diff --git a/.Rbuildignore b/.Rbuildignore
index 95b0e70..1324998 100644
--- a/.Rbuildignore
+++ b/.Rbuildignore
@@ -6,3 +6,9 @@
 ^docs$
 ^pkgdown$
 ^CRAN-SUBMISSION$
+^doc$
+^Meta$
+^examples/temp/
+^tests/temp/
+
+
diff --git a/.gitignore b/.gitignore
index 8c83bbc..ae997c6 100644
--- a/.gitignore
+++ b/.gitignore
@@ -7,3 +7,5 @@
 .o
 .so
 .dll
+/doc/
+/Meta/
diff --git a/CRAN-SUBMISSION b/CRAN-SUBMISSION
index 40039da..efae06a 100644
--- a/CRAN-SUBMISSION
+++ b/CRAN-SUBMISSION
@@ -1,3 +1,3 @@
-Version: 2.1
-Date: 2024-09-14 10:57:51 UTC
-SHA: eb5656ea33fc519c7f43ebe74b0963825b5943c0
+Version: 2.2
+Date: 2024-11-13 18:00:38 UTC
+SHA: 323e03f56d02eec77b7c9d98aa46ed597b3f3b74
diff --git a/DESCRIPTION b/DESCRIPTION
index b23cbc2..f12afd9 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,6 +1,6 @@
 Package: biplotEZ
 Title: EZ-to-Use Biplots
-Version: 2.1
+Version: 2.3
 Authors@R: 
     c(person("Sugnet", "Lubbe", , "muvisu@sun.ac.za", role = c("aut", "cre","cph"),
            comment = c(ORCID = "0000-0003-2762-9944")),
@@ -27,7 +27,7 @@ Description: Provides users with an EZ-to-use platform for representing data
 License: MIT + file LICENSE
 Encoding: UTF-8
 Roxygen: list(markdown = TRUE)
-RoxygenNote: 7.3.2
+RoxygenNote: 7.3.3
 VignetteBuilder: knitr
 Config/testthat/edition: 3
 Suggests: 
@@ -40,14 +40,17 @@ Suggests:
     knitr,
     MASS,
     R.devices,
+    RColorBrewer,
     rgl,
-    rmarkdown,
-    testthat (>= 3.0.0)
+    rmarkdown
 Imports: 
     graphics,
     grDevices,
     plotrix,
+    Rcpp,
     splines,
     stats,
     withr
 NeedsCompilation: yes
+LinkingTo: 
+    Rcpp
diff --git a/NAMESPACE b/NAMESPACE
index 32ac46e..6697b7c 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -3,6 +3,7 @@
 S3method(AoD,biplot)
 S3method(CA,biplot)
 S3method(CVA,biplot)
+S3method(CatPCA,biplot)
 S3method(PCA,biplot)
 S3method(PCO,biplot)
 S3method(classification,biplot)
@@ -12,15 +13,14 @@ S3method(regress,biplot)
 S3method(summary,biplot)
 export(AoD)
 export(CA)
-export(CATPCA)
 export(CLPs)
 export(CLRs)
 export(CVA)
+export(CatPCA)
 export(PCA)
 export(PCO)
 export(alpha.bags)
 export(axes)
-export(axes_coordinates)
 export(biplot)
 export(classification)
 export(classify)
@@ -34,6 +34,8 @@ export(legend.type)
 export(means)
 export(newaxes)
 export(newsamples)
+export(nom.axes)
+export(ord.axes)
 export(prediction)
 export(reflect)
 export(regress)
@@ -41,6 +43,7 @@ export(rotate)
 export(samples)
 export(sqrtManhattan)
 export(translate_axes)
+importFrom(Rcpp,sourceCpp)
 importFrom(grDevices,chull)
 importFrom(grDevices,colorRampPalette)
 importFrom(grDevices,grey)
diff --git a/R/CA.R b/R/CA.R
index 84aa44d..bab9577 100644
--- a/R/CA.R
+++ b/R/CA.R
@@ -18,13 +18,19 @@
 #' \item{Z}{Combined data frame of the row and column coordinates.}
 #' \item{r}{Numer of levels in the row factor.}
 #' \item{c}{Numer of levels in the column factor.}
+#' \item{Dr}{Diagonal matrix of row profiles.}
+#' \item{Dc}{Diagonal matrix of column profiles.}
+#' \item{Drh}{Weighted row profiles.}
+#' \item{Dch}{Weighted column profiles.}
 #' \item{rowcoor}{Row coordinates based on the selected \code{variant}.}
 #' \item{colcoor}{Column coordinates based on the selected \code{variant}.}
-#' \item{P}{Correspondence Matrix}
+#' \item{P}{Correspondence Matrix.}
 #' \item{Smat}{Standardised Pearson residuals.}
 #' \item{SVD}{Singular value decomposition solution: \code{d, u, v}.}
-#' \item{qual}{Quality of the approximation.}
+#' \item{e.vects}{Depending on what was specified in \code{CA} argument.}
+#' \item{dim.biplot}{The dimension of the biplot.}
 #' \item{lambda.val}{The computed lambda value if lambda-scaling is requested.}
+#' \item{gamma}{Contribution of the singular values, based on the CA variant.}
 #'
 #' @seealso [biplot()]
 #'
@@ -130,10 +136,10 @@ CA.biplot <- function(bp, dim.biplot = c(2,1,3), e.vects = 1:ncol(bp$X), variant
   bp$Z <- Z
   bp$r <- r
   bp$c <- c
+  bp$Dr <- Dr
   bp$Dc <- Dc
-  bp$Rc <- Dr
-  bp$Dch <- Dch
   bp$Drh <- Drh
+  bp$Dch <- Dch
   bp$rowcoor <- rowcoor         
   bp$colcoor <- colcoor
   bp$P <- P
diff --git a/R/CATPCA.R b/R/CATPCA.R
index 57fd524..aae96a0 100644
--- a/R/CATPCA.R
+++ b/R/CATPCA.R
@@ -1,40 +1,253 @@
-#' Categorical Principal Component Analysis
+# -------------------------------------------------------------------------------------------
+#' Perform Categorical Principal Components Analysis (CatPCA)
+#'
+#' @description
+#' This function appends the \code{biplot} object with elements resulting from performing CatPCA.
 #'
 #' @param bp an object of class \code{biplot} obtained from preceding function \code{biplot()}.
-#' @param dim.biplot dimension of the biplot. Only values 1, 2 and 3 are accepted, with default \code{2}.
-#' @param e.vects which eigenvectors (principal components) to extract, with default \code{1:dim.biplot}.
-#' @param group.aes vector of the same length as the number of rows in the data matrix
+#' @param cat.type a vector indicating whether each categorical variables is \code{nominal} or \code{ordinal}.
+#' @param dim.biplot the dimension of the biplot. Only values \code{1}, \code{2} and \code{3} are accepted, with default \code{2}.
+#' @param e.vects the vector indicating which eigenvectors (principal components) should be plotted in the biplot, with default \code{1:dim.biplot}.
+#' @param group.aes a vector of the same length as the number of rows in the data matrix
 #'                  for differentiated aesthetics for samples.
-#' @param show.class.means logical, indicating whether group means should be plotted in the biplot.
+#' @param show.class.means a logical value indicating whether group means should be plotted in the biplot.
+#' @param epsilon convergence criteria for iterative algorithm with defaults 1e-6.
+#'
+#' @return An object of class CatPCA with the following elements:
+#' \item{X}{the matrix of the centered and scaled numeric variables.}
+#' \item{Xcat}{the data frame of the categorical variables.}
+#' \item{raw.X}{the original data.}
+#' \item{classes}{the vector of category levels for the class variable. This is to be used for \code{colour}, \code{pch} and \code{cex} specifications.}
+#' \item{na.action}{the vector of observations that have been removed.}
+#' \item{center}{a logical value indicating whether \eqn{\mathbf{X}} is centered.}
+#' \item{scaled}{a logical value indicating whether \eqn{\mathbf{X}} is scaled.}
+#' \item{means}{the vector of means for each numerical variable.}
+#' \item{sd}{the vector of standard deviations for each numerical variable.}
+#' \item{n}{the number of observations.}
+#' \item{p}{the number of variables.}
+#' \item{group.aes}{the vector of category levels for the grouping variable. This is to be used for \code{colour}, \code{pch} and \code{cex} specification.}
+#' \item{g.names}{the descriptive names to be used for group labels.}
+#' \item{g}{the number of groups.}
+#' \item{Title}{the title of the biplot rendered.}
+#' \item{Z}{the matrix with each row containing the details of the points that are plotted (i.e. coordinates).}
+#' \item{Lmat}{the matrix for transformation to the principal components.}
+#' \item{Linv}{the inverse of \eqn{\mathbf{L}}.}
+#' \item{eigenvalues}{the vector of eigenvalues of the covariance matrix of \eqn{\mathbf{X}}.}
+#' \item{all.ax.one.unit}{one unit in the positive direction of each biplot axis.}
+#' \item{ax.type}{one of numeric, ordinal or nominal.}
+#' \item{ax.one.unit}{one unit in the positive direction of each numeric biplot axis.}
+#' \item{nom.levels}{a list with the levels of each nominal variable}
+#' \item{ord.levels}{a list with the levels of each ordinal variable}
+#' \item{e.vects}{the vector indicating which principal components are plotted in the biplot.}
+#' \item{dim.biplot}{the dimension of the biplot.}
+#' \item{class.means}{a logical value indicating whether group means are plotted in the biplot.}
+#' \item{Zmeans}{the matrix of class mean coordinates that are plotted in the biplot.}
+#'
+#' @usage CatPCA(bp, cat.type = NULL, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X),
+#' group.aes = NULL, show.class.means = FALSE, epsilon = 1e-6)
+#' @aliases CatPCA
 #'
-#' @return
-#' an object of class \code{biplot}
-#' 
 #' @export
-#' @usage CATPCA(bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X),
-#' group.aes = NULL, show.class.means = FALSE)
-#' @aliases CATPCA
+#'
+#' @examples
+#' biplot(iris) |> CatPCA()
+#' # create a CatPCA biplot
+#' biplot(data = iris) |> CatPCA() |> plot()
 #' 
+CatPCA <- function (bp, cat.type = NULL, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X), group.aes=NULL, 
+                    show.class.means = FALSE, epsilon = 1e-6)
+{
+  UseMethod("CatPCA")
+}
+
+#' Calculate elements for the CatPCA biplot
+#'
+#' @description This function performs calculations for the construction of a CatPCA biplot.
+#'
+#' @inheritParams CatPCA
+#'
+#' @return an object of class \code{CatPCA}, inherits from classes \code{PCA} and \code{biplot}.
+#' @export
+#'
 #' @examples
-#' CATPCA (iris)
-CATPCA<-function(bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X),
-                 group.aes = NULL, show.class.means = FALSE){
-  indmat  <- function (groep.vec) 
-  {  elements <- levels(factor(groep.vec))
-  Y <- matrix(0, nrow = length(groep.vec), ncol = length(elements))
-  dimnames(Y) <- list(NULL, paste(elements))
-  for (i in 1:length(elements)) Y[groep.vec == elements[i], i] <- 1
-  return(Y)
-  }
-  
-  biplot.check.G <- function (G, n) 
-  {  if (is.null(G)) { G <- matrix(indmat(rep(1, n)), ncol = 1)
-  dimnames(G) <- list(1:n, "AllData")      }
-    if (nrow(G) != n) stop("number of rows of X and G differ")
-    if (is.null(dimnames(G))) dimnames(G) <- list(NULL, paste("class", 1:ncol(G), sep = ""))
-    if (length(dimnames(G)[[2]]) == 0) dimnames(G)[[2]] <- paste("class", 1:ncol(G), sep = "")
-    if (ncol(G) == 1) class.vec <- rep(dimnames(G)[[2]], n) else class.vec <- apply(t(apply(G, 1, function(x) x == max(x))), 1, function(s, G) dimnames(G)[[2]][s], G = G)
-    G
-  }
-  ##Possibly combine these two functions to obtain indicator matrices and overall indicator matrix (could be useful for MCA as well)
+#' biplot(iris) |> CatPCA()
+#' # create a CatPCA biplot
+#' biplot(data = iris) |> CatPCA() |> plot()
+#'
+CatPCA.biplot <- function (bp, cat.type = NULL, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X), group.aes=NULL,
+                        show.class.means = FALSE, epsilon = 1e-6)
+{
+  dim.biplot <- dim.biplot[1]
+  if (dim.biplot != 1 & dim.biplot != 2 & dim.biplot != 3) stop("Only 1D, 2D and 3D biplots")
+  e.vects <- e.vects[1:dim.biplot]
+  if (!is.null(group.aes)) 
+  { bp$group.aes <- factor(group.aes)
+    bp$g.names <-levels(factor(group.aes))
+    bp$g <- length(bp$g.names)
+  }
+  
+  if (!bp$center)
+  {  warning("Any form of PCA requires a centred datamatrix. Your numeric data was centred before computation. Use center = TRUE in the call to biplot()")
+     bp <- biplot (bp$X, center = TRUE, scaled=bp$scaled, bp$classes, bp$group.aes)
+  }
+  X <- bp$X
+  n <- bp$n
+  p <- bp$p
+  p2 <- bp$p2
+  Xcat <- bp$Xcat
+  if (is.null(cat.type)) cat.type <- rep("nom", p2)
+  if (length(cat.type) != p2) stop ("The length of cat.type needs to match the number of columns in Xcat")
+  cat.type <- c("nominal","ordinal")[pmatch (cat.type, c("nominal", "ordinal"), duplicates.ok = TRUE)]
+  if (any(is.na(cat.type))) stop ("Only 'nominal' or 'ordinal' allowed for cat.type.")  
+  
+  Gk <- vector("list", p2)
+  Lk.mat <- vector("list", p2)
+  Lk <- rep(NA, p2)
+  zlist <- vector("list", p2)
+  Hmat <- matrix(nrow = n, ncol = p2)
+  CatLabels <- NULL
+  
+  for (k in 1:p2) 
+  { Gk[[k]] <- indmat(Xcat[, k])
+    CatLabels <- append(CatLabels, dimnames(Gk[[k]])[[2]])
+    Lk[k] <- ncol(Gk[[k]])
+    Lk.mat[[k]] <- t(Gk[[k]]) %*% Gk[[k]]
+  }
+  
+  Gmat <- matrix(unlist(Gk), nrow = n)
+  L.mat <- diag(diag(t(Gmat) %*% Gmat))
+  L.mat.min.half <- diag(diag(L.mat)^-0.5)
+  N.mat <- diag(n) - matrix(1, nrow = n, ncol = n)/n
+  svd.mca <- svd(L.mat.min.half %*% t(Gmat) %*% N.mat %*% Gmat %*% L.mat.min.half/p)
+  z.ini <- svd.mca$v[, 1]
+  names(z.ini) <- CatLabels
+  count <- 0
+  for (k in 1:p2) 
+  {  zlist[[k]] <- as.vector(z.ini[(count + 1):(count + ncol(Gk[[k]]))])
+     names(zlist[[k]]) <- CatLabels[(count + 1):(count + ncol(Gk[[k]]))]
+     count <- count + ncol(Gk[[k]])
+     if (identical(cat.type[k], "ordinal")) 
+       { 
+          gradient <- sign(stats::lm(zlist[[k]] ~ I(1:length(zlist[[k]])))$coef[2])
+          if (gradient>0) zlist[[k]] <- ties (d = 1:length(zlist[[k]]), delta=zlist[[k]])
+          if (gradient<0) zlist[[k]] <- rev(ties (d = 1:length(zlist[[k]]), delta=rev(zlist[[k]])))
+          if (gradient==0) zlist[[k]] <- mean(zlist[[k]])         
+       }
+  }
+  for (k in 1:p2) 
+  { labs <- names(zlist[[k]])
+    scaling.factor <- as.numeric(sqrt(t(zlist[[k]]) %*% t(Gk[[k]]) %*% N.mat %*% Gk[[k]] %*% zlist[[k]]))
+    if (is.na(1/scaling.factor)) scaling.factor <- 1
+    scaling.vec <- rep(scaling.factor, length(zlist[[k]]))
+    if (identical(cat.type[k], "nominal")) zlist[[k]] <- as.vector(zlist[[k]]/scaling.vec)
+    if (identical(cat.type[k], "ordinal")) 
+    {  u.temp <- sum(diag(Lk.mat[[k]]))
+       v.temp <- sum(zlist[[k]] * diag(Lk.mat[[k]]))                       
+       w.temp <- c(t(zlist[[k]]) %*% Lk.mat[[k]] %*% zlist[[k]])
+       b.temp <- sqrt(1/(w.temp - v.temp^2/u.temp))
+       zlist[[k]] <- b.temp * zlist[[k]] - b.temp * v.temp/u.temp
+    }
+    names(zlist[[k]]) <- labs
+    Hmat[, k] <- Gk[[k]] %*% zlist[[k]]
+  }
+  Hmat <- as.matrix(Hmat)
+  dimnames(Hmat) <- dimnames(Xcat)
+  again <- TRUE
+  RSS.old <- NULL
+  Hmat.cent <- cbind(N.mat %*% Hmat, X)
+  iter <- 0
+  while (again) 
+  {  iter <- iter + 1
+     svd.out <- svd(Hmat.cent)
+     if (dim.biplot>1)
+       Yr <- scale(svd.out$u[, e.vects, drop=F] %*% diag(svd.out$d[e.vects]) %*% t(svd.out$v[, e.vects, drop=F]), scale = FALSE, center = TRUE)
+     else
+       Yr <- scale((svd.out$u[, e.vects, drop=F] * svd.out$d[e.vects]) %*% t(svd.out$v[, e.vects, drop=F]), scale = FALSE, center = TRUE)
+     RSS <- sum((Hmat.cent - Yr)^2)
+     if (!is.null(RSS.old)) again <- ((RSS.old - RSS) > epsilon)
+     RSS.old <- RSS
+     if (again) {
+      for (k in 1:p2) {
+        labs <- names(zlist[[k]])
+        if (identical(cat.type[k], "nominal")) {
+          scale.factor <- as.numeric(sqrt(t(Yr[, k]) %*% Gk[[k]] %*% solve(Lk.mat[[k]]) %*% t(Gk[[k]]) %*% Yr[, k]))
+          zlist[[k]] <- as.vector((solve(Lk.mat[[k]]) %*% t(Gk[[k]]) %*% Yr[, k])/scale.factor)
+        }
+        if (identical(cat.type[k], "ordinal")) {
+          zlist[[k]] <- as.vector((solve(Lk.mat[[k]]) %*% t(Gk[[k]]) %*% Yr[, k]))
+          gradient <- sign(stats::lm(zlist[[k]] ~ I(1:length(zlist[[k]])))$coef[2])
+          if (gradient>0) zlist[[k]] <- ties (d = 1:length(zlist[[k]]), delta=zlist[[k]])
+          if (gradient<0) zlist[[k]] <- rev(ties (d = 1:length(zlist[[k]]), delta=rev(zlist[[k]])))
+          if (gradient==0) zlist[[k]] <- mean(zlist[[k]])         
+          u.temp <- sum(diag(Lk.mat[[k]]))
+          v.temp <- sum(zlist[[k]] * diag(Lk.mat[[k]]))
+          w.temp <- c(t(zlist[[k]]) %*% Lk.mat[[k]] %*% zlist[[k]])
+          b.temp <- sqrt(1/(w.temp - v.temp^2/u.temp))
+          zlist[[k]] <- b.temp * zlist[[k]] - b.temp * v.temp/u.temp
+        }
+        names(zlist[[k]]) <- labs
+        Hmat[, k] <- Gk[[k]] %*% zlist[[k]]
+      }
+    }
+    Hmat.cent <- cbind(N.mat %*% Hmat, X)
+  }
+  Lz <- rep(NA, p2)
+  for (i in 1:p2) Lz[i] <- sum(Lk.mat[[i]] %*% zlist[[i]])
+  zLz <- rep(NA, p2)
+  for (i in 1:p2) zLz[i] <- sum(t(zlist[[i]]) %*% Lk.mat[[i]] %*% zlist[[i]])
+  Hmat.cent.svd <- svd(Hmat.cent)
+  
+  V.mat <- Hmat.cent.svd$v
+  U.mat <- Hmat.cent.svd$u
+  Sigma.mat <- diag(Hmat.cent.svd$d)
+  Lmat <- Hmat.cent.svd$v
+  Vr <- Hmat.cent.svd$v[, e.vects, drop = FALSE]
+  Z <- Hmat.cent %*% Hmat.cent.svd$v[, e.vects, drop=F]
+  rownames(Z) <- rownames(X)
+  
+  ax.one.unit <- 1/(diag(Vr %*% t(Vr))) * Vr
+  nom.levels <- ord.levels <- NULL
+  nom.count <- ord.count <- 0
+  for (k in 1:p2)
+  {
+    if (cat.type[k] == "nominal")
+    {
+      nom.count <- nom.count + 1
+      nom.levels[[nom.count]] <- zlist[[k]]
+    }
+    if (cat.type[k] == "ordinal")
+    {
+      ord.count <- ord.count + 1
+      ord.levels[[ord.count]] <- zlist[[k]]
+    }
+  }
+  
+  ax.type <- c(cat.type, rep("numeric",p))
+  num.levels <- apply(Xcat, 2, function(x) nlevels(factor(x)))
+  num.levels <- c(num.levels, rep(1,p))
+  ax.type <- data.frame (ax.type, num.levels)
+  
+  bp$Z <- Z
+  bp$Lmat <- Lmat
+  bp$eigenvalues <- svd.out$d^2
+  bp$all.ax.one.unit <- ax.one.unit
+  bp$ax.type <- ax.type
+  bp$ax.one.unit <- ax.one.unit[ax.type$ax.type=="numeric",]
+  bp$nom.levels <- nom.levels
+  bp$ord.levels <- ord.levels
+  bp$e.vects <- e.vects
+  bp$Vr <- Vr
+  bp$dim.biplot <- dim.biplot
+  if (bp$g == 1) bp$class.means <- FALSE else bp$class.means <- show.class.means
+  if (bp$class.means)
+  {
+    G <- indmat(bp$group.aes)
+    Xmeans <- solve(t(G)%*%G) %*% t(G) %*% X
+    Zmeans <- Xmeans %*% Lmat[,e.vects]
+    bp$Zmeans <- Zmeans
+  }
+  
+  class(bp) <- append(class(bp),"PCA")
+  class(bp) <- append(class(bp),"catPCA")
+  bp
 }
diff --git a/R/PCA.R b/R/PCA.R
index ae79c83..db3b562 100644
--- a/R/PCA.R
+++ b/R/PCA.R
@@ -14,6 +14,7 @@
 #'                           optimally approximated in the biplot. If \code{TRUE}, the correlations between
 #'                           variables are optimally approximated by the cosine of the angles between
 #'                           axes. Default is \code{FALSE}.
+#' @param ... additional arguments.
 #'
 #' @return An object of class PCA with the following elements:
 #' \item{X}{the matrix of the centered and scaled numeric variables.}
@@ -44,8 +45,9 @@
 #'
 #' @seealso [biplot()]
 #'
-#' @usage PCA(bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X),
-#' group.aes = NULL, show.class.means = FALSE, correlation.biplot = FALSE)
+#' @usage PCA(bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X), 
+#'            group.aes=NULL, show.class.means = FALSE,
+#'            correlation.biplot=FALSE, ...)
 #' @aliases PCA
 #'
 #' @export
@@ -58,8 +60,9 @@
 #' # create a PCA biplot
 #' biplot(data = iris) |> PCA() |> plot()
 #' 
-PCA <- function (bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X), group.aes=NULL, show.class.means = FALSE,
-                 correlation.biplot=FALSE)
+PCA <- function (bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X), 
+                 group.aes=NULL, show.class.means = FALSE,
+                 correlation.biplot=FALSE, ...)
 {
   UseMethod("PCA")
 }
@@ -79,7 +82,7 @@ PCA <- function (bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X), group.aes=
 #' biplot(data = iris) |> PCA() |> plot()
 #'
 PCA.biplot <- function (bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X), group.aes=NULL,
-                        show.class.means = FALSE, correlation.biplot=FALSE)
+                        show.class.means = FALSE, correlation.biplot=FALSE, ...)
 {
   
   dim.biplot <- dim.biplot[1]
@@ -105,13 +108,15 @@ PCA.biplot <- function (bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X), gro
   Lmat <- svd.out$v
   Vr <- svd.out$v[, e.vects, drop = FALSE]
 
-  if (correlation.biplot)
-  {
-
-    if (dim.biplot>1) lambda.r <- diag(svd(t(X) %*% X)$d[1:dim.biplot])
-    else lambda.r <- matrix(svd(t(X) %*% X)$d, nrow=1, ncol=1)
+  if (correlation.biplot) {
+    svals <- svd(t(X) %*% X)$d
+    if (dim.biplot > 1) 
+      lambda.r <- diag(svals[1:dim.biplot])
+    else lambda.r <- matrix(svals, nrow = 1, ncol = 1)
+    if (any(diag(lambda.r) < 1e-14)) stop (paste("Your data is of rank <", dim.biplot))
     Z <- sqrt(n - 1) * X %*% Vr %*% sqrt(solve(lambda.r))
-    Lmat <- sqrt(n-1) * Lmat %*% sqrt(solve(diag(svd(t(X) %*% X)$d)))
+    if (n > p) Lmat <- sqrt(n - 1) * Lmat %*% diag(sqrt(ifelse(svals < 1e-14, 0, 1/svals)))
+    else Lmat <- sqrt(n - 1) * Lmat %*% diag(sqrt(ifelse(svals < 1e-14, 0, 1/svals)))[1:n,1:n]
   }
   else { Z <- X %*% Vr }
   rownames(Z) <- rownames(X)
diff --git a/R/RcppExports.R b/R/RcppExports.R
new file mode 100644
index 0000000..d943b0d
--- /dev/null
+++ b/R/RcppExports.R
@@ -0,0 +1,11 @@
+# Generated by using Rcpp::compileAttributes() -> do not edit by hand
+# Generator token: 10BE3573-1514-4C36-9D1C-5A225CD40393
+
+alfunc <- function(BVEC, X, Y, M, MU, LAMBDA, CONST1, CONST2, U, V) {
+    .Call(`_biplotEZ_alfunc`, BVEC, X, Y, M, MU, LAMBDA, CONST1, CONST2, U, V)
+}
+
+optimize_spline <- function(BVEC, X, Y, M, MU, LAMBDA, CONST1, CONST2, U, V, TAU, FTOL, TINY, ITMAX) {
+    .Call(`_biplotEZ_optimize_spline`, BVEC, X, Y, M, MU, LAMBDA, CONST1, CONST2, U, V, TAU, FTOL, TINY, ITMAX)
+}
+
diff --git a/R/aesthetics.R b/R/aesthetics.R
index 639154c..b281a6b 100644
--- a/R/aesthetics.R
+++ b/R/aesthetics.R
@@ -78,7 +78,6 @@ samples <- function (bp,  which = 1:bp$g, col = ez.col, pch = 16,
   g <- bp$g
   n <- bp$n
   p <- bp$p
-  
   if(is.null(which) & length(col)==0) col <- ez.col
   
  if(inherits(bp,"CA")) 
@@ -194,7 +193,8 @@ samples <- function (bp,  which = 1:bp$g, col = ez.col, pch = 16,
 #' This function allows the user to format the aesthetics for the class means or group means.
 #'
 #' @param bp an object of class \code{biplot}.
-#' @param which a vector containing the groups or classes for which the means should be displayed, with default \code{bp$g}.
+#' @param which a vector containing the groups or classes for which the means should be displayed, with default 
+#'              the \code{which} argument of samples.
 #' @param col the colour(s) for the means, with default as the colour of the samples.
 #' @param pch the plotting character(s) for the means, with default \code{15}.
 #' @param cex the character expansion(s) for the means, with default \code{1}.
@@ -225,7 +225,7 @@ samples <- function (bp,  which = 1:bp$g, col = ez.col, pch = 16,
 #' @seealso [biplot()]
 #' 
 #' @usage
-#' means (bp,  which = NULL, col = NULL, pch = 15, cex = 1, label = FALSE,
+#' means (bp,  which =  bp$samples$which, col = NULL, pch = 15, cex = 1, label = FALSE,
 #' label.col = NULL,label.cex = 0.75, label.side = "bottom", label.offset = 0.5,
 #' opacity = 1, shade.darker = TRUE)
 #' @aliases means
@@ -234,11 +234,10 @@ samples <- function (bp,  which = 1:bp$g, col = ez.col, pch = 16,
 #'
 #' @examples biplot(iris[,1:4]) |> PCA() |>
 #'           means(col = "purple", pch = 15, cex = 2) |> plot()
-means <- function (bp,  which = NULL, col = NULL,
+means <- function (bp,  which = bp$samples$which, col = NULL,
                      pch = 15, cex = 1, label = FALSE, label.col=NULL, label.cex = 0.75,
                      label.side = "bottom", label.offset = 0.5, opacity = 1, shade.darker = TRUE)
 {
-  bp$show.class.means <- TRUE
   if (is.null(bp$samples)) bp <- samples(bp)
   g <- bp$g
   
@@ -250,10 +249,9 @@ means <- function (bp,  which = NULL, col = NULL,
     which <- which[which <= g]
     which <- which[which > 0]
   }
-  else if (!is.null(bp$samples$which)) which <- bp$samples$which else which <- 1:g
   class.num <- length(which)
 
-
+  if (!is.null(which))
   if (is.null(col))
   {
     if (max(which)<=length(bp$samples$col)) col <- bp$samples$col[which] else col <- bp$samples$col
@@ -487,6 +485,419 @@ axes <- function (bp, X.names=colnames(bp$X), which = 1:bp$p, col = grey(0.7), l
   bp
 }
 
+# ----------------------------------------------------------------------------------------------
+#' Format aesthetics for the nominal biplot axes
+#'
+#' @description
+#' This function allows the user to format the aesthetics for the nominal biplot axes.
+#'
+#'
+#' @param bp an object of class \code{biplot}.
+#' @param X.names a vector of column names of \code{bp} to specify which axes should be labelled.
+#' @param which a vector containing the columns or variables for which the axes should be displayed, with default \code{1:p}.
+#' @param col a list with each component the colour(s) for the levels of that axis.
+#' @param lwd the line width(s) for the axes, with default \code{1}.
+#' @param lty the line type(s) for the axes, with default \code{1}.
+#' @param label.dir a character string indicating the placement of the axis titles to the side of the figure. One of "\code{Orthog}" for axis titles to appear orthogonal to the side of the figure (default) , "\code{Hor}" for axis titles to appear horizontally or "\code{Paral}" for axis titles to appear parallel to the side of the figure.
+#' @param label.col the colour(s) for the axis labels, with default, \code{col}.
+#' @param label.cex the label expansion for the axis labels, with default \code{0.75}.
+#' @param label.line the distance of the axis title from the side of the figure, with default \code{0.1}.
+#' @param label.offset a four-component numeric vector controlling the distances axis titles are displayed from the side of the figure, with default \code{rep(0,4)}. Sides are numbered \code{1} to \code{4} according to \code{R} conventions.
+#' @param ticks an integer-valued vector indicating the number of tickmarks for each axis, with default \code{5} for each axis.
+#' @param tick.col the colour(s) for the tick marks, with default \code{col}.
+#' @param tick.size a vector specifying the sizes of tick marks for each axis, with default \code{1} for each .
+#' @param tick.label a logical value indicating whether the axes should be labelled, with default \code{TRUE}.
+#' @param tick.label.side a character string indicating the position of the tick label. One of "\code{below}" for the label to appear below the tick mark (default) or "\code{above}" for the label to appear above the tick mark.
+#' @param tick.label.col the colour(s) for the tick mark labels, with default \code{tick.col}.
+#' @param tick.label.cex the label expansion for the tick mark labels, with default \code{0.6}.
+#' @param predict.col the colour(s) for the predicted samples, with default \code{col}.
+#' @param predict.lwd the line width(s) for the predicted samples, with default \code{lwd}.
+#' @param predict.lty the line type(s) for the predicted samples, with default \code{lty}.
+#' @param ax.names a vector of size \code{p} containing user defined titles for the axes.
+#' @param orthogx a numeric vector of size \code{p} specifying the x-coordinate of the parallel transformation of each axis, with default \code{0} for each axis. This is only used when \code{dim.biplot = 2}. 
+#' @param orthogy a numeric vector of size \code{p} specifying the y-coordinate of the parallel transformation of each axis, with default \code{0} for each axis. This is only used when \code{dim.biplot = 2}.
+#'
+#' @return The object of class \code{biplot} will be appended with a list called \code{axes} containing the following elements:
+#' \item{which}{a vector containing the columns for which the axes are displayed.}
+#' \item{col}{the colour(s) of the axes.}
+#' \item{lwd}{the line width(s) of the axes.}
+#' \item{lty}{the line type(s) of the axes.}
+#' \item{label.dir}{the placement of the axis titles to the side of the figure.}
+#' \item{label.col}{the colour(s) of the axis titles.}
+#' \item{label.cex}{the label expansion(s) of the axis titles.}
+#' \item{label.line}{the distance(s) of the axis titles from the side of the figure.}
+#' \item{ticks}{the number of tick marks per axis.}
+#' \item{tick.col}{the colour(s) of the tick marks.}
+#' \item{tick.size}{the size(s) of the tick marks.}
+#' \item{tick.label}{logical value(s) indicating whether axes are labelled.}
+#' \item{tick.label.side}{the position of the tick mark labels.}
+#' \item{tick.label.col}{the colour(s) of the tick mark labels.}
+#' \item{tick.label.cex}{the expansion(s) of the tick mark labels.}
+#' \item{predict.col}{the colour(s) of the predicted samples.}
+#' \item{predict.lty}{the line type(s) of the predicted samples.}
+#' \item{predict.lwd}{the line width(s) of the predicted samples.}
+#' \item{names}{the user defined axis titles.}
+#' \item{orthogx}{the horizontal translations for each axis.}
+#' \item{orthogy}{the vertical translations for each axis.}
+#' \item{vectors}{a logical value indicating whether calibrated axes are plotted.}
+#' 
+#' @seealso [biplot()]
+#'
+#' @usage
+#' nom.axes(bp, X.names=colnames(bp$Xcat)[bp$ax.type$ax.type=="nominal"], 
+#'          which =1:sum(bp$ax.type$ax.type=="nominal"), col = NULL, lwd = 1, 
+#'          lty = 1, label.dir = "Orthog", label.col = "black", label.cex = 0.75, 
+#'          label.line = 0.1, label.offset=rep(0,4), ticks = 5, tick.col = "black", 
+#'          tick.size = 1, tick.label = TRUE, tick.label.side = "below", 
+#'          tick.label.col = tick.col, tick.label.cex = 0.6, predict.col = col, 
+#'          predict.lwd = lwd, predict.lty = lty, ax.names = X.names, 
+#'          orthogx = 0, orthogy = 0)
+#' @aliases nom.axes
+#'
+#' @export
+#'
+#' @examples
+#' biplot(iris) |> CatPCA() |> nom.axes(col=c("blue","magenta","gold")) |> plot()
+#'
+nom.axes <- function (bp, X.names=colnames(bp$Xcat)[bp$ax.type$ax.type=="nominal"], 
+                      which =1:sum(bp$ax.type$ax.type=="nominal"), col = NULL, lwd = 1, 
+                      lty = 1, label.dir = "Orthog", label.col = "black", 
+                      label.cex = 0.75, 
+                      label.line = 0.1, label.offset=rep(0,4), ticks = 5, tick.col = "black", 
+                      tick.size = 1, tick.label = TRUE, tick.label.side = "below",
+                      tick.label.col = tick.col, tick.label.cex = 0.6,
+                      predict.col = col, predict.lwd = lwd, predict.lty = lty, ax.names = X.names,
+                      orthogx = 0, orthogy = 0)
+{
+  if (!requireNamespace("RColorBrewer", quietly = TRUE)) {
+   stop("Package 'RColorBrewer' is required for this function. Please install it.", call. = FALSE)
+  }
+  
+  p <- sum(bp$ax.type$ax.type=="nominal")
+  num.levels.vec <- bp$ax.type$num.levels[bp$ax.type$ax.type == "nominal"]
+  if (!is.null(p))
+  {
+    if (!all(is.numeric(which))) which <- match(which, X.names, nomatch = 0)
+    which <- which[which <= p]
+    which <- which[which > 0]
+    ax.num <- length(which)
+
+    if (is.null(col))
+      col <- c(RColorBrewer::brewer.pal(12,"Set3")[-2], RColorBrewer::brewer.pal(7,"Dark2"))
+    if (!is.list(col))
+    {
+      temp <- vector ("list", ax.num)
+      for (j in 1:ax.num) temp[[j]] <- col
+      col <- temp
+    }
+    if (length(col) < ax.num)
+    {
+      temp <- vector ("list", ax.num)
+      col.length <- length(col)
+      j <- 0
+      while (j < ax.num)
+      {  for (k in 1:col.length) if (k+j<ax.num) temp[[k+1]] <- col[[k]]
+         j <- j + col.length
+      }
+      col <- temp
+    }
+    if (length(col) > ax.num)
+    {
+      temp <- vector ("list", ax.num)
+      for (j in 1:ax.num) temp[[j]] <- col[[j]]
+      col <- temp
+    }
+    num.levels <- num.levels.vec[which]
+    
+    for (j in 1:ax.num)
+      col[[j]] <- col[[j]][ifelse (1:num.levels[j] %% length(col[[j]]) == 0, length(col[[j]]), 
+                                                                          1:num.levels[j] %% length(col[[j]]))]
+
+    lwd.len <- length(lwd)
+    lwd <- lwd[ifelse(1:ax.num%%lwd.len==0,lwd.len,1:ax.num%%lwd.len)]
+    if(is.null(lwd)){lwd <- rep(0, ax.num)}
+    
+    lty.len <- length(lty)
+    lty <- lty[ifelse(1:ax.num%%lty.len==0,lty.len,1:ax.num%%lty.len)]
+    if(is.null(lty)){lty <- rep(0, ax.num)}
+    if (label.dir != "Orthog" & label.dir != "Hor" & label.dir != "Paral")
+      stop("Incorrect specification of axis label direction")
+    
+    label.col.len <- length(label.col)
+    label.col <- label.col[ifelse(1:ax.num%%label.col.len==0,label.col.len,1:ax.num%%label.col.len)]
+    if(is.null(label.col)){label.col <- rep(0, ax.num)}
+    
+    label.cex.len <- length(label.cex)
+    label.cex <- label.cex[ifelse(1:ax.num%%label.cex.len==0,label.cex.len,1:ax.num%%label.cex.len)]
+    if(is.null(label.cex)){label.cex <- rep(0, ax.num)}
+    
+    label.line.len <- length(label.line)
+    label.line <- label.line[ifelse(1:ax.num%%label.line.len==0,label.line.len,1:ax.num%%label.line.len)]
+    if(is.null(label.line)){label.line <- rep(0, ax.num)}
+    
+    ticks.len <- length(ticks)
+    ticks <- ticks[ifelse(1:ax.num%%ticks.len==0,ticks.len,1:ax.num%%ticks.len)]
+    if(is.null(ticks)){ticks <- rep(0, ax.num)}
+    
+    tick.col.len <- length(tick.col)
+    tick.col <- tick.col[ifelse(1:ax.num%%tick.col.len==0,tick.col.len,1:ax.num%%tick.col.len)]
+    if(is.null(tick.col)){tick.col <- rep(0, ax.num)}
+    
+    tick.size.len <- length(tick.size)
+    tick.size <- tick.size[ifelse(1:ax.num%%tick.size.len==0,tick.size.len,1:ax.num%%tick.size.len)]
+    if(is.null(tick.size)){tick.size <- rep(0, ax.num)}
+    
+    tick.label.len <- length(tick.label)
+    tick.label <- tick.label[ifelse(1:ax.num%%tick.label.len==0,tick.label.len,1:ax.num%%tick.label.len)]
+    if(is.null(tick.label)){tick.label <- rep("", ax.num)}
+    
+    tick.label.col.len <- length(tick.label.col)
+    tick.label.col <- tick.label.col[ifelse(1:ax.num%%tick.label.col.len==0,tick.label.col.len,1:ax.num%%tick.label.col.len)]
+    if(is.null(tick.label.col)){tick.label.col <- rep(0, ax.num)}
+    
+    tick.label.cex.len <- length(tick.label.cex)
+    tick.label.cex <- tick.label.cex[ifelse(1:ax.num%%tick.label.cex.len==0,tick.label.cex.len,1:ax.num%%tick.label.cex.len)]
+    if(is.null(tick.label.cex)){tick.label.cex <- rep(0, ax.num)}
+    
+    tick.label.side.len <- length(tick.label.side)
+    tick.label.side <- tick.label.side[ifelse(1:ax.num%%tick.label.side.len==0,tick.label.side.len,1:ax.num%%tick.label.side.len)]
+    if(is.null(tick.label.side)){tick.label.side <- rep(0, ax.num)}
+    
+    predict.col.len <- length(predict.col)
+    predict.col <- predict.col[ifelse(1:ax.num%%predict.col.len==0,predict.col.len,1:ax.num%%predict.col.len)]
+    if(is.null(predict.col)){predict.col <- rep(0, ax.num)}
+    
+    predict.lwd.len <- length(predict.lwd)
+    predict.lwd <- predict.lwd[ifelse(1:ax.num%%predict.lwd.len==0,predict.lwd.len,1:ax.num%%predict.lwd.len)]
+    if(is.null(predict.lwd)){predict.lwd <- rep(0, ax.num)}
+    
+    predict.lty.len <- length(predict.lty)
+    predict.lty <- predict.lty[ifelse(1:ax.num%%predict.lty.len==0,predict.lty.len,1:ax.num%%predict.lty.len)]
+    if(is.null(predict.lty)){predict.lty <- rep(0, ax.num)}
+    
+    ax.names.len <- length(ax.names)
+    ax.names <- ax.names[ifelse(1:p%%ax.names.len==0,ax.names.len,1:p%%ax.names.len)]
+    if(is.null(ax.names)){ax.names <- rep("", p)}
+    
+    orthogx.len <- length(orthogx)
+    orthogx <- orthogx[ifelse(1:p%%orthogx.len==0,orthogx.len,1:p%%orthogx.len)]
+    if(is.null(orthogx)){orthogx <- rep("", p)}
+    
+    orthogy.len <- length(orthogy)
+    orthogy <- orthogx[ifelse(1:p%%orthogy.len==0,orthogy.len,1:p%%orthogy.len)]
+    if(is.null(orthogy)){orthogy <- rep("", p)}
+    
+    bp$nom.axes = list(which = which, col = col, lwd = lwd, lty = lty, label.dir = label.dir, 
+                       label.col = label.col, label.cex = label.cex, label.line = label.line, 
+                       ticks = ticks, tick.col = tick.col, tick.size = tick.size, 
+                       tick.label = tick.label, tick.label.col = tick.label.col, 
+                       tick.label.cex = tick.label.cex, tick.label.side=tick.label.side,
+                       predict.col = predict.col, predict.lty = predict.lty, 
+                       predict.lwd = predict.lwd, names = ax.names, orthogx = orthogx, 
+                       orthogy = orthogy)
+    
+  }
+  else bp$nom.axes <- list(which = NULL)
+  bp
+}
+
+# ----------------------------------------------------------------------------------------------
+#' Format aesthetics for the ordinal biplot axes
+#'
+#' @description
+#' This function allows the user to format the aesthetics for the ordinal biplot axes.
+#'
+#'
+#' @param bp an object of class \code{biplot}.
+#' @param X.names a vector of column names of \code{bp} to specify which axes should be labelled.
+#' @param which a vector containing the columns or variables for which the axes should be displayed, with default \code{1:p}.
+#' @param col the colour(s) for the axes, with default \code{grey(0.7)}. Alternatively, provide a vector of colours corresponding to \code{X.names}.
+#' @param lwd.factor a numeric value for increasing line width for each consecutive level
+#' @param reverse logical indicator to switch the narrow to wide calibration on the axis
+#' @param lwd the line width(s) for the axes, with default \code{1}.
+#' @param lty the line type(s) for the axes, with default \code{1}.
+#' @param label.dir a character string indicating the placement of the axis titles to the side of the figure. One of "\code{Orthog}" for axis titles to appear orthogonal to the side of the figure (default) , "\code{Hor}" for axis titles to appear horizontally or "\code{Paral}" for axis titles to appear parallel to the side of the figure.
+#' @param label.col the colour(s) for the axis labels, with default, \code{col}.
+#' @param label.cex the label expansion for the axis labels, with default \code{0.75}.
+#' @param label.line the distance of the axis title from the side of the figure, with default \code{0.1}.
+#' @param label.offset a four-component numeric vector controlling the distances axis titles are displayed from the side of the figure, with default \code{rep(0,4)}. Sides are numbered \code{1} to \code{4} according to \code{R} conventions.
+#' @param ticks an integer-valued vector indicating the number of tickmarks for each axis, with default \code{5} for each axis.
+#' @param tick.col the colour(s) for the tick marks, with default \code{col}.
+#' @param tick.size a vector specifying the sizes of tick marks for each axis, with default \code{1} for each .
+#' @param tick.label a logical value indicating whether the axes should be labelled, with default \code{TRUE}.
+#' @param tick.label.side a character string indicating the position of the tick label. One of "\code{below}" for the label to appear below the tick mark (default) or "\code{above}" for the label to appear above the tick mark.
+#' @param tick.label.col the colour(s) for the tick mark labels, with default \code{tick.col}.
+#' @param tick.label.cex the label expansion for the tick mark labels, with default \code{0.6}.
+#' @param predict.col the colour(s) for the predicted samples, with default \code{col}.
+#' @param predict.lwd the line width(s) for the predicted samples, with default \code{lwd}.
+#' @param predict.lty the line type(s) for the predicted samples, with default \code{lty}.
+#' @param ax.names a vector of size \code{p} containing user defined titles for the axes.
+#' @param orthogx a numeric vector of size \code{p} specifying the x-coordinate of the parallel transformation of each axis, with default \code{0} for each axis. This is only used when \code{dim.biplot = 2}. 
+#' @param orthogy a numeric vector of size \code{p} specifying the y-coordinate of the parallel transformation of each axis, with default \code{0} for each axis. This is only used when \code{dim.biplot = 2}.
+#'
+#' @return The object of class \code{biplot} will be appended with a list called \code{axes} containing the following elements:
+#' \item{which}{a vector containing the columns for which the axes are displayed.}
+#' \item{col}{the colour(s) of the axes.}
+#' \item{lwd.factor}{the factor with which to increase the line width for each level.}
+#' \item{reverse}{whether the axis goes narrow to wide or vice versa.}
+#' \item{lwd}{the line width(s) of the axes.}
+#' \item{lty}{the line type(s) of the axes.}
+#' \item{label.dir}{the placement of the axis titles to the side of the figure.}
+#' \item{label.col}{the colour(s) of the axis titles.}
+#' \item{label.cex}{the label expansion(s) of the axis titles.}
+#' \item{label.line}{the distance(s) of the axis titles from the side of the figure.}
+#' \item{ticks}{the number of tick marks per axis.}
+#' \item{tick.col}{the colour(s) of the tick marks.}
+#' \item{tick.size}{the size(s) of the tick marks.}
+#' \item{tick.label}{logical value(s) indicating whether axes are labelled.}
+#' \item{tick.label.side}{the position of the tick mark labels.}
+#' \item{tick.label.col}{the colour(s) of the tick mark labels.}
+#' \item{tick.label.cex}{the expansion(s) of the tick mark labels.}
+#' \item{predict.col}{the colour(s) of the predicted samples.}
+#' \item{predict.lty}{the line type(s) of the predicted samples.}
+#' \item{predict.lwd}{the line width(s) of the predicted samples.}
+#' \item{names}{the user defined axis titles.}
+#' \item{orthogx}{the horizontal translations for each axis.}
+#' \item{orthogy}{the vertical translations for each axis.}
+#' \item{vectors}{a logical value indicating whether calibrated axes are plotted.}
+#' 
+#' @usage
+#' ord.axes(bp, X.names=colnames(bp$Xcat)[bp$ax.type$ax.type=="ordinal"], 
+#'          which =1:sum(bp$ax.type$ax.type=="ordinal"), col = grey(0.7), 
+#'          reverse = rep(FALSE, sum(bp$ax.type$ax.type=="ordinal")), lwd.factor = 1.5, 
+#'          lwd = 1, lty = 1, label.dir = "Orthog", label.col = col, label.cex = 0.75, 
+#'          label.line = 0.1, label.offset=rep(0,4), ticks = 5, tick.col = col, 
+#'          tick.size = 1, tick.label = TRUE, tick.label.side = "below", 
+#'          tick.label.col = tick.col, tick.label.cex = 0.6, 
+#'          predict.col = col, predict.lwd = lwd, predict.lty = lty, ax.names = X.names, 
+#'          orthogx = 0, orthogy = 0)
+#' @aliases ord.axes
+#'
+#' @export
+#'
+#' @examples
+#' biplot(iris) |> CatPCA(cat.type = "ord") |> ord.axes(col="purple") |> plot()
+#'
+ord.axes <- function (bp, X.names=colnames(bp$Xcat)[bp$ax.type$ax.type=="ordinal"], 
+                      which =1:sum(bp$ax.type$ax.type=="ordinal"), col = grey(0.7), 
+                      reverse = rep(FALSE, sum(bp$ax.type$ax.type=="ordinal")), lwd.factor = 1.5, 
+                      lwd = 1, lty = 1, label.dir = "Orthog", label.col = col, label.cex = 0.75, 
+                      label.line = 0.1, label.offset=rep(0,4), ticks = 5, tick.col = col, 
+                      tick.size = 1, tick.label = TRUE, tick.label.side = "below",
+                      tick.label.col = tick.col, tick.label.cex = 0.6,
+                      predict.col = col, predict.lwd = lwd, predict.lty = lty, ax.names = X.names,
+                      orthogx = 0, orthogy = 0)
+{
+  p <- sum(bp$ax.type$ax.type=="ordinal")
+  num.levels.vec <- bp$ax.type$num.levels[bp$ax.type$ax.type == "ordinal"]
+  if (!is.null(p))
+  {
+    if (!all(is.numeric(which))) which <- match(which, X.names, nomatch = 0)
+    which <- which[which <= p]
+    which <- which[which > 0]
+    ax.num <- length(which)
+    
+    col.len <- length(col)
+    col <- col[ifelse(1:ax.num%%col.len==0,col.len,1:ax.num%%col.len)]
+    if(is.null(col)){col <- rep(0, ax.num)}
+    
+    lwdf.len <- length(lwd.factor)
+    lwd.factor <- lwd.factor[ifelse(1:ax.num%%lwdf.len==0,lwdf.len,1:ax.num%%lwdf.len)]
+    if(is.null(lwd.factor)){lwd.factor <- rep(0, ax.num)}
+    
+    lwd.len <- length(lwd)
+    lwd <- lwd[ifelse(1:ax.num%%lwd.len==0,lwd.len,1:ax.num%%lwd.len)]
+    if(is.null(lwd)){lwd <- rep(0, ax.num)}
+    
+    rev.len <- length(reverse)
+    reverse <- reverse[ifelse(1:ax.num%%rev.len==0,rev.len,1:ax.num%%rev.len)]
+    if(is.null(reverse)){reverse <- rep(FALSE, ax.num)}
+
+    lty.len <- length(lty)
+    lty <- lty[ifelse(1:ax.num%%lty.len==0,lty.len,1:ax.num%%lty.len)]
+    if(is.null(lty)){lty <- rep(0, ax.num)}
+    if (label.dir != "Orthog" & label.dir != "Hor" & label.dir != "Paral")
+      stop("Incorrect specification of axis label direction")
+    
+    label.col.len <- length(label.col)
+    label.col <- label.col[ifelse(1:ax.num%%label.col.len==0,label.col.len,1:ax.num%%label.col.len)]
+    if(is.null(label.col)){label.col <- rep(0, ax.num)}
+    
+    label.cex.len <- length(label.cex)
+    label.cex <- label.cex[ifelse(1:ax.num%%label.cex.len==0,label.cex.len,1:ax.num%%label.cex.len)]
+    if(is.null(label.cex)){label.cex <- rep(0, ax.num)}
+    
+    label.line.len <- length(label.line)
+    label.line <- label.line[ifelse(1:ax.num%%label.line.len==0,label.line.len,1:ax.num%%label.line.len)]
+    if(is.null(label.line)){label.line <- rep(0, ax.num)}
+    
+    ticks.len <- length(ticks)
+    ticks <- ticks[ifelse(1:ax.num%%ticks.len==0,ticks.len,1:ax.num%%ticks.len)]
+    if(is.null(ticks)){ticks <- rep(0, ax.num)}
+    
+    tick.col.len <- length(tick.col)
+    tick.col <- tick.col[ifelse(1:ax.num%%tick.col.len==0,tick.col.len,1:ax.num%%tick.col.len)]
+    if(is.null(tick.col)){tick.col <- rep(0, ax.num)}
+    
+    tick.size.len <- length(tick.size)
+    tick.size <- tick.size[ifelse(1:ax.num%%tick.size.len==0,tick.size.len,1:ax.num%%tick.size.len)]
+    if(is.null(tick.size)){tick.size <- rep(0, ax.num)}
+    
+    tick.label.len <- length(tick.label)
+    tick.label <- tick.label[ifelse(1:ax.num%%tick.label.len==0,tick.label.len,1:ax.num%%tick.label.len)]
+    if(is.null(tick.label)){tick.label <- rep("", ax.num)}
+    
+    tick.label.col.len <- length(tick.label.col)
+    tick.label.col <- tick.label.col[ifelse(1:ax.num%%tick.label.col.len==0,tick.label.col.len,1:ax.num%%tick.label.col.len)]
+    if(is.null(tick.label.col)){tick.label.col <- rep(0, ax.num)}
+    
+    tick.label.cex.len <- length(tick.label.cex)
+    tick.label.cex <- tick.label.cex[ifelse(1:ax.num%%tick.label.cex.len==0,tick.label.cex.len,1:ax.num%%tick.label.cex.len)]
+    if(is.null(tick.label.cex)){tick.label.cex <- rep(0, ax.num)}
+    
+    tick.label.side.len <- length(tick.label.side)
+    tick.label.side <- tick.label.side[ifelse(1:ax.num%%tick.label.side.len==0,tick.label.side.len,1:ax.num%%tick.label.side.len)]
+    if(is.null(tick.label.side)){tick.label.side <- rep(0, ax.num)}
+    
+    predict.col.len <- length(predict.col)
+    predict.col <- predict.col[ifelse(1:ax.num%%predict.col.len==0,predict.col.len,1:ax.num%%predict.col.len)]
+    if(is.null(predict.col)){predict.col <- rep(0, ax.num)}
+    
+    predict.lwd.len <- length(predict.lwd)
+    predict.lwd <- predict.lwd[ifelse(1:ax.num%%predict.lwd.len==0,predict.lwd.len,1:ax.num%%predict.lwd.len)]
+    if(is.null(predict.lwd)){predict.lwd <- rep(0, ax.num)}
+    
+    predict.lty.len <- length(predict.lty)
+    predict.lty <- predict.lty[ifelse(1:ax.num%%predict.lty.len==0,predict.lty.len,1:ax.num%%predict.lty.len)]
+    if(is.null(predict.lty)){predict.lty <- rep(0, ax.num)}
+    
+    ax.names.len <- length(ax.names)
+    ax.names <- ax.names[ifelse(1:p%%ax.names.len==0,ax.names.len,1:p%%ax.names.len)]
+    if(is.null(ax.names)){ax.names <- rep("", p)}
+    
+    orthogx.len <- length(orthogx)
+    orthogx <- orthogx[ifelse(1:p%%orthogx.len==0,orthogx.len,1:p%%orthogx.len)]
+    if(is.null(orthogx)){orthogx <- rep("", p)}
+    
+    orthogy.len <- length(orthogy)
+    orthogy <- orthogx[ifelse(1:p%%orthogy.len==0,orthogy.len,1:p%%orthogy.len)]
+    if(is.null(orthogy)){orthogy <- rep("", p)}
+    
+    bp$ord.axes = list(which = which, col = col, lwd.factor = lwd.factor, reverse = reverse, 
+                       lwd = lwd, lty = lty, label.dir = label.dir, 
+                       label.col = label.col, label.cex = label.cex, label.line = label.line, 
+                       ticks = ticks, tick.col = tick.col, tick.size = tick.size, 
+                       tick.label = tick.label, tick.label.col = tick.label.col, 
+                       tick.label.cex = tick.label.cex, tick.label.side=tick.label.side,
+                       predict.col = predict.col, predict.lty = predict.lty, 
+                       predict.lwd = predict.lwd, names = ax.names, orthogx = orthogx, 
+                       orthogy = orthogy)
+    
+  }
+  else bp$ord.axes <- list(which = NULL)
+  bp
+}
+
 # ----------------------------------------------------------------------------------------------
 #' Aesthetics for alpha-bags
 #'
@@ -771,12 +1182,47 @@ newsamples <- function (bp,  col = "darkorange1", pch = 1, cex = 1,
      any(label.side!="bottom") | any(label.offset !=0.5) | any(label.cex!=0.75))
     label<-TRUE
   nn <- nrow(bp$Xnew)
-  while (length(col) < nn) col <- c(col, col)
-  col <- as.vector(col[1:nn])
-  while (length(pch) < nn) pch <- c(pch, pch)
-  pch <- as.vector(pch[1:nn])
-  while (length(cex) < nn) cex <- c(cex, cex)
-  cex <- as.vector(cex[1:nn])
+  gg <- bp$new.g
+
+  if (length(col)==1)
+    col <- rep(col, nn)
+  else
+  {
+    col.len <- length(col)
+    col <- col[ifelse(1:gg%%col.len==0,col.len,1:gg%%col.len)]
+    if(is.null(col)){col <- rep(NA, gg)}
+    new.col <- rep(NA, nn)
+    for (j in 1:bp$new.g)
+      new.col[bp$new.group.aes == bp$new.g.names[j]] <- col[j]
+    col <- new.col
+  }
+
+  if (length(pch)==1)
+    pch <- rep(pch, nn)
+  else
+  {
+    pch.len <- length(pch)
+    pch <- pch[ifelse(1:gg%%pch.len==0,pch.len,1:gg%%pch.len)]
+    if(is.null(pch)){pch <- rep(NA, gg)}
+    new.pch <- rep(NA, nn)
+    for (j in 1:bp$new.g)
+      new.pch[bp$new.group.aes == bp$new.g.names[j]] <- pch[j]
+    pch <- new.pch
+  }
+  
+  if (length(cex)==1)
+    cex <- rep(cex, nn)
+  else
+  {
+    cex.len <- length(cex)
+    cex <- cex[ifelse(1:gg%%cex.len==0,cex.len,1:gg%%cex.len)]
+    if(is.null(cex)){cex <- rep(NA, gg)}
+    new.cex <- rep(NA, nn)
+    for (j in 1:bp$new.g)
+      new.cex[bp$new.group.aes == bp$new.g.names[j]] <- cex[j]
+    cex <- new.cex
+  }
+
   if (label[1] == "ggrepel")
   {
     label <- label[1]
diff --git a/R/biplot.R b/R/biplot.R
index 158f93e..6f8c829 100644
--- a/R/biplot.R
+++ b/R/biplot.R
@@ -85,8 +85,10 @@
 #'  * [rotate()]
 #' 
 #' @references
-#' Gabriel, K.R. (1971) The biplot graphic display of matrices with application to principal component analysis. \emph{Biometrika.} 58(3):453–467.<br><br>
-#' Gower, J., Gardner-Lubbe, S. & Le Roux, N. (2011, ISBN: 978-0-470-01255-0) \emph{Understanding Biplots.} Chichester, England: John Wiley & Sons Ltd.<br><br>
+#' Gabriel, K.R. (1971) The biplot graphic display of matrices with application to principal component analysis. \emph{Biometrika.} 58(3):453–467.
+#' 
+#' Gower, J., Gardner-Lubbe, S. & Le Roux, N. (2011, ISBN: 978-0-470-01255-0) \emph{Understanding Biplots.} Chichester, England: John Wiley & Sons Ltd.
+#' 
 #' Gower, J.C. & Hand, D.J.(1996, ISBN: 0-412-71630-5) \emph{Biplots.} London: Chapman & Hall.
 #'
 #' @usage biplot(data, classes = NULL, group.aes = NULL, center = TRUE, scaled = FALSE,
@@ -740,12 +742,14 @@ summary.biplot <- function (object, adequacy = TRUE, axis.predictivity = TRUE,
 #'                containing supplementary data points to be added onto the biplot.
 #' @param newvariable a new data set, similar in structure to the data set supplied to \code{biplot()}
 #'                containing supplementary variables to be added onto the biplot.
+#' @param new.group.aes aesthetics for the new samples
 #'
 #' @return The object of class \code{biplot} will be appended with the following elements:
 #' \item{Xnew.raw}{the new data.}
 #' \item{Xnew}{the matrix of the centered and scaled new numeric variables of new data.}
 #' \item{Xnew.cat}{the matrix of the categorical variables of new data.}
 #' \item{Znew}{the matrix of the coordinates of the new data in the biplot.}
+#' \item{new.group.aes}{aeshetics for the new samples}
 #'
 #' For an object of class \code{CA} the following additional elements will be appended:
 #' \item{newrowcoor}{the matrix of row coordinates of the new data in the biplot.}
@@ -758,7 +762,8 @@ summary.biplot <- function (object, adequacy = TRUE, axis.predictivity = TRUE,
 #' biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = "Symmetric") |> 
 #'      interpolate(newdata = HairEyeColor[,,1]) |> plot()
 #'
-interpolate <- function (bp, newdata=NULL, newvariable=NULL)
+interpolate <- function (bp, newdata=NULL, newvariable=NULL, 
+                         new.group.aes = NULL)
 {
   # New samples 
   if(!is.null(newdata))
@@ -811,7 +816,19 @@ interpolate <- function (bp, newdata=NULL, newvariable=NULL)
       Znew <- Ynew[,bp$e.vects]
     }
     
-    
+    if (!is.null(new.group.aes)) 
+    { 
+      bp$new.group.aes <- factor(new.group.aes)
+      bp$new.g.names <-levels(factor(new.group.aes))
+      bp$new.g <- length(bp$new.g.names)
+    }
+    else
+    {
+      bp$new.group.aes <- factor(rep(1, nrow(Xnew)))
+      bp$new.g.names <-levels(bp$new.group.aes)
+      bp$new.g <- length(bp$new.g.names)
+    }
+
     bp$Xnew.raw <- Xnew.raw
     bp$Xnew <- Xnew
     bp$Xnew.cat <- Xnew.cat
@@ -1013,6 +1030,9 @@ prediction <- function (bp, predict.samples=NULL,predict.means=NULL,which=1:bp$p
 #'   classify(col=c("red","blue","orange"),opacity=0.1) |> plot()
 classify <- function(bp, classify.regions = TRUE, col=ez.col, opacity=0.4, borders = FALSE)
 {
+  if (!requireNamespace("caret", quietly = TRUE)) {
+   stop("Package 'caret' is required for this function. Please install it.", call. = FALSE)
+  }
   if (inherits(bp, "CVA"))
   {
     while (length(col) < bp$g) col <- c(col, col)
diff --git a/R/biplotEZ-package.R b/R/biplotEZ-package.R
index d95718a..0b92bb4 100644
--- a/R/biplotEZ-package.R
+++ b/R/biplotEZ-package.R
@@ -54,5 +54,7 @@
 #' @importFrom graphics points
 #' @importFrom graphics text
 #' @importFrom grDevices colorRampPalette
+#' @importFrom Rcpp sourceCpp
+#' @useDynLib biplotEZ, .registration = TRUE
 ## usethis namespace: end
 NULL
diff --git a/R/calibrate_axes.R b/R/calibrate_axes.R
deleted file mode 100644
index 5aa838f..0000000
--- a/R/calibrate_axes.R
+++ /dev/null
@@ -1,59 +0,0 @@
-#' Calibrate Biplot Axes
-#' 
-#' Convenience function to obtain the coordinates of the calibrated ticks marks on the biplot
-#' 
-#' @param x an object of class \code{biplot}
-#'
-#' @return An ordered list containing the coordinates the of tick marks to plotted on the biplot
-#' @export
-#'
-#' @examples
-#' x<-biplot(iris) |> PCA()
-#' coordinates<-axes_coordinates(x)
-axes_coordinates<-function(x){
-  Z <- x$Z
-  if(!inherits(x,"CA")) {
-    if (is.null(x$axes)) x <- axes(x)}
-  ax.aes <- x$axes
-  if (length(ax.aes$which) > 0)
-  {
-    if (!is.null(x$Lmat))
-      if (nrow(x$Lmat) == ncol(x$Lmat)) 
-        Xhat <- x$Z %*% solve(x$Lmat)[x$e.vects,]
-    else Xhat <- x$X
-    else
-      Xhat <- x$X
-    if (x$scaled) Xhat <- scale(Xhat, center=FALSE, scale=1/x$sd)
-    if (x$center) Xhat <- scale(Xhat, center=-1*x$means, scale=FALSE)
-    
-    if(!is.null(x$PCOaxes)) 
-    { if (x$PCOaxes == "splines") # Only for PCO - if axes (type) is set to splines.  
-    {
-      z.axes <- lapply(1:length(ax.aes$which), biplot.spline.axis, Z, x$raw.X, 
-                       means=x$means, sd=x$sd, n.int=ax.aes$ticks, 
-                       spline.control=x$spline.control)
-
-      
-    } 
-      else if(x$PCOaxes == "regression") # Only for PCO - if axes (type) is set to regression. 
-      {
-        z.axes <- lapply(1:length(ax.aes$which), .calibrate.axis, Xhat, x$means, x$sd, x$ax.one.unit, ax.aes$which,
-                         ax.aes$ticks, ax.aes$orthogx, ax.aes$orthogy)
-        
-        for(i in 1:length(z.axes)){
-          z.axes[[i]]<-z.axes[[i]][[1]]
-        }
-      }
-    } 
-    else 
-    { # Otherwise calibrate linear axes
-      z.axes <- lapply(1:length(ax.aes$which), .calibrate.axis, Xhat, x$means, x$sd, x$ax.one.unit, ax.aes$which,
-                       ax.aes$ticks, ax.aes$orthogx, ax.aes$orthogy)
-      for(i in 1:length(z.axes)){
-        z.axes[[i]]<-z.axes[[i]][[1]]
-      }
-    }
-  }
-  
-  return(z.axes)
-}
\ No newline at end of file
diff --git a/R/clouds.R b/R/clouds.R
index 70a5873..af25f24 100644
--- a/R/clouds.R
+++ b/R/clouds.R
@@ -153,7 +153,7 @@ density1D <- function(bp,which = NULL, h = "nrd0", kernel="gaussian",
 #' \item{lwd}{vector of line widths for the \eqn{\alpha}-bags.}
 #'
 #' @references
-#' Gower, J., Gardner-Lubbe, S. & Le Roux, N. (2011, ISBN: 978-0-470-01255-0) \emph{Understanding Biplots.} Chichester, England: John Wiley & Sons Ltd.<br><br>
+#' Gower, J., Gardner-Lubbe, S. & Le Roux, N. (2011, ISBN: 978-0-470-01255-0) \emph{Understanding Biplots.} Chichester, England: John Wiley & Sons Ltd.
 #'
 #' @export
 #' @usage alpha.bags(bp, alpha = 0.95, which = NULL, col = ez.col[which], lty = 1,
@@ -168,6 +168,9 @@ alpha.bags <- function(bp, alpha=0.95, which = NULL, col = ez.col[which], lty =
                        lwd = 1, max = 2500, trace = TRUE, opacity = 0.25,
                        outlying=FALSE)
 { 
+  if (!requireNamespace("geometry", quietly = TRUE)) {
+     stop("Package 'geometry' is required for this function. Please install it.", call. = FALSE)
+   }
   g <- bp$g
   g.names <- bp$g.names
   if (is.null(which)) which <- 1:g
@@ -564,6 +567,14 @@ calc.alpha.bags <- function (x, y, aa=0.95, na.rm = TRUE, approx.limit = 2500, p
   }
   xydata <- if (missing(y)) x
   else cbind(x, y)
+  if (all(!is.na(apply(xydata,2,stats::sd))))
+  if (any(apply(xydata,2,stats::sd)<1e-15))
+  {
+    xy <- apply(xydata, 2, mean)
+    xy <- jitter(rbind (xy, xy, xy))
+    return (list(xy=xy))
+  }
+    
   if (is.data.frame(xydata)) xydata <- as.matrix(xydata)
   if (any(is.na(xydata))) {
     if (na.rm) {
diff --git a/R/plot2D.R b/R/plot2D.R
index 1842a16..9a7d28c 100644
--- a/R/plot2D.R
+++ b/R/plot2D.R
@@ -74,7 +74,6 @@
                       group.aes = group.aes, pch = rep(NA,n),
                       col = rep(NA,n), cex = rep(NA,n),
                       cex.vec, Z)
-
     for(j in 1:length(sample.aes$which))
     {
       ZZ$pch[group.aes==g.names[sample.aes$which[j]]] = sample.aes$pch[j]
@@ -176,41 +175,45 @@
   if(!any(invals))
     return()
   ZZ <- Z[sample.aes$which,]
-
-  toetsers<-invals[sample.aes$which]
-  if (sample.aes$label[1]=="ggrepel")
+  
+  if (nrow(ZZ) > 0)
   {
-    for (j in 1:nrow(ggrepel.labs$coords)){
-      graphics::text(ggrepel.labs$coords[j, 1], ggrepel.labs$coords[j, 2], 
-                     labels = ggrepel.labs$coords[j,3],
-                     cex = sample.aes$label.cex[ggrepel.labs$visible[j]],
-                     col = sample.aes$label.col[ggrepel.labs$visible[j]])
+    toetsers<-invals[sample.aes$which]
+    
+    if (sample.aes$label[1]=="ggrepel")
+    {
+      for (j in 1:nrow(ggrepel.labs$coords)){
+        graphics::text(ggrepel.labs$coords[j, 1], ggrepel.labs$coords[j, 2], 
+                       labels = ggrepel.labs$coords[j,3],
+                       cex = sample.aes$label.cex[ggrepel.labs$visible[j]],
+                       col = sample.aes$label.col[ggrepel.labs$visible[j]])
+      }
+      for (j in ggrepel.labs$textlines)
+      { 
+        label.val <- rownames(ZZ)[j]
+        label.xy <- ggrepel.labs$coords[match(label.val, ggrepel.labs$coords[,3]),1:2]
+        graphics::lines (x=c(label.xy[1],ZZ[j,1]), y=c(label.xy[2],ZZ[j,2]), col=sample.aes$label.col[j])
+      }
     }
-    for (j in ggrepel.labs$textlines)
-    { 
-      label.val <- rownames(ZZ)[j]
-      label.xy <- ggrepel.labs$coords[match(label.val, ggrepel.labs$coords[,3]),1:2]
-      graphics::lines (x=c(label.xy[1],ZZ[j,1]), y=c(label.xy[2],ZZ[j,2]), col=sample.aes$label.col[j])
+    else
+    {
+      Z.labels <- rownames(Z)[sample.aes$which]
+      for (j in 1:length(sample.aes$label.side))
+      { if(!toetsers[j])
+        next
+        text.pos <- match(sample.aes$label.side[j], c("bottom", "left", "top", "right"))
+        if (sample.aes$label[j]) graphics::text(ZZ[j, 1], ZZ[j, 2], labels = Z.labels[j],
+                                                cex = sample.aes$label.cex[j], col = sample.aes$label.col[j],
+                                                pos = text.pos, offset = sample.aes$label.offset[j])
+      }
     }
-  }
-  else
-  {
-    Z.labels <- rownames(Z)[sample.aes$which]
-    for (j in 1:length(sample.aes$label.side))
-    { if(!toetsers[j])
+    for (j in 1:length(sample.aes$which)){
+      if(!toetsers[j])
         next
-      text.pos <- match(sample.aes$label.side[j], c("bottom", "left", "top", "right"))
-    if (sample.aes$label[j]) graphics::text(ZZ[j, 1], ZZ[j, 2], labels = Z.labels[j],
-                                            cex = sample.aes$label.cex[j], col = sample.aes$label.col[j],
-                                            pos = text.pos, offset = sample.aes$label.offset[j])
+      graphics::points(x = Z[sample.aes$which[j], 1], y = Z[sample.aes$which[j], 2],
+                       pch = sample.aes$pch[j], col = sample.aes$col[j], cex = sample.aes$cex[j])
     }
   }
-  for (j in 1:length(sample.aes$which)){
-    if(!toetsers[j])
-      next
-    graphics::points(x = Z[sample.aes$which[j], 1], y = Z[sample.aes$which[j], 2],
-                     pch = sample.aes$pch[j], col = sample.aes$col[j], cex = sample.aes$cex[j])
-  }
 }
 
 #' Title
@@ -352,6 +355,61 @@
 
 
 
+
+#----------
+#' .calibrate.cat.axis
+#'
+#' @param j Index of axis to calibrate
+#' @param axes.rows 
+#' @param ax.which 
+#' @param ax.orthogxvec 
+#' @param ax.orthogyvec 
+#' @param markers
+#'
+#' @noRd
+.calibrate.cat.axis <- function (j, axes.rows, ax.which, ax.orthogxvec, ax.orthogyvec,
+                                 markers)
+{
+  ax.num <- ax.which[j]
+  ax.direction <- axes.rows[ax.num,]
+  r <- ncol(axes.rows)
+  ax.orthog <- rbind(ax.orthogxvec, ax.orthogyvec)
+  if (nrow(ax.orthog) < r)    ax.orthog <- rbind(ax.orthog, 0)
+  if (nrow(axes.rows) > 1)    phi.vec <- diag(1 / diag(axes.rows %*% t(axes.rows))) %*% axes.rows %*% ax.orthog[, ax.num]
+  else  phi.vec <- (1 / (axes.rows %*% t(axes.rows))) %*% axes.rows %*% ax.orthog[, ax.num]
+
+  std.range <- range(markers[[ax.num]])
+  std.ax.tick.label.min <-  min(markers[[ax.num]]) - (std.range[2] - std.range[1])
+  std.ax.tick.label.max <-  max(markers[[ax.num]]) + (std.range[2] - std.range[1])
+  axis.vals <- c(std.ax.tick.label.min, markers[[ax.num]], std.ax.tick.label.max)
+
+  number.points <- length(axis.vals)
+  axis.points <- matrix(0, nrow = number.points, ncol = r)
+  for (i in 1:r)
+    axis.points[, i] <-  ax.orthog[i, ax.num] + (axis.vals - phi.vec[ax.num]) * ax.direction[i]
+  rownames(axis.points)  <- c("", names(markers[[ax.num]]), "")
+
+  #slope = delta y / delta x of two datapoints
+  slope <- (axis.points[1, 2] - axis.points[2, 2]) / (axis.points[1, 1] - axis.points[2, 1])
+  #if slope is infinite then all x-values are same
+  v <- NULL
+  if (is.na(slope))
+  {  v <- axis.points[1, 1]
+     slope = NULL
+  }
+  else if (abs(slope) == Inf)
+       {  v <- axis.points[1, 1]
+          slope = NULL
+       }
+  
+  #y=mx+c... c=y-mx
+  intercept <- axis.points[1, 2] - slope * axis.points[1, 1]
+  
+  retvals <- list(coords = axis.points, a = intercept, b = slope, v = v)
+  return(retvals)
+}
+
+
 #' Insert tick marks and label - called by .marker.func
 #'
 #' @param x x-coo of tick
@@ -366,14 +424,14 @@
 #' @param offset REMOVE
 #' @param label.col color of label
 #' @param cex Bigness of label
-#' @param label_pos 1 for above -1 for below
+#' @param label.pos 1 for above -1 for below
 #'
 #' @return inserts tick marks and label to plot
 #' @noRd
 .marker.label <- function(x, y, grad, marker.val, 
                              expand = 1, col, label.on.off, 
                              label.col, cex,
-                             label_pos=-1,usr)
+                             label.pos=-1,usr)
 {
   
   #get fraction of plot width and expand
@@ -382,14 +440,14 @@
   if (grad == "v"){
     graphics::lines(rep(x, 2), c(y - d, y + d), col = col)
     if (label.on.off == 1) 
-      graphics::text(x, y - label_pos(d+2.5*mm), label = marker.val,
+      graphics::text(x, y - label.pos(d+2.5*mm), label = marker.val,
                      col = label.col, 
                      cex = cex)
   }
   if (grad == "h"){
     graphics::lines(c(x - d, x + d), rep(y, 2), col = col)
     if (label.on.off == 1) 
-      graphics::text(x - label_pos*(d+2.5*mm), y, label = marker.val, 
+      graphics::text(x - label.pos*(d+2.5*mm), y, label = marker.val, 
                      col = label.col, cex = cex,
                      srt=90)
   }
@@ -406,14 +464,14 @@
     
     if (label.on.off == 1){
       if(grad>0)
-        graphics::text(x+label_pos*(2.5*x_shift+b), 
-                       y+label_pos*(2.5*y_shift+a), 
+        graphics::text(x+label.pos*(2.5*x_shift+b), 
+                       y+label.pos*(2.5*y_shift+a), 
                        label = marker.val, 
                        col = label.col,
                        cex = cex,srt=180+(90+atan(grad)*180/pi))
       
       if(grad<0)
-        graphics::text(x-label_pos*(2.5*x_shift+b), y-label_pos*(2.5*y_shift+a), 
+        graphics::text(x-label.pos*(2.5*x_shift+b), y-label.pos*(2.5*y_shift+a), 
                        label = marker.val, 
                        col = label.col,
                        cex = cex,srt=(90+atan(grad)*180/pi))
@@ -439,20 +497,17 @@
 #' @return prints markers to plot
 #' @noRd
 .marker.func <- function(vec, coef, col, tick.size, 
-                         label_pos, label.col, cex,
+                         label.pos, label.col, cex,
                          usr)
 {
 
-  if(label_pos=="below")
-    label_pos<--1
-  if(label_pos=="above")
-    label_pos<- 1
+  if(label.pos=="below")     label.pos<--1
+  if(label.pos=="above")    label.pos<- 1
   
-
   ## vec = [x_coo, y_coo, marker val, show]
   ## coef = [intercept, slope]
-  x <- vec[1]
-  y <- vec[2]
+  x <- as.numeric(vec[1])
+  y <- as.numeric(vec[2])
   marker.val <- vec[3]
   label.on.off <- vec[4]
   if (is.na(coef[2]))
@@ -460,20 +515,20 @@
                      expand = tick.size, col = col, 
                      label.on.off = label.on.off, 
                      label.col = label.col, 
-                     cex = cex,usr=usr, label_pos=label_pos)
+                     cex = cex,usr=usr, label.pos=label.pos)
   
   else if (coef[2] == 0) # line is verticle
     .marker.label(x, y, grad = "v", marker.val, 
                      expand = tick.size, col = col, 
                      label.on.off = label.on.off,
                      label.col = label.col,
-                     cex = cex, usr=usr,label_pos=label_pos)
+                     cex = cex, usr=usr,label.pos=label.pos)
   else
     .marker.label(x, y, grad = -1/coef[2], marker.val, 
                      expand = tick.size, col = col, 
                      label.on.off = label.on.off, 
                      label.col = label.col, 
-                     cex = cex, usr=usr,label_pos=label_pos)
+                     cex = cex, usr=usr,label.pos=label.pos)
 }
 
 
@@ -503,60 +558,90 @@
      marker.mat <- marker.mat[rev(order(marker.mat[, 3])), ]
      x.vals <- marker.mat[, 1]
      y.vals <- marker.mat[, 2]
+     k <- nrow(marker.mat)
   
-     lin.coef<-c(a=this.axis$a,b=this.axis$b)
      if (is.null(this.axis$b))
        graphics::abline(v = this.axis$v, col = ax.aes$col[i], lwd = ax.aes$lwd[i], lty = ax.aes$lty[i])
      else
-       graphics::abline(coef=lin.coef, col = ax.aes$col[i], lwd = ax.aes$lwd[i], lty = ax.aes$lty[i])
-    if (ax.aes$label.dir == "Hor") {  graphics::par(las = 1)
-                                      adjust <- c(0.5, 1, 0.5, 0)       }
-    if (ax.aes$label.dir == "Orthog") { graphics::par(las = 2)
-                                        adjust <- c(1, 1, 0, 0)         }
-    if (ax.aes$label.dir == "Paral") {  graphics::par(las = 0)
-                                        adjust <- c(0.5, 0.5, 0.5, 0.5) }
-    h <- nrow(marker.mat)
-    if (is.null(this.axis$b))
-     { if (y.vals[1] < y.vals[h])
-         graphics::mtext(text = ax.aes$names[i], side = 1, line = ax.aes$label.line[i], adj = adjust[1], at = x.vals[1], col = ax.aes$label.col[i], cex = ax.aes$label.cex[i])
+       graphics::abline(coef=c(this.axis$a, this.axis$b), col = ax.aes$col[i], lwd = ax.aes$lwd[i], lty = ax.aes$lty[i])
+     if (ax.aes$label.dir == "Hor") 
+     {  graphics::par(las = 1)
+       adjust <- c(0.5, 1, 0.5, 0)       
+     }
+     if (ax.aes$label.dir == "Orthog") 
+     {  graphics::par(las = 2)
+       adjust <- c(1, 1, 0, 0)         
+     }
+     if (ax.aes$label.dir == "Paral") 
+     {  graphics::par(las = 0)
+       adjust <- c(0.5, 0.5, 0.5, 0.5) 
+     }
+     
+     if (is.null(this.axis$b))
+     {  if (y.vals[1] < y.vals[k])
+          graphics::mtext(text = ax.aes$names[i], side = 1, line = ax.aes$label.line[i], 
+                       adj = adjust[1], at = x.vals[1], col = ax.aes$label.col[i], 
+                       cex = ax.aes$label.cex[i])
        else
-         graphics::mtext(text = ax.aes$names[i], side = 3, line = ax.aes$label.line[i], adj = adjust[3], at = y.vals[1], col = ax.aes$label.col[i], cex = ax.aes$label.cex[i])
+         graphics::mtext(text = ax.aes$names[i], side = 3, line = ax.aes$label.line[i], 
+                         adj = adjust[3], at = y.vals[1], col = ax.aes$label.col[i], 
+                         cex = ax.aes$label.cex[i])
      }
-    else
-      { y1.ster <- lin.coef[2] * usr[1] + lin.coef[1]
-        y2.ster <- lin.coef[2] * usr[2] + lin.coef[1]
-        x1.ster <- (usr[3] - lin.coef[1])/lin.coef[2]
-        x2.ster <- (usr[4] - lin.coef[1])/lin.coef[2]
-        if (lin.coef[2] == 0)
-          { if (x.vals[1] < x.vals[h])
-              graphics::mtext(text = ax.aes$names[i], side = 2, line = ax.aes$label.line[i], adj = adjust[2], at = y.vals[1], col = ax.aes$label.col[i], cex = ax.aes$label.cex[i])
-            else
-              graphics::mtext(text = ax.aes$names[i], side = 4, line = ax.aes$label.line[i], adj = adjust[4], at = y.vals[1], col = ax.aes$label.col[i], cex = ax.aes$label.cex[i])
-          }
-        if (lin.coef[2] > 0)
-          {  if (x.vals[1] < x.vals[h])
-               if (y1.ster <= usr[4] & y1.ster >= usr[3])
-                 graphics::mtext(text = ax.aes$names[i], side = 2, line = ax.aes$label.line[i], adj = adjust[2], at = y1.ster, col = ax.aes$label.col[i], cex = ax.aes$label.cex[i])
-               else
-                 graphics::mtext(text = ax.aes$names[i], side = 1, line = ax.aes$label.line[i], adj = adjust[1], at = x1.ster, col = ax.aes$label.col[i], cex = ax.aes$label.cex[i])
-               else if (y2.ster <= usr[4] & y2.ster >= usr[3])
-                      graphics::mtext(text = ax.aes$names[i], side = 4, line = ax.aes$label.line[i], adj = adjust[4], at = y2.ster, col = ax.aes$label.col[i], cex = ax.aes$label.cex[i])
-                    else
-                      graphics::mtext(text = ax.aes$names[i], side = 3, line = ax.aes$label.line[i], adj = adjust[3], at = x2.ster, col = ax.aes$label.col[i], cex = ax.aes$label.cex[i])
-          }
-        if (lin.coef[2] < 0)
-          {  if (x.vals[1] < x.vals[h])
-               if (y1.ster <= usr[4] & y1.ster >= usr[3])
-                 graphics::mtext(text = ax.aes$names[i], side = 2, line = ax.aes$label.line[i], adj = adjust[2], at = y1.ster, col = ax.aes$label.col[i], cex = ax.aes$label.cex[i])
-               else
-                 graphics::mtext(text = ax.aes$names[i], side = 3, line = ax.aes$label.line[i], adj = adjust[3], at = x2.ster, col = ax.aes$label.col[i], cex = ax.aes$label.cex[i])
-             else if (y2.ster <= usr[4] & y2.ster >= usr[3])
-                    graphics::mtext(text = ax.aes$names[i], side = 4, line = ax.aes$label.line[i], adj = adjust[4], at = y2.ster, col = ax.aes$label.col[i], cex = ax.aes$label.cex[i])
-                  else
-                    graphics::mtext(text = ax.aes$names[i], side = 1, line = ax.aes$label.line[i], adj = adjust[1], at = x1.ster, col = ax.aes$label.col[i], cex = ax.aes$label.cex[i])
+     else
+     {  y1.ster <- this.axis$b * usr[1] + this.axis$a
+        y2.ster <- this.axis$b * usr[2] + this.axis$a
+        x1.ster <- (usr[3] - this.axis$a)/this.axis$b
+        x2.ster <- (usr[4] - this.axis$a)/this.axis$b
+        if (this.axis$b == 0)
+        { if (x.vals[1] < x.vals[k])
+            graphics::mtext(text = ax.aes$names[i], side = 2, line = ax.aes$label.line[i], 
+                            adj = adjust[2], at = y.vals[1], col = ax.aes$label.col[i], 
+                            cex = ax.aes$label.cex[i])
+          else
+            graphics::mtext(text = ax.aes$names[i], side = 4, line = ax.aes$label.line[i], 
+                            adj = adjust[4], at = y.vals[1], col = ax.aes$label.col[i], 
+                            cex = ax.aes$label.cex[i])
+        }
+        if (this.axis$b > 0)
+         {  if (x.vals[1] < x.vals[k])
+              if (y1.ster <= usr[4] & y1.ster >= usr[3])
+                graphics::mtext(text = ax.aes$names[i], side = 2, line = ax.aes$label.line[i], 
+                                adj = adjust[2], at = y1.ster, col = ax.aes$label.col[i], 
+                                cex = ax.aes$label.cex[i])
+              else
+                graphics::mtext(text = ax.aes$names[i], side = 1, line = ax.aes$label.line[i], 
+                                adj = adjust[1], at = x1.ster, col = ax.aes$label.col[i], 
+                                cex = ax.aes$label.cex[i])
+            else if (y2.ster <= usr[4] & y2.ster >= usr[3])
+                   graphics::mtext(text = ax.aes$names[i], side = 4, line = ax.aes$label.line[i], 
+                                   adj = adjust[4], at = y2.ster, col = ax.aes$label.col[i], 
+                                   cex = ax.aes$label.cex[i])
+                 else
+                   graphics::mtext(text = ax.aes$names[i], side = 3, line = ax.aes$label.line[i], 
+                                   adj = adjust[3], at = x2.ster, col = ax.aes$label.col[i], 
+                                   cex = ax.aes$label.cex[i])
           }
-     }
-  
+        if (this.axis$b < 0)
+        {  if (x.vals[1] < x.vals[k])
+             if (y1.ster <= usr[4] & y1.ster >= usr[3])
+               graphics::mtext(text = ax.aes$names[i], side = 2, line = ax.aes$label.line[i], 
+                               adj = adjust[2], at = y1.ster, col = ax.aes$label.col[i], 
+                               cex = ax.aes$label.cex[i])
+             else
+               graphics::mtext(text = ax.aes$names[i], side = 3, line = ax.aes$label.line[i], 
+                               adj = adjust[3], at = x2.ster, col = ax.aes$label.col[i], 
+                               cex = ax.aes$label.cex[i])
+           else if (y2.ster <= usr[4] & y2.ster >= usr[3])
+                  graphics::mtext(text = ax.aes$names[i], side = 4, line = ax.aes$label.line[i], 
+                                  adj = adjust[4], at = y2.ster, col = ax.aes$label.col[i], 
+                                  cex = ax.aes$label.cex[i])
+                else
+                  graphics::mtext(text = ax.aes$names[i], side = 1, line = ax.aes$label.line[i], 
+                                  adj = adjust[1], at = x1.ster, col = ax.aes$label.col[i], 
+                                  cex = ax.aes$label.cex[i])
+         }
+      }
+     
   invals <- x.vals < usr[2] & x.vals > usr[1] & y.vals < usr[4] & y.vals > usr[3]
   std.markers <- marker.mat[invals, 3]
   if (is.numeric(std.markers)) std.markers <- zapsmall(std.markers)
@@ -565,18 +650,308 @@
   if (ax.aes$tick.label[i]) label.on.off <- rep(1, sum(invals))  else label.on.off <- rep(0, sum(invals))
   if (!ax.aes$tick.label[i]) label.on.off[c(1, length(label.on.off))] <- 1
   if(sum(invals)>0) apply(data.frame(x.vals, y.vals, std.markers, label.on.off), 1, .marker.func,
-                          coef = lin.coef, col = ax.aes$tick.col[i], tick.size = ax.aes$tick.size[i],
-                          label.col = ax.aes$tick.label.col[i], label_pos=ax.aes$tick.label.side[i],
+                          coef = c(this.axis$a, this.axis$b), col = ax.aes$tick.col[i], tick.size = ax.aes$tick.size[i],
+                          label.col = ax.aes$tick.label.col[i], label.pos=ax.aes$tick.label.side[i],
                           cex = ax.aes$tick.label.cex[i], usr=usr)
   
   
   if(ax.num %in% predict_which)
     {
-      if (!is.null(predict.mat)) apply(cbind(predict.mat,y.vals[1]), 1, .predict.func, coef = lin.coef,col=ax.aes$predict.col,lwd=ax.aes$predict.lwd,lty=ax.aes$predict.lty)
+      if (!is.null(predict.mat)) apply(cbind(predict.mat,y.vals[1]), 1, .predict.func, coef = c(this.axis$a, this.axis$b),
+                                       col=ax.aes$predict.col,lwd=ax.aes$predict.lwd,lty=ax.aes$predict.lty)
+    }
+  }
+}
+
+#' Plot linear nominal axes on biplots
+#'
+#' @param z.axes list containing all the info to draw axis. see below
+#' @param ax.aes Axis aestetics
+#' @param predict.mat Xhat
+#' @param too.small cutoff: predictivity smaller than cutoff not plotted
+#' @param usr plot dim
+#'
+#' z.axes:    List containing following components for each axis:
+#' $coords:   Tick mark coordinates
+#' $a $b $v:  Intercept, slope, vertical
+#' 
+#' @noRd
+.nom.axes.plot <- function(z.axes, ax.aes, predict.mat, too.small, usr, predict_which)
+{
+  for (i in 1:length(ax.aes$which))
+  {  ax.num <- ax.aes$which[i]
+     if (!is.null(too.small)) if (ax.num %in% too.small) next
+     this.axis <- z.axes[[i]]
+     marker.mat <- this.axis$coords
+     marker.mat <- marker.mat[order(marker.mat[, 1]), ]
+  
+     ends.mat <- c(usr[1], NA)
+     k <- nrow(marker.mat)
+     for (j in 2:nrow(marker.mat))
+       ends.mat <- rbind (ends.mat, (marker.mat[j,1:2] + marker.mat[j-1,1:2])/2)
+     ends.mat <- rbind (ends.mat, c(usr[2],NA))
+     x.vals <- marker.mat[, 1]
+     y.vals <- marker.mat[, 2]
+     
+     if (ends.mat[1,1] < ends.mat[2,1]) ends.mat[2,] <- ends.mat[1,]
+     ends.mat <- ends.mat[-1,]
+     if (ends.mat[k,1] > ends.mat[k-1,1]) ends.mat[k-1,] <- ends.mat[k,]
+     ends.mat <- ends.mat[-k,]
+
+     if (is.null(this.axis$b))
+     {
+       ends.mat[1,1] <- ends.mat[nrow(ends.mat),1] <- 0
+       ends.mat[1,2] <- usr[3]
+       ends.mat[nrow(ends.mat),2] <- usr[4]
+       # graphics::abline(v = this.axis$v, col = ax.aes$col[i], lwd = ax.aes$lwd[i], lty = ax.aes$lty[i])
+     }
+     else
+     {
+       ends.mat[1,2] <- this.axis$a + ends.mat[1,1]*this.axis$b
+       ends.mat[nrow(ends.mat),2] <- this.axis$a + ends.mat[nrow(ends.mat),1]*this.axis$b
+     }
+     
+     if (ax.aes$label.dir == "Hor") 
+     {  graphics::par(las = 1)
+        adjust <- c(0.5, 1, 0.5, 0)       
+     }
+     if (ax.aes$label.dir == "Orthog") 
+     {  graphics::par(las = 2)
+        adjust <- c(1, 1, 0, 0)         
+     }
+     if (ax.aes$label.dir == "Paral") 
+     {  graphics::par(las = 0)
+        adjust <- c(0.5, 0.5, 0.5, 0.5) 
+     }
+     
+     if (is.null(this.axis$b))
+     {  if (y.vals[1] < y.vals[k])
+          graphics::mtext(text = ax.aes$names[i], side = 1, line = ax.aes$label.line[i], 
+                          adj = adjust[1], at = x.vals[1], col = ax.aes$label.col[i], 
+                          cex = ax.aes$label.cex[i])
+        else
+          graphics::mtext(text = ax.aes$names[i], side = 3, line = ax.aes$label.line[i], 
+                          adj = adjust[3], at = y.vals[1], col = ax.aes$label.col[i], 
+                          cex = ax.aes$label.cex[i])
+     }
+     else
+     {  y1.ster <- this.axis$b * usr[1] + this.axis$a
+        y2.ster <- this.axis$b * usr[2] + this.axis$a
+        x1.ster <- (usr[3] - this.axis$a)/this.axis$b
+        x2.ster <- (usr[4] - this.axis$a)/this.axis$b
+        if (this.axis$b == 0)
+        { if (x.vals[1] < x.vals[k])
+              graphics::mtext(text = ax.aes$names[i], side = 2, line = ax.aes$label.line[i], 
+                              adj = adjust[2], at = y.vals[1], col = ax.aes$label.col[i], 
+                              cex = ax.aes$label.cex[i])
+          else
+            graphics::mtext(text = ax.aes$names[i], side = 4, line = ax.aes$label.line[i], 
+                            adj = adjust[4], at = y.vals[1], col = ax.aes$label.col[i], 
+                            cex = ax.aes$label.cex[i])
+        }
+        if (this.axis$b > 0)
+        {  if (x.vals[1] < x.vals[k])
+             if (y1.ster <= usr[4] & y1.ster >= usr[3])
+               graphics::mtext(text = ax.aes$names[i], side = 2, line = ax.aes$label.line[i], 
+                               adj = adjust[2], at = y1.ster, col = ax.aes$label.col[i], 
+                               cex = ax.aes$label.cex[i])
+             else
+               graphics::mtext(text = ax.aes$names[i], side = 1, line = ax.aes$label.line[i], 
+                               adj = adjust[1], at = x1.ster, col = ax.aes$label.col[i], 
+                               cex = ax.aes$label.cex[i])
+           else if (y2.ster <= usr[4] & y2.ster >= usr[3])
+                  graphics::mtext(text = ax.aes$names[i], side = 4, line = ax.aes$label.line[i], 
+                                  adj = adjust[4], at = y2.ster, col = ax.aes$label.col[i], 
+                                  cex = ax.aes$label.cex[i])
+                else
+                   graphics::mtext(text = ax.aes$names[i], side = 3, line = ax.aes$label.line[i], 
+                                   adj = adjust[3], at = x2.ster, col = ax.aes$label.col[i], 
+                                   cex = ax.aes$label.cex[i])
+        }
+    if (this.axis$b < 0)
+    {  if (x.vals[1] < x.vals[k])
+         if (y1.ster <= usr[4] & y1.ster >= usr[3])
+           graphics::mtext(text = ax.aes$names[i], side = 2, line = ax.aes$label.line[i], 
+                           adj = adjust[2], at = y1.ster, col = ax.aes$label.col[i], 
+                           cex = ax.aes$label.cex[i])
+         else
+           graphics::mtext(text = ax.aes$names[i], side = 3, line = ax.aes$label.line[i], 
+                           adj = adjust[3], at = x2.ster, col = ax.aes$label.col[i], 
+                           cex = ax.aes$label.cex[i])
+       else if (y2.ster <= usr[4] & y2.ster >= usr[3])
+              graphics::mtext(text = ax.aes$names[i], side = 4, line = ax.aes$label.line[i], 
+                              adj = adjust[4], at = y2.ster, col = ax.aes$label.col[i], 
+                              cex = ax.aes$label.cex[i])
+            else
+              graphics::mtext(text = ax.aes$names[i], side = 1, line = ax.aes$label.line[i], 
+                              adj = adjust[1], at = x1.ster, col = ax.aes$label.col[i], 
+                              cex = ax.aes$label.cex[i])
+    }
+  }
+  for (j in 2:nrow(ends.mat))
+  {
+     graphics::lines (x = ends.mat[(-1:0)+j, 1], y = ends.mat[(-1:0)+j, 2],
+                      col = ax.aes$col[[i]][j-1], lwd = 2*ax.aes$lwd[i], lty=ax.aes$lty[i])
+    .marker.func (vec = c(marker.mat[j,], rownames(marker.mat)[j], 1), 
+                  coef = c(this.axis$a, this.axis$b), col = ax.aes$tick.col,
+                  tick.size = 0, label.pos = ax.aes$tick.label.side[i], label.col = ax.aes$tick.label.col, 
+                  cex = ax.aes$tick.label.cex, usr = usr)
+  }
+
+    if(ax.num %in% predict_which)
+    {
+      if (!is.null(predict.mat)) apply(cbind(predict.mat,y.vals[1]), 1, .predict.func, 
+                                       coef = c(this.axis$a, this.axis$b), col=ax.aes$predict.col,
+                                       lwd=ax.aes$predict.lwd,lty=ax.aes$predict.lty)
     }
   }
 }
 
+#' Plot linear ordinal axes on biplots
+#'
+#' @param z.axes list containing all the info to draw axis. see below
+#' @param ax.aes Axis aestetics
+#' @param predict.mat Xhat
+#' @param too.small cutoff: predictivity smaller than cutoff not plotted
+#' @param usr plot dim
+#'
+#' z.axes:    List containing following components for each axis:
+#' $coords:   Tick mark coordinates
+#' $a $b $v:  Intercept, slope, vertical
+#' 
+#' @noRd
+.ord.axes.plot <- function(z.axes, ax.aes, predict.mat, too.small, usr, predict_which)
+{
+  for (i in 1:length(ax.aes$which))
+  {  ax.num <- ax.aes$which[i]
+     if (!is.null(too.small)) if (ax.num %in% too.small) next
+     this.axis <- z.axes[[i]]
+     marker.mat <- this.axis$coords
+     marker.mat <- marker.mat[order(marker.mat[, 1]), ]
+  
+     ends.mat <- c(usr[1], NA)
+     k <- nrow(marker.mat)
+     for (j in 2:nrow(marker.mat))
+       ends.mat <- rbind (ends.mat, (marker.mat[j,1:2] + marker.mat[j-1,1:2])/2)
+     ends.mat <- rbind (ends.mat, c(usr[2],NA))
+     x.vals <- marker.mat[, 1]
+     y.vals <- marker.mat[, 2]
+  
+     if (ends.mat[1,1] < ends.mat[2,1]) ends.mat[2,] <- ends.mat[1,]
+     ends.mat <- ends.mat[-1,]
+     if (ends.mat[k,1] > ends.mat[k-1,1]) ends.mat[k-1,] <- ends.mat[k,]
+     ends.mat <- ends.mat[-k,]
+  
+     if (is.null(this.axis$b))
+     {
+       ends.mat[1,1] <- ends.mat[nrow(ends.mat),1] <- 0
+       ends.mat[1,2] <- usr[3]
+       ends.mat[nrow(ends.mat),2] <- usr[4]
+     }
+     else
+     {
+       ends.mat[1,2] <- this.axis$a + ends.mat[1,1]*this.axis$b
+       ends.mat[nrow(ends.mat),2] <- this.axis$a + ends.mat[nrow(ends.mat),1]*this.axis$b
+     }
+  
+     if (ax.aes$label.dir == "Hor") 
+     {  graphics::par(las = 1)
+        adjust <- c(0.5, 1, 0.5, 0)       
+     }
+     if (ax.aes$label.dir == "Orthog") 
+     {  graphics::par(las = 2)
+        adjust <- c(1, 1, 0, 0)         
+     }
+     if (ax.aes$label.dir == "Paral") 
+     {  graphics::par(las = 0)
+        adjust <- c(0.5, 0.5, 0.5, 0.5) 
+     }
+  
+     if (is.null(this.axis$b))
+     {  if (y.vals[1] < y.vals[k])
+          graphics::mtext(text = ax.aes$names[i], side = 1, line = ax.aes$label.line[i], 
+                          adj = adjust[1], at = x.vals[1], col = ax.aes$label.col[i], 
+                          cex = ax.aes$label.cex[i])
+        else
+          graphics::mtext(text = ax.aes$names[i], side = 3, line = ax.aes$label.line[i], 
+                          adj = adjust[3], at = y.vals[1], col = ax.aes$label.col[i], 
+                          cex = ax.aes$label.cex[i])
+     }
+     else
+       {  y1.ster <- this.axis$b * usr[1] + this.axis$a
+          y2.ster <- this.axis$b * usr[2] + this.axis$a
+          x1.ster <- (usr[3] - this.axis$a)/this.axis$b
+          x2.ster <- (usr[4] - this.axis$a)/this.axis$b
+          if (this.axis$b == 0)
+          { if (x.vals[1] < x.vals[k])
+              graphics::mtext(text = ax.aes$names[i], side = 2, line = ax.aes$label.line[i], 
+                              adj = adjust[2], at = y.vals[1], col = ax.aes$label.col[i], 
+                              cex = ax.aes$label.cex[i])
+            else
+              graphics::mtext(text = ax.aes$names[i], side = 4, line = ax.aes$label.line[i], 
+                              adj = adjust[4], at = y.vals[1], col = ax.aes$label.col[i], 
+                              cex = ax.aes$label.cex[i])
+          }
+          if (this.axis$b > 0)
+          {  if (x.vals[1] < x.vals[k])
+               if (y1.ster <= usr[4] & y1.ster >= usr[3])
+                 graphics::mtext(text = ax.aes$names[i], side = 2, line = ax.aes$label.line[i], 
+                                 adj = adjust[2], at = y1.ster, col = ax.aes$label.col[i], 
+                                 cex = ax.aes$label.cex[i])
+               else
+                 graphics::mtext(text = ax.aes$names[i], side = 1, line = ax.aes$label.line[i], 
+                                 adj = adjust[1], at = x1.ster, col = ax.aes$label.col[i], 
+                                 cex = ax.aes$label.cex[i])
+             else if (y2.ster <= usr[4] & y2.ster >= usr[3])
+                    graphics::mtext(text = ax.aes$names[i], side = 4, line = ax.aes$label.line[i], 
+                                    adj = adjust[4], at = y2.ster, col = ax.aes$label.col[i], 
+                                    cex = ax.aes$label.cex[i])
+                  else
+                    graphics::mtext(text = ax.aes$names[i], side = 3, line = ax.aes$label.line[i], 
+                                    adj = adjust[3], at = x2.ster, col = ax.aes$label.col[i], 
+                                    cex = ax.aes$label.cex[i])
+          }
+          if (this.axis$b < 0)
+          {  if (x.vals[1] < x.vals[k])
+               if (y1.ster <= usr[4] & y1.ster >= usr[3])
+                 graphics::mtext(text = ax.aes$names[i], side = 2, line = ax.aes$label.line[i], 
+                                 adj = adjust[2], at = y1.ster, col = ax.aes$label.col[i], 
+                                 cex = ax.aes$label.cex[i])
+               else
+                 graphics::mtext(text = ax.aes$names[i], side = 3, line = ax.aes$label.line[i], 
+                                 adj = adjust[3], at = x2.ster, col = ax.aes$label.col[i], 
+                                 cex = ax.aes$label.cex[i])
+             else if (y2.ster <= usr[4] & y2.ster >= usr[3])
+                    graphics::mtext(text = ax.aes$names[i], side = 4, line = ax.aes$label.line[i], 
+                                    adj = adjust[4], at = y2.ster, col = ax.aes$label.col[i], 
+                                    cex = ax.aes$label.cex[i])
+                  else
+                    graphics::mtext(text = ax.aes$names[i], side = 1, line = ax.aes$label.line[i], 
+                                    adj = adjust[1], at = x1.ster, col = ax.aes$label.col[i], 
+                                    cex = ax.aes$label.cex[i])
+          }
+       }
+  if (ax.aes$reverse[i]) lwd.vec <- (nrow(ends.mat)-1):1 else lwd.vec <- 1:(nrow(ends.mat)-1)
+  lwd.vec <- lwd.vec * ax.aes$lwd.factor[i]
+  for (j in 2:nrow(ends.mat))
+  {
+    graphics::lines (x = ends.mat[(-1:0)+j, 1], y = ends.mat[(-1:0)+j, 2],
+                     col = ax.aes$col[i], lwd = lwd.vec[j-1], lty=ax.aes$lty[i])
+    .marker.func (vec = c(marker.mat[j,], rownames(marker.mat)[j], 1), 
+                  coef = c(this.axis$a, this.axis$b), col = ax.aes$tick.col,
+                  tick.size = 0, label.pos = ax.aes$tick.label.side[i], label.col = ax.aes$tick.label.col, 
+                  cex = ax.aes$tick.label.cex, usr = usr)
+  }
+  
+  if(ax.num %in% predict_which)
+  {
+    if (!is.null(predict.mat)) apply(cbind(predict.mat,y.vals[1]), 1, .predict.func, 
+                                     coef = c(this.axis$a, this.axis$b), col=ax.aes$predict.col,
+                                     lwd=ax.aes$predict.lwd,lty=ax.aes$predict.lty)
+  }
+  }
+}
+
 .CLPs.plot <- function (coords, colvec, cexvec)
 {
   text (x=coords[,1], y=coords[,2], labels=rownames(coords), col=colvec, cex=cexvec)
@@ -638,6 +1013,15 @@
 #' @noRd
 .get.ggrepel.coords <- function(df)
 {
+  if (!requireNamespace("ggplot2", quietly = TRUE)) {
+    stop("Package 'ggplot2' is required for this function. Please install it.", call. = FALSE)
+   }
+  if (!requireNamespace("ggrepel", quietly = TRUE)) {
+     stop("Package 'ggrepel' is required for this function. Please install it.", call. = FALSE)
+   }
+  if (!requireNamespace("grid", quietly = TRUE)) {
+     stop("Package 'grid' is required for this function. Please install it.", call. = FALSE)
+   }
   pp <- ggplot2::ggplot (df, ggplot2::aes(df$x,df$y,label=df$z)) + 
            ggplot2::geom_point() + 
            ggrepel::geom_text_repel()
@@ -686,12 +1070,11 @@
 
 }
 
-
 #' calibrate spline based axes on biplots
 #'
 #' @param j Index of the axis to be calibrated in the data
 #' @param X Coordinates of the samples on the biplot space
-#' @param Ytilde Raw data used to construct the biplot
+#' @param Y Raw data used to construct the biplot
 #' @param means column means of the raw data
 #' @param sd Column standard deviations of the data
 #' @param n.int the number of tick marks per axis
@@ -699,16 +1082,15 @@
 #' @param dmeth Argument unused
 #' @param ... additional arguments
 #' 
-#' @useDynLib biplotEZ, .registration = TRUE
-#'
 #' @noRd
+
+
+
 biplot.spline.axis <- function(j, X, Y, means, sd, 
-                               n.int, spline.control, dmeth=0, ... )
-{
+                               n.int, spline.control, dmeth=0, ... ){
   n <- nrow(X)
   p <- ncol(X)
-  if (n > 103)
-    {  
+  if (n > 103){  
       my.sample <- sample (1:n, size=103, replace=F)
       X <- X[my.sample,]
       Y <- Y[my.sample,]
@@ -743,8 +1125,7 @@ biplot.spline.axis <- function(j, X, Y, means, sd,
   mu <- unique(mu)
   nmu <- length(mu)
   
-  if (v>0)
-  {
+  if (v>0){
     knots <- seq.int(from=0,to=1,length.out=v+2)[-c(1,v+2)]
     knots <- stats::quantile(y,knots)
     M <- splines::bs(mu,knots=knots,degree=u,intercept=FALSE)
@@ -757,56 +1138,44 @@ biplot.spline.axis <- function(j, X, Y, means, sd,
   const1 <- sum(y^2)
   const2 <- sum(X^2)/(n*p)
   TotalNumberOfLossFunctionCalls <- 0
-  
-  optimtouse <- function(Bvec)
-  {
+  optimtouse <- function(Bvec) {
     timetemp <- proc.time()[3]
-    LOSS <- 1.0
-    LOSS1 <- 1.0
-    Ind <- rep(1,n)
-    pred <- rep(0,nmu)
-    deltmp <- 0
-    tau <- tau
-    #.5 # the choice of tau seems to affect perfomance quite substantially.
-    # tau is used to specify the points on the inital simplex.
-    Ay <- rep(0,(u+v)*p+1)
-    TEMPVK <- rep(0,(u+v)*p)
-    iter1 <- 0
-    iter <- 0
-    ERRO <- 0
-    
-    # Prepare for Fortran subroutine
-    storage.mode(X) <- "double"
-    storage.mode(Ind) <- "integer"
-    storage.mode(mu) <- "double"
-    storage.mode(pred) <- "double"
-    storage.mode(y) <- "double"
-    storage.mode(M) <- "double"
-    storage.mode(Bvec) <- "double"
-    storage.mode(Ay) <- "double"
-    storage.mode(TEMPVK) <- "double"
   
+      # Use Rcpp optimize_spline function
+    returned_data <- optimize_spline(
+      BVEC = Bvec, 
+      X = X, 
+      Y = y, 
+      M = M, 
+      MU = mu,
+      LAMBDA = lambda, 
+      CONST1 = const1, 
+      CONST2 = const2,
+      U = u, 
+      V = v, 
+      TAU = tau, 
+      FTOL = ftol, 
+      TINY = tiny, 
+      ITMAX = itmax
+    )
     
-    returned_data <-.Fortran('L',LOSS=as.double(LOSS),X=X,n=as.integer(n),p=as.integer(p),nmu=as.integer(nmu),Ind=Ind,
-                            mu=mu,pred=pred,lambda=as.double(lambda),y=y,const1=as.double(const1),const2=as.double(const2),u=as.integer(u),
-                            v=as.integer(v),M=M,Bvec=Bvec,tau=as.double(tau),Ay=Ay,TEMPVEK=TEMPVK,iter=as.integer(iter),
-                            ftol=as.double(ftol),LOSS1=as.double(LOSS1),iter1=as.integer(iter1),fout = as.integer(ERRO),
-                            const3=as.double(tiny), itmax=as.integer(itmax))
-    if(returned_data$fout > 0)
-    {
-      cat("Fout is: ", returned_data$fout, "\n")
-      warning("Increase itmax for Fortran \n")
+    if(returned_data$ERRO > 0) {
+      cat("  Warning: Error code =", returned_data$ERRO, "\n")
     }
     
-    B <- matrix(returned_data$Bvec,ncol=p)
-    Z <- M%*%B 
+    aa <- list(
+      BestValue = returned_data$LOSS,
+      BestSolution = returned_data$BVEC,
+      ConvergenceCode = returned_data$ERRO,
+      iter1 = returned_data$ITER1,
+      iter = returned_data$ITER,
+      TimeTaken = proc.time()[3] - timetemp
+    )
     
-    aa <- list(BestValue=returned_data$LOSS,BestSolution=returned_data$Bvec,ConvergenceCode=returned_data$fout, iter1=returned_data$iter1,
-             iter=returned_data$iter,TimeTaken=proc.time()[3]-timetemp)
     aa
   }
-  EuclidDist2 <- function (X, Y) 
-  {
+
+  EuclidDist2 <- function (X, Y) {
     n <- nrow(X)
     m <- nrow(Y)
     bx <- rowSums(X^2)
@@ -838,29 +1207,24 @@ biplot.spline.axis <- function(j, X, Y, means, sd,
   test.iter1 <- temp$iter1
   
   ### Last best coefficients perturbed
-  for (gammacounter in 2:(gamma+1))
-  {
-    if (nSameSolutionConsecutively>=bigsigmaactivate)
-    {
+  for (gammacounter in 2:(gamma+1)){
+    if (nSameSolutionConsecutively>=bigsigmaactivate){
       temp <- optimtouse(outBestSolutions[,which.min(outBestValues)]+stats::rnorm((u+v)*2,mean=0,sd=bigsigma))
       BigSigmaActivations <- c(BigSigmaActivations,gammacounter)
     }
     else temp <- optimtouse(outBestSolutions[,which.min(outBestValues)]+stats::rnorm((u+v)*2,mean=0,sd=smallsigma))
     outTimeTaken[gammacounter] <- temp$TimeTaken
     tempSquaredDistances <- EuclidDist2(matrix(temp$BestSolution,nrow=1),t(outBestSolutions[,1:DistinctSolutions]))
-    if (any(tempSquaredDistances<eps))
-    {
+    if (any(tempSquaredDistances<eps)){
       BestSolutionsIndices[gammacounter] <- tempAA<-which.min(tempSquaredDistances)
       BestSolutionsFrequency[tempAA] <- BestSolutionsFrequency[tempAA]+1
       if (!is.na(PreviousBestSolution) && tempAA==PreviousBestSolution) nSameSolutionConsecutively<-nSameSolutionConsecutively+1
-      else
-      {
+      else{
         PreviousBestSolution <- tempAA
         nSameSolutionConsecutively <- 0
       }
     }
-    else
-    {
+    else{
       DistinctSolutions <- DistinctSolutions+1
       outBestValues[DistinctSolutions] <- temp$BestValue
       outBestSolutions[,DistinctSolutions] <- temp$BestSolution
@@ -878,6 +1242,9 @@ biplot.spline.axis <- function(j, X, Y, means, sd,
 }
 
 
+
+
+
 #' Plot nonlinear axes on biplots
 #'
 #' @param z.axes list containing all the info to draw axis.
@@ -950,7 +1317,7 @@ biplot.spline.axis <- function(j, X, Y, means, sd,
           coef = coef.mat[j, ],
           col = ax.style$tick.col[i],
           tick.size = ax.style$tick.size[i],
-          label_pos = ax.style$tick.label.side[i],
+          label.pos = ax.style$tick.label.side[i],
           #pos = ax.style$tick.label.pos[i],
           #offset = ax.style$tick.label.offset[i],
           label.col = ax.style$tick.label.col[i],
diff --git a/R/plotting.R b/R/plotting.R
index 576851b..23e89a6 100644
--- a/R/plotting.R
+++ b/R/plotting.R
@@ -6,6 +6,7 @@
 #' @param axis.predictivity either a logical or a numeric value between \code{0} and \code{1}. If it is a numeric value, this value is used as threshold so that only axes with axis predictivity larger than the threshold is displayed. If \code{axis.predictivity = TRUE}, the axis colour is 'diluted' in proportion with the axis predictivity.
 #' @param sample.predictivity either a logical or a numeric value between 0 and 1. If it is a numeric value, this value is used as threshold so that only samples with sample predictivity larger than the threshold is displayed. If \code{sample.predictivity = TRUE}, the sample size is shrinked in proportion with the sample predictivity.
 #' @param zoom a logical value allowing the user to select an area to zoom into.
+#' @param add a logical value allowing the user to add the biplot to a current plot. If \code{add = TRUE} the argument \code{zoom} is inactive.
 #' @param xlim the horizontal limits of the plot.
 #' @param ylim the vertical limits of the plot.
 #' @param ... additional arguments.
@@ -17,15 +18,17 @@
 #' @examples
 #' biplot (iris[,1:4]) |> PCA() |> plot()
 plot.biplot <- function(x, exp.factor=1.2, axis.predictivity=NULL, sample.predictivity=NULL,
-                        zoom=FALSE, xlim = NULL, ylim = NULL, ...)
+                        zoom = FALSE, add = FALSE, xlim = NULL, ylim = NULL, ...)
 {
+  
   #----- See all the internal functions in utility_2D.R
   if (is.null(x$Z)) stop ("Add a biplot method before generating a plot")
     else Z <- x$Z
 
   #aesthetics for samples
   if (is.null(x$samples)) x <- samples(x) 
-  
+
+  if (add) zoom <- FALSE  
   if(zoom)
     grDevices::dev.new()
 
@@ -63,6 +66,9 @@ plot.biplot <- function(x, exp.factor=1.2, axis.predictivity=NULL, sample.predic
   ggrepel.new <- ggrepel.means <- ggrepel.samples <- NULL
   if (do.ggrepel)
   {
+    if (!requireNamespace("R.devices", quietly = TRUE)) {
+       stop("Package 'R.devices' is required for this function. Please install it.", call. = FALSE)
+    }
     out <- R.devices::suppressGraphics(.get.ggrepel.coords(df))
     if (n.newsamples>n.means) ggrepel.new <-list(coords = out$coords[out$visible>n.newsamples & out$visible<n.means+1,,drop=F],
                                                  visible = out$visible[out$visible>n.newsamples & out$visible<n.means+1]-n.means,
@@ -100,6 +106,7 @@ plot.biplot <- function(x, exp.factor=1.2, axis.predictivity=NULL, sample.predic
       }
       
       # Start with empty plot
+      if (!add)
       plot(Z[, 1] * exp.factor, Z[, 2] * exp.factor, xlim = xlim, ylim = ylim,
            xaxt = "n", yaxt = "n", xlab = "", ylab = "", type = "n", xaxs = "i", yaxs = "i", asp = 1)
 
@@ -118,7 +125,6 @@ plot.biplot <- function(x, exp.factor=1.2, axis.predictivity=NULL, sample.predic
         }
 
       # Classification Regions - this should be plotted first. 
-      # if(!is.null(x$classify)) x <- classify(x)
       classify.aes <- x$classify$aes
       
       if(!is.null(x$classify$classify.regions)) {
@@ -181,15 +187,6 @@ plot.biplot <- function(x, exp.factor=1.2, axis.predictivity=NULL, sample.predic
       {
         if (length(ax.aes$which) > 0)
           {
-          if (!is.null(x$Lmat))
-              if (nrow(x$Lmat) == ncol(x$Lmat)) 
-                Xhat <- x$Z %*% solve(x$Lmat)[x$e.vects,]
-              else Xhat <- x$X
-            else
-              Xhat <- x$X
-            if (x$scaled) Xhat <- scale(Xhat, center=FALSE, scale=1/x$sd)
-            if (x$center) Xhat <- scale(Xhat, center=-1*x$means, scale=FALSE)
-            
             if(!is.null(x$PCOaxes)) 
               { if (x$PCOaxes == "splines") # Only for PCO - if axes (type) is set to splines.  
                   {
@@ -201,15 +198,17 @@ plot.biplot <- function(x, exp.factor=1.2, axis.predictivity=NULL, sample.predic
                   } 
                 else if(x$PCOaxes == "regression") # Only for PCO - if axes (type) is set to regression. 
                        {
-                         z.axes <- lapply(1:length(ax.aes$which), .calibrate.axis, Xhat, x$means, x$sd, x$ax.one.unit, ax.aes$which,
-                                        ax.aes$ticks, ax.aes$orthogx, ax.aes$orthogy)
+                         z.axes <- lapply(1:length(ax.aes$which), .calibrate.axis, x$X, x$means, 
+                                          x$sd, x$ax.one.unit, ax.aes$which, ax.aes$ticks, 
+                                          ax.aes$orthogx, ax.aes$orthogy)
                         .lin.axes.plot(z.axes, ax.aes, predict.mat, too.small,usr=usr,predict_which=x$predict$which)
                        }
               } 
             else 
               { # Otherwise calibrate linear axes
-                z.axes <- lapply(1:length(ax.aes$which), .calibrate.axis, Xhat, x$means, x$sd, x$ax.one.unit, ax.aes$which,
-                               ax.aes$ticks, ax.aes$orthogx, ax.aes$orthogy)
+                z.axes <- lapply(1:length(ax.aes$which), .calibrate.axis, x$X, x$means, x$sd, 
+                                 x$ax.one.unit, ax.aes$which, ax.aes$ticks, 
+                                 ax.aes$orthogx, ax.aes$orthogy)
                 .lin.axes.plot(z.axes, ax.aes, predict.mat, too.small,usr=usr,predict_which=x$predict$which)
               }
             }
@@ -226,13 +225,56 @@ plot.biplot <- function(x, exp.factor=1.2, axis.predictivity=NULL, sample.predic
       if (length(new.ax.aes$which) > 0)
       {
         
-        z.axes.new <- lapply(1:length(new.ax.aes$which), .calibrate.axis, 
-                             x$newvariable, x$new.means, x$new.sd, x$new.ax.one.unit, new.ax.aes$which,
+        z.axes.new <- lapply(1:length(new.ax.aes$which), .calibrate.axis, x$newvariable, 
+                             x$new.means, x$new.sd, x$new.ax.one.unit, new.ax.aes$which,
                              new.ax.aes$ticks, new.ax.aes$orthogx, new.ax.aes$orthogy)
-        .lin.axes.plot(z.axes.new, new.ax.aes, predict.mat, too.small, usr=usr, predict_which=x$predict$which)
+        .lin.axes.plot(z.axes.new, new.ax.aes, predict.mat, too.small, usr=usr, 
+                       predict_which=x$predict$which)
       }
       }
-      
+        
+      # Nominal and ordinal axes
+      if(inherits(x,"catPCA"))
+      {
+        if (sum(x$ax.type == "nominal") > 0)
+        {
+          nom.one.unit <- x$all.ax.one.unit[x$ax.type$ax.type == "nominal",,drop = FALSE]
+          if (is.null(x$nom.axes)) x <- nom.axes(x)
+
+          z.axes <- lapply(1:length(x$nom.axes$which), .calibrate.cat.axis, 
+                           nom.one.unit, x$nom.axes$which, x$nom.axes$orthogx, 
+                           x$nom.axes$orthogy, x$nom.levels)
+          .nom.axes.plot(z.axes, x$nom.axes, predict.mat, too.small,
+                         usr = usr, predict_which = x$predict$which)
+        }
+
+        if (sum(x$ax.type == "ordinal") > 0)
+        {
+          ord.one.unit <- x$all.ax.one.unit[x$ax.type$ax.type == "ordinal",,drop = FALSE]
+          if (is.null(x$ord.axes)) x <- ord.axes(x)
+          for (j in 1:length(x$ord.levels))
+          {
+            current.markers <- x$ord.levels[[j]]
+            i <- 1
+            while (i < length(current.markers) - 1)
+            {
+              if (abs(current.markers[i]-current.markers[i+1]) < 1.5*.Machine$double.eps)
+              {
+                names(current.markers[i]) <- paste(names(current.markers[i]),
+                                                   names(current.markers[i+1]), sep="*")
+                current.markers <- current.markers[-(i+1)]
+              }
+              else i <- i + 1
+            }
+            x$ord.levels[[j]] <- current.markers
+          }
+          z.axes <- lapply(1:length(x$ord.axes$which), .calibrate.cat.axis,  
+                           ord.one.unit, x$ord.axes$which, x$ord.axes$orthogx, 
+                           x$ord.axes$orthogy, x$ord.levels)
+          .ord.axes.plot(z.axes, x$ord.axes, predict.mat, too.small,
+                         usr = usr,predict_which = x$predict$which)
+        }
+      }
       
       # Fit measures 
       too.small <- NULL
@@ -329,6 +371,9 @@ plot.biplot <- function(x, exp.factor=1.2, axis.predictivity=NULL, sample.predic
 plot3D <- function(bp,
                     exp.factor = 1.2,...)
 {
+  if (!requireNamespace("rgl", quietly = TRUE)) {
+     stop("Package 'rgl' is required for this function. Please install it.", call. = FALSE)
+   }
   
   if (is.null(bp$Z)) stop ("Add a biplot method before generating a plot")
   else Z <- bp$Z
@@ -408,7 +453,9 @@ if(!inherits(bp,"CA")){
   
   }
   
-
+  # Nominal and ordinal axes
+  if(inherits(bp,"catPCA")) stop ("catPCA not implemented for 3D biplots")
+    
   # Bags 
   
   
@@ -520,6 +567,9 @@ plot1D <-  function(bp, exp.factor = 1.2,...)
     }
     }
 
+    # Nominal and ordinal axes
+    if(inherits(bp,"catPCA")) stop ("catPCA not implemented for 1D biplots")
+
     # Predictions of points with lines down to the axes.
     if (!is.null(predict.mat)){
 
diff --git a/R/translate_axes.R b/R/translate_axes.R
index c732687..67495a6 100644
--- a/R/translate_axes.R
+++ b/R/translate_axes.R
@@ -35,6 +35,9 @@
 #' dist[7] <- 0.4
 #' bp |> translate_axes(delta = 0.2, distances=dist) |> plot()
 translate_axes<-function(bp, delta=0,swop=FALSE,distances=NULL){
+  if (!requireNamespace("cluster", quietly = TRUE)) {
+     stop("Package 'cluster' is required for this function. Please install it.", call. = FALSE)
+   }
   p<-bp$p
   m<-bp$ax.one.unit[,2]/bp$ax.one.unit[,1] #slopes of the axes
   thetas<-atan(m)                         #angles of the axes
diff --git a/R/utility.R b/R/utility.R
index 2752c5f..9e9e86e 100644
--- a/R/utility.R
+++ b/R/utility.R
@@ -413,4 +413,34 @@ extended.matching.coefficient <- function (X)
     Dmat <- Dmat + matrix (1, nrow=n, ncol=n) - Gk %*% t(Gk)
   }
   stats::as.dist(sqrt(Dmat))
-}
\ No newline at end of file
+}
+
+#' Applies primary or secondary approach to ties
+#'
+#' @param d observed dissimilarities
+#' @param delta given dissimilarities to match (order)
+#' @param method either \code{primary} or \code{secondary} approach to ties
+#'
+#' @returns a vector of ordered values
+#'
+ties <- function (d, delta, method = c("primary", "secondary")) 
+{
+  method <- method[1]
+  if (!(identical(method, "primary") | identical(method, "secondary"))) stop("method must be either 'primary' or 'secondary' ")
+  if (is.null(names(delta))) labels <- 1:length(delta) else labels <- names(delta)
+  pairs <- data.frame(d, delta, labels)
+  if (identical(method, "primary")) pairs <- pairs[order(d, delta), ]
+  if (identical(method, "secondary")) pairs <- pairs[order(d), ]
+  z <- as.vector(pairs[, 2])
+  names(z) <- pairs[, 3]
+  while (!all(order(z) == (1:length(z)))) 
+  {  block.vec <- rep(1, length(z))
+  block.num <- 1
+  for (i in 2:length(z)) 
+  {  if (z[i] > z[i - 1]) block.num <- block.num + 1
+  block.vec[i] <- block.num
+  }
+  for (i in 1:max(block.vec)) z[block.vec == i] <- mean(z[block.vec == i])
+  }
+  z
+}
diff --git a/README.Rmd b/README.Rmd
index 55cde2b..ba90985 100644
--- a/README.Rmd
+++ b/README.Rmd
@@ -15,9 +15,6 @@ knitr::opts_chunk$set(
 
 # biplotEZ
 
-<!-- badges: start -->
-<!-- badges: end -->
-
 The goal of biplotEZ is to provide users an EZ-to-use platform for
 visually representing their data with biplots. Currently, this package
 includes principal component analysis (PCA) and canonical variate
diff --git a/README.md b/README.md
index 362eca6..65d3167 100644
--- a/README.md
+++ b/README.md
@@ -13,6 +13,7 @@ analysis (CVA) biplots. This is accompanied by various formatting
 options for the samples and axes. Alpha-bags and concentration ellipses
 are included for visual enhancements and interpretation.
 
+
 ## Installation
 
 You can install the development version of biplotEZ like this:
diff --git a/_pkgdown.yml b/_pkgdown.yml
new file mode 100644
index 0000000..5b1d790
--- /dev/null
+++ b/_pkgdown.yml
@@ -0,0 +1,21 @@
+template:
+  bootstrap: 5
+navbar:
+ components:
+   articles:
+    text: Articles
+    menu:
+    - text: biplotEZ
+      href: articles/biplotEZ.html
+    - text: biplotEZ enhancements
+      href: articles/biplotEZ_enhancements.html
+    - text: Multi-dimensional scaling
+      href: articles/MDS.html
+    - text: Biplots for separating classes
+      href: articles/Class_separation.html
+    - text: Categorical biplots
+      href: articles/CA_in_biplotEZ.html
+    - text: One dimensional biplots
+      href: articles/Biplots_in_1D.html
+    - text: Three dimensional biplots
+      href: articles/Biplots_in_3D.html
\ No newline at end of file
diff --git a/biplotEZ.Rproj b/biplotEZ.Rproj
index 21a4da0..4b726bb 100644
--- a/biplotEZ.Rproj
+++ b/biplotEZ.Rproj
@@ -1,4 +1,5 @@
 Version: 1.0
+ProjectId: 19a4037d-9088-49bb-bddb-bbc5a80cabdc
 
 RestoreWorkspace: Default
 SaveWorkspace: Default
diff --git a/docs/404.html b/docs/404.html
index 54624f2..547fff5 100644
--- a/docs/404.html
+++ b/docs/404.html
@@ -4,127 +4,88 @@
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
-<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Page not found (404) • biplotEZ</title>
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-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">2.1</span>
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+<body>
+    <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
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+    <li><a class="dropdown-item" href="articles/Biplots_in_3D.html">Three dimensional biplots</a></li>
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+<ul class="navbar-nav">
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+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="search.json">
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+  </main>
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-      <footer><div class="copyright">
-  <p></p>
-<p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
-  <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p>
+<div class="pkgdown-footer-right">
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 </html>
diff --git a/docs/CNAME b/docs/CNAME
new file mode 100644
index 0000000..09e131f
--- /dev/null
+++ b/docs/CNAME
@@ -0,0 +1 @@
+www.biplotez.org
\ No newline at end of file
diff --git a/docs/LICENSE-text.html b/docs/LICENSE-text.html
index 7479159..d776643 100644
--- a/docs/LICENSE-text.html
+++ b/docs/LICENSE-text.html
@@ -1,98 +1,65 @@
 <!DOCTYPE html>
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+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>License • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="apple-touch-icon.png"><link rel="icon" sizes="any" href="favicon.ico"><link rel="manifest" href="site.webmanifest"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="License"><meta property="og:image" content="/logo.png"></head><body>
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+<li class="nav-item dropdown">
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+  <ul class="dropdown-menu" aria-labelledby="dropdown-articles"><li><a class="dropdown-item" href="articles/biplotEZ.html">biplotEZ</a></li>
+    <li><a class="dropdown-item" href="articles/biplotEZ_enhancements.html">biplotEZ enhancements</a></li>
+    <li><a class="dropdown-item" href="articles/MDS.html">Multi-dimensional scaling</a></li>
+    <li><a class="dropdown-item" href="articles/Class_separation.html">Biplots for separating classes</a></li>
+    <li><a class="dropdown-item" href="articles/CA_in_biplotEZ.html">Categorical biplots</a></li>
+    <li><a class="dropdown-item" href="articles/Biplots_in_1D.html">One dimensional biplots</a></li>
+    <li><a class="dropdown-item" href="articles/Biplots_in_3D.html">Three dimensional biplots</a></li>
   </ul></li>
-      </ul><ul class="nav navbar-nav navbar-right"></ul></div><!--/.nav-collapse -->
-  </div><!--/.container -->
-</div><!--/.navbar -->
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="search.json"></form></li>
+      </ul></div>
 
-      
 
-      </header><div class="row">
-  <div class="contents col-md-9">
-    <div class="page-header">
-      <h1>License</h1>
+  </div>
+</nav><div class="container template-title-body">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="logo.png" class="logo" alt=""><h1>License</h1>
+
     </div>
 
 <pre>YEAR: 2024
 COPYRIGHT HOLDER: biplotEZ authors
 </pre>
 
-  </div>
+  </main></div>
 
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
-    </nav></div>
 
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-
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-      <footer><div class="copyright">
-  <p></p><p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.2.</p>
 </div>
 
-<div class="pkgdown">
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diff --git a/docs/LICENSE.html b/docs/LICENSE.html
index ddc7ee5..817c01d 100644
--- a/docs/LICENSE.html
+++ b/docs/LICENSE.html
@@ -1,68 +1,43 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>MIT License • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="apple-touch-icon-60x60.png"><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="bootstrap-toc.css"><script src="bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="pkgdown.css" rel="stylesheet"><script src="pkgdown.js"></script><meta property="og:title" content="MIT License"><meta property="og:image" content="/logo.png"><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>MIT License • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="apple-touch-icon.png"><link rel="icon" sizes="any" href="favicon.ico"><link rel="manifest" href="site.webmanifest"><script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="deps/headroom-0.11.0/headroom.min.js"></script><script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="deps/search-1.0.0/fuse.min.js"></script><script src="deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="pkgdown.js"></script><meta property="og:title" content="MIT License"><meta property="og:image" content="/logo.png"></head><body>
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+    <li><a class="dropdown-item" href="articles/CA_in_biplotEZ.html">Categorical biplots</a></li>
+    <li><a class="dropdown-item" href="articles/Biplots_in_1D.html">One dimensional biplots</a></li>
+    <li><a class="dropdown-item" href="articles/Biplots_in_3D.html">Three dimensional biplots</a></li>
   </ul></li>
-      </ul><ul class="nav navbar-nav navbar-right"></ul></div><!--/.nav-collapse -->
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-</div><!--/.navbar -->
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="search.json"></form></li>
+      </ul></div>
 
-      
 
-      </header><div class="row">
-  <div class="contents col-md-9">
-    <div class="page-header">
-      <h1>MIT License</h1>
+  </div>
+</nav><div class="container template-title-body">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="logo.png" class="logo" alt=""><h1>MIT License</h1>
+
     </div>
 
 <div id="mit-license" class="section level1">
@@ -73,30 +48,22 @@ <h1>MIT License</h1>
 <p>THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.</p>
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+  </main></div>
 
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
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+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
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-      
 
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-  <div class="col-md-9 contents">
-    <div class="page-header toc-ignore">
-      <h1 data-toc-skip>Biplots in 1D</h1>
+
+
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Biplots in 1D</h1>
             
       
-      
-      <div class="hidden name"><code>Biplots_in_1D.Rmd</code></div>
 
+      <div class="d-none name"><code>Biplots_in_1D.Rmd</code></div>
     </div>
 
     
@@ -112,6 +83,10 @@ <h2 id="one-dimensional-pca-biplot">One-dimensional PCA biplot<a class="anchor"
 </h2>
 <p>One-dimensional PCA biplots are obtained by specifying
 <code>dim.biplot = 1</code> in the call to <code><a href="../reference/PCA.html">PCA()</a></code>.</p>
+<p>The one-dimensional representation of the data is displayed by the
+colour points on the top horizontal line. The accompanying calibrated
+variable axes are displayed as horizontal lines below. The variable name
+is displayed on the side to which the variable increases.</p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">$</span><span class="va">Species</span>,dim.biplot <span class="op">=</span> <span class="fl">1</span><span class="op">)</span>  <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-2-1.png" width="672"></p>
@@ -137,7 +112,7 @@ <h3 id="classification-using-classify">Classification using <code>classify()</co
 <div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">bp</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CVA.html">CVA</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span>,dim.biplot <span class="op">=</span> <span class="fl">1</span><span class="op">)</span><span class="op">|&gt;</span></span>
 <span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
-<span>  <span class="fu"><a href="../reference/classify.html">classify</a></span><span class="op">(</span>borders <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">|&gt;</span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<span>  <span class="fu"><a href="../reference/classify.html">classify</a></span><span class="op">(</span>borders <span class="op">=</span> <span class="cn">TRUE</span>,opacity <span class="op">=</span> <span class="fl">1</span><span class="op">)</span><span class="op">|&gt;</span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-4-1.png" width="672"></p>
 <p>The <code><a href="https://rdrr.io/r/base/print.html" class="external-link">print()</a></code> function provides the misclassification
 rate, as well as the confusion matrix, of the CVA classifier applied to
@@ -160,8 +135,28 @@ <h3 id="classification-using-classify">Classification using <code>classify()</co
 </div>
 </div>
 <div class="section level2">
-<h2 id="adding-new-samples">Adding new samples<a class="anchor" aria-label="anchor" href="#adding-new-samples"></a>
+<h2 id="one-dimensional-ca-biplot">One-dimensional CA biplot<a class="anchor" aria-label="anchor" href="#one-dimensional-ca-biplot"></a>
+</h2>
+<p>Similarly for a CA 1d biplot, <code>dim.biplot = 1</code> is
+specified in the call to <code><a href="../reference/CA.html">CA()</a></code>. The one-dimensional biplot
+is constructed from the first columns of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐔</mi><msup><mi>𝚲</mi><mi>𝛄</mi></msup></mrow><annotation encoding="application/x-tex">\mathbf{U\Lambda^\gamma}</annotation></semantics></math>
+and <span class="math inline">$&amp;\mathbf{V\Lambda^{1-\gamma}}$</span>.</p>
+<p>Consider the <code>HairEyeColor</code> example again as discussed in
+<code>CA in biplotEZ</code>:</p>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CA.html">CA</a></span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Princ"</span>, </span>
+<span>  dim.biplot<span class="op">=</span><span class="fl">1</span>, lambda.scal <span class="op">=</span> <span class="cn">T</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-6-1.png" width="672"></p>
+</div>
+<div class="section level2">
+<h2 id="the-function-interpolate">The function <code>interpolate()</code><a class="anchor" aria-label="anchor" href="#the-function-interpolate"></a>
 </h2>
+<p><code><a href="../reference/interpolate.html">interpolate()</a></code> allows for new observations or axes to be
+added to the biplot.</p>
+<div class="section level3">
+<h3 id="the-function-newsamples">The function <code>newsamples()</code><a class="anchor" aria-label="anchor" href="#the-function-newsamples"></a>
+</h3>
 <p>The process of adding new samples to the biplot, called interpolation
 utilises the functions <code><a href="../reference/interpolate.html">interpolate()</a></code> and
 <code><a href="../reference/newsamples.html">newsamples()</a></code>. These functions work in the same way as in
@@ -171,14 +166,14 @@ <h2 id="adding-new-samples">Adding new samples<a class="anchor" aria-label="anch
 interpolated. The function <code><a href="../reference/newsamples.html">newsamples()</a></code> operates the same
 way as <code><a href="../reference/samples.html">samples()</a></code> in that the user can specify the
 aesthetics of the interpolated samples.</p>
-<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">50</span>,<span class="fl">101</span><span class="op">:</span><span class="fl">150</span><span class="op">)</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span><span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>dim.biplot <span class="op">=</span> <span class="fl">1</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/interpolate.html">interpolate</a></span><span class="op">(</span>newdata <span class="op">=</span> <span class="va">iris</span><span class="op">[</span><span class="fl">51</span><span class="op">:</span><span class="fl">100</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/newsamples.html">newsamples</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"purple"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-6-1.png" width="672"></p>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-7-1.png" width="672"></p>
 </div>
-<div class="section level2">
-<h2 id="adding-new-variables">Adding new variables<a class="anchor" aria-label="anchor" href="#adding-new-variables"></a>
-</h2>
+<div class="section level3">
+<h3 id="the-function-newaxes">The function <code>newaxes()</code><a class="anchor" aria-label="anchor" href="#the-function-newaxes"></a>
+</h3>
 <p>To interpolate new variables to the biplot, the function
 <code><a href="../reference/interpolate.html">interpolate()</a></code> and <code><a href="../reference/newaxes.html">newaxes()</a></code> are called. The
 function <code><a href="../reference/interpolate.html">interpolate()</a></code> accepts the argument
@@ -187,15 +182,19 @@ <h2 id="adding-new-variables">Adding new variables<a class="anchor" aria-label="
 the new variables to be interpolated. The function
 <code><a href="../reference/newaxes.html">newaxes()</a></code> allows the user to specify the aesthetics of the
 interpolated variables.</p>
-<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">3</span><span class="op">]</span><span class="op">)</span><span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>dim.biplot <span class="op">=</span> <span class="fl">1</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/interpolate.html">interpolate</a></span><span class="op">(</span>newvariable <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/newaxes.html">newaxes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"darkred"</span>,X.new.names <span class="op">=</span> <span class="st">"Petal.Width"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-7-1.png" width="672"></p>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-8-1.png" width="672"></p>
+</div>
 </div>
 <div class="section level2">
-<h2 id="predicting-samples">Predicting samples<a class="anchor" aria-label="anchor" href="#predicting-samples"></a>
+<h2 id="the-function-prediction">The function <code>prediction()</code><a class="anchor" aria-label="anchor" href="#the-function-prediction"></a>
 </h2>
+<div class="section level3">
+<h3 id="predicting-samples">Predicting Samples<a class="anchor" aria-label="anchor" href="#predicting-samples"></a>
+</h3>
 <p>To add the prediction of samples on the biplot, the
 <code><a href="../reference/prediction.html">prediction()</a></code> function is used. The
 <code>predict.samples</code> argument takes in a vector indicating
@@ -204,16 +203,16 @@ <h2 id="predicting-samples">Predicting samples<a class="anchor" aria-label="anch
 for samples 100 to 150 are shown. The aesthetics for the display of the
 predictions are arguments in the <code><a href="../reference/axes.html">axes()</a></code> function:
 <code>predict.col</code> and <code>predict.lwd</code>.</p>
-<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">$</span><span class="va">Species</span>,dim.biplot <span class="op">=</span> <span class="fl">1</span>,show.class.means <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span>,predict.col <span class="op">=</span> <span class="st">"darkred"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/prediction.html">prediction</a></span><span class="op">(</span>predict.samples<span class="op">=</span><span class="fl">100</span><span class="op">:</span><span class="fl">150</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-8-1.png" width="672"></p>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-9-1.png" width="672"></p>
 </div>
-<div class="section level2">
-<h2 id="predicting-group-means">Predicting group means<a class="anchor" aria-label="anchor" href="#predicting-group-means"></a>
-</h2>
+<div class="section level3">
+<h3 id="predicting-group-means">Predicting Group Means<a class="anchor" aria-label="anchor" href="#predicting-group-means"></a>
+</h3>
 <p>Similarly, to add the prediction of group means, the function
 <code><a href="../reference/prediction.html">prediction()</a></code> is used. The argument
 <code>predict.means</code> takes in a vector specifying which group
@@ -221,12 +220,13 @@ <h2 id="predicting-group-means">Predicting group means<a class="anchor" aria-lab
 predicted. Important to note that the argument
 <code>show.class.means</code> must be set to TRUE in the
 <code><a href="../reference/PCA.html">PCA()</a></code> function.</p>
-<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">$</span><span class="va">Species</span>,dim.biplot <span class="op">=</span> <span class="fl">1</span>,show.class.means <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
-<span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span>,predict.col <span class="op">=</span> <span class="st">"darkred"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span>,predict.col <span class="op">=</span> <span class="st">"darkred"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/means.html">means</a></span><span class="op">(</span>label<span class="op">=</span><span class="cn">TRUE</span>,which<span class="op">=</span><span class="fl">1</span><span class="op">:</span><span class="fl">3</span><span class="op">)</span><span class="op">|&gt;</span></span>
 <span>  <span class="fu"><a href="../reference/prediction.html">prediction</a></span><span class="op">(</span>predict.means <span class="op">=</span> <span class="fl">1</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-9-1.png" width="672"></p>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-10-1.png" width="672"></p>
+</div>
 </div>
 <div class="section level2">
 <h2 id="ellipses-and-alpha-bags">Ellipses and Alpha bags<a class="anchor" aria-label="anchor" href="#ellipses-and-alpha-bags"></a>
@@ -236,49 +236,117 @@ <h2 id="ellipses-and-alpha-bags">Ellipses and Alpha bags<a class="anchor" aria-l
 concentration ellipses are simply a confidence interval. The
 concentration interval is indicated using rectangles spanning the range
 of the interval.</p>
-<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span>,dim.biplot <span class="op">=</span> <span class="fl">1</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/ellipses.html">ellipses</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span>
 <span><span class="co">#&gt; Computing 1.96 -ellipse for setosa </span></span>
 <span><span class="co">#&gt; Computing 1.96 -ellipse for versicolor </span></span>
 <span><span class="co">#&gt; Computing 1.96 -ellipse for virginica</span></span></code></pre></div>
-<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-10-1.png" width="672"></p>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-11-1.png" width="672"></p>
 <p>The one-dimensional representation of an Alpha bag will simply be an
 empirical interval. The empirical interval is indicated using rectangles
 spanning the range of the interval.</p>
-<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span>,dim.biplot <span class="op">=</span> <span class="fl">1</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/alpha.bags.html">alpha.bags</a></span><span class="op">(</span>alpha <span class="op">=</span> <span class="fl">0.7</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span>
 <span><span class="co">#&gt; Computing 0.7 -bag for setosa </span></span>
 <span><span class="co">#&gt; Computing 0.7 -bag for versicolor </span></span>
 <span><span class="co">#&gt; Computing 0.7 -bag for virginica</span></span></code></pre></div>
-<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-11-1.png" width="672"></p>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-12-1.png" width="672"></p>
 </div>
 <div class="section level2">
-<h2 id="group-densities">Group Densities<a class="anchor" aria-label="anchor" href="#group-densities"></a>
+<h2 id="the-function-density1d">The function <code>density1D()</code><a class="anchor" aria-label="anchor" href="#the-function-density1d"></a>
 </h2>
-<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
+<p>Overlapping points make the distribution of points on the scatter
+line difficult to identify. <code><a href="../reference/density1D.html">density1D()</a></code> uses kernel density
+estimation (KDE), which adds a density plot to the one-dimensional
+biplot.</p>
+<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>dim.biplot <span class="op">=</span> <span class="fl">1</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/density1D.html">density1D</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-13-1.png" width="672"></p>
+<p>This KDE may be too smooth to display the distribution of the data.
+By changing the parameters of the KDE, we are able to address this
+issue. The bandwidth and kernel used in <code><a href="../reference/density1D.html">density1D()</a></code> are
+controlled by the arguments <code>h=</code> and <code>kernel=</code>,
+respectively. The bandwidth <code>h</code> can take any positive value,
+see <code><a href="https://rdrr.io/r/stats/density.html" class="external-link">?stats::density</a></code> for more detail. <code>kernel</code>
+can take on any kernel supported by <code><a href="https://rdrr.io/r/stats/density.html" class="external-link">stats::density()</a></code>.</p>
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>dim.biplot <span class="op">=</span> <span class="fl">1</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">'black'</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/density1D.html">density1D</a></span><span class="op">(</span>h <span class="op">=</span> <span class="fl">0.5</span> ,kernel <span class="op">=</span> <span class="st">"triangular"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-14-1.png" width="672"></p>
+<p>The high concentration of observations in the right of the plot now
+becomes evident. To further explore the distributions of the
+observations, we may want to explore the density of groupings in the
+data. To do this, simply specify the <code>group.aes=</code> argument in
+<code><a href="../reference/PCA.html">PCA()</a></code>. Here the density of the three species of iris is
+displayed.</p>
+<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span>,dim.biplot <span class="op">=</span> <span class="fl">1</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span></span>
-<span>  <span class="fu"><a href="../reference/density1D.html">density1D</a></span><span class="op">(</span>which <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">1</span>,<span class="fl">2</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-12-1.png" width="672"></p>
+<span>  <span class="fu"><a href="../reference/density1D.html">density1D</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-15-1.png" width="672"></p>
+<p>To only display the density of certain groups, use the
+<code>which=</code> argument in <code><a href="../reference/density1D.html">density1D()</a></code>.</p>
+<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span>,dim.biplot <span class="op">=</span> <span class="fl">1</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/density1D.html">density1D</a></span><span class="op">(</span>which <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-16-1.png" width="672"></p>
 </div>
 <div class="section level2">
-<h2 id="legend">Legend<a class="anchor" aria-label="anchor" href="#legend"></a>
+<h2 id="the-function-legend-type">The function <code>legend.type()</code><a class="anchor" aria-label="anchor" href="#the-function-legend-type"></a>
 </h2>
-<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CVA.html">CVA</a></span><span class="op">(</span>classes  <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span>,dim.biplot <span class="op">=</span> <span class="fl">1</span>, show.class.means <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
-<span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/density1D.html">density1D</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/samples.html">samples</a></span><span class="op">(</span>opacity<span class="op">=</span><span class="fl">0.5</span><span class="op">)</span><span class="op">|&gt;</span> <span class="fu"><a href="../reference/classify.html">classify</a></span><span class="op">(</span>borders <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">|&gt;</span> <span class="fu"><a href="../reference/alpha.bags.html">alpha.bags</a></span><span class="op">(</span><span class="op">)</span><span class="op">|&gt;</span></span>
-<span>  <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>samples <span class="op">=</span> <span class="cn">TRUE</span>,means <span class="op">=</span> <span class="cn">TRUE</span>, bags <span class="op">=</span> <span class="cn">TRUE</span>, ellipses <span class="op">=</span> <span class="cn">TRUE</span>,new <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span>
+<p><code>legend.type</code> adds a legend to the plot. A separate legend
+is created for each of the elements by setting each of
+<code>samples</code>, <code>means</code>, <code>bags</code> and
+<code>ellipses</code> equal to <code>TRUE</code>. Here, we add a legend
+for the samples.</p>
+<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes  <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span>,dim.biplot <span class="op">=</span> <span class="fl">1</span>, show.class.means <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/density1D.html">density1D</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/samples.html">samples</a></span><span class="op">(</span>opacity<span class="op">=</span><span class="fl">0.5</span><span class="op">)</span><span class="op">|&gt;</span> <span class="fu"><a href="../reference/alpha.bags.html">alpha.bags</a></span><span class="op">(</span><span class="op">)</span><span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>samples <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span>
+<span><span class="co">#&gt; Computing 0.95 -bag for setosa </span></span>
+<span><span class="co">#&gt; Computing 0.95 -bag for versicolor </span></span>
+<span><span class="co">#&gt; Computing 0.95 -bag for virginica</span></span></code></pre></div>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-17-1.png" width="672"></p>
+<p>If other legends are added, they will overlap with the elements of
+the plot as displayed below.</p>
+<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes  <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span>,dim.biplot <span class="op">=</span> <span class="fl">1</span>, show.class.means <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/density1D.html">density1D</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/samples.html">samples</a></span><span class="op">(</span>opacity<span class="op">=</span><span class="fl">0.5</span><span class="op">)</span><span class="op">|&gt;</span> <span class="fu"><a href="../reference/alpha.bags.html">alpha.bags</a></span><span class="op">(</span><span class="op">)</span><span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>samples <span class="op">=</span> <span class="cn">TRUE</span>,means <span class="op">=</span> <span class="cn">TRUE</span>, bags <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span>
+<span><span class="co">#&gt; Computing 0.95 -bag for setosa </span></span>
+<span><span class="co">#&gt; Computing 0.95 -bag for versicolor </span></span>
+<span><span class="co">#&gt; Computing 0.95 -bag for virginica</span></span></code></pre></div>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-18-1.png" width="672"></p>
+<p>By specifying <code>new=TRUE</code>, the legends will be displayed on
+a new plot.</p>
+<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes  <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span>,dim.biplot <span class="op">=</span> <span class="fl">1</span>, show.class.means <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/density1D.html">density1D</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/samples.html">samples</a></span><span class="op">(</span>opacity<span class="op">=</span><span class="fl">0.5</span><span class="op">)</span><span class="op">|&gt;</span> <span class="fu"><a href="../reference/alpha.bags.html">alpha.bags</a></span><span class="op">(</span><span class="op">)</span><span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>samples <span class="op">=</span> <span class="cn">TRUE</span>,means <span class="op">=</span> <span class="cn">TRUE</span>, bags <span class="op">=</span> <span class="cn">TRUE</span>, new<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span>
 <span><span class="co">#&gt; Computing 0.95 -bag for setosa </span></span>
 <span><span class="co">#&gt; Computing 0.95 -bag for versicolor </span></span>
 <span><span class="co">#&gt; Computing 0.95 -bag for virginica</span></span></code></pre></div>
-<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-13-1.png" width="672"><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-13-2.png" width="672"></p>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-19-1.png" width="672"><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-19-2.png" width="672"></p>
+<p>For the CVA biplot <code>legend.type</code> also displays a legend
+for classification regions if `</p>
+<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">bp</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CVA.html">CVA</a></span><span class="op">(</span>classes  <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span>,dim.biplot <span class="op">=</span> <span class="fl">1</span>, show.class.means <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/classify.html">classify</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/density1D.html">density1D</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/samples.html">samples</a></span><span class="op">(</span>opacity<span class="op">=</span><span class="fl">0.5</span><span class="op">)</span><span class="op">|&gt;</span> <span class="fu"><a href="../reference/alpha.bags.html">alpha.bags</a></span><span class="op">(</span><span class="op">)</span><span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>samples <span class="op">=</span> <span class="cn">TRUE</span>,means <span class="op">=</span> <span class="cn">TRUE</span>, bags <span class="op">=</span> <span class="cn">TRUE</span>, regions <span class="op">=</span> <span class="cn">TRUE</span>, new<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span> <span class="co">#</span></span>
+<span><span class="co">#&gt; Computing 0.95 -bag for setosa </span></span>
+<span><span class="co">#&gt; Computing 0.95 -bag for versicolor </span></span>
+<span><span class="co">#&gt; Computing 0.95 -bag for virginica</span></span></code></pre></div>
+<p><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-20-1.png" width="672"><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-20-2.png" width="672"><img src="Biplots_in_1D_files/figure-html/unnamed-chunk-20-3.png" width="672"></p>
 </div>
 <div class="section level2">
-<h2 id="fit-measures">Fit measures<a class="anchor" aria-label="anchor" href="#fit-measures"></a>
+<h2 id="the-function-fit-measures">The function <code>fit.measures()</code><a class="anchor" aria-label="anchor" href="#the-function-fit-measures"></a>
 </h2>
 <p><code><a href="../reference/fit.measures.html">fit.measures()</a></code> calculates measures of fit for the
 biplot. Passing a biplot object which has been piped to
@@ -289,21 +357,21 @@ <h2 id="fit-measures">Fit measures<a class="anchor" aria-label="anchor" href="#f
 Predictivity.</li>
 <li>For each sample: Sample Predictivity</li>
 </ul>
-<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">a</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span>,dim.biplot <span class="op">=</span> <span class="fl">1</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/fit.measures.html">fit.measures</a></span><span class="op">(</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">a</span><span class="op">)</span></span>
 <span><span class="co">#&gt; Object of class biplot, based on 150 samples and 5 variables.</span></span>
 <span><span class="co">#&gt; 4 numeric variables.</span></span>
 <span><span class="co">#&gt; 1 categorical variable.</span></span>
 <span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Quality of fit = 92.5% </span></span>
-<span><span class="co">#&gt; Adequacy of variables:</span></span>
+<span><span class="co">#&gt; Quality of fit in 1 dimension(s) = 92.5% </span></span>
+<span><span class="co">#&gt; Adequacy of variables in 1 dimension(s):</span></span>
 <span><span class="co">#&gt; Sepal.Length  Sepal.Width Petal.Length  Petal.Width </span></span>
 <span><span class="co">#&gt;  0.130600269  0.007144055  0.733884527  0.128371149 </span></span>
-<span><span class="co">#&gt; Axis predictivity:</span></span>
+<span><span class="co">#&gt; Axis predictivity in 1 dimension(s):</span></span>
 <span><span class="co">#&gt; Sepal.Length  Sepal.Width Petal.Length  Petal.Width </span></span>
 <span><span class="co">#&gt;    0.8053299    0.1590003    0.9957524    0.9342141 </span></span>
-<span><span class="co">#&gt; Sample predictivity:</span></span>
+<span><span class="co">#&gt; Sample predictivity in 1 dimension(s):</span></span>
 <span><span class="co">#&gt;            1            2            3            4            5            6 </span></span>
 <span><span class="co">#&gt; 0.9859320755 0.9885358364 0.9974032622 0.9858701194 0.9843168833 0.8999107868 </span></span>
 <span><span class="co">#&gt;            7            8            9           10           11           12 </span></span>
@@ -359,35 +427,26 @@ <h2 id="fit-measures">Fit measures<a class="anchor" aria-label="anchor" href="#f
 <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
 </h2>
 </div>
-  </div>
-
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-
-        <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
-    </nav>
-</div>
-
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside>
 </div>
 
 
 
-      <footer><div class="copyright">
-  <p></p>
-<p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
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-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.</p>
+<div class="pkgdown-footer-right">
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-      
 
-      </header><script src="Biplots_in_3D_files/htmlwidgets-1.6.4/htmlwidgets.js"></script><script src="Biplots_in_3D_files/rglWebGL-binding-1.3.1/rglWebGL.js"></script><link href="Biplots_in_3D_files/rglwidgetClass-1.3.1/rgl.css" rel="stylesheet">
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-  <div class="col-md-9 contents">
-    <div class="page-header toc-ignore">
-      <h1 data-toc-skip>Biplots in 3D</h1>
+<script src="Biplots_in_3D_files/htmlwidgets-1.6.4/htmlwidgets.js"></script><script src="Biplots_in_3D_files/rglWebGL-binding-1.3.18/rglWebGL.js"></script><link href="Biplots_in_3D_files/rglwidgetClass-1.3.18/rgl.css" rel="stylesheet">
+<script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/rglClass.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/utils.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/buffer.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/subscenes.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/shaders.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/shadersrc.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/textures.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/projection.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/mouse.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/init.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/pieces.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/draw.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/controls.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/selection.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/rglTimer.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/pretty.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/axes.src.js"></script><script src="Biplots_in_3D_files/rglwidgetClass-1.3.18/animation.src.js"></script><script src="Biplots_in_3D_files/CanvasMatrix4-1.3.18/CanvasMatrix.src.js"></script><div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Biplots in 3D</h1>
             
       
-      
-      <div class="hidden name"><code>Biplots_in_3D.Rmd</code></div>
 
+      <div class="d-none name"><code>Biplots_in_3D.Rmd</code></div>
     </div>
 
     
     
 <div class="section level2">
-<h2 id="pca-3d-biplot">PCA 3d biplot<a class="anchor" aria-label="anchor" href="#pca-3d-biplot"></a>
+<h2 id="pca-3d-biplot">PCA 3D biplot<a class="anchor" aria-label="anchor" href="#pca-3d-biplot"></a>
 </h2>
 <p>Three-dimensional PCA biplots are obtained by specifying
 <code>dim.biplot = 3</code> in the call to <code><a href="../reference/PCA.html">PCA()</a></code>. The
@@ -117,31 +87,13 @@ <h2 id="pca-3d-biplot">PCA 3d biplot<a class="anchor" aria-label="anchor" href="
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">$</span><span class="va">Species</span>,dim.biplot <span class="op">=</span> <span class="fl">3</span><span class="op">)</span> <span class="op">|&gt;</span></span>
 <span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg 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(point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n      if (uFogMode > 1)\n        fogF = mix(uFogParms.w, 1.0, fogF);\n      fogF = fogF*uFogParms.z;\n      if (uFogMode == 2)\n        fogF = 1.0 - exp(-fogF);\n      // Docs are wrong: use (density*c)^2, not density*c^2\n      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n      else if (uFogMode == 3)\n        fogF = 1.0 - exp(-fogF*fogF);\n      fogF = clamp(fogF, 0.0, 1.0);\n      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n    } else gl_FragColor = fragColor;\n#else\n    gl_FragColor = fragColor;\n#endif // HAS_FOG\n    \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true}},"evals":[],"jsHooks":[]}</script><p id="rgl86731-aria" hidden>
-</p>
-</div>
-</div>
-<div class="section level2">
-<h2 id="cva-3d-biplot">CVA 3d biplot<a class="anchor" aria-label="anchor" href="#cva-3d-biplot"></a>
-</h2>
-<p>Similarly for a CVA 3d biplot, <code>dim.biplot = 3</code> is
-specified in the call to <code><a href="../reference/CVA.html">CVA()</a></code>.</p>
-<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CVA.html">CVA</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">iris</span><span class="op">$</span><span class="va">Species</span>,dim.biplot <span class="op">=</span> <span class="fl">3</span><span class="op">)</span> <span class="op">|&gt;</span></span>
-<span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span>
-<span><span class="co">#&gt; Warning in CVA.biplot(biplot(iris), classes = iris$Species, dim.biplot = 3):</span></span>
-<span><span class="co">#&gt; The dimension of the canonical space &lt; dim.biplot sample.opt method used for</span></span>
-<span><span class="co">#&gt; additional dimension(s).</span></span></code></pre></div>
-<div class="figure">
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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = 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USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg 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(point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n      if (uFogMode > 1)\n        fogF = mix(uFogParms.w, 1.0, fogF);\n      fogF = fogF*uFogParms.z;\n      if (uFogMode == 2)\n        fogF = 1.0 - exp(-fogF);\n      // Docs are wrong: use (density*c)^2, not density*c^2\n      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n      else if (uFogMode == 3)\n        fogF = 1.0 - exp(-fogF*fogF);\n      fogF = clamp(fogF, 0.0, 1.0);\n      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n    } else gl_FragColor = fragColor;\n#else\n    gl_FragColor = fragColor;\n#endif // HAS_FOG\n    \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true},"fastTransparency":true},"evals":[],"jsHooks":[]}</script><p id="rgl14395-aria" hidden>
 </p>
 </div>
-</div>
-<div class="section level2">
-<h2 id="adding-new-samples">Adding new samples<a class="anchor" aria-label="anchor" href="#adding-new-samples"></a>
-</h2>
+<div class="section level3">
+<h3 id="adding-new-samples">Adding new samples<a class="anchor" aria-label="anchor" href="#adding-new-samples"></a>
+</h3>
 <p>The process of adding new samples to the biplot, called interpolation
 utilises the functions <code><a href="../reference/interpolate.html">interpolate()</a></code> and
 <code><a href="../reference/newsamples.html">newsamples()</a></code>. These functions work in the same way as in
@@ -151,18 +103,18 @@ <h2 id="adding-new-samples">Adding new samples<a class="anchor" aria-label="anch
 interpolated. The function <code><a href="../reference/newsamples.html">newsamples()</a></code> operates the same
 way as <code><a href="../reference/samples.html">samples()</a></code> in that the user can specify the
 aesthetics of the interpolated samples.</p>
-<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">100</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span><span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>dim.biplot <span class="op">=</span> <span class="fl">3</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/interpolate.html">interpolate</a></span><span class="op">(</span>newdata <span class="op">=</span> <span class="va">iris</span><span class="op">[</span><span class="fl">101</span><span class="op">:</span><span class="fl">150</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/newsamples.html">newsamples</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"purple"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n      if (uFogMode > 1)\n        fogF = mix(uFogParms.w, 1.0, fogF);\n      fogF = fogF*uFogParms.z;\n      if (uFogMode == 2)\n        fogF = 1.0 - exp(-fogF);\n      // Docs are wrong: use (density*c)^2, not density*c^2\n      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n      else if (uFogMode == 3)\n        fogF = 1.0 - exp(-fogF*fogF);\n      fogF = clamp(fogF, 0.0, 1.0);\n      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n    } else gl_FragColor = fragColor;\n#else\n    gl_FragColor = fragColor;\n#endif // HAS_FOG\n    \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true},"fastTransparency":true},"evals":[],"jsHooks":[]}</script><p id="rgl42263-aria" hidden>
 </p>
 </div>
 </div>
-<div class="section level2">
-<h2 id="adding-new-variables">Adding new variables<a class="anchor" aria-label="anchor" href="#adding-new-variables"></a>
-</h2>
+<div class="section level3">
+<h3 id="adding-new-variables">Adding new variables<a class="anchor" aria-label="anchor" href="#adding-new-variables"></a>
+</h3>
 <p>To interpolate new variables to the biplot, the function
 <code><a href="../reference/interpolate.html">interpolate()</a></code> and <code><a href="../reference/newaxes.html">newaxes()</a></code> are called. The
 function <code><a href="../reference/interpolate.html">interpolate()</a></code> accepts the argument
@@ -171,19 +123,19 @@ <h2 id="adding-new-variables">Adding new variables<a class="anchor" aria-label="
 the new variables to be interpolated. The function
 <code><a href="../reference/newaxes.html">newaxes()</a></code> allows the user to specify the aesthetics of the
 interpolated variables.</p>
-<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">3</span><span class="op">]</span><span class="op">)</span><span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>dim.biplot <span class="op">=</span> <span class="fl">3</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/interpolate.html">interpolate</a></span><span class="op">(</span>newvariable <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/newaxes.html">newaxes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"darkred"</span>,X.new.names <span class="op">=</span> <span class="st">"Petal.Width"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg 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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - 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luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n      if (uFogMode > 1)\n        fogF = mix(uFogParms.w, 1.0, fogF);\n      fogF = fogF*uFogParms.z;\n      if (uFogMode == 2)\n        fogF = 1.0 - exp(-fogF);\n      // Docs are wrong: use (density*c)^2, not density*c^2\n      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n      else if (uFogMode == 3)\n        fogF = 1.0 - exp(-fogF*fogF);\n      fogF = clamp(fogF, 0.0, 1.0);\n      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n    } else gl_FragColor = fragColor;\n#else\n    gl_FragColor = fragColor;\n#endif // HAS_FOG\n    \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true},"fastTransparency":true},"evals":[],"jsHooks":[]}</script><p id="rgl7296-aria" hidden>
 </p>
 </div>
 </div>
-<div class="section level2">
-<h2 id="predicting-samples">Predicting samples<a class="anchor" aria-label="anchor" href="#predicting-samples"></a>
-</h2>
+<div class="section level3">
+<h3 id="predicting-samples">Predicting samples<a class="anchor" aria-label="anchor" href="#predicting-samples"></a>
+</h3>
 <p>To add the prediction of samples on the biplot, the
 <code><a href="../reference/prediction.html">prediction()</a></code> function is used. The
 <code>predict.samples</code> argument takes in a vector indicating
@@ -194,19 +146,19 @@ <h2 id="predicting-samples">Predicting samples<a class="anchor" aria-label="anch
 variables 1 and 4. The aesthetics for the display of the predictions are
 arguments in the <code><a href="../reference/axes.html">axes()</a></code> function: <code>predict.col</code>
 and <code>predict.lwd</code>.</p>
-<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">$</span><span class="va">Species</span>,dim.biplot <span class="op">=</span> <span class="fl">3</span>,show.class.means <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span>,predict.col <span class="op">=</span> <span class="st">"orange"</span><span class="op">)</span> <span class="op">|&gt;</span>  </span>
 <span>  <span class="fu"><a href="../reference/prediction.html">prediction</a></span><span class="op">(</span>predict.samples<span class="op">=</span><span class="fl">100</span><span class="op">:</span><span class="fl">150</span>,which <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">1</span>,<span class="fl">4</span><span class="op">)</span><span class="op">)</span>  <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
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USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = 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projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 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USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg 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vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - 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luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - 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 </p>
 </div>
 </div>
-<div class="section level2">
-<h2 id="predicting-group-means">Predicting group means<a class="anchor" aria-label="anchor" href="#predicting-group-means"></a>
-</h2>
+<div class="section level3">
+<h3 id="predicting-group-means">Predicting group means<a class="anchor" aria-label="anchor" href="#predicting-group-means"></a>
+</h3>
 <p>Similarly, to add the prediction of group means, the function
 <code><a href="../reference/prediction.html">prediction()</a></code> is used. The argument
 <code>predict.means</code> takes in a vector specifying which group
@@ -214,23 +166,23 @@ <h2 id="predicting-group-means">Predicting group means<a class="anchor" aria-lab
 predicted. Important to note that the argument
 <code>show.class.means</code> must be set to TRUE in the
 <code><a href="../reference/PCA.html">PCA()</a></code> function.</p>
-<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">$</span><span class="va">Species</span>,dim.biplot <span class="op">=</span> <span class="fl">3</span>,show.class.means <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span>,predict.col <span class="op">=</span> <span class="st">"darkred"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/prediction.html">prediction</a></span><span class="op">(</span>predict.means <span class="op">=</span> <span class="fl">1</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = 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vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n      if (uFogMode > 1)\n        fogF = mix(uFogParms.w, 1.0, fogF);\n      fogF = fogF*uFogParms.z;\n      if (uFogMode == 2)\n        fogF = 1.0 - exp(-fogF);\n      // Docs are wrong: use (density*c)^2, not density*c^2\n      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n      else if (uFogMode == 3)\n        fogF = 1.0 - exp(-fogF*fogF);\n      fogF = clamp(fogF, 0.0, 1.0);\n      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n    } else gl_FragColor = fragColor;\n#else\n    gl_FragColor = fragColor;\n#endif // HAS_FOG\n    \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true},"fastTransparency":true},"evals":[],"jsHooks":[]}</script><p id="rgl43254-aria" hidden>
 </p>
 </div>
 </div>
-<div class="section level2">
-<h2 id="ellipses">Ellipses<a class="anchor" aria-label="anchor" href="#ellipses"></a>
-</h2>
-<p>Ellipses are added to a 3d biplot using the <code><a href="../reference/ellipses.html">ellipses()</a></code>
-function which works in the same way as a 2d biplot.</p>
-<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<div class="section level3">
+<h3 id="ellipses">Ellipses<a class="anchor" aria-label="anchor" href="#ellipses"></a>
+</h3>
+<p>Ellipses are added to a 3D biplot using the <code><a href="../reference/ellipses.html">ellipses()</a></code>
+function which works in the same way as a 2D biplot.</p>
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span>,dim.biplot <span class="op">=</span> <span class="fl">3</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/ellipses.html">ellipses</a></span><span class="op">(</span>kappa <span class="op">=</span> <span class="fl">3</span>,opacity <span class="op">=</span> <span class="fl">0.5</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span>
@@ -238,40 +190,95 @@ <h2 id="ellipses">Ellipses<a class="anchor" aria-label="anchor" href="#ellipses"
 <span><span class="co">#&gt; Computing 3 -ellipse for versicolor </span></span>
 <span><span class="co">#&gt; Computing 3 -ellipse for virginica</span></span></code></pre></div>
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Pf0A6r6EwzDAjTVevTR39b5E+TDAdCiJvmCp/763+TfAPmgVvs68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4my/HfGpvr+vOz61r2O/i+vRvnYCTz7d2Fe/J3rNvuIz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rUbr8AAAAApufbvlYvZ78AAAAA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\nAj/RKE0/AhmfPjdMDz9VjUQ/1JyfPkDHGT/3e0g/vqUkPuyUDD8f5F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lWJRP+Gx1b6k4ea+E/lJP0VMub4gWaK+uWpgP7xm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\n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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - 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z3AYpY3P5/H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\nzhxzvgCzYL/Q/JK+XX/CvPsldb99Fya+E4qtvEaNfL+Ixoi+K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tHK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\nd76TUWu/A2HEu69IwL6EQW2/0F2vPcg+ZL5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sQ+ToZ3vjnXTb8bDgs/x3ijvkzQSr+cHwU/zuPavQxcY7/i3eQ+IxPRvZIZ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\n+Z42P47VAj/RKE0/AhmfP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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n      if (uFogMode > 1)\n        fogF = mix(uFogParms.w, 1.0, fogF);\n      fogF = fogF*uFogParms.z;\n      if (uFogMode == 2)\n        fogF = 1.0 - exp(-fogF);\n      // Docs are wrong: use (density*c)^2, not density*c^2\n      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n      else if (uFogMode == 3)\n        fogF = 1.0 - exp(-fogF*fogF);\n      fogF = clamp(fogF, 0.0, 1.0);\n      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n    } else gl_FragColor = fragColor;\n#else\n    gl_FragColor = fragColor;\n#endif // HAS_FOG\n    \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true},"fastTransparency":true},"evals":[],"jsHooks":[]}</script><p id="rgl79174-aria" hidden>
 </p>
 </div>
 </div>
-  </div>
-
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-
-        <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
-    </nav>
 </div>
-
+<div class="section level2">
+<h2 id="cva-3d-biplot">CVA 3d biplot<a class="anchor" aria-label="anchor" href="#cva-3d-biplot"></a>
+</h2>
+<p>Similarly for a CVA 3D biplot, <code>dim.biplot = 3</code> is
+specified in the call to <code><a href="../reference/CVA.html">CVA()</a></code>.</p>
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CVA.html">CVA</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">iris</span><span class="op">$</span><span class="va">Species</span>,dim.biplot <span class="op">=</span> <span class="fl">3</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span>
+<span><span class="co">#&gt; Warning in CVA.biplot(biplot(iris), classes = iris$Species, dim.biplot = 3):</span></span>
+<span><span class="co">#&gt; The dimension of the canonical space &lt; dim.biplot sample.opt method used for</span></span>
+<span><span class="co">#&gt; additional dimension(s).</span></span></code></pre></div>
+<div class="figure">
+<div id="rgl46013" style="width:672px;height:576px;" class="rglWebGL html-widget" role="img" aria-labelledby="rgl46013-aria"></div>
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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - 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+</p>
+</div>
+</div>
+<div class="section level2">
+<h2 id="ca-3d-biplot">CA 3D biplot<a class="anchor" aria-label="anchor" href="#ca-3d-biplot"></a>
+</h2>
+<p>As with <code><a href="../reference/PCA.html">PCA()</a></code>, three-dimensional CA biplots are obtained
+by specifying <code>dim.biplot = 3</code> in the call to
+<code><a href="../reference/CA.html">CA()</a></code>. Again, an interactive biplot will be drawn in a
+separate <code>rgl</code> window.</p>
+<p>Consider the <code>HairEyeColor</code> example again as discussed in
+<code>CA in biplotEZ</code>:</p>
+<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="../reference/CA.html">CA</a></span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Symmetric"</span>, dim.biplot <span class="op">=</span> <span class="fl">3</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/samples.html">samples</a></span><span class="op">(</span>col<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"darkred"</span>,<span class="st">"forestgreen"</span><span class="op">)</span>, pch<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">15</span>,<span class="fl">17</span><span class="op">)</span>, label.col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<div class="figure">
+<div id="rgl20859" style="width:672px;height:576px;" class="rglWebGL html-widget" role="img" aria-labelledby="rgl20859-aria"></div>
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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n      if (uFogMode > 1)\n        fogF = mix(uFogParms.w, 1.0, fogF);\n      fogF = fogF*uFogParms.z;\n      if (uFogMode == 2)\n        fogF = 1.0 - exp(-fogF);\n      // Docs are wrong: use (density*c)^2, not density*c^2\n      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n      else if (uFogMode == 3)\n        fogF = 1.0 - exp(-fogF*fogF);\n      fogF = clamp(fogF, 0.0, 1.0);\n      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n    } else gl_FragColor = fragColor;\n#else\n    gl_FragColor = fragColor;\n#endif // HAS_FOG\n    \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true},"fastTransparency":true},"evals":[],"jsHooks":[]}</script><p id="rgl20859-aria" hidden>
+</p>
+</div>
+<p>We also illustrate the three dimensional CA biplot of the
+<code>SA Crime</code> example:</p>
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">SACrime</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">matrix</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">1235</span>,<span class="fl">432</span>,<span class="fl">1824</span>,<span class="fl">1322</span>,<span class="fl">573</span>,<span class="fl">588</span>,<span class="fl">624</span>,<span class="fl">169</span>,<span class="fl">629</span>,<span class="fl">34479</span>,<span class="fl">16833</span>,<span class="fl">46993</span>,<span class="fl">30606</span>,<span class="fl">13670</span>,</span>
+<span>              <span class="fl">16849</span>,<span class="fl">15861</span>,<span class="fl">9898</span>,<span class="fl">24915</span>,<span class="fl">2160</span>,<span class="fl">939</span>,<span class="fl">5257</span>,<span class="fl">4946</span>,<span class="fl">722</span>,<span class="fl">1271</span>,<span class="fl">881</span>,<span class="fl">775</span>,<span class="fl">1844</span>,<span class="fl">5946</span>,</span>
+<span>              <span class="fl">4418</span>,<span class="fl">15117</span>,<span class="fl">10258</span>,<span class="fl">5401</span>,<span class="fl">4273</span>,<span class="fl">4987</span>,<span class="fl">1956</span>,<span class="fl">10639</span>,<span class="fl">29508</span>,<span class="fl">15705</span>,<span class="fl">62703</span>,<span class="fl">37203</span>,</span>
+<span>              <span class="fl">11857</span>,<span class="fl">18855</span>,<span class="fl">14722</span>,<span class="fl">4924</span>,<span class="fl">42376</span>,<span class="fl">604</span>,<span class="fl">156</span>,<span class="fl">7466</span>,<span class="fl">3889</span>,<span class="fl">203</span>,<span class="fl">664</span>,<span class="fl">291</span>,<span class="fl">5</span>,<span class="fl">923</span>,<span class="fl">19875</span>,</span>
+<span>              <span class="fl">19885</span>,<span class="fl">57153</span>,<span class="fl">29410</span>,<span class="fl">11024</span>,<span class="fl">12202</span>,<span class="fl">10406</span>,<span class="fl">5431</span>,<span class="fl">32663</span>,<span class="fl">7086</span>,<span class="fl">4193</span>,<span class="fl">22152</span>,<span class="fl">9264</span>,<span class="fl">3760</span>,</span>
+<span>              <span class="fl">4752</span>,<span class="fl">3863</span>,<span class="fl">1337</span>,<span class="fl">8578</span>,<span class="fl">7929</span>,<span class="fl">4525</span>,<span class="fl">12348</span>,<span class="fl">24174</span>,<span class="fl">3198</span>,<span class="fl">1770</span>,<span class="fl">7004</span>,<span class="fl">2201</span>,<span class="fl">45985</span>,<span class="fl">764</span>,</span>
+<span>              <span class="fl">427</span>,<span class="fl">1501</span>,<span class="fl">1197</span>,<span class="fl">215</span>,<span class="fl">251</span>,<span class="fl">345</span>,<span class="fl">213</span>,<span class="fl">1850</span>,<span class="fl">3515</span>,<span class="fl">879</span>,<span class="fl">3674</span>,<span class="fl">4713</span>,<span class="fl">696</span>,<span class="fl">835</span>,<span class="fl">917</span>,<span class="fl">422</span>,<span class="fl">2836</span>,</span>
+<span>              <span class="fl">88</span>,<span class="fl">59</span>,<span class="fl">174</span>,<span class="fl">76</span>,<span class="fl">31</span>,<span class="fl">61</span>,<span class="fl">117</span>,<span class="fl">32</span>,<span class="fl">257</span>,<span class="fl">5499</span>,<span class="fl">2628</span>,<span class="fl">8073</span>,<span class="fl">6502</span>,<span class="fl">2816</span>,<span class="fl">2635</span>,<span class="fl">3017</span>,<span class="fl">1020</span>,<span class="fl">4000</span>,</span>
+<span>              <span class="fl">8939</span>,<span class="fl">4501</span>,<span class="fl">50970</span>,<span class="fl">24290</span>,<span class="fl">2447</span>,<span class="fl">5907</span>,<span class="fl">5528</span>,<span class="fl">1175</span>,<span class="fl">14555</span><span class="op">)</span>,nrow<span class="op">=</span><span class="fl">9</span>, ncol<span class="op">=</span><span class="fl">14</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/dimnames.html" class="external-link">dimnames</a></span><span class="op">(</span><span class="va">SACrime</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"ECpe"</span>, <span class="st">"FrSt"</span>, <span class="st">"Gaut"</span>, <span class="st">"KZN"</span>,  <span class="st">"Limp"</span>, <span class="st">"Mpml"</span>, <span class="st">"NWst"</span>, <span class="st">"NCpe"</span>,</span>
+<span>                            <span class="st">"WCpe"</span><span class="op">)</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"Arsn"</span>, <span class="st">"AGBH"</span>, <span class="st">"AtMr"</span>, <span class="st">"BNRs"</span>, <span class="st">"BRs"</span>,  <span class="st">"CrJk"</span>,</span>
+<span>                                              <span class="st">"CmAs"</span>, <span class="st">"CmRb"</span>, <span class="st">"DrgR"</span>, <span class="st">"InAs"</span>, <span class="st">"Mrd"</span>, <span class="st">"PubV"</span>, </span>
+<span>                                              <span class="st">"Rape"</span>, <span class="st">"RAC"</span> <span class="op">)</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/dimnames.html" class="external-link">dimnames</a></span><span class="op">(</span><span class="va">SACrime</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="st">"Provinces"</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/dimnames.html" class="external-link">dimnames</a></span><span class="op">(</span><span class="va">SACrime</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="fl">2</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="st">"Crimes"</span></span></code></pre></div>
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">SACrime</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CA.html">CA</a></span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Symmetric"</span>, dim.biplot <span class="op">=</span> <span class="fl">3</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span><span class="fu"><a href="../reference/samples.html">samples</a></span><span class="op">(</span>col<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"royalblue"</span>,<span class="st">"darkred"</span><span class="op">)</span>, pch<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">15</span>,<span class="fl">17</span><span class="op">)</span>, label.col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<div class="figure">
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vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n      if (uFogMode > 1)\n        fogF = mix(uFogParms.w, 1.0, fogF);\n      fogF = fogF*uFogParms.z;\n      if (uFogMode == 2)\n        fogF = 1.0 - exp(-fogF);\n      // Docs are wrong: use (density*c)^2, not density*c^2\n      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n      else if (uFogMode == 3)\n        fogF = 1.0 - exp(-fogF*fogF);\n      fogF = clamp(fogF, 0.0, 1.0);\n      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n    } else gl_FragColor = fragColor;\n#else\n    gl_FragColor = fragColor;\n#endif // HAS_FOG\n    \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true},"fastTransparency":true},"evals":[],"jsHooks":[]}</script><p id="rgl15091-aria" hidden>
+</p>
+</div>
+</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside>
 </div>
 
 
 
-      <footer><div class="copyright">
-  <p></p>
-<p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
-  <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.</p>
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.2.</p>
 </div>
 
-      </footer>
+    </footer>
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-  
 
 
-  
+
 
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 </html>
diff --git a/docs/articles/Biplots_in_3D_files/CanvasMatrix4-1.3.18/CanvasMatrix.src.js b/docs/articles/Biplots_in_3D_files/CanvasMatrix4-1.3.18/CanvasMatrix.src.js
new file mode 100644
index 0000000..2bfbd58
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/CanvasMatrix4-1.3.18/CanvasMatrix.src.js
@@ -0,0 +1,729 @@
+/* globals CanvasMatrix4: true */
+/* globals WebGLFloatArray */
+/* jshint eqeqeq: false */
+/*
+ * Copyright (C) 2009 Apple Inc. All Rights Reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
+ * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+ * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL APPLE INC. OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
+ * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+ * Copyright (2016) Duncan Murdoch - fixed CanvasMatrix4.ortho,
+ * cleaned up.
+ */
+/*
+    CanvasMatrix4 class
+
+    This class implements a 4x4 matrix. It has functions which
+    duplicate the functionality of the OpenGL matrix stack and
+    glut functions.
+
+    IDL:
+
+    [
+        Constructor(in CanvasMatrix4 matrix),           // copy passed matrix into new CanvasMatrix4
+        Constructor(in sequence<float> array)           // create new CanvasMatrix4 with 16 floats (row major)
+        Constructor()                                   // create new CanvasMatrix4 with identity matrix
+    ]
+    interface CanvasMatrix4 {
+        attribute float m11;
+        attribute float m12;
+        attribute float m13;
+        attribute float m14;
+        attribute float m21;
+        attribute float m22;
+        attribute float m23;
+        attribute float m24;
+        attribute float m31;
+        attribute float m32;
+        attribute float m33;
+        attribute float m34;
+        attribute float m41;
+        attribute float m42;
+        attribute float m43;
+        attribute float m44;
+
+        void load(in CanvasMatrix4 matrix);                 // copy the values from the passed matrix
+        void load(in sequence<float> array);                // copy 16 floats into the matrix
+        sequence<float> getAsArray();                       // return the matrix as an array of 16 floats
+        WebGLFloatArray getAsCanvasFloatArray();           // return the matrix as a WebGLFloatArray with 16 values
+        void makeIdentity();                                // replace the matrix with identity
+        void transpose();                                   // replace the matrix with its transpose
+        void invert();                                      // replace the matrix with its inverse
+
+        void translate(in float x, in float y, in float z); // multiply the matrix by passed translation values on the right
+        void scale(in float x, in float y, in float z);     // multiply the matrix by passed scale values on the right
+        void rotate(in float angle,                         // multiply the matrix by passed rotation values on the right
+                    in float x, in float y, in float z);    // (angle is in degrees)
+        void multRight(in CanvasMatrix matrix);             // multiply the matrix by the passed matrix on the right
+        void multLeft(in CanvasMatrix matrix);              // multiply the matrix by the passed matrix on the left
+        void ortho(in float left, in float right,           // multiply the matrix by the passed ortho values on the right
+                   in float bottom, in float top,
+                   in float near, in float far);
+        void frustum(in float left, in float right,         // multiply the matrix by the passed frustum values on the right
+                     in float bottom, in float top,
+                     in float near, in float far);
+        void perspective(in float fovy, in float aspect,    // multiply the matrix by the passed perspective values on the right
+                         in float zNear, in float zFar);
+        void lookat(in float eyex, in float eyey, in float eyez,    // multiply the matrix by the passed lookat
+                    in float ctrx, in float ctry, in float ctrz,    // values on the right
+                    in float upx, in float upy, in float upz);
+    }
+*/
+
+CanvasMatrix4 = function(m)
+{
+    if (typeof m == 'object') {
+        if ("length" in m && m.length >= 16) {
+            this.load(m[0], m[1], m[2], m[3], m[4], m[5], m[6], m[7], m[8], m[9], m[10], m[11], m[12], m[13], m[14], m[15]);
+            return;
+        }
+        else if (m instanceof CanvasMatrix4) {
+            this.load(m);
+            return;
+        }
+    }
+    this.makeIdentity();
+};
+
+CanvasMatrix4.prototype.load = function()
+{
+    if (arguments.length == 1 && typeof arguments[0] == 'object') {
+        var matrix = arguments[0];
+
+        if ("length" in matrix && matrix.length == 16) {
+            this.m11 = matrix[0];
+            this.m12 = matrix[1];
+            this.m13 = matrix[2];
+            this.m14 = matrix[3];
+
+            this.m21 = matrix[4];
+            this.m22 = matrix[5];
+            this.m23 = matrix[6];
+            this.m24 = matrix[7];
+
+            this.m31 = matrix[8];
+            this.m32 = matrix[9];
+            this.m33 = matrix[10];
+            this.m34 = matrix[11];
+
+            this.m41 = matrix[12];
+            this.m42 = matrix[13];
+            this.m43 = matrix[14];
+            this.m44 = matrix[15];
+            return;
+        }
+
+        if (arguments[0] instanceof CanvasMatrix4) {
+
+            this.m11 = matrix.m11;
+            this.m12 = matrix.m12;
+            this.m13 = matrix.m13;
+            this.m14 = matrix.m14;
+
+            this.m21 = matrix.m21;
+            this.m22 = matrix.m22;
+            this.m23 = matrix.m23;
+            this.m24 = matrix.m24;
+
+            this.m31 = matrix.m31;
+            this.m32 = matrix.m32;
+            this.m33 = matrix.m33;
+            this.m34 = matrix.m34;
+
+            this.m41 = matrix.m41;
+            this.m42 = matrix.m42;
+            this.m43 = matrix.m43;
+            this.m44 = matrix.m44;
+            return;
+        }
+    }
+
+    this.makeIdentity();
+};
+
+CanvasMatrix4.prototype.getAsArray = function()
+{
+    return [
+        this.m11, this.m12, this.m13, this.m14,
+        this.m21, this.m22, this.m23, this.m24,
+        this.m31, this.m32, this.m33, this.m34,
+        this.m41, this.m42, this.m43, this.m44
+    ];
+};
+
+CanvasMatrix4.prototype.getAsWebGLFloatArray = function()
+{
+    return new WebGLFloatArray(this.getAsArray());
+};
+
+CanvasMatrix4.prototype.makeIdentity = function()
+{
+    this.m11 = 1;
+    this.m12 = 0;
+    this.m13 = 0;
+    this.m14 = 0;
+
+    this.m21 = 0;
+    this.m22 = 1;
+    this.m23 = 0;
+    this.m24 = 0;
+
+    this.m31 = 0;
+    this.m32 = 0;
+    this.m33 = 1;
+    this.m34 = 0;
+
+    this.m41 = 0;
+    this.m42 = 0;
+    this.m43 = 0;
+    this.m44 = 1;
+};
+
+CanvasMatrix4.prototype.transpose = function()
+{
+    var tmp = this.m12;
+    this.m12 = this.m21;
+    this.m21 = tmp;
+
+    tmp = this.m13;
+    this.m13 = this.m31;
+    this.m31 = tmp;
+
+    tmp = this.m14;
+    this.m14 = this.m41;
+    this.m41 = tmp;
+
+    tmp = this.m23;
+    this.m23 = this.m32;
+    this.m32 = tmp;
+
+    tmp = this.m24;
+    this.m24 = this.m42;
+    this.m42 = tmp;
+
+    tmp = this.m34;
+    this.m34 = this.m43;
+    this.m43 = tmp;
+};
+
+CanvasMatrix4.prototype.invert = function()
+{
+    // Calculate the 4x4 determinant
+    // If the determinant is zero,
+    // then the inverse matrix is not unique.
+    var det = this._determinant4x4();
+
+    if (Math.abs(det) < 1e-8)
+        return null;
+
+    this._makeAdjoint();
+
+    // Scale the adjoint matrix to get the inverse
+    this.m11 /= det;
+    this.m12 /= det;
+    this.m13 /= det;
+    this.m14 /= det;
+
+    this.m21 /= det;
+    this.m22 /= det;
+    this.m23 /= det;
+    this.m24 /= det;
+
+    this.m31 /= det;
+    this.m32 /= det;
+    this.m33 /= det;
+    this.m34 /= det;
+
+    this.m41 /= det;
+    this.m42 /= det;
+    this.m43 /= det;
+    this.m44 /= det;
+};
+
+CanvasMatrix4.prototype.translate = function(x,y,z)
+{
+    if (x === undefined)
+        x = 0;
+    if (y === undefined)
+        y = 0;
+    if (z === undefined)
+        z = 0;
+
+    var matrix = new CanvasMatrix4();
+    matrix.m41 = x;
+    matrix.m42 = y;
+    matrix.m43 = z;
+
+    this.multRight(matrix);
+};
+
+CanvasMatrix4.prototype.scale = function(x,y,z)
+{
+    if (x === undefined)
+        x = 1;
+    if (z === undefined) {
+        if (y === undefined) {
+            y = x;
+            z = x;
+        }
+        else
+            z = 1;
+    }
+    else if (y === undefined)
+        y = x;
+
+    var matrix = new CanvasMatrix4();
+    matrix.m11 = x;
+    matrix.m22 = y;
+    matrix.m33 = z;
+
+    this.multRight(matrix);
+};
+
+CanvasMatrix4.prototype.rotate = function(angle,x,y,z)
+{
+    // angles are in degrees. Switch to radians
+    angle = angle / 180 * Math.PI;
+
+    angle /= 2;
+    var sinA = Math.sin(angle);
+    var cosA = Math.cos(angle);
+    var sinA2 = sinA * sinA;
+
+    // normalize
+    var length = Math.sqrt(x * x + y * y + z * z);
+    if (length === 0) {
+        // bad vector, just use something reasonable
+        x = 0;
+        y = 0;
+        z = 1;
+    } else if (length != 1) {
+        x /= length;
+        y /= length;
+        z /= length;
+    }
+
+    var mat = new CanvasMatrix4();
+
+    // optimize case where axis is along major axis
+    if (x == 1 && y === 0 && z === 0) {
+        mat.m11 = 1;
+        mat.m12 = 0;
+        mat.m13 = 0;
+        mat.m21 = 0;
+        mat.m22 = 1 - 2 * sinA2;
+        mat.m23 = 2 * sinA * cosA;
+        mat.m31 = 0;
+        mat.m32 = -2 * sinA * cosA;
+        mat.m33 = 1 - 2 * sinA2;
+        mat.m14 = mat.m24 = mat.m34 = 0;
+        mat.m41 = mat.m42 = mat.m43 = 0;
+        mat.m44 = 1;
+    } else if (x === 0 && y == 1 && z === 0) {
+        mat.m11 = 1 - 2 * sinA2;
+        mat.m12 = 0;
+        mat.m13 = -2 * sinA * cosA;
+        mat.m21 = 0;
+        mat.m22 = 1;
+        mat.m23 = 0;
+        mat.m31 = 2 * sinA * cosA;
+        mat.m32 = 0;
+        mat.m33 = 1 - 2 * sinA2;
+        mat.m14 = mat.m24 = mat.m34 = 0;
+        mat.m41 = mat.m42 = mat.m43 = 0;
+        mat.m44 = 1;
+    } else if (x === 0 && y === 0 && z == 1) {
+        mat.m11 = 1 - 2 * sinA2;
+        mat.m12 = 2 * sinA * cosA;
+        mat.m13 = 0;
+        mat.m21 = -2 * sinA * cosA;
+        mat.m22 = 1 - 2 * sinA2;
+        mat.m23 = 0;
+        mat.m31 = 0;
+        mat.m32 = 0;
+        mat.m33 = 1;
+        mat.m14 = mat.m24 = mat.m34 = 0;
+        mat.m41 = mat.m42 = mat.m43 = 0;
+        mat.m44 = 1;
+    } else {
+        var x2 = x*x;
+        var y2 = y*y;
+        var z2 = z*z;
+
+        mat.m11 = 1 - 2 * (y2 + z2) * sinA2;
+        mat.m12 = 2 * (x * y * sinA2 + z * sinA * cosA);
+        mat.m13 = 2 * (x * z * sinA2 - y * sinA * cosA);
+        mat.m21 = 2 * (y * x * sinA2 - z * sinA * cosA);
+        mat.m22 = 1 - 2 * (z2 + x2) * sinA2;
+        mat.m23 = 2 * (y * z * sinA2 + x * sinA * cosA);
+        mat.m31 = 2 * (z * x * sinA2 + y * sinA * cosA);
+        mat.m32 = 2 * (z * y * sinA2 - x * sinA * cosA);
+        mat.m33 = 1 - 2 * (x2 + y2) * sinA2;
+        mat.m14 = mat.m24 = mat.m34 = 0;
+        mat.m41 = mat.m42 = mat.m43 = 0;
+        mat.m44 = 1;
+    }
+    this.multRight(mat);
+};
+
+CanvasMatrix4.prototype.multRight = function(mat)
+{
+    var m11 = (this.m11 * mat.m11 + this.m12 * mat.m21 +
+               this.m13 * mat.m31 + this.m14 * mat.m41);
+    var m12 = (this.m11 * mat.m12 + this.m12 * mat.m22 +
+               this.m13 * mat.m32 + this.m14 * mat.m42);
+    var m13 = (this.m11 * mat.m13 + this.m12 * mat.m23 +
+               this.m13 * mat.m33 + this.m14 * mat.m43);
+    var m14 = (this.m11 * mat.m14 + this.m12 * mat.m24 +
+               this.m13 * mat.m34 + this.m14 * mat.m44);
+
+    var m21 = (this.m21 * mat.m11 + this.m22 * mat.m21 +
+               this.m23 * mat.m31 + this.m24 * mat.m41);
+    var m22 = (this.m21 * mat.m12 + this.m22 * mat.m22 +
+               this.m23 * mat.m32 + this.m24 * mat.m42);
+    var m23 = (this.m21 * mat.m13 + this.m22 * mat.m23 +
+               this.m23 * mat.m33 + this.m24 * mat.m43);
+    var m24 = (this.m21 * mat.m14 + this.m22 * mat.m24 +
+               this.m23 * mat.m34 + this.m24 * mat.m44);
+
+    var m31 = (this.m31 * mat.m11 + this.m32 * mat.m21 +
+               this.m33 * mat.m31 + this.m34 * mat.m41);
+    var m32 = (this.m31 * mat.m12 + this.m32 * mat.m22 +
+               this.m33 * mat.m32 + this.m34 * mat.m42);
+    var m33 = (this.m31 * mat.m13 + this.m32 * mat.m23 +
+               this.m33 * mat.m33 + this.m34 * mat.m43);
+    var m34 = (this.m31 * mat.m14 + this.m32 * mat.m24 +
+               this.m33 * mat.m34 + this.m34 * mat.m44);
+
+    var m41 = (this.m41 * mat.m11 + this.m42 * mat.m21 +
+               this.m43 * mat.m31 + this.m44 * mat.m41);
+    var m42 = (this.m41 * mat.m12 + this.m42 * mat.m22 +
+               this.m43 * mat.m32 + this.m44 * mat.m42);
+    var m43 = (this.m41 * mat.m13 + this.m42 * mat.m23 +
+               this.m43 * mat.m33 + this.m44 * mat.m43);
+    var m44 = (this.m41 * mat.m14 + this.m42 * mat.m24 +
+               this.m43 * mat.m34 + this.m44 * mat.m44);
+
+    this.m11 = m11;
+    this.m12 = m12;
+    this.m13 = m13;
+    this.m14 = m14;
+
+    this.m21 = m21;
+    this.m22 = m22;
+    this.m23 = m23;
+    this.m24 = m24;
+
+    this.m31 = m31;
+    this.m32 = m32;
+    this.m33 = m33;
+    this.m34 = m34;
+
+    this.m41 = m41;
+    this.m42 = m42;
+    this.m43 = m43;
+    this.m44 = m44;
+};
+
+CanvasMatrix4.prototype.multLeft = function(mat)
+{
+    var m11 = (mat.m11 * this.m11 + mat.m12 * this.m21 +
+               mat.m13 * this.m31 + mat.m14 * this.m41);
+    var m12 = (mat.m11 * this.m12 + mat.m12 * this.m22 +
+               mat.m13 * this.m32 + mat.m14 * this.m42);
+    var m13 = (mat.m11 * this.m13 + mat.m12 * this.m23 +
+               mat.m13 * this.m33 + mat.m14 * this.m43);
+    var m14 = (mat.m11 * this.m14 + mat.m12 * this.m24 +
+               mat.m13 * this.m34 + mat.m14 * this.m44);
+
+    var m21 = (mat.m21 * this.m11 + mat.m22 * this.m21 +
+               mat.m23 * this.m31 + mat.m24 * this.m41);
+    var m22 = (mat.m21 * this.m12 + mat.m22 * this.m22 +
+               mat.m23 * this.m32 + mat.m24 * this.m42);
+    var m23 = (mat.m21 * this.m13 + mat.m22 * this.m23 +
+               mat.m23 * this.m33 + mat.m24 * this.m43);
+    var m24 = (mat.m21 * this.m14 + mat.m22 * this.m24 +
+               mat.m23 * this.m34 + mat.m24 * this.m44);
+
+    var m31 = (mat.m31 * this.m11 + mat.m32 * this.m21 +
+               mat.m33 * this.m31 + mat.m34 * this.m41);
+    var m32 = (mat.m31 * this.m12 + mat.m32 * this.m22 +
+               mat.m33 * this.m32 + mat.m34 * this.m42);
+    var m33 = (mat.m31 * this.m13 + mat.m32 * this.m23 +
+               mat.m33 * this.m33 + mat.m34 * this.m43);
+    var m34 = (mat.m31 * this.m14 + mat.m32 * this.m24 +
+               mat.m33 * this.m34 + mat.m34 * this.m44);
+
+    var m41 = (mat.m41 * this.m11 + mat.m42 * this.m21 +
+               mat.m43 * this.m31 + mat.m44 * this.m41);
+    var m42 = (mat.m41 * this.m12 + mat.m42 * this.m22 +
+               mat.m43 * this.m32 + mat.m44 * this.m42);
+    var m43 = (mat.m41 * this.m13 + mat.m42 * this.m23 +
+               mat.m43 * this.m33 + mat.m44 * this.m43);
+    var m44 = (mat.m41 * this.m14 + mat.m42 * this.m24 +
+               mat.m43 * this.m34 + mat.m44 * this.m44);
+
+    this.m11 = m11;
+    this.m12 = m12;
+    this.m13 = m13;
+    this.m14 = m14;
+
+    this.m21 = m21;
+    this.m22 = m22;
+    this.m23 = m23;
+    this.m24 = m24;
+
+    this.m31 = m31;
+    this.m32 = m32;
+    this.m33 = m33;
+    this.m34 = m34;
+
+    this.m41 = m41;
+    this.m42 = m42;
+    this.m43 = m43;
+    this.m44 = m44;
+};
+
+CanvasMatrix4.prototype.ortho = function(left, right, bottom, top, near, far)
+{
+    var tx = (left + right) / (left - right);
+    var ty = (top + bottom) / (bottom - top);
+    var tz = (far + near) / (near - far);
+
+    var matrix = new CanvasMatrix4();
+    matrix.m11 = 2 / (right - left);
+    matrix.m12 = 0;
+    matrix.m13 = 0;
+    matrix.m14 = 0;
+    matrix.m21 = 0;
+    matrix.m22 = 2 / (top - bottom);
+    matrix.m23 = 0;
+    matrix.m24 = 0;
+    matrix.m31 = 0;
+    matrix.m32 = 0;
+    matrix.m33 = -2 / (far - near);
+    matrix.m34 = 0;
+    matrix.m41 = tx;
+    matrix.m42 = ty;
+    matrix.m43 = tz;
+    matrix.m44 = 1;
+
+    this.multRight(matrix);
+};
+
+CanvasMatrix4.prototype.frustum = function(left, right, bottom, top, near, far)
+{
+    var matrix = new CanvasMatrix4();
+    var A = (right + left) / (right - left);
+    var B = (top + bottom) / (top - bottom);
+    var C = -(far + near) / (far - near);
+    var D = -(2 * far * near) / (far - near);
+
+    matrix.m11 = (2 * near) / (right - left);
+    matrix.m12 = 0;
+    matrix.m13 = 0;
+    matrix.m14 = 0;
+
+    matrix.m21 = 0;
+    matrix.m22 = 2 * near / (top - bottom);
+    matrix.m23 = 0;
+    matrix.m24 = 0;
+
+    matrix.m31 = A;
+    matrix.m32 = B;
+    matrix.m33 = C;
+    matrix.m34 = -1;
+
+    matrix.m41 = 0;
+    matrix.m42 = 0;
+    matrix.m43 = D;
+    matrix.m44 = 0;
+
+    this.multRight(matrix);
+};
+
+CanvasMatrix4.prototype.perspective = function(fovy, aspect, zNear, zFar)
+{
+    var top = Math.tan(fovy * Math.PI / 360) * zNear;
+    var bottom = -top;
+    var left = aspect * bottom;
+    var right = aspect * top;
+    this.frustum(left, right, bottom, top, zNear, zFar);
+};
+
+CanvasMatrix4.prototype.lookat = function(eyex, eyey, eyez, centerx, centery, centerz, upx, upy, upz)
+{
+    var matrix = new CanvasMatrix4(),
+        xx, xy, xz;
+
+    // Make rotation matrix
+
+    // Z vector
+    var zx = eyex - centerx;
+    var zy = eyey - centery;
+    var zz = eyez - centerz;
+    var mag = Math.sqrt(zx * zx + zy * zy + zz * zz);
+    if (mag) {
+        zx /= mag;
+        zy /= mag;
+        zz /= mag;
+    }
+
+    // Y vector
+    var yx = upx;
+    var yy = upy;
+    var yz = upz;
+
+    // X vector = Y cross Z
+    xx =  yy * zz - yz * zy;
+    xy = -yx * zz + yz * zx;
+    xz =  yx * zy - yy * zx;
+
+    // Recompute Y = Z cross X
+    yx = zy * xz - zz * xy;
+    yy = -zx * xz + zz * xx;
+    yx = zx * xy - zy * xx;
+
+    // cross product gives area of parallelogram, which is < 1.0 for
+    // non-perpendicular unit-length vectors; so normalize x, y here
+
+    mag = Math.sqrt(xx * xx + xy * xy + xz * xz);
+    if (mag) {
+        xx /= mag;
+        xy /= mag;
+        xz /= mag;
+    }
+
+    mag = Math.sqrt(yx * yx + yy * yy + yz * yz);
+    if (mag) {
+        yx /= mag;
+        yy /= mag;
+        yz /= mag;
+    }
+
+    matrix.m11 = xx;
+    matrix.m12 = xy;
+    matrix.m13 = xz;
+    matrix.m14 = 0;
+
+    matrix.m21 = yx;
+    matrix.m22 = yy;
+    matrix.m23 = yz;
+    matrix.m24 = 0;
+
+    matrix.m31 = zx;
+    matrix.m32 = zy;
+    matrix.m33 = zz;
+    matrix.m34 = 0;
+
+    matrix.m41 = 0;
+    matrix.m42 = 0;
+    matrix.m43 = 0;
+    matrix.m44 = 1;
+    matrix.translate(-eyex, -eyey, -eyez);
+
+    this.multRight(matrix);
+};
+
+// Support functions
+CanvasMatrix4.prototype._determinant2x2 = function(a, b, c, d)
+{
+    return a * d - b * c;
+};
+
+CanvasMatrix4.prototype._determinant3x3 = function(a1, a2, a3, b1, b2, b3, c1, c2, c3)
+{
+    return a1 * this._determinant2x2(b2, b3, c2, c3) -
+         b1 * this._determinant2x2(a2, a3, c2, c3) +
+         c1 * this._determinant2x2(a2, a3, b2, b3);
+};
+
+CanvasMatrix4.prototype._determinant4x4 = function()
+{
+    var a1 = this.m11;
+    var b1 = this.m12;
+    var c1 = this.m13;
+    var d1 = this.m14;
+
+    var a2 = this.m21;
+    var b2 = this.m22;
+    var c2 = this.m23;
+    var d2 = this.m24;
+
+    var a3 = this.m31;
+    var b3 = this.m32;
+    var c3 = this.m33;
+    var d3 = this.m34;
+
+    var a4 = this.m41;
+    var b4 = this.m42;
+    var c4 = this.m43;
+    var d4 = this.m44;
+
+    return a1 * this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4) -
+         b1 * this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4) +
+         c1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4) -
+         d1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
+};
+
+CanvasMatrix4.prototype._makeAdjoint = function()
+{
+    var a1 = this.m11;
+    var b1 = this.m12;
+    var c1 = this.m13;
+    var d1 = this.m14;
+
+    var a2 = this.m21;
+    var b2 = this.m22;
+    var c2 = this.m23;
+    var d2 = this.m24;
+
+    var a3 = this.m31;
+    var b3 = this.m32;
+    var c3 = this.m33;
+    var d3 = this.m34;
+
+    var a4 = this.m41;
+    var b4 = this.m42;
+    var c4 = this.m43;
+    var d4 = this.m44;
+
+    // Row column labeling reversed since we transpose rows & columns
+    this.m11  =   this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4);
+    this.m21  = - this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4);
+    this.m31  =   this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4);
+    this.m41  = - this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
+
+    this.m12  = - this._determinant3x3(b1, b3, b4, c1, c3, c4, d1, d3, d4);
+    this.m22  =   this._determinant3x3(a1, a3, a4, c1, c3, c4, d1, d3, d4);
+    this.m32  = - this._determinant3x3(a1, a3, a4, b1, b3, b4, d1, d3, d4);
+    this.m42  =   this._determinant3x3(a1, a3, a4, b1, b3, b4, c1, c3, c4);
+
+    this.m13  =   this._determinant3x3(b1, b2, b4, c1, c2, c4, d1, d2, d4);
+    this.m23  = - this._determinant3x3(a1, a2, a4, c1, c2, c4, d1, d2, d4);
+    this.m33  =   this._determinant3x3(a1, a2, a4, b1, b2, b4, d1, d2, d4);
+    this.m43  = - this._determinant3x3(a1, a2, a4, b1, b2, b4, c1, c2, c4);
+
+    this.m14  = - this._determinant3x3(b1, b2, b3, c1, c2, c3, d1, d2, d3);
+    this.m24  =   this._determinant3x3(a1, a2, a3, c1, c2, c3, d1, d2, d3);
+    this.m34  = - this._determinant3x3(a1, a2, a3, b1, b2, b3, d1, d2, d3);
+    this.m44  =   this._determinant3x3(a1, a2, a3, b1, b2, b3, c1, c2, c3);
+};
diff --git a/docs/articles/Biplots_in_3D_files/rglWebGL-binding-1.3.1/rglWebGL.js b/docs/articles/Biplots_in_3D_files/rglWebGL-binding-1.3.1/rglWebGL.js
new file mode 100644
index 0000000..52c8fe6
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglWebGL-binding-1.3.1/rglWebGL.js
@@ -0,0 +1,79 @@
+/* el is the div, holding the rgl object as el.rglinstance,
+     which holds x as el.rglinstance.scene
+   x is the JSON encoded rglwidget.
+*/
+
+
+HTMLWidgets.widget({
+
+  name: 'rglWebGL',
+
+  type: 'output',
+
+  factory: function(el, width, height) {
+    el.width = width;
+    el.height = height;
+    var rgl = new rglwidgetClass(),
+        onchangeselection = function(e) {
+          for (var i = 0; i < rgl.scene.crosstalk.sel_handle.length; i++)
+            rgl.clearBrush(except = e.rglSubsceneId);
+          rgl.selection(e, false);
+        },
+        onchangefilter = function(e) {
+          rgl.selection(e, true);
+        };
+    
+    return { 
+      renderValue: function(x) {
+        var i, pel, player, groups,
+            inShiny = (typeof Shiny !== "undefined");
+      
+        x.crosstalk.group = groups = [].concat(x.crosstalk.group);
+        x.crosstalk.id = [].concat(x.crosstalk.id);
+        x.crosstalk.key = [].concat(x.crosstalk.key);
+        x.crosstalk.sel_handle = new Array(groups.length);
+        x.crosstalk.fil_handle = new Array(groups.length);
+        x.crosstalk.selection = [];
+        for (i = 0; i < groups.length; i++) {
+          x.crosstalk.sel_handle[i] = new crosstalk.SelectionHandle(groups[i], {sharedId: x.crosstalk.id[i]});
+          x.crosstalk.sel_handle[i].on("change", onchangeselection);
+          x.crosstalk.fil_handle[i] = new crosstalk.FilterHandle(groups[i], {sharedId: x.crosstalk.id[i]});
+          x.crosstalk.fil_handle[i].on("change", onchangefilter);
+        }
+        if (inShiny) {
+          // Shiny calls this multiple times, so we need extra cleanup
+          // between
+          rgl.sphere = undefined;
+        }
+        rgl.initialize(el, x);
+        rgl.initGL();
+  
+  /* We might have been called after (some of) the players were rendered.
+     We need to make sure we respond to their initial values. */
+
+        if (typeof x.players !== "undefined") {
+          var players = [].concat(x.players);
+          for (i = 0; i < players.length; i++) {
+            pel = document.getElementById(players[i]);
+            if (pel) {
+              player = pel.rglPlayer;
+              if (player && (!player.initialized || inShiny)) {
+                rgl.Player(pel, player);
+                player.initialized = true;
+              }
+            }
+          }
+        }
+        rgl.drag = 0;
+        rgl.drawScene();
+      },
+
+      resize: function(width, height) {
+        el.width = width;
+        el.height = height;
+        el.rglinstance.resize(el);
+        el.rglinstance.drawScene();
+      }
+    };
+  }
+});
diff --git a/docs/articles/Biplots_in_3D_files/rglWebGL-binding-1.3.18/rglWebGL.js b/docs/articles/Biplots_in_3D_files/rglWebGL-binding-1.3.18/rglWebGL.js
new file mode 100644
index 0000000..52c8fe6
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglWebGL-binding-1.3.18/rglWebGL.js
@@ -0,0 +1,79 @@
+/* el is the div, holding the rgl object as el.rglinstance,
+     which holds x as el.rglinstance.scene
+   x is the JSON encoded rglwidget.
+*/
+
+
+HTMLWidgets.widget({
+
+  name: 'rglWebGL',
+
+  type: 'output',
+
+  factory: function(el, width, height) {
+    el.width = width;
+    el.height = height;
+    var rgl = new rglwidgetClass(),
+        onchangeselection = function(e) {
+          for (var i = 0; i < rgl.scene.crosstalk.sel_handle.length; i++)
+            rgl.clearBrush(except = e.rglSubsceneId);
+          rgl.selection(e, false);
+        },
+        onchangefilter = function(e) {
+          rgl.selection(e, true);
+        };
+    
+    return { 
+      renderValue: function(x) {
+        var i, pel, player, groups,
+            inShiny = (typeof Shiny !== "undefined");
+      
+        x.crosstalk.group = groups = [].concat(x.crosstalk.group);
+        x.crosstalk.id = [].concat(x.crosstalk.id);
+        x.crosstalk.key = [].concat(x.crosstalk.key);
+        x.crosstalk.sel_handle = new Array(groups.length);
+        x.crosstalk.fil_handle = new Array(groups.length);
+        x.crosstalk.selection = [];
+        for (i = 0; i < groups.length; i++) {
+          x.crosstalk.sel_handle[i] = new crosstalk.SelectionHandle(groups[i], {sharedId: x.crosstalk.id[i]});
+          x.crosstalk.sel_handle[i].on("change", onchangeselection);
+          x.crosstalk.fil_handle[i] = new crosstalk.FilterHandle(groups[i], {sharedId: x.crosstalk.id[i]});
+          x.crosstalk.fil_handle[i].on("change", onchangefilter);
+        }
+        if (inShiny) {
+          // Shiny calls this multiple times, so we need extra cleanup
+          // between
+          rgl.sphere = undefined;
+        }
+        rgl.initialize(el, x);
+        rgl.initGL();
+  
+  /* We might have been called after (some of) the players were rendered.
+     We need to make sure we respond to their initial values. */
+
+        if (typeof x.players !== "undefined") {
+          var players = [].concat(x.players);
+          for (i = 0; i < players.length; i++) {
+            pel = document.getElementById(players[i]);
+            if (pel) {
+              player = pel.rglPlayer;
+              if (player && (!player.initialized || inShiny)) {
+                rgl.Player(pel, player);
+                player.initialized = true;
+              }
+            }
+          }
+        }
+        rgl.drag = 0;
+        rgl.drawScene();
+      },
+
+      resize: function(width, height) {
+        el.width = width;
+        el.height = height;
+        el.rglinstance.resize(el);
+        el.rglinstance.drawScene();
+      }
+    };
+  }
+});
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/animation.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/animation.src.js
new file mode 100644
index 0000000..cdca347
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/animation.src.js
@@ -0,0 +1,153 @@
+/**
+     * Methods related to animations
+     * @name ___METHODS_FOR_ANIMATION___
+     * @memberof rglwidgetClass
+     * @kind function
+     * @instance
+     */
+    /**
+     * Binary search
+     * @param x - x coordinates in increasing order
+     * @param newx - value to find, assumed to be in the range of x
+     * @result index of largest x value below newx
+     */
+    rglwidgetClass.bisect = function(x, newx) {
+      var lo = 0, hi = x.length - 1, mid;
+      while (lo < hi - 1) {
+        mid = Math.round((lo + hi)/2);
+        if (x[mid] < newx)
+          lo = mid;
+        else
+          hi = mid;
+      }
+      return lo;
+    };
+    
+    /**
+     * Step interpolation (constant outside bounds)
+     * @param x - x coordinates in increasing order
+     * @param v - values at x; either a vector or matrix
+     * @param newx - value at which to evaluate
+     */
+    rglwidgetClass.step = function(x, v, newx) {
+      var n, lo;
+      if (newx <= x[0])
+        return v[0];    
+      n = x.length;
+      if (newx >= x[n-1])
+        return v[n-1];
+      lo = this.bisect(x, newx);
+      return v[lo];
+    };
+    
+    /**
+     * Linear interpolation (constant outside bounds)
+     * @param x - x coordinates in increasing order
+     * @param v - values at x; either a vector or matrix
+     * @param newx - value at which to evaluate
+     */
+    rglwidgetClass.lerp = function(x, v, newx) {
+      var i, n, lo, hi, alpha, result;
+      if (newx <= x[0])
+        return v[0];    
+      n = x.length;
+      if (newx >= x[n-1])
+        return v[n-1];
+      lo = this.bisect(x, newx);
+      if (newx === x[lo])
+        return v[lo];
+      hi = lo + 1;
+      if (newx === x[hi])
+        return v[hi];
+      alpha = (newx - x[lo])/(x[hi] - x[lo]);
+      result = v[lo];
+      n = result.length;
+      if (typeof n !== "undefined") {
+        for (i = 0; i < n; i++)
+          result[i] = (1 - alpha)*result[i] + alpha*v[hi][i];
+      } else
+        result = (1 - alpha)*result + alpha*v[hi];
+      return result;
+    };
+    
+    /**
+     * Spherical linear interpolation (constant outside bounds)
+     * @param x - x coordinates in increasing order
+     * @param v - a matrix of unit quaternions
+     * @param newx - value at which to evaluate
+     */
+    rglwidgetClass.slerp = function(x, v, newx) {
+      var n, lo, hi, alpha, result,
+          p0, p1, dot, Omega, alpha0, alpha1, len;
+      if (newx <= x[0])
+        return v[0];    
+      if (newx >= x[n-1])
+        return v[n-1];
+      lo = this.bisect(x, newx);
+      if (newx === x[lo])
+        return v[lo];
+      hi = lo + 1;
+      if (newx === x[hi])
+        return v[hi];
+      p0 = v[lo];
+      p1 = v[hi];
+      dot = p0[0]*p1[0] + 
+            p0[1]*p1[1] +
+            p0[2]*p1[2] +
+            p0[3]*p1[3];
+      if (dot < 0) {
+        p1 = [-p1[0], -p1[1], -p1[2], -p1[3]];
+        dot = -dot;
+      }
+      if (dot >= 1)
+        result = p1;
+      else {
+        alpha = (newx - x[lo])/(x[hi] - x[lo]);
+        Omega = Math.acos(dot);
+        alpha0 = Math.sin((1 - alpha)*Omega);
+        alpha1 = Math.sin(alpha*Omega);
+        result = [alpha0*p0[0] + alpha1*p1[0],
+                  alpha0*p0[1] + alpha1*p1[1],
+                  alpha0*p0[2] + alpha1*p1[2],
+                  alpha0*p0[3] + alpha1*p1[3]];
+      }
+      len = Math.sqrt(result[0]*result[0] +
+                      result[1]*result[1] +
+                      result[2]*result[2] +
+                      result[3]*result[3]);
+      return [result[0]/len,
+              result[1]/len,
+              result[2]/len,
+              result[3]/len];
+    };
+
+    /**
+     * Rotate using unit quaternion
+     * @param q - a single unit quaternion
+     */
+    rglwidgetClass.rotateByQuaternion = function(M, q) {
+
+    var xx = q[0]*q[0],
+        xy = q[0]*q[1],
+        xz = q[0]*q[2],
+        xw = q[0]*q[3],
+        yy = q[1]*q[1],
+        yz = q[1]*q[2],
+        yw = q[1]*q[3],
+        zz = q[2]*q[2],
+        zw = q[2]*q[3],
+        matrix = new CanvasMatrix4();
+      matrix.m11 = 1 - 2*(yy + zz);
+      matrix.m12 = 2*(xy + zw);
+      matrix.m13 = 2*(xz - yw);
+        
+      matrix.m21 = 2*(xy - zw);
+      matrix.m22 = 1 - 2*(xx + zz);
+      matrix.m23 = 2*(yz + xw);
+
+      matrix.m31 = 2*(xz + yw);
+      matrix.m32 = 2*(yz - xw);
+      matrix.m33 = 1 - 2*(xx + yy);
+
+      M.multRight(matrix);      
+    };
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/axes.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/axes.src.js
new file mode 100644
index 0000000..8fc17e8
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/axes.src.js
@@ -0,0 +1,441 @@
+    /**
+     * Methods related to axes
+     * @name ___METHODS_FOR_AXES___
+     * @memberof rglwidgetClass
+     * @kind function
+     * @instance
+     */
+     
+    /**
+     * Choose edges for ticks
+     * @param { Matrix } prmv - projection-model-view matrix
+     */
+    rglwidgetClass.prototype.getTickEdges = function(prmv){
+      var vertices = [[0,0,0,1], [0,0,1,1],
+                      [0,1,0,1], [0,1,1,1],
+                      [1,0,0,1], [1,0,1,1],
+                      [1,1,0,1], [1,1,1,1]], 
+           dim, i, j, k, edges, hull, step, result = [], proj = [],
+
+        // Filter to edges that are on sides that would
+        // be shown with a filled backing.
+        
+      has_back = function(edge) {
+          var normals = [[], []],
+              verts = [vertices[edge[0]], 
+                       vertices[edge[1]]], 
+              normal, m, n;
+          n = 0;
+          for (m=0; m<3; m++) {
+            if (verts[0][m] === verts[1][m]) {
+              normals[n] = [0,0,0,1];
+              normals[n][m] = 2*verts[0][m] - 1;
+              n++;
+            }
+          }
+          for (n=0; n<2; n++) {
+            normal = rglwidgetClass.multVM(normals[n], self.normMatrix);
+            if (normal[2] < 0 ||
+                (normal[2] === 0 && normal[0] < 0))
+              return true;
+          }
+          return false;
+        }, self = this;
+        
+      for (i = 0; i < vertices.length; i++) {
+        proj[i] = rglwidgetClass.multVM(vertices[i], prmv);
+        proj[i][0] = proj[i][0]/proj[i][3];
+        proj[i][1] = proj[i][1]/proj[i][3];
+        proj[i][2] = i;
+      }
+      hull = rglwidgetClass.chull(proj.slice());  
+      for (i = 0; i < hull.length; i++)
+        hull[i] = hull[i][2];
+      hull.push(hull[0]);
+      for (dim = 0; dim < 3; dim++) { 
+        edges = [];
+        step = Math.pow(2, 2-dim);
+        for (i = 0; i < 4; i++) {
+          j = (dim === 0) ? i : (dim === 1) ? i + 2*(i>1) : 2*i;
+          for (k = 0; k < hull.length - 1; k++) {
+            if ((hull[k] === j && hull[k+1] === j + step) ||
+                (hull[k] === j+step && hull[k+1] === j))
+          
+              edges.push([j, j+step], [j+step, j]);
+          }
+        }
+
+        edges = edges.filter(has_back);
+        
+        // Find the edge with a vertex closest
+        // to the bottom left corner
+        if (edges.length) {
+          var best, best2, val = Infinity, newval;
+          for (i = 0; i < edges.length; i++) {
+            j = edges[i][0];
+            newval = proj[j][0] + proj[j][1];
+            if (newval < val) {
+              best = j;
+              best2 = edges[i][1];
+              val = newval;
+            }
+          }
+          if (typeof best !== "undefined") {
+            result[dim] = vertices[best].slice(0,3);
+            result[dim][dim] = undefined;
+          } else
+            result[dim] = undefined;
+        }
+      }
+      return result;
+    };
+    
+    /**
+     * Choose tick locations
+     * @param { Object } obj - The bboxdeco
+    */
+    rglwidgetClass.prototype.getTickLocations = function(obj){
+      var dim, i, limits, locations = [], result = [[],[],[]], value,
+          len, delta, range, bbox = obj.bbox;
+      obj.needsAxisCallback = false;
+      for (dim = 0; dim < 3; dim++) {
+        limits = bbox.slice(2*dim, 2*dim + 2);
+        range = limits[1] - limits[0];
+        switch(obj.axes.mode[dim]) {
+        case "custom":
+          for (i=0; i < obj.vertices.length; i++) {
+            value = (obj.vertices[i][dim] - limits[0])/range;
+            if (typeof value !== "undefined" &&
+                !isNaN(value))
+              result[dim].push(value);
+          }
+          break;
+        case "fixedstep":
+          len = Math.floor(range/obj.axes.step[dim]);
+          delta = obj.axes.step[dim];
+          for (i = 0; i < len; i++)
+            result[dim].push(i*delta);          
+          break;
+        case "fixednum":
+          len = obj.axes.nticks[dim];
+          delta = (len > 1) ? range/(len-1) : 0;
+          for (i = 0; i < len; i++)
+            result[dim].push(i*delta/range);
+          break;
+        case "pretty":
+          locations = this.R_pretty(limits[0], limits[1], obj.axes.nticks[dim],
+                                  3, // min_n
+                                  0.75, // shrink_sml
+                                  [1.5, 2.75], // high_u_fact
+                                  0, // eps_correction
+                                  0); // return_bounds)  
+          for (i = locations.lo; i <= locations.up; i++) {
+            value = (i*locations.unit - limits[0])/range;
+            if (0 < value && value < 1)
+              result[dim].push(value);
+          }
+          break;
+        case "user":
+          obj.needsAxisCallback = true;
+          break;
+        }
+      }
+      return result;
+    };
+    
+    /**
+     * Set tick vertices
+     * @param { Object } ticks - the tick object
+     * @param { Array }  edges - Which edges get the ticks?
+    */
+    rglwidgetClass.prototype.getTickVertices = function(ticks) {
+      var dim, i, j, vertices = [], locations, 
+          edges = ticks.edges, edge;
+      for (dim = 0; dim < 3; dim++) {
+        locations = ticks.locations[dim];
+        if (locations.length)
+          for (i = 0; i < locations.length; i++) 
+            if (typeof edges[dim] !== "undefined") {
+              edge = edges[dim].slice();
+              edge[dim] = locations[i];
+              vertices.push(edge);
+              edge = edge.slice();
+              for (j = 0; j < 3; j++)       
+                if ((dim < 2 && j === 1 - dim) || 
+                    (dim === 2 && j === 0))
+                  edge[j] += 2*(edge[j] - 0.5)/ticks.axes.marklen[dim];
+              vertices.push(edge);
+            }
+        }
+      ticks.vertices = vertices;
+      ticks.vertexCount = vertices.length;
+      ticks.values = new Float32Array(rglwidgetClass.flatten(vertices));
+      ticks.initialized = false;
+    };
+    
+    /**
+     * Set tick label positions
+     * @param { Object } obj - the bbox object
+    */
+    rglwidgetClass.prototype.placeTickLabels = function(obj) {
+      var ticks = obj.ticks, labels = obj.labels, i,j,k,
+          vertices = [], tickvertices = ticks.vertices, 
+          vertex, locations, dim, edges = obj.ticks.edges;
+      j = 0;
+      for (dim = 0; dim < 3; dim++) {
+        if (typeof edges[dim] === "undefined") 
+          continue;
+        locations = ticks.locations[dim];
+        if (locations.length)
+          for (i = 0; i < locations.length; i++) {
+            if (isNaN(locations[i]))
+              continue;
+            while (j < tickvertices.length && 
+                   tickvertices[j][dim] !== locations[i]) j++;
+            if (j >= tickvertices.length)
+              break;
+            vertex = tickvertices[j].slice();
+            for (k = 0; k < 3; k++)
+              vertex[k] += 2*(tickvertices[j+1][k] - vertex[k]);
+            vertices.push(vertex);
+            j += 2;
+          }
+        }
+      labels.vertices = vertices;
+      labels.centers = labels.vertices;
+      labels.initialized = false;
+    };  
+     
+    /**
+     * Set tick labels
+     * @param { Object } obj - the bbox object
+     */ 
+    rglwidgetClass.prototype.setTickLabels = function(obj) {
+      var ticks = obj.ticks, mode, locations, labels = [],
+      start = 0, nticks, dim, i, limits, range, values, max,
+      edges = obj.ticks.edges;
+      for (dim = 0; dim < 3; dim++) {
+        if (typeof edges[dim] === "undefined") 
+          continue;
+        mode = obj.axes.mode[dim];
+        nticks = obj.axes.nticks[dim]; // used on input only for custom!
+        if (mode === "custom") 
+          labels = labels.concat(obj.texts.slice(start, start + nticks));
+        else {
+          limits = obj.bbox.slice(2*dim, 2*(dim+1));
+          range = limits[1] - limits[0];
+          locations = ticks.locations[dim];
+          max = -Infinity;
+          values = [];
+          for (i = 0; i < locations.length; i++) {
+            values.push(limits[0] + range*locations[i]);
+            max = Math.max(max, Math.abs(values[i]));
+          }
+          for (i = 0; i < locations.length; i++) {
+            if (Math.abs(values[i])/max < Math.pow(10, -5))
+              values[i] = 0;
+            labels.push(rglwidgetClass.signif(values[i], 4).toString());
+          }
+          obj.axes.nticks[dim] = locations.length;  
+        }
+        start += nticks;
+      }
+      obj.labels.texts = labels;
+    };
+
+    /**
+     * Set bboxdeco bbox and center vector 
+     * @param { Object } obj - the bbox object
+     */ 
+    rglwidgetClass.prototype.setBbox = function(obj, subscene) {
+      var i, expand, center = [], bbox;
+      if (!obj.initialized)
+        this.initBBox(obj);
+        
+      bbox = [].concat(subscene.par3d.bbox);
+      for (i = 0; i < 3; i++) {
+        expand = obj.axes.expand[i];
+        center[i] = (bbox[2*i] + bbox[2*i + 1])/2;
+        bbox[2*i] = center[i] - expand*(bbox[2*i + 1] - center[i]);
+        bbox[2*i+1] = center[i] + expand*(bbox[2*i + 1] - center[i]);
+      }
+      obj.bbox = bbox;
+      obj.center = center;
+    };
+
+    rglwidgetClass.prototype.setBBoxMatrices = function(obj) {
+      var saved = {normMatrix: new CanvasMatrix4(this.normMatrix),
+                   mvMatrix: new CanvasMatrix4(this.mvMatrix)},
+          bboxNorm, bboxMV, bbox = obj.bbox, scale;
+          
+      bboxNorm = new CanvasMatrix4();
+      scale = [bbox[1]-bbox[0], bbox[3]-bbox[2], bbox[5]-bbox[4]];
+      bboxNorm.scale(1/scale[0], 1/scale[1], 1/scale[2]);
+      bboxNorm.multRight(saved.normMatrix);
+      this.normMatrix = bboxNorm;
+
+      bboxMV = new CanvasMatrix4();
+      bboxMV.scale(scale[0], scale[1], scale[2]);
+      bboxMV.translate(bbox[0], bbox[2], bbox[4]);
+      bboxMV.multRight(saved.mvMatrix);
+      this.mvMatrix = obj.mvMatrix = bboxMV;
+      
+      if (this.prmvMatrix === null)
+        saved.prmvMatrix = null;
+      else
+        saved.prmvMatrix = new CanvasMatrix4(this.prmvMatrix);
+        
+      this.setprmvMatrix();
+      obj.prmvMatrix = this.prmvMatrix;
+      
+      return saved;
+    };
+    
+    rglwidgetClass.prototype.restoreBBoxMatrices = function(saved) {
+      this.normMatrix = saved.normMatrix;
+      this.mvMatrix   = saved.mvMatrix;
+      this.prmvMatrix = saved.prmvMatrix;
+    };
+    
+    rglwidgetClass.prototype.getMarginParameters = function(bboxdeco, material) {
+      // Assume we've run this.setBbox(bboxdeco, subscene);
+      var bbox = bboxdeco.bbox,
+          edge = [].concat(material.edge),
+          saved, edges, i, 
+          at = material.margin, line, level, trans, scale;
+
+      if (material.floating) {
+        saved = this.setBBoxMatrices(bboxdeco);
+        edges = this.getTickEdges(this.prmvMatrix)[at];
+        this.restoreBBoxMatrices(saved);
+        if (typeof edges !== "undefined")
+          for (i = 0; i < 3; i++) {
+            if (edges[i] < 1) edges[i] = -1;
+              edge[i] = edge[i]*edges[i];
+        } else
+          return undefined;
+      }
+      switch(at) {
+      case 0: line = 1;
+              level = 2;
+              break;
+      case 1: line = 0;
+              level = 2;
+              break;
+      case 2: line = 0;
+              level = 1;
+              break;
+      }
+      scale = [edge[0]*(bbox[1]-bbox[0])/bboxdeco.axes.marklen[0], 
+               edge[1]*(bbox[3]-bbox[2])/bboxdeco.axes.marklen[1], 
+               edge[2]*(bbox[5]-bbox[4])/bboxdeco.axes.marklen[2]];
+      trans = [edge[0] === 1 ? bbox[1] : bbox[0],
+               edge[1] === 1 ? bbox[3] : bbox[2],
+               edge[2] === 1 ? bbox[5] : bbox[4]];
+      return {at: at, line: line, level: level, trans: trans, scale: scale};        
+    };
+    
+    rglwidgetClass.prototype.fixVertex = function(orig, parms, center, bbox) {
+      var vertex = [0,0,0];
+      if (rglwidgetClass.missing(orig[0]))
+        vertex[parms.at] = center[parms.at];
+      else if (orig[0] === "-Inf")
+        vertex[parms.at] = bbox[2*parms.at];
+      else if (orig[0] === "Inf")
+        vertex[parms.at] = bbox[2*parms.at + 1];
+      else
+        vertex[parms.at] = orig[0];
+      vertex[parms.line] = parms.scale[parms.line]*orig[1] + 
+          parms.trans[parms.line];
+      vertex[parms.level] = parms.scale[parms.level]*orig[2] + 
+          parms.trans[parms.level];
+      return vertex;
+    };
+    
+    rglwidgetClass.prototype.fixNormal = function(orig, parms) {
+      var vertex = [0,0,0];
+      vertex[parms.at] = orig[0];
+      vertex[parms.line] = orig[1]/parms.scale[parms.line];
+      vertex[parms.level] = orig[2]/parms.scale[parms.level];
+      return vertex;
+    };
+
+    rglwidgetClass.prototype.marginVecToDataVec = function(obj, subscene) {
+      var bboxdeco = this.getBBoxDeco(subscene),
+          center, bbox, parms, parmsjson,
+          orig = obj.orig, 
+          vertices = [], normals = [],
+          centers = [], i, vertex;
+      if (typeof orig === "undefined") {
+        orig = {vert: obj.vertices,
+                norm: obj.normals,
+                cent: obj.centers,
+                doNormals: typeof obj.normals !== "undefined",
+                doCenters: typeof obj.centers !== "undefined",
+                parms: ""
+               };
+        obj.orig = orig;
+      }
+
+      if (typeof bboxdeco !== "undefined") {
+        this.setBbox(bboxdeco, subscene);
+        center = bboxdeco.center;
+        bbox = bboxdeco.bbox;
+        parms = this.getMarginParameters(bboxdeco, obj.material);
+        if (typeof parms === "undefined")
+          return false;  /* axis is not currently shown */
+        
+        parmsjson = JSON.stringify(parms);
+        if (parmsjson === orig.parms)
+          return true;  /* nothing has changed */
+    
+        orig.parms = parmsjson;
+        
+        for (i=0; i < orig.vert.length; i++) {
+          vertex = this.fixVertex(orig.vert[i], parms, center, bbox);
+          vertices.push(vertex);
+        }
+        obj.vertices = vertices;
+        if (orig.doNormals) {
+          for (i=0; i < orig.norm.length; i++) {
+            vertex = this.fixNormal(orig.norm[i], parms);
+            normals.push(vertex);
+          }
+          obj.normals = normals;
+        }
+        if (orig.doCenters) {
+          for (i=0; i < orig.cent.length; i++) {
+            vertex = this.fixVertex(orig.cent[i], parms, center, bbox);
+            centers.push(vertex);
+          }
+          obj.centers = centers;
+        }
+        
+        obj.initialized = false;
+        return true;
+      } else {
+        console.warn("bboxdeco not found");
+        return false;
+      }
+    };
+
+    rglwidgetClass.prototype.doAxisCallback = function(obj, edges) {
+      var i, j, code, axis, fn;
+      for (i = 0; i < 3; i++) {
+        if (obj.axes.mode[i] === "user") {
+          axis = ["x", "y", "z"][i];
+          if (typeof obj.callbacks !== "undefined" &&
+              typeof (code = obj.callbacks[axis]) !== "undefined") {
+            if (typeof edges[i] !== "undefined")
+              for (j = 0; j < 3; j++)
+                if (typeof edges[i][j] !== "undefined")
+                  axis = axis + (edges[i][j] > 0 ? "+" : "-");
+            
+          /* jshint evil:true */
+            fn = Function('"use strict";return (' + code + ')')();
+          /* jshint evil:false */
+            fn.call(this, axis);
+          }
+        }
+      }
+    };
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/buffer.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/buffer.src.js
new file mode 100644
index 0000000..13d2e1a
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/buffer.src.js
@@ -0,0 +1,182 @@
+/**
+     * Methods related to buffered data
+     * @name ___METHODS_FOR_BUFFERS___
+     * @memberof rglwidgetClass
+     * @kind function
+     * @instance
+     */
+    /**
+     * Detect rglBuffered object
+     * @param { Object } obj - vertices or similar 
+     */
+    rglwidgetClass.prototype.isBuffered = function(obj) {
+      return typeof obj === "string";
+    };
+
+    /* The next two functions are taken from 
+     
+     https://developer.mozilla.org/en-US/docs/Web/JavaScript/Base64_encoding_and_decoding
+     
+     They were written by Mozilla Contributors and dedicated
+     to the public domain under CC0. */
+     
+    /* Array of bytes to Base64 string decoding */
+    rglwidgetClass.prototype.b64ToUint6 = function(nChr) {
+      return nChr > 64 && nChr < 91 ? nChr - 65 : 
+             nChr > 96 && nChr < 123 ? nChr - 71 : 
+             nChr > 47 && nChr < 58 ? nChr + 4 : 
+             nChr === 43 ? 62 : 
+             nChr === 47 ? 63 : 
+             0;
+    };
+
+    /* jshint bitwise:false */
+    rglwidgetClass.prototype.base64DecToArr = function(sBase64, nBlocksSize) {
+      var sB64Enc = sBase64.replace(/[^A-Za-z0-9\+\/]/g, ""),
+        nInLen = sB64Enc.length, 
+        nOutLen = nBlocksSize ? Math.ceil((nInLen * 3 + 1 >> 2) / nBlocksSize) * nBlocksSize : nInLen * 3 + 1 >> 2, 
+        taBytes = new Uint8Array(nOutLen);
+      for (var nMod3, nMod4, nUint24 = 0, nOutIdx = 0, nInIdx = 0; nInIdx < nInLen; nInIdx++) {
+        nMod4 = nInIdx & 3;
+        nUint24 |= this.b64ToUint6(sB64Enc.charCodeAt(nInIdx)) << 6 * (3 - nMod4);
+        if (nMod4 === 3 || nInLen - nInIdx === 1) {
+          for (nMod3 = 0; nMod3 < 3 && nOutIdx < nOutLen; nMod3++, nOutIdx++) {
+            taBytes[nOutIdx] = nUint24 >>> (16 >>> nMod3 & 24) & 255;
+          }
+          nUint24 = 0;
+        }
+      }
+      return taBytes;
+    };
+    /* jshint bitwise:true */
+    
+    rglwidgetClass.prototype.getArrayBuffer = function(base64) {
+      return this.base64DecToArr(base64, 4).buffer;
+    };
+
+    rglwidgetClass.prototype.getBufferedData = function(v) {
+      return this.readAccessor(parseInt(v, 10), this.scene.buffer);
+    };
+    
+    rglwidgetClass.prototype.readAccessor = function(acc, buf) {
+      var typeSignedByte = 5120, 
+          typeUnsignedByte = 5121, 
+          typeSignedShort = 5122, 
+          typeUnsignedShort = 5123, 
+          typeSignedInt = 5124, 
+          typeUnsignedInt = 5125, 
+          typeFloat = 5126, 
+          typeDouble = 5130, 
+          accessor = buf.accessors[acc], 
+          bufferView = buf.bufferViews[accessor.bufferView], 
+          buffer = buf.buffers[bufferView.buffer], 
+          bytes, 
+          lens = {
+            SCALAR: 1,
+            VEC2: 2,
+            VEC3: 3,
+            VEC4: 4,
+            MAT2: 4,
+            MAT3: 9,
+            MAT4: 16
+          }, 
+          rowsizes = {
+            SCALAR: 1,
+            VEC2: 2,
+            VEC3: 3,
+            VEC4: 4,
+            MAT2: 2,
+            MAT3: 3,
+            MAT4: 4
+          }, 
+          offset = 0, 
+          len = lens[accessor.type], 
+          rowsize = rowsizes[accessor.type], 
+          count = len * accessor.count, 
+          nrows = count / rowsize, 
+          values, arr = [], row, i, j, k;
+          
+      if (typeof buffer.bytes === "string") 
+        buffer.bytes = this.getArrayBuffer(buffer.bytes);
+        
+      bytes = buffer.bytes;
+      
+      if (typeof accessor.byteOffset !== "undefined") 
+        offset += accessor.byteOffset;
+        
+      if (typeof bufferView.byteOffset !== "undefined") 
+        offset += bufferView.byteOffset;
+        
+      switch (accessor.componentType) {
+       case typeSignedByte:
+        values = new Int8Array(buffer.bytes, offset, count);
+        break;
+
+       case typeUnsignedByte:
+        values = new Uint8Array(buffer.bytes, offset, count);
+        break;
+
+       case typeSignedShort:
+        values = new Int16Array(buffer.bytes, offset, count);
+        break;
+
+       case typeUnsignedShort:
+        values = new Uint16Array(buffer.bytes, offset, count);
+        break;
+
+       case typeSignedInt:
+        values = new Int32Array(buffer.bytes, offset, count);
+        break;
+
+       case typeUnsignedInt:
+        values = new Uint32Array(buffer.bytes, offset, count);
+        break;
+
+       case typeFloat:
+        values = new Float32Array(buffer.bytes, offset, count);
+        break;
+
+       case typeDouble:
+        values = new Float64Array(buffer.bytes, offset, count);
+        break;
+      }
+
+      /* This is all very inefficient, but is convenient
+             to work with the old code. */
+      k = 0;
+      for (i = 0; i < nrows; i++) {
+        row = [];
+        for (j = 0; j < rowsize; j++) {
+          if (accessor.normalized) {
+            switch(accessor.componentType) {
+              case typeSignedByte:
+                row.push(Math.max(values[k++]/127, -1.0));
+                break;
+              case typeSignedShort:
+                row.push(Math.max(values[k++]/32767, -1.0));
+                break;
+              case typeUnsignedByte:
+                row.push(values[k++]/255);
+                break;
+              case typeUnsignedShort:
+                row.push(values[k++]/65535);
+                break;
+            }
+          } else
+            row.push(values[k++]);
+        }
+        arr.push(row);
+      }
+      return arr;
+    };
+    
+    rglwidgetClass.prototype.expandBufferedFields = function(obj) {
+      /* this list needs to match the one in convertScene.R */
+      var fields = ["vertices", "normals", "indices", 
+                    "texcoords", "colors", "centers"], i, field;
+      for (i = 0; i < fields.length; i++) {
+        field = obj[fields[i]];
+        if (this.isBuffered(field))
+          obj[fields[i]] = this.getBufferedData(field);
+      }
+    };
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/controls.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/controls.src.js
new file mode 100644
index 0000000..ffc7be8
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/controls.src.js
@@ -0,0 +1,591 @@
+
+    /**
+     * Change the displayed subset
+     * @param { Object } el - Element of the control; not used.
+     * @param { Object } control - The subset control data.
+     */
+    rglwidgetClass.prototype.subsetSetter = function(el, control) {
+      if (typeof control.subscenes === "undefined" ||
+          control.subscenes === null)
+        control.subscenes = this.scene.rootSubscene;
+      var value = Math.round(control.value),
+          subscenes = [].concat(control.subscenes),
+          fullset = [].concat(control.fullset),
+          i, j, subsceneid,
+          adds = [], deletes = [];
+      if (rglwidgetClass.missing(value))
+        value = control.value = 0;
+      if (control.accumulate)
+        for (i=0; i <= value; i++)
+          adds = adds.concat(control.subsets[i]);
+      else
+        adds = adds.concat(control.subsets[value]);
+      deletes = fullset.filter(function(x) { return adds.indexOf(x) < 0; });
+      for (i = 0; i < subscenes.length; i++) {
+        subsceneid = subscenes[i];
+        if (typeof this.getObj(subsceneid) === "undefined")
+          this.alertOnce("typeof object is undefined");
+        for (j = 0; j < adds.length; j++)
+          this.addToSubscene(adds[j], subsceneid);
+        for (j = 0; j < deletes.length; j++)
+          this.delFromSubscene(deletes[j], subsceneid);
+      }
+    };
+
+    /**
+     * Change the requested property
+     * @param { Object } el - Element of the control; not used.
+     * @param { Object } control - The property setter control data.
+     */
+    rglwidgetClass.prototype.propertySetter = function(el, control)  {
+      var value = control.value,
+          values = [].concat(control.values),
+          svals = [].concat(control.param),
+          direct = values[0] === null,
+          entries = [].concat(control.entries),
+          ncol = entries.length,
+          nrow = values.length/ncol,
+          properties = rglwidgetClass.repeatToLen(control.properties, ncol),
+          objids = rglwidgetClass.repeatToLen(control.objids, ncol),
+          property, objid = objids[0],
+          obj = this.getObj(objid),
+          propvals, i, j, v1, v2, p, entry, gl, needsBinding,
+          newprop, newid,
+
+          getPropvals = function() {
+            if (property === "userMatrix")
+              return obj.par3d.userMatrix.getAsArray();
+            else if (property === "scale" || property === "FOV" || property === "zoom")
+              return [].concat(obj.par3d[property]);
+            else
+              return [].concat(obj[property]);
+          },
+
+          putPropvals = function(newvals) {
+            if (newvals.length === 1)
+              newvals = newvals[0];
+            if (property === "userMatrix")
+              obj.par3d.userMatrix.load(newvals);
+            else if (property === "scale" || property === "FOV" || property === "zoom")
+              obj.par3d[property] = newvals;
+            else
+              obj[property] = newvals;
+          };
+
+      if (direct && typeof value === "undefined")
+        return;
+
+      if (control.interp) {
+        values = values.slice(0, ncol).concat(values).
+                 concat(values.slice(ncol*(nrow-1), ncol*nrow));
+        svals = [-Infinity].concat(svals).concat(Infinity);
+        for (i = 1; i < svals.length; i++) {
+          if (value <= svals[i]) {
+            if (svals[i] === Infinity)
+              p = 1;
+            else
+              p = (svals[i] - value)/(svals[i] - svals[i-1]);
+            break;
+          }
+        }
+      } else if (!direct) {
+        value = Math.round(value);
+      }
+
+      for (j=0; j<entries.length; j++) {
+        entry = entries[j];
+        newprop = properties[j];
+        newid = objids[j];
+
+        if (newprop !== property || newid !== objid) {
+          if (typeof property !== "undefined")
+            putPropvals(propvals);
+          property = newprop;
+          objid = newid;
+          obj = this.getObj(objid);
+          propvals = getPropvals();
+        }
+        if (control.interp) {
+          v1 = values[ncol*(i-1) + j];
+          v2 = values[ncol*i + j];
+          this.setElement(propvals, entry, p*v1 + (1-p)*v2);
+        } else if (!direct) {
+          this.setElement(propvals, entry, values[ncol*value + j]);
+        } else {
+          this.setElement(propvals, entry, value[j]);
+        }
+      }
+      putPropvals(propvals);
+
+      needsBinding = [];
+      for (j=0; j < entries.length; j++) {
+        if (properties[j] === "values" &&
+            needsBinding.indexOf(objids[j]) === -1) {
+          needsBinding.push(objids[j]);
+        }
+      }
+      for (j=0; j < needsBinding.length; j++) {
+        gl = this.gl || this.initGL();
+        obj = this.getObj(needsBinding[j]);
+        gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
+        gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW);
+      }
+    };
+
+    /**
+     * Change the requested vertices
+     * @param { Object } el - Element of the control; not used.
+     * @param { Object } control - The vertext setter control data.
+     */
+    rglwidgetClass.prototype.vertexSetter = function(el, control)  {
+      var svals = [].concat(control.param),
+          j, k, p, a, propvals, stride, ofs, obj, entry,
+          attrib, vertex, varies,
+          ofss    = {x:"vofs", y:"vofs", z:"vofs",
+                     red:"cofs", green:"cofs", blue:"cofs",
+                     alpha:"cofs", radii:"radofs",
+                     nx:"nofs", ny:"nofs", nz:"nofs",
+                     ox:"oofs", oy:"oofs", oz:"oofs",
+                     ts:"tofs", tt:"tofs"},
+          pos     = {x:0, y:1, z:2,
+                     red:0, green:1, blue:2,
+                     alpha:3,radii:0,
+                     nx:0, ny:1, nz:2,
+                     ox:0, oy:1, oz:2,
+                     ts:0, tt:1},
+        values = control.values,
+        direct = values === null,
+        ncol,
+        interp = control.interp,
+        vertices = [].concat(control.vertices),
+        attributes = [].concat(control.attributes),
+        value = control.value, newval, aliases, alias;
+
+      ncol = Math.max(vertices.length, attributes.length);
+
+      if (!ncol)
+        return;
+
+      vertices = rglwidgetClass.repeatToLen(vertices, ncol);
+      attributes = rglwidgetClass.repeatToLen(attributes, ncol);
+
+      if (direct)
+        interp = false;
+
+      /* JSON doesn't pass Infinity */
+      svals[0] = -Infinity;
+      svals[svals.length - 1] = Infinity;
+
+      for (j = 1; j < svals.length; j++) {
+        if (value <= svals[j]) {
+          if (interp) {
+            if (svals[j] === Infinity)
+              p = 1;
+            else
+              p = (svals[j] - value)/(svals[j] - svals[j-1]);
+          } else {
+            if (svals[j] - value > value - svals[j-1])
+              j = j - 1;
+          }
+          break;
+        }
+      }
+
+      obj = this.getObj(control.objid);
+      // First, make sure color attributes vary in original
+      if (typeof obj.vOffsets !== "undefined") {
+      	varies = true;
+        for (k = 0; k < ncol; k++) {
+          attrib = attributes[k];
+          if (typeof attrib !== "undefined") {
+            ofs = obj.vOffsets[ofss[attrib]];
+            if (ofs < 0) {
+              switch(attrib) {
+              	case "alpha":
+              	case "red":
+              	case "green":
+              	case "blue":
+              	  obj.colors = [obj.colors[0], obj.colors[0]];
+              	  break;
+              }
+              varies = false;
+            }
+          }
+        }
+        if (!varies)
+          this.initObjId(control.objid);
+      }
+      propvals = obj.values;
+      aliases = obj.alias;
+      if (typeof aliases === "undefined")
+        aliases = [];
+      for (k=0; k<ncol; k++) {
+        if (direct) {
+          newval = value;
+        } else if (interp) {
+          newval = p*values[j-1][k] + (1-p)*values[j][k];
+        } else {
+          newval = values[j][k];
+        }      	
+        attrib = attributes[k];
+        vertex = vertices[k];
+        alias = aliases[vertex];
+        if (obj.type === "planes" || obj.type === "clipplanes") {
+          ofs = ["nx", "ny", "nz", "offset"].indexOf(attrib);
+          if (ofs >= 0) {
+            if (ofs < 3) {
+              if (obj.normals[vertex][ofs] !== newval) {  // Assume no aliases here...
+              	obj.normals[vertex][ofs] = newval;
+              	obj.initialized = false;
+              }
+            } else {
+              if (obj.offsets[vertex][0] !== newval) {
+              	obj.offsets[vertex][0] = newval;
+              	obj.initialized = false;
+              }
+            }
+            continue;
+          }
+        }
+        // Not a plane setting...
+        ofs = obj.vOffsets[ofss[attrib]];
+        if (ofs < 0)
+          this.alertOnce("Attribute '"+attrib+"' not found in object "+control.objid);
+        else {
+          stride = obj.vOffsets.stride;
+          ofs = ofs + pos[attrib];
+          entry = vertex*stride + ofs;
+          propvals[entry] = newval;
+          if (typeof alias !== "undefined")
+            for (a = 0; a < alias.length; a++)
+              propvals[alias[a]*stride + ofs] = newval;
+        }
+      }
+      if (typeof obj.buf !== "undefined") {
+        var gl = this.gl || this.initGL();
+        gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
+        gl.bufferData(gl.ARRAY_BUFFER, propvals, gl.STATIC_DRAW);
+      }
+    };
+
+    /**
+     * Change the requested vertex properties by age
+     * @param { Object } el - Element of the control; not used.
+     * @param { Object } control - The age setter control data.
+     */
+    rglwidgetClass.prototype.ageSetter = function(el, control) {
+      var objids = [].concat(control.objids),
+          nobjs = objids.length,
+          time = control.value,
+          births = [].concat(control.births),
+          ages = [].concat(control.ages),
+          steps = births.length,
+          j = Array(steps),
+          p = Array(steps),
+          i, k, l, age, j0, propvals, stride, ofs, objid, obj,
+          attrib, dim, varies, alias, aliases, a, d,
+          attribs = ["colors", "alpha", "radii", "vertices",
+                     "normals", "origins", "texcoords",
+                     "x", "y", "z",
+                     "red", "green", "blue"],
+          ofss    = ["cofs", "cofs", "radofs", "vofs",
+                     "nofs", "oofs", "tofs",
+                     "vofs", "vofs", "vofs",
+                     "cofs", "cofs", "cofs"],
+          dims    = [3,1,1,3,
+                     3,2,2,
+                     1,1,1,
+                     1,1,1],
+          pos     = [0,3,0,0,
+                     0,0,0,
+                     0,1,2,
+                     0,1,2];
+      /* Infinity doesn't make it through JSON */
+      ages[0] = -Infinity;
+      ages[ages.length-1] = Infinity;
+      for (i = 0; i < steps; i++) {
+        if (births[i] !== null) {  // NA in R becomes null
+          age = time - births[i];
+          for (j0 = 1; age > ages[j0]; j0++);
+          if (ages[j0] === Infinity)
+            p[i] = 1;
+          else if (ages[j0] > ages[j0-1])
+            p[i] = (ages[j0] - age)/(ages[j0] - ages[j0-1]);
+          else
+            p[i] = 0;
+          j[i] = j0;
+        }
+      }
+      // First, make sure color attributes vary in original
+      for (l = 0; l < nobjs; l++) {
+      	objid = objids[l];
+      	obj = this.getObj(objid);
+      	varies = true;
+        if (typeof obj.vOffsets === "undefined")
+          continue;
+        for (k = 0; k < attribs.length; k++) {
+          attrib = control[attribs[k]];
+          if (typeof attrib !== "undefined") {
+            ofs = obj.vOffsets[ofss[k]];
+            if (ofs < 0) {
+              switch(attribs[k]) {
+              	case "colors":
+              	case "alpha":
+              	case "red":
+              	case "green":
+              	case "blue":
+              	  obj.colors = [obj.colors[0], obj.colors[0]];
+              	  break;
+              }
+              varies = false;
+            }
+          }
+        }
+        if (!varies)
+          this.initObjId(objid);
+      }
+      for (l = 0; l < nobjs; l++) {
+        objid = objids[l];
+        obj = this.getObj(objid);
+        if (typeof obj.vOffsets === "undefined")
+          continue;
+        aliases = obj.alias;
+        if (typeof aliases === "undefined")
+          aliases = [];
+        propvals = obj.values;
+        stride = obj.vOffsets.stride;
+        for (k = 0; k < attribs.length; k++) {
+          attrib = control[attribs[k]];
+          if (typeof attrib !== "undefined") {
+            ofs = obj.vOffsets[ofss[k]];
+            if (ofs >= 0) {
+              dim = dims[k];
+              ofs = ofs + pos[k];
+              for (i = 0; i < steps; i++) {
+              	alias = aliases[i];
+                if (births[i] !== null) {
+                  for (d=0; d < dim; d++) {
+                    propvals[i*stride + ofs + d] = p[i]*attrib[dim*(j[i]-1) + d] + (1-p[i])*attrib[dim*j[i] + d];
+                    if (typeof alias !== "undefined")
+                      for (a=0; a < alias.length; a++)
+                        propvals[alias[a]*stride + ofs + d] = propvals[i*stride + ofs + d];
+                  }
+                }
+              }
+            } else
+              this.alertOnce("\'"+attribs[k]+"\' property not found in object "+objid);
+          }
+        }
+        obj.values = propvals;
+        if (typeof obj.buf !== "undefined") {
+          var gl = this.gl || this.initGL();
+          gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
+          gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW);
+        }
+      }
+    };
+
+    /**
+     * Bridge to old style control
+     * @param { Object } el - Element of the control; not used.
+     * @param { Object } control - The bridge control data.
+     */
+    rglwidgetClass.prototype.oldBridge = function(el, control) {
+      var attrname, global = window[control.prefix + "rgl"];
+      if (global)
+        for (attrname in global)
+          this[attrname] = global[attrname];
+      window[control.prefix + "rgl"] = this;
+    };
+
+    /**
+     * Set up a player control
+     * @param { Object } el - The player control element
+     * @param { Object } control - The player data.
+     */
+    rglwidgetClass.prototype.Player = function(el, control) {
+      var
+        self = this,
+        components = [].concat(control.components),
+        buttonLabels = [].concat(control.buttonLabels),
+
+        Tick = function() { /* "this" will be a timer */
+          var i,
+              nominal = this.value,
+              slider = this.Slider,
+              labels = this.outputLabels,
+              output = this.Output,
+              step;
+          if (typeof slider !== "undefined" && nominal !== slider.value)
+            slider.value = nominal;
+          if (typeof output !== "undefined") {
+            step = Math.round((nominal - output.sliderMin)/output.sliderStep);
+            if (labels !== null) {
+              output.innerHTML = labels[step];
+            } else {
+              step = step*output.sliderStep + output.sliderMin;
+              output.innerHTML = step.toPrecision(output.outputPrecision);
+            }
+          }
+          for (i=0; i < this.actions.length; i++) {
+            this.actions[i].value = nominal;
+          }
+          self.applyControls(el, this.actions, false);
+          self.drawScene();
+        },
+
+        OnSliderInput = function() { /* "this" will be the slider */
+          this.rgltimer.value = Number(this.value);
+          this.rgltimer.Tick();
+        },
+
+        addSlider = function(min, max, step, value) {
+          var slider = document.createElement("input");
+          slider.type = "range";
+          slider.min = min;
+          slider.max = max;
+          slider.step = step;
+          slider.value = value;
+          slider.oninput = OnSliderInput;
+          slider.sliderActions = control.actions;
+          slider.sliderScene = this;
+          slider.className = "rgl-slider";
+          slider.id = el.id + "-slider";
+          el.rgltimer.Slider = slider;
+          slider.rgltimer = el.rgltimer;
+          el.appendChild(slider);
+        },
+
+        addLabel = function(labels, min, step, precision) {
+          var output = document.createElement("output");
+          output.sliderMin = min;
+          output.sliderStep = step;
+          output.outputPrecision = precision;
+          output.className = "rgl-label";
+          output.id = el.id + "-label";
+          el.rgltimer.Output = output;
+          el.rgltimer.outputLabels = labels;
+          el.appendChild(output);
+        },
+
+        addButton = function(which, label, active) {
+          var button = document.createElement("input"),
+              onclicks = {Reverse: function() { this.rgltimer.reverse();},
+                    Play: function() { this.rgltimer.play();
+                                       this.value = this.rgltimer.enabled ? this.inactiveValue : this.activeValue; },
+                   Slower: function() { this.rgltimer.slower(); },
+                   Faster: function() { this.rgltimer.faster(); },
+                   Reset: function() { this.rgltimer.reset(); },
+              	   Step:  function() { this.rgltimer.step(); }
+              };
+          button.rgltimer = el.rgltimer;
+          button.type = "button";
+          button.value = label;
+          button.activeValue = label;
+          button.inactiveValue = active;
+          if (which === "Play")
+            button.rgltimer.PlayButton = button;
+          button.onclick = onclicks[which];
+          button.className = "rgl-button";
+          button.id = el.id + "-" + which;
+          el.appendChild(button);
+        };
+
+        if (typeof control.reinit !== "undefined" && control.reinit !== null) {
+          control.actions.reinit = control.reinit;
+        }
+        el.rgltimer = new rgltimerClass(Tick, control.start, control.interval, control.stop,
+                                        control.step, control.value, control.rate, control.loop, control.actions);
+        for (var i=0; i < components.length; i++) {
+          switch(components[i]) {
+            case "Slider": addSlider(control.start, control.stop,
+                                   control.step, control.value);
+              break;
+            case "Label": addLabel(control.labels, control.start,
+                                   control.step, control.precision);
+              break;
+            default:
+              addButton(components[i], buttonLabels[i], control.pause);
+          }
+        }
+        el.rgltimer.Tick();
+    };
+
+    /**
+     * Apply all registered controls
+     * @param { Object } el - DOM element of the control
+     * @param { Object } x - List of actions to apply
+     * @param { boolean } [draw=true] - Whether to redraw after applying
+     */
+    rglwidgetClass.prototype.applyControls = function(el, x, draw) {
+      var self = this, reinit = x.reinit, i, control, type;
+      for (i = 0; i < x.length; i++) {
+        control = x[i];
+        type = control.type;
+        self[type](el, control);
+      }
+      if (typeof reinit !== "undefined" && reinit !== null) {
+        reinit = [].concat(reinit);
+        for (i = 0; i < reinit.length; i++)
+          self.getObj(reinit[i]).initialized = false;
+      }
+      if (typeof draw === "undefined" || draw)
+        self.drawScene();
+    };
+
+    /**
+     * Handler for scene change
+     * @param { Object } message - What sort of scene change to do?
+     */
+    rglwidgetClass.prototype.sceneChangeHandler = function(message) {
+      var self = document.getElementById(message.elementId).rglinstance,
+          objs = message.objects, mat = message.material,
+          root = message.rootSubscene,
+          initSubs = message.initSubscenes,
+          redraw = message.redrawScene,
+          skipRedraw = message.skipRedraw,
+          deletes, subs, allsubs = [], i,j;
+      if (typeof message.delete !== "undefined") {
+        deletes = [].concat(message.delete);
+        if (typeof message.delfromSubscenes !== "undefined")
+          subs = [].concat(message.delfromSubscenes);
+        else
+          subs = [];
+        for (i = 0; i < deletes.length; i++) {
+          for (j = 0; j < subs.length; j++) {
+            self.delFromSubscene(deletes[i], subs[j]);
+          }
+          delete self.scene.objects[deletes[i]];
+        }
+      }
+      if (typeof objs !== "undefined") {
+        Object.keys(objs).forEach(function(key){
+          key = parseInt(key, 10);
+          self.scene.objects[key] = objs[key];
+          self.initObjId(key);
+          var obj = self.getObj(key),
+              subs = [].concat(obj.inSubscenes), k;
+          allsubs = allsubs.concat(subs);
+          for (k = 0; k < subs.length; k++)
+            self.addToSubscene(key, subs[k]);
+        });
+      }
+      if (typeof mat !== "undefined") {
+        self.scene.material = mat;
+      }
+      if (typeof root !== "undefined") {
+        self.scene.rootSubscene = root;
+      }
+      if (typeof initSubs !== "undefined")
+        allsubs = allsubs.concat(initSubs);
+      allsubs = self.unique(allsubs);
+      for (i = 0; i < allsubs.length; i++) {
+        self.initSubscene(allsubs[i]);
+      }
+      if (typeof skipRedraw !== "undefined") {
+        root = self.getObj(self.scene.rootSubscene);
+        root.par3d.skipRedraw = skipRedraw;
+      }
+      if (redraw)
+        self.drawScene();
+    };
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/draw.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/draw.src.js
new file mode 100644
index 0000000..11b098a
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/draw.src.js
@@ -0,0 +1,1376 @@
+    /**
+     * Methods related to drawing
+     * @name ___METHODS_FOR_DRAWING___
+     * @memberof rglwidgetClass
+     * @kind function
+     * @instance
+     */
+     
+    /**
+     * Start drawing
+     * @returns { boolean } Previous state
+     */
+    rglwidgetClass.prototype.startDrawing = function() {
+    	var value = this.drawing;
+    	this.drawing = true;
+    	return value;
+    };
+
+    /**
+     * Stop drawing and check for context loss
+     * @param { boolean } saved - Previous state
+     */
+    rglwidgetClass.prototype.stopDrawing = function(saved) {
+      this.drawing = saved;
+      if (!saved && this.gl && this.gl.isContextLost())
+        this.restartCanvas();
+    };
+
+    /**
+     * Update the triangles used to display a plane
+     * @param { number } id - id of the plane
+     * @param { Object } bbox - bounding box in which to display the plane
+     */
+    rglwidgetClass.prototype.planeUpdateTriangles = function(obj, bbox) {
+      var perms = [[0,0,1], [1,2,2], [2,1,0]],
+          x, xrow, elem, A, d, nhits, i, j, k, u, v, w, intersect, which, v0, v2, vx, reverse,
+          face1 = [], face2 = [], normals = [],
+          nPlanes = obj.normals.length, idx, center;
+      obj.bbox = bbox;
+      obj.vertices = [];
+      obj.centers = [];
+      obj.initialized = false;
+      for (elem = 0; elem < nPlanes; elem++) {
+//    Vertex Av = normal.getRecycled(elem);
+        x = [];
+        A = obj.normals[elem];
+        d = obj.offsets[elem][0];
+        nhits = 0;
+        for (i=0; i<3; i++)
+          for (j=0; j<2; j++)
+            for (k=0; k<2; k++) {
+              u = perms[0][i];
+              v = perms[1][i];
+              w = perms[2][i];
+              if (A[w] !== 0.0) {
+                intersect = -(d + A[u]*bbox[j+2*u] + A[v]*bbox[k+2*v])/A[w];
+                if (bbox[2*w] < intersect && intersect < bbox[1+2*w]) {
+                  xrow = [];
+                  xrow[u] = bbox[j+2*u];
+                  xrow[v] = bbox[k+2*v];
+                  xrow[w] = intersect;
+                  x.push(xrow);
+                  face1[nhits] = j + 2*u;
+                  face2[nhits] = k + 2*v;
+                  nhits++;
+                }
+              }
+            }
+
+            if (nhits > 3) {
+            /* Re-order the intersections so the triangles work */
+              for (i=0; i<nhits-2; i++) {
+                which = 0; /* initialize to suppress warning */
+                for (j=i+1; j<nhits; j++) {
+                  if (face1[i] === face1[j] || face1[i] === face2[j] ||
+                      face2[i] === face1[j] || face2[i] === face2[j] ) {
+                    which = j;
+                    break;
+                  }
+                }
+                if (which > i+1) {
+                  rglwidgetClass.swap(x, i+1, which);
+                  rglwidgetClass.swap(face1, i+1, which);
+                  rglwidgetClass.swap(face2, i+1, which);
+                }
+              }
+            }
+            if (nhits >= 3) {
+      /* Put in order so that the normal points out the FRONT of the faces */
+              v0 = [x[0][0] - x[1][0] , x[0][1] - x[1][1], x[0][2] - x[1][2]];
+              v2 = [x[2][0] - x[1][0] , x[2][1] - x[1][1], x[2][2] - x[1][2]];
+              /* cross-product */
+              vx = rglwidgetClass.xprod(v0, v2);
+              reverse = rglwidgetClass.dotprod(vx, A) > 0;
+
+              for (i=0; i<nhits-2; i++) {
+                obj.vertices.push(x[0]);
+                center = [];
+                for (k = 0; k<3; k++)
+                  center.push(x[0][k]/3);
+                normals.push(A);
+                for (j=1; j<3; j++) {
+                  idx = i + (reverse ? 3-j : j);
+                  obj.vertices.push(x[idx]);
+                  for (k=0; k<3; k++)
+                    center[k] += x[idx][k]/3;
+                  normals.push(A);
+                }
+                obj.centers.push(center);
+              }
+            }
+      }
+      obj.pnormals = normals;
+    };
+    
+    rglwidgetClass.prototype.mode4type = {points : "POINTS",
+                     linestrip : "LINE_STRIP",
+                     abclines : "LINES",
+                     lines : "LINES",
+                     sprites : "TRIANGLES",
+                     planes : "TRIANGLES",
+                     text : "TRIANGLES",
+                     quads : "TRIANGLES",
+                     surface : "TRIANGLES",
+                     triangles : "TRIANGLES",
+                     sphere : "TRIANGLES"
+    };
+    
+    /**
+     * Disable unused arrays
+     * @param { Object } obj - Object to work with
+     * @param { Array } enabled - Array indicating which are enabled
+     */
+    rglwidgetClass.prototype.disableArrays = function(obj, enabled) {
+      var gl = this.gl || this.initGL(),
+          objLocs = ["normLoc", "texLoc", "ofsLoc", "pointLoc", "nextLoc"],
+          thisLocs = ["posLoc", "colLoc"], i, attr;
+      for (i = 0; i < objLocs.length; i++) 
+        if (enabled[objLocs[i]]) gl.disableVertexAttribArray(obj[objLocs[i]]);
+      for (i = 0; i < thisLocs.length; i++)
+        if (enabled[thisLocs[i]]) gl.disableVertexAttribArray(this[objLocs[i]]);
+      if (typeof obj.userAttributes !== "undefined") {
+      	for (attr in obj.userAttribSizes) {  // Not all attributes may have been used
+      	  gl.disableVertexAttribArray( obj.userAttribLocations[attr] );
+      	}
+      }
+    };
+
+    /**
+     * Start drawing the scene
+     */    
+    rglwidgetClass.prototype.doStartScene = function() {
+      var gl = this.gl || this.initGL();
+      gl.enable(gl.DEPTH_TEST);
+      gl.depthFunc(gl.LEQUAL);
+      gl.clearDepth(1.0);
+      gl.clearColor(1,1,1,1);
+      gl.depthMask(true); // Must be true before clearing depth buffer
+      /* jshint bitwise: false */
+      gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);
+      /* jshint bitwise: true */
+    };
+    
+    /**
+     * Set gl depth test based on object's material
+     * @param { Object } obj - object to use
+     */
+    rglwidgetClass.prototype.doDepthTest = function(obj) {
+      var gl = this.gl,
+          tests = {never: gl.NEVER,
+                   less:  gl.LESS,
+                   equal: gl.EQUAL,
+                   lequal:gl.LEQUAL,
+                   greater: gl.GREATER,
+                   notequal: gl.NOTEQUAL,
+                   gequal: gl.GEQUAL,
+                   always: gl.ALWAYS},
+           test = tests[this.getMaterial(obj, "depth_test")];
+      gl.depthFunc(test);
+    };    
+    
+    /**
+     * Set polygon offset for an obj
+     * @param { object } obj - object to use
+     */
+    rglwidgetClass.prototype.doPolygonOffset = function(obj) { 
+      var gl = this.gl;
+      if (typeof obj.polygon_offset !== "undefined") {
+        gl.polygonOffset(obj.polygon_offset[0],
+                          obj.polygon_offset[1]);
+        gl.enable(gl.POLYGON_OFFSET_FILL);
+      } else
+        gl.disable(gl.POLYGON_OFFSET_FILL);
+    };
+    
+    /**
+     * Do code for clipping
+     * @param { object } obj - Object to work with
+     * @param { object } subscene - Subscene to work with
+     */
+    rglwidgetClass.prototype.doClipping = function(obj, subscene) {
+      var gl = this.gl,
+          clipcheck = 0,
+          clipplaneids = subscene.clipplanes,
+          clip, i,j, n = this.countClipplanes(),
+          clipplanedata; 
+          
+      if (n > 0) {
+        clipplanedata = new Float32Array(4*n);
+        for (i=0; i < clipplaneids.length; i++) {
+          clip = this.getObj(clipplaneids[i]);
+          for (j=0; j < clip.offsets.length; j++) {
+            clipplanedata.set(clip.IMVClip[j], clipcheck);
+            clipcheck += 4;
+          }
+        }
+      
+        // Leftovers are initialized to zero, which is fine
+        gl.uniform4fv(obj.clipLoc, clipplanedata);
+      }
+    };
+    
+    /**
+     * Do code for lighting
+     * @param { object } obj - Object to work with
+     * @param { object } subscene - Subscene to work with
+     */
+    rglwidgetClass.prototype.doLighting = function(obj, subscene) {
+    var gl = this.gl, i, j, n, light,
+      ambient, specular, diffuse, lightDir, viewpoint, finite,
+      ambient0, specular0;
+
+      gl.uniform3fv( obj.emissionLoc, obj.emission);
+      gl.uniform1f( obj.shininessLoc, obj.shininess);
+      while ((typeof subscene.lights === "undefined" ||
+              subscene.lights.length === 0) && 
+             typeof subscene.parent !== "undefined")
+        subscene = this.getObj(subscene.parent);
+
+      if (typeof subscene.lights === "undefined")
+        return;
+        
+      n = subscene.lights.length;
+        
+      ambient = new Float32Array(3*n);
+      specular = new Float32Array(3*n);
+      diffuse = new Float32Array(3*n);
+      lightDir = new Float32Array(3*n);
+      viewpoint = new Int32Array(n);
+      finite = new Int32Array(n);
+          
+      for (i=0; i < n; i++) {
+        light = this.getObj(subscene.lights[i]);
+        if (!light.initialized) this.initObj(light);
+        ambient0 = this.componentProduct(light.ambient, obj.ambient);
+        specular0 = this.componentProduct(light.specular, obj.specular);
+        for (j=0; j < 3; j++) {
+          ambient[3*i + j] = ambient0[j];
+          specular[3*i + j] = specular0[j];
+          diffuse[3*i + j] = light.diffuse[j];
+          lightDir[3*i + j] = light.lightDir[j];
+        }
+        viewpoint[i] = light.viewpoint;
+        finite[i] = light.finite;
+      }
+        
+      for (i = n; i < obj.nlights; i++) {
+        for (j = 0; j < 3; j++) {
+          ambient[3*i + j] = 0.0;
+          specular[3*i + j] = 0.0;
+          diffuse[3*i + j] = 0.0;
+        }
+      }
+        
+      gl.uniform3fv( obj.ambientLoc, ambient);
+      gl.uniform3fv( obj.specularLoc, specular);
+      gl.uniform3fv( obj.diffuseLoc, diffuse);
+      gl.uniform3fv( obj.lightDirLoc, lightDir);
+      gl.uniform1iv( obj.viewpointLoc, viewpoint);
+      gl.uniform1iv( obj.finiteLoc, finite);
+    };
+    
+    /**
+     * Do code for colors
+     * @param { object } obj - Object to work with
+     */
+    rglwidgetClass.prototype.doColors = function(obj) {
+      var gl = this.gl;
+      if (obj.colorCount === 1) {
+        gl.disableVertexAttribArray( this.colLoc );
+        gl.vertexAttrib4fv( this.colLoc, new Float32Array(obj.onecolor));
+        return false;
+      } else {
+        gl.enableVertexAttribArray( this.colLoc );
+        gl.vertexAttribPointer(this.colLoc, 4, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.cofs);
+        return true;
+      }
+    };
+    
+    /**
+     * Do code for normals
+     * @param { object } obj - Object to work with
+     */
+    rglwidgetClass.prototype.doNormals = function(obj) {
+      var gl = this.gl;
+      if (obj.vOffsets.nofs >= 0) {
+        gl.enableVertexAttribArray( obj.normLoc );
+        gl.vertexAttribPointer(obj.normLoc, 3, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.nofs);
+        return true;
+      } else
+        return false;
+    };
+    
+    /**
+     * Do code for vNormal
+     * @param { object } obj - Object to work with
+     */
+    rglwidgetClass.prototype.doNormMat = function(obj) {
+      var gl = this.gl;
+        
+      gl.uniformMatrix4fv( obj.normMatLoc, false, new Float32Array(this.normMatrix.getAsArray()) );
+    };
+    
+    /**
+     * Do code for textures
+     * @param { object } obj - Object to work with
+     */    
+    rglwidgetClass.prototype.doTexture = function(obj) {
+      var gl = this.gl, 
+          is_sphere = obj.type === "sphere";
+        gl.enableVertexAttribArray( obj.texLoc );
+        if (is_sphere)
+          gl.vertexAttribPointer(obj.texLoc, 2, gl.FLOAT, false, 4*this.sphere.vOffsets.stride, 4*this.sphere.vOffsets.tofs);
+        else
+          gl.vertexAttribPointer(obj.texLoc, 2, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.tofs);
+        gl.activeTexture(gl.TEXTURE0);
+        gl.bindTexture(gl.TEXTURE_2D, obj.texture);
+        gl.uniform1i( obj.sampler, 0);
+        return true;
+    };
+    
+    /**
+     * Do code for user attributes
+     * @param { object } obj - Object to work with
+     */    
+    rglwidgetClass.prototype.doUserAttributes = function(obj) {
+      if (typeof obj.userAttributes !== "undefined") {
+        var gl = this.gl;
+      	for (var attr in obj.userAttribSizes) {  // Not all attributes may have been used
+      	  gl.enableVertexAttribArray( obj.userAttribLocations[attr] );
+      	  gl.vertexAttribPointer( obj.userAttribLocations[attr], obj.userAttribSizes[attr],
+      	  			  gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.userAttribOffsets[attr]);
+      	}
+      }
+    };
+
+    /**
+     * Do code for user uniforms
+     * @param { object } obj - Object to work with
+     */    
+    rglwidgetClass.prototype.doUserUniforms = function(obj) {
+      var gl = this.gl, attr;
+      if (typeof obj.userUniforms !== "undefined") {
+      	for (attr in obj.userUniformLocations) {
+      	  var loc = obj.userUniformLocations[attr];
+      	  if (loc !== null) {
+      	    var uniform = obj.userUniforms[attr];
+      	    if (typeof uniform !== "undefined") {
+      	      var dim = rglwidgetClass.arrayDim(uniform);
+      	      if (dim.length === 0)
+      	        gl.uniform1f(loc, uniform);
+      	      else if (dim.length === 1) {
+      	        uniform = new Float32Array(uniform);
+      	        switch(uniform.length) {
+      	      	  case 2: gl.uniform2fv(loc, uniform); break;
+      	      	  case 3: gl.uniform3fv(loc, uniform); break;
+      	      	  case 4: gl.uniform4fv(loc, uniform); break;
+      	      	  default: console.warn("bad uniform length");
+      	        }
+      	      } else if (dim.length === 2 && dim[0] === 4 && dim[1] === 4)
+      	        gl.uniformMatrix4fv(loc, false, new Float32Array(rglwidgetClass.flatten(uniform)));
+      	      else if (dim.length === 2) {
+      	        uniform = new Float32Array(rglwidgetClass.flatten(uniform));
+      	        switch(dim[[1]]) {
+      	          case 1: gl.uniform1fv(loc, uniform); break;
+      	          case 2: gl.uniform2fv(loc, uniform); break;
+      	          case 3: gl.uniform3fv(loc, uniform); break;
+      	          case 4: gl.uniform4fv(loc, uniform); break;
+      	          default: console.warn("bad uniform column count");
+      	        }
+      	      } else
+      	        console.warn("unsupported uniform shape");
+      	    }
+      	  }
+      	}
+      }
+      if (typeof obj.userTextures !== "undefined") {
+        var has_texture = rglwidgetClass.isSet(obj.flags, rglwidgetClass.f_has_texture),
+              texnum = has_texture - 1;
+        for (attr in obj.userTextures) {
+      	  var texture = obj.userTextures[attr];
+      	  if (texture.sampler !== null) {
+      	    texnum += 1;
+      	    gl.activeTexture(gl.TEXTURE0 + texnum);
+            gl.bindTexture(gl.TEXTURE_2D, texture.texture);
+            gl.uniform1i( texture.sampler, texnum);
+      	  }
+      	}
+      }
+    };
+
+    /**
+     * Load indices for complex drawing
+     * @param { object } obj - Object to work with
+     * @param { numeric } pass - Which pass of drawing?
+     * @param { array } indices - Indices to draw
+     */    
+    rglwidgetClass.prototype.doLoadIndices = function(obj, pass, indices) {
+      var gl = this.gl,
+          f = obj.f[pass],
+          type = obj.type,
+          fat_lines = rglwidgetClass.isSet(obj.flags, rglwidgetClass.f_fat_lines),
+          fnew, step;
+      switch(type){
+        case "points":
+          step = 1;
+          break;
+        case "abclines":
+        case "lines":
+          if (fat_lines)
+            step = 6;
+          else
+            step = 2;
+          break;
+        case "linestrip":
+          if (fat_lines)
+            step = 6;
+          else
+            step = 1;
+          break;
+        case "sphere":
+        case "planes":
+        case "triangles":
+          step = 3;
+          break;
+        case "text":
+        case "sprites":
+        case "quads":
+        case "surface":
+          step = 6;
+          break;
+        default:
+          console.error("loadIndices for "+type);
+          return 0;
+      }
+      if (obj.index_uint)
+        fnew = new Uint32Array(step * indices.length);
+      else
+        fnew = new Uint16Array(step * indices.length);
+      for (var i = 0; i < indices.length; i++) {
+        for (var j = 0; j < step; j++) {
+          fnew[step*i + j] = f[step*indices[i] + j];
+        }
+      }
+      gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, fnew, gl.DYNAMIC_DRAW);
+      return fnew.length;
+    };
+
+    /**
+     * Do code for depth masking
+     * @param { boolean } mask - whether to mask
+     */
+    rglwidgetClass.prototype.doMasking = function(mask) {
+      var gl = this.gl;
+      gl.depthMask(mask);
+    };
+
+    /**
+     * Do code for alpha blending
+     * @param { boolean }  blend - Whether to blend.
+     * @param { integer }  objid - Object id
+     */    
+    rglwidgetClass.prototype.doBlending = function(blend, objid) {
+      var gl = this.gl, blendfunc, obj, 
+        blends =  {zero: gl.ZERO,
+                   one:  gl.ONE,
+                   src_color: gl.SRC_COLOR,
+                   one_minus_src_color: gl.ONE_MINUS_SRC_COLOR,
+                   dst_color: gl.DST_COLOR,
+                   one_minus_dst_color: gl.ONE_MINUS_DST_COLOR,
+                   src_alpha: gl.SRC_ALPHA,
+                   one_minus_src_alpha: gl.ONE_MINUS_SRC_ALPHA,
+                   dst_alpha: gl.DST_ALPHA,
+                   one_minus_dst_alpha: gl.ONE_MINUS_DST_ALPHA,
+                   constant_color: gl.CONSTANT_COLOR,
+                   one_minus_constant_color: gl.ONE_MINUS_CONSTANT_COLOR,
+                   constant_alpha: gl.CONSTANT_ALPHA,
+                   one_minus_constant_alpha: gl.ONE_MINUS_CONSTANT_ALPHA,
+                   src_alpha_saturate: gl.SRC_ALPHA_SATURATE};
+      if (blend) {
+        obj = this.getObj(objid);
+        blendfunc = this.getMaterial(obj, "blend");
+        gl.blendFuncSeparate(blends[blendfunc[0]],
+                             blends[blendfunc[1]],
+                             gl.ONE, gl.ONE);
+        gl.enable(gl.BLEND);
+      } else {
+        gl.disable(gl.BLEND);
+      }
+    };
+    
+    /**
+     * Set up for fog in the subscene
+     * @param { object } obj - background object
+     * @param { object } subscene - which subscene
+     */
+    rglwidgetClass.prototype.doFog = function(obj, subscene) {
+      var gl = this.gl, fogmode, color, 
+          observer = subscene.par3d.observer[2],
+          sintheta = Math.sin(subscene.par3d.FOV*Math.PI/180/2),
+          parms = [this.frustum.near - 2*observer,
+                   this.frustum.far - 2*observer,
+                   this.fogScale,
+                   (1-sintheta)/(1+sintheta)];
+      if (typeof this.fogType === "undefined")
+        this.fogType = "none";
+      if (typeof this.fogScale === "undefined")
+        parms[2] = 1;
+      if (sintheta === 0)
+        parms[3] = 1/3;
+      switch(this.fogType){
+        case "none": fogmode = 0; break;
+        case "linear": 
+          fogmode = 1; break;
+        case "exp":  
+          fogmode = 2; break;
+        case "exp2": 
+          fogmode = 3;
+          break;
+        default: console.error("Unknown fogtype "+this.fogType);
+      }
+      gl.uniform1i(obj.uFogMode, fogmode);
+      color = this.fogColor;
+      gl.uniform3f(obj.uFogColor, color[0], color[1], color[2]);
+      gl.uniform4f(obj.uFogParms, parms[0], parms[1], parms[2], parms[3]);
+    };
+
+    /* The draw methods are called twice.  When 
+       this.opaquePass is true, they should draw opaque parts
+       of the scene, and return the list of transparent
+       pieces.  Here context is the context array on input,
+       modified when the matrices are changed.
+       When this.opaquePass is false, the context argument
+       contains a "piece", i.e. an ordered list of parts
+       of the object to draw. */
+
+    /**
+     * Draw simple object
+     * @param { object } obj - Object to draw
+     * @param { object } subscene - which subscene
+     * @param { array } context - Which context are we in?
+     */       
+    rglwidgetClass.prototype.drawSimple = function(obj, subscene, context) {
+      var 
+          fl,
+          is_transparent,
+          type = obj.type,
+          gl = this.gl || this.initGL(),
+          count,
+          pass, mode, pmode,
+          enabled = {};
+        
+      if (!obj.initialized)
+        this.initObj(obj);
+        
+      if (this.texturesLoading)
+        return[];
+
+      count = obj.vertexCount;
+      if (!count)
+        return [];
+    
+      fl = obj.defFlags;
+      is_transparent = fl.is_transparent || obj.someHidden;
+      
+      if (is_transparent && this.opaquePass)
+        return this.getPieces(context, obj.id, 0, obj);
+
+      this.doDepthTest(obj);
+      
+      this.doMasking(this.getMaterial(obj, "depth_mask"));
+            
+      gl.useProgram(obj.prog);
+
+      this.doPolygonOffset(obj);
+
+      gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
+
+      gl.uniformMatrix4fv( obj.prMatLoc, false, new Float32Array(this.prMatrix.getAsArray()) );
+      gl.uniformMatrix4fv( obj.mvMatLoc, false, new Float32Array(this.mvMatrix.getAsArray()) );
+
+      this.doClipping(obj, subscene);
+
+      if (fl.needs_vnormal)
+        this.doNormMat(obj);
+        
+      if (fl.is_lit)
+        this.doLighting(obj, subscene);
+
+      if (fl.has_fog)
+        this.doFog(obj, subscene);
+
+      this.doUserAttributes(obj);
+
+      this.doUserUniforms(obj);
+ 
+      gl.enableVertexAttribArray( this.posLoc );
+      enabled.posLoc = true;
+        
+      if (fl.has_texture || obj.type === "text")
+        enabled.texLoc = this.doTexture(obj);
+
+      enabled.colLoc = this.doColors(obj);
+      enabled.normLoc = this.doNormals(obj);
+
+      if (fl.fixed_size) {
+        gl.uniform3f( obj.textScaleLoc, 0.75/this.vp.width, 0.75/this.vp.height, 1.0);
+      }
+      
+      if (fl.fixed_quads) {
+        gl.enableVertexAttribArray( obj.ofsLoc );
+        enabled.ofsLoc = true;
+        gl.vertexAttribPointer(obj.ofsLoc, 3, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.oofs);
+      }
+
+      for (pass = 0; pass < obj.passes; pass++) {
+      	pmode = obj.pmode[pass];
+        if (pmode === "culled")
+          continue;
+
+      	mode = fl.fat_lines && (fl.is_lines || pmode === "lines") ? "TRIANGLES" : this.mode4type[type];
+
+      	if (fl.is_twosided) {
+      	  gl.uniform1i(obj.frontLoc, pass !== 0);
+      	  if (fl.has_normals) {
+      	    gl.uniformMatrix4fv(obj.invPrMatLoc, false, new Float32Array(this.invPrMatrix.getAsArray()));
+      	  }
+      	}
+
+        gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[pass]);
+        if (!this.opaquePass) {
+          if (type === "sphere" && obj.fastTransparency)
+            count = this.doLoadIndices(obj, pass, this.sphere.fastpieces[0].indices);
+          else
+            count = this.doLoadIndices(obj, pass, context.indices);
+        } else {
+          count = obj.f[pass].length;
+          gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, obj.f[pass], gl.STATIC_DRAW);
+        }
+      	if (!fl.is_lines && pmode === "lines" && !fl.fat_lines) {
+          mode = "LINES";
+        } else if (pmode === "points") {
+          mode = "POINTS";
+        }
+                          
+        if ((fl.is_lines || pmode === "lines") && fl.fat_lines) {
+          gl.enableVertexAttribArray(obj.pointLoc);
+          enabled.pointLoc = true;
+          gl.vertexAttribPointer(obj.pointLoc, 2, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.pointofs);
+          gl.enableVertexAttribArray(obj.nextLoc );
+          enabled.nextLoc = true;
+          gl.vertexAttribPointer(obj.nextLoc, 3, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.nextofs);
+          gl.uniform1f(obj.aspectLoc, this.vp.width/this.vp.height);
+          gl.uniform1f(obj.lwdLoc, this.getMaterial(obj, "lwd")/this.vp.height);
+        }
+
+        gl.vertexAttribPointer(this.posLoc,  3, gl.FLOAT, false, 4*obj.vOffsets.stride,  4*obj.vOffsets.vofs);
+
+        gl.drawElements(gl[mode], count, obj.index_uint ? gl.UNSIGNED_INT : gl.UNSIGNED_SHORT, 0);
+      }
+      this.disableArrays(obj, enabled);
+      return [];
+    };
+
+    /**
+     * Draw planes object
+     * @param { object } obj - Object to draw
+     * @param { object } subscene - which subscene
+     * @param { array } context - Which context are we in?
+     */      
+    rglwidgetClass.prototype.drawPlanes = function(obj, subscene, context) {
+      if (this.opaquePass && (obj.bbox !== subscene.par3d.bbox || !obj.initialized)) {
+          this.planeUpdateTriangles(obj, subscene.par3d.bbox);
+      }
+      return this.drawSimple(obj, subscene, context);
+   };
+
+    /**
+     * @param { object } obj - object to draw
+     * @param { object } subscene 
+     * @param { array } context 
+     * @description
+     * Draw spheres in a subscene<br>
+     * 
+     * Drawing spheres happens in six ways:<br>
+     * 1 opaquepass, not transparent:  transform and draw this.sphere count times<br>
+     * 2 opaquepass, transparent, not fast: transform & collect sphere pieces count times<br>
+     * 3 opaquepass, transparent, fast:  order the centres into separate pieces, order this.sphere once<br>
+     * 4 not opaquepass, not transparent:  do nothing<br>
+     * 5 not opaquepass, transparent, not fast:  transform for one sphere, draw one merged piece<br>
+     * 6 not opaquepass, transparent, fast:  transform for one sphere, draw this.sphere in fixed order.<br>
+     **/
+
+    rglwidgetClass.prototype.drawSpheres = function(obj, subscene, context) {
+      var flags = obj.flags,
+          is_transparent = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_transparent),
+          sphereMV, baseofs, ofs, sscale, i,
+          count, nc, scount, scale, indices, sphereNorm,
+          enabled = {}, drawing,
+          saveNorm = new CanvasMatrix4(this.normMatrix),
+          saveMV = new CanvasMatrix4(this.mvMatrix),
+          savePRMV = null,
+          result = [], idx, margin = obj.material.margin;
+ 
+      if (typeof margin !== "undefined")
+        if (!this.marginVecToDataVec(obj, subscene))
+          return [];
+
+      if (!obj.initialized)
+        this.initObj(obj);
+
+      count = obj.vertexCount;
+      if (!count) 
+        return [];
+        
+      is_transparent = is_transparent || obj.someHidden;
+
+      if (!this.opaquePass && !is_transparent)
+        return [];
+        
+      if (this.prmvMatrix !== null)
+        savePRMV = new CanvasMatrix4(this.prmvMatrix);
+      
+      scale = subscene.par3d.scale;        
+      sphereNorm = new CanvasMatrix4();
+      sphereNorm.scale(scale[0], scale[1], scale[2]);
+      sphereNorm.multRight(saveNorm);
+      this.normMatrix = sphereNorm;
+
+      if (this.opaquePass) {
+        context = context.slice();
+        context.push(obj.id);
+      } 
+      
+      drawing = this.opaquePass !== is_transparent;
+      if (drawing) {
+        nc = obj.colorCount;
+        if (nc === 1) {
+          this.sphere.onecolor = obj.onecolor;
+        }
+      }
+      
+      this.initShapeFromObj(this.sphere, obj);
+
+      if (!this.opaquePass && obj.fastTransparency && typeof this.sphere.fastpieces === "undefined") {
+        this.sphere.fastpieces = this.getPieces(context.context, obj.id, 0, this.sphere);
+        this.sphere.fastpieces = this.sortPieces(this.sphere.fastpieces);
+        this.sphere.fastpieces = this.mergePieces(this.sphere.fastpieces);
+      }
+
+      if (this.opaquePass)
+        scount = count;
+      else {
+        indices = context.indices;
+        if (obj.fastTransparency)
+          scount = indices.length;  /* Each item gives the center of a whole sphere */
+        else
+          scount = 1;               /* Each item is a fragment of the sphere, at location subid */
+      }
+      for (i = 0; i < scount; i++) {
+        sphereMV = new CanvasMatrix4();
+        if (this.opaquePass)
+          idx = i;
+        else if (obj.fastTransparency)
+          idx = indices[i];
+        else
+          idx = context.subid;
+        if (typeof idx === "undefined")
+          console.error("idx is undefined");
+        baseofs = idx*obj.vOffsets.stride;
+        ofs = baseofs + obj.vOffsets.radofs;
+        sscale = obj.values[ofs];
+
+        sphereMV.scale(sscale/scale[0], sscale/scale[1], sscale/scale[2]);
+        sphereMV.translate(obj.values[baseofs],
+                             obj.values[baseofs+1],
+                             obj.values[baseofs+2]);
+        sphereMV.multRight(saveMV);
+        this.mvMatrix = sphereMV;
+        this.setnormMatrix2();
+        this.setprmvMatrix();
+        if (drawing) {
+          if (nc > 1) {
+            this.sphere.onecolor = obj.values.slice(baseofs + obj.vOffsets.cofs, baseofs + obj.vOffsets.cofs + 4);
+          }
+          this.drawSimple(this.sphere, subscene, context);
+        } else 
+          result = result.concat(this.getSpherePieces(context, i, obj));
+      }
+      if (drawing)
+        this.disableArrays(obj, enabled);
+      this.normMatrix = saveNorm;
+      this.mvMatrix = saveMV;
+      this.prmvMatrix = savePRMV;
+        
+      return result;
+    };
+    
+    /**
+     * Prepare clipplanes for drawing
+     * @param { object } obj - clip planes object
+     */
+    rglwidgetClass.prototype.drawClipplanes = function(obj) {
+      var count = obj.offsets.length,
+        IMVClip = [];
+      for (var i=0; i < count; i++) {
+        IMVClip[i] = rglwidgetClass.multMV(this.invMatrix, obj.vClipplane.slice(4*i, 4*(i+1)));
+      }
+      obj.IMVClip = IMVClip;
+      return [];
+    };
+
+    /**
+     * Prepare linestrip for drawing
+     * @param { object } obj - line strip object
+     * @param { object } subscene 
+     * @param { array } context 
+     */    
+    rglwidgetClass.prototype.drawLinestrip = function(obj, subscene, context) {
+      var origIndices, i, j, margin = obj.material.margin;
+ 
+      if (typeof margin !== "undefined") 
+        if (!this.marginVecToDataVec(obj, subscene))
+          return [];
+          
+      if (this.opaquePass)
+        return this.drawSimple(obj, subscene, context);
+      origIndices = context.indices.slice();
+      for (i=0; i < origIndices.length; i++) {
+        j = origIndices[i];
+        if (j < obj.centers.length - 1) {
+          context.indices = [j, j+1];
+          this.drawSimple(obj, subscene, context);
+        }
+      }
+      context.indices = origIndices;
+      return [];
+    };
+          
+    /**
+     * Draw a sprites object in a subscene
+     * @param { object } obj - object to draw
+     * @param { object } subscene
+     * @param { object } context
+     */
+    rglwidgetClass.prototype.drawSprites = function(obj, subscene, context) {
+      var flags = obj.flags,
+          is_transparent = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_transparent),
+          sprites3d = rglwidgetClass.isSet(flags, rglwidgetClass.f_sprites_3d),
+          fixed_size = rglwidgetClass.isSet(flags, rglwidgetClass.f_fixed_size),
+          rotating = rglwidgetClass.isSet(flags, rglwidgetClass.f_rotating),
+          i,j,
+          origMV = new CanvasMatrix4( this.mvMatrix ),
+          origPRMV = null,
+          origPR,
+          pos, radius, userMatrix,
+          result = [], margin = obj.material.margin;
+ 
+      if (typeof margin !== "undefined")
+        if (!this.marginVecToDataVec(obj, subscene))
+          return [];
+
+      if (!sprites3d) 
+        return this.drawSimple(obj, subscene, context);
+      
+      if (!obj.initialized)
+        this.initObj(obj);
+
+      if (!obj.vertexCount)
+        return [];
+    
+      is_transparent = is_transparent || obj.someHidden;
+      
+      var norigs = obj.vertices.length,
+          savenorm = new CanvasMatrix4(this.normMatrix),
+          iOrig, adj, offset;
+
+      userMatrix = obj.userMatrix;
+                   
+      if (this.opaquePass) {
+        context = context.slice();
+        context.push(obj.id);
+      } else
+        norigs = 1;
+          
+      if (this.prmvMatrix !== null)
+         origPRMV = new CanvasMatrix4( this.prmvMatrix );
+
+      offset = obj.offset;
+      
+      if (fixed_size && !rotating) {
+        origPR = this.prMatrix;
+        this.prMatrix = new CanvasMatrix4();
+      }
+        
+      for (iOrig=0; iOrig < norigs; iOrig++) {
+        if (this.opaquePass)
+          j = iOrig;
+        else
+          j = context.subid;
+        pos = [].concat(obj.vertices[j]).concat(1.0);
+        radius = obj.radii.length > 1 ? obj.radii[j][0] : obj.radii[0][0];
+        this.mvMatrix = new CanvasMatrix4(userMatrix);
+        adj = this.getAdj(obj, j, offset);
+        this.mvMatrix.translate(1 - 2*adj[0], 1 - 2*adj[1], 1 - 2*adj[2]);
+        this.mvMatrix.scale(radius, radius, radius);
+        
+        if (fixed_size) {
+          var viewport = subscene.par3d.viewport,
+            winwidth = viewport.width*this.canvas.width,
+            winheight = viewport.height*this.canvas.height,
+            scalex = 27/winwidth, scaley = 27/winheight,
+              scale = Math.sqrt(scalex * scaley);
+          if (!rotating) {
+            pos = rglwidgetClass.multVM(pos, origMV);
+            pos = rglwidgetClass.multVM(pos, origPR);
+            this.mvMatrix.scale(scalex, scaley, scale);
+          } else {
+            scale = 4.0 * scale * subscene.par3d.zoom;
+            this.mvMatrix.scale(scale, scale, scale);
+          }
+          this.mvMatrix.translate(pos[0]/pos[3], pos[1]/pos[3], pos[2]/pos[3]);
+          if (rotating)
+            this.mvMatrix.multRight(origMV);
+        } else {
+          if (!rotating) {
+            pos = rglwidgetClass.multVM(pos, origMV);
+            this.mvMatrix.translate(pos[0]/pos[3], pos[1]/pos[3], pos[2]/pos[3]);
+          } else {
+            this.mvMatrix.translate(pos[0]/pos[3], pos[1]/pos[3], pos[2]/pos[3]);
+            this.mvMatrix.multRight(origMV);
+          }
+        }
+        this.setnormMatrix2();
+        this.setprmvMatrix();
+      
+        j = iOrig % obj.shapefirst.length;
+        var first = obj.shapefirst[j];
+        
+        for (i=0; i < obj.shapelens[j]; i++)
+          if (this.opaquePass)
+            result = result.concat(this.drawObjId(obj.objects[first + i], subscene.id, context.concat(j)));
+          else
+            this.drawObjId(obj.objects[i], subscene.id, context);
+      }
+      this.normMatrix = savenorm;
+      this.mvMatrix = origMV;
+      if (fixed_size && !rotating)
+        this.prMatrix = origPR;
+      if (origPRMV !== null)
+        this.prmvMatrix = origPRMV;
+      return result;
+    };
+    
+    /**
+     * Draw object that might be in margin
+     * @param { Object } obj - text object to draw
+     * @param { Object } subscene - subscene holding it
+     * @param { Object } context - context for drawing
+     */
+    rglwidgetClass.prototype.drawMarginal = function(obj, subscene, context) {
+      var margin = obj.material.margin;
+ 
+      if (typeof margin !== "undefined") 
+        if (!this.marginVecToDataVec(obj, subscene))
+          return [];
+          
+      return this.drawSimple(obj, subscene, context);
+    };
+    
+    /**
+     * Draw bounding box and decorations
+     * @param { Object } obj - bboxdeco to draw
+     * @param { Object } subscene - subscene holding it
+     * @param { Object } context - context for drawing
+     */
+    rglwidgetClass.prototype.drawBBox = function(obj, subscene, context) {
+      var flags = obj.flags,
+          is_transparent = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_transparent),
+          scale, bbox, indices,
+          enabled = {}, drawing,
+          result = [], idx, center, edges,
+          saved;
+
+      if (!obj.initialized)
+        this.initBBox(obj);
+      
+      is_transparent = is_transparent || obj.someHidden;
+
+      if (!this.opaquePass && !is_transparent)
+        return result;
+      
+      this.setBbox(obj, subscene);
+      
+      saved = this.setBBoxMatrices(obj);
+      
+      bbox = obj.bbox;
+      center = obj.center;
+
+      scale = [bbox[1]-bbox[0], bbox[3]-bbox[2], bbox[5]-bbox[4]];
+
+      if (!obj.cube.initialized) {
+        this.initObj(obj.cube);
+      }
+
+      if (this.opaquePass) {
+        context = context.slice();
+        context.push(obj.id);
+      } 
+      
+      drawing = this.opaquePass !== is_transparent;
+      this.cube.onecolor = obj.cube.onecolor;
+      this.initShapeFromObj(this.cube, obj.cube);
+
+      if (!this.opaquePass)
+        indices = context.indices;
+
+      if (this.opaquePass)
+        idx = 0;
+      else
+        idx = context.subid;
+      if (typeof idx === "undefined")
+        console.error("idx is undefined");
+
+      if (drawing) {
+        this.drawSimple(this.cube, subscene, context);
+      } else 
+        result = result.concat(this.getCubePieces(context, obj));
+
+      if (!obj.ticks.initialized) {
+        obj.ticks.locations = this.getTickLocations(obj);
+        obj.ticks.edges = undefined;
+      }
+      edges = this.getTickEdges(this.prmvMatrix);
+      if (obj.needsAxisCallback) 
+        this.doAxisCallback(obj, edges);
+      if (!obj.ticks.edges || edges.toString() !== obj.ticks.edges.toString()) {
+        obj.ticks.edges = edges;
+        this.getTickVertices(obj.ticks);
+        this.placeTickLabels(obj);
+        this.setTickLabels(obj);
+      }
+      if (!obj.ticks.initialized) {
+        this.initObj(obj.ticks);
+        this.initObj(obj.labels);
+      }
+        
+      if (drawing) {
+        this.drawSimple(obj.ticks, subscene, context);
+        this.drawSimple(obj.labels, subscene, context);
+
+        this.disableArrays(obj, enabled);
+      } else {
+        result = result.concat(this.drawSimple(obj.ticks, subscene, context));
+        result = result.concat(this.drawSimple(obj.labels, subscene, context));
+      }
+
+      this.restoreBBoxMatrices(saved);
+        
+      return result;
+    };
+    
+    /**
+     * Use ids to choose object to draw
+     * @param { numeric } id - object to draw
+     * @param { numeric } subscene
+     * @param { array } context
+     */   
+    rglwidgetClass.prototype.drawObjId = function(id, subsceneid, context) {
+      if (typeof id !== "number")
+        this.alertOnce("drawObjId id is "+typeof id);
+
+      return this.drawObj(this.getObj(id), this.getObj(subsceneid), context);
+   };
+   
+    /**
+     * Draw an object in a subscene
+     * @param { object } obj - object to draw
+     * @param { object } subscene
+     * @param { array } context
+     */
+    rglwidgetClass.prototype.drawObj = function(obj, subscene, context) {
+      switch(obj.type) {
+        case "abclines":
+        case "surface":
+          return this.drawSimple(obj, subscene, context);
+        case "points":
+        case "lines":  
+        case "triangles":
+        case "quads":
+        case "text":
+          return this.drawMarginal(obj, subscene, context);
+        case "linestrip":
+          return this.drawLinestrip(obj, subscene, context);
+        case "planes":
+          return this.drawPlanes(obj, subscene, context);
+        case "spheres":
+          return this.drawSpheres(obj, subscene, context);
+        case "clipplanes":
+          return this.drawClipplanes(obj);
+        case "sprites":
+          return this.drawSprites(obj, subscene, context);
+        case "light":
+          return [];
+        case "bboxdeco":
+          return this.drawBBox(obj, subscene, context);
+      }
+      
+      console.error("drawObj for type = "+obj.type);
+    };
+
+    /**
+     * Draw the background for a subscene
+     * @param { number } id - id of background object
+     * @param { number } subsceneid - id of subscene
+     */
+    rglwidgetClass.prototype.drawBackground = function(id, subsceneid, context) {
+      var gl = this.gl || this.initGL(),
+          obj = this.getObj(id),
+          subscene,
+          bg, i, savepr, saveinvpr, savemv, savenorm, m, bbox, result = [], 
+          savedm = gl.getParameter(gl.DEPTH_WRITEMASK),
+          savedt = gl.isEnabled(gl.DEPTH_TEST),
+          saveblend = gl.isEnabled(gl.BLEND);
+
+      if (!obj.initialized)
+        this.initObj(obj);
+
+      if (obj.colors.length) {
+        bg = obj.colors[0];
+        gl.depthMask(true);
+        gl.clear(gl.DEPTH_BUFFER_BIT);
+        gl.clearColor(bg[0], bg[1], bg[2], bg[3]);
+        gl.clear(gl.COLOR_BUFFER_BIT);
+        this.fogColor = bg;
+      } else {
+        this.fogColor = [0,0,0,0];
+        obj.colors = [[0,0,0,0]];
+      }
+  
+      this.fogType = obj.fogtype;
+      this.fogScale = obj.fogscale;
+      gl.disable(gl.BLEND);
+      gl.disable(gl.DEPTH_TEST);
+      gl.depthMask(false);
+      if (typeof obj.quad !== "undefined") {
+        savepr = this.prMatrix;
+        saveinvpr = this.invPrMatrix;
+        savemv = this.mvMatrix;
+        savenorm = this.normMatrix;
+        this.prMatrix = new CanvasMatrix4();
+        this.invPrMatrix = new CanvasMatrix4();
+        this.mvMatrix = new CanvasMatrix4();
+        this.normMatrix = new CanvasMatrix4();
+        for (i=0; i < obj.quad.length; i++)
+          result = result.concat(this.drawObjId(obj.quad[i], subsceneid));
+        this.prMatrix = savepr;
+        this.invPrMatrix = saveinvpr;
+        this.mvMatrix = savemv;
+        this.normMatrix = savenorm;
+
+      } else if (obj.sphere) {
+        subscene = this.getObj(subsceneid);
+        savemv = this.mvMatrix;
+        savenorm = this.normMatrix;
+        bbox = subscene.par3d.bbox;
+        var center = [(bbox[0] + bbox[1])/2, 
+                  (bbox[2] + bbox[3])/2, 
+                  (bbox[4] + bbox[5])/2, 1],
+            scale = subscene.par3d.scale,
+            ranges = [bbox[1] - bbox[0], 
+                  bbox[3] - bbox[2],
+                  bbox[5] - bbox[4]],
+            avgscale = rglwidgetClass.vlen(ranges)/Math.sqrt(3),
+            aspect = [ranges[0]*scale[0]/avgscale,
+                      ranges[1]*scale[1]/avgscale,
+                      ranges[2]*scale[2]/avgscale],
+            maxaspect = Math.max(aspect[0], aspect[1], aspect[2]),
+            zoom = subscene.par3d.zoom;
+        m = new CanvasMatrix4();
+        m.rotate(90, 1, 0, 0);
+        m.scale(zoom*2.0*maxaspect*ranges[0]/aspect[0], 
+                zoom*2.0*maxaspect*ranges[1]/aspect[1],
+                zoom*2.0*maxaspect*ranges[2]/aspect[2]);
+        m.translate(center[0], center[1], center[2]);
+        m.multRight(savemv);
+        center = rglwidgetClass.multVM(center, savemv);
+        m.translate(-center[0], -center[1], -center[2]);
+        m.scale(1, 1, 0.25/zoom);
+        m.translate(center[0], center[1], center[2]);
+        this.mvMatrix = m;
+        this.initShapeFromObj(this.sphere, obj);
+        this.sphere.onecolor = obj.colors.length > 1 ? obj.colors[1] : obj.colors[0];
+        
+        this.normMatrix = new CanvasMatrix4();
+        
+        this.setnormMatrix2();
+        this.setprmvMatrix();
+        
+        result = result.concat(this.drawSimple(this.sphere, subscene, context));
+        this.mvMatrix = savemv;
+        this.normMatrix = savenorm;
+      }
+      gl.depthMask(savedm);
+      if (savedt)
+        gl.enable(gl.DEPTH_TEST);
+      if (saveblend)
+        gl.enable(gl.BLEND);
+      return result;
+    };
+
+    /**
+     * Draw a subscene
+     * @param { number } subsceneid - id of subscene
+     * @param { array } context 
+     */
+    rglwidgetClass.prototype.drawSubscene = function(subsceneid, context) {
+      var sub = this.getObj(subsceneid),
+          objects = this.scene.objects,
+          clipids = sub.clipplanes,
+          subids = sub.objects,
+          subscene_has_faces = false,
+          subscene_needs_sorting = false,
+          flags, i, obj, result = [];
+          
+      if (sub.par3d.skipRedraw)
+        return result;
+      
+      if (this.opaquePass) {
+        for (i=0; i < subids.length; i++) {
+      	  obj = objects[subids[i]];
+          flags = obj.flags;
+          if (typeof flags !== "undefined") {
+            subscene_has_faces = subscene_has_faces || 
+                            (rglwidgetClass.isSet(flags, rglwidgetClass.f_is_lit) &&
+                            !rglwidgetClass.isSet(flags, rglwidgetClass.f_fixed_quads));
+            obj.is_transparent = obj.someHidden || 
+              rglwidgetClass.isSet(flags, rglwidgetClass.f_is_transparent);
+            subscene_needs_sorting = subscene_needs_sorting || 
+              obj.is_transparent ||
+              rglwidgetClass.isSet(flags, rglwidgetClass.f_depth_sort);
+          }
+        }
+      }
+
+      this.setViewport(subsceneid);
+
+      this.setprMatrix(subsceneid);
+      this.setInvPrMatrix();
+      this.setmvMatrix(subsceneid);
+      this.setnormMatrix2();
+      this.setprmvMatrix();
+      this.invMatrix = new CanvasMatrix4(this.mvMatrix);
+      this.invMatrix.invert();
+      
+      if (this.opaquePass) {
+        context = context.slice();
+        context.push(subsceneid);
+        
+        this.doBlending(false);
+        this.subsceneid = subsceneid;
+        if (typeof this.sphere !== "undefined") // reset this.sphere.fastpieces; it will be recreated if needed
+          this.sphere.fastpieces = undefined;
+        if (typeof sub.backgroundId !== "undefined")
+          result = result.concat(this.drawBackground(sub.backgroundId, subsceneid, context));
+      }
+
+      if (subids.length) {
+            
+        if (clipids.length > 0) {
+          for (i = 0; i < clipids.length; i++)
+            this.drawObjId(clipids[i], subsceneid);
+        }
+        
+        subids = sub.opaque.concat(sub.transparent);
+        if (this.opaquePass) {
+          for (i = 0; i < subids.length; i++)
+            result = result.concat(this.drawObjId(subids[i], subsceneid, context));
+          subids = sub.subscenes;
+          for (i = 0; i < subids.length; i++)
+            result = result.concat(this.drawSubscene(subids[i], context));
+        }
+      }
+      return result;
+    };
+    
+    /**
+     * Set the context for drawing transparently
+     * @param { array } context
+     */
+    rglwidgetClass.prototype.setContext = function(context) {
+      var result = [], objid, obj, type;
+      context = context.slice();
+      context.reverse();
+      while (context.length > 0) {
+        objid = context.pop();
+        obj = this.getObj(objid);
+        type = obj.type;
+        switch (type) {
+          case "subscene":
+            this.drawSubscene(objid, false);
+            break;
+          case "sprites":
+            result = result.concat(context.pop());
+            break;
+          case "spheres":
+            // this.initSphereFromObj(obj);  // FIXME:  not needed?
+            break;
+          case "bboxdeco":
+            result = result.concat(context.pop());
+            break;
+          default:
+            console.error("bad type '", type, "' in setContext");
+        }
+      }
+      return result;
+    };
+    
+    /**
+     * Draw the transparent pieces of a scene
+     * @param {object} pieces
+     */
+    rglwidgetClass.prototype.drawPieces = function(pieces) {
+      var i, prevcontext = [], context;
+      for (i = 0; i < pieces.length; i++) {
+        context = pieces[i].context.slice();
+        if (context !== prevcontext) {
+          prevcontext = context.slice();
+          context = this.setContext(context);
+          this.doBlending(true, pieces[i].objid);
+        }
+        this.drawObjId(pieces[i].objid, this.subsceneid, 
+                       pieces[i]);
+      }
+    };
+ 
+    /**
+     * Draw the whole scene
+     */
+    rglwidgetClass.prototype.drawScene = function() {
+      var wasDrawing = this.startDrawing(),
+          pieces;
+      if (!wasDrawing) {
+        if (this.select.state !== "inactive")
+          this.selectionChanged();
+
+        this.doStartScene();
+        this.opaquePass = true;
+        pieces = this.drawSubscene(this.scene.rootSubscene, []);
+        this.opaquePass = false;
+        pieces = this.sortPieces(pieces);
+        pieces = this.mergePieces(pieces);
+        this.drawPieces(pieces);
+      }
+      this.stopDrawing(wasDrawing);
+    };
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/init.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/init.src.js
new file mode 100644
index 0000000..3e4c448
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/init.src.js
@@ -0,0 +1,1338 @@
+    /**
+     * Methods related to initialization
+     * @name ___METHODS_FOR_INITIALIZATION___
+     * @memberof rglwidgetClass
+     * @kind function
+     * @instance
+     */
+     
+    /**
+     * Initial test for WebGL
+     */
+    rglwidgetClass.prototype.initGL0 = function() {
+      if (!window.WebGLRenderingContext){
+        this.alertOnce("Your browser does not support WebGL. See http://get.webgl.org");
+        return;
+      }
+    };
+
+    /**
+     * Initialize WebGL
+     * @returns { Object } the WebGL context
+     */
+    rglwidgetClass.prototype.initGL = function() {
+      var self = this, success = false;
+      if (this.gl) {
+      	if (!this.drawing && this.gl.isContextLost())
+          this.restartCanvas();
+        else
+          return this.gl;
+      }
+      // if (!this.isInBrowserViewport()) return; Return what??? At this point we know this.gl is null.
+      this.canvas.addEventListener("webglcontextrestored",
+        this.onContextRestored, false);
+      this.canvas.addEventListener("webglcontextlost",
+        this.onContextLost, false);
+      this.gl = this.canvas.getContext("webgl", this.webGLoptions) ||
+               this.canvas.getContext("experimental-webgl", this.webGLoptions);
+      success = !!(this.gl && this.gl instanceof WebGLRenderingContext);
+      if (!success)
+        this.alertOnce("Your browser does not support WebGL. See http://get.webgl.org"); 
+      this.index_uint = this.gl.getExtension("OES_element_index_uint");
+      var save = this.startDrawing();
+      Object.keys(this.scene.objects).forEach(function(key){
+        self.initObjId(parseInt(key, 10));
+        });
+      this.stopDrawing(save);
+      return this.gl;
+    };
+
+    /**
+     * Resize the display to match element
+     * @param { Object } el - DOM element to match
+     */
+    rglwidgetClass.prototype.resize = function(el) {
+      this.canvas.width = el.width;
+      this.canvas.height = el.height;
+    };
+
+    /**
+     * Initialize the sphere object
+     */
+    rglwidgetClass.prototype.initSphere = function(sections, segments) {
+      var v = [], phi = [], theta = [], it = [], centers = [],
+           i, j, k, ind, result = {};
+       
+      for (i = 0; i <= sections; i++) {
+        phi.push(i/sections - 0.5);
+      }
+
+      for (j = 0; j <= segments; j++) {
+        theta.push(2*j/segments);
+        for (i = 0; i <= sections; i++) {
+          /* These are [x,y,z,s,t]: */
+          v.push([Math.sin(Math.PI*theta[j]) * Math.cos(Math.PI*phi[i]),
+                  Math.sin(Math.PI*phi[i]),
+                  Math.cos(Math.PI*theta[j]) * Math.cos(Math.PI*phi[i]),                               
+                  theta[j]/2,
+                  phi[i] + 0.5]);
+           // console.log("xyzst="+v[v.length-1]);
+        }
+      }
+      result.values = new Float32Array(rglwidgetClass.flatten(v));
+      result.vertexCount = v.length;
+      
+      for (j = 0; j < segments; j++) {
+        for (i = 0; i < sections; i++) {
+          ind = i + (sections + 1)*j;
+          if (i > 0)                       // Not south pole
+            it.push([ind, 
+                     ind + sections + 1,
+                     ind + 1]);
+          if (i < sections - 1)             // Not north pole
+            it.push([ind + sections + 1, 
+                     ind + sections + 2,
+                     ind + 1]);
+        }
+      }
+      result.it = new Uint16Array(rglwidgetClass.flatten(it));
+      
+      for (i = 0; i < it.length; i++) {
+        centers.push([0,0,0]);
+        for (j = 0; j < 3; j++) { // x,y,z
+          for (k = 0; k < 3; k++) {// vertices
+            centers[i][j] += v[it[i][k]][j]/3;
+          }
+        }
+      }
+      result.centers = centers;
+      
+      result.vOffsets = {vofs:0, cofs:-1, nofs:0, radofs:-1, oofs:-1,
+                         tofs:3, nextofs:-1, pointofs:-1, stride:5};
+
+      result.f = [];
+      result.indices = {};
+
+      result.colorCount = 1;
+      result.type = "sphere";
+      this.sphere = result;
+      this.initShapeGL(this.sphere);
+    };
+
+    /**
+     * Initialize the cube object
+     */
+    rglwidgetClass.prototype.initCube = function() {
+   var v = [[0, 0, 0], [1, 0, 0], 
+            [0, 1, 0], [1, 1, 0], 
+            [0, 0, 1], [1, 0, 1],
+            [0, 1, 1], [1, 1, 1]],
+          ib = [[0, 2, 3, 1], 
+                [2, 6, 7, 3], 
+                [1, 3, 7, 5], 
+                [0, 4, 6, 2], 
+                [0, 1, 5, 4], 
+                [4, 5, 7, 6]], 
+          centers = [], i, j, k, 
+          i0, i1, i2,
+          normal, result = {};
+       
+      for (i = 0; i < ib.length; i++) {
+        centers.push([0,0,0]);
+        for (j = 0; j < 3; j++) { // x,y,z
+          for (k = 0; k < 4; k++) {// vertices
+            centers[i][j] += v[ib[i][k]][j]/4;
+          }
+        }
+      }
+      result.centers = centers; 
+      result.values = new Float32Array(6*4*3*2);
+      result.vertexCount = 24;
+      result.vertices = new Array(24);
+      result.normals = new Array(24);
+      for (i=0; i < 6; i++) {
+        for (j=0; j < 4; j++) {
+          i0 = ib[i][j];
+          result.vertices[4*i + j] = v[i0];
+          i1 = ib[i][(j + 1) % 4];
+          i2 = ib[i][(j + 2) % 4];
+          if (j === 0)
+            normal = rglwidgetClass.normalize(rglwidgetClass.xprod(rglwidgetClass.vdiff(v[i1], v[i0]),
+                                  rglwidgetClass.vdiff(v[i2], v[i0])));
+          result.normals[4*i + j] = normal;
+          for (k=0; k < 3; k++) {
+            result.values[i*24 + j*6 + k] = v[i0][k];
+            result.values[i*24 + j*6 + 3 + k] = normal[k];
+          }
+        }
+        for (j=0; j<4; j++)
+          ib[i][j] = 4*i + j;
+      }
+      result.ib = new Uint16Array(rglwidgetClass.flatten(ib));
+      
+      result.vOffsets = {vofs:0, cofs:-1, nofs:3, radofs:-1, oofs:-1,
+                         tofs:-1, nextofs:-1, pointofs:-1, stride:6};
+
+      result.f = [];
+      result.indices = {};
+
+      result.colorCount = 1;
+      result.type = "quads";
+      this.cube = result;
+      this.initShapeGL(this.cube);
+    };
+    
+
+    /**
+     * Do the gl part of initializing the sphere and cube
+     */
+    rglwidgetClass.prototype.initShapeGL = function(shape) {
+      var gl = this.gl || this.initGL();
+      if (gl.isContextLost()) return;
+      shape.buf = gl.createBuffer();
+      gl.bindBuffer(gl.ARRAY_BUFFER, shape.buf);
+      gl.bufferData(gl.ARRAY_BUFFER, shape.values, gl.STATIC_DRAW);
+      shape.ibuf = [gl.createBuffer(), gl.createBuffer()];
+      return;
+    };
+
+    /* Initialize common sphere object from spheres object
+    */
+    rglwidgetClass.prototype.initShapeFromObj = function(shape, obj) {
+      var i, pass, f, mode, self = this,
+        /* This function selects things that would be
+           the back, ignoring perspective -- this is what 
+           we want for the bounding box decoration. */
+        is_back = function(i) {
+                var normal = [].concat(shape.normals[i]),
+                  pt = shape.vertices[i];
+                normal.push(-rglwidgetClass.dotprod(normal, pt));
+                normal = rglwidgetClass.multVM(normal, self.normMatrix);
+                return normal[2] < 0 || (normal[2] === 0 && normal[0] < 0);
+              }; 
+      shape.ofsLoc = obj.ofsLoc;
+      shape.texLoc = obj.texLoc;
+      shape.texture = obj.texture;
+      shape.sampler = obj.sampler;
+      shape.uFogMode = obj.uFogMode;
+      shape.uFogColor = obj.uFogColor;
+      shape.uFogParms = obj.uFogParms;
+      shape.userAttribLocations = obj.userAttribLocations;
+      shape.userUniformLocations = obj.userUniformLocations;
+      shape.normLoc = obj.normLoc;
+      shape.invPrMatLoc = obj.invPrMatLoc;
+      shape.clipLoc = obj.clipLoc;
+      shape.nextLoc = obj.nextLoc;
+      shape.pointLoc = obj.pointLoc;
+      shape.aspectLoc = obj.aspectLoc;
+      shape.lwdLoc = obj.lwdLoc;
+      shape.prog = obj.prog;
+      shape.material = obj.material;
+      shape.flags = obj.flags;
+      shape.defFlags = obj.defFlags;
+      shape.someHidden = obj.someHidden;
+      shape.fastTransparency = obj.fastTransparency;
+      shape.nlights = obj.nlights;
+      shape.emission = obj.emission;
+      shape.emissionLoc = obj.emissionLoc;
+      shape.shininess = obj.shininess;
+      shape.shininessLoc = obj.shininessLoc;
+      shape.ambient = obj.ambient;
+      shape.ambientLoc = obj.ambientLoc;
+      shape.specular = obj.specular;
+      shape.specularLoc = obj.specularLoc;
+      shape.diffuse = obj.diffuse;
+      shape.diffuseLoc = obj.diffuseLoc;
+      shape.lightDir = obj.lightDir;
+      shape.lightDirLoc = obj.lightDirLoc;
+      shape.viewpoint = obj.viewpoint;
+      shape.viewpointLoc = obj.viewpointLoc;
+      shape.finite = obj.finite;
+      shape.finiteLoc = obj.finiteLoc;
+      shape.prMatLoc = obj.prMatLoc;
+      shape.mvMatLoc = obj.mvMatLoc;
+      shape.normMatLoc = obj.normMatLoc;
+      shape.frontLoc = obj.frontLoc;
+      shape.index_uint = false;
+      shape.is_transparent = obj.is_transparent;
+      shape.ignoreExtent = obj.ignoreExtent;
+      if (shape.passes !== obj.passes ||
+          JSON.stringify( shape.pmode) !== JSON.stringify(obj.pmode)) {
+        shape.passes = obj.passes;
+        shape.pmode = obj.pmode;
+        for (pass = 0; pass < obj.passes; pass++) {
+          mode =  shape.pmode[pass];
+          if (typeof  shape.indices[mode] === "undefined") {
+            f = [];
+            switch (mode) {
+            case "culled": break;
+            case "points":
+              f.length =  shape.vertexCount;
+              for (i=0; i < f.length; i++)
+                f[i] = i;
+              break;
+            case "lines":
+              if (typeof shape.it !== "undefined") {
+                f.length = 2* shape.it.length;
+      	        for (i=0; i <  shape.it.length/3; i++) {
+      	          f[6*i] =  shape.it[3*i];
+      	          f[6*i + 1] =  shape.it[3*i + 1];
+      	          f[6*i + 2] =  shape.it[3*i + 1];
+      	          f[6*i + 3] =  shape.it[3*i + 2];
+      	          f[6*i + 4] =  shape.it[3*i + 2];
+      	          f[6*i + 5] =  shape.it[3*i];
+      	        }
+              } else {
+                f.length = 2*shape.ib.length;
+                for (i=0; i < shape.ib.length/4; i++) {
+                  f[8*i] = shape.ib[4*i];
+                  f[8*i + 1] = shape.ib[4*i + 1];
+                  f[8*i + 2] = shape.ib[4*i + 1];
+                  f[8*i + 3] = shape.ib[4*i + 2];
+                  f[8*i + 4] = shape.ib[4*i + 2];
+                  f[8*i + 5] = shape.ib[4*i + 3];
+                  f[8*i + 6] = shape.ib[4*i + 3];
+                  f[8*i + 7] = shape.ib[4*i];
+                }
+              }
+      	      break;
+      	    case "filled":
+      	      if (typeof shape.it !== "undefined")
+      	        f =  shape.it;
+      	      else if (typeof shape.ib !== "undefined") {
+      	        f.length = 1.5*shape.ib.length;
+                for (i=0; i < shape.ib.length/4; i++) {
+                  f[6*i] = shape.ib[4*i];
+                  f[6*i+1] = shape.ib[4*i + 1];
+                  f[6*i+2] = shape.ib[4*i + 2];
+                  f[6*i+3] = shape.ib[4*i];
+                  f[6*i+4] = shape.ib[4*i + 2];
+                  f[6*i+5] = shape.ib[4*i + 3];
+                }      	        
+      	      }
+      	      break;
+      	    }              
+            shape.indices[mode] = new Uint16Array(f);
+          }
+        }
+      }       
+      for (pass = 0; pass < obj.passes; pass++) {
+        mode =  shape.pmode[pass];
+        shape.f[pass] =  shape.indices[mode];
+        if (typeof obj.draw_front !== "undefined" &&
+            !obj.draw_front) {
+          shape.f[pass] = shape.f[pass].filter(is_back);   
+        }
+      }
+      // console.log("Names in  shapes not in  shape:"+JSON.stringify(rglwidgetClass.keydiff(obj,  shape)));
+       shape.initialized = true;
+    };
+
+    /**
+     * Initialize a subscene
+     * @param { number } id - id of subscene.
+     */
+    rglwidgetClass.prototype.initSubscene = function(id) {
+      var sub = this.getObj(id),
+          i, obj;
+
+      if (sub.type !== "subscene")
+        return;
+
+      sub.par3d.userMatrix = this.toCanvasMatrix4(sub.par3d.userMatrix);
+      sub.par3d.userProjection = this.toCanvasMatrix4(sub.par3d.userProjection);
+      sub.par3d.userProjection.transpose();
+      sub.par3d.listeners = [].concat(sub.par3d.listeners);
+      sub.backgroundId = undefined;
+      sub.subscenes = [];
+      sub.clipplanes = [];
+      sub.transparent = [];
+      sub.opaque = [];
+      sub.lights = [];
+      sub.needsBegin = true;
+      if (typeof sub.objects !== "undefined")
+        sub.objects = [].concat(sub.objects); /* make sure it's an array */
+      for (i=0; i < sub.objects.length; i++) {
+        obj = this.getObj(sub.objects[i]);
+        if (typeof obj === "undefined") {
+          sub.objects.splice(i, 1);
+          i--;
+        } else if (obj.type === "background")
+          sub.backgroundId = obj.id;
+        else
+          sub[this.whichList(obj.id)].push(obj.id);
+      }
+    };
+    
+    rglwidgetClass.prototype.initBBox = function(obj) {
+      if (!this.cube)
+        this.initCube();
+      obj.cube = {id: obj.id + 0.1,
+                    type: "quads",
+                    flags: obj.flags,
+                    material: obj.material,
+                    colors: [obj.colors[0]],
+                    vertices: this.cube.vertices,
+                    normals: this.cube.normals,
+                    draw_front: obj.draw_front,
+                    initialized: false
+        };
+      if (this.getMaterial(obj.cube, "front") !==
+          this.getMaterial(obj.cube, "back"))
+        /* jshint bitwise: false */  
+        obj.cube.flags |= rglwidgetClass.f_is_twosided;
+        /* jshint bitwise: true */
+      this.scene.objects[obj.cube.id] = obj.cube;
+      obj.ticks = {id: obj.id + 0.2,
+                     type: "lines",
+                     flags: rglwidgetClass.f_has_fog,
+                     material: obj.material,
+                     colors: (obj.colors.length > 1 ? [obj.colors[1]] : [obj.colors[0]]),
+                     axes: obj.axes,
+                     initialized: false
+      };
+      this.scene.objects[obj.ticks.id] = obj.ticks;
+      obj.labels = {id: obj.id + 0.3,
+                     type: "text",
+                     flags: rglwidgetClass.f_has_fog + 
+                            rglwidgetClass.f_fixed_size + 
+                            rglwidgetClass.f_fixed_quads,
+                     material: {lit: false},
+                     colors: (obj.colors.length > 1 ? [obj.colors[1]] : [obj.colors[0]]),
+                     cex: [[1]],
+                     family: [["sans"]],
+                     font: [[1]],
+                     adj: [[0.5, 0.5, 0.5]],
+                     ignoreExtent: true,
+                     initialized: false
+      };
+      this.scene.objects[obj.labels.id] = obj.labels;
+      obj.initialized = true;
+    };
+    
+    rglwidgetClass.prototype.initBackground = function(obj) {
+      var material, fl = obj.defFlags;
+      if (typeof obj.ids !== "undefined")
+        obj.quad = rglwidgetClass.flatten([].concat(obj.ids));
+      else if (obj.sphere) {
+        fl.has_normals = true;
+        fl.needs_vnormal = true;
+        obj.defFlags = fl;
+        material = obj.material;
+        material.front = "culled";
+        obj.vertices = [[0,0,0]];
+        obj.texcoords = [[0,0]];
+      }  
+    };
+
+    /**
+     * Initialize object for display
+     * @param { number } id - id of object to initialize
+     */
+    rglwidgetClass.prototype.initObjId = function(id) {
+      if (typeof id !== "number") {
+        this.alertOnce("initObj id is "+typeof id);
+      }
+      return this.initObj(this.getObj(id));
+    };
+
+    /**
+     * Initialize object for display
+     * @param { Object } obj - object to initialize
+     */
+    rglwidgetClass.prototype.initObj = function(obj) {
+      var type = obj.type, 
+          flags = obj.flags,
+          normals = obj.normals,
+          round_points = (typeof obj.material === "undefined") ?
+            false : this.getMaterial(obj, "point_antialias"),
+          has_indices = typeof obj.indices !== "undefined",
+          has_spheres = type === "spheres" || 
+                        (type === "background" && obj.sphere),
+          sprites_3d = rglwidgetClass.isSet(flags, rglwidgetClass.f_sprites_3d),
+          depth_sort = rglwidgetClass.isSet(flags, rglwidgetClass.f_depth_sort),
+          gl = this.gl || this.initGL(),
+          fl, polygon_offset,
+          texinfo, drawtype, nclipplanes, f, nrows, oldrows,
+          i,j,v,v1,v2, mat, uri, matobj, pass, pmode,
+          dim, nx, nz, nrow, shaders;
+
+    obj.initialized = true;
+    
+    obj.someHidden = false; // used in selection
+    
+    this.expandBufferedFields(obj);
+    
+    if (type === "subscene")
+      return;
+      
+    obj.defFlags = fl = rglwidgetClass.getDefFlags(flags, type, normals, round_points);
+  
+    obj.is_transparent = fl.is_transparent;
+  
+    if (type === "bboxdeco")
+      return this.initBBox(obj);
+      
+    if (has_spheres && typeof this.sphere === "undefined")
+      this.initSphere(16, 16);
+
+    if (type === "light") {
+      obj.ambient = new Float32Array(obj.colors[0].slice(0,3));
+      obj.diffuse = new Float32Array(obj.colors[1].slice(0,3));
+      obj.specular = new Float32Array(obj.colors[2].slice(0,3));
+      obj.lightDir = new Float32Array(obj.vertices[0]);
+      return;
+    }
+
+    if (type === "clipplanes") {
+      obj.vClipplane = rglwidgetClass.flatten(rglwidgetClass.cbind(obj.normals, obj.offsets));
+      return;
+    }
+
+    if (type === "background") {
+      this.initBackground(obj);
+      if (!obj.sphere)
+        return;
+    }
+
+    polygon_offset = this.getMaterial(obj, "polygon_offset");
+    if (polygon_offset[0] !== 0 || polygon_offset[1] !== 0)
+      obj.polygon_offset = polygon_offset;
+
+    if (fl.is_transparent) {
+      depth_sort = ["triangles", "quads", "surface",
+                    "spheres", "sprites", "text",
+                    "planes"].indexOf(type) >= 0;
+    }
+    
+    if (fl.is_brush)
+      this.initSelection(obj.id);
+
+    if (typeof obj.vertices === "undefined")
+      obj.vertices = [];
+
+    v = obj.vertices;
+    if (has_indices)
+      obj.vertexCount = obj.indices.length;
+    else
+      obj.vertexCount = v.length;
+      
+    if (!obj.vertexCount) return;
+
+    if (fl.is_twosided && !fl.has_normals && type !== "background") {
+      if (typeof obj.userAttributes === "undefined")
+        obj.userAttributes = {};
+      v1 = Array(v.length);
+      v2 = Array(v.length);
+      if (obj.type === "triangles" || obj.type === "quads") {
+      	if (obj.type === "triangles")
+      	  nrow = 3;
+      	else
+      	  nrow = 4;
+        for (i=0; i<Math.floor(v.length/nrow); i++)
+          for (j=0; j<nrow; j++) {
+            v1[nrow*i + j] = v[nrow*i + ((j+1) % nrow)];
+            v2[nrow*i + j] = v[nrow*i + ((j+2) % nrow)];
+          }
+      } else if (obj.type === "surface") {
+        dim = obj.dim[0];
+        nx = dim[0];
+        nz = dim[1];
+        for (j=0; j<nx; j++) {
+          for (i=0; i<nz; i++) {
+            if (i+1 < nz && j+1 < nx) {
+              v2[j + nx*i] = v[j + nx*(i+1)];
+              v1[j + nx*i] = v[j+1 + nx*(i+1)];
+            } else if (i+1 < nz) {
+              v2[j + nx*i] = v[j-1 + nx*i];
+              v1[j + nx*i] = v[j + nx*(i+1)];
+            } else {
+              v2[j + nx*i] = v[j + nx*(i-1)];
+              v1[j + nx*i] = v[j-1 + nx*(i-1)];
+            }
+          }
+        }
+      }
+      obj.userAttributes.aPos1 = v1;
+      obj.userAttributes.aPos2 = v2;
+    }
+
+    if (!sprites_3d) {
+      if (gl.isContextLost()) return;
+      if (typeof obj.prog !== "undefined") {
+        gl.deleteProgram(obj.prog);
+        obj.prog = undefined;
+      }
+      
+      shaders = this.getShaders(obj);
+      
+      obj.prog = gl.createProgram();
+      gl.attachShader(obj.prog, this.getShader( gl.VERTEX_SHADER,
+                      shaders.vertex ));
+      gl.attachShader(obj.prog, this.getShader( gl.FRAGMENT_SHADER,
+                      shaders.fragment ));
+      //  Force aPos to location 0, aCol to location 1
+      gl.bindAttribLocation(obj.prog, 0, "aPos");
+      gl.bindAttribLocation(obj.prog, 1, "aCol");
+      gl.linkProgram(obj.prog);
+      var linked = gl.getProgramParameter(obj.prog, gl.LINK_STATUS);
+      if (!linked) {
+
+        // An error occurred while linking
+        var lastError = gl.getProgramInfoLog(obj.prog);
+        console.warn("Error in program linking:" + lastError);
+
+        gl.deleteProgram(obj.prog);
+        return;
+      }
+    }
+
+    if (type === "text") {
+      texinfo = this.drawTextToCanvas(obj.texts,
+                                      rglwidgetClass.flatten(obj.cex),
+                                      rglwidgetClass.flatten(obj.family),
+                                      rglwidgetClass.flatten(obj.family));
+    }
+
+    if (fl.fixed_quads && !sprites_3d) {
+      obj.ofsLoc = gl.getAttribLocation(obj.prog, "aOfs");
+    }
+
+    if (fl.has_texture || type === "text") {
+      if (!obj.texture) {
+        obj.texture = gl.createTexture();
+        // This is a trick from https://stackoverflow.com/a/19748905/2554330 to avoid warnings
+        gl.bindTexture(gl.TEXTURE_2D, obj.texture);
+        gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, 1, 1, 0, gl.RGBA, gl.UNSIGNED_BYTE,
+              new Uint8Array([255,255,255, 255])); // white
+      }
+      obj.texLoc = gl.getAttribLocation(obj.prog, "aTexcoord");
+      obj.sampler = gl.getUniformLocation(obj.prog, "uSampler");
+    }
+    
+    if (fl.has_fog && !sprites_3d) {
+      obj.uFogMode = gl.getUniformLocation(obj.prog, "uFogMode");
+      obj.uFogColor = gl.getUniformLocation(obj.prog, "uFogColor");
+      obj.uFogParms = gl.getUniformLocation(obj.prog, "uFogParms");
+    }
+
+    if (fl.has_texture) {
+      mat = obj.material;
+      if (typeof mat.uri !== "undefined")
+        uri = mat.uri;
+      else if (typeof mat.uriElementId === "undefined") {
+        matobj = this.getObj(mat.uriId);
+        if (typeof matobj !== "undefined") {
+          uri = matobj.material.uri;
+        } else {
+          uri = "";
+        }
+      } else
+        uri = document.getElementById(mat.uriElementId).rglinstance.getObj(mat.uriId).material.uri;
+
+      this.loadImageToTexture(uri, obj.texture);
+    }
+
+    if (type === "text") {
+      this.handleLoadedTexture(obj.texture, this.textureCanvas);
+    }
+
+    var stride = 3, nc, cofs, nofs, radofs, oofs, tofs, vnew, fnew,
+        nextofs = -1, pointofs = -1, alias, colors, key, selection,
+        filter, adj, offset, attr, last, options, 
+        len, current;
+
+    obj.alias = undefined;
+    
+    colors = obj.colors;
+
+    j = this.scene.crosstalk.id.indexOf(obj.id);
+    if (j >= 0) {
+      key = this.scene.crosstalk.key[j];
+      options = this.scene.crosstalk.options[j];
+      colors = colors.slice(0); 
+      for (i = 0; i < v.length; i++)
+        colors[i] = obj.colors[i % obj.colors.length].slice(0);
+      if ( (selection = this.scene.crosstalk.selection) &&
+           (selection.length || !options.selectedIgnoreNone) )
+        for (i = 0; i < v.length; i++) {
+          if (!selection.includes(key[i])) {
+            if (options.deselectedColor)
+              colors[i] = options.deselectedColor.slice(0);
+            colors[i][3] = colors[i][3]*options.deselectedFade;   /* default: mostly transparent if not selected */
+          } else if (options.selectedColor)
+            colors[i] = options.selectedColor.slice(0);
+        }
+      if ( (filter = this.scene.crosstalk.filter) )
+        for (i = 0; i < v.length; i++) 
+          if (!filter.includes(key[i])) {
+            if (options.filteredColor)
+              colors[i] = options.filteredColor.slice(0);
+            colors[i][3] = colors[i][3]*options.filteredFade;   /* default: completely hidden if filtered */
+          }
+    }  
+    
+    nc = obj.colorCount = colors.length;
+    if (nc > 1) {
+      cofs = stride;
+      stride = stride + 4;
+      v = rglwidgetClass.cbind(v, colors);
+    } else {
+      cofs = -1;
+      obj.onecolor = rglwidgetClass.flatten(colors);
+    }
+
+    if (fl.has_normals && !has_spheres) {
+      nofs = stride;
+      stride = stride + 3;
+      v = rglwidgetClass.cbind(v, typeof obj.pnormals !== "undefined" ? obj.pnormals : obj.normals);
+    } else
+      nofs = -1;
+
+    if (typeof obj.radii !== "undefined") {
+      radofs = stride;
+      stride = stride + 1;
+      // FIXME:  always concat the radii?
+      if (obj.radii.length === v.length) {
+        v = rglwidgetClass.cbind(v, obj.radii);
+      } else if (obj.radii.length === 1) {
+        v = v.map(function(row) { return row.concat(obj.radii[0]);});
+      }
+    } else
+      radofs = -1;
+      
+    // Add default indices
+    if (has_indices) {
+      f = Array(obj.indices.length);
+      for (i = 0; i < f.length; i++)
+        f[i] = obj.indices[i] - 1;
+    } else {
+      f = Array(v.length);
+      for (i = 0; i < v.length; i++)
+        f[i] = i;
+    }
+    obj.f = [f,f];
+
+    if (type === "sprites" && !sprites_3d) {
+      tofs = stride;
+      stride += 2;
+      oofs = stride;
+      stride += 3;
+      vnew = new Array(4*v.length);
+      fnew = new Array(4*v.length);
+      alias = new Array(v.length);
+      var rescale = fl.fixed_size ? 72 : 1,
+          size = obj.radii, s = rescale*size[0]/2;
+      last = v.length;
+      f = obj.f[0];
+      obj.adj = rglwidgetClass.flatten(obj.adj);
+      if (typeof obj.pos !== "undefined") {
+        obj.pos = rglwidgetClass.flatten(obj.pos);
+        offset = obj.adj[0];
+      } else
+        offset = 0;
+      for (i=0; i < v.length; i++) {
+        adj = this.getAdj(obj, i, offset);
+        if (size.length > 1)
+          s = rescale*size[i]/2;
+        adj[0] = 2*s*(adj[0] - 0.5);
+        adj[1] = 2*s*(adj[1] - 0.5);
+        adj[2] = 2*s*(adj[2] - 0.5);
+        vnew[i]  = v[i].concat([0,0]).concat([-s-adj[0],
+                                              -s-adj[1],
+                                              -adj[2]]);
+        fnew[4*i] = f[i];
+        vnew[last]= v[i].concat([1,0]).concat([s-adj[0],
+                                              -s-adj[1],
+                                              -adj[2]]);
+        fnew[4*i+1] = last++;
+        vnew[last]= v[i].concat([1,1]).concat([s-adj[0],
+                                               s-adj[1],
+                                               -adj[2]]);
+        fnew[4*i+2] = last++;
+        vnew[last]= v[i].concat([0,1]).concat([-s-adj[0],
+                                                s-adj[1],
+                                                -adj[2]]);
+        fnew[4*i+3] = last++;
+        alias[i] = [last-3, last-2, last-1];
+      }
+      v = vnew;
+      obj.vertexCount = v.length;
+      obj.f = [fnew, fnew];
+    } else if (type === "text") {
+      tofs = stride;
+      stride += 2;
+      oofs = stride;
+      stride += 3;
+      vnew = new Array(4*v.length);
+      f = obj.f[0];
+      fnew = new Array(4*f.length);
+      alias = new Array(v.length);
+      last = v.length;
+      adj = rglwidgetClass.flatten(obj.adj);
+      if (typeof obj.pos !== "undefined") {
+        obj.pos = rglwidgetClass.flatten(obj.pos);
+        offset = adj[0];
+      } else
+        offset = 0;
+      for (i=0; i < v.length; i++) {
+        adj = this.getAdj(obj, i, offset, obj.texts[i]);
+        vnew[i]  = v[i].concat([0,-0.5]).concat(adj);
+        fnew[4*i] = f[i];
+        vnew[last] = v[i].concat([1,-0.5]).concat(adj);
+        fnew[4*i+1] = last++;
+        vnew[last] = v[i].concat([1, 1.5]).concat(adj);
+        fnew[4*i+2] = last++;
+        vnew[last] = v[i].concat([0, 1.5]).concat(adj);
+        fnew[4*i+3] = last++;
+        alias[i] = [last-3, last-2, last-1];
+        for (j=0; j < 4; j++) {
+          v1 = vnew[fnew[4*i+j]];
+          v1[oofs] = 2*(v1[tofs]-v1[oofs])*texinfo.widths[i];
+          v1[oofs+1] = 2*(v1[tofs+1]-v1[oofs+1])*texinfo.textHeights[i];
+          v1[oofs+2] = 2*(0.5-v1[oofs+2])*texinfo.textHeights[i]/1000.0;
+          v1[tofs] = (texinfo.offsetsx[i] + v1[tofs]*texinfo.widths[i])/texinfo.canvasX;
+          v1[tofs+1] = 1.0-(texinfo.offsetsy[i] -
+              v1[tofs+1]*texinfo.textHeights[i])/texinfo.canvasY;
+          vnew[fnew[4*i+j]] = v1;
+        }
+      }
+      v = vnew;
+      obj.vertexCount = v.length;
+      obj.f = [fnew, fnew];
+    } else if (typeof obj.texcoords !== "undefined") {
+      tofs = stride;
+      stride += 2;
+      oofs = -1;
+      v = rglwidgetClass.cbind(v, obj.texcoords);
+    } else {
+      tofs = -1;
+      oofs = -1;
+    }
+    
+    obj.alias = alias;
+                          
+    if (typeof obj.userAttributes !== "undefined") {
+      obj.userAttribOffsets = {};
+      obj.userAttribLocations = {};
+      obj.userAttribSizes = {};
+      for (attr in obj.userAttributes) {
+      	obj.userAttribLocations[attr] = gl.getAttribLocation(obj.prog, attr);
+      	if (obj.userAttribLocations[attr] >= 0) { // Attribute may not have been used
+      	  obj.userAttribOffsets[attr] = stride;
+      	  v = rglwidgetClass.cbind(v, obj.userAttributes[attr]);
+      	  stride = v[0].length;
+      	  obj.userAttribSizes[attr] = stride - obj.userAttribOffsets[attr];
+      	} else
+      	  console.warn("attribute '"+attr+"' not found in object "+obj.id+".");
+      }
+    }
+
+    if (typeof obj.userUniforms !== "undefined" ||
+        typeof obj.userTextures !== "undefined") {
+      obj.userUniformLocations = {};
+      for (attr in obj.userUniforms) {
+        obj.userUniformLocations[attr] = gl.getUniformLocation(obj.prog, attr);
+        if (obj.userUniformLocations[attr] === null)
+          console.warn("uniform '"+attr+"' not found in object "+obj.id+".");
+      }
+      for (attr in obj.userTextures) {
+        var texture = obj.userTextures[attr];
+        texture.texture = gl.createTexture();
+        // This is a trick from https://stackoverflow.com/a/19748905/2554330 to avoid warnings
+        gl.bindTexture(gl.TEXTURE_2D, texture.texture);
+        gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, 1, 1, 0, gl.RGBA, gl.UNSIGNED_BYTE,
+              new Uint8Array([255,255,255, 255])); // white
+        texture.sampler = gl.getUniformLocation(obj.prog, attr);
+        if (texture.sampler === null)
+          console.warn("sampler '"+attr+"' not found in object "+obj.id+".");
+        uri = texture.uri;
+        this.loadImageToTexture(uri, texture.texture);
+      }
+    }
+
+    if (sprites_3d) {
+      obj.userMatrix = new CanvasMatrix4();
+      obj.userMatrix.load(rglwidgetClass.flatten(obj.usermatrix));
+      obj.objects = rglwidgetClass.flatten([].concat(obj.ids));
+      fl.is_lit = false;
+      obj.adj = rglwidgetClass.flatten(obj.adj);
+      
+      if (typeof obj.pos !== "undefined") {
+        obj.pos = rglwidgetClass.flatten(obj.pos);
+        obj.offset = obj.adj[0];
+      } else
+        obj.offset = 0;
+        
+      var shapenum = rglwidgetClass.flatten(obj.shapenum);
+      obj.shapelens = [];
+      obj.shapefirst = [];
+      obj.shapefirst.push(0);
+      len = 0;
+      current = 0;
+      for (i = 0; i < shapenum.length; i++) {
+        if (shapenum[i] === shapenum[current]) {
+          len++;
+        } else {
+          obj.shapelens.push(len);
+          len = 1;
+          current = i;
+          obj.shapefirst.push(i);
+        }
+      }
+      obj.shapelens.push(len);
+        
+      for (i=0; i < obj.objects.length; i++)
+        this.initObjId(obj.objects[i]);
+    }
+
+    nclipplanes = this.countClipplanes();
+    if (nclipplanes && !sprites_3d) {
+      obj.clipLoc = gl.getUniformLocation(obj.prog,"vClipplane");
+    }
+
+    if (fl.is_lit) {
+      obj.emissionLoc = gl.getUniformLocation(obj.prog, "emission");
+      obj.emission = new Float32Array(this.stringToRgb(this.getMaterial(obj, "emission")));
+      obj.shininessLoc = gl.getUniformLocation(obj.prog, "shininess");
+      obj.shininess = this.getMaterial(obj, "shininess");
+      obj.nlights = this.countLights();
+      if (obj.nlights > 0) {
+        obj.ambient = new Float32Array(this.stringToRgb(this.getMaterial(obj, "ambient")));
+        obj.specular = new Float32Array(this.stringToRgb(this.getMaterial(obj, "specular")));
+        obj.ambientLoc = gl.getUniformLocation(obj.prog, "ambient");
+        obj.specularLoc = gl.getUniformLocation(obj.prog, "specular");
+        obj.diffuseLoc = gl.getUniformLocation(obj.prog, "diffuse" );
+        obj.lightDirLoc = gl.getUniformLocation(obj.prog, "lightDir");
+        obj.viewpointLoc = gl.getUniformLocation(obj.prog, "viewpoint");
+        obj.finiteLoc = gl.getUniformLocation(obj.prog, "finite" );
+      }
+    }
+    
+    obj.passes = fl.is_twosided + 1;
+    obj.pmode = new Array(obj.passes);
+    for (pass = 0; pass < obj.passes; pass++) {
+      if (type === "triangles" || type === "quads" || type === "surface" || has_spheres)
+      	pmode = this.getMaterial(obj, (pass === 0) ? "front" : "back");
+      else pmode = "filled";
+      obj.pmode[pass] = pmode;
+    }
+    if (!has_spheres) {
+      obj.f.length = obj.passes;
+      for (pass = 0; pass < obj.passes; pass++) {
+      	f = fnew = obj.f[pass];
+        pmode = obj.pmode[pass];
+      	if (pmode === "culled")
+      	  fnew = [];
+        else if (pmode === "points") {
+          // stay with default
+        } else if ((type === "quads" || type === "text" ||
+             type === "sprites") && !sprites_3d) {
+          nrows = Math.floor(obj.vertexCount/4);
+          if (pmode === "filled") {
+            fnew = Array(6*nrows);
+            for (i=0; i < nrows; i++) {
+              fnew[6*i] = f[4*i];
+              fnew[6*i+1] = f[4*i + 1];
+              fnew[6*i+2] = f[4*i + 2];
+              fnew[6*i+3] = f[4*i];
+              fnew[6*i+4] = f[4*i + 2];
+              fnew[6*i+5] = f[4*i + 3];
+            }
+          } else {
+            fnew = Array(8*nrows);
+            for (i=0; i < nrows; i++) {
+              fnew[8*i] = f[4*i];
+              fnew[8*i+1] = f[4*i + 1];
+              fnew[8*i+2] = f[4*i + 1];
+              fnew[8*i+3] = f[4*i + 2];
+              fnew[8*i+4] = f[4*i + 2];
+              fnew[8*i+5] = f[4*i + 3];
+              fnew[8*i+6] = f[4*i + 3];
+              fnew[8*i+7] = f[4*i];
+            }
+          }
+        } else if (type === "triangles") {
+          nrows = Math.floor(obj.vertexCount/3);
+          if (pmode === "filled") {
+            fnew = Array(3*nrows);
+            for (i=0; i < fnew.length; i++) {
+              fnew[i] = f[i];
+            }
+          } else if (pmode === "lines") {
+            fnew = Array(6*nrows);
+      	    for (i=0; i < nrows; i++) {
+      	      fnew[6*i] = f[3*i];
+      	      fnew[6*i + 1] = f[3*i + 1];
+      	      fnew[6*i + 2] = f[3*i + 1];
+      	      fnew[6*i + 3] = f[3*i + 2];
+      	      fnew[6*i + 4] = f[3*i + 2];
+      	      fnew[6*i + 5] = f[3*i];
+      	    }
+          }
+        } else if (has_spheres) {
+          // default
+        } else if (type === "surface") {
+          dim = obj.dim[0];
+          nx = dim[0];
+          nz = dim[1];
+          if (pmode === "filled") {
+            fnew = [];
+            for (j=0; j<nx-1; j++) {
+              for (i=0; i<nz-1; i++) {
+                fnew.push(f[j + nx*i],
+                       f[j + nx*(i+1)],
+                       f[j + 1 + nx*(i+1)],
+                       f[j + nx*i],
+                       f[j + 1 + nx*(i+1)],
+                       f[j + 1 + nx*i]);
+              }
+            }
+          } else if (pmode === "lines") {
+            fnew = [];
+            for (j=0; j<nx; j++) {
+              for (i=0; i<nz; i++) {
+                if (i+1 < nz)
+                  fnew.push(f[j + nx*i],
+                         f[j + nx*(i+1)]);
+                if (j+1 < nx)
+                  fnew.push(f[j + nx*i],
+                         f[j+1 + nx*i]);
+              }
+            }
+          }
+        }
+        obj.f[pass] = fnew;
+        if (depth_sort) {
+          drawtype = "DYNAMIC_DRAW";
+        } else {
+          drawtype = "STATIC_DRAW";
+        }
+      }
+    }
+    
+    if (fl.fat_lines) {
+      alias = undefined;
+      obj.nextLoc = gl.getAttribLocation(obj.prog, "aNext");
+      obj.pointLoc = gl.getAttribLocation(obj.prog, "aPoint");
+      obj.aspectLoc = gl.getUniformLocation(obj.prog, "uAspect");
+      obj.lwdLoc = gl.getUniformLocation(obj.prog, "uLwd");
+      // Expand vertices to turn each segment into a pair of triangles
+        
+      	for (pass = 0; pass < obj.passes; pass++) {
+      	  f = obj.f[pass];	
+          oldrows = f.length;
+      	  if (obj.pmode[pass] === "lines") 
+      	    break;
+      	}
+      
+      if (type === "linestrip") 
+        nrows = 4*(oldrows - 1); 
+      else
+        nrows = 2*oldrows;
+      vnew = new Array(nrows);
+      fnew = new Array(1.5*nrows);
+      
+      // We're going to turn each pair of vertices into 4 new ones, with the "next" and "pt" attributes
+      // added.
+      // We do this by copying the originals in the first pass, adding the new attributes, then in a 
+      // second pass add new vertices at the end.
+
+      for (i = 0; i < v.length; i++) {
+        vnew[i] = v[i].concat([0,0,0,0,0]); 
+      }
+
+      nextofs = stride;
+      pointofs = stride + 3;
+      stride = stride + 5;
+            
+      // Now add the extras
+      var ind, k;
+      last = v.length - 1;
+      ind = 0;
+      alias = new Array(f.length);
+      for (i = 0; i < f.length; i++)
+        alias[i] = [];
+      for (i = 0; i < f.length - 1; i++) {
+      	if (type !== "linestrip" && i % 2 === 1)
+      	  continue;
+      	k = ++last;
+      	vnew[k] = vnew[f[i]].slice();
+      	for (j=0; j<3; j++)
+      	  vnew[k][nextofs + j] = vnew[f[i+1]][j];
+      	vnew[k][pointofs] = -1;
+      	vnew[k][pointofs+1] = -1;
+      	fnew[ind] = k;
+      	last++;
+      	vnew[last] = vnew[k].slice();
+      	vnew[last][pointofs] = 1;
+      	fnew[ind+1] = last;
+      	alias[f[i]].push(last-1, last);
+      	last++;
+      	k = last;
+      	vnew[k] = vnew[f[i+1]].slice();
+      	for (j=0; j<3; j++)
+      	  vnew[k][nextofs + j] = vnew[f[i]][j];
+      	vnew[k][pointofs] = -1;
+      	vnew[k][pointofs+1] = 1;
+      	fnew[ind+2] = k;
+      	fnew[ind+3] = fnew[ind+1];
+      	last++;
+      	vnew[last] = vnew[k].slice();
+      	vnew[last][pointofs] = 1;
+      	fnew[ind+4] = last;
+      	fnew[ind+5] = fnew[ind+2];
+      	ind += 6;
+      	alias[f[i+1]].push(last-1, last);
+      }
+      vnew.length = last+1;
+      v = vnew;
+      obj.vertexCount = v.length;
+      if (typeof alias !== "undefined" && typeof obj.alias !== "undefined") {  // Already have aliases from previous section?
+        var oldalias = obj.alias, newalias = Array(obj.alias.length);
+        for (i = 0; i < newalias.length; i++) {
+          newalias[i] = oldalias[i].slice();
+          for (j = 0; j < oldalias[i].length; j++)
+            Array.prototype.push.apply(newalias[i], alias[oldalias[j]]); // pushes each element 
+        }
+        obj.alias = newalias;
+      } else
+        obj.alias = alias;
+      
+      for (pass = 0; pass < obj.passes; pass++)
+      	if (type === "lines" || type === "linestrip" || obj.pmode[pass] === "lines") {
+          obj.f[pass] = fnew;
+        }
+      
+      if (depth_sort) 
+        drawtype = "DYNAMIC_DRAW";
+      else
+        drawtype = "STATIC_DRAW";
+    }
+    
+      for (pass = 0; pass < obj.passes; pass++) {
+        if (obj.vertexCount > 65535) {
+          if (this.index_uint) {
+            obj.f[pass] = new Uint32Array(obj.f[pass]);
+            obj.index_uint = true;
+          } else
+            this.alertOnce("Object has "+obj.vertexCount+" vertices, not supported in this browser.");
+        } else {
+          obj.f[pass] = new Uint16Array(obj.f[pass]);
+          obj.index_uint = false;
+        }
+      }
+    
+    if (stride !== v[0].length) {
+      this.alertOnce("problem in stride calculation");
+    }
+
+    obj.vOffsets = {vofs:0, cofs:cofs, nofs:nofs, radofs:radofs, oofs:oofs, tofs:tofs,
+                    nextofs:nextofs, pointofs:pointofs, stride:stride};
+
+    obj.values = new Float32Array(rglwidgetClass.flatten(v));
+
+    if (!has_spheres && !sprites_3d) {
+      obj.buf = gl.createBuffer();
+      gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
+      gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW); //
+      obj.ibuf = Array(obj.passes);
+      obj.ibuf[0] = gl.createBuffer();
+      gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[0]);
+      gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, obj.f[0], gl[drawtype]);
+      if (fl.is_twosided) {
+      	obj.ibuf[1] = gl.createBuffer();
+      	gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[1]);
+      	gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, obj.f[1], gl[drawtype]);
+      }
+    }
+
+    if (!sprites_3d) {
+      obj.mvMatLoc = gl.getUniformLocation(obj.prog, "mvMatrix");
+      obj.prMatLoc = gl.getUniformLocation(obj.prog, "prMatrix");
+
+      if (fl.fixed_size) {
+        obj.textScaleLoc = gl.getUniformLocation(obj.prog, "textScale");
+      }
+    }
+
+    if (fl.needs_vnormal) {
+      obj.normLoc = gl.getAttribLocation(obj.prog, "aNorm");
+      obj.normMatLoc = gl.getUniformLocation(obj.prog, "normMatrix");
+    }
+
+    if (fl.is_twosided) {
+      obj.frontLoc = gl.getUniformLocation(obj.prog, "front");
+      if (fl.has_normals)
+        obj.invPrMatLoc = gl.getUniformLocation(obj.prog, "invPrMatrix");
+    }
+  };
+    
+    /**
+     * Initialize the DOM object
+     * @param { Object } el - the DOM object
+     * @param { Object } x - the scene data sent by JSON from R
+     */
+    rglwidgetClass.prototype.initialize = function(el, x) {
+      this.textureCanvas = document.createElement("canvas");
+      this.textureCanvas.style.display = "block";
+      this.scene = x;
+      this.normMatrix = new CanvasMatrix4();
+      this.invPrMatrix = new CanvasMatrix4();
+      this.saveMat = {};
+      this.distance = null;
+      this.posLoc = 0;
+      this.colLoc = 1;
+      if (el) {
+        el.rglinstance = this;
+        this.el = el;
+        this.webGLoptions = el.rglinstance.scene.webGLoptions;
+        this.initCanvas();
+      }
+      if (typeof Shiny !== "undefined") {
+        var self = this;
+        Shiny.addCustomMessageHandler("shinyGetPar3d",
+          function(message) {
+            var i, param, 
+                subscene = self.getObj(message.subscene),
+                parameters = [].concat(message.parameters),
+                result = {tag: message.tag, subscene: message.subscene};
+            if (typeof subscene !== "undefined") {
+              for (i = 0; i < parameters.length; i++) {
+                param = parameters[i];
+                result[param] = subscene.par3d[param];
+              }
+            } else {
+              console.log("subscene "+message.subscene+" undefined.");
+            }
+            Shiny.setInputValue("par3d:shinyPar3d", result, {priority: "event"});
+          });
+          
+        Shiny.addCustomMessageHandler("shinySetPar3d",
+          function(message) {
+            var param = message.parameter, 
+                subscene = self.getObj(message.subscene);
+            if (typeof subscene !== "undefined") {
+              subscene.par3d[param] = message.value;
+              subscene.initialized = false;
+              self.drawScene();
+            } else {
+              console.log("subscene "+message.subscene+" undefined.");
+            }
+          });
+          
+        Shiny.addCustomMessageHandler("resetBrush",
+          function(message) {
+            if (message === self.scene.selectionInput) {
+              self.clearBrush(null);
+              self.recordSelection(0);
+            }
+          });
+      }
+    };
+    
+    /**
+     * Restart the WebGL canvas
+     */
+    rglwidgetClass.prototype.restartCanvas = function() {
+      var newcanvas = document.createElement("canvas"),
+          self = this, 
+          labelid = this.el.getAttribute("aria-labelledby");
+      newcanvas.width = this.el.width;
+      newcanvas.height = this.el.height;
+      newcanvas.setAttribute("aria-labelledby", 
+        labelid);
+        
+      if (typeof this.scene.altText !== "undefined") {
+        // We're in Shiny, so alter the label
+        var label = document.getElementById(labelid);
+        if (label)
+          label.innerHTML = this.scene.altText;
+      }
+      newcanvas.addEventListener("webglcontextrestored",
+        this.onContextRestored, false);
+      newcanvas.addEventListener("webglcontextlost",
+        this.onContextLost, false);
+      while (this.el.firstChild) {
+        this.el.removeChild(this.el.firstChild);
+      }
+      this.el.appendChild(newcanvas);
+      this.canvas = newcanvas;
+      if (this.scene.javascript) {
+        /* jshint evil:true */
+        Function('"use strict";' + this.scene.javascript)();
+        /* jshint evil:false */
+      }
+      this.setMouseHandlers();
+      if (this.gl) 
+        Object.keys(this.scene.objects).forEach(function(key){
+          self.getObj(parseInt(key, 10)).texture = undefined; 
+          });
+      this.gl = null;
+    };
+
+    /**
+     * Initialize the WebGL canvas
+     */
+    rglwidgetClass.prototype.initCanvas = function() {
+      this.restartCanvas();
+      var objs = this.scene.objects,
+          self = this;
+          
+      /* These hold context specific data.  In Shiny, they   
+         need to be deleted.  Elsewhere, they don't exist
+         and these are no-ops. */
+         
+      delete this.cube;
+      delete this.sphere;
+      
+      Object.keys(objs).forEach(function(key){
+        self.initSubscene(parseInt(key, 10));
+      });
+
+      this.onContextRestored = function() {
+        self.initGL();
+        self.drawScene();
+      };
+
+      this.onContextLost = function(event) {
+        if (!self.drawing)
+          this.gl = null;
+        event.preventDefault();
+      };
+
+      this.initGL0();
+      this.lazyLoadScene = function() {
+      	if (typeof self.slide === "undefined")
+      	  self.slide = self.getSlide();
+      	if (self.isInBrowserViewport()) {
+      	  if (!self.gl || self.gl.isContextLost())
+      	    self.initGL();
+      	  self.drawScene();
+      	}
+      };
+      window.addEventListener("DOMContentLoaded", this.lazyLoadScene, false);
+      window.addEventListener("load", this.lazyLoadScene, false);
+      window.addEventListener("resize", this.lazyLoadScene, false);
+      window.addEventListener("scroll", this.lazyLoadScene, false);
+      this.slide = this.getSlide();
+      if (this.slide) {
+        if (typeof this.slide.rgl === "undefined")
+          this.slide.rgl = [this];
+        else
+          this.slide.rgl.push(this);
+        if (this.scene.context.rmarkdown) 
+          if (this.scene.context.rmarkdown === "ioslides_presentation") {
+            this.slide.setAttribute("slideenter", "this.rgl.forEach(function(scene) { scene.lazyLoadScene.call(window);})");
+          } else if (this.scene.context.rmarkdown === "slidy_presentation") {
+            // This method would also work in ioslides, but it gets triggered
+            // something like 5 times per slide for every slide change, so
+            // you'd need a quicker function than lazyLoadScene.
+            var MutationObserver = window.MutationObserver || window.WebKitMutationObserver || window.MozMutationObserver,
+            observer = new MutationObserver(function(mutations) {
+              mutations.forEach(function() {
+                self.slide.rgl.forEach(function(scene) { scene.lazyLoadScene.call(window); });});});
+            observer.observe(this.slide, { attributes: true, attributeFilter:["class"] });
+          }
+      }
+    };
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/mouse.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/mouse.src.js
new file mode 100644
index 0000000..ca992f8
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/mouse.src.js
@@ -0,0 +1,569 @@
+    /**
+     * Methods related to mouse handling
+     * @name ___METHODS_FOR_MOUSE_HANDLING___
+     * @memberof rglwidgetClass
+     * @kind function
+     * @instance
+     */
+     
+    rglwidgetClass.prototype.getCursor = function(mode) {
+      switch(mode) {
+        case "none": 
+          return "none";
+        case "trackball":
+        case "xAxis":
+        case "yAxis":
+        case "zAxis":
+        case "polar":
+          return "grab";
+        case "selecting":
+          return "crosshair";
+        case "fov":
+        case "zoom":
+          return "zoom-in";
+        case "user":
+          return "default";
+      }
+      return "dragging";
+    };
+    
+    /**
+     * Set mouse mode for a subscene
+     * @param { string } mode - name of mode
+     * @param { number } button - button number (0 to 4)
+     * @param { number } subscene - subscene id number
+     * @param { number } stayActive - if truthy, don't clear brush
+     */
+    rglwidgetClass.prototype.setMouseMode = function(mode, button, subscene, stayActive) {
+      var sub = this.getObj(subscene),
+          which = ["none", "left", "right", "middle", "wheel"][button];
+      if (!stayActive && sub.par3d.mouseMode[which] === "selecting")
+        this.clearBrush(null);
+      sub.par3d.mouseMode[which] = mode;
+      if (button === 1 || (button === 0 && mode !== "none"))
+        this.canvas.style.cursor = this.getCursor(mode);
+      if (button === 0 && mode !== "none")
+        sub.needsBegin = mode;
+    };
+
+    /**
+     * Compute mouse coordinates relative to current canvas
+     * @returns { Object }
+     * @param { Object } event - event object from mouse click
+     */
+    rglwidgetClass.prototype.relMouseCoords = function(event) {
+      var rect = this.canvas.getBoundingClientRect();
+      return {x:event.clientX-rect.left, y:event.clientY-rect.top};
+    };
+    
+    /**
+     * Send mouse selection to Shiny
+     */
+    rglwidgetClass.prototype.recordSelection = function(subid) {
+      var result = {};
+      if (typeof this.select !== "undefined" && 
+          typeof this.select.state !== "undefined" &&
+          this.select.state !== "inactive") {
+        result = { subscene: subid,
+                   state: this.select.state,
+                   region: this.select.region
+                 };
+        this.setmvMatrix(subid);
+        result.model = this.mvMatrix;
+        this.setprMatrix(subid);
+        result.proj = this.prMatrix;
+        this.getViewport(subid);
+        result.view = this.vp;
+      } else
+        result.state = "inactive";
+      Shiny.setInputValue(this.scene.selectionInput + ":shinyMouse3d", result);
+    }; 
+
+    /**
+     * Set mouse handlers for the scene
+     */
+    rglwidgetClass.prototype.setMouseHandlers = function() {
+      var self = this, activeSubscene, handler,
+          handlers = {}, drag = 0;
+
+      handlers.rotBase = 0;
+
+      self.screenToVector = function(x, y) {
+        var viewport = self.getObj(activeSubscene).par3d.viewport,
+          width = viewport.width*self.canvas.width,
+          height = viewport.height*self.canvas.height,
+          radius = Math.max(width, height)/2.0,
+          cx = width/2.0,
+          cy = height/2.0,
+          px = (x-cx)/radius,
+          py = (y-cy)/radius,
+          plen = Math.sqrt(px*px+py*py);
+        if (plen > 1.e-6) {
+          px = px/plen;
+          py = py/plen;
+        }
+        var angle = (Math.SQRT2 - plen)/Math.SQRT2*Math.PI/2,
+          z = Math.sin(angle),
+          zlen = Math.sqrt(1.0 - z*z);
+        px = px * zlen;
+        py = py * zlen;
+        return [px, py, z];
+      };
+
+      handlers.trackballdown = function(x,y) {
+        var activeSub = self.getObj(activeSubscene),
+            activeModel = self.getObj(self.useid(activeSub.id, "model")),
+            i, l = activeModel.par3d.listeners;
+        handlers.rotBase = self.screenToVector(x, y);
+        self.saveMat = [];
+        for (i = 0; i < l.length; i++) {
+          activeSub = self.getObj(l[i]);
+          activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
+        }
+        self.canvas.style.cursor = "grabbing";
+      };
+
+      handlers.trackballmove = function(x,y) {
+        var rotCurrent = self.screenToVector(x,y),
+            rotBase = handlers.rotBase,
+            dot = rotBase[0]*rotCurrent[0] +
+                  rotBase[1]*rotCurrent[1] +
+                  rotBase[2]*rotCurrent[2],
+            angle = Math.acos( dot/rglwidgetClass.vlen(rotBase)/rglwidgetClass.vlen(rotCurrent) )*180.0/Math.PI,
+            axis = rglwidgetClass.xprod(rotBase, rotCurrent),
+            objects = self.scene.objects,
+            activeSub = self.getObj(activeSubscene),
+            activeModel = self.getObj(self.useid(activeSub.id, "model")),
+            l = activeModel.par3d.listeners,
+            i;
+        if (angle === 0.0)
+          return;    
+        for (i = 0; i < l.length; i++) {
+          activeSub = self.getObj(l[i]);
+          activeSub.par3d.userMatrix.load(objects[l[i]].saveMat);
+          activeSub.par3d.userMatrix.rotate(angle, axis[0], axis[1], axis[2]);
+        }
+        self.drawScene();
+      };
+      handlers.trackballend = 0;
+
+      self.clamp = function(x, lo, hi) {
+      	return Math.max(lo, Math.min(x, hi));
+      };
+
+      self.screenToPolar = function(x,y) {
+        var viewport = self.getObj(activeSubscene).par3d.viewport,
+          width = viewport.width*self.canvas.width,
+          height = viewport.height*self.canvas.height,
+    	  r = Math.min(width, height)/2,
+    	  dx = self.clamp(x - width/2, -r, r),
+    	  dy = self.clamp(y - height/2, -r, r);
+    	  return [Math.asin(dx/r), Math.asin(-dy/r)];
+      };
+
+      handlers.polardown = function(x,y) {
+        var activeSub = self.getObj(activeSubscene),
+            activeModel = self.getObj(self.useid(activeSub.id, "model")),
+            i, l = activeModel.par3d.listeners;
+        handlers.dragBase = self.screenToPolar(x, y);
+        self.saveMat = [];
+        for (i = 0; i < l.length; i++) {
+          activeSub = self.getObj(l[i]);
+          activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
+          activeSub.camBase = [-Math.atan2(activeSub.saveMat.m13, activeSub.saveMat.m11),
+                               Math.atan2(activeSub.saveMat.m32, activeSub.saveMat.m22)];
+        }
+        self.canvas.style.cursor = "grabbing";
+      };
+
+      handlers.polarmove = function(x,y) {
+        var dragCurrent = self.screenToPolar(x,y),
+            activeSub = self.getObj(activeSubscene),
+            activeModel = self.getObj(self.useid(activeSub.id, "model")),
+            objects = self.scene.objects,
+            l = activeModel.par3d.listeners,
+            i, j, changepos = [];
+        for (i = 0; i < l.length; i++) {
+          activeSub = self.getObj(l[i]);
+          for (j=0; j<2; j++)
+            changepos[j] = -(dragCurrent[j] - handlers.dragBase[j]);
+          activeSub.par3d.userMatrix.makeIdentity();
+          activeSub.par3d.userMatrix.rotate(changepos[0]*180/Math.PI, 0,-1,0);
+          activeSub.par3d.userMatrix.multRight(objects[l[i]].saveMat);
+          activeSub.par3d.userMatrix.rotate(changepos[1]*180/Math.PI, -1,0,0);
+        }
+        self.drawScene();
+      };
+      handlers.polarend = 0;
+
+      handlers.axisdown = function(x) {
+        handlers.rotBase = self.screenToVector(x, self.canvas.height/2);
+        var activeSub = self.getObj(activeSubscene),
+            activeModel = self.getObj(self.useid(activeSub.id, "model")),
+            i, l = activeModel.par3d.listeners;
+        for (i = 0; i < l.length; i++) {
+          activeSub = self.getObj(l[i]);
+          activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
+        }
+        self.canvas.style.cursor = "grabbing";
+      };
+
+      handlers.axismove = function(x) {
+        var rotCurrent = self.screenToVector(x, self.canvas.height/2),
+            rotBase = handlers.rotBase,
+            angle = (rotCurrent[0] - rotBase[0])*180/Math.PI,
+            rotMat = new CanvasMatrix4();
+        rotMat.rotate(angle, handlers.axis[0], handlers.axis[1], handlers.axis[2]);
+        var activeSub = self.getObj(activeSubscene),
+            activeModel = self.getObj(self.useid(activeSub.id, "model")),
+            i, l = activeModel.par3d.listeners;
+        for (i = 0; i < l.length; i++) {
+          activeSub = self.getObj(l[i]);
+          activeSub.par3d.userMatrix.load(activeSub.saveMat);
+          activeSub.par3d.userMatrix.multLeft(rotMat);
+        }
+        self.drawScene();
+      };
+      handlers.axisend = 0;
+
+      handlers.y0zoom = 0;
+      handlers.zoomdown = function(x, y) {
+        var activeSub = self.getObj(activeSubscene),
+          activeProjection = self.getObj(self.useid(activeSub.id, "projection")),
+          i, l = activeProjection.par3d.listeners;
+        handlers.y0zoom = y;
+        for (i = 0; i < l.length; i++) {
+          activeSub = self.getObj(l[i]);
+          activeSub.zoom0 = Math.log(activeSub.par3d.zoom);
+        }
+        self.canvas.style.cursor = "zoom-in";
+      };
+      handlers.zoommove = function(x, y) {
+        var activeSub = self.getObj(activeSubscene),
+            activeProjection = self.getObj(self.useid(activeSub.id, "projection")),
+            i, l = activeProjection.par3d.listeners;
+        for (i = 0; i < l.length; i++) {
+          activeSub = self.getObj(l[i]);
+          activeSub.par3d.zoom = Math.exp(activeSub.zoom0 + (y-handlers.y0zoom)/self.canvas.height);
+        }
+        self.drawScene();
+      };
+      handlers.zoomend = 0;
+
+      handlers.y0fov = 0;
+      handlers.fovdown = function(x, y) {
+        handlers.y0fov = y;
+        var activeSub = self.getObj(activeSubscene),
+          activeProjection = self.getObj(self.useid(activeSub.id, "projection")),
+          i, l = activeProjection.par3d.listeners;
+        for (i = 0; i < l.length; i++) {
+          activeSub = self.getObj(l[i]);
+          activeSub.fov0 = activeSub.par3d.FOV;
+        }
+        self.canvas.style.cursor = "zoom-in";
+      };
+      handlers.fovmove = function(x, y) {
+        var activeSub = self.getObj(activeSubscene),
+            activeProjection = self.getObj(self.useid(activeSub.id, "projection")),
+            i, l = activeProjection.par3d.listeners;
+        for (i = 0; i < l.length; i++) {
+          activeSub = self.getObj(l[i]);
+          activeSub.par3d.FOV = Math.max(1, Math.min(179, activeSub.fov0 +
+             180*(y-handlers.y0fov)/self.canvas.height));
+        }
+        self.drawScene();
+      };
+      handlers.fovend = 0;
+      
+      handlers.selectingdown = function(x, y) {
+      	var viewport = self.getObj(activeSubscene).par3d.viewport,
+      	  width = viewport.width*self.canvas.width,
+      	  height = viewport.height*self.canvas.height, 
+          p = {x: 2.0*x/width - 1.0, y: 2.0*y/height - 1.0};
+      	self.select.region = {p1: p, p2: p};
+      	if (self.select.subscene && self.select.subscene !== activeSubscene)
+      	  self.delFromSubscene(self.scene.brushId, self.select.subscene);
+      	self.select.subscene = activeSubscene;
+      	self.addToSubscene(self.scene.brushId, activeSubscene);
+      	self.select.state = "changing";
+      	if (typeof self.scene.brushId !== "undefined")
+      	  self.getObj(self.scene.brushId).initialized = false;
+      	if (typeof self.scene.selectionInput !== "undefined")
+      	  self.recordSelection(activeSubscene); 
+      	self.drawScene();
+      	self.canvas.style.cursor = "crosshair";
+      };
+      
+      handlers.selectingmove = function(x, y) {
+      	var viewport = self.getObj(activeSubscene).par3d.viewport,
+      	  width = viewport.width*self.canvas.width,
+      	  height = viewport.height*self.canvas.height;
+      	if (self.select.state === "inactive") 
+      	  return;
+      	self.select.region.p2 = {x: 2.0*x/width - 1.0, y: 2.0*y/height - 1.0};
+      	if (typeof self.scene.brushId !== "undefined")
+      	  self.getObj(self.scene.brushId).initialized = false;
+      	if (typeof self.scene.selectionInput !== "undefined")
+      	  self.recordSelection(activeSubscene);
+      	self.drawScene();
+      };
+      
+      handlers.selectingend = 0;
+      /* jshint evil:true */
+      handlers.userdown = function(x, y) {
+        var sub = self.getObj(activeSubscene),
+            code = sub.callbacks[drag].begin;
+        if (code) {
+          var fn = Function('"use strict";return (' + code + ')')();
+          fn.call(self, x, y);
+        }
+      };
+      
+      handlers.usermove = function(x, y) {
+        var sub = self.getObj(activeSubscene),
+            code = sub.callbacks[drag].update;
+        if (code) {
+          var fn = Function('"use strict";return (' + code + ')')();
+          fn.call(self, x, y);
+        }
+      };
+      
+      handlers.userend = function() {
+        var sub = self.getObj(activeSubscene),
+            code = sub.callbacks[drag].end;
+        if (code) {
+          var fn = Function('"use strict";return (' + code + ')')();
+          fn.call(self);
+        }
+      };
+
+      self.canvas.onpointerdown = function ( ev ){
+        // pointers and mice differ in capture rules; 
+        // act like a mouse.
+        if (ev.target.hasPointerCapture(ev.pointerId))
+          ev.target.releasePointerCapture(ev.pointerId);
+          
+        if (!ev.which) // Use w3c defns in preference to MS
+        switch (ev.button) {
+          case 0: ev.which = 1; break;
+          case 1:
+          case 4: ev.which = 2; break;
+          case 2: ev.which = 3;
+        }
+        drag = ["none", "left", "middle", "right", "wheel"][ev.which];
+        var coords = self.relMouseCoords(ev);
+        coords.y = self.canvas.height-coords.y;
+        activeSubscene = self.whichSubscene(coords);
+        var sub = self.getObj(activeSubscene), f;
+        handler = sub.par3d.mouseMode[drag];
+        switch (handler) {
+        case "xAxis":
+          handler = "axis";
+          handlers.axis = [1.0, 0.0, 0.0];
+          break;
+        case "yAxis":
+          handler = "axis";
+          handlers.axis = [0.0, 1.0, 0.0];
+          break;
+        case "zAxis":
+          handler = "axis";
+          handlers.axis = [0.0, 0.0, 1.0];
+          break;
+        }
+        f = handlers[handler + "down"];
+        if (f) {
+          coords = self.translateCoords(activeSubscene, coords);
+          f.call(self, coords.x, coords.y);
+          ev.preventDefault();
+        } else
+          console.warn("Mouse handler '" + handler + "' is not implemented.");
+
+      };
+
+      self.canvas.onpointerup = function ( ev ){
+        if ( !drag ) return;
+        var f = handlers[handler + "end"];
+        if (f) {
+          f.call(self);
+          ev.preventDefault();
+        }
+        drag = 0;
+        handlers.onpointermove( ev );
+      };
+
+      self.canvas.onpointerout = self.canvas.onpointerup;
+
+      handlers.onpointermove = function ( ev ) {
+        var coords = self.relMouseCoords(ev), sub, f;
+        coords.y = self.canvas.height - coords.y;
+        if (ev.buttons === 0) {
+          activeSubscene = self.whichSubscene(coords);
+          drag = "none";
+          sub = self.getObj(activeSubscene);
+          handler = sub.par3d.mouseMode.none;
+          if (handler !== "none") {
+            if (sub.needsBegin) {
+              f = handlers[handler + "down"];
+              if (f) {
+                coords = self.translateCoords(activeSubscene, coords);
+                f.call(self, coords.x, coords.y);
+              }
+              sub.needsBegin = 0;
+            }
+            self.canvas.style.cursor = self.getCursor(sub.par3d.mouseMode.none);
+          } else {
+            self.canvas.style.cursor = self.getCursor(sub.par3d.mouseMode.left);  
+            return;
+          }
+        }
+        f = handlers[handler + "move"];
+        if (f) {
+          coords = self.translateCoords(activeSubscene, coords);
+          f.call(self, coords.x, coords.y);
+        }
+      };
+      
+
+      self.canvas.onpointerenter = function() {
+        self.canvas.addEventListener("pointermove",               handlers.onpointermove);
+      };
+      
+      self.canvas.onpointerleave = function() {
+        self.canvas.removeEventListener("pointermove",
+          handlers.onpointermove);
+      };
+
+      handlers.setZoom = function(ds) {
+        var i;
+        if (typeof activeSubscene === "undefined")
+          activeSubscene = self.scene.rootSubscene;
+        var activeSub = self.getObj(activeSubscene),
+            activeProjection = self.getObj(self.useid(activeSub.id, "projection")),
+            l = activeProjection.par3d.listeners;
+
+        for (i = 0; i < l.length; i++) {
+          activeSub = self.getObj(l[i]);
+          activeSub.par3d.zoom *= ds;
+        }
+        self.drawScene();
+      };
+      
+      handlers.pushwheel = function(ev) {
+        ev.deltaY = -ev.deltaY;
+        handlers.pullwheel(ev);
+      };
+      
+      handlers.pullwheel = function(ev) {
+        var del = 1.05;
+        if (ev.shiftKey) del = 1.005;
+        var ds = ev.deltaY < 0 ? del : (1 / del);
+        handlers.setZoom(ds);
+      };
+      
+      handlers.user2wheel = function(ev) {
+        var sub = self.getObj(activeSubscene),
+            code = sub.callbacks.wheel.rotate;
+        if (code) {
+          var fn = Function('"use strict";return (' + code + ')')();
+          /* jshint evil:false */
+          fn.call(self, ev.deltaY < 0 ? 1 : 2);
+        }        
+      };
+        
+      handlers.wheelHandler = function(ev) {
+        var coords = self.relMouseCoords(ev);
+        coords.y = self.canvas.height - coords.y;
+        activeSubscene = self.whichSubscene(coords);
+        var sub = self.getObj(activeSubscene), f,
+            handler = sub.par3d.mouseMode.wheel,
+            evlocal;
+            
+        ev.deltaY = ev.deltaY || ev.detail || ev.deltaX || ev.wheelDelta;
+                      
+        switch(handler) {
+          case "none": break;
+          case "push":
+          case "pull":
+          case "user2":
+            f = handlers[handler + "wheel"];
+            if (f) {
+              evlocal = {};
+              evlocal.deltaY = ev.deltaY;
+              evlocal.shiftKey = ev.shiftKey;
+              evlocal.preventDefault = function() { ev.preventDefault(); };
+              f.call(self, evlocal);
+            }
+            break;
+          default: 
+            evlocal = {};
+            evlocal.preventDefault = function() { ev.preventDefault(); };
+            evlocal.which = 4;
+            evlocal.clientX = self.canvas.width/2;
+            evlocal.clientY = self.canvas.height/2;
+            self.canvas.onpointerdown(evlocal);
+            evlocal.clientX += ev.deltaX;
+            evlocal.clientY += ev.deltaY;
+            handlers.onpointermove(evlocal);
+            self.canvas.onpointerup(evlocal);
+        }
+        ev.preventDefault();
+      };
+      
+      handlers.get_finger_dist = function(ev) {
+        var diffX = ev.touches[0].clientX - ev.touches[1].clientX,
+            diffY = ev.touches[0].clientY - ev.touches[1].clientY;
+        return Math.sqrt(diffX * diffX + diffY * diffY); 
+      };
+      
+      handlers.touchstart = function(ev) {
+        var touch = ev.touches[0],
+          mouseEvent = new MouseEvent("pointerdown",
+            {
+              clientX: touch.clientX,
+              clientY: touch.clientY
+            });
+        ev.preventDefault();
+        if (ev.touches.length === 2) {
+          var coords = self.relMouseCoords(touch);
+          coords.y = self.canvas.height-coords.y;
+          activeSubscene = self.whichSubscene(coords);
+          handlers.finger_dist0 = handlers.get_finger_dist(ev);
+          handlers.zoomdown(coords.x, coords.y);
+        }
+        self.dispatchEvent(mouseEvent);
+      };
+      
+      handlers.touchend = function(ev) {
+        var mouseEvent;
+        ev.preventDefault();
+        if (ev.touches.length === 1) {
+          mouseEvent = new MouseEvent("pointerup", {});
+          self.dispatchEvent(mouseEvent);
+        }
+      };
+      
+      handlers.touchmove = function(ev) {
+        var touch = ev.touches[0],
+          mouseEvent;
+        ev.preventDefault();
+        if (ev.touches.length > 1) {
+          var coords = self.relMouseCoords(touch),
+              new_dist = handlers.get_finger_dist(ev);
+          coords.y = self.canvas.height*Math.log(handlers.finger_dist0/new_dist) + handlers.y0zoom;
+          handlers.zoommove(coords.x, coords.y);
+        } else {
+          mouseEvent = new MouseEvent("pointermove",
+          {
+            clientX: touch.clientX,
+            clientY: touch.clientY
+          });
+          self.dispatchEvent(mouseEvent);
+        }
+      };
+
+      self.canvas.addEventListener("DOMMouseScroll", handlers.wheelHandler, false);
+      self.canvas.addEventListener("mousewheel", handlers.wheelHandler, false);
+      self.canvas.addEventListener("touchstart", handlers.touchstart, {passive: false});
+      self.canvas.addEventListener("touchend", handlers.touchend, {passive: false});
+      self.canvas.addEventListener("touchmove", handlers.touchmove, {passive: false});
+	  };
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/pieces.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/pieces.src.js
new file mode 100644
index 0000000..c6a5724
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/pieces.src.js
@@ -0,0 +1,162 @@
+/**
+ * Methods related to drawing transparent objects
+ * @name ___METHODS_FOR_TRANSPARENCY___
+ * @memberof rglwidgetClass
+ * @kind function
+ * @instance
+
+ * These functions order the centers of displayed objects so they
+ * can be drawn using the painters algorithm, necessary to support
+ * transparency.  
+
+ * Note that objid is not obj.id when drawing spheres.
+ */
+
+/**
+ * Break objects into pieces
+ * @returns { array } Array of pieces
+ */
+    rglwidgetClass.prototype.getPieces = function(context, objid, subid, obj) {
+      var n = obj.centers.length,
+          depth,
+          result = new Array(n),
+          z, w, i,
+          meandepth = 0;
+      context = context.slice();
+          
+      for(i=0; i<n; i++) {
+        z = this.prmvMatrix.m13*obj.centers[i][0] +
+            this.prmvMatrix.m23*obj.centers[i][1] +
+            this.prmvMatrix.m33*obj.centers[i][2] +
+            this.prmvMatrix.m43;
+        w = this.prmvMatrix.m14*obj.centers[i][0] +
+            this.prmvMatrix.m24*obj.centers[i][1] +
+            this.prmvMatrix.m34*obj.centers[i][2] +
+            this.prmvMatrix.m44;
+        depth = z/w;
+        meandepth += depth;
+        result[i] = {context: context, 
+                     objid: objid,
+                     subid: subid,
+                     index: i, 
+                     depth: depth,
+                     meandepth: 0};
+      }
+      meandepth /= n;
+      for (i=0; i<n; i++)
+        result[i].meandepth = meandepth;
+      return result;    
+    };
+    
+    /**
+     * Get pieces from sphere
+     * @returns { object }
+     * @param { array } context - 
+     * @param { numeric } subid - subscene
+     * @param { object } obj - spheres object
+     */
+    rglwidgetClass.prototype.getSpherePieces = function(context, subid, obj)
+    {
+      if (obj.fastTransparency) 
+        if (subid === 0) // Only compute pieces once
+          return this.getPieces(context, obj.id, -1, obj);
+        else
+          return [];
+      else
+        return this.getPieces(context, obj.id, subid, this.sphere);
+    };
+    
+   /**
+     * Get pieces from cube
+     * @returns { object }
+     * @param { array } context - 
+     * @param { numeric } subid - subscene
+     * @param { object } obj - spheres object
+     */
+    rglwidgetClass.prototype.getCubePieces = function(context, obj)
+    {
+      return this.getPieces(context, obj.id, 0, this.cube);
+    };
+    
+    /**
+     * Merge pieces that can be drawn in one call
+     * @returns { object }
+     * @param { array } pieces - The pieces to merge
+     */
+    rglwidgetClass.prototype.mergePieces = function(pieces) {
+      var result = [];
+      if (pieces.length > 0) {
+        var i,
+          thiscontext = pieces[0].context, 
+          thisobjid = pieces[0].objid, 
+          thissubid = pieces[0].subid,
+          indices = [];
+        for (i= 0; i < pieces.length; i++) {
+          if (pieces[i].context !== thiscontext || 
+              pieces[i].objid !== thisobjid ||
+              pieces[i].subid !== thissubid) {
+            result.push({context: thiscontext, objid: thisobjid,
+                         subid: thissubid, indices: indices});
+            thiscontext = pieces[i].context;
+            thisobjid = pieces[i].objid;
+            thissubid = pieces[i].subid;
+            indices = [];
+          }
+          indices.push(pieces[i].index);
+        }
+        result.push({context: thiscontext, objid: thisobjid,
+                                subid: thissubid,
+                                indices: indices});
+      }
+      return result;
+    };
+
+    /**
+     * Sort pieces by depth
+     * @returns { array }
+     * @param { array } pieces - array of pieces 
+     */
+    rglwidgetClass.prototype.sortPieces = function(pieces) {
+      var fastTransparency = this.scene.fastTransparency,
+          compare = function(i,j) {
+          var c1, c2,
+              diff = fastTransparency ? j.meandepth - i.meandepth : j.depth - i.depth;
+              
+        // Check for different object depths     
+        if (diff !== 0.0)
+          return diff;
+          
+        // At this point we are either on the same object or
+        // two different objects that are at the same mean
+        // depth.  Context changes are expensive so arbitrarily
+        // split the two objects.
+        
+        // Check for different objects
+        diff = j.objid - i.objid;
+        if (diff !== 0)
+          return diff;
+          
+        // Check for different nested objects 
+        c1 = j.context.slice();
+        c2 = i.context.slice();
+        diff = c1.length - c2.length; 
+        while (diff === 0 && c1.length > 0) {
+          diff = c1.pop() - c2.pop();
+        }
+        if (diff !== 0)
+          return diff;
+          
+        // Both pieces are in the same object, so
+        // check for different piece depths
+        // If fastTransparency is not set, this is redundant,
+        // but a test would probably be slower.
+        
+        diff = j.depth - i.depth;
+
+        return diff;
+        
+      }, result = [];
+      if (pieces.length) 
+        result = pieces.sort(compare);
+      return result;
+    };
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/pretty.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/pretty.src.js
new file mode 100644
index 0000000..5f9145a
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/pretty.src.js
@@ -0,0 +1,163 @@
+/**
+ * Pretty function from R
+ * @name ___PRETTY_FROM_R___
+ * @memberof rglwidgetClass
+ * @kind function
+ * @instance
+ */
+
+
+/* This file is translated from pretty.c, which was
+ taken from the R sources, r61744 of src/appl/pretty.c,
+ with minimal changes */
+
+/*
+ *  R : A Computer Language for Statistical Data Analysis
+ *  Copyright (C) 1995-2012  The R Core Team
+ *
+ *  This program is free software; you can redistribute it and/or modify
+ *  it under the terms of the GNU General Public License as published by
+ *  the Free Software Foundation; either version 2 of the License, or
+ *  (at your option) any later version.
+ *
+ *  This program is distributed in the hope that it will be useful,
+ *  but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *  GNU General Public License for more details.
+ *
+ *  You should have received a copy of the GNU General Public License
+ *  along with this program; if not, a copy is available at
+ *  http://www.r-project.org/Licenses/
+ */
+
+/**     
+ * Construct pretty values to cover an interval
+ * @param { number } lo - lower end of interval
+ * @param { number } up - upper end of interval
+ * @param { number } ndiv - requested number of divisions
+ * @param { number } min_n - minimum divisions
+ * @param { number } shrink_sml - if too many cells, amount to shrink by
+ * @param { number } high_u_fact - bias in favour of larger units
+ * @param { number } eps_correction - correction to bounds
+ * @param { Boolean } return_bounds - whether to return bounds
+ * @description
+ * Pretty Intervals
+
+ * Constructs m "pretty" values which cover the given interval	*lo <= *up
+ *	m ~= *ndiv + 1	(i.e., ndiv := approximate number of INTERVALS)
+ *
+ * It is not quite clear what should happen for	 *lo = *up;
+ * S itself behaves quite funilly, then.
+ *
+ * In my opinion, a proper 'pretty' should always ensure
+ * *lo < *up, and hence *ndiv >=1 in the result.
+ * However, in S and here, we allow  *lo == *up, and *ndiv = 0.
+ * Note however, that we are NOT COMPATIBLE to S. [Martin M.]
+ *
+ * NEW (0.63.2): ns, nu are double (==> no danger of integer overflow)
+ *
+ * We determine
+ * if the interval (up - lo) is ``small'' [<==>	 i_small == TRUE, below].
+ * For the ``i_small'' situation, there is a parameter  shrink_sml,
+ * the factor by which the "scale" is shrunk.		~~~~~~~~~~
+ * It is advisable to set it to some (smaller) integer power of 2,
+ * since this enables exact floating point division.
+ */
+rglwidgetClass.prototype.R_pretty = function(
+  lo, up, ndiv, min_n, shrink_sml, high_u_fact,
+  eps_correction, return_bounds) {
+  /* From version 0.65 on, we had rounding_eps := 1e-5, before, r..eps = 0
+   * 1e-7 is consistent with seq.default() */
+  var rounding_eps = 1e-7,  h = high_u_fact[0],
+                                           h5 = high_u_fact[1], 
+                                                           dx, cell, unit, base, U, ns, nu, k, i_small,
+                                                           DBL_EPSILON = Number.EPSILON,
+                                                           DBL_MIN = Number.MIN_VALUE,
+                                                           DBL_MAX = Number.MAX_VALUE;
+  
+  dx = up - lo;
+  /* cell := "scale"	here */
+  if (dx === 0 && up === 0) { /*  up == lo == 0	 */
+  cell = 1;
+    i_small = true;
+  } else {
+    cell = Math.max(Math.abs(lo), Math.abs(up));
+    /* U = upper bound on cell/unit */
+    U = (1 + (h5 >= 1.5*h+0.5)) ? 1/(1+h) : 1.5/(1+h5);
+    /* added times 3, as several calculations here */
+    i_small = dx < cell * U * Math.max(1,ndiv) * DBL_EPSILON *3;
+  }
+  
+  /*OLD: cell = FLT_EPSILON+ dx / *ndiv; FLT_EPSILON = 1.192e-07 */
+  if(i_small) {
+    if(cell > 10)
+      cell = 9 + cell/10;
+    cell *= shrink_sml;
+    if(min_n > 1) cell /= min_n;
+  } else {
+    cell = dx;
+    if(ndiv > 1) cell /= ndiv;
+  }
+  
+  if(cell < 20*DBL_MIN) {
+    /* warning(_("Internal(pretty()): very small range.. corrected")); */
+    cell = 20*DBL_MIN;
+  } else if(cell * 10 > DBL_MAX) {
+    /* warning(_("Internal(pretty()): very large range.. corrected")); */
+    cell = 0.1*DBL_MAX;
+  }
+  base = Math.pow(10, Math.floor(Math.log10(cell))); /* base <= cell < 10*base */
+    
+    /* unit : from { 1,2,5,10 } * base
+     *	 such that |u - cell| is small,
+     * favoring larger (if h > 1, else smaller)  u  values;
+     * favor '5' more than '2'  if h5 > h  (default h5 = .5 + 1.5 h) */
+    unit = base;
+    if((U = 2*base)-cell <  h*(cell-unit)) { unit = U;
+      if((U = 5*base)-cell < h5*(cell-unit)) { unit = U;
+        if((U =10*base)-cell <  h*(cell-unit)) unit = U; }}
+    /* Result: c := cell,  u := unit,  b := base
+     *	c in [	1,	      (2+ h) /(1+h) ] b ==> u=  b
+     *	c in ( (2+ h)/(1+h),  (5+2h5)/(1+h5)] b ==> u= 2b
+     *	c in ( (5+2h)/(1+h), (10+5h) /(1+h) ] b ==> u= 5b
+     *	c in ((10+5h)/(1+h),	         10 ) b ==> u=10b
+     *
+     *	===>	2/5 *(2+h)/(1+h)  <=  c/u  <=  (2+h)/(1+h)	*/
+    
+    ns = Math.floor(lo/unit+rounding_eps);
+    nu = Math.ceil (up/unit-rounding_eps);
+    
+    if(eps_correction && (eps_correction > 1 || !i_small)) {
+      if(lo !== 0.0) lo *= (1- DBL_EPSILON); else lo = -DBL_MIN;
+      if(up !== 0.0) up *= (1+ DBL_EPSILON); else up = +DBL_MIN;
+    }
+    
+    while(ns*unit > lo + rounding_eps*unit) ns--;
+    
+    while(nu*unit < up - rounding_eps*unit) nu++;
+    
+    k = Math.floor(0.5 + nu - ns);
+    if(k < min_n) {
+      /* ensure that	nu - ns	 == min_n */
+      
+      k = min_n - k;
+      if(ns >= 0) {
+        nu += k/2;
+        ns -= k/2 + k%2;/* ==> nu-ns = old(nu-ns) + min_n -k = min_n */
+      } else {
+        ns -= k/2;
+        nu += k/2 + k%2;
+      }
+      ndiv = min_n;
+    } else {
+      ndiv = k;
+    }
+    if(return_bounds) { /* if()'s to ensure that result covers original range */
+      if(ns * unit < lo) lo = ns * unit;
+      if(nu * unit > up) up = nu * unit;
+    } else {
+      lo = ns;
+      up = nu;
+    }
+    return {lo:lo, up:up, ndiv:ndiv, unit:unit};
+};
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/projection.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/projection.src.js
new file mode 100644
index 0000000..4fc59c7
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/projection.src.js
@@ -0,0 +1,148 @@
+    /**
+     * Methods related to projections
+     * @name ___METHODS_FOR_PROJECTIONS___
+     * @memberof rglwidgetClass
+     * @kind function
+     * @instance
+     */
+     
+    /**
+     * Get the viewport
+     */
+     
+    rglwidgetClass.prototype.getViewport = function(id) {
+      var vp = this.getObj(id).par3d.viewport,
+         x = vp.x*this.canvas.width,
+         y = vp.y*this.canvas.height,
+         width = vp.width*this.canvas.width,
+         height = vp.height*this.canvas.height;
+       this.vp = {x:x, y:y, width:width, height:height};
+    };
+    
+    /**
+     * Set the gl viewport and scissor test
+     * @param { number } id - id of subscene
+     */
+    rglwidgetClass.prototype.setViewport = function(id) {
+       var gl = this.gl || this.initGL();
+       this.getViewport(id);
+       gl.viewport(this.vp.x, this.vp.y, this.vp.width, this.vp.height);
+       gl.scissor(this.vp.x, this.vp.y, this.vp.width, this.vp.height);
+       gl.enable(gl.SCISSOR_TEST);
+     };
+
+    /**
+     * Set the projection matrix for a subscene
+     * @param { number } id - id of subscene
+     */
+    rglwidgetClass.prototype.setprMatrix = function(id) {
+       var subscene = this.getObj(id),
+          embedding = subscene.embeddings.projection;
+       if (embedding === "replace")
+         this.prMatrix.makeIdentity();
+       else
+         this.setprMatrix(subscene.parent);
+       if (embedding === "inherit")
+         return;
+       // This is based on the Frustum::enclose code from geom.cpp
+       var bbox = subscene.par3d.bbox,
+           scale = subscene.par3d.scale,
+           ranges = [(bbox[1]-bbox[0])*scale[0]/2,
+                     (bbox[3]-bbox[2])*scale[1]/2,
+                     (bbox[5]-bbox[4])*scale[2]/2],
+           radius = Math.sqrt(this.sumsq(ranges))*1.1; // A bit bigger to handle labels
+       if (radius <= 0) radius = 1;
+       var observer = subscene.par3d.observer,
+           distance = observer[2],
+           FOV = subscene.par3d.FOV, ortho = FOV === 0,
+           t = ortho ? 1 : Math.tan(FOV*Math.PI/360),
+           near = distance - radius,
+           far = distance + radius,
+           hlen,
+           aspect = this.vp.width/this.vp.height,
+           z = subscene.par3d.zoom,
+           userProjection = subscene.par3d.userProjection;
+       if (far < 0.0)
+         far = 1.0;
+       if (near < far/100.0)
+         near = far/100.0;
+       this.frustum = {near:near, far:far};
+       hlen = t*near;
+       if (ortho) {
+         if (aspect > 1)
+           this.prMatrix.ortho(-hlen*aspect*z, hlen*aspect*z,
+                          -hlen*z, hlen*z, near, far);
+         else
+           this.prMatrix.ortho(-hlen*z, hlen*z,
+                          -hlen*z/aspect, hlen*z/aspect,
+                          near, far);
+       } else {
+         if (aspect > 1)
+           this.prMatrix.frustum(-hlen*aspect*z, hlen*aspect*z,
+                          -hlen*z, hlen*z, near, far);
+         else
+           this.prMatrix.frustum(-hlen*z, hlen*z,
+                          -hlen*z/aspect, hlen*z/aspect,
+                          near, far);
+       }
+       this.prMatrix.multRight(userProjection);
+     };
+
+    /**
+     * Set the model-view matrix for a subscene
+     * @param { number } id - id of the subscene
+     */
+    rglwidgetClass.prototype.setmvMatrix = function(id) {
+       var observer = this.getObj(id).par3d.observer;
+       this.mvMatrix.makeIdentity();
+       this.setmodelMatrix(id);
+       this.mvMatrix.translate(-observer[0], -observer[1], -observer[2]);
+
+     };
+
+    /**
+     * Set the model matrix for a subscene
+     * @param { number } id - id of the subscene
+     */
+    rglwidgetClass.prototype.setmodelMatrix = function(id) {
+      var subscene = this.getObj(id),
+          embedding = subscene.embeddings.model;
+      if (embedding === "replace") {
+        var bbox = subscene.par3d.bbox,
+            center = [(bbox[0]+bbox[1])/2,
+                      (bbox[2]+bbox[3])/2,
+                      (bbox[4]+bbox[5])/2];
+        this.mvMatrix.translate(-center[0], -center[1], -center[2]);
+      }
+      if (embedding !== "inherit") {
+        var scale = subscene.par3d.scale;
+        this.mvMatrix.scale(scale[0], scale[1], scale[2]);
+        this.mvMatrix.multRight( subscene.par3d.userMatrix );
+      }
+      if (embedding !== "replace")
+        this.setmodelMatrix(subscene.parent);
+     };
+
+    /**
+     * Set the normals matrix for a subscene
+     * @param { number } subsceneid - id of the subscene
+     */
+     rglwidgetClass.prototype.setnormMatrix2 = function() {
+       this.normMatrix = new CanvasMatrix4(this.mvMatrix);
+       this.normMatrix.invert();
+       this.normMatrix.transpose();
+     };
+
+    /**
+     * Set the combined projection-model-view matrix
+     */
+    rglwidgetClass.prototype.setprmvMatrix = function() {
+       this.prmvMatrix = new CanvasMatrix4( this.mvMatrix );
+       this.prmvMatrix.multRight( this.prMatrix );
+     };
+
+    rglwidgetClass.prototype.setInvPrMatrix = function() {
+      this.invPrMatrix = new CanvasMatrix4( this.prMatrix );
+      this.invPrMatrix.invert();
+      this.invPrMatrix.transpose();
+    };
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/rgl.css b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/rgl.css
new file mode 100644
index 0000000..b22aaf6
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/rgl.css
@@ -0,0 +1,21 @@
+.rglPlayer {
+  width: auto;
+  height: auto;
+}
+
+.rglPlayer .rgl-button {
+  width: auto;
+  display: inline-block;
+  font-size: 75%;
+}
+
+.rglPlayer .rgl-slider {
+  display: inline-block;
+  width: 30%;
+}
+
+.rglPlayer .rgl-label {
+  display: inline;
+  padding-left: 6px;
+  padding-right: 6px;
+}
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/rglClass.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/rglClass.src.js
new file mode 100644
index 0000000..475300e
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/rglClass.src.js
@@ -0,0 +1,71 @@
+//// To generate the help pages for this library, use
+
+// jsdoc --template /usr/local/lib/node_modules/foodoc/template *.src.js -R README.md -c JSDoc.json
+
+// To test, set environment variable RGL_DEBUGGING=true
+// before building.
+
+/* globals rglwidgetClass: true */
+
+/**
+ * The class of an rgl widget
+ * @class
+*/
+rglwidgetClass = function() {
+    this.canvas = null;
+    this.userMatrix = new CanvasMatrix4();
+    this.types = [];
+    this.prMatrix = new CanvasMatrix4();
+    this.mvMatrix = new CanvasMatrix4();
+    this.vp = null;
+    this.prmvMatrix = null;
+    this.origs = null;
+    this.gl = null;
+    this.scene = null;
+    this.select = {state: "inactive", subscene: null, region: {p1: {x:0, y:0}, p2: {x:0, y:0}}};
+    this.drawing = false;
+};
+
+    rglwidgetClass.f_is_lit = 1;
+    rglwidgetClass.f_is_smooth = 2;
+    rglwidgetClass.f_has_texture = 4;
+    rglwidgetClass.f_depth_sort = 8;
+    rglwidgetClass.f_fixed_quads = 16;
+    rglwidgetClass.f_is_transparent = 32;
+    rglwidgetClass.f_is_lines = 64;
+    rglwidgetClass.f_sprites_3d = 128;
+    rglwidgetClass.f_is_subscene = 256;
+    rglwidgetClass.f_is_clipplanes = 512;
+    rglwidgetClass.f_fixed_size = 1024;
+    rglwidgetClass.f_is_points = 2048;
+    rglwidgetClass.f_is_twosided = 4096;
+    rglwidgetClass.f_fat_lines = 8192;
+    rglwidgetClass.f_is_brush = 16384;
+    rglwidgetClass.f_has_fog = 32768;
+    rglwidgetClass.f_rotating = 65536;
+    
+    rglwidgetClass.prototype.fogNone = 0;
+    rglwidgetClass.prototype.fogLinear = 1;
+    rglwidgetClass.prototype.fogExp = 2;
+    rglwidgetClass.prototype.fogExp2 = 3;
+
+    /**
+     * Methods related to obsolete approaches.
+     * @name ___OBSOLETE_METHODS___
+     * @memberof rglwidgetClass
+     * @kind function
+     * @instance
+     */
+     
+    /**
+     * Start the writeWebGL scene. This is only used by writeWebGL; rglwidget has
+       no debug element.
+     */
+    rglwidgetClass.prototype.start = function() {
+      if (typeof this.prefix !== "undefined") {
+        this.debugelement = document.getElementById(this.prefix + "debug");
+        this.debug("");
+      }
+      this.drag = 0;
+      this.drawScene();
+    };
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/rglTimer.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/rglTimer.src.js
new file mode 100644
index 0000000..1091556
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/rglTimer.src.js
@@ -0,0 +1,155 @@
+
+/* globals rgltimerClass: true */
+
+/**
+ * The class of an rgl timer object
+ * @class
+*/
+
+/**
+ * Construct an rgltimerClass object
+ * @constructor
+ * @param { function } Tick - action when timer fires
+ * @param { number } startTime - nominal start time in seconds
+ * @param { number } interval - seconds between updates
+ * @param { number } stopTime - nominal stop time in seconds
+ * @param { number } stepSize - nominal step size
+ * @param { number } value - current nominal time
+ * @param { number } rate - nominal units per second
+ * @param { string } loop - "none", "cycle" or "oscillate"
+ * @param { Object } actions - list of actions
+ */
+rgltimerClass = function(Tick, startTime, interval, stopTime, stepSize, value, rate, loop, actions) {
+  this.enabled = false;
+  this.timerId = 0;
+  /** nominal start time in seconds */
+  this.startTime = startTime;   
+  /** current nominal time */      
+  this.value = value;
+  /** seconds between updates */                 
+  this.interval = interval;
+  /** nominal stop time */           
+  this.stopTime = stopTime;
+  /** nominal step size */           
+  this.stepSize = stepSize;
+  /** nominal units per second */           
+  this.rate = rate;
+  /** "none", "cycle", or "oscillate" */                   
+  this.loop = loop;
+  /** real world start time */                   
+  this.realStart = undefined;
+  /** multiplier for fast-forward or reverse */         
+  this.multiplier = 1;                
+  this.actions = actions;
+  this.Tick = Tick;
+};
+
+
+    /**
+     * Methods related to players
+     * @name ___METHODS_FOR_PLAYERS___
+     * @memberof rgltimerClass
+     * @kind function
+     * @instance
+     */
+
+  /**
+   * Start playing
+   * @memberof rgltimerClass
+   */
+  rgltimerClass.prototype.play = function() {
+    if (this.enabled) {
+      this.enabled = false;
+      window.clearInterval(this.timerId);
+      this.timerId = 0;
+      return;
+    }
+    var tick = function(self) {
+      var now = new Date();
+      self.value = self.multiplier*self.rate*(now - self.realStart)/1000 + self.startTime;
+      self.forceToRange();
+      if (typeof self.Tick !== "undefined") {
+        self.Tick(self.value);
+      }
+
+    };
+    this.realStart = new Date() - 1000*(this.value - this.startTime)/this.rate/this.multiplier;
+    this.timerId = window.setInterval(tick, 1000*this.interval, this);
+    this.enabled = true;
+  };
+
+  /**
+   * Force value into legal range
+   */
+  rgltimerClass.prototype.forceToRange = function() {
+    if (this.value > this.stopTime + this.stepSize/2 || this.value < this.startTime - this.stepSize/2) {
+      if (!this.loop) {
+        this.reset();
+      } else {
+        var cycle = this.stopTime - this.startTime + this.stepSize,
+            newval = (this.value - this.startTime) % cycle + this.startTime;
+        if (newval < this.startTime) {
+          newval += cycle;
+        }
+        this.realStart += (this.value - newval)*1000/this.multiplier/this.rate;
+        this.value = newval;
+      }
+    }
+  };
+
+  /**
+   * Reset to start values
+   */
+  rgltimerClass.prototype.reset = function() {
+    this.value = this.startTime;
+    this.newmultiplier(1);
+    if (typeof this.Tick !== "undefined") {
+        this.Tick(this.value);
+    }
+    if (this.enabled)
+      this.play();  /* really pause... */
+    if (typeof this.PlayButton !== "undefined")
+      this.PlayButton.value = "Play";
+  };
+
+  /**
+   * Increase the multiplier to play faster
+   */
+  rgltimerClass.prototype.faster = function() {
+    this.newmultiplier(Math.SQRT2*this.multiplier);
+  };
+
+  /**
+   * Decrease the multiplier to play slower
+   */
+  rgltimerClass.prototype.slower = function() {
+    this.newmultiplier(this.multiplier/Math.SQRT2);
+  };
+
+  /**
+   * Change sign of multiplier to reverse direction
+   */
+  rgltimerClass.prototype.reverse = function() {
+    this.newmultiplier(-this.multiplier);
+  };
+
+  /**
+   * Set multiplier for play speed
+   * @param { number } newmult - new value
+   */
+  rgltimerClass.prototype.newmultiplier = function(newmult) {
+    if (newmult !== this.multiplier) {
+      this.realStart += 1000*(this.value - this.startTime)/this.rate*(1/this.multiplier - 1/newmult);
+      this.multiplier = newmult;
+    }
+  };
+
+  /**
+   * Take one step
+   */
+  rgltimerClass.prototype.step = function() {
+    this.value += this.rate*this.multiplier;
+    this.forceToRange();
+    if (typeof this.Tick !== "undefined")
+      this.Tick(this.value);
+  };
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/selection.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/selection.src.js
new file mode 100644
index 0000000..a45e09e
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/selection.src.js
@@ -0,0 +1,129 @@
+    /**
+     * Methods related to selection
+     * @name ___METHODS_FOR_SELECTION___
+     * @memberof rglwidgetClass
+     * @kind function
+     * @instance
+     */
+     
+    /**
+     * Respond to brush change
+     */
+    rglwidgetClass.prototype.selectionChanged = function() {
+      var i, j, k, id, subid = this.select.subscene, subscene,
+          objids, obj,
+          p1 = this.select.region.p1, p2 = this.select.region.p2,
+          filter, selection = [], handle, keys, xmin, x, xmax, ymin, y, ymax, z, v,
+          someHidden;
+      if (!subid)
+        return;
+      subscene = this.getObj(subid);
+      objids = subscene.objects;
+      filter = this.scene.crosstalk.filter;
+      this.setmvMatrix(subid);
+      this.setprMatrix(subid);
+      this.setprmvMatrix();
+      xmin = Math.min(p1.x, p2.x);
+      xmax = Math.max(p1.x, p2.x);
+      ymin = Math.min(p1.y, p2.y);
+      ymax = Math.max(p1.y, p2.y);
+      for (i = 0; i < objids.length; i++) {
+      	id = objids[i];
+      	j = this.scene.crosstalk.id.indexOf(id);
+      	if (j >= 0) {
+      	  keys = this.scene.crosstalk.key[j];
+      	  obj = this.getObj(id);
+      	  someHidden = false;
+      	  for (k = 0; k < keys.length; k++) {
+      	    if (filter && filter.indexOf(keys[k]) < 0) {
+      	      someHidden = true;
+      	      continue;
+      	    }
+      	    v = [].concat(obj.vertices[k]).concat(1.0);
+            v = rglwidgetClass.multVM(v, this.prmvMatrix);
+            x = v[0]/v[3];
+            y = v[1]/v[3];
+            z = v[2]/v[3];
+            if (xmin <= x && x <= xmax && ymin <= y && y <= ymax && -1.0 <= z && z <= 1.0) {
+              selection.push(keys[k]);
+            } else
+              someHidden = true;
+      	  }
+      	  obj.someHidden = someHidden && (filter || selection.length);
+      	  obj.initialized = false;
+      	  /* Who should we notify?  Only shared data in the current subscene, or everyone? */
+      	  if (!this.equalArrays(selection, this.scene.crosstalk.selection)) {
+      	    handle = this.scene.crosstalk.sel_handle[j];
+      	    handle.set(selection, {rglSubsceneId: this.select.subscene});
+      	  }
+      	}
+      }
+    };
+    
+    /**
+     * Respond to selection or filter change from crosstalk
+     * @param { Object } event - crosstalk event
+     * @param { boolean } filter - filter or selection?
+     */
+    rglwidgetClass.prototype.selection = function(event, filter) {
+      	var i, j, ids, obj, keys, crosstalk = this.scene.crosstalk,
+      	    selection, someHidden;
+
+      	// Record the message and find out if this event makes some objects have mixed values:
+      	
+      	crosstalk = this.scene.crosstalk;
+      	
+      	if (filter) {
+      	  filter = crosstalk.filter = event.value;
+      	  selection = crosstalk.selection;
+      	} else {  
+          selection = crosstalk.selection = event.value;
+          filter = crosstalk.filter;
+      	}
+        ids = crosstalk.id;
+        for (i = 0; i < ids.length ; i++) {
+          obj = this.getObj(ids[i]);
+          obj.initialized = false;
+          keys = crosstalk.key[i];
+          someHidden = false;
+          for (j = 0; j < keys.length && !someHidden; j++) {
+            if ((filter && filter.indexOf(keys[j]) < 0) ||
+                (selection.length && selection.indexOf(keys[j]) < 0))
+                someHidden = true;
+          }
+          obj.someHidden = someHidden;
+        }
+        this.drawScene();
+    };
+    
+    /**
+     * Clear the selection brush
+     * @param { number } except - Subscene that should ignore this request
+     */
+    rglwidgetClass.prototype.clearBrush = function(except) {
+      if (this.select.subscene !== except) {
+        this.select.region = {p1: {x:Infinity, y:Infinity}, 
+                              p2: {x:Infinity, y:Infinity}};
+        this.selectionChanged();
+        this.select.state = "inactive";
+        this.delFromSubscene(this.scene.brushId, this.select.subscene);
+      }
+      this.drawScene();
+    };
+    
+    /**
+     * Set the vertices in the selection box object
+     */
+    rglwidgetClass.prototype.initSelection = function(id) {
+      if (typeof this.select.region === "undefined")
+        return;
+      var obj = this.getObj(id),
+          p1 = this.select.region.p1,
+          p2 = this.select.region.p2;
+          
+      obj.vertices = [[p1.x, p1.y, 0.0],
+                      [p2.x, p1.y, 0.0],
+                      [p2.x, p2.y, 0.0],
+                      [p1.x, p2.y, 0.0],
+                      [p1.x, p1.y, 0.0]];
+    };
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/shaders.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/shaders.src.js
new file mode 100644
index 0000000..e646678
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/shaders.src.js
@@ -0,0 +1,183 @@
+    /**
+     * Methods related to shaders
+     * @name ___METHODS_FOR_SHADERS___
+     * @memberof rglwidgetClass
+     * @kind function
+     * @instance
+     */
+     
+    /**
+     * Get flags that will end up as shader defines.
+     * Static method so it can be called from R
+     */
+    rglwidgetClass.getDefFlags = function(flags, type, normals, round_points) {
+      var f = {};
+      f.fat_lines = rglwidgetClass.isSet(flags, rglwidgetClass.f_fat_lines);
+      f.fixed_quads = rglwidgetClass.isSet(flags, rglwidgetClass.f_fixed_quads);
+      f.fixed_size = rglwidgetClass.isSet(flags, rglwidgetClass.f_fixed_size);
+      f.has_fog = rglwidgetClass.isSet(flags, rglwidgetClass.f_has_fog);
+      f.has_normals = (typeof normals !== "undefined") ||
+                        type === "spheres";
+      f.has_texture = rglwidgetClass.isSet(flags, rglwidgetClass.f_has_texture);
+      f.is_brush = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_brush);
+      f.is_lines = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_lines);
+      f.is_lit = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_lit);
+      f.is_points = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_points);
+      f.is_transparent = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_transparent);
+      f.is_twosided = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_twosided);
+      f.needs_vnormal = !rglwidgetClass.isSet(flags, rglwidgetClass.f_sprites_3d) &&
+        (f.is_lit && !f.fixed_quads && !f.is_brush) || (f.is_twosided && f.has_normals);
+      f.rotating = rglwidgetClass.isSet(flags, rglwidgetClass.f_rotating);
+      f.round_points = round_points;
+      return f;
+    };
+     
+    
+    /**
+     * Generate the defines for the shader code for an object.
+     * 
+     * This is a static method so it can be called from R.
+     * 
+     * @returns {string}
+     * @param  id - id of object
+     * @param  type - type of object
+     * @param  flags - object flags
+     * @param  nclipplanes - number of clipping planes in scene 
+     *         (may not all be active)
+     * @param  nlights - number of lights in scene (ditto)
+     * @param  normals - normals for object
+     * @param  pointSize - point size for object 
+     * @param  textype - texture type for object 
+     * @param  antialias - use antialiasing?
+     */
+    rglwidgetClass.getDefines = function(id, type, flags,
+      nclipplanes, nlights, normals, pointSize, textype,
+      texmode, texenvmap, antialias, fl) {
+      var
+        title, defines;
+      
+      if (typeof fl === "undefined")
+        fl = rglwidgetClass.getDefFlags(flags, type, normals, antialias);
+        
+      title = "  /* ****** "+type+" object "+id+" shader ****** */\n";
+      
+      defines = "#define NCLIPPLANES " + nclipplanes + "\n"+
+                "#define NLIGHTS " + nlights + "\n";
+      
+      if (fl.fat_lines)
+        defines = defines + "#define FAT_LINES 1\n";
+      
+      if (fl.fixed_quads)
+        defines = defines + "#define FIXED_QUADS 1\n";
+
+      if (fl.fixed_size)
+        defines = defines + "#define FIXED_SIZE 1\n";
+
+      if (fl.has_fog)
+        defines = defines + "#define HAS_FOG 1\n";
+        
+      if (fl.has_normals)
+        defines = defines + "#define HAS_NORMALS 1\n";
+        
+      if (fl.has_texture) {
+        defines = defines + "#define HAS_TEXTURE 1\n";
+        defines = defines + "#define TEXTURE_" + textype + "\n";
+        defines = defines + "#define TEXMODE_" + texmode + "\n";
+        if (texenvmap)
+          defines = defines + "#define USE_ENVMAP 1\n";
+      }
+      
+      if (fl.is_brush)
+        defines = defines + "#define IS_BRUSH 1\n";  
+
+      if (type === "linestrip")
+        defines = defines + "#define IS_LINESTRIP 1\n";         
+
+      if (fl.is_lit)
+        defines = defines + "#define IS_LIT 1\n"; 
+      
+      if (fl.is_points) {
+        defines = defines + "#define IS_POINTS 1\n";
+        defines = defines + "#define POINTSIZE " + Number.parseFloat(pointSize).toFixed(1) + "\n";
+      }
+        
+      if (type === "sprites")
+        defines = defines + "#define IS_SPRITES 1\n";
+        
+      if (type === "text")
+        defines = defines + "#define IS_TEXT 1\n";
+
+      if (fl.is_transparent)
+        defines = defines + "#define IS_TRANSPARENT 1\n"; 
+        
+      if (fl.is_twosided)
+        defines = defines + "#define IS_TWOSIDED 1\n";
+        
+      if (fl.needs_vnormal)
+        defines = defines + "#define NEEDS_VNORMAL 1\n";
+
+      if (fl.rotating)
+        defines = defines + "#define ROTATING 1\n";
+        
+      if (fl.round_points)        
+        defines = defines + "#define ROUND_POINTS 1\n";   
+
+      // console.log(result);
+      return title + defines;
+    };
+
+    /**
+     * Create code for vertex and fragment shaders
+     * @returns {Object}
+     * @param { number } shaderType - gl code for shader type
+     * @param { string } code - code for the shader
+     */
+    rglwidgetClass.prototype.getShaders = function(obj) {
+      var header, 
+        vertex = obj.userVertexShader, 
+        fragment = obj.userFragmentShader;
+      
+      header = rglwidgetClass.getDefines(
+        obj.id, obj.type, obj.flags, 
+        this.countClipplanes(), this.countLights(), 
+        obj.normals, 
+        this.getMaterial(obj, "size"), 
+        this.getMaterial(obj, "textype"),
+        this.getMaterial(obj, "texmode"),
+        this.getMaterial(obj, "texenvmap"),
+        this.getMaterial(obj, "point_antialias"),
+        obj.defFlags
+      );
+
+      if (typeof vertex === "undefined")
+        vertex = rglwidgetClass.rgl_vertex_shader();
+        
+      if (typeof fragment === "undefined") 
+        fragment = rglwidgetClass.rgl_fragment_shader();
+
+//      console.log("vertex:");
+//      console.log(header + vertex);
+//      console.log("fragment:");
+//      console.log(header + fragment);
+      
+      return {vertex: header + vertex,
+              fragment: header + fragment};
+    };
+    
+    
+    /**
+     * Call gl functions to create and compile shader from code
+     * @returns {Object}
+     * @param { number } shaderType - gl code for shader type
+     * @param { string } code - code for the shader
+     */
+    rglwidgetClass.prototype.getShader = function(shaderType, code) {
+        var gl = this.gl, shader;
+        shader = gl.createShader(shaderType);
+        gl.shaderSource(shader, code);
+        gl.compileShader(shader);
+        if (!gl.getShaderParameter(shader, gl.COMPILE_STATUS) && !gl.isContextLost())
+            alert(gl.getShaderInfoLog(shader));
+        return shader;
+    };
+
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/shadersrc.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/shadersrc.src.js
new file mode 100644
index 0000000..ccf93d4
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/shadersrc.src.js
@@ -0,0 +1,455 @@
+rglwidgetClass.rgl_vertex_shader = function() {
+return  "#line 2 1\n"+
+"// File 1 is the vertex shader\n"+
+"#ifdef GL_ES\n"+
+"#ifdef GL_FRAGMENT_PRECISION_HIGH\n"+
+"precision highp float;\n"+
+"#else\n"+
+"precision mediump float;\n"+
+"#endif\n"+
+"#endif\n"+
+"\n"+
+"attribute vec3 aPos;\n"+
+"attribute vec4 aCol;\n"+
+"uniform mat4 mvMatrix;\n"+
+"uniform mat4 prMatrix;\n"+
+"varying vec4 vCol;\n"+
+"varying vec4 vPosition;\n"+
+"\n"+
+"#ifdef NEEDS_VNORMAL\n"+
+"attribute vec3 aNorm;\n"+
+"uniform mat4 normMatrix;\n"+
+"varying vec4 vNormal;\n"+
+"#endif\n"+
+"\n"+
+"#if defined(HAS_TEXTURE) || defined (IS_TEXT)\n"+
+"attribute vec2 aTexcoord;\n"+
+"varying vec2 vTexcoord;\n"+
+"#endif\n"+
+"\n"+
+"#ifdef FIXED_SIZE\n"+
+"uniform vec3 textScale;\n"+
+"#endif\n"+
+"\n"+
+"#ifdef FIXED_QUADS\n"+
+"attribute vec3 aOfs;\n"+
+"#endif\n"+
+"\n"+
+"#ifdef IS_TWOSIDED\n"+
+"#ifdef HAS_NORMALS\n"+
+"varying float normz;\n"+
+"uniform mat4 invPrMatrix;\n"+
+"#else\n"+
+"attribute vec3 aPos1;\n"+
+"attribute vec3 aPos2;\n"+
+"varying float normz;\n"+
+"#endif\n"+
+"#endif // IS_TWOSIDED\n"+
+"\n"+
+"#ifdef FAT_LINES\n"+
+"attribute vec3 aNext;\n"+
+"attribute vec2 aPoint;\n"+
+"varying vec2 vPoint;\n"+
+"varying float vLength;\n"+
+"uniform float uAspect;\n"+
+"uniform float uLwd;\n"+
+"#endif\n"+
+"\n"+
+"#ifdef USE_ENVMAP\n"+
+"varying vec3 vReflection;\n"+
+"#endif\n"+
+"\n"+
+"void main(void) {\n"+
+"  \n"+
+"#ifndef IS_BRUSH\n"+
+"#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n"+
+"  vPosition = mvMatrix * vec4(aPos, 1.);\n"+
+"#endif\n"+
+"  \n"+
+"#ifndef FIXED_QUADS\n"+
+"  gl_Position = prMatrix * vPosition;\n"+
+"#endif\n"+
+"#endif // !IS_BRUSH\n"+
+"  \n"+
+"#ifdef IS_POINTS\n"+
+"  gl_PointSize = POINTSIZE;\n"+
+"#endif\n"+
+"  \n"+
+"  vCol = aCol;\n"+
+"  \n"+
+"// USE_ENVMAP implies NEEDS_VNORMAL\n"+
+"\n"+
+"#ifdef NEEDS_VNORMAL\n"+
+"  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n"+
+"#endif\n"+
+"\n"+
+"#ifdef USE_ENVMAP\n"+
+"  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n"+
+"                        normalize(vNormal.xyz/vNormal.w)));\n"+
+"#endif\n"+
+"  \n"+
+"#ifdef IS_TWOSIDED\n"+
+"#ifdef HAS_NORMALS\n"+
+"  /* normz should be calculated *after* projection */\n"+
+"  normz = (invPrMatrix*vNormal).z;\n"+
+"#else\n"+
+"  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n"+
+"  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n"+
+"  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n"+
+"  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n"+
+"  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n"+
+"#endif\n"+
+"#endif // IS_TWOSIDED\n"+
+"  \n"+
+"#ifdef NEEDS_VNORMAL\n"+
+"  vNormal = vec4(normalize(vNormal.xyz), 1);\n"+
+"#endif\n"+
+"  \n"+
+"#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n"+
+"  vTexcoord = aTexcoord;\n"+
+"#endif\n"+
+"  \n"+
+"#if defined(FIXED_SIZE) && !defined(ROTATING)\n"+
+"  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n"+
+"  pos = pos/pos.w;\n"+
+"  gl_Position = pos + vec4(aOfs*textScale, 0.);\n"+
+"#endif\n"+
+"  \n"+
+"#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n"+
+"  vec4 pos = mvMatrix * vec4(aPos, 1.);\n"+
+"  pos = pos/pos.w + vec4(aOfs,  0.);\n"+
+"  gl_Position = prMatrix*pos;\n"+
+"#endif\n"+
+"  \n"+
+"#ifdef FAT_LINES\n"+
+"  /* This code was inspired by Matt Deslauriers' code in \n"+
+"   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n"+
+"  vec2 aspectVec = vec2(uAspect, 1.0);\n"+
+"  mat4 projViewModel = prMatrix * mvMatrix;\n"+
+"  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n"+
+"  currentProjected = currentProjected/currentProjected.w;\n"+
+"  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n"+
+"  vec2 currentScreen = currentProjected.xy * aspectVec;\n"+
+"  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n"+
+"  float len = uLwd;\n"+
+"  vec2 dir = vec2(1.0, 0.0);\n"+
+"  vPoint = aPoint;\n"+
+"  vLength = length(nextScreen - currentScreen)/2.0;\n"+
+"  vLength = vLength/(vLength + len);\n"+
+"  if (vLength > 0.0) {\n"+
+"    dir = normalize(nextScreen - currentScreen);\n"+
+"  }\n"+
+"  vec2 normal = vec2(-dir.y, dir.x);\n"+
+"  dir.x /= uAspect;\n"+
+"  normal.x /= uAspect;\n"+
+"  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n"+
+"  gl_Position = currentProjected + offset;\n"+
+"#endif\n"+
+"  \n"+
+"#ifdef IS_BRUSH\n"+
+"  gl_Position = vec4(aPos, 1.);\n"+
+"#endif\n"+
+"}\n" ;};
+rglwidgetClass.rgl_fragment_shader = function() {
+return  "#line 2 2\n"+
+"// File 2 is the fragment shader\n"+
+"#ifdef GL_ES\n"+
+"#ifdef GL_FRAGMENT_PRECISION_HIGH\n"+
+"precision highp float;\n"+
+"#else\n"+
+"precision mediump float;\n"+
+"#endif\n"+
+"#endif\n"+
+"varying vec4 vCol; // carries alpha\n"+
+"varying vec4 vPosition;\n"+
+"#if defined(HAS_TEXTURE) || defined (IS_TEXT)\n"+
+"varying vec2 vTexcoord;\n"+
+"uniform sampler2D uSampler;\n"+
+"#endif\n"+
+"\n"+
+"#ifdef HAS_FOG\n"+
+"uniform int uFogMode;\n"+
+"uniform vec3 uFogColor;\n"+
+"uniform vec4 uFogParms;\n"+
+"#endif\n"+
+"\n"+
+"#if defined(IS_LIT) && !defined(FIXED_QUADS)\n"+
+"varying vec4 vNormal;\n"+
+"#endif\n"+
+"\n"+
+"#if NCLIPPLANES > 0\n"+
+"uniform vec4 vClipplane[NCLIPPLANES];\n"+
+"#endif\n"+
+"\n"+
+"#if NLIGHTS > 0\n"+
+"uniform mat4 mvMatrix;\n"+
+"#endif\n"+
+"\n"+
+"#ifdef IS_LIT\n"+
+"uniform vec3 emission;\n"+
+"uniform float shininess;\n"+
+"#if NLIGHTS > 0\n"+
+"uniform vec3 ambient[NLIGHTS];\n"+
+"uniform vec3 specular[NLIGHTS]; // light*material\n"+
+"uniform vec3 diffuse[NLIGHTS];\n"+
+"uniform vec3 lightDir[NLIGHTS];\n"+
+"uniform bool viewpoint[NLIGHTS];\n"+
+"uniform bool finite[NLIGHTS];\n"+
+"#endif\n"+
+"#endif // IS_LIT\n"+
+"\n"+
+"#ifdef IS_TWOSIDED\n"+
+"uniform bool front;\n"+
+"varying float normz;\n"+
+"#endif\n"+
+"\n"+
+"#ifdef FAT_LINES\n"+
+"varying vec2 vPoint;\n"+
+"varying float vLength;\n"+
+"#endif\n"+
+"\n"+
+"#ifdef USE_ENVMAP\n"+
+"varying vec3 vReflection;\n"+
+"#endif\n"+
+"\n"+
+"void main(void) {\n"+
+"  vec4 fragColor;\n"+
+"#ifdef FAT_LINES\n"+
+"  vec2 point = vPoint;\n"+
+"  bool neg = point.y < 0.0;\n"+
+"  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n"+
+"                 -(point.y - vLength)/(1.0 - vLength);\n"+
+"#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n"+
+"  if (neg && length(point) <= 1.0) discard;\n"+
+"#endif\n"+
+"  point.y = min(point.y, 0.0);\n"+
+"  if (length(point) > 1.0) discard;\n"+
+"#endif // FAT_LINES\n"+
+"  \n"+
+"#ifdef ROUND_POINTS\n"+
+"  vec2 coord = gl_PointCoord - vec2(0.5);\n"+
+"  if (length(coord) > 0.5) discard;\n"+
+"#endif\n"+
+"  \n"+
+"#if NCLIPPLANES > 0\n"+
+"  for (int i = 0; i < NCLIPPLANES; i++)\n"+
+"    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n"+
+"#endif\n"+
+"    \n"+
+"#ifdef FIXED_QUADS\n"+
+"    vec3 n = vec3(0., 0., 1.);\n"+
+"#elif defined(IS_LIT)\n"+
+"    vec3 n = normalize(vNormal.xyz);\n"+
+"#endif\n"+
+"    \n"+
+"#ifdef IS_TWOSIDED\n"+
+"    if ((normz <= 0.) != front) discard;\n"+
+"#endif\n"+
+"\n"+
+"#ifdef IS_LIT\n"+
+"    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n"+
+"    vec3 lightdir;\n"+
+"    vec4 colDiff;\n"+
+"    vec3 halfVec;\n"+
+"    vec4 lighteffect = vec4(emission, 0.);\n"+
+"    vec3 col;\n"+
+"    float nDotL;\n"+
+"#ifdef FIXED_QUADS\n"+
+"    n = -faceforward(n, n, eye);\n"+
+"#endif\n"+
+"    \n"+
+"#if NLIGHTS > 0\n"+
+"    // Simulate two-sided lighting\n"+
+"    if (n.z < 0.0)\n"+
+"      n = -n;\n"+
+"    for (int i=0;i<NLIGHTS;i++) {\n"+
+"      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n"+
+"      lightdir = lightDir[i];\n"+
+"      if (!viewpoint[i]) {\n"+
+"        if (finite[i]) {\n"+
+"          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n"+
+"        } else {\n"+
+"          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n"+
+"        }\n"+
+"      }\n"+
+"      if (!finite[i]) {\n"+
+"        halfVec = normalize(lightdir + eye);\n"+
+"      } else {\n"+
+"        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n"+
+"        halfVec = normalize(lightdir + eye);\n"+
+"      }\n"+
+"      col = ambient[i];\n"+
+"      nDotL = dot(n, lightdir);\n"+
+"      col = col + max(nDotL, 0.) * colDiff.rgb;\n"+
+"      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n"+
+"      lighteffect = lighteffect + vec4(col, colDiff.a);\n"+
+"    }\n"+
+"#endif\n"+
+"    \n"+
+"#else // not IS_LIT\n"+
+"    vec4 colDiff = vCol;\n"+
+"    vec4 lighteffect = colDiff;\n"+
+"#endif\n"+
+"    \n"+
+"#ifdef IS_TEXT\n"+
+"    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n"+
+"#endif\n"+
+"    \n"+
+"#ifdef HAS_TEXTURE\n"+
+"\n"+
+"// These calculations use the definitions from \n"+
+"// https://docs.gl/gl3/glTexEnv\n"+
+"\n"+
+"#ifdef USE_ENVMAP\n"+
+"    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n"+
+"    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n"+
+"#else\n"+
+"    vec4 textureColor = texture2D(uSampler, vTexcoord);\n"+
+"#endif\n"+
+"\n"+
+"#ifdef TEXTURE_rgb\n"+
+"\n"+
+"#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n"+
+"    textureColor = vec4(textureColor.rgb, lighteffect.a);\n"+
+"#endif \n"+
+"\n"+
+"#ifdef TEXMODE_modulate\n"+
+"    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n"+
+"#endif\n"+
+"\n"+
+"#ifdef TEXMODE_blend\n"+
+"    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n"+
+"#endif\n"+
+"\n"+
+"#ifdef TEXMODE_add\n"+
+"    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n"+
+"#endif\n"+
+"\n"+
+"#endif //TEXTURE_rgb\n"+
+"        \n"+
+"#ifdef TEXTURE_rgba\n"+
+"\n"+
+"#ifdef TEXMODE_replace\n"+
+"// already done\n"+
+"#endif \n"+
+"\n"+
+"#ifdef TEXMODE_modulate\n"+
+"    textureColor = lighteffect*textureColor;\n"+
+"#endif\n"+
+"\n"+
+"#ifdef TEXMODE_decal\n"+
+"    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n"+
+"                     textureColor.a*textureColor.rgb, \n"+
+"                     lighteffect.a);\n"+
+"#endif\n"+
+"\n"+
+"#ifdef TEXMODE_blend\n"+
+"    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n"+
+"                    lighteffect.a*textureColor.a);\n"+
+"#endif\n"+
+"\n"+
+"#ifdef TEXMODE_add\n"+
+"    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n"+
+"                    lighteffect.a*textureColor.a);\n"+
+"#endif\n"+
+"    \n"+
+"#endif //TEXTURE_rgba\n"+
+"    \n"+
+"#ifdef TEXTURE_alpha\n"+
+"    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n"+
+"\n"+
+"#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n"+
+"    textureColor = vec4(lighteffect.rgb, luminance);\n"+
+"#endif \n"+
+"\n"+
+"#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n"+
+"    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n"+
+"#endif\n"+
+" \n"+
+"#endif // TEXTURE_alpha\n"+
+"    \n"+
+"// The TEXTURE_luminance values are not from that reference    \n"+
+"#ifdef TEXTURE_luminance\n"+
+"    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n"+
+"\n"+
+"#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n"+
+"    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n"+
+"#endif \n"+
+"\n"+
+"#ifdef TEXMODE_modulate\n"+
+"    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n"+
+"#endif\n"+
+"\n"+
+"#ifdef TEXMODE_blend\n"+
+"    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n"+
+"                        lighteffect.a);\n"+
+"#endif\n"+
+"\n"+
+"#ifdef TEXMODE_add\n"+
+"    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n"+
+"#endif\n"+
+"\n"+
+"#endif // TEXTURE_luminance\n"+
+" \n"+
+"    \n"+
+"#ifdef TEXTURE_luminance_alpha\n"+
+"    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n"+
+"\n"+
+"#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n"+
+"    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n"+
+"#endif \n"+
+"\n"+
+"#ifdef TEXMODE_modulate\n"+
+"    textureColor = vec4(luminance*lighteffect.rgb, \n"+
+"                        textureColor.a*lighteffect.a);\n"+
+"#endif\n"+
+"\n"+
+"#ifdef TEXMODE_blend\n"+
+"    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n"+
+"                        textureColor.a*lighteffect.a);\n"+
+"#endif\n"+
+"\n"+
+"#ifdef TEXMODE_add\n"+
+"    textureColor = vec4(luminance + lighteffect.rgb, \n"+
+"                        textureColor.a*lighteffect.a);\n"+
+"\n"+
+"#endif\n"+
+"\n"+
+"#endif // TEXTURE_luminance_alpha\n"+
+"    \n"+
+"    fragColor = textureColor;\n"+
+"\n"+
+"#elif defined(IS_TEXT)\n"+
+"    if (textureColor.a < 0.1)\n"+
+"      discard;\n"+
+"    else\n"+
+"      fragColor = textureColor;\n"+
+"#else\n"+
+"    fragColor = lighteffect;\n"+
+"#endif // HAS_TEXTURE\n"+
+"    \n"+
+"#ifdef HAS_FOG\n"+
+"    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n"+
+"    // In Exp and Exp2: use density = density/far\n"+
+"    // fogF will be the proportion of fog\n"+
+"    // Initialize it to the linear value\n"+
+"    float fogF;\n"+
+"    if (uFogMode > 0) {\n"+
+"      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n"+
+"      if (uFogMode > 1)\n"+
+"        fogF = mix(uFogParms.w, 1.0, fogF);\n"+
+"      fogF = fogF*uFogParms.z;\n"+
+"      if (uFogMode == 2)\n"+
+"        fogF = 1.0 - exp(-fogF);\n"+
+"      // Docs are wrong: use (density*c)^2, not density*c^2\n"+
+"      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n"+
+"      else if (uFogMode == 3)\n"+
+"        fogF = 1.0 - exp(-fogF*fogF);\n"+
+"      fogF = clamp(fogF, 0.0, 1.0);\n"+
+"      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n"+
+"    } else gl_FragColor = fragColor;\n"+
+"#else\n"+
+"    gl_FragColor = fragColor;\n"+
+"#endif // HAS_FOG\n"+
+"    \n"+
+"}\n" ;};
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/subscenes.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/subscenes.src.js
new file mode 100644
index 0000000..fc6e05d
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/subscenes.src.js
@@ -0,0 +1,179 @@
+    /**
+     * Methods related to subscenes
+     * @name ___METHODS_FOR_SUBSCENES___
+     * @memberof rglwidgetClass
+     * @kind function
+     * @instance
+     */
+
+    /**
+     * Is a particular id in a subscene?
+     * @returns { boolean }
+     * @param {number} id Which id?
+     * @param {number} subscene Which subscene id?
+     */
+    rglwidgetClass.prototype.inSubscene = function(id, subscene) {
+      return this.getObj(subscene).objects.indexOf(id) > -1;
+    };
+
+    /**
+     * Translate from window coordinates to viewport coordinates
+     * @returns { Object } translated coordinates
+     * @param { number } subsceneid - which subscene to use?
+     * @param { Object } coords - point to translate
+     */
+    rglwidgetClass.prototype.translateCoords = function(subsceneid, coords) {
+      var viewport = this.getObj(subsceneid).par3d.viewport;
+      return {x: coords.x - viewport.x*this.canvas.width,
+              y: coords.y - viewport.y*this.canvas.height};
+    };
+
+    /**
+     * Check whether point is in viewport of subscene
+     * @returns {boolean}
+     * @param { Object } coords - screen coordinates of point
+     * @param { number } subsceneid - subscene to check
+     */
+    rglwidgetClass.prototype.inViewport = function(coords, subsceneid) {
+      var viewport = this.getObj(subsceneid).par3d.viewport,
+        x0 = coords.x - viewport.x*this.canvas.width,
+        y0 = coords.y - viewport.y*this.canvas.height;
+      return 0 <= x0 && x0 <= viewport.width*this.canvas.width &&
+             0 <= y0 && y0 <= viewport.height*this.canvas.height;
+    };
+
+    /**
+     * Find which subscene contains a point
+     * @returns { number } subscene id
+     * @param { Object } coords - coordinates of point
+     */
+    rglwidgetClass.prototype.whichSubscene = function(coords) {
+      var self = this,
+          recurse = function(subsceneid) {
+            var subscenes = self.getChildSubscenes(subsceneid), i, id;
+            for (i=0; i < subscenes.length; i++) {
+              id = recurse(subscenes[i]);
+              if (typeof(id) !== "undefined")
+                return(id);
+            }
+            if (self.inViewport(coords, subsceneid))
+              return(subsceneid);
+            else
+              return undefined;
+          },
+          rootid = this.scene.rootSubscene,
+          result = recurse(rootid);
+      if (typeof(result) === "undefined")
+        result = rootid;
+      return result;
+    };
+
+    /**
+     * Add an id to a subscene.
+     * @param {number} id Which id?
+     * @param {number} subscene Which subscene id?
+     */
+    rglwidgetClass.prototype.addToSubscene = function(id, subscene) {
+      var thelist,
+          thesub = this.getObj(subscene),
+          ids = [id],
+          obj = this.getObj(id), i;
+      if (typeof obj !== "undefined" && typeof (obj.newIds) !== "undefined") {
+        ids = ids.concat(obj.newIds);
+      }
+      thesub.objects = [].concat(thesub.objects);
+      for (i = 0; i < ids.length; i++) {
+        id = ids[i];
+        if (thesub.objects.indexOf(id) === -1) {
+          thelist = this.whichList(id);
+          thesub.objects.push(id);
+          thesub[thelist].push(id);
+        }
+      }
+    };
+
+    /**
+     * Delete an id from a subscene
+     * @param { number } id - the id to add
+     * @param { number } subscene - the id of the subscene
+     */
+    rglwidgetClass.prototype.delFromSubscene = function(id, subscene) {
+      var thelist,
+          thesub = this.getObj(subscene),
+          obj = this.getObj(id),
+          ids = [id], i, j;
+      if (typeof obj !== "undefined" && typeof (obj.newIds) !== "undefined")
+        ids = ids.concat(obj.newIds);
+      thesub.objects = [].concat(thesub.objects); // It might be a scalar
+      for (j=0; j<ids.length;j++) {
+        id = ids[j];
+        i = thesub.objects.indexOf(id);
+        if (i > -1) {
+          thesub.objects.splice(i, 1);
+          thelist = this.whichList(id);
+          i = thesub[thelist].indexOf(id);
+          thesub[thelist].splice(i, 1);
+        }
+      }
+    };
+
+    /**
+     * Set the ids in a subscene
+     * @param { number[] } ids - the ids to set
+     * @param { number } subsceneid - the id of the subscene
+     */
+    rglwidgetClass.prototype.setSubsceneEntries = function(ids, subsceneid) {
+      var sub = this.getObj(subsceneid);
+      sub.objects = ids;
+      this.initSubscene(subsceneid);
+    };
+
+    /**
+     * Get the ids in a subscene
+     * @returns {number[]}
+     * @param { number } subscene - the id of the subscene
+     */
+    rglwidgetClass.prototype.getSubsceneEntries = function(subscene) {
+      return this.getObj(subscene).objects;
+    };
+
+    /**
+     * Get the ids of the subscenes within a subscene
+     * @returns { number[] }
+     * @param { number } subscene - the id of the subscene
+     */
+    rglwidgetClass.prototype.getChildSubscenes = function(subscene) {
+      return this.getObj(subscene).subscenes;
+    };
+
+    /**
+     * Find a particular subscene by inheritance
+     * @returns { number } id of subscene to use
+     * @param { number } subsceneid - child subscene
+     * @param { string } type - type of inheritance:  "projection" or "model"
+     */
+    rglwidgetClass.prototype.useid = function(subsceneid, type) {
+      var sub = this.getObj(subsceneid);
+      if (sub.embeddings[type] === "inherit")
+        return(this.useid(sub.parent, type));
+      else
+        return subsceneid;
+    };
+
+    /**
+     * Find bboxdeco for a subscene
+     * @returns { number } id of bboxdeco, or undefined if none
+     * @param { number } sub- subscene
+     */
+    rglwidgetClass.prototype.getBBoxDeco = function(sub) {
+      var objects = sub.objects, i, obj;
+      for (i = 0; i < objects.length; i++) {
+        obj = this.getObj(objects[i]);
+        if (obj.type === "bboxdeco")
+          return obj;
+      }
+      if (sub.parent) 
+        return this.getBBoxDeco(this.getObj(sub.parent));
+      else
+        return undefined;
+    };
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/textures.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/textures.src.js
new file mode 100644
index 0000000..3cf32d3
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/textures.src.js
@@ -0,0 +1,173 @@
+    /**
+     * Methods related to textures
+     * @name ___METHODS_FOR_TEXTURES___
+     * @memberof rglwidgetClass
+     * @kind function
+     * @instance
+     */
+     
+    rglwidgetClass.prototype.getTexFilter = function(filter) {
+      var gl = this.gl || this.initGL();
+      switch(filter) {
+        case "nearest": return gl.NEAREST;
+        case "linear": return gl.LINEAR;
+        case "nearest.mipmap.nearest": return gl.NEAREST_MIPMAP_NEAREST;
+        case "linear.mipmap.nearest": return gl.LINEAR_MIPMAP_NEAREST;
+        case "nearest.mipmap.linear": return gl.NEAREST_MIPMAP_LINEAR;
+        case "linear.mipmap.linear": return gl.LINEAR_MIPMAP_LINEAR;
+        default: console.error("Unknown filter: "+filter);
+      }
+    };
+     
+    /**
+     * Handle a texture after its image has been loaded
+     * @param { Object } texture - the gl texture object
+     * @param { Object } textureCanvas - the canvas holding the image
+     */
+    rglwidgetClass.prototype.handleLoadedTexture = function(texture, textureCanvas) {
+      var gl = this.gl || this.initGL();
+      gl.pixelStorei(gl.UNPACK_FLIP_Y_WEBGL, true);
+
+      gl.bindTexture(gl.TEXTURE_2D, texture);
+      gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, gl.RGBA, gl.UNSIGNED_BYTE, textureCanvas);
+      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.LINEAR);
+      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.LINEAR_MIPMAP_NEAREST);
+      gl.generateMipmap(gl.TEXTURE_2D);
+
+      gl.bindTexture(gl.TEXTURE_2D, null);
+    };
+
+    /**
+     * Get maximum dimension of texture in current browser.
+     * @returns {number}
+     */
+    rglwidgetClass.prototype.getMaxTexSize = function() {
+      var gl = this.gl || this.initGL();	
+      return Math.min(4096, gl.getParameter(gl.MAX_TEXTURE_SIZE));
+    };
+    
+    /**
+     * Load an image to a texture
+     * @param { string } uri - The image location
+     * @param { Object } texture - the gl texture object
+     */
+    rglwidgetClass.prototype.loadImageToTexture = function(uri, texture) {
+      var canvas = this.textureCanvas,
+          ctx = canvas.getContext("2d"),
+          image = new Image(),
+          self = this;
+
+       image.onload = function() {
+
+         var w = image.width,
+             h = image.height,
+             canvasX = self.getPowerOfTwo(w),
+             canvasY = self.getPowerOfTwo(h),
+             maxTexSize = self.getMaxTexSize();
+         while (canvasX > 1 && canvasY > 1 && (canvasX > maxTexSize || canvasY > maxTexSize)) {
+           canvasX /= 2;
+           canvasY /= 2;
+         }
+         canvas.width = canvasX;
+         canvas.height = canvasY;
+         ctx.imageSmoothingEnabled = true;
+         ctx.drawImage(image, 0, 0, canvasX, canvasY);
+         self.handleLoadedTexture(texture, canvas);
+         self.texturesLoading -= 1;
+         if (!self.texturesLoading)
+           self.drawScene();
+       };
+       if (!self.texturesLoading)
+         self.texturesLoading = 0; // may have been undefined
+       self.texturesLoading += 1;
+       image.src = uri;
+     };
+
+    /**
+     * Draw text to the texture canvas
+     * @returns { Object } object with text measurements
+     * @param { string } text - the text
+     * @param { number } cex - expansion
+     * @param { string } family - font family
+     * @param { number } font - font number
+     */
+    rglwidgetClass.prototype.drawTextToCanvas = function(text, cex, family, font) {
+       var canvasX, canvasY,
+           scaling = 20,
+           textColour = "white",
+
+           backgroundColour = "rgba(0,0,0,0)",
+           canvas = this.textureCanvas,
+           ctx = canvas.getContext("2d"),
+           i, textHeight = 0, textHeights = [], width, widths = [], 
+           offsetx, offsety = 0, line, lines = [], offsetsx = [],
+           offsetsy = [], lineoffsetsy = [], fontStrings = [],
+           maxTexSize = this.getMaxTexSize(),
+           getFontString = function(i) {
+             textHeights[i] = scaling*cex[i];
+             var fontString = textHeights[i] + "px",
+                 family0 = family[i],
+                 font0 = font[i];
+             if (family0 === "sans")
+               family0 = "sans-serif";
+             else if (family0 === "mono")
+               family0 = "monospace";
+             fontString = fontString + " " + family0;
+             if (font0 === 2 || font0 === 4)
+               fontString = "bold " + fontString;
+             if (font0 === 3 || font0 === 4)
+               fontString = "italic " + fontString;
+             return fontString;
+           };
+       cex = rglwidgetClass.repeatToLen(cex, text.length);
+       family = rglwidgetClass.repeatToLen(family, text.length);
+       font = rglwidgetClass.repeatToLen(font, text.length);
+
+       canvasX = 1;
+       line = -1;
+       offsetx = maxTexSize;
+       for (i = 0; i < text.length; i++)  {
+         ctx.font = fontStrings[i] = getFontString(i);
+         width = widths[i] = ctx.measureText(text[i]).width;
+         if (offsetx + width > maxTexSize) {
+           offsety = offsety + 2*textHeight;
+           if (line >= 0)
+             lineoffsetsy[line] = offsety;
+           line += 1;
+           if (offsety > maxTexSize)
+             console.error("Too many strings for texture.");
+           textHeight = 0;
+           offsetx = 0;
+         }
+         textHeight = Math.max(textHeight, textHeights[i]);
+         offsetsx[i] = offsetx;
+         offsetx += width;
+         canvasX = Math.max(canvasX, offsetx);
+         lines[i] = line;
+       }
+       offsety = lineoffsetsy[line] = offsety + 2*textHeight;
+       for (i = 0; i < text.length; i++) {
+       	 offsetsy[i] = lineoffsetsy[lines[i]];
+       }
+       
+       canvasX = this.getPowerOfTwo(canvasX);
+       canvasY = this.getPowerOfTwo(offsety);
+
+       canvas.width = canvasX;
+       canvas.height = canvasY;
+
+       ctx.fillStyle = backgroundColour;
+       ctx.fillRect(0, 0, ctx.canvas.width, ctx.canvas.height);
+
+       ctx.textBaseline = "alphabetic";
+       for(i = 0; i < text.length; i++) {
+         ctx.font = fontStrings[i];
+         ctx.fillStyle = textColour;
+         ctx.textAlign = "left";
+         ctx.fillText(text[i], offsetsx[i],  offsetsy[i]);
+       }
+       return {canvasX:canvasX, canvasY:canvasY,
+               widths:widths, textHeights:textHeights,
+               offsetsx:offsetsx, offsetsy:offsetsy};
+     };
+
diff --git a/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/utils.src.js b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/utils.src.js
new file mode 100644
index 0000000..00bc5fc
--- /dev/null
+++ b/docs/articles/Biplots_in_3D_files/rglwidgetClass-1.3.18/utils.src.js
@@ -0,0 +1,654 @@
+    /**
+     * Utility methods
+     * @name ___UTILITY_METHODS___
+     * @memberof rglwidgetClass
+     * @kind function
+     * @instance
+     */
+     
+    /**
+     * Multiply matrix by vector
+     * @returns {number[]}
+     * @param M {number[][]} Left operand
+     * @param v {number[]} Right operand
+     */
+    rglwidgetClass.multMV = function(M, v) {
+        return [ M.m11 * v[0] + M.m12 * v[1] + M.m13 * v[2] + M.m14 * v[3],
+                 M.m21 * v[0] + M.m22 * v[1] + M.m23 * v[2] + M.m24 * v[3],
+                 M.m31 * v[0] + M.m32 * v[1] + M.m33 * v[2] + M.m34 * v[3],
+                 M.m41 * v[0] + M.m42 * v[1] + M.m43 * v[2] + M.m44 * v[3]
+               ];
+    };
+    
+    /**
+     * Multiply row vector by Matrix
+     * @returns {number[]}
+     * @param v {number[]} left operand
+     * @param M {number[][]} right operand
+     */
+    rglwidgetClass.multVM = function(v, M) {
+        return [ M.m11 * v[0] + M.m21 * v[1] + M.m31 * v[2] + M.m41 * v[3],
+                 M.m12 * v[0] + M.m22 * v[1] + M.m32 * v[2] + M.m42 * v[3],
+                 M.m13 * v[0] + M.m23 * v[1] + M.m33 * v[2] + M.m43 * v[3],
+                 M.m14 * v[0] + M.m24 * v[1] + M.m34 * v[2] + M.m44 * v[3]
+               ];
+    };
+    
+    /**
+     * Euclidean length of a vector
+     * @returns {number}
+     * @param v {number[]}
+     */
+    rglwidgetClass.vlen = function(v) {
+      return Math.sqrt(rglwidgetClass.dotprod(v, v));
+    };
+
+    /**
+     * Dot product of two vectors
+     * @instance rglwidgetClass
+     * @returns {number}
+     * @param a {number[]}
+     * @param b {number[]}
+     */
+    rglwidgetClass.dotprod = function(a, b) {
+      return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
+    };
+
+    /**
+     * Cross product of two vectors
+     * @returns {number[]}
+     * @param a {number[]}
+     * @param b {number[]}
+     */
+    rglwidgetClass.xprod = function(a, b) {
+      return [a[1]*b[2] - a[2]*b[1],
+          a[2]*b[0] - a[0]*b[2],
+          a[0]*b[1] - a[1]*b[0]];
+    };
+
+    /**
+     * Bind vectors or matrices by columns
+     * @returns {number[][]}
+     * @param a {number[][]}
+     * @param b {number[]|number[][]}
+     */
+    rglwidgetClass.cbind = function(a, b) {
+      if (b.length < a.length)
+        b = rglwidgetClass.repeatToLen(b, a.length);
+      else if (a.length < b.length)
+        a = rglwidgetClass.repeatToLen(a, b.length);
+      return a.map(function(currentValue, index) {
+            return [].concat(currentValue).concat(b[index]);
+      });
+    };
+
+    /**
+     * Swap elements
+     * @returns {any[]}
+     * @param a {any[]}
+     * @param i {number} Element to swap
+     * @param j {number} Other element to swap
+     */
+    rglwidgetClass.swap = function(a, i, j) {
+      var temp = a[i];
+      a[i] = a[j];
+      a[j] = temp;
+    };
+
+    /**
+     * Flatten a matrix into a vector
+     * @returns {any[]}
+     * @param a {any[][]}
+     */
+    rglwidgetClass.flatten = function(arr, result) {
+      var value;
+      if (typeof result === "undefined") result = [];
+      for (var i = 0, length = arr.length; i < length; i++) {
+        value = arr[i];
+        if (Array.isArray(value)) {
+          rglwidgetClass.flatten(value, result);
+        } else {
+          result.push(value);
+        }
+      }
+      return result;
+    };
+
+    /**
+     * set element of 1d or 2d array as if it was flattened.
+     * Column major, zero based!
+     * @returns {any[]|any[][]}
+     * @param {any[]|any[][]} a - array
+     * @param {number} i - element
+     * @param {any} value
+     */
+    rglwidgetClass.prototype.setElement = function(a, i, value) {
+      if (Array.isArray(a[0])) {
+        var dim = a.length,
+            col = Math.floor(i/dim),
+            row = i % dim;
+        a[row][col] = value;
+      } else {
+        a[i] = value;
+      }
+    };
+
+    /**
+     * Transpose an array
+     * @returns {any[][]}
+     * @param {any[][]} a
+     */
+    rglwidgetClass.prototype.transpose = function(a) {
+      var newArray = [],
+          n = a.length,
+          m = a[0].length,
+          i;
+      for(i = 0; i < m; i++){
+        newArray.push([]);
+      }
+
+      for(i = 0; i < n; i++){
+        for(var j = 0; j < m; j++){
+          newArray[j].push(a[i][j]);
+        }
+      }
+      return newArray;
+    };
+
+    /**
+     * Calculate sum of squares of a numeric vector
+     * @returns {number}
+     * @param {number[]} x
+     */
+    rglwidgetClass.prototype.sumsq = function(x) {
+      var result = 0, i;
+      for (i=0; i < x.length; i++)
+        result += x[i]*x[i];
+      return result;
+    };
+
+    /**
+     * Convert a matrix to a CanvasMatrix4
+     * @returns {CanvasMatrix4}
+     * @param {number[][]|number[]} mat
+     */
+    rglwidgetClass.prototype.toCanvasMatrix4 = function(mat) {
+      if (mat instanceof CanvasMatrix4)
+        return mat;
+      var result = new CanvasMatrix4();
+      mat = rglwidgetClass.flatten(this.transpose(mat));
+      result.load(mat);
+      return result;
+    };
+
+    /**
+     * Convert an R-style numeric colour string to an rgb vector
+     * @returns {number[]}
+     * @param {string} s
+     */
+    /* jshint bitwise:false */ 
+    rglwidgetClass.prototype.stringToRgb = function(s) {
+      s = s.replace("#", "");
+      var bigint = parseInt(s, 16);
+      return [((bigint >> 16) & 255)/255,
+              ((bigint >> 8) & 255)/255,
+               (bigint & 255)/255];
+    };
+    /* jshint bitwise:true */
+    /**
+     * Which list does a particular id come from?
+     * @returns { string }
+     * @param {number} id The id to look up.
+     */
+    rglwidgetClass.prototype.whichList = function(id) {
+      var obj = this.getObj(id),
+          flags = obj.flags;
+        if (obj.type === "light")
+          return "lights";
+        if (rglwidgetClass.isSet(flags, rglwidgetClass.f_is_subscene))
+            return "subscenes";
+        if (rglwidgetClass.isSet(flags, rglwidgetClass.f_is_clipplanes))
+            return "clipplanes";
+        if (rglwidgetClass.isSet(flags, rglwidgetClass.f_is_transparent))
+            return "transparent";
+        return "opaque";
+    };
+    
+    /**
+     * Take a component-by-component product of two 3 vectors
+     * @returns {number[]}
+     * @param {number[]} x
+     * @param {number[]} y
+     */
+    rglwidgetClass.prototype.componentProduct = function(x, y) {
+      if (typeof y === "undefined") {
+        this.alertOnce("Bad arg to componentProduct");
+      }
+      var result = new Float32Array(3), i;
+      for (i = 0; i<3; i++)
+        result[i] = x[i]*y[i];
+      return result;
+    };
+
+    /**
+     * Get next higher power of two
+     * @returns { number }
+     * @param { number } value - input value
+     */
+    rglwidgetClass.prototype.getPowerOfTwo = function(value) {
+      var pow = 1;
+      while(pow<value) {
+        pow *= 2;
+      }
+      return pow;
+    };
+
+    /**
+     * Unique entries
+     * @returns { any[] }
+     * @param { any[] } arr - An array
+     */
+    rglwidgetClass.prototype.unique = function(arr) {
+      arr = [].concat(arr);
+      return arr.filter(function(value, index, self) {
+        return self.indexOf(value) === index;
+      });
+    };
+
+    /**
+     * Shallow compare of arrays
+     * @returns { boolean }
+     * @param { any[] } a - An array
+     * @param { any[] } b - Another array
+     */
+    rglwidgetClass.prototype.equalArrays = function(a, b) {
+      return a === b || (a && b &&
+                      a.length === b.length &&
+                      a.every(function(v, i) {return v === b[i];}));
+    };
+    
+    /**
+     * Repeat an array to a desired length
+     * @returns {any[]}
+     * @param {any | any[]} arr The input array
+     * @param {number} len The desired output length
+     */
+    rglwidgetClass.repeatToLen = function(arr, len) {
+      arr = [].concat(arr);
+      if (!arr.length) 
+        throw new RangeError("array is length 0");
+      while (arr.length < len/2)
+        arr = arr.concat(arr);
+      return arr.concat(arr.slice(0, len - arr.length));
+    };
+
+    /**
+     * Give a single alert message, not to be repeated.
+     * @param {string} msg  The message to give.
+     */
+    rglwidgetClass.prototype.alertOnce = function(msg) {
+      // debugger;
+      if (typeof this.alerted !== "undefined")
+        return;
+      this.alerted = true;
+      alert(msg);
+    };
+
+    /**
+     * Get an object by id number.
+     * @returns { Object }
+     * @param {number} id
+     */
+    rglwidgetClass.prototype.getObj = function(id) {
+      if (typeof id !== "number") {
+        this.alertOnce("getObj id is "+typeof id);
+      }
+      return this.scene.objects[id];
+    };
+
+    /**
+     * Get ids of a particular type from a subscene or the whole scene
+     * @returns { number[] }
+     * @param {string} type What type of object?
+     * @param {number} subscene  Which subscene?  If not given, find in the whole scene
+     */
+    rglwidgetClass.prototype.getIdsByType = function(type, subscene) {
+      var
+        result = [], i, self = this, ids;
+      if (typeof subscene === "undefined") {
+        Object.keys(this.scene.objects).forEach(
+          function(key) {
+            key = parseInt(key, 10);
+            if (self.getObj(key).type === type)
+              result.push(key);
+          });
+      } else {
+        ids = this.getObj(subscene).objects;
+        for (i=0; i < ids.length; i++) {
+          if (this.getObj(ids[i]).type === type) {
+            result.push(ids[i]);
+          }
+        }
+      }
+      return result;
+    };
+
+    /**
+     * Get a particular material property for an obj
+     * @returns { any }
+     * @param {object} obj  Which object?
+     * @param {string} property Which material property?
+     */
+    rglwidgetClass.prototype.getMaterial = function(obj, property) {
+      var mat;
+      if (typeof obj.material === "undefined")
+        console.error("material undefined");
+      mat = obj.material[property];
+      if (typeof mat === "undefined")
+          mat = this.scene.material[property];
+      return mat;
+    };
+    
+   /**
+     * Get a particular material property for an id
+     * @returns { any }
+     * @param {number} id  Which object?
+     * @param {string} property Which material property?
+     */
+    rglwidgetClass.prototype.getMaterialId = function(id, property) {
+      var obj = this.getObj(id);
+      return this.getMaterial(obj, property);
+    };
+
+    rglwidgetClass.prototype.getAdj = function (obj, index, offset, text) {
+      var len, pos;
+      if (typeof obj.pos === "undefined")
+        return rglwidgetClass.flatten(obj.adj);
+      pos = obj.pos[index % obj.pos.length];
+      switch(pos) {
+        case 0: return [0.5, 0.5, 0.5];
+        case 1: return [0.5, 1 + offset, 0.5];
+        case 3: return [0.5, -offset, 0.5];
+        case 5: return [0.5, 0.5, -offset];
+        case 6: return [0.5, 0.5, 1 + offset];
+        case 2: 
+        case 4: if (typeof text === "undefined")
+                  len = 1;
+                else
+                  len = text.length;
+                if (pos === 2)
+                  return [1 + offset/len, 0.5, 0.5];
+                else
+                  return [-offset/len, 0.5, 0.5];
+      }
+    };
+
+    /**
+     * Count clipping planes in a scene
+     * @returns {number}
+     */
+    rglwidgetClass.prototype.countClipplanes = function() {
+      var self = this,
+          bound = 0;
+      
+      Object.keys(this.scene.objects).forEach(
+        function(key) {
+          var obj = self.getObj(parseInt(key, 10));
+          if (obj.type === "clipplanes")
+            bound = bound + obj.offsets.length;
+        });
+      return bound;
+    };
+
+    /**
+     * Count clipping plane objects in a scene
+     * @returns {number}
+     */
+    rglwidgetClass.prototype.countClipplaneObjs = function() {
+      return this.countObjs("clipplanes");
+    };
+
+    /**
+     * Count lights in a scene
+     * @returns { number }
+     */
+    rglwidgetClass.prototype.countLights = function() {
+      return this.countObjs("light");
+    };
+
+    /**
+     * Count objects of specific type in a scene
+     * @returns { number }
+     * @param { string } type - Type of object to count
+     */
+    rglwidgetClass.prototype.countObjs = function(type) {
+      var self = this,
+          bound = 0;
+
+      Object.keys(this.scene.objects).forEach(
+        function(key) {
+          if (self.getObj(parseInt(key, 10)).type === type)
+            bound = bound + 1;
+        });
+      return bound;
+    };
+
+    /**
+     * Display a debug message
+     * @param { string } msg - The message to display
+     * @param { Object } [img] - Image to insert before message
+     */
+    rglwidgetClass.prototype.debug = function(msg, img) {
+      if (typeof this.debugelement !== "undefined" && this.debugelement !== null) {
+        this.debugelement.innerHTML = msg;
+        if (typeof img !== "undefined") {
+          this.debugelement.insertBefore(img, this.debugelement.firstChild);
+        }
+      } else if (msg !== "")
+        alert(msg);
+    };
+
+    /**
+     * If we are in an ioslides or slidy presentation, get the
+     * DOM element of the current slide
+     * @returns { Object }
+     */
+    rglwidgetClass.prototype.getSlide = function() {
+      var result = this.el, done = false;
+      while (result && !done && this.scene.context.rmarkdown) {
+      	switch(this.scene.context.rmarkdown) {
+          case "ioslides_presentation":
+            if (result.tagName === "SLIDE") return result;
+            break;
+          case "slidy_presentation":
+            if (result.tagName === "DIV" && result.classList.contains("slide"))
+              return result;
+            break;
+          default: return null;
+      	}
+      	result = result.parentElement;
+      }
+      return null;
+    };
+
+    /**
+     * Is this scene visible in the browser?
+     * @returns { boolean }
+     */
+    rglwidgetClass.prototype.isInBrowserViewport = function() {
+      var rect = this.canvas.getBoundingClientRect(),
+          windHeight = (window.innerHeight || document.documentElement.clientHeight),
+          windWidth = (window.innerWidth || document.documentElement.clientWidth);
+      if (this.scene.context && this.scene.context.rmarkdown !== null) {
+      	if (this.slide)
+      	  return (this.scene.context.rmarkdown === "ioslides_presentation" &&
+      	          this.slide.classList.contains("current")) ||
+      	         (this.scene.context.rmarkdown === "slidy_presentation" &&
+      	          !this.slide.classList.contains("hidden"));
+      }
+      return (
+      	rect.top >= -windHeight &&
+      	rect.left >= -windWidth &&
+      	rect.bottom <= 2*windHeight &&
+      	rect.right <= 2*windWidth);
+    };
+    
+    rglwidgetClass.keydiff = function(obj1, obj2) {
+      var keys = Object.keys(obj1), i, result = [];
+      for (i=0;i<keys.length;i++) {
+        if (typeof obj1[keys[i]] !== "undefined" &&
+            typeof obj2[keys[i]] === "undefined")
+          result.push(keys[i]);
+      }
+      return result;
+    };
+
+    rglwidgetClass.isSet = function(flags, flag) {
+      /* jshint bitwise: false */
+      return (flags & flag) !== 0;
+      /* jshint bitwise: true */
+    };
+    
+    rglwidgetClass.prototype.user2window = function(p, subid) {
+      var m, v = [].concat(p);
+      
+      this.setmvMatrix(subid);
+      m = new CanvasMatrix4(this.mvMatrix);
+      v = rglwidgetClass.multVM(v, m);
+      this.setprMatrix(subid);
+      m = new CanvasMatrix4(this.prMatrix);
+      v = rglwidgetClass.multVM(v, m);
+      this.getViewport(subid);
+      v[0] = v[0]*0.5/v[3] + 0.5 + this.vp.x/this.vp.width;
+      v[1] = v[1]*0.5/v[3] + 0.5 + this.vp.y/this.vp.height;
+      v[2] = (1 + v[2]/v[3])*0.5;
+      return v.slice(0, 3);
+    };
+
+    /**
+     * Andrew's convex hull algorithm. 
+     * From Wikipedia, used under Creative Commons Attribution-ShareAlike License
+     * @returns { Array } Indices of convex hull points
+     */
+    rglwidgetClass.chull = function(points) {
+      function cross(a, b, o) {
+        return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0]);
+      }
+        
+      points.sort(function(a, b) {
+        return a[0] === b[0] ? a[1] - b[1] : a[0] - b[0];
+      });
+
+      var lower = [], upper = [];
+      for (var i = 0; i < points.length; i++) {
+        while (lower.length >= 2 && cross(lower[lower.length - 2], lower[lower.length - 1], points[i]) <= 0) {
+          lower.pop();
+        }
+        lower.push(points[i]);
+      }
+
+      for (i = points.length - 1; i >= 0; i--) {
+        while (upper.length >= 2 && cross(upper[upper.length - 2], upper[upper.length - 1], points[i]) <= 0) {
+          upper.pop();
+        }
+        upper.push(points[i]);
+      }
+
+      upper.pop();
+      lower.pop();
+      return lower.concat(upper);
+    };
+    
+    /**
+     * Round number to given precision
+     * @param { number } x
+     * @param { number } digits
+     * @returns { number } 
+     */
+    rglwidgetClass.signif = function(x, digits) { 
+      return parseFloat(x.toPrecision(digits));
+    };
+      
+    /**
+     * Check for NA, NaN, undefined, or null
+     * @param x
+     * @returns { bool }
+     */
+    rglwidgetClass.missing = function(x) {
+      return x !== "-Inf" && x !== "Inf" &&
+             (isNaN(x) || x === null || typeof(x) === "undefined");
+    };
+
+    /**
+     * Write matrix to log
+     * @param M
+     */
+    rglwidgetClass.logMatrix = function(M) {
+      console.log("matrix(c("+M.m11+","+M.m12+","+M.m13+","+M.m14+",\n"+
+                              M.m21+","+M.m22+","+M.m23+","+M.m24+",\n"+
+                              M.m31+","+M.m32+","+M.m33+","+M.m34+",\n"+
+                              M.m41+","+M.m42+","+M.m43+","+M.m44+"), byrow=TRUE, ncol=4)");
+    };
+    
+    /**
+     * Write vector to log
+     * @param {vector} v
+     */
+     
+    rglwidgetClass.logVec3 = function(v) {
+      console.log("c("+v[0]+","+v[1]+","+v[2]+")");
+    };
+    
+    /**
+     * Sum two vectors
+     * @param {vector} x
+     * @param {vector} y
+     */
+     rglwidgetClass.vsum = function(x, y) {
+       var i, result = [].concat(x);
+       for (i = 0; i < y.length; i++)
+         result[i] += y[i];
+        return result;
+     };
+     
+    /**
+     * difference of two vectors
+     * @param {vector} x
+     * @param {vector} y
+     */
+     rglwidgetClass.vdiff = function(x, y) {
+        return rglwidgetClass.vsum(x, rglwidgetClass.vscale(y, -1));
+     };
+
+    /**
+     * Scale a vector
+     * @param {number} s
+     * @param {vector} x
+     */
+     rglwidgetClass.vscale = function(x, s) {
+       var i, result = [].concat(x);
+       for (i = 0; i < x.length; i++)
+         result[i] *= s;
+        return result;
+     };
+    
+    /**
+     * Normalize a vector
+     * @param {vector} v
+     */
+    rglwidgetClass.normalize = function(v) {
+      return rglwidgetClass.vscale(v, 1/rglwidgetClass.vlen(v));
+    };
+    
+    /**
+     * Compute the dimensions of a regular array
+     * without checking that it is regular
+     */ 
+    rglwidgetClass.arrayDim = function(arr) {
+      var result = [];
+      while (typeof arr.length !== "undefined") {
+        result = result.concat(arr.length);
+        arr = arr[0];
+      }
+      return result;
+    };
diff --git a/docs/articles/CA_in_biplotEZ.html b/docs/articles/CA_in_biplotEZ.html
index 9925e32..b237143 100644
--- a/docs/articles/CA_in_biplotEZ.html
+++ b/docs/articles/CA_in_biplotEZ.html
@@ -4,101 +4,72 @@
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+    <li><a class="dropdown-item" href="../articles/MDS.html">Multi-dimensional scaling</a></li>
+    <li><a class="dropdown-item" href="../articles/Class_separation.html">Biplots for separating classes</a></li>
+    <li><a class="dropdown-item" href="../articles/CA_in_biplotEZ.html">Categorical biplots</a></li>
+    <li><a class="dropdown-item" href="../articles/Biplots_in_1D.html">One dimensional biplots</a></li>
+    <li><a class="dropdown-item" href="../articles/Biplots_in_3D.html">Three dimensional biplots</a></li>
   </ul>
 </li>
       </ul>
-<ul class="nav navbar-nav navbar-right"></ul>
+<ul class="navbar-nav">
+<li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json">
+</form></li>
+      </ul>
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-<!--/.nav-collapse -->
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+</nav><div class="container template-article">
+
+
 
-      
 
-      </header><div class="row">
-  <div class="col-md-9 contents">
-    <div class="page-header toc-ignore">
-      <h1 data-toc-skip>CA in biplotEZ</h1>
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>CA in biplotEZ</h1>
             
       
-      
-      <div class="hidden name"><code>CA_in_biplotEZ.Rmd</code></div>
 
+      <div class="d-none name"><code>CA_in_biplotEZ.Rmd</code></div>
     </div>
 
     
@@ -111,11 +82,13 @@ <h2 id="what-is-a-correspondence-analysis">What is a Correspondence Analysis?<a
 frequency table. Numerous variants of CA are available for the
 application to diverse problems, the interested reader is referred to:
 <span class="citation">Gower, Lubbe, and Roux (2011)</span>, <span class="citation">Beh and Lombardo (2014)</span>.</p>
-<p>In <code>biplotEZ</code> focus will be places on three
-<em>EZ</em>-to-use versions based on the Pearson residuals (<span class="citation">Gower, Lubbe, and Roux (2011)</span>: Page 300).</p>
+<p>In this vignette, focus will be placed on three <em>EZ</em>-to-use
+versions based on the Pearson residuals (<span class="citation">Gower,
+Lubbe, and Roux (2011)</span> :300).</p>
 <p>Now, the two-way frequency table is also referred to as the data
-matrix: <span class="math inline">\(\mathbf{X}:r\times c\)</span>. This
-data matrix is different from the continuous case used for the
+matrix:
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐗</mi><mo>:</mo><mi>r</mi><mo>×</mo><mi>c</mi></mrow><annotation encoding="application/x-tex">\mathbf{X}:r\times c</annotation></semantics></math>.
+This data matrix is different from the continuous case used for the
 <code><a href="../reference/PCA.html">PCA()</a></code> and <code><a href="../reference/CVA.html">CVA()</a></code> examples, as it represents the
 cross-tabulations of two categorical variables (i.e. factors), each with
 a finite number of levels (i.e response values). The elements of the
@@ -125,104 +98,131 @@ <h2 id="what-is-a-correspondence-analysis">What is a Correspondence Analysis?<a
 the hair and eye color of male and female statistics students. For the
 purpose of this example only the male students will be considered:</p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">X</span> <span class="op">&lt;-</span> <span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">1</span><span class="op">]</span></span>
+<code class="sourceCode R"><span><span class="va">X</span> <span class="op">&lt;-</span> <span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span></span>
 <span><span class="va">X</span></span>
 <span><span class="co">#&gt;        Eye</span></span>
 <span><span class="co">#&gt; Hair    Brown Blue Hazel Green</span></span>
-<span><span class="co">#&gt;   Black    32   11    10     3</span></span>
-<span><span class="co">#&gt;   Brown    53   50    25    15</span></span>
-<span><span class="co">#&gt;   Red      10   10     7     7</span></span>
-<span><span class="co">#&gt;   Blond     3   30     5     8</span></span></code></pre></div>
-<p>The grand total of the table <span class="math inline">\(N\)</span>
+<span><span class="co">#&gt;   Black    36    9     5     2</span></span>
+<span><span class="co">#&gt;   Brown    66   34    29    14</span></span>
+<span><span class="co">#&gt;   Red      16    7     7     7</span></span>
+<span><span class="co">#&gt;   Blond     4   64     5     8</span></span></code></pre></div>
+<p>The grand total of the table
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>N</mi><annotation encoding="application/x-tex">N</annotation></semantics></math>
 is obtained from the total of all frequencies:</p>
-<p><span class="math display">\[
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><munderover><mo>∑</mo><mrow><mi>r</mi><mo>=</mo><mn>1</mn></mrow><mi>R</mi></munderover><munderover><mo>∑</mo><mrow><mi>c</mi><mo>=</mo><mn>1</mn></mrow><mi>C</mi></munderover><msub><mi>x</mi><mrow><mi>r</mi><mi>c</mi></mrow></msub><mo>=</mo><mi>N</mi></mrow><annotation encoding="application/x-tex">
 \sum_{r=1}^{R}\sum_{c=1}^{C}x_{rc}=N
-\]</span></p>
+</annotation></semantics></math></p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">N</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="va">X</span><span class="op">)</span></span>
 <span><span class="va">N</span></span>
-<span><span class="co">#&gt; [1] 279</span></span></code></pre></div>
+<span><span class="co">#&gt; [1] 313</span></span></code></pre></div>
 <p>It is common to work with the proportions rather than the frequencies
-in terms of the correspondence matrix, <span class="math inline">\(\mathbf{P}\)</span>:</p>
-<p><span class="math display">\[
+in terms of the correspondence matrix,
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐏</mi><annotation encoding="application/x-tex">\mathbf{P}</annotation></semantics></math>:</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐏</mi><mo>=</mo><mfrac><mi>𝐗</mi><mi>N</mi></mfrac></mrow><annotation encoding="application/x-tex">
 \mathbf{P}=\frac{\mathbf{X}}{N}
-\]</span></p>
+</annotation></semantics></math></p>
 <div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">P</span> <span class="op">&lt;-</span> <span class="va">X</span><span class="op">/</span><span class="va">N</span></span>
 <span><span class="va">P</span></span>
 <span><span class="co">#&gt;        Eye</span></span>
-<span><span class="co">#&gt; Hair         Brown       Blue      Hazel      Green</span></span>
-<span><span class="co">#&gt;   Black 0.11469534 0.03942652 0.03584229 0.01075269</span></span>
-<span><span class="co">#&gt;   Brown 0.18996416 0.17921147 0.08960573 0.05376344</span></span>
-<span><span class="co">#&gt;   Red   0.03584229 0.03584229 0.02508961 0.02508961</span></span>
-<span><span class="co">#&gt;   Blond 0.01075269 0.10752688 0.01792115 0.02867384</span></span></code></pre></div>
-<p>Other useful summaries of <span class="math inline">\(\mathbf{P}\)</span> include the row and column
-masses (for arbitrary row and column <span class="math inline">\(r\)</span> and <span class="math inline">\(c\)</span>, respectively), also expressed as
-diagonal matrices:</p>
-<p><span class="math display">\[
+<span><span class="co">#&gt; Hair          Brown        Blue       Hazel       Green</span></span>
+<span><span class="co">#&gt;   Black 0.115015974 0.028753994 0.015974441 0.006389776</span></span>
+<span><span class="co">#&gt;   Brown 0.210862620 0.108626198 0.092651757 0.044728435</span></span>
+<span><span class="co">#&gt;   Red   0.051118211 0.022364217 0.022364217 0.022364217</span></span>
+<span><span class="co">#&gt;   Blond 0.012779553 0.204472843 0.015974441 0.025559105</span></span></code></pre></div>
+<p>Other useful summaries of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐏</mi><annotation encoding="application/x-tex">\mathbf{P}</annotation></semantics></math>
+include the row and column masses (for arbitrary row and column
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>r</mi><annotation encoding="application/x-tex">r</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>c</mi><annotation encoding="application/x-tex">c</annotation></semantics></math>,
+respectively), also expressed as diagonal matrices:</p>
+<p><span class="math display">$$
 \mathbf{r}_r = \sum_{c=1}^{C}p_{rc}; \hspace{0.5 cm}
 \mathbf{c}_c = \sum_{r=1}^{R}p_{rc}\\
 \mathbf{r}=\mathbf{P1}; \hspace{0.5 cm}
 \mathbf{c}=\mathbf{P}^\prime\mathbf{1}
-\]</span></p>
+$$</span></p>
 <div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">rMass</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/colSums.html" class="external-link">rowSums</a></span><span class="op">(</span><span class="va">P</span><span class="op">)</span></span>
 <span><span class="va">rMass</span></span>
 <span><span class="co">#&gt;     Black     Brown       Red     Blond </span></span>
-<span><span class="co">#&gt; 0.2007168 0.5125448 0.1218638 0.1648746</span></span></code></pre></div>
-<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">cMass</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/colSums.html" class="external-link">colSums</a></span><span class="op">(</span><span class="va">P</span><span class="op">)</span></span>
+<span><span class="co">#&gt; 0.1661342 0.4568690 0.1182109 0.2587859</span></span>
+<span><span class="va">cMass</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/colSums.html" class="external-link">colSums</a></span><span class="op">(</span><span class="va">P</span><span class="op">)</span></span>
 <span><span class="va">cMass</span></span>
-<span><span class="co">#&gt;     Brown      Blue     Hazel     Green </span></span>
-<span><span class="co">#&gt; 0.3512545 0.3620072 0.1684588 0.1182796</span></span></code></pre></div>
+<span><span class="co">#&gt;      Brown       Blue      Hazel      Green </span></span>
+<span><span class="co">#&gt; 0.38977636 0.36421725 0.14696486 0.09904153</span></span></code></pre></div>
 <p>Diagonal matrices:</p>
-<p><span class="math display">\[
+<p><span class="math display">$$
 \mathbf{D_r}=\text{diag}(\mathbf{r}); \hspace{0.5 cm}
 \mathbf{D_c}=\text{diag}(\mathbf{c})
-\]</span></p>
-<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+$$</span></p>
+<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">Dr</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/diag.html" class="external-link">diag</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/apply.html" class="external-link">apply</a></span><span class="op">(</span><span class="va">P</span>, <span class="fl">1</span>, <span class="va">sum</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="va">Dr</span></span>
-<span><span class="co">#&gt;           [,1]      [,2]      [,3]      [,4]</span></span>
-<span><span class="co">#&gt; [1,] 0.2007168 0.0000000 0.0000000 0.0000000</span></span>
-<span><span class="co">#&gt; [2,] 0.0000000 0.5125448 0.0000000 0.0000000</span></span>
-<span><span class="co">#&gt; [3,] 0.0000000 0.0000000 0.1218638 0.0000000</span></span>
-<span><span class="co">#&gt; [4,] 0.0000000 0.0000000 0.0000000 0.1648746</span></span></code></pre></div>
-<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">Dc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/diag.html" class="external-link">diag</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/apply.html" class="external-link">apply</a></span><span class="op">(</span><span class="va">P</span>, <span class="fl">2</span>, <span class="va">sum</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="co">#&gt;           [,1]     [,2]      [,3]      [,4]</span></span>
+<span><span class="co">#&gt; [1,] 0.1661342 0.000000 0.0000000 0.0000000</span></span>
+<span><span class="co">#&gt; [2,] 0.0000000 0.456869 0.0000000 0.0000000</span></span>
+<span><span class="co">#&gt; [3,] 0.0000000 0.000000 0.1182109 0.0000000</span></span>
+<span><span class="co">#&gt; [4,] 0.0000000 0.000000 0.0000000 0.2587859</span></span>
+<span><span class="va">Dc</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/diag.html" class="external-link">diag</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/apply.html" class="external-link">apply</a></span><span class="op">(</span><span class="va">P</span>, <span class="fl">2</span>, <span class="va">sum</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="va">Dc</span></span>
-<span><span class="co">#&gt;           [,1]      [,2]      [,3]      [,4]</span></span>
-<span><span class="co">#&gt; [1,] 0.3512545 0.0000000 0.0000000 0.0000000</span></span>
-<span><span class="co">#&gt; [2,] 0.0000000 0.3620072 0.0000000 0.0000000</span></span>
-<span><span class="co">#&gt; [3,] 0.0000000 0.0000000 0.1684588 0.0000000</span></span>
-<span><span class="co">#&gt; [4,] 0.0000000 0.0000000 0.0000000 0.1182796</span></span></code></pre></div>
+<span><span class="co">#&gt;           [,1]      [,2]      [,3]       [,4]</span></span>
+<span><span class="co">#&gt; [1,] 0.3897764 0.0000000 0.0000000 0.00000000</span></span>
+<span><span class="co">#&gt; [2,] 0.0000000 0.3642173 0.0000000 0.00000000</span></span>
+<span><span class="co">#&gt; [3,] 0.0000000 0.0000000 0.1469649 0.00000000</span></span>
+<span><span class="co">#&gt; [4,] 0.0000000 0.0000000 0.0000000 0.09904153</span></span></code></pre></div>
 <p>In order to obtain the first form of the row and column coordinates,
 the singular value decomposition (SVD) of the matrix of standardised
-Pearson residuals (<span class="math inline">\(\mathbf{S}\)</span>) is
-computed:</p>
-<p><span class="math display">\[
+Pearson residuals
+(<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐒</mi><annotation encoding="application/x-tex">\mathbf{S}</annotation></semantics></math>)
+is computed:</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable><mtr><mtd columnalign="right" style="text-align: right"><mtext mathvariant="normal">SVD</mtext><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐒</mi><mo stretchy="true" form="postfix">)</mo></mrow></mtd><mtd columnalign="left" style="text-align: left"><mo>=</mo><mtext mathvariant="normal">SVD</mtext><mrow><mo stretchy="true" form="prefix">(</mo><msubsup><mi>𝐃</mi><mi>𝐫</mi><mrow><mi mathvariant="bold">−</mi><mfrac><mn>𝟏</mn><mn>𝟐</mn></mfrac></mrow></msubsup><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐏</mi><mo>−</mo><mrow><mi>𝐫</mi><msup><mi>𝐜</mi><mi mathvariant="bold">′</mi></msup></mrow><mo stretchy="true" form="postfix">)</mo></mrow><msubsup><mi>𝐃</mi><mi>𝐜</mi><mrow><mi mathvariant="bold">−</mi><mfrac><mn>𝟏</mn><mn>𝟐</mn></mfrac></mrow></msubsup><mo stretchy="true" form="postfix">)</mo></mrow></mtd></mtr><mtr><mtd columnalign="right" style="text-align: right"></mtd><mtd columnalign="left" style="text-align: left"><mo>=</mo><mrow><mi>𝐔</mi><mi>𝚲</mi><msup><mi>𝐕</mi><mi mathvariant="bold">′</mi></msup></mrow></mtd></mtr></mtable><annotation encoding="application/x-tex">
 \begin{aligned}
-\text{SVD}(\mathbf{S}) &amp;=
-\text{SVD}\left(\mathbf{D_r^{-\frac{1}{2}}}(\mathbf{P}-\mathbf{rc^\prime})\mathbf{D_c^{-\frac{1}{2}}}\right)\\&amp;=
-\mathbf{U\Lambda V^\prime}
+\text{SVD}(\mathbf{S}) &amp;= \text{SVD}\left(\mathbf{D_r^{-\frac{1}{2}}}(\mathbf{P}-\mathbf{rc^\prime})\mathbf{D_c^{-\frac{1}{2}}}\right)\\&amp;= \mathbf{U\Lambda V^\prime}
 \end{aligned}
-\]</span> The return value for the Standardised pearson residuals is
-<code>Smat</code> and the singular value decomposition,
-<code>SVD</code>.</p>
-<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">Smat</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">sqrt</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/solve.html" class="external-link">solve</a></span><span class="op">(</span><span class="va">Dr</span><span class="op">)</span><span class="op">)</span><span class="op"><a href="https://rdrr.io/r/base/matmult.html" class="external-link">%*%</a></span><span class="op">(</span><span class="va">P</span><span class="op">-</span><span class="op">(</span><span class="va">Dr</span> <span class="op"><a href="https://rdrr.io/r/base/matmult.html" class="external-link">%*%</a></span><span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">matrix</a></span><span class="op">(</span><span class="fl">1</span>, nrow <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">nrow</a></span><span class="op">(</span><span class="va">X</span><span class="op">)</span>, ncol <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">X</span><span class="op">)</span><span class="op">)</span> <span class="op"><a href="https://rdrr.io/r/base/matmult.html" class="external-link">%*%</a></span>  <span class="va">Dc</span><span class="op">)</span><span class="op">)</span><span class="op"><a href="https://rdrr.io/r/base/matmult.html" class="external-link">%*%</a></span><span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">sqrt</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/solve.html" class="external-link">solve</a></span><span class="op">(</span><span class="va">Dc</span><span class="op">)</span><span class="op">)</span></span>
-<span><span class="va">svd.out</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/svd.html" class="external-link">svd</a></span><span class="op">(</span><span class="va">Smat</span><span class="op">)</span></span></code></pre></div>
-<p>This is linked to the <span class="math inline">\(\chi^2\)</span>-statistic to determine whether the
-two categorical variables (i.e. the rows and columns of the contingency
-table) are independent. The expected frequencies represented by the
-product of the row and column masses (<span class="math inline">\(\mathbf{rc^\prime}\)</span>).</p>
+</annotation></semantics></math> The return value for the Standardised
+pearson residuals is <code>Smat</code> and the singular value
+decomposition, <code>SVD</code>.</p>
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">Smat</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">sqrt</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/solve.html" class="external-link">solve</a></span><span class="op">(</span><span class="va">Dr</span><span class="op">)</span><span class="op">)</span><span class="op"><a href="https://rdrr.io/r/base/matmult.html" class="external-link">%*%</a></span><span class="op">(</span><span class="va">P</span><span class="op">-</span><span class="op">(</span><span class="va">Dr</span> <span class="op"><a href="https://rdrr.io/r/base/matmult.html" class="external-link">%*%</a></span><span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">matrix</a></span><span class="op">(</span><span class="fl">1</span>, nrow <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">nrow</a></span><span class="op">(</span><span class="va">X</span><span class="op">)</span>, </span>
+<span>    ncol <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">X</span><span class="op">)</span><span class="op">)</span> <span class="op"><a href="https://rdrr.io/r/base/matmult.html" class="external-link">%*%</a></span>  <span class="va">Dc</span><span class="op">)</span><span class="op">)</span><span class="op"><a href="https://rdrr.io/r/base/matmult.html" class="external-link">%*%</a></span><span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">sqrt</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/solve.html" class="external-link">solve</a></span><span class="op">(</span><span class="va">Dc</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="va">svd.out</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/svd.html" class="external-link">svd</a></span><span class="op">(</span><span class="va">Smat</span><span class="op">)</span></span>
+<span><span class="va">svd.out</span></span>
+<span><span class="co">#&gt; $d</span></span>
+<span><span class="co">#&gt; [1] 5.499629e-01 1.806424e-01 7.541748e-02 8.574459e-17</span></span>
+<span><span class="co">#&gt; </span></span>
+<span><span class="co">#&gt; $u</span></span>
+<span><span class="co">#&gt;            [,1]       [,2]        [,3]      [,4]</span></span>
+<span><span class="co">#&gt; [1,] -0.3832205  0.7807477 -0.27828196 0.4075956</span></span>
+<span><span class="co">#&gt; [2,] -0.3195599 -0.2982325  0.59335474 0.6759209</span></span>
+<span><span class="co">#&gt; [3,] -0.1736837 -0.5332073 -0.75320188 0.3438181</span></span>
+<span><span class="co">#&gt; [4,]  0.8490333  0.1310737 -0.05635808 0.5087101</span></span>
+<span><span class="co">#&gt; </span></span>
+<span><span class="co">#&gt; $v</span></span>
+<span><span class="co">#&gt;             [,1]       [,2]        [,3]      [,4]</span></span>
+<span><span class="co">#&gt; [1,] -0.61837991  0.4547976 -0.14487614 0.6243207</span></span>
+<span><span class="co">#&gt; [2,]  0.75797511  0.2307003  0.08963172 0.6035041</span></span>
+<span><span class="co">#&gt; [3,] -0.20612962 -0.5898626  0.68015284 0.3833600</span></span>
+<span><span class="co">#&gt; [4,]  0.02430218 -0.6260980 -0.71300012 0.3147086</span></span></code></pre></div>
+<p>This is linked to the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>χ</mi><mn>2</mn></msup><annotation encoding="application/x-tex">\chi^2</annotation></semantics></math>-statistic
+to determine whether the two categorical variables (i.e. the rows and
+columns of the contingency table) are independent. The expected
+frequencies represented by the product of the row and column masses
+(<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐫</mi><msup><mi>𝐜</mi><mi mathvariant="bold">′</mi></msup></mrow><annotation encoding="application/x-tex">\mathbf{rc^\prime}</annotation></semantics></math>).</p>
 <p>Furthermore, since the weights of certain objects might be
 substantially different from others which could result in a distorted
-approximation in lower dimension, the <span class="math inline">\(\chi^2\)</span>-distance, also referred to as the
-weighted Euclidean distance, is rather used to measure distances in CA.
-This is an intuitive decision as it follows from the <span class="math inline">\(\chi^2\)</span>-statistic to test the independence
-between two categorical variables, in this case the independence between
-the rows and columns of the contingency table. (<span class="citation">Beh and Lombardo (2014)</span>, <span class="citation">Greenacre (2017)</span>).</p>
+approximation in lower dimension, the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>χ</mi><mn>2</mn></msup><annotation encoding="application/x-tex">\chi^2</annotation></semantics></math>-distance,
+also referred to as the weighted Euclidean distance, is rather used to
+measure distances in CA. This is an intuitive decision as it follows
+from the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>χ</mi><mn>2</mn></msup><annotation encoding="application/x-tex">\chi^2</annotation></semantics></math>-statistic
+to test the independence between two categorical variables, in this case
+the independence between the rows and columns of the contingency table.
+(<span class="citation">Beh and Lombardo (2014)</span>, <span class="citation">Greenacre (2017)</span>).</p>
 </div>
 <div class="section level2">
 <h2 id="ca-biplot">CA biplot<a class="anchor" aria-label="anchor" href="#ca-biplot"></a>
@@ -235,55 +235,118 @@ <h3 id="coordinates">Coordinates<a class="anchor" aria-label="anchor" href="#coo
 constructed. This means that the contribution of the singular values
 should be different for the row and column coordinates. (<span class="citation">Gabriel (1971)</span>) The standard coordinates are
 expressed by:</p>
-<p><span class="math display">\[
+<p><span class="math display">$$
 \begin{aligned}
 \text{Row standard coordinates:} \hspace{0.5 cm}&amp;\mathbf{U}\\
 \text{Column standard coordinates:} \hspace{0.5 cm}&amp;\mathbf{V}
 \end{aligned}
-\]</span></p>
+$$</span></p>
 <p>The principal coordinates are expressed by:</p>
-<p><span class="math display">\[
+<p><span class="math display">$$
 \begin{aligned}
 \text{Row principal coordinates:} \hspace{0.5
 cm}&amp;\mathbf{U\Lambda}\\
 \text{Column principal coordinates:} \hspace{0.5
 cm}&amp;\mathbf{V\Lambda}
 \end{aligned}
-\]</span></p>
+$$</span></p>
 <p>By including the singular values the magnitude of the association
 between the variables are incorporated in the scaling of the
 coordinates.</p>
 <p>In the <code>ca()</code> function the argument <code>variant</code>
 allows the user to choose between three types of CA biplots:
 <code>Princ</code>, <code>Stand</code> and <code>Symmetric</code>.</p>
-<p><span class="math display">\[
+<p><span class="math display">$$
 \begin{aligned}
 \text{Row coordinates:} \hspace{0.5 cm}&amp;\mathbf{U\Lambda^\gamma}\\
 \text{Column coordinates:} \hspace{0.5
 cm}&amp;\mathbf{V\Lambda^{1-\gamma}}
 \end{aligned}
-\]</span> The row standard (i.e. column principal) coordinate biplot:
-<code>Stand</code>, results from <span class="math inline">\(\gamma=0\)</span>.</p>
+$$</span> The row standard (i.e. column principal) coordinate biplot:
+<code>Stand</code>, results from
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>γ</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\gamma=0</annotation></semantics></math>.</p>
 <p>The row principal (i.e. column standard) coordinate biplot:
-<code>Princ</code>, results from <span class="math inline">\(\gamma=1\)</span>.</p>
+<code>Princ</code>, results from
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>γ</mi><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\gamma=1</annotation></semantics></math>.</p>
 <p>The symmetric plot in which row and column coordinates are scaled
-equally: <code>Symmetric</code>, results from <span class="math inline">\(\gamma=0.5\)</span>.</p>
+equally: <code>Symmetric</code>, results from
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>γ</mi><mo>=</mo><mn>0.5</mn></mrow><annotation encoding="application/x-tex">\gamma=0.5</annotation></semantics></math>.</p>
 <p>The return value is <code>rowcoor</code> and <code>colcoor</code>,
 respectively.</p>
-<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">gamma</span> <span class="op">&lt;-</span> <span class="fl">0</span></span>
 <span><span class="va">rowcoor</span> <span class="op">&lt;-</span> <span class="va">svd.out</span><span class="op">[[</span><span class="fl">2</span><span class="op">]</span><span class="op">]</span><span class="op"><a href="https://rdrr.io/r/base/matmult.html" class="external-link">%*%</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/diag.html" class="external-link">diag</a></span><span class="op">(</span><span class="va">svd.out</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">)</span><span class="op">^</span><span class="va">gamma</span><span class="op">)</span></span>
 <span><span class="va">colcoor</span> <span class="op">&lt;-</span> <span class="va">svd.out</span><span class="op">[[</span><span class="fl">3</span><span class="op">]</span><span class="op">]</span><span class="op"><a href="https://rdrr.io/r/base/matmult.html" class="external-link">%*%</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/diag.html" class="external-link">diag</a></span><span class="op">(</span><span class="va">svd.out</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">)</span><span class="op">^</span><span class="op">(</span><span class="fl">1</span><span class="op">-</span><span class="va">gamma</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 </div>
 <div class="section level3">
-<h3 id="the-quality-of-the-biplot-display">The quality of the biplot display<a class="anchor" aria-label="anchor" href="#the-quality-of-the-biplot-display"></a>
+<h3 id="lambda-scaling">Lambda scaling<a class="anchor" aria-label="anchor" href="#lambda-scaling"></a>
+</h3>
+<p>As presented in <span class="citation">Gower, Lubbe, and Roux
+(2011)</span> :24, when constructing a biplot representing the rows of a
+coordinate matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐀</mi><annotation encoding="application/x-tex">\mathbf{A}</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>𝐁</mi><mi>′</mi></msup><annotation encoding="application/x-tex">\mathbf{B}^\prime</annotation></semantics></math>.
+Take note that the inner product is invariant when
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐀</mi><annotation encoding="application/x-tex">\mathbf{A}</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐁</mi><annotation encoding="application/x-tex">\mathbf{B}</annotation></semantics></math>
+are scaled inversely by
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>λ</mi><annotation encoding="application/x-tex">\lambda</annotation></semantics></math>.</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi>𝐀</mi><mi>𝐁</mi></mrow><mo>=</mo><mrow><mo stretchy="true" form="prefix">(</mo><mi>λ</mi><mi>𝐀</mi><mo stretchy="true" form="postfix">)</mo></mrow><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐁</mi><mi>/</mi><mi>λ</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">
+\mathbf{AB} = (\lambda\mathbf{A})(\mathbf{B}/\lambda)
+</annotation></semantics></math> An arbitrary value of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>λ</mi><annotation encoding="application/x-tex">\lambda</annotation></semantics></math>
+can be selected or an <em>optimal</em> value could be to ensure that the
+average squared distance of the points in
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi><mi>𝐀</mi></mrow><annotation encoding="application/x-tex">\lambda\mathbf{A}</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐁</mi><mi>/</mi><mi>λ</mi></mrow><annotation encoding="application/x-tex">\mathbf{B}/\lambda</annotation></semantics></math>
+is equal.</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>λ</mi><mn>4</mn></msup><mo>=</mo><mfrac><mi>r</mi><mi>c</mi></mfrac><mfrac><mrow><mrow><mo stretchy="true" form="prefix">|</mo><mo stretchy="true" form="postfix">|</mo></mrow><mi>𝐁</mi><msup><mrow><mo stretchy="true" form="prefix">|</mo><mo stretchy="true" form="postfix">|</mo></mrow><mn>2</mn></msup></mrow><mrow><mrow><mo stretchy="true" form="prefix">|</mo><mo stretchy="true" form="postfix">|</mo></mrow><mi>𝐀</mi><msup><mrow><mo stretchy="true" form="prefix">|</mo><mo stretchy="true" form="postfix">|</mo></mrow><mn>2</mn></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">
+\lambda^4 =\frac{r}{c}\frac{||\mathbf{B}||^2}{||\mathbf{A}||^2}
+</annotation></semantics></math></p>
+<p>The default setting is to not apply lambda-scaling
+(i.e. <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\lambda=1</annotation></semantics></math>).</p>
+<p>The return value is <code>lambda.val</code>.</p>
+</div>
+<div class="section level3">
+<h3 id="measures-of-fit">Measures of fit<a class="anchor" aria-label="anchor" href="#measures-of-fit"></a>
 </h3>
-<p>This is measured by the ratio of the variance explained (sum of the
-squared singular values of the utilised (<span class="math inline">\(M\)</span>) components) and the total variance
-(sum of all squared singular values (<span class="math inline">\(p\)</span>)).</p>
-<p><span class="math display">\[
+<p><code>quality</code>, <code>adequacy</code>,
+<code>row.predictivities</code> and <code>column.predictivities</code>
+are available for CA biplots.</p>
+<p>As explained in the biplotEZ vignette, the quality of the biplot is
+measured by the ratio of the variance explained (sum of the squared
+singular values of the utilised
+(<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>M</mi><annotation encoding="application/x-tex">M</annotation></semantics></math>)
+components) and the total variance (sum of all squared singular values
+(<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>p</mi><annotation encoding="application/x-tex">p</annotation></semantics></math>)).</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mfrac><mrow><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><msubsup><mi>λ</mi><mi>m</mi><mn>2</mn></msubsup></mrow><mrow><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>p</mi></munderover><msubsup><mi>λ</mi><mi>m</mi><mn>2</mn></msubsup></mrow></mfrac><annotation encoding="application/x-tex">
 \frac{\sum_{m=1}^{M}\lambda_m^2}{\sum_{m=1}^{p}\lambda_m^2}
-\]</span> The return value is <code>qual</code>.</p>
+</annotation></semantics></math> The <code>adequacy</code> refers to the
+representation of the variables. In <code><a href="../reference/CA.html">CA()</a></code> the factor
+variable represented in the columns is treated as the variables and is
+calculated as explained in the biplotEZ vignette:</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>𝐕</mi><mi>r</mi></msub><msub><mi>𝐕</mi><mi>r</mi></msub><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐕</mi><mi>𝐕</mi></mrow><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow></mfrac><mo>=</mo><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>𝐕</mi><mi>r</mi></msub><msub><mi>𝐕</mi><mi>r</mi></msub><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">
+ \frac{diag(\mathbf{V}_r\mathbf{V}_r')}{diag(\mathbf{VV}')}= diag(\mathbf{V}_r\mathbf{V}_r')
+</annotation></semantics></math></p>
+<p>The predictivities provide a measure of how well the original values
+are recovered from the biplot. An element that is well represented will
+have a predictivity close to one, indicating that the row or column
+variable values from prediction is close to the observed values. If an
+element is poorly represented, the predicted values will be very
+different from the original values and the predictivity value will be
+close to zero.</p>
+<p>The <code>row.predictivities</code> are calculated as follows (<span class="citation">Gower, Lubbe, and Roux (2011)</span> :299):</p>
+<p><span class="math display">$$
+diag(\mathbf{U}\mathbf{\Sigma}\mathbf{J}\mathbf{\Sigma}\mathbf{U}')[diag(\mathbf{U}\mathbf{\Sigma}\mathbf{\Sigma}\mathbf{U}')]^{-1}\\
+=diag(\mathbf{U}\mathbf{\Sigma}^2\mathbf{J}\mathbf{U}')[diag(\mathbf{U}\mathbf{\Sigma^2}\mathbf{U}')]^{-1}
+$$</span></p>
+<p>The <code>col.predictivities</code> are calculated as follows (<span class="citation">Gower, Lubbe, and Roux (2011)</span> :299):</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐕</mi><msup><mi>𝚺</mi><mn>2</mn></msup><mi>𝐉</mi><mi>𝐕</mi><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow><msup><mrow><mo stretchy="true" form="prefix">[</mo><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐕</mi><msup><mi>𝚺</mi><mn>𝟐</mn></msup><mi>𝐕</mi><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo stretchy="true" form="postfix">]</mo></mrow><mrow><mi>−</mi><mn>1</mn></mrow></msup></mrow><annotation encoding="application/x-tex">
+diag(\mathbf{V}\mathbf{\Sigma}^2\mathbf{J}\mathbf{V}')[diag(\mathbf{V}\mathbf{\Sigma^2}\mathbf{V}')]^{-1}
+</annotation></semantics></math></p>
 </div>
 </div>
 <div class="section level2">
@@ -301,8 +364,8 @@ <h3 id="variantprinc">
 <code>Variant="Princ"</code><a class="anchor" aria-label="anchor" href="#variantprinc"></a>
 </h3>
 <p>The default CA biplot is a row principal coordinate biplot:</p>
-<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">1</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CA.html">CA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CA.html">CA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="CA_in_biplotEZ_files/figure-html/unnamed-chunk-9-1.png" width="672"></p>
 </div>
 <div class="section level3">
@@ -310,39 +373,153 @@ <h3 id="variantstand">
 <code>Variant="Stand"</code><a class="anchor" aria-label="anchor" href="#variantstand"></a>
 </h3>
 <p>To construct the CA biplot for row standard coordinates:</p>
-<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">ca.out</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">1</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CA.html">CA</a></span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Stand"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">ca.out</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CA.html">CA</a></span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Stand"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="CA_in_biplotEZ_files/figure-html/unnamed-chunk-10-1.png" width="672"></p>
-<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">ca.out</span><span class="op">$</span><span class="va">qual</span></span>
-<span><span class="co">#&gt; [1] 99.73298</span></span></code></pre></div>
 </div>
 <div class="section level3">
 <h3 id="variantsymmetric">
 <code>Variant="Symmetric"</code><a class="anchor" aria-label="anchor" href="#variantsymmetric"></a>
 </h3>
 <p>To construct the symmetric CA map:</p>
-<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">ca.out</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">1</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CA.html">CA</a></span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Symmetric"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">ca.out</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="../reference/CA.html">CA</a></span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Symmetric"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="CA_in_biplotEZ_files/figure-html/unnamed-chunk-11-1.png" width="672"></p>
-<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">ca.out</span><span class="op">$</span><span class="va">qual</span></span>
-<span><span class="co">#&gt; [1] 99.73298</span></span></code></pre></div>
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">ca.out</span><span class="op">$</span><span class="va">lambda.val</span></span>
+<span><span class="co">#&gt; [1] 1</span></span></code></pre></div>
+</div>
+<div class="section level3">
+<h3 id="measures-of-fit-1">Measures of fit<a class="anchor" aria-label="anchor" href="#measures-of-fit-1"></a>
+</h3>
+<p>The <code>fit.mesaures()</code> function should be utilised to obtain
+the specific fit measures explained above.</p>
+<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">ca.out</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="../reference/CA.html">CA</a></span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Symmetric"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/fit.measures.html">fit.measures</a></span><span class="op">(</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="st">"Quality"</span><span class="op">)</span></span>
+<span><span class="co">#&gt; [1] "Quality"</span></span>
+<span><span class="va">ca.out</span><span class="op">$</span><span class="va">quality</span></span>
+<span><span class="co">#&gt; [1] 0.9833094</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="st">"Adequacy"</span><span class="op">)</span></span>
+<span><span class="co">#&gt; [1] "Adequacy"</span></span>
+<span><span class="va">ca.out</span><span class="op">$</span><span class="va">adequacy</span></span>
+<span><span class="co">#&gt;        Brown   Blue  Hazel  Green</span></span>
+<span><span class="co">#&gt; Dim 1 0.3824 0.5745 0.0425 0.0006</span></span>
+<span><span class="co">#&gt; Dim 2 0.5892 0.6277 0.3904 0.3926</span></span>
+<span><span class="co">#&gt; Dim 3 0.6102 0.6358 0.8530 0.9010</span></span>
+<span><span class="co">#&gt; Dim 4 1.0000 1.0000 1.0000 1.0000</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="st">"Row predictivities"</span><span class="op">)</span></span>
+<span><span class="co">#&gt; [1] "Row predictivities"</span></span>
+<span><span class="va">ca.out</span><span class="op">$</span><span class="va">row.predictivities</span></span>
+<span><span class="co">#&gt;        Black  Brown    Red  Blond</span></span>
+<span><span class="co">#&gt; Dim 1 0.6860 0.8630 0.4219 0.9974</span></span>
+<span><span class="co">#&gt; Dim 2 0.9932 0.9441 0.8508 0.9999</span></span>
+<span><span class="co">#&gt; Dim 3 1.0000 1.0000 1.0000 1.0000</span></span>
+<span><span class="co">#&gt; Dim 4 1.0000 1.0000 1.0000 1.0000</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="st">"Column predictivities"</span><span class="op">)</span></span>
+<span><span class="co">#&gt; [1] "Column predictivities"</span></span>
+<span><span class="va">ca.out</span><span class="op">$</span><span class="va">col.predictivities</span></span>
+<span><span class="co">#&gt;        Brown   Blue  Hazel  Green</span></span>
+<span><span class="co">#&gt; Dim 1 0.9439 0.9898 0.4789 0.0113</span></span>
+<span><span class="co">#&gt; Dim 2 0.9990 0.9997 0.9020 0.8177</span></span>
+<span><span class="co">#&gt; Dim 3 1.0000 1.0000 1.0000 1.0000</span></span>
+<span><span class="co">#&gt; Dim 4 1.0000 1.0000 1.0000 1.0000</span></span></code></pre></div>
+</div>
+<div class="section level3">
+<h3 id="interpolating-new-samples">Interpolating new samples<a class="anchor" aria-label="anchor" href="#interpolating-new-samples"></a>
+</h3>
+<p>Adding cross-tabulations of the two categorical variables to the plot
+is facilitated by the function <code><a href="../reference/interpolate.html">interpolate()</a></code>. Note that the
+additional variables to be interpolated did not contribute to the
+construction of the biplot. This is the reason why <span class="citation">Greenacre (2017)</span> term these supplementary
+points.</p>
+<p>The function <code><a href="../reference/interpolate.html">interpolate()</a></code> accepts a matrix or data
+frame containing the samples and variables to be interpolated. The
+argument <code>newdata</code> containing the samples to be interpolated
+needs to have a similar structure to the data set sent to
+<code><a href="../reference/biplot.html">biplot()</a></code>. If <code><a href="../reference/biplot.html">biplot()</a></code> received a data frame,
+<code>newdata</code> can be either another data frame or a matrix
+containing the subset of numerical variables.</p>
+<p>The function <code><a href="../reference/newsamples.html">newsamples()</a></code> operates similar to
+<code><a href="../reference/samples.html">samples()</a></code> and enables aesthetic changes to the new
+samples.</p>
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CA.html">CA</a></span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Symmetric"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="../reference/samples.html">samples</a></span><span class="op">(</span>pch <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>,<span class="fl">2</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/interpolate.html">interpolate</a></span><span class="op">(</span>newdata <span class="op">=</span> <span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">1</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="../reference/newsamples.html">newsamples</a></span><span class="op">(</span>col <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"orange"</span>,<span class="st">"purple"</span><span class="op">)</span>, pch <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">15</span>,<span class="fl">17</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span>      </span></code></pre></div>
+<p><img src="CA_in_biplotEZ_files/figure-html/unnamed-chunk-13-1.png" width="672"></p>
 </div>
 <div class="section level3">
 <h3 id="aesthetics-and-legend">Aesthetics and legend<a class="anchor" aria-label="anchor" href="#aesthetics-and-legend"></a>
 </h3>
 <p>The <code><a href="https://rdrr.io/r/base/sample.html" class="external-link">sample()</a></code> function should be utilised to specify the
 colours, plotting characters and expansion of the samples.</p>
-<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CA.html">CA</a></span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Princ"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
-<span>  <span class="fu"><a href="../reference/samples.html">samples</a></span><span class="op">(</span>col<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan"</span>,<span class="st">"purple"</span><span class="op">)</span>, pch<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">15</span>,<span class="fl">17</span><span class="op">)</span>, label.side<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"bottom"</span>,<span class="st">"top"</span><span class="op">)</span>, </span>
-<span>          label.cex<span class="op">=</span><span class="fl">1</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>samples <span class="op">=</span> <span class="cn">TRUE</span>, new <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-<p><img src="CA_in_biplotEZ_files/figure-html/unnamed-chunk-12-1.png" width="672"><img src="CA_in_biplotEZ_files/figure-html/unnamed-chunk-12-2.png" width="672"></p>
-<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
+<span>  <span class="fu"><a href="../reference/samples.html">samples</a></span><span class="op">(</span>col <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan"</span>,<span class="st">"purple"</span><span class="op">)</span>, pch <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">15</span>,<span class="fl">17</span><span class="op">)</span>, label.side <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"bottom"</span>,<span class="st">"top"</span><span class="op">)</span>, </span>
+<span>          label.cex <span class="op">=</span> <span class="fl">1</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>samples <span class="op">=</span> <span class="cn">TRUE</span>, new <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<p><img src="CA_in_biplotEZ_files/figure-html/unnamed-chunk-14-1.png" width="672"><img src="CA_in_biplotEZ_files/figure-html/unnamed-chunk-14-2.png" width="672"></p>
+<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CA.html">CA</a></span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Symmetric"</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
-<span>  <span class="fu"><a href="../reference/samples.html">samples</a></span><span class="op">(</span>col<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"forestgreen"</span>,<span class="st">"magenta"</span><span class="op">)</span>, pch<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">12</span>,<span class="fl">17</span><span class="op">)</span>, label.side<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"top"</span>,<span class="st">"bottom"</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>samples <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-<p><img src="CA_in_biplotEZ_files/figure-html/unnamed-chunk-13-1.png" width="672"></p>
+<span>  <span class="fu"><a href="../reference/samples.html">samples</a></span><span class="op">(</span>col <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"forestgreen"</span>,<span class="st">"magenta"</span><span class="op">)</span>, pch <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">12</span>,<span class="fl">17</span><span class="op">)</span>, </span>
+<span>          label.side <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"top"</span>,<span class="st">"bottom"</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>samples <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<p><img src="CA_in_biplotEZ_files/figure-html/unnamed-chunk-15-1.png" width="672"></p>
+</div>
+<div class="section level3">
+<h3 id="additional-example">Additional example<a class="anchor" aria-label="anchor" href="#additional-example"></a>
+</h3>
+<p>Consider the South African Crime data set 2008, extracted from the
+South African police website (<a href="http://www.saps.gov.za/" class="external-link uri">http://www.saps.gov.za/</a>). <span class="citation">Gower,
+Lubbe, and Roux (2011)</span> :312.</p>
+<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">SACrime</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">matrix</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">1235</span>,<span class="fl">432</span>,<span class="fl">1824</span>,<span class="fl">1322</span>,<span class="fl">573</span>,<span class="fl">588</span>,<span class="fl">624</span>,<span class="fl">169</span>,<span class="fl">629</span>,<span class="fl">34479</span>,<span class="fl">16833</span>,<span class="fl">46993</span>,<span class="fl">30606</span>,<span class="fl">13670</span>,</span>
+<span>              <span class="fl">16849</span>,<span class="fl">15861</span>,<span class="fl">9898</span>,<span class="fl">24915</span>,<span class="fl">2160</span>,<span class="fl">939</span>,<span class="fl">5257</span>,<span class="fl">4946</span>,<span class="fl">722</span>,<span class="fl">1271</span>,<span class="fl">881</span>,<span class="fl">775</span>,<span class="fl">1844</span>,<span class="fl">5946</span>,</span>
+<span>              <span class="fl">4418</span>,<span class="fl">15117</span>,<span class="fl">10258</span>,<span class="fl">5401</span>,<span class="fl">4273</span>,<span class="fl">4987</span>,<span class="fl">1956</span>,<span class="fl">10639</span>,<span class="fl">29508</span>,<span class="fl">15705</span>,<span class="fl">62703</span>,<span class="fl">37203</span>,</span>
+<span>              <span class="fl">11857</span>,<span class="fl">18855</span>,<span class="fl">14722</span>,<span class="fl">4924</span>,<span class="fl">42376</span>,<span class="fl">604</span>,<span class="fl">156</span>,<span class="fl">7466</span>,<span class="fl">3889</span>,<span class="fl">203</span>,<span class="fl">664</span>,<span class="fl">291</span>,<span class="fl">5</span>,<span class="fl">923</span>,<span class="fl">19875</span>,</span>
+<span>              <span class="fl">19885</span>,<span class="fl">57153</span>,<span class="fl">29410</span>,<span class="fl">11024</span>,<span class="fl">12202</span>,<span class="fl">10406</span>,<span class="fl">5431</span>,<span class="fl">32663</span>,<span class="fl">7086</span>,<span class="fl">4193</span>,<span class="fl">22152</span>,<span class="fl">9264</span>,<span class="fl">3760</span>,</span>
+<span>              <span class="fl">4752</span>,<span class="fl">3863</span>,<span class="fl">1337</span>,<span class="fl">8578</span>,<span class="fl">7929</span>,<span class="fl">4525</span>,<span class="fl">12348</span>,<span class="fl">24174</span>,<span class="fl">3198</span>,<span class="fl">1770</span>,<span class="fl">7004</span>,<span class="fl">2201</span>,<span class="fl">45985</span>,<span class="fl">764</span>,</span>
+<span>              <span class="fl">427</span>,<span class="fl">1501</span>,<span class="fl">1197</span>,<span class="fl">215</span>,<span class="fl">251</span>,<span class="fl">345</span>,<span class="fl">213</span>,<span class="fl">1850</span>,<span class="fl">3515</span>,<span class="fl">879</span>,<span class="fl">3674</span>,<span class="fl">4713</span>,<span class="fl">696</span>,<span class="fl">835</span>,<span class="fl">917</span>,<span class="fl">422</span>,<span class="fl">2836</span>,</span>
+<span>              <span class="fl">88</span>,<span class="fl">59</span>,<span class="fl">174</span>,<span class="fl">76</span>,<span class="fl">31</span>,<span class="fl">61</span>,<span class="fl">117</span>,<span class="fl">32</span>,<span class="fl">257</span>,<span class="fl">5499</span>,<span class="fl">2628</span>,<span class="fl">8073</span>,<span class="fl">6502</span>,<span class="fl">2816</span>,<span class="fl">2635</span>,<span class="fl">3017</span>,<span class="fl">1020</span>,<span class="fl">4000</span>,</span>
+<span>              <span class="fl">8939</span>,<span class="fl">4501</span>,<span class="fl">50970</span>,<span class="fl">24290</span>,<span class="fl">2447</span>,<span class="fl">5907</span>,<span class="fl">5528</span>,<span class="fl">1175</span>,<span class="fl">14555</span><span class="op">)</span>,nrow<span class="op">=</span><span class="fl">9</span>, ncol<span class="op">=</span><span class="fl">14</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/dimnames.html" class="external-link">dimnames</a></span><span class="op">(</span><span class="va">SACrime</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"ECpe"</span>, <span class="st">"FrSt"</span>, <span class="st">"Gaut"</span>, <span class="st">"KZN"</span>,  <span class="st">"Limp"</span>, <span class="st">"Mpml"</span>, <span class="st">"NWst"</span>, <span class="st">"NCpe"</span>,</span>
+<span>                            <span class="st">"WCpe"</span><span class="op">)</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"Arsn"</span>, <span class="st">"AGBH"</span>, <span class="st">"AtMr"</span>, <span class="st">"BNRs"</span>, <span class="st">"BRs"</span>,  <span class="st">"CrJk"</span>,</span>
+<span>                                              <span class="st">"CmAs"</span>, <span class="st">"CmRb"</span>, <span class="st">"DrgR"</span>, <span class="st">"InAs"</span>, <span class="st">"Mrd"</span>, <span class="st">"PubV"</span>, </span>
+<span>                                              <span class="st">"Rape"</span>, <span class="st">"RAC"</span> <span class="op">)</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/dimnames.html" class="external-link">dimnames</a></span><span class="op">(</span><span class="va">SACrime</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="st">"Provinces"</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/dimnames.html" class="external-link">dimnames</a></span><span class="op">(</span><span class="va">SACrime</span><span class="op">)</span><span class="op">)</span><span class="op">[[</span><span class="fl">2</span><span class="op">]</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="st">"Crimes"</span></span>
+<span><span class="va">SACrime</span></span>
+<span><span class="co">#&gt;          Crimes</span></span>
+<span><span class="co">#&gt; Provinces Arsn  AGBH AtMr  BNRs   BRs CrJk  CmAs  CmRb  DrgR InAs  Mrd PubV</span></span>
+<span><span class="co">#&gt;      ECpe 1235 34479 2160  5946 29508  604 19875  7086  7929  764 3515   88</span></span>
+<span><span class="co">#&gt;      FrSt  432 16833  939  4418 15705  156 19885  4193  4525  427  879   59</span></span>
+<span><span class="co">#&gt;      Gaut 1824 46993 5257 15117 62703 7466 57153 22152 12348 1501 3674  174</span></span>
+<span><span class="co">#&gt;      KZN  1322 30606 4946 10258 37203 3889 29410  9264 24174 1197 4713   76</span></span>
+<span><span class="co">#&gt;      Limp  573 13670  722  5401 11857  203 11024  3760  3198  215  696   31</span></span>
+<span><span class="co">#&gt;      Mpml  588 16849 1271  4273 18855  664 12202  4752  1770  251  835   61</span></span>
+<span><span class="co">#&gt;      NWst  624 15861  881  4987 14722  291 10406  3863  7004  345  917  117</span></span>
+<span><span class="co">#&gt;      NCpe  169  9898  775  1956  4924    5  5431  1337  2201  213  422   32</span></span>
+<span><span class="co">#&gt;      WCpe  629 24915 1844 10639 42376  923 32663  8578 45985 1850 2836  257</span></span>
+<span><span class="co">#&gt;          Crimes</span></span>
+<span><span class="co">#&gt; Provinces Rape   RAC</span></span>
+<span><span class="co">#&gt;      ECpe 5499  8939</span></span>
+<span><span class="co">#&gt;      FrSt 2628  4501</span></span>
+<span><span class="co">#&gt;      Gaut 8073 50970</span></span>
+<span><span class="co">#&gt;      KZN  6502 24290</span></span>
+<span><span class="co">#&gt;      Limp 2816  2447</span></span>
+<span><span class="co">#&gt;      Mpml 2635  5907</span></span>
+<span><span class="co">#&gt;      NWst 3017  5528</span></span>
+<span><span class="co">#&gt;      NCpe 1020  1175</span></span>
+<span><span class="co">#&gt;      WCpe 4000 14555</span></span></code></pre></div>
+<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">SACrime</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="../reference/CA.html">CA</a></span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Symmetric"</span>, lambda.scal <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="../reference/samples.html">samples</a></span><span class="op">(</span>col <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"cyan"</span>,<span class="st">"purple"</span><span class="op">)</span>, pch <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">15</span>,<span class="fl">17</span><span class="op">)</span>, label.side <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"bottom"</span>,<span class="st">"top"</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>samples <span class="op">=</span> <span class="cn">TRUE</span>, new <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<p><img src="CA_in_biplotEZ_files/figure-html/unnamed-chunk-17-1.png" width="672"><img src="CA_in_biplotEZ_files/figure-html/unnamed-chunk-17-2.png" width="672"></p>
 </div>
 </div>
 <div class="section level2">
@@ -368,35 +545,26 @@ <h2 class="unnumbered" id="references">References<a class="anchor" aria-label="a
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+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside>
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+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
-  <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.</p>
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.2.</p>
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diff --git a/docs/articles/Class_separation.html b/docs/articles/Class_separation.html
index 260a16d..838493d 100644
--- a/docs/articles/Class_separation.html
+++ b/docs/articles/Class_separation.html
@@ -4,107 +4,81 @@
 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
 <meta charset="utf-8">
 <meta http-equiv="X-UA-Compatible" content="IE=edge">
-<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
 <title>Class separation • biplotEZ</title>
-<!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png">
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-<!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.1/jquery.min.js" integrity="sha512-v2CJ7UaYy4JwqLDIrZUI/4hqeoQieOmAZNXBeQyjo21dadnwR+8ZaIJVT8EE2iyI61OV8e6M8PP2/4hpQINQ/g==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous">
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-  <div class="col-md-9 contents">
-    <div class="page-header toc-ignore">
-      <h1 data-toc-skip>Class separation</h1>
+
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Class separation</h1>
             
       
-      
-      <div class="hidden name"><code>Class_separation.Rmd</code></div>
 
+      <div class="d-none name"><code>Class_separation.Rmd</code></div>
     </div>
 
     
     
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">biplotEZ</span><span class="op">)</span></span>
+<span><span class="co">#&gt; Welcome to biplotEZ! </span></span>
+<span><span class="co">#&gt; This package is used to construct biplots </span></span>
+<span><span class="co">#&gt; Run ?biplot or vignette() for more information</span></span>
 <span><span class="co">#&gt; </span></span>
 <span><span class="co">#&gt; Attaching package: 'biplotEZ'</span></span>
 <span><span class="co">#&gt; The following object is masked from 'package:stats':</span></span>
@@ -120,139 +94,193 @@ <h1 data-toc-skip>Class separation</h1>
 <div class="section level2">
 <h2 id="what-is-a-cva-biplot">What is a CVA biplot<a class="anchor" aria-label="anchor" href="#what-is-a-cva-biplot"></a>
 </h2>
-<p>Consider a data matrix <span class="math inline">\(\mathbf{X}:n
-\times p\)</span> containing data on <span class="math inline">\(n\)</span> objects and <span class="math inline">\(p\)</span> variables. In addition, a vector <span class="math inline">\(\mathbf{g}:n \times 1\)</span> contains
-information on class membership of each observation. Let <span class="math inline">\(G\)</span> indicate the total number of classes.
-CVA is closely related to linear discriminant anlaysis, in that the
-<span class="math inline">\(p\)</span> variables are transformed to
-<span class="math inline">\(p\)</span> new variables, called canonical
-variates, such that the classes are optimally separated in the canonical
-space. By optimally separated, we mean maximising the between class
-variance, relative to the within class variance. This can be formulated
-as follows:</p>
-<p>Let <span class="math inline">\(\mathbf{G}:n \times G\)</span> be an
-indicator matrix with <span class="math inline">\(g_{ij} = 0\)</span>
-unless observation <span class="math inline">\(i\)</span> belongs to
-class <span class="math inline">\(j\)</span> and then <span class="math inline">\(g_{ij} = 1\)</span>. The matrix <span class="math inline">\(\mathbf{G'G}\)</span> is a diagonal matrix
-containing the number of observations per class on the diagonal. We can
-form the matrix of class means <span class="math inline">\(\bar{\mathbf{X}}:G \times p =
-(\mathbf{G'G})^{-1} \mathbf{G'X}\)</span>. With the usual
-analysis of variance the total variance can be decomposed into a between
-class variance and within class variance:</p>
-<p><span class="math display">\[
+<p>Consider a data matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐗</mi><mo>:</mo><mi>n</mi><mo>×</mo><mi>p</mi></mrow><annotation encoding="application/x-tex">\mathbf{X}:n \times p</annotation></semantics></math>
+containing data on
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>n</mi><annotation encoding="application/x-tex">n</annotation></semantics></math>
+objects and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>p</mi><annotation encoding="application/x-tex">p</annotation></semantics></math>
+variables. In addition, a vector
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐠</mi><mo>:</mo><mi>n</mi><mo>×</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\mathbf{g}:n \times 1</annotation></semantics></math>
+contains information on class membership of each observation. Let
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>G</mi><annotation encoding="application/x-tex">G</annotation></semantics></math>
+indicate the total number of classes. CVA is closely related to linear
+discriminant anlaysis, in that the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>p</mi><annotation encoding="application/x-tex">p</annotation></semantics></math>
+variables are transformed to
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>p</mi><annotation encoding="application/x-tex">p</annotation></semantics></math>
+new variables, called canonical variates, such that the classes are
+optimally separated in the canonical space. By optimally separated, we
+mean maximising the between class variance, relative to the within class
+variance. This can be formulated as follows:</p>
+<p>Let
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐆</mi><mo>:</mo><mi>n</mi><mo>×</mo><mi>G</mi></mrow><annotation encoding="application/x-tex">\mathbf{G}:n \times G</annotation></semantics></math>
+be an indicator matrix with
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>g</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">g_{ij} = 0</annotation></semantics></math>
+unless observation
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>i</mi><annotation encoding="application/x-tex">i</annotation></semantics></math>
+belongs to class
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>j</mi><annotation encoding="application/x-tex">j</annotation></semantics></math>
+and then
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>g</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">g_{ij} = 1</annotation></semantics></math>.
+The matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐆</mi><mi mathvariant="bold">′</mi><mi>𝐆</mi></mrow><annotation encoding="application/x-tex">\mathbf{G'G}</annotation></semantics></math>
+is a diagonal matrix containing the number of observations per class on
+the diagonal. We can form the matrix of class means
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mo>:</mo><mi>G</mi><mo>×</mo><mi>p</mi><mo>=</mo><msup><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐆</mi><mi mathvariant="bold">′</mi><mi>𝐆</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow><mrow><mi>−</mi><mn>1</mn></mrow></msup><mrow><mi>𝐆</mi><mi mathvariant="bold">′</mi><mi>𝐗</mi></mrow></mrow><annotation encoding="application/x-tex">\bar{\mathbf{X}}:G \times p = (\mathbf{G'G})^{-1} \mathbf{G'X}</annotation></semantics></math>.
+With the usual analysis of variance the total variance can be decomposed
+into a between class variance and within class variance:</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐓</mi><mo>=</mo><mi>𝐁</mi><mo>+</mo><mi>𝐖</mi></mrow><annotation encoding="application/x-tex">
 \mathbf{T} = \mathbf{B} + \mathbf{W}
-\]</span></p>
-<p><span class="math display">\[
-\mathbf{X'X} = \mathbf{\bar{\mathbf{X}}'C \bar{\mathbf{X}}} +
-\mathbf{X' [I - G(G'G)^{-1}C(G'G)^{-1}G'] X}
-\]</span></p>
-<p>The default choice for the centring matrix <span class="math inline">\(\mathbf{C = G'G}\)</span> leads to the
-simplification</p>
-<p><span class="math display">\[
-\mathbf{X'X} = \mathbf{\bar{\mathbf{X}}'G'G
-\bar{\mathbf{X}}} + \mathbf{X' [I - G(G'G)^{-1}G'] X}.
-\]</span></p>
-<p>Other options are <span class="math inline">\(\mathbf{C = I}\)</span>
-and <span class="math inline">\(\mathbf{C} = (\mathbf{I}_G -
-\frac{1}{G}\mathbf{11'})\)</span>. To find the canonical variates we
-want to maximise the ratio</p>
-<p><span class="math display">\[
+</annotation></semantics></math></p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi>𝐗</mi><mi mathvariant="bold">′</mi><mi>𝐗</mi></mrow><mo>=</mo><mrow><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mi mathvariant="bold">′</mi><mi>𝐂</mi><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover></mrow><mo>+</mo><mrow><mi>𝐗</mi><mi mathvariant="bold">′</mi><mrow><mo stretchy="true" form="prefix" mathvariant="bold">[</mo><mi>𝐈</mi><mo mathvariant="bold">−</mo><mi>𝐆</mi><msup><mrow><mo stretchy="true" form="prefix" mathvariant="bold">(</mo><mi>𝐆</mi><mi mathvariant="bold">′</mi><mi>𝐆</mi><mo stretchy="true" form="postfix" mathvariant="bold">)</mo></mrow><mrow><mi mathvariant="bold">−</mi><mn>𝟏</mn></mrow></msup><mi>𝐂</mi><msup><mrow><mo stretchy="true" form="prefix" mathvariant="bold">(</mo><mi>𝐆</mi><mi mathvariant="bold">′</mi><mi>𝐆</mi><mo stretchy="true" form="postfix" mathvariant="bold">)</mo></mrow><mrow><mi mathvariant="bold">−</mi><mn>𝟏</mn></mrow></msup><mi>𝐆</mi><mi mathvariant="bold">′</mi><mo stretchy="true" form="postfix" mathvariant="bold">]</mo></mrow><mi>𝐗</mi></mrow></mrow><annotation encoding="application/x-tex">
+\mathbf{X'X} = \mathbf{\bar{\mathbf{X}}'C \bar{\mathbf{X}}} + \mathbf{X' [I - G(G'G)^{-1}C(G'G)^{-1}G'] X}
+</annotation></semantics></math></p>
+<p>The default choice for the centring matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐂</mi><mo mathvariant="bold">=</mo><mi>𝐆</mi><mi mathvariant="bold">′</mi><mi>𝐆</mi></mrow><annotation encoding="application/x-tex">\mathbf{C = G'G}</annotation></semantics></math>
+leads to the simplification</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi>𝐗</mi><mi mathvariant="bold">′</mi><mi>𝐗</mi></mrow><mo>=</mo><mrow><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mi mathvariant="bold">′</mi><mi>𝐆</mi><mi mathvariant="bold">′</mi><mi>𝐆</mi><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover></mrow><mo>+</mo><mrow><mi>𝐗</mi><mi mathvariant="bold">′</mi><mrow><mo stretchy="true" form="prefix" mathvariant="bold">[</mo><mi>𝐈</mi><mo mathvariant="bold">−</mo><mi>𝐆</mi><msup><mrow><mo stretchy="true" form="prefix" mathvariant="bold">(</mo><mi>𝐆</mi><mi mathvariant="bold">′</mi><mi>𝐆</mi><mo stretchy="true" form="postfix" mathvariant="bold">)</mo></mrow><mrow><mi mathvariant="bold">−</mi><mn>𝟏</mn></mrow></msup><mi>𝐆</mi><mi mathvariant="bold">′</mi><mo stretchy="true" form="postfix" mathvariant="bold">]</mo></mrow><mi>𝐗</mi></mrow><mi>.</mi></mrow><annotation encoding="application/x-tex">
+\mathbf{X'X} = \mathbf{\bar{\mathbf{X}}'G'G \bar{\mathbf{X}}} + \mathbf{X' [I - G(G'G)^{-1}G'] X}.
+</annotation></semantics></math></p>
+<p>Other options are
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐂</mi><mo mathvariant="bold">=</mo><mi>𝐈</mi></mrow><annotation encoding="application/x-tex">\mathbf{C = I}</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐂</mi><mo>=</mo><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>𝐈</mi><mi>G</mi></msub><mo>−</mo><mfrac><mn>1</mn><mi>G</mi></mfrac><mrow><mn>𝟏𝟏</mn><mi mathvariant="bold">′</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">\mathbf{C} = (\mathbf{I}_G - \frac{1}{G}\mathbf{11'})</annotation></semantics></math>.
+To find the canonical variates we want to maximise the ratio</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mfrac><mrow><mi>𝐦</mi><mi mathvariant="bold">′</mi><mi>𝐁</mi><mi>𝐦</mi></mrow><mrow><mi>𝐦</mi><mi mathvariant="bold">′</mi><mi>𝐖</mi><mi>𝐦</mi></mrow></mfrac><annotation encoding="application/x-tex">
 \frac{\mathbf{m'Bm}}{\mathbf{m'Wm}}
-\]</span></p>
-<p>subject to <span class="math inline">\(\mathbf{m'Wm} =
-1\)</span>. It can be shown that this leads to the following equivalent
-eigen equations:</p>
-<p><span class="math display">\[
+</annotation></semantics></math></p>
+<p>subject to
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi>𝐦</mi><mi mathvariant="bold">′</mi><mi>𝐖</mi><mi>𝐦</mi></mrow><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\mathbf{m'Wm} = 1</annotation></semantics></math>.
+It can be shown that this leads to the following equivalent eigen
+equations:</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>𝐖</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup><mrow><mi>𝐁</mi><mi>𝐌</mi></mrow><mo>=</mo><mrow><mi>𝐌</mi><mi>𝚲</mi></mrow></mrow><annotation encoding="application/x-tex">
 \mathbf{W}^{-1}\mathbf{BM} = \mathbf{M \Lambda} \tag{1}
-\]</span></p>
-<p><span class="math display">\[
+</annotation></semantics></math></p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi>𝐁</mi><mi>𝐌</mi></mrow><mo>=</mo><mrow><mi>𝐖</mi><mi>𝐌</mi><mi>𝚲</mi></mrow></mrow><annotation encoding="application/x-tex">
 \mathbf{BM} = \mathbf{WM \Lambda}
-\]</span></p>
-<p><span class="math display">\[
-(\mathbf{W}^{-\frac{1}{2}} \mathbf{B} \mathbf{W}^{-\frac{1}{2}})
-\mathbf{M} = (\mathbf{W}^{-\frac{1}{2}} \mathbf{M}) \mathbf{\Lambda}
-\]</span></p>
-<p>with <span class="math inline">\(\mathbf{M'BM}=
-\mathbf{\Lambda}\)</span> and <span class="math inline">\(\mathbf{M'WM}= \mathbf{I}\)</span>.</p>
-<p>Since the matrix <span class="math inline">\(\mathbf{W}^{-\frac{1}{2}} \mathbf{B}
-\mathbf{W}^{-\frac{1}{2}}\)</span> is symmetric and positive
-semi-definite the eigenvalues in the matrix <span class="math inline">\(\mathbf{\Lambda}\)</span> are positive and
-ordered. The rank of <span class="math inline">\(\mathbf{B} = min(p,
-G-1)\)</span> so that only the first <span class="math inline">\(rank(\mathbf{B})\)</span> eigenvalues are
-non-zero. We form the canonical variates with the transformation</p>
-<p><span class="math display">\[
+</annotation></semantics></math></p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo stretchy="true" form="prefix">(</mo><msup><mi>𝐖</mi><mrow><mi>−</mi><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></msup><mi>𝐁</mi><msup><mi>𝐖</mi><mrow><mi>−</mi><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></msup><mo stretchy="true" form="postfix">)</mo></mrow><mi>𝐌</mi><mo>=</mo><mrow><mo stretchy="true" form="prefix">(</mo><msup><mi>𝐖</mi><mrow><mi>−</mi><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></msup><mi>𝐌</mi><mo stretchy="true" form="postfix">)</mo></mrow><mi>𝚲</mi></mrow><annotation encoding="application/x-tex">
+(\mathbf{W}^{-\frac{1}{2}} \mathbf{B} \mathbf{W}^{-\frac{1}{2}}) \mathbf{M} = (\mathbf{W}^{-\frac{1}{2}} \mathbf{M}) \mathbf{\Lambda}
+</annotation></semantics></math></p>
+<p>with
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi>𝐌</mi><mi mathvariant="bold">′</mi><mi>𝐁</mi><mi>𝐌</mi></mrow><mo>=</mo><mi>𝚲</mi></mrow><annotation encoding="application/x-tex">\mathbf{M'BM}= \mathbf{\Lambda}</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi>𝐌</mi><mi mathvariant="bold">′</mi><mi>𝐖</mi><mi>𝐌</mi></mrow><mo>=</mo><mi>𝐈</mi></mrow><annotation encoding="application/x-tex">\mathbf{M'WM}= \mathbf{I}</annotation></semantics></math>.</p>
+<p>Since the matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>𝐖</mi><mrow><mi>−</mi><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></msup><mi>𝐁</mi><msup><mi>𝐖</mi><mrow><mi>−</mi><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></msup></mrow><annotation encoding="application/x-tex">\mathbf{W}^{-\frac{1}{2}} \mathbf{B} \mathbf{W}^{-\frac{1}{2}}</annotation></semantics></math>
+is symmetric and positive semi-definite the eigenvalues in the matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝚲</mi><annotation encoding="application/x-tex">\mathbf{\Lambda}</annotation></semantics></math>
+are positive and ordered. The rank of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐁</mi><mo>=</mo><mi>m</mi><mi>i</mi><mi>n</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>p</mi><mo>,</mo><mi>G</mi><mo>−</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">\mathbf{B} = min(p, G-1)</annotation></semantics></math>
+so that only the first
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi><mi>a</mi><mi>n</mi><mi>k</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐁</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">rank(\mathbf{B})</annotation></semantics></math>
+eigenvalues are non-zero. We form the canonical variates with the
+transformation</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mi>𝐘</mi><mo accent="true">‾</mo></mover><mo>=</mo><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mi>𝐌</mi><mi>.</mi></mrow><annotation encoding="application/x-tex">
 \bar{\mathbf{Y}} = \bar{\mathbf{X}}\mathbf{M}.
-\]</span></p>
+</annotation></semantics></math></p>
 <p>To construct a 2D biplot, we plot the first two canonical variates
-<span class="math inline">\(\bar{\mathbf{Z}} =
-\bar{\mathbf{X}}\mathbf{MJ}_2\)</span> where <span class="math inline">\(\mathbf{J}_2' = \begin{bmatrix} \mathbf{I}_2
-&amp; \mathbf{0} \end{bmatrix}\)</span>. We add the individual sample
-points with the same transformation</p>
-<p><span class="math display">\[
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mi>𝐙</mi><mo accent="true">‾</mo></mover><mo>=</mo><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><msub><mrow><mi>𝐌</mi><mi>𝐉</mi></mrow><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\bar{\mathbf{Z}} = \bar{\mathbf{X}}\mathbf{MJ}_2</annotation></semantics></math>
+where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝐉</mi><mn>2</mn></msub><mi>′</mi><mo>=</mo><mrow><mo stretchy="true" form="prefix">[</mo><mtable><mtr><mtd columnalign="center" style="text-align: center"><msub><mi>𝐈</mi><mn>2</mn></msub></mtd><mtd columnalign="center" style="text-align: center"><mn>𝟎</mn></mtd></mtr></mtable><mo stretchy="true" form="postfix">]</mo></mrow></mrow><annotation encoding="application/x-tex">\mathbf{J}_2' = \begin{bmatrix} \mathbf{I}_2 &amp; \mathbf{0} \end{bmatrix}</annotation></semantics></math>.
+We add the individual sample points with the same transformation</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐙</mi><mo>=</mo><mi>𝐗</mi><msub><mrow><mi>𝐌</mi><mi>𝐉</mi></mrow><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">
 \mathbf{Z} = \mathbf{X}\mathbf{MJ}_2
-\]</span> where <span class="math display">\[
+</annotation></semantics></math> where
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝐉</mi><mn>2</mn></msub><mo>=</mo><mrow><mo stretchy="true" form="prefix">[</mo><mtable><mtr><mtd columnalign="center" style="text-align: center"><msub><mi>𝐈</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd columnalign="center" style="text-align: center"><mn>𝟎</mn></mtd></mtr></mtable><mo stretchy="true" form="postfix">]</mo></mrow><mi>.</mi></mrow><annotation encoding="application/x-tex">
 \mathbf{J}_2 = \begin{bmatrix}
                 \mathbf{I}_2\\
                 \mathbf{0}
                \end{bmatrix}.
-\]</span> Interpolation of a new sample <span class="math inline">\(\mathbf{x}^*:p \times 1\)</span> follows as <span class="math inline">\({\mathbf{z}^*}':2 \times 1
-={\mathbf{x}^*}' \mathbf{MJ}_2\)</span>. Using the inverse
-transformation <span class="math inline">\(\mathbf{x}' =
-\mathbf{y}'\mathbf{M}^{-1}\)</span>, all the points that will
-predict <span class="math inline">\(\mu\)</span> for variable <span class="math inline">\(j\)</span> will have the form</p>
-<p><span class="math display">\[
+</annotation></semantics></math> Interpolation of a new sample
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>𝐱</mi><mo>*</mo></msup><mo>:</mo><mi>p</mi><mo>×</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\mathbf{x}^*:p \times 1</annotation></semantics></math>
+follows as
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>𝐳</mi><mo>*</mo></msup><mi>′</mi><mo>:</mo><mn>2</mn><mo>×</mo><mn>1</mn><mo>=</mo><msup><mi>𝐱</mi><mo>*</mo></msup><mi>′</mi><msub><mrow><mi>𝐌</mi><mi>𝐉</mi></mrow><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">{\mathbf{z}^*}':2 \times 1 ={\mathbf{x}^*}' \mathbf{MJ}_2</annotation></semantics></math>.
+Using the inverse transformation
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐱</mi><mi>′</mi><mo>=</mo><mi>𝐲</mi><mi>′</mi><msup><mi>𝐌</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup></mrow><annotation encoding="application/x-tex">\mathbf{x}' = \mathbf{y}'\mathbf{M}^{-1}</annotation></semantics></math>,
+all the points that will predict
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>μ</mi><annotation encoding="application/x-tex">\mu</annotation></semantics></math>
+for variable
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>j</mi><annotation encoding="application/x-tex">j</annotation></semantics></math>
+will have the form</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi><mo>=</mo><mi>𝐲</mi><mi>′</mi><msup><mi>𝐌</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup><msub><mi>𝐞</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">
 \mu = \mathbf{y}'\mathbf{M}^{-1} \mathbf{e}_j
-\]</span></p>
-<p>where <span class="math inline">\(\mathbf{e}_j\)</span> is a vector
-of zeros with a one in position <span class="math inline">\(j\)</span>.
-All the points in the 2D biplot that predict the value <span class="math inline">\(\mu\)</span> will have</p>
-<p><span class="math display">\[
-\mu = \begin{bmatrix} z_1 &amp; z_2 &amp; 0 &amp; \dots &amp;
-0\end{bmatrix}\mathbf{M}^{-1} \mathbf{e}_j
-\]</span></p>
+</annotation></semantics></math></p>
+<p>where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐞</mi><mi>j</mi></msub><annotation encoding="application/x-tex">\mathbf{e}_j</annotation></semantics></math>
+is a vector of zeros with a one in position
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>j</mi><annotation encoding="application/x-tex">j</annotation></semantics></math>.
+All the points in the 2D biplot that predict the value
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>μ</mi><annotation encoding="application/x-tex">\mu</annotation></semantics></math>
+will have</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi><mo>=</mo><mrow><mo stretchy="true" form="prefix">[</mo><mtable><mtr><mtd columnalign="center" style="text-align: center"><msub><mi>z</mi><mn>1</mn></msub></mtd><mtd columnalign="center" style="text-align: center"><msub><mi>z</mi><mn>2</mn></msub></mtd><mtd columnalign="center" style="text-align: center"><mn>0</mn></mtd><mtd columnalign="center" style="text-align: center"><mi>…</mi></mtd><mtd columnalign="center" style="text-align: center"><mn>0</mn></mtd></mtr></mtable><mo stretchy="true" form="postfix">]</mo></mrow><msup><mi>𝐌</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup><msub><mi>𝐞</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">
+\mu = \begin{bmatrix} z_1 &amp; z_2 &amp; 0 &amp; \dots &amp; 0\end{bmatrix}\mathbf{M}^{-1} \mathbf{e}_j
+</annotation></semantics></math></p>
 <p>defining the prediction line as</p>
-<p><span class="math display">\[
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi><mo>=</mo><msub><mi>𝐳</mi><mi>μ</mi></msub><mi>′</mi><msub><mi>𝐉</mi><mn>2</mn></msub><msup><mi>𝐌</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup><msub><mi>𝐞</mi><mi>j</mi></msub><mi>.</mi></mrow><annotation encoding="application/x-tex">
 \mu = \mathbf{z}_{\mu}' \mathbf{J}_2 \mathbf{M}^{-1} \mathbf{e}_j.
-\]</span></p>
-<p>Writing <span class="math inline">\(\mathbf{h}_{(j)} = \mathbf{J}_2
-\mathbf{M}^{-1} \mathbf{e}_j\)</span> the construction of biplot axes is
-similar to the discussion in the biplotEZ vignette for PCA biplots. The
-direction of the axis is given by <span class="math inline">\(\mathbf{h}_{(j)}\)</span>. To find the
-intersection of the prediction line with <span class="math inline">\(\mathbf{h}_{(j)}\)</span> we note that <span class="math display">\[
-\mathbf{z}'_{(\mu)}\mathbf{h}_{(j)} = \| \mathbf{z}_{(\mu)} \|^2 \|
-\mathbf{h}_{(j)} \|^2 cos(\mathbf{z}_{(\mu)},\mathbf{h}_{(j)}) =
-\| \mathbf{p} \|^2 \| \mathbf{h}_{(j)} \|^2
-\]</span> where <span class="math inline">\(\mathbf{p}\)</span> is the
-length of the orthogonal projection of <span class="math inline">\(\mathbf{z}_{(\mu)}\)</span> on <span class="math inline">\(\mathbf{h}_{(j)}\)</span>.</p>
-<p>Since <span class="math inline">\(\mathbf{p}\)</span> is along <span class="math inline">\(\mathbf{h}_{(j)}\)</span> we can write <span class="math inline">\(\mathbf{p} = c\mathbf{h}_{(j)}\)</span> and all
-points on the prediction line <span class="math inline">\(\mu =
-\mathbf{z}'_{\mu}\mathbf{h}_{(j)}\)</span> project on the same point
-<span class="math inline">\(c_{\mu}\mathbf{h}_{(j)}\)</span>. We solve
-for <span class="math inline">\(c_{\mu}\)</span> from <span class="math display">\[
-\mu = \mathbf{z}'_{\mu}\mathbf{h}_{(j)}=\| \mathbf{p} \|^2 \|
-\mathbf{h}_{(j)} \|^2 =
-\| c_{\mu}\mathbf{h}_{(j)} \|^2 \| \mathbf{h}_{(j)} \|^2
-\]</span></p>
-<p><span class="math display">\[
+</annotation></semantics></math></p>
+<p>Writing
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo>=</mo><msub><mi>𝐉</mi><mn>2</mn></msub><msup><mi>𝐌</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup><msub><mi>𝐞</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">\mathbf{h}_{(j)} = \mathbf{J}_2 \mathbf{M}^{-1} \mathbf{e}_j</annotation></semantics></math>
+the construction of biplot axes is similar to the discussion in the
+biplotEZ vignette for PCA biplots. The direction of the axis is given by
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><annotation encoding="application/x-tex">\mathbf{h}_{(j)}</annotation></semantics></math>.
+To find the intersection of the prediction line with
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><annotation encoding="application/x-tex">\mathbf{h}_{(j)}</annotation></semantics></math>
+we note that
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐳</mi><msub><mi>′</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>μ</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo>=</mo><mo stretchy="false" form="postfix">∥</mo><msub><mi>𝐳</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>μ</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup><mo stretchy="false" form="postfix">∥</mo><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup><mi>c</mi><mi>o</mi><mi>s</mi><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>𝐳</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>μ</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo>,</mo><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mo stretchy="false" form="postfix">∥</mo><mi>𝐩</mi><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup><mo stretchy="false" form="postfix">∥</mo><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">
+\mathbf{z}'_{(\mu)}\mathbf{h}_{(j)} = \| \mathbf{z}_{(\mu)} \|^2 \| \mathbf{h}_{(j)} \|^2 cos(\mathbf{z}_{(\mu)},\mathbf{h}_{(j)}) = 
+\| \mathbf{p} \|^2 \| \mathbf{h}_{(j)} \|^2 
+</annotation></semantics></math> where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐩</mi><annotation encoding="application/x-tex">\mathbf{p}</annotation></semantics></math>
+is the length of the orthogonal projection of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐳</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>μ</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><annotation encoding="application/x-tex">\mathbf{z}_{(\mu)}</annotation></semantics></math>
+on
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><annotation encoding="application/x-tex">\mathbf{h}_{(j)}</annotation></semantics></math>.</p>
+<p>Since
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐩</mi><annotation encoding="application/x-tex">\mathbf{p}</annotation></semantics></math>
+is along
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><annotation encoding="application/x-tex">\mathbf{h}_{(j)}</annotation></semantics></math>
+we can write
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐩</mi><mo>=</mo><mi>c</mi><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow><annotation encoding="application/x-tex">\mathbf{p} = c\mathbf{h}_{(j)}</annotation></semantics></math>
+and all points on the prediction line
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi><mo>=</mo><mi>𝐳</mi><msub><mi>′</mi><mi>μ</mi></msub><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow><annotation encoding="application/x-tex">\mu = \mathbf{z}'_{\mu}\mathbf{h}_{(j)}</annotation></semantics></math>
+project on the same point
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>c</mi><mi>μ</mi></msub><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow><annotation encoding="application/x-tex">c_{\mu}\mathbf{h}_{(j)}</annotation></semantics></math>.
+We solve for
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>c</mi><mi>μ</mi></msub><annotation encoding="application/x-tex">c_{\mu}</annotation></semantics></math>
+from
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi><mo>=</mo><mi>𝐳</mi><msub><mi>′</mi><mi>μ</mi></msub><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo>=</mo><mo stretchy="false" form="postfix">∥</mo><mi>𝐩</mi><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup><mo stretchy="false" form="postfix">∥</mo><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup><mo>=</mo><mo stretchy="false" form="postfix">∥</mo><msub><mi>c</mi><mi>μ</mi></msub><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup><mo stretchy="false" form="postfix">∥</mo><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">
+\mu = \mathbf{z}'_{\mu}\mathbf{h}_{(j)}=\| \mathbf{p} \|^2 \| \mathbf{h}_{(j)} \|^2 = 
+\| c_{\mu}\mathbf{h}_{(j)} \|^2 \| \mathbf{h}_{(j)} \|^2 
+</annotation></semantics></math></p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>c</mi><mi>μ</mi></msub><mo>=</mo><mfrac><mi>μ</mi><mrow><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mi>′</mi><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow></mfrac><mi>.</mi></mrow><annotation encoding="application/x-tex">
 c_{\mu} = \frac{\mu}{\mathbf{h}_{(j)}'\mathbf{h}_{(j)}}.
-\]</span> If we select ‘nice’ scale markers <span class="math inline">\(\tau_{1}, \tau_{2}, \cdots \tau_{k}\)</span> for
-variable <span class="math inline">\(j\)</span>, then <span class="math inline">\(\tau_{h}-\bar{x}_j = \mu_{h}\)</span> and
-positions of these scale markers on <span class="math inline">\(\mathbf{h}_{(j)}\)</span> are given by <span class="math inline">\(p_{\mu_{1}}, p_{\mu_{2}}, \cdots
-p_{\mu_{k}}\)</span> with <span class="math display">\[
-p_{\mu_h} = c_{\mu_h}\mathbf{h}_{(j)}
-=  \frac{\mu_h}{\mathbf{h}_{(j)}'\mathbf{h}_{(j)}}\mathbf{h}_{(j)}
-\]</span></p>
-<p><span class="math display">\[
-= \frac{\mu_h}{\mathbf{e}_{(j)}' \mathbf{M'}^{-1} \mathbf{J}
-\mathbf{M}^{-1} \mathbf{e}_{(j)}}\ \mathbf{J}_2 \mathbf{M}^{-1}
-\mathbf{e}_{(j)}
-\]</span></p>
-<p>with <span class="math display">\[
+</annotation></semantics></math> If we select ‘nice’ scale markers
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>τ</mi><mn>1</mn></msub><mo>,</mo><msub><mi>τ</mi><mn>2</mn></msub><mo>,</mo><mi>⋯</mi><msub><mi>τ</mi><mi>k</mi></msub></mrow><annotation encoding="application/x-tex">\tau_{1}, \tau_{2}, \cdots \tau_{k}</annotation></semantics></math>
+for variable
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>j</mi><annotation encoding="application/x-tex">j</annotation></semantics></math>,
+then
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>τ</mi><mi>h</mi></msub><mo>−</mo><msub><mover><mi>x</mi><mo accent="true">‾</mo></mover><mi>j</mi></msub><mo>=</mo><msub><mi>μ</mi><mi>h</mi></msub></mrow><annotation encoding="application/x-tex">\tau_{h}-\bar{x}_j = \mu_{h}</annotation></semantics></math>
+and positions of these scale markers on
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><annotation encoding="application/x-tex">\mathbf{h}_{(j)}</annotation></semantics></math>
+are given by
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><msub><mi>μ</mi><mn>1</mn></msub></msub><mo>,</mo><msub><mi>p</mi><msub><mi>μ</mi><mn>2</mn></msub></msub><mo>,</mo><mi>⋯</mi><msub><mi>p</mi><msub><mi>μ</mi><mi>k</mi></msub></msub></mrow><annotation encoding="application/x-tex">p_{\mu_{1}}, p_{\mu_{2}}, \cdots p_{\mu_{k}}</annotation></semantics></math>
+with
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><msub><mi>μ</mi><mi>h</mi></msub></msub><mo>=</mo><msub><mi>c</mi><msub><mi>μ</mi><mi>h</mi></msub></msub><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo>=</mo><mfrac><msub><mi>μ</mi><mi>h</mi></msub><mrow><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mi>′</mi><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow></mfrac><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow><annotation encoding="application/x-tex">
+p_{\mu_h} = c_{\mu_h}\mathbf{h}_{(j)} =  \frac{\mu_h}{\mathbf{h}_{(j)}'\mathbf{h}_{(j)}}\mathbf{h}_{(j)}
+</annotation></semantics></math></p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>=</mo><mfrac><msub><mi>μ</mi><mi>h</mi></msub><mrow><msub><mi>𝐞</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mi>′</mi><msup><mrow><mi>𝐌</mi><mi mathvariant="bold">′</mi></mrow><mrow><mi>−</mi><mn>1</mn></mrow></msup><mi>𝐉</mi><msup><mi>𝐌</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup><msub><mi>𝐞</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow></mfrac><mspace width="0.222em"></mspace><msub><mi>𝐉</mi><mn>2</mn></msub><msup><mi>𝐌</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup><msub><mi>𝐞</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow><annotation encoding="application/x-tex">
+= \frac{\mu_h}{\mathbf{e}_{(j)}' \mathbf{M'}^{-1} \mathbf{J} \mathbf{M}^{-1} \mathbf{e}_{(j)}}\ \mathbf{J}_2 \mathbf{M}^{-1} \mathbf{e}_{(j)}
+</annotation></semantics></math></p>
+<p>with
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐉</mi><mo>=</mo><mrow><mo stretchy="true" form="prefix">[</mo><mtable><mtr><mtd columnalign="center" style="text-align: center"><msub><mi>𝐈</mi><mn>2</mn></msub></mtd><mtd columnalign="center" style="text-align: center"><mn>𝟎</mn></mtd></mtr><mtr><mtd columnalign="center" style="text-align: center"><mn>𝟎</mn></mtd><mtd columnalign="center" style="text-align: center"><mn>𝟎</mn></mtd></mtr></mtable><mo stretchy="true" form="postfix">]</mo></mrow><mi>.</mi></mrow><annotation encoding="application/x-tex">
 \mathbf{J} = \begin{bmatrix}
               \mathbf{I}_2 &amp; \mathbf{0}\\
               \mathbf{0} &amp; \mathbf{0}
              \end{bmatrix}.
-\]</span></p>
+</annotation></semantics></math></p>
 </div>
 <div class="section level2">
 <h2 id="the-function-cva">The function <code>CVA()</code><a class="anchor" aria-label="anchor" href="#the-function-cva"></a>
@@ -261,15 +289,20 @@ <h2 id="the-function-cva">The function <code>CVA()</code><a class="anchor" aria-
 optimally separating the classes according to <code>state.region</code>
 we call</p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CVA.html">CVA</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">state.region</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="../reference/CVA.html">CVA</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">state.region</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="Class_separation_files/figure-html/unnamed-chunk-2-1.png" width="672"></p>
-<p>Fitting <span class="math inline">\(\alpha\)</span>-bags to the
-classes makes it easier to compare class overlap and separation. For a
-detailed discussion on <span class="math inline">\(\alpha\)</span>-bags,
+<p>Fitting
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bags
+to the classes makes it easier to compare class overlap and separation.
+For a detailed discussion on
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bags,
 see the <em>biplotEZ</em> vignette.</p>
 <div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CVA.html">CVA</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">state.region</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/alpha.bags.html">alpha.bags</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
-<span>  <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span> <span class="op">(</span>bags <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span>
+<span>  <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span> <span class="op">(</span>bags <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span>
 <span><span class="co">#&gt; Computing 0.95 -bag for Northeast </span></span>
 <span><span class="co">#&gt; Computing 0.95 -bag for South </span></span>
 <span><span class="co">#&gt; Computing 0.95 -bag for North Central </span></span>
@@ -287,7 +320,8 @@ <h2 id="the-function-means">The function <code>means()</code><a class="anchor" a
 <div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/CVA.html">CVA</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">state.division</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
-<span>  <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>means <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<span>  <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>means <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="Class_separation_files/figure-html/unnamed-chunk-4-1.png" width="672"></p>
 <p>Instead of adding a legend, we can choose to label the class means.
 Furthermore, the colour of each class mean defaults to the colour of the
@@ -296,7 +330,8 @@ <h2 id="the-function-means">The function <code>means()</code><a class="anchor" a
 <div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/CVA.html">CVA</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">state.division</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
-<span>  <span class="fu"><a href="../reference/means.html">means</a></span><span class="op">(</span>label <span class="op">=</span> <span class="cn">TRUE</span>, col <span class="op">=</span> <span class="st">"olivedrab"</span>, pch <span class="op">=</span> <span class="fl">15</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<span>  <span class="fu"><a href="../reference/means.html">means</a></span><span class="op">(</span>label <span class="op">=</span> <span class="cn">TRUE</span>, col <span class="op">=</span> <span class="st">"olivedrab"</span>, pch <span class="op">=</span> <span class="fl">15</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="Class_separation_files/figure-html/unnamed-chunk-5-1.png" width="672"></p>
 <p>If we choose to only show the class means for the central states, the
 argument <code>which</code> is used either indicating the number(s) in
@@ -334,6 +369,22 @@ <h2 id="the-function-means">The function <code>means()</code><a class="anchor" a
 <p><img src="Class_separation_files/figure-html/unnamed-chunk-8-1.png" width="672"></p>
 </div>
 <div class="section level2">
+<h2 id="the-function-classify">The function <code>classify()</code><a class="anchor" aria-label="anchor" href="#the-function-classify"></a>
+</h2>
+<p>Classification regions can be added to the CVA biplot with the
+function <code><a href="../reference/classify.html">classify()</a></code>. The argument
+<code>classify.regions</code> must be set equal to <code>TRUE</code> to
+render the regions in the plot. Other arguments such as
+<code>col</code>, <code>opacity</code> and <code>borders</code> allows
+to change the aesthetics of the regions.</p>
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="../reference/CVA.html">CVA</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">state.division</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/classify.html">classify</a></span><span class="op">(</span>classify.regions <span class="op">=</span> <span class="cn">TRUE</span>,opacity <span class="op">=</span> <span class="fl">0.2</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<p><img src="Class_separation_files/figure-html/unnamed-chunk-9-1.png" width="672"></p>
+</div>
+<div class="section level2">
 <h2 id="the-functions-fit-measures-and-summary">The functions <code>fit.measures()</code> and
 <code>summary()</code><a class="anchor" aria-label="anchor" href="#the-functions-fit-measures-and-summary"></a>
 </h2>
@@ -343,45 +394,55 @@ <h2 id="the-functions-fit-measures-and-summary">The functions <code>fit.measures
 <code><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary()</a></code>.</p>
 <p>Canonical variate analysis can be considered as a transformation of
 the original variables to the canonical space followed by constructing a
-PCA biplot of canonical variables. The matrix of class means <span class="math inline">\(\bar{\mathbf{X}} = (\mathbf{G'G})^{-1}
-\mathbf{G'X}\)</span> is transformed to <span class="math inline">\(\mathbf{\bar{X}L}\)</span> where <span class="math inline">\(\mathbf{L}\)</span> is a non-singular matrix such
-that <span class="math inline">\(\mathbf{LL'=W}^{-1}\)</span>.
-Pricipal component analysis finds the orthogonal matrix <span class="math inline">\(\mathbf{V}\)</span> such that</p>
-<p><span class="math display">\[
+PCA biplot of canonical variables. The matrix of class means
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mo>=</mo><msup><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐆</mi><mi mathvariant="bold">′</mi><mi>𝐆</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow><mrow><mi>−</mi><mn>1</mn></mrow></msup><mrow><mi>𝐆</mi><mi mathvariant="bold">′</mi><mi>𝐗</mi></mrow></mrow><annotation encoding="application/x-tex">\bar{\mathbf{X}} = (\mathbf{G'G})^{-1} \mathbf{G'X}</annotation></semantics></math>
+is transformed to
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mi>𝐋</mi></mrow><annotation encoding="application/x-tex">\mathbf{\bar{X}L}</annotation></semantics></math>
+where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐋</mi><annotation encoding="application/x-tex">\mathbf{L}</annotation></semantics></math>
+is a non-singular matrix such that
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mrow><mi>𝐋</mi><mi>𝐋</mi><mi mathvariant="bold">′</mi><mo mathvariant="bold">=</mo><mi>𝐖</mi></mrow><mrow><mi>−</mi><mn>1</mn></mrow></msup><annotation encoding="application/x-tex">\mathbf{LL'=W}^{-1}</annotation></semantics></math>.
+Pricipal component analysis finds the orthogonal matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐕</mi><annotation encoding="application/x-tex">\mathbf{V}</annotation></semantics></math>
+such that</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo stretchy="true" form="prefix" mathvariant="bold">(</mo><mi>𝐋</mi><mi mathvariant="bold">′</mi><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mi mathvariant="bold">′</mi><mi>𝐂</mi><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mi>𝐋</mi><mo stretchy="true" form="postfix" mathvariant="bold">)</mo></mrow><mi>𝐕</mi><mo mathvariant="bold">=</mo><mi>𝐕</mi><mi>𝚲</mi></mrow><annotation encoding="application/x-tex">
 \mathbf{(L'\bar{X}'C\bar{X}L)V=V \Lambda}
-\]</span></p>
-<p>where <span class="math inline">\(\mathbf{M = LV}\)</span> as defined
-in section 1. The predicted values for the class means is given by</p>
-<p><span class="math display">\[
+</annotation></semantics></math></p>
+<p>where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐌</mi><mo mathvariant="bold">=</mo><mi>𝐋</mi><mi>𝐕</mi></mrow><annotation encoding="application/x-tex">\mathbf{M = LV}</annotation></semantics></math>
+as defined in section 1. The predicted values for the class means is
+given by</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mo accent="true">̂</mo></mover><mo>=</mo><mrow><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mi>𝐌</mi><mi>𝐉</mi></mrow><msup><mi>𝐌</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup><mi>.</mi></mrow><annotation encoding="application/x-tex">
 \mathbf{\hat{\bar{X}}} = \mathbf{\bar{X}MJ}\mathbf{M}^{-1}.
-\]</span></p>
+</annotation></semantics></math></p>
 <div class="section level3">
 <h3 id="overall-quality-of-fit">Overall quality of fit<a class="anchor" aria-label="anchor" href="#overall-quality-of-fit"></a>
 </h3>
 <p>Based on the two-step process described above, there are two measures
 of quality of fit. The quality of the approximation of the canonical
-variables <span class="math inline">\(\mathbf{\bar{X}L}\)</span> in the
-<span class="math inline">\(2\)</span>-dimensional display is given
-by</p>
-<p><span class="math display">\[
-Quality (canonical \: variables) = \frac{tr(\mathbf{\Lambda
-J})}{tr(\mathbf{\Lambda)}}
-\]</span> and the quality of the approximation of the original variables
-<span class="math inline">\(\mathbf{\bar{X}}\)</span> in the 2D CVA
-biplot is given by</p>
-<p><span class="math display">\[
-Quality (original \: variables) = \frac{tr(\mathbf{\Lambda
-J})}{tr(\mathbf{\Lambda)}}
-\]</span></p>
+variables
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mi>𝐋</mi></mrow><annotation encoding="application/x-tex">\mathbf{\bar{X}L}</annotation></semantics></math>
+in the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>2</mn><annotation encoding="application/x-tex">2</annotation></semantics></math>-dimensional
+display is given by</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi><mi>u</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>t</mi><mi>y</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>c</mi><mi>a</mi><mi>n</mi><mi>o</mi><mi>n</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>l</mi><mspace width="0.222em"></mspace><mi>v</mi><mi>a</mi><mi>r</mi><mi>i</mi><mi>a</mi><mi>b</mi><mi>l</mi><mi>e</mi><mi>s</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mfrac><mrow><mi>t</mi><mi>r</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝚲</mi><mi>𝐉</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>t</mi><mi>r</mi><mo stretchy="false" form="prefix">(</mo><mrow><mi>𝚲</mi><mo stretchy="false" form="postfix" mathvariant="bold">)</mo></mrow></mrow></mfrac></mrow><annotation encoding="application/x-tex">
+Quality (canonical \: variables) = \frac{tr(\mathbf{\Lambda J})}{tr(\mathbf{\Lambda)}}
+</annotation></semantics></math> and the quality of the approximation of
+the original variables
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><annotation encoding="application/x-tex">\mathbf{\bar{X}}</annotation></semantics></math>
+in the 2D CVA biplot is given by</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi><mi>u</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>t</mi><mi>y</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>o</mi><mi>r</mi><mi>i</mi><mi>g</mi><mi>i</mi><mi>n</mi><mi>a</mi><mi>l</mi><mspace width="0.222em"></mspace><mi>v</mi><mi>a</mi><mi>r</mi><mi>i</mi><mi>a</mi><mi>b</mi><mi>l</mi><mi>e</mi><mi>s</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mfrac><mrow><mi>t</mi><mi>r</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝚲</mi><mi>𝐉</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>t</mi><mi>r</mi><mo stretchy="false" form="prefix">(</mo><mrow><mi>𝚲</mi><mo stretchy="false" form="postfix" mathvariant="bold">)</mo></mrow></mrow></mfrac></mrow><annotation encoding="application/x-tex">
+Quality (original \: variables) = \frac{tr(\mathbf{\Lambda J})}{tr(\mathbf{\Lambda)}}
+</annotation></semantics></math></p>
 </div>
 <div class="section level3">
 <h3 id="adequacy-of-representation-of-variables">Adequacy of representation of variables<a class="anchor" aria-label="anchor" href="#adequacy-of-representation-of-variables"></a>
 </h3>
 <p>The adequacy with which each of the variables is represented in the
 biplot is given by the elementwise ratios</p>
-<p><span class="math display">\[
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>d</mi><mi>e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi>y</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐌</mi><mi>𝐉</mi><mi>𝐌</mi><mi mathvariant="bold">′</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐌</mi><mi>𝐌</mi><mi mathvariant="bold">′</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow></mfrac><mi>.</mi></mrow><annotation encoding="application/x-tex">
 Adequacy = \frac{diag(\mathbf{MJM'})}{diag(\mathbf{MM'})}.
-\]</span></p>
+</annotation></semantics></math></p>
 </div>
 <div class="section level3">
 <h3 id="predictivity">Predictivity<a class="anchor" aria-label="anchor" href="#predictivity"></a>
@@ -396,20 +457,18 @@ <h5 id="axis-predictivity">Axis predictivity<a class="anchor" aria-label="anchor
 </h5>
 <p>The elementwise ratios for the predictivity of each of the axes are
 given by</p>
-<p><span class="math display">\[
-axis \: predictivity =
-\frac{diag(\mathbf{\hat{\bar{X}}}'\mathbf{C\hat{\bar{X}}})}{diag(\mathbf{\bar{X}}'\mathbf{C\bar{X}})}.
-\]</span></p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mi>x</mi><mi>i</mi><mi>s</mi><mspace width="0.222em"></mspace><mi>p</mi><mi>r</mi><mi>e</mi><mi>d</mi><mi>i</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mover><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mo accent="true">̂</mo></mover><mi>′</mi><mrow><mi>𝐂</mi><mover><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mo accent="true">̂</mo></mover></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mi>′</mi><mrow><mi>𝐂</mi><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow></mfrac><mi>.</mi></mrow><annotation encoding="application/x-tex">
+axis \: predictivity = \frac{diag(\mathbf{\hat{\bar{X}}}'\mathbf{C\hat{\bar{X}}})}{diag(\mathbf{\bar{X}}'\mathbf{C\bar{X}})}.
+</annotation></semantics></math></p>
 </div>
 <div class="section level5">
 <h5 id="class-predictivity">Class predictivity<a class="anchor" aria-label="anchor" href="#class-predictivity"></a>
 </h5>
 <p>Similarly for each of the class means the elementwise ratio is
 computed from</p>
-<p><span class="math display">\[
-class \: predictivity =
-\frac{diag(\mathbf{C}^{\frac{1}{2}}\mathbf{\hat{\bar{X}}}'\mathbf{W^{-1}}\mathbf{\hat{\bar{X}}}\mathbf{C}^{\frac{1}{2}})}{diag(\mathbf{C}^{\frac{1}{2}}\mathbf{\bar{X}}'\mathbf{W^{-1}}\mathbf{\bar{X}}\mathbf{C}^{\frac{1}{2}})}.
-\]</span></p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mspace width="0.222em"></mspace><mi>p</mi><mi>r</mi><mi>e</mi><mi>d</mi><mi>i</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><msup><mi>𝐂</mi><mfrac><mn>1</mn><mn>2</mn></mfrac></msup><mover><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mo accent="true">̂</mo></mover><mi>′</mi><msup><mi>𝐖</mi><mrow><mi mathvariant="bold">−</mi><mn>𝟏</mn></mrow></msup><mover><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mo accent="true">̂</mo></mover><msup><mi>𝐂</mi><mfrac><mn>1</mn><mn>2</mn></mfrac></msup><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><msup><mi>𝐂</mi><mfrac><mn>1</mn><mn>2</mn></mfrac></msup><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><mi>′</mi><msup><mi>𝐖</mi><mrow><mi mathvariant="bold">−</mi><mn>𝟏</mn></mrow></msup><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><msup><mi>𝐂</mi><mfrac><mn>1</mn><mn>2</mn></mfrac></msup><mo stretchy="true" form="postfix">)</mo></mrow></mrow></mfrac><mi>.</mi></mrow><annotation encoding="application/x-tex">
+class \: predictivity = \frac{diag(\mathbf{C}^{\frac{1}{2}}\mathbf{\hat{\bar{X}}}'\mathbf{W^{-1}}\mathbf{\hat{\bar{X}}}\mathbf{C}^{\frac{1}{2}})}{diag(\mathbf{C}^{\frac{1}{2}}\mathbf{\bar{X}}'\mathbf{W^{-1}}\mathbf{\bar{X}}\mathbf{C}^{\frac{1}{2}})}.
+</annotation></semantics></math></p>
 </div>
 </div>
 <div class="section level4">
@@ -417,20 +476,19 @@ <h4 id="within-class-predictivity">Within class predictivity<a class="anchor" ar
 </h4>
 <p>We define the matrix of samples as deviations from their class means
 as</p>
-<p><span class="math display">\[
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐈</mi><mo mathvariant="bold">−</mo><mi>𝐇</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow><mi>𝐗</mi><mo>=</mo><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>𝐈</mi><mi>n</mi></msub><mo>−</mo><mi>𝐆</mi><msup><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐆</mi><mi mathvariant="bold">′</mi><mi>𝐆</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow><mrow><mi>−</mi><mn>1</mn></mrow></msup><mi>𝐆</mi><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow><mi>𝐗</mi></mrow><annotation encoding="application/x-tex">
 (\mathbf{I-H})\mathbf{X}=(\mathbf{I}_n-\mathbf{G}(\mathbf{G'G})^{-1}\mathbf{G}')\mathbf{X}
-\]</span></p>
-<p>where <span class="math inline">\(\mathbf{H} =
-\mathbf{G}(\mathbf{G'G})^{-1}\mathbf{G}'\)</span>.</p>
+</annotation></semantics></math></p>
+<p>where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐇</mi><mo>=</mo><mi>𝐆</mi><msup><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐆</mi><mi mathvariant="bold">′</mi><mi>𝐆</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow><mrow><mi>−</mi><mn>1</mn></mrow></msup><mi>𝐆</mi><mi>′</mi></mrow><annotation encoding="application/x-tex">\mathbf{H} = \mathbf{G}(\mathbf{G'G})^{-1}\mathbf{G}'</annotation></semantics></math>.</p>
 <div class="section level5">
 <h5 id="within-class-axis-predictivity">Within class axis predictivity<a class="anchor" aria-label="anchor" href="#within-class-axis-predictivity"></a>
 </h5>
 <p>The within class axis predictivity is computed as the elementwise
 ratios</p>
-<p><span class="math display">\[
-within \: class \: axis \: predictivity =
-\frac{diag(\mathbf{\hat{X}}'(\mathbf{I-H)\hat{X}})}{diag(\mathbf{X}'(\mathbf{I-H)X})}.
-\]</span></p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mi>i</mi><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mspace width="0.222em"></mspace><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mspace width="0.222em"></mspace><mi>a</mi><mi>x</mi><mi>i</mi><mi>s</mi><mspace width="0.222em"></mspace><mi>p</mi><mi>r</mi><mi>e</mi><mi>d</mi><mi>i</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mi>′</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐈</mi><mo mathvariant="bold">−</mo><mi>𝐇</mi><mo stretchy="false" form="postfix" mathvariant="bold">)</mo><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mo stretchy="false" form="prefix">(</mo><mi>𝐗</mi><mi>′</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐈</mi><mo mathvariant="bold">−</mo><mi>𝐇</mi><mo stretchy="false" form="postfix" mathvariant="bold">)</mo><mi>𝐗</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow></mfrac><mi>.</mi></mrow><annotation encoding="application/x-tex">
+within \: class \: axis \: predictivity = \frac{diag(\mathbf{\hat{X}}'(\mathbf{I-H)\hat{X}})}{diag(\mathbf{X}'(\mathbf{I-H)X})}.
+</annotation></semantics></math></p>
 </div>
 <div class="section level5">
 <h5 id="within-class-sample-predictivity">Within class sample predictivity<a class="anchor" aria-label="anchor" href="#within-class-sample-predictivity"></a>
@@ -438,49 +496,48 @@ <h5 id="within-class-sample-predictivity">Within class sample predictivity<a cla
 <p>Unlike PCA biplots, sample predictivity for CVA biplots are computed
 for the observations expressed as deviations from their class means. The
 elementwise ratios is obtained from</p>
-<p><span class="math display">\[
-within \: class \: axis \: predictivity =
-\frac{diag(\mathbf{(I-H)\hat{X}}\mathbf{W}^{-1}\mathbf{\hat{X}'(I-H)})}{diag(\mathbf{(I-H)X}\mathbf{W}^{-1}\mathbf{X'(I-H)})}.
-\]</span> To display the fit measures, we create a <code>biplot</code>
-object with the measures added by the function
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mi>i</mi><mi>t</mi><mi>h</mi><mi>i</mi><mi>n</mi><mspace width="0.222em"></mspace><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mspace width="0.222em"></mspace><mi>a</mi><mi>x</mi><mi>i</mi><mi>s</mi><mspace width="0.222em"></mspace><mi>p</mi><mi>r</mi><mi>e</mi><mi>d</mi><mi>i</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mrow><mo stretchy="true" form="prefix" mathvariant="bold">(</mo><mi>𝐈</mi><mo mathvariant="bold">−</mo><mi>𝐇</mi><mo stretchy="true" form="postfix" mathvariant="bold">)</mo></mrow><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover></mrow><msup><mi>𝐖</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup><mrow><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mi mathvariant="bold">′</mi><mrow><mo stretchy="true" form="prefix" mathvariant="bold">(</mo><mi>𝐈</mi><mo mathvariant="bold">−</mo><mi>𝐇</mi><mo stretchy="true" form="postfix" mathvariant="bold">)</mo></mrow></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mrow><mo stretchy="true" form="prefix" mathvariant="bold">(</mo><mi>𝐈</mi><mo mathvariant="bold">−</mo><mi>𝐇</mi><mo stretchy="true" form="postfix" mathvariant="bold">)</mo></mrow><mi>𝐗</mi></mrow><msup><mi>𝐖</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup><mrow><mi>𝐗</mi><mi mathvariant="bold">′</mi><mrow><mo stretchy="true" form="prefix" mathvariant="bold">(</mo><mi>𝐈</mi><mo mathvariant="bold">−</mo><mi>𝐇</mi><mo stretchy="true" form="postfix" mathvariant="bold">)</mo></mrow></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow></mfrac><mi>.</mi></mrow><annotation encoding="application/x-tex">
+within \: class \: axis \: predictivity = \frac{diag(\mathbf{(I-H)\hat{X}}\mathbf{W}^{-1}\mathbf{\hat{X}'(I-H)})}{diag(\mathbf{(I-H)X}\mathbf{W}^{-1}\mathbf{X'(I-H)})}.
+</annotation></semantics></math> To display the fit measures, we create
+a <code>biplot</code> object with the measures added by the function
 <code><a href="../reference/fit.measures.html">fit.measures()</a></code> and call <code><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary()</a></code>.</p>
-<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">obj</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>       <span class="fu"><a href="../reference/CVA.html">CVA</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">state.division</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>       <span class="fu"><a href="../reference/fit.measures.html">fit.measures</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span></span>
 <span>       <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-<p><img src="Class_separation_files/figure-html/unnamed-chunk-9-1.png" width="672"></p>
-<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<p><img src="Class_separation_files/figure-html/unnamed-chunk-10-1.png" width="672"></p>
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span> <span class="op">(</span><span class="va">obj</span><span class="op">)</span></span>
 <span><span class="co">#&gt; Object of class biplot, based on 50 samples and 8 variables.</span></span>
 <span><span class="co">#&gt; 8 numeric variables.</span></span>
 <span><span class="co">#&gt; 9 classes: New England Middle Atlantic South Atlantic East South Central West South Central East North Central West North Central Mountain Pacific </span></span>
 <span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Quality of fit of canonical variables = 70.7% </span></span>
-<span><span class="co">#&gt; Quality of fit of original variables = 70.5% </span></span>
-<span><span class="co">#&gt; Adequacy of variables:</span></span>
+<span><span class="co">#&gt; Quality of fit of canonical variables in 2 dimension(s) = 70.7% </span></span>
+<span><span class="co">#&gt; Quality of fit of original variables in 2 dimension(s) = 70.5% </span></span>
+<span><span class="co">#&gt; Adequacy of variables in 2 dimension(s):</span></span>
 <span><span class="co">#&gt; Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost </span></span>
 <span><span class="co">#&gt; 0.41716176 0.15621549 0.16136381 0.09759664 0.19426796 0.55332679 0.50497634 </span></span>
 <span><span class="co">#&gt;       Area </span></span>
 <span><span class="co">#&gt; 0.40661470 </span></span>
-<span><span class="co">#&gt; Axis predictivity:</span></span>
+<span><span class="co">#&gt; Axis predictivity in 2 dimension(s):</span></span>
 <span><span class="co">#&gt; Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost </span></span>
 <span><span class="co">#&gt;  0.1859124  0.4019427  0.8195756  0.6925389  0.7685373  0.9506355  0.7819324 </span></span>
 <span><span class="co">#&gt;       Area </span></span>
 <span><span class="co">#&gt;  0.8458143 </span></span>
-<span><span class="co">#&gt; Class predictivity:</span></span>
+<span><span class="co">#&gt; Class predictivity in 2 dimension(s):</span></span>
 <span><span class="co">#&gt;        New England    Middle Atlantic     South Atlantic East South Central </span></span>
 <span><span class="co">#&gt;          0.7922047          0.6570417          0.8191791          0.8777759 </span></span>
 <span><span class="co">#&gt; West South Central East North Central West North Central           Mountain </span></span>
 <span><span class="co">#&gt;          0.7416085          0.6370315          0.3265978          0.6825966 </span></span>
 <span><span class="co">#&gt;            Pacific </span></span>
 <span><span class="co">#&gt;          0.6700194 </span></span>
-<span><span class="co">#&gt; Within class axis predictivity:</span></span>
+<span><span class="co">#&gt; Within class axis predictivity in 2 dimension(s):</span></span>
 <span><span class="co">#&gt; Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost </span></span>
 <span><span class="co">#&gt; 0.04212318 0.09357501 0.25675620 0.19900223 0.29474972 0.75215233 0.31027358 </span></span>
 <span><span class="co">#&gt;       Area </span></span>
 <span><span class="co">#&gt; 0.12741853 </span></span>
-<span><span class="co">#&gt; Within class sample predictivity:</span></span>
+<span><span class="co">#&gt; Within class sample predictivity in 2 dimension(s):</span></span>
 <span><span class="co">#&gt;        Alabama         Alaska        Arizona       Arkansas     California </span></span>
 <span><span class="co">#&gt;    0.722548912    0.163442379    0.333341120    0.268976273    0.229139828 </span></span>
 <span><span class="co">#&gt;       Colorado    Connecticut       Delaware        Florida        Georgia </span></span>
@@ -508,7 +565,7 @@ <h5 id="within-class-sample-predictivity">Within class sample predictivity<a cla
 <code><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot()</a></code> is optional. It is further possible to select which
 fit measures to display in the <code><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary()</a></code> function where all
 measures default to <code>TRUE</code>.</p>
-<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">obj</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>       <span class="fu"><a href="../reference/CVA.html">CVA</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">state.region</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>       <span class="fu"><a href="../reference/fit.measures.html">fit.measures</a></span><span class="op">(</span><span class="op">)</span></span>
@@ -518,14 +575,14 @@ <h5 id="within-class-sample-predictivity">Within class sample predictivity<a cla
 <span><span class="co">#&gt; 8 numeric variables.</span></span>
 <span><span class="co">#&gt; 4 classes: Northeast South North Central West </span></span>
 <span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Quality of fit of canonical variables = 91.9% </span></span>
-<span><span class="co">#&gt; Quality of fit of original variables = 95.3% </span></span>
-<span><span class="co">#&gt; Axis predictivity:</span></span>
+<span><span class="co">#&gt; Quality of fit of canonical variables in 2 dimension(s) = 91.9% </span></span>
+<span><span class="co">#&gt; Quality of fit of original variables in 2 dimension(s) = 95.3% </span></span>
+<span><span class="co">#&gt; Axis predictivity in 2 dimension(s):</span></span>
 <span><span class="co">#&gt; Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost </span></span>
 <span><span class="co">#&gt;  0.9873763  0.9848608  0.8757913  0.9050208  0.9955088  0.9970346  0.9558192 </span></span>
 <span><span class="co">#&gt;       Area </span></span>
 <span><span class="co">#&gt;  0.9344651 </span></span>
-<span><span class="co">#&gt; Class predictivity:</span></span>
+<span><span class="co">#&gt; Class predictivity in 2 dimension(s):</span></span>
 <span><span class="co">#&gt;     Northeast         South North Central          West </span></span>
 <span><span class="co">#&gt;     0.8031465     0.9985089     0.6449906     0.9988469</span></span></code></pre></div>
 </div>
@@ -535,43 +592,58 @@ <h5 id="within-class-sample-predictivity">Within class sample predictivity<a cla
 <div class="section level2">
 <h2 id="additional-cva-dimensions">Additional CVA dimensions<a class="anchor" aria-label="anchor" href="#additional-cva-dimensions"></a>
 </h2>
-<p>It was mentioned that the eigen equation (1) has <span class="math inline">\(min(p, G-1)\)</span> non-zero eigenvalues. This
-implies that the CVA biplot for <span class="math inline">\(G=2\)</span>
+<p>It was mentioned that the eigen equation (1) has
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mi>i</mi><mi>n</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>p</mi><mo>,</mo><mi>G</mi><mo>−</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">min(p, G-1)</annotation></semantics></math>
+non-zero eigenvalues. This implies that the CVA biplot for
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi><mo>=</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">G=2</annotation></semantics></math>
 groups, reduces to a single dimension. If we write</p>
-<p><span class="math display">\[
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐌</mi><mo>=</mo><mrow><mo stretchy="true" form="prefix">[</mo><mtable><mtr><mtd columnalign="center" style="text-align: center"><msub><mi>𝐦</mi><mn>1</mn></msub></mtd><mtd columnalign="center" style="text-align: center"><msup><mi>𝐌</mi><mo>*</mo></msup></mtd></mtr></mtable><mo stretchy="true" form="postfix">]</mo></mrow></mrow><annotation encoding="application/x-tex">
 \mathbf{M} = \begin{bmatrix}
              \mathbf{m}_1 &amp; \mathbf{M}^*
              \end{bmatrix}
-\]</span> the columns of <span class="math inline">\(\mathbf{M}^*\)</span> forms a basis for the
-orthogonal complement of the canonical space defined by <span class="math inline">\(\mathbf{m}\)</span>_1. The argument
-<code>low.dim</code> determines how to uniquely define the second and
-third dimensions. By default <code>low.dim = "sample.opt"</code> which
-selects the dimensions by minimising total squared reconstruction error
-for samples.</p>
-<p>The representation of the canonical variates <span class="math inline">\(\bar{\mathbf{Z}} =
-\bar{\mathbf{X}}\mathbf{m}_1\)</span> are exact in the first dimension,
-but not the representation of the individual samples <span class="math inline">\({\mathbf{Z}} = {\mathbf{X}}\mathbf{m}_1\)</span>.
-If we define <span class="math inline">\(\mathbf{\hat{X}} =
-\mathbf{XMJ}\mathbf{M}^{-1}\)</span> with <span class="math inline">\(\mathbf{J}\)</span> a square matrix of zeros
-except for a <span class="math inline">\(1\)</span> in the first
-diagonal position, then the total square reconstruction error for
-samples is given by</p>
-<p><span class="math display">\[
-TSRES =
-tr{(\mathbf{X}-\mathbf{\hat{X}})'(\mathbf{X}-\mathbf{\hat{X}})}.
-\]</span> Define <span class="math display">\[
+</annotation></semantics></math> the columns of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>𝐌</mi><mo>*</mo></msup><annotation encoding="application/x-tex">\mathbf{M}^*</annotation></semantics></math>
+forms a basis for the orthogonal complement of the canonical space
+defined by
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐦</mi><annotation encoding="application/x-tex">\mathbf{m}</annotation></semantics></math>_1.
+The argument <code>low.dim</code> determines how to uniquely define the
+second and third dimensions. By default
+<code>low.dim = "sample.opt"</code> which selects the dimensions by
+minimising total squared reconstruction error for samples.</p>
+<p>The representation of the canonical variates
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mi>𝐙</mi><mo accent="true">‾</mo></mover><mo>=</mo><mover><mi>𝐗</mi><mo accent="true">‾</mo></mover><msub><mi>𝐦</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">\bar{\mathbf{Z}} = \bar{\mathbf{X}}\mathbf{m}_1</annotation></semantics></math>
+are exact in the first dimension, but not the representation of the
+individual samples
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐙</mi><mo>=</mo><mi>𝐗</mi><msub><mi>𝐦</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">{\mathbf{Z}} = {\mathbf{X}}\mathbf{m}_1</annotation></semantics></math>.
+If we define
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mo>=</mo><mrow><mi>𝐗</mi><mi>𝐌</mi><mi>𝐉</mi></mrow><msup><mi>𝐌</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup></mrow><annotation encoding="application/x-tex">\mathbf{\hat{X}} = \mathbf{XMJ}\mathbf{M}^{-1}</annotation></semantics></math>
+with
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐉</mi><annotation encoding="application/x-tex">\mathbf{J}</annotation></semantics></math>
+a square matrix of zeros except for a
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>1</mn><annotation encoding="application/x-tex">1</annotation></semantics></math>
+in the first diagonal position, then the total square reconstruction
+error for samples is given by</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mi>S</mi><mi>R</mi><mi>E</mi><mi>S</mi><mo>=</mo><mi>t</mi><mi>r</mi><mrow><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐗</mi><mo>−</mo><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mo stretchy="true" form="postfix">)</mo></mrow><mi>′</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐗</mi><mo>−</mo><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mi>.</mi></mrow><annotation encoding="application/x-tex">
+TSRES = tr{(\mathbf{X}-\mathbf{\hat{X}})'(\mathbf{X}-\mathbf{\hat{X}})}.
+</annotation></semantics></math> Define
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>𝐌</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup><mo>=</mo><mrow><mo stretchy="true" form="prefix">[</mo><mtable><mtr><mtd columnalign="center" style="text-align: center"><msup><mi>𝐌</mi><mrow><mo stretchy="true" form="prefix">(</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow></msup><mo>:</mo><mrow><mo stretchy="true" form="prefix">(</mo><mi>G</mi><mo>−</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow><mo>×</mo><mi>p</mi></mtd></mtr><mtr><mtd columnalign="center" style="text-align: center"><msup><mi>𝐌</mi><mrow><mo stretchy="true" form="prefix">(</mo><mn>2</mn><mo stretchy="true" form="postfix">)</mo></mrow></msup><mo>:</mo><mrow><mo stretchy="true" form="prefix">(</mo><mi>p</mi><mo>−</mo><mi>G</mi><mo>+</mo><mn>1</mn><mo stretchy="true" form="postfix">)</mo></mrow><mo>×</mo><mi>p</mi></mtd></mtr></mtable><mo stretchy="true" form="postfix">]</mo></mrow></mrow><annotation encoding="application/x-tex">
 \mathbf{M}^{-1} = \begin{bmatrix}
 \mathbf{M}^{(1)}:(G-1) \times p \\
 \mathbf{M}^{(2)}: (p-G+1) \times p
 \end{bmatrix}
-\]</span></p>
-<p>then <span class="math inline">\(TSRES\)</span> is minimised when</p>
-<p><span class="math display">\[
+</annotation></semantics></math></p>
+<p>then
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mi>S</mi><mi>R</mi><mi>E</mi><mi>S</mi></mrow><annotation encoding="application/x-tex">TSRES</annotation></semantics></math>
+is minimised when</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>𝐌</mi><mrow><mi>o</mi><mi>p</mi><mi>t</mi></mrow></msup><mo>=</mo><mrow><mo stretchy="true" form="prefix">[</mo><mtable><mtr><mtd columnalign="center" style="text-align: center"><msub><mi>𝐌</mi><mn>1</mn></msub></mtd><mtd columnalign="center" style="text-align: center"><msup><mi>𝐌</mi><mo>*</mo></msup><mi>𝐕</mi></mtd></mtr></mtable><mo stretchy="true" form="postfix">]</mo></mrow></mrow><annotation encoding="application/x-tex">
   \mathbf{M}^{opt} = \begin{bmatrix}
   \mathbf{M}_1 &amp; \mathbf{M}^*\mathbf{V}
   \end{bmatrix}
-\]</span></p>
-<pre><code>where $\mathbf{V}$ is the matrix of right singular vectors of $\mathbf{M}^{(2)}\mathbf{M}^{(2)'}$. </code></pre>
+</annotation></semantics></math></p>
+<p>where where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐕</mi><annotation encoding="application/x-tex">\mathbf{V}</annotation></semantics></math>
+is the matrix of right singular vectors of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>𝐌</mi><mrow><mo stretchy="true" form="prefix">(</mo><mn>2</mn><mo stretchy="true" form="postfix">)</mo></mrow></msup><msup><mi>𝐌</mi><mrow><mrow><mo stretchy="true" form="prefix">(</mo><mn>2</mn><mo stretchy="true" form="postfix">)</mo></mrow><mi>′</mi></mrow></msup></mrow><annotation encoding="application/x-tex">\mathbf{M}^{(2)}\mathbf{M}^{(2)'}</annotation></semantics></math>.</p>
 <div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">state.2group</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/ifelse.html" class="external-link">ifelse</a></span><span class="op">(</span><span class="va">state.division</span> <span class="op">==</span> <span class="st">"New England"</span> <span class="op">|</span> </span>
 <span>                       <span class="va">state.division</span> <span class="op">==</span> <span class="st">"Middle Atlantic"</span>  <span class="op">|</span></span>
@@ -582,18 +654,19 @@ <h2 id="additional-cva-dimensions">Additional CVA dimensions<a class="anchor" ar
 <span><span class="co">#&gt; Warning in CVA.biplot(biplot(state.x77), state.2group): The dimension of the</span></span>
 <span><span class="co">#&gt; canonical space &lt; dim.biplot sample.opt method used for additional</span></span>
 <span><span class="co">#&gt; dimension(s).</span></span></code></pre></div>
-<p><img src="Class_separation_files/figure-html/unnamed-chunk-11-1.png" width="672"></p>
-<p><span class="citation">@leRouxLubbe2024</span> discuss an alternative
-method for obtaining additional dimensions. When assuming underlying
-normal distributions, the Bhattacharyya distance can be optimised. This
-method is specific to the two class case and cannot be utilised to find
-a third dimension in a 3D CVA biplot with three classes.</p>
+<p><img src="Class_separation_files/figure-html/unnamed-chunk-12-1.png" width="672"></p>
+<p><span class="citation">le Roux and Gardner-Lubbe (2024)</span>
+discuss an alternative method for obtaining additional dimensions. When
+assuming underlying normal distributions, the Bhattacharyya distance can
+be optimised. This method is specific to the two class case and cannot
+be utilised to find a third dimension in a 3D CVA biplot with three
+classes.</p>
 <div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span> <span class="op">(</span><span class="va">state.x77</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/CVA.html">CVA</a></span> <span class="op">(</span><span class="va">state.2group</span>, low.dim<span class="op">=</span><span class="st">"Bha"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>means<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span>
 <span><span class="co">#&gt; Warning in CVA.biplot(biplot(state.x77), state.2group, low.dim = "Bha"): The</span></span>
 <span><span class="co">#&gt; dimension of the canonical space &lt; dim.biplot Bhattacharyya.dist method used</span></span>
 <span><span class="co">#&gt; for additional dimension(s).</span></span></code></pre></div>
-<p><img src="Class_separation_files/figure-html/unnamed-chunk-12-1.png" width="672"></p>
+<p><img src="Class_separation_files/figure-html/unnamed-chunk-13-1.png" width="672"></p>
 </div>
 <div class="section level2">
 <h2 id="analysis-of-distance-aod">Analysis of Distance (AoD)<a class="anchor" aria-label="anchor" href="#analysis-of-distance-aod"></a>
@@ -602,39 +675,56 @@ <h2 id="analysis-of-distance-aod">Analysis of Distance (AoD)<a class="anchor" ar
 decomposes the total sum of squared distances into a sum of squared
 distances between class means component and a sum of squared distances
 within classes component.</p>
-<p>Consider any Euclidean embeddable distance metric <span class="math inline">\(\psi_{ij}=\psi(\mathbf{x}_i,\mathbf{x}_j)\)</span>.
+<p>Consider any Euclidean embeddable distance metric
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ψ</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><mi>ψ</mi><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>𝐱</mi><mi>i</mi></msub><mo>,</mo><msub><mi>𝐱</mi><mi>j</mi></msub><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">\psi_{ij}=\psi(\mathbf{x}_i,\mathbf{x}_j)</annotation></semantics></math>.
 For a Euclidean embeddable metric it is possible to find high
-dimensional coordinates <span class="math inline">\(\mathbf{y}_i\)</span> and <span class="math inline">\(\mathbf{y}_j\)</span> such that the Euclidean
-distance between <span class="math inline">\(\mathbf{y}_i\)</span> and
-<span class="math inline">\(\mathbf{y}_j\)</span> is equal to <span class="math inline">\(\psi_{ij}\)</span>. Let the matrix <span class="math inline">\(\mathbf{\tilde\Psi}\)</span> contain the values
-<span class="math inline">\(-\frac{1}2{}\psi_{ij}^2\)</span> and
-similarly <span class="math inline">\(\mathbf{\tilde\Delta}\)</span> the
-values <span class="math inline">\(-\frac{1}2{}\delta_{hk}^2\)</span>
-where <span class="math inline">\(\delta_{hk}\)</span> represent the
-distance between class means <span class="math inline">\(h\)</span> and
-<span class="math inline">\(k\)</span>.</p>
-<p><span class="math display">\[
+dimensional coordinates
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐲</mi><mi>i</mi></msub><annotation encoding="application/x-tex">\mathbf{y}_i</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐲</mi><mi>j</mi></msub><annotation encoding="application/x-tex">\mathbf{y}_j</annotation></semantics></math>
+such that the Euclidean distance between
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐲</mi><mi>i</mi></msub><annotation encoding="application/x-tex">\mathbf{y}_i</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐲</mi><mi>j</mi></msub><annotation encoding="application/x-tex">\mathbf{y}_j</annotation></semantics></math>
+is equal to
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>ψ</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><annotation encoding="application/x-tex">\psi_{ij}</annotation></semantics></math>.
+Let the matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>𝚿</mi><mo accent="true">̃</mo></mover><annotation encoding="application/x-tex">\mathbf{\tilde\Psi}</annotation></semantics></math>
+contain the values
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>−</mi><mfrac><mn>1</mn><mn>2</mn></mfrac><mrow></mrow><msubsup><mi>ψ</mi><mrow><mi>i</mi><mi>j</mi></mrow><mn>2</mn></msubsup></mrow><annotation encoding="application/x-tex">-\frac{1}2{}\psi_{ij}^2</annotation></semantics></math>
+and similarly
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>𝚫</mi><mo accent="true">̃</mo></mover><annotation encoding="application/x-tex">\mathbf{\tilde\Delta}</annotation></semantics></math>
+the values
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>−</mi><mfrac><mn>1</mn><mn>2</mn></mfrac><mrow></mrow><msubsup><mi>δ</mi><mrow><mi>h</mi><mi>k</mi></mrow><mn>2</mn></msubsup></mrow><annotation encoding="application/x-tex">-\frac{1}2{}\delta_{hk}^2</annotation></semantics></math>
+where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>δ</mi><mrow><mi>h</mi><mi>k</mi></mrow></msub><annotation encoding="application/x-tex">\delta_{hk}</annotation></semantics></math>
+represent the distance between class means
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>h</mi><annotation encoding="application/x-tex">h</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>k</mi><annotation encoding="application/x-tex">k</annotation></semantics></math>.</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐓</mi><mo>=</mo><mi>𝐁</mi><mo>+</mo><mi>𝐖</mi></mrow><annotation encoding="application/x-tex">
 \mathbf{T} = \mathbf{B} + \mathbf{W}
-\]</span></p>
-<p><span class="math display">\[
-\mathbf{1'\tilde\Psi1} = \mathbf{n'\tilde\Delta n} +
-\sum_{k=1}^{G} \frac{n}{n_k}
-\mathbf{g}_k'\mathbf{\tilde\Psi}\mathbf{g}_k
-\]</span> where <span class="math inline">\(\mathbf{n}=\mathbf{(G'G)1}\)</span>. Thus, AoD
-differs from CVA in allowing any Euclidean embeddable measure of
-inter-class distance. As with CVA, these distances may be represented in
-maps with point representing the class means, supplemented by additional
-points representing the within-group variation. Principal coordinate
-analysis is performed, only on the <span class="math inline">\(G \times
-G\)</span> matrix <span class="math inline">\(\mathbf{\tilde\Delta}\)</span>.</p>
+</annotation></semantics></math></p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mn>𝟏</mn><mi mathvariant="bold">′</mi><mover><mi>𝚿</mi><mo accent="true">̃</mo></mover><mn>𝟏</mn></mrow><mo>=</mo><mrow><mi>𝐧</mi><mi mathvariant="bold">′</mi><mover><mi>𝚫</mi><mo accent="true">̃</mo></mover><mi>𝐧</mi></mrow><mo>+</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>G</mi></munderover><mfrac><mi>n</mi><msub><mi>n</mi><mi>k</mi></msub></mfrac><msub><mi>𝐠</mi><mi>k</mi></msub><mi>′</mi><mover><mi>𝚿</mi><mo accent="true">̃</mo></mover><msub><mi>𝐠</mi><mi>k</mi></msub></mrow><annotation encoding="application/x-tex">
+\mathbf{1'\tilde\Psi1} = \mathbf{n'\tilde\Delta n} + \sum_{k=1}^{G} \frac{n}{n_k} \mathbf{g}_k'\mathbf{\tilde\Psi}\mathbf{g}_k
+</annotation></semantics></math> where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐧</mi><mo>=</mo><mrow><mrow><mo stretchy="true" form="prefix" mathvariant="bold">(</mo><mi>𝐆</mi><mi mathvariant="bold">′</mi><mi>𝐆</mi><mo stretchy="true" form="postfix" mathvariant="bold">)</mo></mrow><mn>𝟏</mn></mrow></mrow><annotation encoding="application/x-tex">\mathbf{n}=\mathbf{(G'G)1}</annotation></semantics></math>.
+Thus, AoD differs from CVA in allowing any Euclidean embeddable measure
+of inter-class distance. As with CVA, these distances may be represented
+in maps with point representing the class means, supplemented by
+additional points representing the within-group variation. Principal
+coordinate analysis is performed, only on the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi><mo>×</mo><mi>G</mi></mrow><annotation encoding="application/x-tex">G \times G</annotation></semantics></math>
+matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>𝚫</mi><mo accent="true">̃</mo></mover><annotation encoding="application/x-tex">\mathbf{\tilde\Delta}</annotation></semantics></math>.</p>
 <div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/AoD.html">AoD</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">state.region</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-<p><img src="Class_separation_files/figure-html/unnamed-chunk-13-1.png" width="672"></p>
+<p><img src="Class_separation_files/figure-html/unnamed-chunk-14-1.png" width="672"></p>
 <p>By default linear regression biplot axes are fitted to the plot.
 Alternatively, spline axes can be constructed.</p>
 <div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/AoD.html">AoD</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">state.region</span>, axes <span class="op">=</span> <span class="st">"splines"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-<p><img src="Class_separation_files/figure-html/unnamed-chunk-14-1.png" width="672"></p>
+<p><img src="Class_separation_files/figure-html/unnamed-chunk-15-1.png" width="672"></p>
 <pre><code><span><span class="co">#&gt; Calculating spline axis for variable 1 </span></span>
 <span><span class="co">#&gt; Calculating spline axis for variable 2 </span></span>
 <span><span class="co">#&gt; Calculating spline axis for variable 3 </span></span>
@@ -649,7 +739,7 @@ <h2 id="analysis-of-distance-aod">Analysis of Distance (AoD)<a class="anchor" ar
 <div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/AoD.html">AoD</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">state.region</span>, axes <span class="op">=</span> <span class="st">"splines"</span>, dist.func<span class="op">=</span><span class="va">sqrtManhattan</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
-<p><img src="Class_separation_files/figure-html/unnamed-chunk-15-1.png" width="672"></p>
+<p><img src="Class_separation_files/figure-html/unnamed-chunk-16-1.png" width="672"></p>
 <pre><code><span><span class="co">#&gt; Calculating spline axis for variable 1 </span></span>
 <span><span class="co">#&gt; Calculating spline axis for variable 2 </span></span>
 <span><span class="co">#&gt; Calculating spline axis for variable 3 </span></span>
@@ -660,38 +750,36 @@ <h2 id="analysis-of-distance-aod">Analysis of Distance (AoD)<a class="anchor" ar
 <span><span class="co">#&gt; Calculating spline axis for variable 8</span></span></code></pre>
 </div>
 <div class="section level2">
-<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
+<h2 class="unnumbered" id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
 </h2>
+<div id="refs" class="references csl-bib-body hanging-indent" entry-spacing="0">
+<div id="ref-leRouxLubbe2024" class="csl-entry">
+le Roux, N. J, and S. Gardner-Lubbe. 2024. <span>“A Two-Group Canonical
+Variate Analysis Biplot for an Optimal Display of Bothmeans and
+Cases.”</span> <em>Advances in Data Analysis and Classification</em>.
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-      <h1 data-toc-skip>MDS</h1>
+
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>MDS</h1>
             
       
-      
-      <div class="hidden name"><code>MDS.Rmd</code></div>
 
+      <div class="d-none name"><code>MDS.Rmd</code></div>
     </div>
 
     
     
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va">biplotEZ</span><span class="op">)</span></span>
+<span><span class="co">#&gt; Welcome to biplotEZ! </span></span>
+<span><span class="co">#&gt; This package is used to construct biplots </span></span>
+<span><span class="co">#&gt; Run ?biplot or vignette() for more information</span></span>
 <span><span class="co">#&gt; </span></span>
 <span><span class="co">#&gt; Attaching package: 'biplotEZ'</span></span>
 <span><span class="co">#&gt; The following object is masked from 'package:stats':</span></span>
@@ -116,14 +90,15 @@ <h1 data-toc-skip>MDS</h1>
 <h2 id="what-is-mds">What is MDS<a class="anchor" aria-label="anchor" href="#what-is-mds"></a>
 </h2>
 <p>In general, multidimensional scaling deals with constructing a low
-dimensional map of <span class="math inline">\(n\)</span> samples such
-that the Euclidean distances between the samples match a given set of
-dissimilarities <span class="math inline">\(\mathbf{\Delta}:n \times
-n\)</span> as closely as possible. Here the focus is on Principal
-Coordinate Analysis (PCO), an approach based on the singular value
-decomposition of a matrix. However, the regression biplot provides a
-general structure for fitting any 2D map of samples with biplot
-axes.</p>
+dimensional map of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>n</mi><annotation encoding="application/x-tex">n</annotation></semantics></math>
+samples such that the Euclidean distances between the samples match a
+given set of dissimilarities
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝚫</mi><mo>:</mo><mi>n</mi><mo>×</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">\mathbf{\Delta}:n \times n</annotation></semantics></math>
+as closely as possible. Here the focus is on Principal Coordinate
+Analysis (PCO), an approach based on the singular value decomposition of
+a matrix. However, the regression biplot provides a general structure
+for fitting any 2D map of samples with biplot axes.</p>
 </div>
 <div class="section level2">
 <h2 id="regression-biplot">Regression biplot<a class="anchor" aria-label="anchor" href="#regression-biplot"></a>
@@ -133,18 +108,23 @@ <h2 id="regression-biplot">Regression biplot<a class="anchor" aria-label="anchor
 should contain the data set that will be used to construct the biplot
 axes. The second argument <code>Z</code> contains the coordinates of the
 samples in the MDS map. By default linear regression axes will be fitted
-to the plot. If <span class="math inline">\(\mathbf{X}\)</span> denote
-the data matrix, the directions of the biplot axes are found by solving
-the regression equation</p>
-<p><span class="math display">\[
+to the plot. If
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐗</mi><annotation encoding="application/x-tex">\mathbf{X}</annotation></semantics></math>
+denote the data matrix, the directions of the biplot axes are found by
+solving the regression equation</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐗</mi><mo>=</mo><mrow><mi>𝐙</mi><mi>𝐇</mi></mrow><mi>′</mi><mo>+</mo><mi>𝐄</mi><mi>.</mi></mrow><annotation encoding="application/x-tex">
 \mathbf{X} = \mathbf{ZH}' + \mathbf{E}.
-\]</span> The matrix <span class="math inline">\(\mathbf{H}'=(\mathbf{Z'Z})^{-1}\mathbf{Z'X}\)</span>
+</annotation></semantics></math> The matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐇</mi><mi>′</mi><mo>=</mo><msup><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐙</mi><mi mathvariant="bold">′</mi><mi>𝐙</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow><mrow><mi>−</mi><mn>1</mn></mrow></msup><mrow><mi>𝐙</mi><mi mathvariant="bold">′</mi><mi>𝐗</mi></mrow></mrow><annotation encoding="application/x-tex">\mathbf{H}'=(\mathbf{Z'Z})^{-1}\mathbf{Z'X}</annotation></semantics></math>
 and calibration of the axes proceed analogous to equation (2) in the
-biplotEZ vignette. The coordinates of the marker <span class="math inline">\(/mu\)</span> on biplot axis <span class="math inline">\(j\)</span> is given as follows</p>
-<p><span class="math display">\[
-p_{\mu}
-=  \frac{\mu}{\mathbf{h}_{(j)}'\mathbf{h}_{(j)}}\mathbf{h}_{(j)}.
-\]</span></p>
+biplotEZ vignette. The coordinates of the marker
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>/</mi><mi>m</mi><mi>u</mi></mrow><annotation encoding="application/x-tex">/mu</annotation></semantics></math>
+on biplot axis
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>j</mi><annotation encoding="application/x-tex">j</annotation></semantics></math>
+is given as follows</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>μ</mi></msub><mo>=</mo><mfrac><mi>μ</mi><mrow><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mi>′</mi><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow></mfrac><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mi>.</mi></mrow><annotation encoding="application/x-tex">
+p_{\mu} =  \frac{\mu}{\mathbf{h}_{(j)}'\mathbf{h}_{(j)}}\mathbf{h}_{(j)}.
+</annotation></semantics></math></p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">rock</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/regress.html">regress</a></span><span class="op">(</span>Z <span class="op">=</span> <span class="fu">MASS</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/MASS/man/sammon.html" class="external-link">sammon</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/dist.html" class="external-link">dist</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/scale.html" class="external-link">scale</a></span><span class="op">(</span><span class="va">rock</span><span class="op">)</span>, method<span class="op">=</span><span class="st">"manhattan"</span><span class="op">)</span><span class="op">)</span><span class="op">$</span><span class="va">points</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
@@ -155,11 +135,15 @@ <h2 id="regression-biplot">Regression biplot<a class="anchor" aria-label="anchor
 <span><span class="co">#&gt; stress after  30 iters: 0.01078, magic = 0.500</span></span></code></pre></div>
 <p><img src="MDS_files/figure-html/unnamed-chunk-2-1.png" width="672"></p>
 <p>More flexibility is provided by approximating the biplot axes using
-B-splines. A calibrated trajectory represented in a matrix <span class="math inline">\(\mathbf{H}:m \times 2\)</span> snakes through the
-samples points <span class="math inline">\(\mathbf{Z}\)</span> such that
-the marker on the trajectory which is closest to a particular sample
-gives the predicted value of that sample for the particular variable. To
-retain smoothness of the trajectory <span class="math inline">\(\mathbf{H}\)</span>, B-splines are used.</p>
+B-splines. A calibrated trajectory represented in a matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐇</mi><mo>:</mo><mi>m</mi><mo>×</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">\mathbf{H}:m \times 2</annotation></semantics></math>
+snakes through the samples points
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐙</mi><annotation encoding="application/x-tex">\mathbf{Z}</annotation></semantics></math>
+such that the marker on the trajectory which is closest to a particular
+sample gives the predicted value of that sample for the particular
+variable. To retain smoothness of the trajectory
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐇</mi><annotation encoding="application/x-tex">\mathbf{H}</annotation></semantics></math>,
+B-splines are used.</p>
 <div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">rock</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/regress.html">regress</a></span><span class="op">(</span>Z <span class="op">=</span> <span class="fu">MASS</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/MASS/man/sammon.html" class="external-link">sammon</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/dist.html" class="external-link">dist</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/scale.html" class="external-link">scale</a></span><span class="op">(</span><span class="va">rock</span><span class="op">)</span>, method<span class="op">=</span><span class="st">"manhattan"</span><span class="op">)</span><span class="op">)</span><span class="op">$</span><span class="va">points</span>,</span>
@@ -178,36 +162,54 @@ <h2 id="regression-biplot">Regression biplot<a class="anchor" aria-label="anchor
 <div class="section level2">
 <h2 id="principal-coordinate-analysis-pco-biplots">Principal Coordinate Analysis (PCO) biplots<a class="anchor" aria-label="anchor" href="#principal-coordinate-analysis-pco-biplots"></a>
 </h2>
-<p>Let <span class="math inline">\(\mathbf{\tilde\Delta}\)</span> be the
-<span class="math inline">\(n \times n\)</span> matrix containing the
-values <span class="math inline">\(-\frac{1}{2}\delta_{ij}^2\)</span>
-where <span class="math inline">\(\delta_{ij}\)</span> represent the
-dissimilarity between objects <span class="math inline">\(i\)</span> and
-<span class="math inline">\(j\)</span>. If it is possible to find a set
-of coordinates <span class="math inline">\(\mathbf{Y}:n\times m\)</span>
-where typically <span class="math inline">\(m = n-1\)</span> such that
-the Euclidean distances between the rows of <span class="math inline">\(\mathbf{Y}\)</span> exactly match the
-dissimilarities <span class="math inline">\(\delta_{ij}\)</span>, the
-dissimilarity is known as a Euclidean embeddable distance metric. <span class="citation">J. C. Gower (1982)</span> shows that if the distances
-<span class="math inline">\(\delta_{ij}\)</span> are Euclidean
-embeddable, then</p>
-<p><span class="math display">\[
-(\mathbf{I}-\mathbf{1s}')\mathbf{\tilde\Delta}
-(\mathbf{I}-\mathbf{s1}')
-\]</span></p>
+<p>Let
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>𝚫</mi><mo accent="true">̃</mo></mover><annotation encoding="application/x-tex">\mathbf{\tilde\Delta}</annotation></semantics></math>
+be the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">n \times n</annotation></semantics></math>
+matrix containing the values
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>−</mi><mfrac><mn>1</mn><mn>2</mn></mfrac><msubsup><mi>δ</mi><mrow><mi>i</mi><mi>j</mi></mrow><mn>2</mn></msubsup></mrow><annotation encoding="application/x-tex">-\frac{1}{2}\delta_{ij}^2</annotation></semantics></math>
+where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>δ</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><annotation encoding="application/x-tex">\delta_{ij}</annotation></semantics></math>
+represent the dissimilarity between objects
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>i</mi><annotation encoding="application/x-tex">i</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>j</mi><annotation encoding="application/x-tex">j</annotation></semantics></math>.
+If it is possible to find a set of coordinates
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐘</mi><mo>:</mo><mi>n</mi><mo>×</mo><mi>m</mi></mrow><annotation encoding="application/x-tex">\mathbf{Y}:n\times m</annotation></semantics></math>
+where typically
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mo>=</mo><mi>n</mi><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">m = n-1</annotation></semantics></math>
+such that the Euclidean distances between the rows of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐘</mi><annotation encoding="application/x-tex">\mathbf{Y}</annotation></semantics></math>
+exactly match the dissimilarities
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>δ</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><annotation encoding="application/x-tex">\delta_{ij}</annotation></semantics></math>,
+the dissimilarity is known as a Euclidean embeddable distance metric.
+<span class="citation">J. C. Gower (1982)</span> shows that if the
+distances
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>δ</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><annotation encoding="application/x-tex">\delta_{ij}</annotation></semantics></math>
+are Euclidean embeddable, then</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐈</mi><mo>−</mo><mrow><mn>𝟏</mn><mi>𝐬</mi></mrow><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow><mover><mi>𝚫</mi><mo accent="true">̃</mo></mover><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐈</mi><mo>−</mo><mrow><mi>𝐬</mi><mn>𝟏</mn></mrow><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">
+(\mathbf{I}-\mathbf{1s}')\mathbf{\tilde\Delta} (\mathbf{I}-\mathbf{s1}')
+</annotation></semantics></math></p>
 <p>is positive semi-definite.</p>
-<p>The Euclidean representation of the samples is obtained as <span class="math inline">\(\mathbf{Y=V\Lambda}^{\frac{1}{2}}\)</span> where
-<span class="math inline">\((\mathbf{I}-\mathbf{1s}')\mathbf{\tilde\Delta}
-(\mathbf{I}-\mathbf{s1}') = \mathbf{V \Lambda V'}\)</span>.
-Since the coordinates in <span class="math inline">\(\mathbf{Y}\)</span>
-is already referred to their principal axes with <span class="math inline">\(\mathbf{Y'Y=\Lambda}\)</span>, the
-representation of the samples in a 2D biplot is obtained from the first
-two columns of <span class="math inline">\(\mathbf{Y}\)</span>.</p>
+<p>The Euclidean representation of the samples is obtained as
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mrow><mi>𝐘</mi><mo mathvariant="bold">=</mo><mi>𝐕</mi><mi>𝚲</mi></mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></msup><annotation encoding="application/x-tex">\mathbf{Y=V\Lambda}^{\frac{1}{2}}</annotation></semantics></math>
+where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐈</mi><mo>−</mo><mrow><mn>𝟏</mn><mi>𝐬</mi></mrow><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow><mover><mi>𝚫</mi><mo accent="true">̃</mo></mover><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐈</mi><mo>−</mo><mrow><mi>𝐬</mi><mn>𝟏</mn></mrow><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mrow><mi>𝐕</mi><mi>𝚲</mi><mi>𝐕</mi><mi mathvariant="bold">′</mi></mrow></mrow><annotation encoding="application/x-tex">(\mathbf{I}-\mathbf{1s}')\mathbf{\tilde\Delta} (\mathbf{I}-\mathbf{s1}') = \mathbf{V \Lambda V'}</annotation></semantics></math>.
+Since the coordinates in
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐘</mi><annotation encoding="application/x-tex">\mathbf{Y}</annotation></semantics></math>
+is already referred to their principal axes with
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐘</mi><mi mathvariant="bold">′</mi><mi>𝐘</mi><mo mathvariant="bold">=</mo><mi>𝚲</mi></mrow><annotation encoding="application/x-tex">\mathbf{Y'Y=\Lambda}</annotation></semantics></math>,
+the representation of the samples in a 2D biplot is obtained from the
+first two columns of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐘</mi><annotation encoding="application/x-tex">\mathbf{Y}</annotation></semantics></math>.</p>
 <p>In addition to the exact biplot axis representations discussed in
 <span class="citation">J. C. Gower, Lubbe, and Roux (2011)</span>
 approximate axes can be obtained. Linear axes are fitted with the
-regression method. The variables in the data matrix <span class="math inline">\(\mathbf{X}:n \times p\)</span> can be represented
-as biplot axes in the PCO biplot with the sample points <span class="math inline">\(\mathbf{Z=V\Lambda}^{\frac{1}{2}}\mathbf{J}_2\)</span>
+regression method. The variables in the data matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐗</mi><mo>:</mo><mi>n</mi><mo>×</mo><mi>p</mi></mrow><annotation encoding="application/x-tex">\mathbf{X}:n \times p</annotation></semantics></math>
+can be represented as biplot axes in the PCO biplot with the sample
+points
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow><mi>𝐙</mi><mo mathvariant="bold">=</mo><mi>𝐕</mi><mi>𝚲</mi></mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></msup><msub><mi>𝐉</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\mathbf{Z=V\Lambda}^{\frac{1}{2}}\mathbf{J}_2</annotation></semantics></math>
 according to the regression method discussed in section 2 above.</p>
 <div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">rock</span>, scale <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCO.html">PCO</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
@@ -224,17 +226,20 @@ <h2 id="principal-coordinate-analysis-pco-biplots">Principal Coordinate Analysis
 <span><span class="co">#&gt; Calculating spline axis for variable 4</span></span></code></pre>
 <p>By default the distance metric used for the analysis is Euclidean
 distance. The user can also specify the distance matrix
-<code>Dmat</code> as an <span class="math inline">\(n \times n\)</span>
+<code>Dmat</code> as an
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">n \times n</annotation></semantics></math>
 matrix of a <code>dist</code> object. As illustration of a metric that
 is Euclidean embeddable, the Clark’s distance</p>
-<p><span class="math display">\[
-\delta_{ij}^2 =
-\sum_{k=1}^{p}\left(\frac{x_{ik}-x_{jk}}{x_{ik}+x_{jk}}\right)^2
-\]</span></p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>δ</mi><mrow><mi>i</mi><mi>j</mi></mrow><mn>2</mn></msubsup><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>p</mi></munderover><msup><mrow><mo stretchy="true" form="prefix">(</mo><mfrac><mrow><msub><mi>x</mi><mrow><mi>i</mi><mi>k</mi></mrow></msub><mo>−</mo><msub><mi>x</mi><mrow><mi>j</mi><mi>k</mi></mrow></msub></mrow><mrow><msub><mi>x</mi><mrow><mi>i</mi><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>x</mi><mrow><mi>j</mi><mi>k</mi></mrow></msub></mrow></mfrac><mo stretchy="true" form="postfix">)</mo></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">
+\delta_{ij}^2 = \sum_{k=1}^{p}\left(\frac{x_{ik}-x_{jk}}{x_{ik}+x_{jk}}\right)^2
+</annotation></semantics></math></p>
 <p>as defined by <span class="citation">John C. Gower and Ngouenet
 (2005)</span> is calculated below and used for constructing a PCO
 biplot. Note that the metric is only defined for strictly positive
-values, so that the data is scaled to values between <span class="math inline">\(1\)</span> and <span class="math inline">\(2\)</span>.</p>
+values, so that the data is scaled to values between
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>1</mn><annotation encoding="application/x-tex">1</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>2</mn><annotation encoding="application/x-tex">2</annotation></semantics></math>.</p>
 <div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">Clark.dist</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">X</span><span class="op">)</span></span>
 <span><span class="op">{</span></span>
@@ -264,10 +269,9 @@ <h2 id="principal-coordinate-analysis-pco-biplots">Principal Coordinate Analysis
 <span><span class="co">#&gt; {</span></span>
 <span><span class="co">#&gt;     sqrt(stats::dist(X, method = "manhattan"))</span></span>
 <span><span class="co">#&gt; }</span></span>
-<span><span class="co">#&gt; &lt;bytecode: 0x00000209c33a73e0&gt;</span></span>
-<span><span class="co">#&gt; &lt;environment: namespace:biplotEZ&gt;</span></span></code></pre></div>
-<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">rock</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCO.html">PCO</a></span><span class="op">(</span>dist.func <span class="op">=</span> <span class="va">sqrtManhattan</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
+<span><span class="co">#&gt; &lt;bytecode: 0x000001fc00ec0e68&gt;</span></span>
+<span><span class="co">#&gt; &lt;environment: namespace:biplotEZ&gt;</span></span>
+<span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">rock</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCO.html">PCO</a></span><span class="op">(</span>dist.func <span class="op">=</span> <span class="va">sqrtManhattan</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="MDS_files/figure-html/unnamed-chunk-7-1.png" width="672"></p>
 </div>
 <div class="section level2">
@@ -289,35 +293,26 @@ <h2 class="unnumbered" id="references">References<a class="anchor" aria-label="a
 </div>
 </div>
 </div>
-  </div>
-
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-
-        <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
-    </nav>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside>
 </div>
 
-</div>
 
 
-
-      <footer><div class="copyright">
-  <p></p>
-<p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
-  <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.</p>
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.2.</p>
 </div>
 
-      </footer>
+    </footer>
 </div>
 
-  
 
 
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 </html>
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@@ -110,94 +81,172 @@ <h1 data-toc-skip>biplotEZ</h1>
 <div class="section level2">
 <h2 id="what-is-a-pca-biplot">What is a PCA biplot<a class="anchor" aria-label="anchor" href="#what-is-a-pca-biplot"></a>
 </h2>
-<p>Consider a data matrix <span class="math inline">\(\mathbf{X}^{*}:n
-\times p\)</span> containing data on <span class="math inline">\(n\)</span> objects and <span class="math inline">\(p\)</span> variables. To produce a 2D biplot, we
-need to optimally approximate <span class="math inline">\(\mathbf{X} =
-(\mathbf{I}_n-\frac{1}{n}\mathbf{11}')\mathbf{X}^{*}\)</span>
-(typically of rank <span class="math inline">\(p\)</span> with <span class="math inline">\(p&lt;n\)</span>) with a rank <span class="math inline">\(2\)</span> matrix. In terms of the least squares
-error, we want to</p>
-<p><span class="math display">\[
+<p>Consider a data matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>𝐗</mi><mo>*</mo></msup><mo>:</mo><mi>n</mi><mo>×</mo><mi>p</mi></mrow><annotation encoding="application/x-tex">\mathbf{X}^{*}:n \times p</annotation></semantics></math>
+containing data on
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>n</mi><annotation encoding="application/x-tex">n</annotation></semantics></math>
+objects and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>p</mi><annotation encoding="application/x-tex">p</annotation></semantics></math>
+variables. To produce a 2D biplot, we need to optimally approximate
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐗</mi><mo>=</mo><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>𝐈</mi><mi>n</mi></msub><mo>−</mo><mfrac><mn>1</mn><mi>n</mi></mfrac><mn>𝟏𝟏</mn><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow><msup><mi>𝐗</mi><mo>*</mo></msup></mrow><annotation encoding="application/x-tex">\mathbf{X} = (\mathbf{I}_n-\frac{1}{n}\mathbf{11}')\mathbf{X}^{*}</annotation></semantics></math>
+(typically of rank
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>p</mi><annotation encoding="application/x-tex">p</annotation></semantics></math>
+with
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo>&lt;</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">p&lt;n</annotation></semantics></math>)
+with a rank
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>2</mn><annotation encoding="application/x-tex">2</annotation></semantics></math>
+matrix. In terms of the least squares error, we want to</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mi>i</mi><mi>n</mi><mo stretchy="false" form="postfix">∥</mo><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mo>−</mo><mi>𝐗</mi><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">
 min \| \hat{\mathbf{X}}-\mathbf{X} \|^2
-\]</span> where <span class="math inline">\(rank(\hat{\mathbf{X}})=2\)</span>. It was shown by
-<span class="citation">Eckart and Young (1936)</span> that if the
-singular value decomposition of <span class="math inline">\(\mathbf{X} =
-\mathbf{UDV'}\)</span> then <span class="math display">\[
+</annotation></semantics></math> where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi><mi>a</mi><mi>n</mi><mi>k</mi><mrow><mo stretchy="true" form="prefix">(</mo><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">rank(\hat{\mathbf{X}})=2</annotation></semantics></math>.
+It was shown by <span class="citation">Eckart and Young (1936)</span>
+that if the singular value decomposition of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐗</mi><mo>=</mo><mrow><mi>𝐔</mi><mi>𝐃</mi><mi>𝐕</mi><mi mathvariant="bold">′</mi></mrow></mrow><annotation encoding="application/x-tex">\mathbf{X} = \mathbf{UDV'}</annotation></semantics></math>
+then
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mo>=</mo><mrow><mi>𝐔</mi><mi>𝐉</mi><mi>𝐃</mi><mi>𝐉</mi><mi>𝐕</mi><mi mathvariant="bold">′</mi></mrow></mrow><annotation encoding="application/x-tex">
 \hat{\mathbf{X}} = \mathbf{UJDJV'}
-\]</span> with <span class="math display">\[
+</annotation></semantics></math> with
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐉</mi><mo>=</mo><mrow><mo stretchy="true" form="prefix">[</mo><mtable><mtr><mtd columnalign="center" style="text-align: center"><msub><mi>𝐈</mi><mn>2</mn></msub></mtd><mtd columnalign="center" style="text-align: center"><mn>𝟎</mn></mtd></mtr><mtr><mtd columnalign="center" style="text-align: center"><mn>𝟎</mn></mtd><mtd columnalign="center" style="text-align: center"><mn>𝟎</mn></mtd></mtr></mtable><mo stretchy="true" form="postfix">]</mo></mrow></mrow><annotation encoding="application/x-tex">
 \mathbf{J} = \begin{bmatrix}
               \mathbf{I}_2 &amp; \mathbf{0}\\
               \mathbf{0} &amp; \mathbf{0}
              \end{bmatrix}
-\]</span> essentially selecting only the first two columns of <span class="math inline">\(\mathbf{U}\)</span>, the diagonal matrix of the
-first (largest) two singular values and the first two rows of <span class="math inline">\(\mathbf{V}'\)</span>. Define <span class="math display">\[
+</annotation></semantics></math> essentially selecting only the first
+two columns of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐔</mi><annotation encoding="application/x-tex">\mathbf{U}</annotation></semantics></math>,
+the diagonal matrix of the first (largest) two singular values and the
+first two rows of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐕</mi><mi>′</mi></mrow><annotation encoding="application/x-tex">\mathbf{V}'</annotation></semantics></math>.
+Define
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝐉</mi><mn>2</mn></msub><mo>=</mo><mrow><mo stretchy="true" form="prefix">[</mo><mtable><mtr><mtd columnalign="center" style="text-align: center"><msub><mi>𝐈</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd columnalign="center" style="text-align: center"><mn>𝟎</mn></mtd></mtr></mtable><mo stretchy="true" form="postfix">]</mo></mrow></mrow><annotation encoding="application/x-tex">
 \mathbf{J}_2 = \begin{bmatrix}
                 \mathbf{I}_2\\
                 \mathbf{0}
                \end{bmatrix}
-\]</span> then <span class="math inline">\(\mathbf{J}_2\mathbf{J}_2'
-= \mathbf{J}\)</span> and we can write <span class="math inline">\(\hat{\mathbf{X}} =
-(\mathbf{UDJ}_2)(\mathbf{VJ}_2)'\)</span>.</p>
+</annotation></semantics></math> then
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>𝐉</mi><mn>2</mn></msub><msub><mi>𝐉</mi><mn>2</mn></msub><mi>′</mi><mo>=</mo><mi>𝐉</mi></mrow><annotation encoding="application/x-tex">\mathbf{J}_2\mathbf{J}_2' = \mathbf{J}</annotation></semantics></math>
+and we can write
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mo>=</mo><mrow><mo stretchy="true" form="prefix">(</mo><msub><mrow><mi>𝐔</mi><mi>𝐃</mi><mi>𝐉</mi></mrow><mn>2</mn></msub><mo stretchy="true" form="postfix">)</mo></mrow><mrow><mo stretchy="true" form="prefix">(</mo><msub><mrow><mi>𝐕</mi><mi>𝐉</mi></mrow><mn>2</mn></msub><mo stretchy="true" form="postfix">)</mo></mrow><mi>′</mi></mrow><annotation encoding="application/x-tex">\hat{\mathbf{X}} = (\mathbf{UDJ}_2)(\mathbf{VJ}_2)'</annotation></semantics></math>.</p>
 <p><span class="citation">Gabriel (1971)</span> shows that any rank
-<span class="math inline">\(2\)</span> matrix can be written as <span class="math display">\[\begin{equation}
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>2</mn><annotation encoding="application/x-tex">2</annotation></semantics></math>
+matrix can be written as
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mo>=</mo><mi>𝐆</mi><mi>𝐇</mi><mi>′</mi></mrow><annotation encoding="application/x-tex">\begin{equation}
   \hat{\mathbf{X}} = \mathbf{G} \mathbf{H}' \tag{1}
-\end{equation}\]</span> where <span class="math inline">\(\mathbf{G}:n
-\times 2\)</span> and <span class="math inline">\(\mathbf{H}:p \times
-2\)</span>.The <span class="math inline">\(n\)</span> rows of <span class="math inline">\(\mathbf{G}\)</span> provide the <span class="math inline">\(n\)</span> pairs of 2D coordinates representing
-the rows of <span class="math inline">\(\hat{\mathbf{X}}\)</span> and
-the <span class="math inline">\(p\)</span> rows of <span class="math inline">\(\mathbf{H}\)</span> provide the <span class="math inline">\(p\)</span> pairs of 2D coordinates representing
-the columns of <span class="math inline">\(\hat{\mathbf{X}}\)</span>.
-Since <span class="math inline">\(\hat{\mathbf{X}} =
-(\mathbf{UDJ}_2)(\mathbf{VJ}_2)'\)</span>, by setting <span class="math inline">\(\mathbf{G}=\mathbf{UDJ}_2\)</span> and <span class="math inline">\(\mathbf{H}=\mathbf{VJ}_2\)</span> we obtains the
-best least squares approximation of <span class="math inline">\(\mathbf{X}\)</span>. <span class="citation">Gabriel (1971)</span> further shows that the
+\end{equation}</annotation></semantics></math> where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐆</mi><mo>:</mo><mi>n</mi><mo>×</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">\mathbf{G}:n \times 2</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐇</mi><mo>:</mo><mi>p</mi><mo>×</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">\mathbf{H}:p \times 2</annotation></semantics></math>.The
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>n</mi><annotation encoding="application/x-tex">n</annotation></semantics></math>
+rows of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐆</mi><annotation encoding="application/x-tex">\mathbf{G}</annotation></semantics></math>
+provide the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>n</mi><annotation encoding="application/x-tex">n</annotation></semantics></math>
+pairs of 2D coordinates representing the rows of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><annotation encoding="application/x-tex">\hat{\mathbf{X}}</annotation></semantics></math>
+and the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>p</mi><annotation encoding="application/x-tex">p</annotation></semantics></math>
+rows of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐇</mi><annotation encoding="application/x-tex">\mathbf{H}</annotation></semantics></math>
+provide the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>p</mi><annotation encoding="application/x-tex">p</annotation></semantics></math>
+pairs of 2D coordinates representing the columns of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><annotation encoding="application/x-tex">\hat{\mathbf{X}}</annotation></semantics></math>.
+Since
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mo>=</mo><mrow><mo stretchy="true" form="prefix">(</mo><msub><mrow><mi>𝐔</mi><mi>𝐃</mi><mi>𝐉</mi></mrow><mn>2</mn></msub><mo stretchy="true" form="postfix">)</mo></mrow><mrow><mo stretchy="true" form="prefix">(</mo><msub><mrow><mi>𝐕</mi><mi>𝐉</mi></mrow><mn>2</mn></msub><mo stretchy="true" form="postfix">)</mo></mrow><mi>′</mi></mrow><annotation encoding="application/x-tex">\hat{\mathbf{X}} = (\mathbf{UDJ}_2)(\mathbf{VJ}_2)'</annotation></semantics></math>,
+by setting
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐆</mi><mo>=</mo><msub><mrow><mi>𝐔</mi><mi>𝐃</mi><mi>𝐉</mi></mrow><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\mathbf{G}=\mathbf{UDJ}_2</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐇</mi><mo>=</mo><msub><mrow><mi>𝐕</mi><mi>𝐉</mi></mrow><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\mathbf{H}=\mathbf{VJ}_2</annotation></semantics></math>
+we obtains the best least squares approximation of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐗</mi><annotation encoding="application/x-tex">\mathbf{X}</annotation></semantics></math>.
+<span class="citation">Gabriel (1971)</span> further shows that the
 approximation of distances between the rows are optimal, while the
 approximation of correlations by the cosines between the angles of the
-rows of <span class="math inline">\(\mathbf{H}\)</span> is
-sub-optimal.</p>
-<p>The rows of <span class="math inline">\(\mathbf{G}\)</span> is
-plotted as points, representing the samples. The rows of <span class="math inline">\(\mathbf{H}\)</span> provide the directions of the
-axes for the variables. Since we have <span class="math display">\[
-x^{*}_{ij}-\bar{x}_j = x_{ij} \approx \hat{x}_{ij} =
-\mathbf{g}_{(i)}'\mathbf{h}_{(j)}
-\]</span> all the values that will predict <span class="math inline">\(\mu\)</span> for variable <span class="math inline">\(j\)</span> is of the form <span class="math display">\[
+rows of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐇</mi><annotation encoding="application/x-tex">\mathbf{H}</annotation></semantics></math>
+is sub-optimal.</p>
+<p>The rows of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐆</mi><annotation encoding="application/x-tex">\mathbf{G}</annotation></semantics></math>
+is plotted as points, representing the samples. The rows of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐇</mi><annotation encoding="application/x-tex">\mathbf{H}</annotation></semantics></math>
+provide the directions of the axes for the variables. Since we have
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>x</mi><mrow><mi>i</mi><mi>j</mi></mrow><mo>*</mo></msubsup><mo>−</mo><msub><mover><mi>x</mi><mo accent="true">‾</mo></mover><mi>j</mi></msub><mo>=</mo><msub><mi>x</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>≈</mo><msub><mover><mi>x</mi><mo accent="true">̂</mo></mover><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><msub><mi>𝐠</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>i</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mi>′</mi><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow><annotation encoding="application/x-tex">
+x^{*}_{ij}-\bar{x}_j = x_{ij} \approx \hat{x}_{ij} = \mathbf{g}_{(i)}'\mathbf{h}_{(j)}
+</annotation></semantics></math> all the values that will predict
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>μ</mi><annotation encoding="application/x-tex">\mu</annotation></semantics></math>
+for variable
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>j</mi><annotation encoding="application/x-tex">j</annotation></semantics></math>
+is of the form
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi><mo>=</mo><mi>𝐠</mi><msub><mi>′</mi><mi>μ</mi></msub><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow><annotation encoding="application/x-tex">
 \mu = \mathbf{g}'_{\mu}\mathbf{h}_{(j)}
-\]</span> which defines a straight line orthogonal to <span class="math inline">\(\mathbf{h}_{(j)}\)</span> in the biplot space (see
-the dotted red line in Figure 1(a)). To find the intersection of this
-prediction line with <span class="math inline">\(\mathbf{h}_{(j)}\)</span> we note that <span class="math display">\[
-\mathbf{g}'_{(i)}\mathbf{h}_{(j)} = \| \mathbf{g}_{(i)} \| \|
-\mathbf{h}_{(j)} \| cos(\mathbf{g}_{(i)},\mathbf{h}_{(j)}) =
-\| \mathbf{p} \| \| \mathbf{h}_{(j)} \|
-\]</span> where <span class="math inline">\(\mathbf{p}\)</span> is the
-length of the orthogonal projection of <span class="math inline">\(\mathbf{g}_{(i)}\)</span> on <span class="math inline">\(\mathbf{h}_{(j)}\)</span>. This is illustrated in
-Figure 1(b) with triangle ABC: <span class="math inline">\(cos(\theta) =
-\frac{AC}{AB}\)</span> or <span class="math inline">\(AC = AB
-cos(\theta)\)</span> The length of <span class="math inline">\(AC\)</span>, written as <span class="math inline">\(\| \mathbf{p} \|\)</span> is equal to the cosine
-times the length of <span class="math inline">\(AB\)</span>, i.e. <span class="math inline">\(cos(\mathbf{g}_{(i)},\mathbf{h}_{(j)}) \|
-\mathbf{g}_{(i)} \|\)</span>.</p>
+</annotation></semantics></math> which defines a straight line
+orthogonal to
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><annotation encoding="application/x-tex">\mathbf{h}_{(j)}</annotation></semantics></math>
+in the biplot space (see the dotted red line in Figure 1(a)). To find
+the intersection of this prediction line with
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><annotation encoding="application/x-tex">\mathbf{h}_{(j)}</annotation></semantics></math>
+we note that
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐠</mi><msub><mi>′</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>i</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo>=</mo><mo stretchy="false" form="postfix">∥</mo><msub><mi>𝐠</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>i</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo stretchy="false" form="postfix">∥</mo><mo stretchy="false" form="postfix">∥</mo><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo stretchy="false" form="postfix">∥</mo><mi>c</mi><mi>o</mi><mi>s</mi><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>𝐠</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>i</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo>,</mo><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mo stretchy="false" form="postfix">∥</mo><mi>𝐩</mi><mo stretchy="false" form="postfix">∥</mo><mo stretchy="false" form="postfix">∥</mo><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo stretchy="false" form="postfix">∥</mo></mrow><annotation encoding="application/x-tex">
+\mathbf{g}'_{(i)}\mathbf{h}_{(j)} = \| \mathbf{g}_{(i)} \| \| \mathbf{h}_{(j)} \| cos(\mathbf{g}_{(i)},\mathbf{h}_{(j)}) = 
+\| \mathbf{p} \| \| \mathbf{h}_{(j)} \| 
+</annotation></semantics></math> where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐩</mi><annotation encoding="application/x-tex">\mathbf{p}</annotation></semantics></math>
+is the length of the orthogonal projection of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐠</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>i</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><annotation encoding="application/x-tex">\mathbf{g}_{(i)}</annotation></semantics></math>
+on
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><annotation encoding="application/x-tex">\mathbf{h}_{(j)}</annotation></semantics></math>.
+This is illustrated in Figure 1(b) with triangle ABC:
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>c</mi><mi>o</mi><mi>s</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>θ</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mfrac><mrow><mi>A</mi><mi>C</mi></mrow><mrow><mi>A</mi><mi>B</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">cos(\theta) = \frac{AC}{AB}</annotation></semantics></math>
+or
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>C</mi><mo>=</mo><mi>A</mi><mi>B</mi><mi>c</mi><mi>o</mi><mi>s</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>θ</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">AC = AB cos(\theta)</annotation></semantics></math>
+The length of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">AC</annotation></semantics></math>,
+written as
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="postfix">∥</mo><mi>𝐩</mi><mo stretchy="false" form="postfix">∥</mo></mrow><annotation encoding="application/x-tex">\| \mathbf{p} \|</annotation></semantics></math>
+is equal to the cosine times the length of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>B</mi></mrow><annotation encoding="application/x-tex">AB</annotation></semantics></math>,
+i.e. <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>c</mi><mi>o</mi><mi>s</mi><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>𝐠</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>i</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo>,</mo><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo stretchy="true" form="postfix">)</mo></mrow><mo stretchy="false" form="postfix">∥</mo><msub><mi>𝐠</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>i</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo stretchy="false" form="postfix">∥</mo></mrow><annotation encoding="application/x-tex">cos(\mathbf{g}_{(i)},\mathbf{h}_{(j)}) \| \mathbf{g}_{(i)} \|</annotation></semantics></math>.</p>
 <div class="figure">
 <img src="axis_calibration.png" alt="Figure 1: Calibration of biplot axes." width="100%"><p class="caption">
 Figure 1: Calibration of biplot axes.
 </p>
 </div>
-<p>Since <span class="math inline">\(\mathbf{p}\)</span> is along <span class="math inline">\(\mathbf{h}_{(j)}\)</span> we can write <span class="math inline">\(\mathbf{p} = c\mathbf{h}_{(j)}\)</span> and all
-points on the prediction line <span class="math inline">\(\mu =
-\mathbf{g}'_{\mu}\mathbf{h}_{(j)}\)</span> project on the same point
-<span class="math inline">\(c_{\mu}\mathbf{h}_{(j)}\)</span>. We solve
-for <span class="math inline">\(c_{\mu}\)</span> from <span class="math display">\[
-\mu = \mathbf{g}'_{\mu}\mathbf{h}_{(j)}=\| \mathbf{p} \| \|
-\mathbf{h}_{(j)} \| =
+<p>Since
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐩</mi><annotation encoding="application/x-tex">\mathbf{p}</annotation></semantics></math>
+is along
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><annotation encoding="application/x-tex">\mathbf{h}_{(j)}</annotation></semantics></math>
+we can write
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐩</mi><mo>=</mo><mi>c</mi><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow><annotation encoding="application/x-tex">\mathbf{p} = c\mathbf{h}_{(j)}</annotation></semantics></math>
+and all points on the prediction line
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi><mo>=</mo><mi>𝐠</mi><msub><mi>′</mi><mi>μ</mi></msub><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow><annotation encoding="application/x-tex">\mu = \mathbf{g}'_{\mu}\mathbf{h}_{(j)}</annotation></semantics></math>
+project on the same point
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>c</mi><mi>μ</mi></msub><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow><annotation encoding="application/x-tex">c_{\mu}\mathbf{h}_{(j)}</annotation></semantics></math>.
+We solve for
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>c</mi><mi>μ</mi></msub><annotation encoding="application/x-tex">c_{\mu}</annotation></semantics></math>
+from
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi><mo>=</mo><mi>𝐠</mi><msub><mi>′</mi><mi>μ</mi></msub><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo>=</mo><mo stretchy="false" form="postfix">∥</mo><mi>𝐩</mi><mo stretchy="false" form="postfix">∥</mo><mo stretchy="false" form="postfix">∥</mo><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo stretchy="false" form="postfix">∥</mo><mo>=</mo><mo stretchy="false" form="postfix">∥</mo><msub><mi>c</mi><mi>μ</mi></msub><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo stretchy="false" form="postfix">∥</mo><mo stretchy="false" form="postfix">∥</mo><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo stretchy="false" form="postfix">∥</mo></mrow><annotation encoding="application/x-tex">
+\mu = \mathbf{g}'_{\mu}\mathbf{h}_{(j)}=\| \mathbf{p} \| \| \mathbf{h}_{(j)} \| = 
 \| c_{\mu}\mathbf{h}_{(j)} \| \| \mathbf{h}_{(j)} \|
-\]</span></p>
-<p><span class="math display">\[
+</annotation></semantics></math></p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>c</mi><mi>μ</mi></msub><mo>=</mo><mfrac><mi>μ</mi><mrow><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mi>′</mi><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow></mfrac><mi>.</mi></mrow><annotation encoding="application/x-tex">
 c_{\mu} = \frac{\mu}{\mathbf{h}_{(j)}'\mathbf{h}_{(j)}}.
-\]</span> If we select ‘nice’ scale markers <span class="math inline">\(\tau_{1}, \tau_{2}, \cdots \tau_{k}\)</span> for
-variable <span class="math inline">\(j\)</span>, then <span class="math inline">\(\tau_{h}-\bar{x}_j = \mu_{h}\)</span> and
-positions of these scale markers on <span class="math inline">\(\mathbf{h}_{(j)}\)</span> are given by <span class="math inline">\(p_{\mu_{1}}, p_{\mu_{2}}, \cdots
-p_{\mu_{k}}\)</span> with <span class="math display">\[
-p_{\mu_h} = c_{\mu_h}\mathbf{h}_{(j)}
-=  \frac{\mu_h}{\mathbf{h}_{(j)}'\mathbf{h}_{(j)}}\mathbf{h}_{(j)}
-\tag{2}
-\]</span> To obtain a PCA biplot of the <span class="math inline">\(48\times 4\)</span> rock data in <code>R</code> we
-call</p>
+</annotation></semantics></math> If we select ‘nice’ scale markers
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>τ</mi><mn>1</mn></msub><mo>,</mo><msub><mi>τ</mi><mn>2</mn></msub><mo>,</mo><mi>⋯</mi><msub><mi>τ</mi><mi>k</mi></msub></mrow><annotation encoding="application/x-tex">\tau_{1}, \tau_{2}, \cdots \tau_{k}</annotation></semantics></math>
+for variable
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>j</mi><annotation encoding="application/x-tex">j</annotation></semantics></math>,
+then
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>τ</mi><mi>h</mi></msub><mo>−</mo><msub><mover><mi>x</mi><mo accent="true">‾</mo></mover><mi>j</mi></msub><mo>=</mo><msub><mi>μ</mi><mi>h</mi></msub></mrow><annotation encoding="application/x-tex">\tau_{h}-\bar{x}_j = \mu_{h}</annotation></semantics></math>
+and positions of these scale markers on
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><annotation encoding="application/x-tex">\mathbf{h}_{(j)}</annotation></semantics></math>
+are given by
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><msub><mi>μ</mi><mn>1</mn></msub></msub><mo>,</mo><msub><mi>p</mi><msub><mi>μ</mi><mn>2</mn></msub></msub><mo>,</mo><mi>⋯</mi><msub><mi>p</mi><msub><mi>μ</mi><mi>k</mi></msub></msub></mrow><annotation encoding="application/x-tex">p_{\mu_{1}}, p_{\mu_{2}}, \cdots p_{\mu_{k}}</annotation></semantics></math>
+with
+<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><msub><mi>μ</mi><mi>h</mi></msub></msub><mo>=</mo><msub><mi>c</mi><msub><mi>μ</mi><mi>h</mi></msub></msub><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mo>=</mo><mfrac><msub><mi>μ</mi><mi>h</mi></msub><mrow><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub><mi>′</mi><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow></mfrac><msub><mi>𝐡</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>j</mi><mo stretchy="true" form="postfix">)</mo></mrow></msub></mrow><annotation encoding="application/x-tex">
+p_{\mu_h} = c_{\mu_h}\mathbf{h}_{(j)} =  \frac{\mu_h}{\mathbf{h}_{(j)}'\mathbf{h}_{(j)}}\mathbf{h}_{(j)} \tag{2}
+</annotation></semantics></math> To obtain a PCA biplot of the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>48</mn><mo>×</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">48\times 4</annotation></semantics></math>
+rock data in <code>R</code> we call</p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">rock</span>, scale <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="biplotEZ_files/figure-html/unnamed-chunk-3-1.png" width="672"></p>
@@ -243,14 +292,12 @@ <h2 id="the-function-biplot">The function <code>biplot()</code><a class="anchor"
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.data</span><span class="op">)</span>                 <span class="co"># centred, but no scaling</span></span>
 <span><span class="co">#&gt; Object of class biplot, based on 50 samples and 9 variables.</span></span>
 <span><span class="co">#&gt; 8 numeric variables.</span></span>
-<span><span class="co">#&gt; 1 categorical variable.</span></span></code></pre></div>
-<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.data</span>, scale <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>   <span class="co"># centered and scaled</span></span>
+<span><span class="co">#&gt; 1 categorical variable.</span></span>
+<span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.data</span>, scale <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>   <span class="co"># centered and scaled</span></span>
 <span><span class="co">#&gt; Object of class biplot, based on 50 samples and 9 variables.</span></span>
 <span><span class="co">#&gt; 8 numeric variables.</span></span>
-<span><span class="co">#&gt; 1 categorical variable.</span></span></code></pre></div>
-<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.data</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="co"># no centring (usually not recommended) or scaling</span></span>
+<span><span class="co">#&gt; 1 categorical variable.</span></span>
+<span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.data</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="co"># no centring (usually not recommended) or scaling</span></span>
 <span><span class="co">#&gt; Object of class biplot, based on 50 samples and 9 variables.</span></span>
 <span><span class="co">#&gt; 8 numeric variables.</span></span>
 <span><span class="co">#&gt; 1 categorical variable.</span></span></code></pre></div>
@@ -259,53 +306,42 @@ <h2 id="the-function-biplot">The function <code>biplot()</code><a class="anchor"
 has no effect on the <code>print method</code>. It does however have an
 effect on the components of the object of class <code>biplot</code> in
 the output.</p>
-<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">out</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.data</span><span class="op">)</span>                 <span class="co"># centred, but no scaling</span></span>
 <span><span class="va">out</span><span class="op">$</span><span class="va">center</span></span>
-<span><span class="co">#&gt; [1] TRUE</span></span></code></pre></div>
-<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span><span class="op">$</span><span class="va">scaled</span></span>
-<span><span class="co">#&gt; [1] FALSE</span></span></code></pre></div>
-<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span><span class="op">$</span><span class="va">means</span></span>
+<span><span class="co">#&gt; [1] TRUE</span></span>
+<span><span class="va">out</span><span class="op">$</span><span class="va">scaled</span></span>
+<span><span class="co">#&gt; [1] FALSE</span></span>
+<span><span class="va">out</span><span class="op">$</span><span class="va">means</span></span>
 <span><span class="co">#&gt; Population     Income Illiteracy   Life.Exp     Murder    HS.Grad      Frost </span></span>
 <span><span class="co">#&gt;  4246.4200  4435.8000     1.1700    70.8786     7.3780    53.1080   104.4600 </span></span>
 <span><span class="co">#&gt;       Area </span></span>
-<span><span class="co">#&gt; 70735.8800</span></span></code></pre></div>
-<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span><span class="op">$</span><span class="va">sd</span></span>
-<span><span class="co">#&gt; [1] 1 1 1 1 1 1 1 1</span></span></code></pre></div>
-<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.data</span>, scale <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>   <span class="co"># centered and scaled</span></span>
+<span><span class="co">#&gt; 70735.8800</span></span>
+<span><span class="va">out</span><span class="op">$</span><span class="va">sd</span></span>
+<span><span class="co">#&gt; [1] 1 1 1 1 1 1 1 1</span></span>
+<span><span class="va">out</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.data</span>, scale <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>   <span class="co"># centered and scaled</span></span>
 <span><span class="va">out</span><span class="op">$</span><span class="va">center</span></span>
-<span><span class="co">#&gt; [1] TRUE</span></span></code></pre></div>
-<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span><span class="op">$</span><span class="va">scaled</span></span>
-<span><span class="co">#&gt; [1] TRUE</span></span></code></pre></div>
-<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span><span class="op">$</span><span class="va">means</span></span>
+<span><span class="co">#&gt; [1] TRUE</span></span>
+<span><span class="va">out</span><span class="op">$</span><span class="va">scaled</span></span>
+<span><span class="co">#&gt; [1] TRUE</span></span>
+<span><span class="va">out</span><span class="op">$</span><span class="va">means</span></span>
 <span><span class="co">#&gt; Population     Income Illiteracy   Life.Exp     Murder    HS.Grad      Frost </span></span>
 <span><span class="co">#&gt;  4246.4200  4435.8000     1.1700    70.8786     7.3780    53.1080   104.4600 </span></span>
 <span><span class="co">#&gt;       Area </span></span>
-<span><span class="co">#&gt; 70735.8800</span></span></code></pre></div>
-<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span><span class="op">$</span><span class="va">sd</span></span>
+<span><span class="co">#&gt; 70735.8800</span></span>
+<span><span class="va">out</span><span class="op">$</span><span class="va">sd</span></span>
 <span><span class="co">#&gt;   Population       Income   Illiteracy     Life.Exp       Murder      HS.Grad </span></span>
 <span><span class="co">#&gt; 4.464491e+03 6.144699e+02 6.095331e-01 1.342394e+00 3.691540e+00 8.076998e+00 </span></span>
 <span><span class="co">#&gt;        Frost         Area </span></span>
-<span><span class="co">#&gt; 5.198085e+01 8.532730e+04</span></span></code></pre></div>
-<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.data</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="co"># no centring (usually not recommended) or scaling</span></span>
+<span><span class="co">#&gt; 5.198085e+01 8.532730e+04</span></span>
+<span><span class="va">out</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.data</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="co"># no centring (usually not recommended) or scaling</span></span>
 <span><span class="va">out</span><span class="op">$</span><span class="va">center</span></span>
-<span><span class="co">#&gt; [1] FALSE</span></span></code></pre></div>
-<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span><span class="op">$</span><span class="va">scaled</span></span>
-<span><span class="co">#&gt; [1] FALSE</span></span></code></pre></div>
-<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span><span class="op">$</span><span class="va">means</span></span>
-<span><span class="co">#&gt; [1] 0 0 0 0 0 0 0 0</span></span></code></pre></div>
-<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span><span class="op">$</span><span class="va">sd</span></span>
+<span><span class="co">#&gt; [1] FALSE</span></span>
+<span><span class="va">out</span><span class="op">$</span><span class="va">scaled</span></span>
+<span><span class="co">#&gt; [1] FALSE</span></span>
+<span><span class="va">out</span><span class="op">$</span><span class="va">means</span></span>
+<span><span class="co">#&gt; [1] 0 0 0 0 0 0 0 0</span></span>
+<span><span class="va">out</span><span class="op">$</span><span class="va">sd</span></span>
 <span><span class="co">#&gt; [1] 1 1 1 1 1 1 1 1</span></span></code></pre></div>
 <p>Note that the components <code>means</code> and <code>sd</code> only
 contain the sample means and sample sds when either/or
@@ -323,12 +359,11 @@ <h3 id="using-biplot-with-princomp-or-prcomp">Using <code>biplot()</code> with <
 can be piped into the biplot function, where the piping implies that the
 argument <code>data</code> now takes the value of an object of class
 <code>prcomp</code> or <code>princomp</code>.</p>
-<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/princomp.html" class="external-link">princomp</a></span><span class="op">(</span><span class="va">state.x77</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="op">)</span></span>
 <span><span class="co">#&gt; Object of class biplot, based on 50 samples and 8 variables.</span></span>
-<span><span class="co">#&gt; 8 numeric variables.</span></span></code></pre></div>
-<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/prcomp.html" class="external-link">prcomp</a></span><span class="op">(</span><span class="va">state.x77</span>, scale.<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="op">)</span></span>
+<span><span class="co">#&gt; 8 numeric variables.</span></span>
+<span><span class="va">out</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/prcomp.html" class="external-link">prcomp</a></span><span class="op">(</span><span class="va">state.x77</span>, scale.<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">out</span><span class="op">$</span><span class="va">raw.X</span>,<span class="fl">3</span><span class="op">)</span>,<span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">tail</a></span><span class="op">(</span><span class="va">out</span><span class="op">$</span><span class="va">raw.X</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="co">#&gt;               Population Income Illiteracy Life Exp Murder HS Grad Frost   Area</span></span>
 <span><span class="co">#&gt; Alabama             3615   3624        2.1    69.05   15.1    41.3    20  50708</span></span>
@@ -336,9 +371,8 @@ <h3 id="using-biplot-with-princomp-or-prcomp">Using <code>biplot()</code> with <
 <span><span class="co">#&gt; Arizona             2212   4530        1.8    70.55    7.8    58.1    15 113417</span></span>
 <span><span class="co">#&gt; West Virginia       1799   3617        1.4    69.48    6.7    41.6   100  24070</span></span>
 <span><span class="co">#&gt; Wisconsin           4589   4468        0.7    72.48    3.0    54.5   149  54464</span></span>
-<span><span class="co">#&gt; Wyoming              376   4566        0.6    70.29    6.9    62.9   173  97203</span></span></code></pre></div>
-<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">out</span><span class="op">$</span><span class="va">X</span>,<span class="fl">3</span><span class="op">)</span>,<span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">tail</a></span><span class="op">(</span><span class="va">out</span><span class="op">$</span><span class="va">X</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span></span>
+<span><span class="co">#&gt; Wyoming              376   4566        0.6    70.29    6.9    62.9   173  97203</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">out</span><span class="op">$</span><span class="va">X</span>,<span class="fl">3</span><span class="op">)</span>,<span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">tail</a></span><span class="op">(</span><span class="va">out</span><span class="op">$</span><span class="va">X</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="co">#&gt;                Population      Income Illiteracy   Life Exp     Murder</span></span>
 <span><span class="co">#&gt; Alabama       -0.14143156 -1.32113867   1.525758 -1.3621937  2.0918101</span></span>
 <span><span class="co">#&gt; Alaska        -0.86939802  3.05824562   0.541398 -1.1685098  1.0624293</span></span>
@@ -352,21 +386,17 @@ <h3 id="using-biplot-with-princomp-or-prcomp">Using <code>biplot()</code> with <
 <span><span class="co">#&gt; Arizona        0.6180514 -1.72101848  0.5002047</span></span>
 <span><span class="co">#&gt; West Virginia -1.4247868 -0.08580083 -0.5469045</span></span>
 <span><span class="co">#&gt; Wisconsin      0.1723413  0.85685405 -0.1906996</span></span>
-<span><span class="co">#&gt; Wyoming        1.2123316  1.31856256  0.3101835</span></span></code></pre></div>
-<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span><span class="op">$</span><span class="va">center</span></span>
-<span><span class="co">#&gt; [1] TRUE</span></span></code></pre></div>
-<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span><span class="op">$</span><span class="va">scaled</span></span>
-<span><span class="co">#&gt; [1] TRUE</span></span></code></pre></div>
-<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span><span class="op">$</span><span class="va">means</span></span>
+<span><span class="co">#&gt; Wyoming        1.2123316  1.31856256  0.3101835</span></span>
+<span><span class="va">out</span><span class="op">$</span><span class="va">center</span></span>
+<span><span class="co">#&gt; [1] TRUE</span></span>
+<span><span class="va">out</span><span class="op">$</span><span class="va">scaled</span></span>
+<span><span class="co">#&gt; [1] TRUE</span></span>
+<span><span class="va">out</span><span class="op">$</span><span class="va">means</span></span>
 <span><span class="co">#&gt; Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost </span></span>
 <span><span class="co">#&gt;  4246.4200  4435.8000     1.1700    70.8786     7.3780    53.1080   104.4600 </span></span>
 <span><span class="co">#&gt;       Area </span></span>
-<span><span class="co">#&gt; 70735.8800</span></span></code></pre></div>
-<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">out</span><span class="op">$</span><span class="va">sd</span></span>
+<span><span class="co">#&gt; 70735.8800</span></span>
+<span><span class="va">out</span><span class="op">$</span><span class="va">sd</span></span>
 <span><span class="co">#&gt;   Population       Income   Illiteracy     Life Exp       Murder      HS Grad </span></span>
 <span><span class="co">#&gt; 4.464491e+03 6.144699e+02 6.095331e-01 1.342394e+00 3.691540e+00 8.076998e+00 </span></span>
 <span><span class="co">#&gt;        Frost         Area </span></span>
@@ -379,14 +409,14 @@ <h2 id="the-functions-pca-plot-and-legend-type">The functions <code>PCA()</code>
 </h2>
 <p>The first argument to the function <code><a href="../reference/PCA.html">PCA()</a></code> is an object of
 class <code>biplot</code>, i.e. the output of the <code><a href="../reference/biplot.html">biplot()</a></code>
-function. By default we c onstruct a 2D biplot (argument
+function. By default we construct a 2D biplot (argument
 <code>dim.biplot = 2</code>) of the first two principal components
 (argument <code>e.vects = 1:2</code>). The <code>group.aes</code>
 argument, if not specified in the function <code><a href="../reference/biplot.html">biplot()</a></code>, allows
 a grouping argument for the sample aesthetics. A PCA biplot of the
 <code>state.x77</code> data with colouring according to
 <code>state.region</code> is obtained as follows:</p>
-<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">state.region</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="biplotEZ_files/figure-html/unnamed-chunk-10-1.png" width="672"></p>
@@ -395,31 +425,48 @@ <h2 id="the-functions-pca-plot-and-legend-type">The functions <code>PCA()</code>
 additional components are present in the <code>PCA</code> object. The
 matrix <code>Z</code> contains the coordinates of the sample points,
 while the matrix <code>Vr</code> contains the “coordinates” for the
-variables. In the notation of equation (1), Z=<span class="math inline">\(\mathbf{G}:n \times 2\)</span> and Vr=<span class="math inline">\(\mathbf{H}:p \times 2\)</span>. The component
-<code>Xhat</code> is the matrix <span class="math inline">\(\hat{\mathbf{X}}\)</span> on the left hand side of
-equation (1). The final component <code>ax.one.unit</code> contains as
-rows the expression in equation (2) with <span class="math inline">\(\mu_h=1\)</span>, in other words, one unit in the
-positive direction of the biplot axis.</p>
+variables. In the notation of equation (1),
+Z=<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐆</mi><mo>:</mo><mi>n</mi><mo>×</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">\mathbf{G}:n \times 2</annotation></semantics></math>
+and
+Vr=<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐇</mi><mo>:</mo><mi>p</mi><mo>×</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">\mathbf{H}:p \times 2</annotation></semantics></math>.
+The component <code>Xhat</code> is the matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><annotation encoding="application/x-tex">\hat{\mathbf{X}}</annotation></semantics></math>
+on the left hand side of equation (1). The final component
+<code>ax.one.unit</code> contains as rows the expression in equation (2)
+with
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>μ</mi><mi>h</mi></msub><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\mu_h=1</annotation></semantics></math>,
+in other words, one unit in the positive direction of the biplot
+axis.</p>
 <p>By piping the <code>PCA</code> class object (inheriting from class
 <code>biplot</code>) to the generic <code><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot()</a></code> function, the
 <code><a href="../reference/plot.biplot.html">plot.biplot()</a></code> function constructs the biplot on the
 graphical device. To add a legend to the biplot, we call</p>
-<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">state.region</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>samples <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="biplotEZ_files/figure-html/unnamed-chunk-11-1.png" width="672"></p>
-<p>It was mentioned in section 1 that the default choice <span class="math inline">\(\mathbf{G}=\mathbf{UDJ}_2\)</span> and <span class="math inline">\(\mathbf{H}=\mathbf{VJ}_2\)</span> provides an
-exact representation of the distances between the rows of <span class="math inline">\(\mathbf{\hat{X}}\)</span> which is an optimal
-approximation in the least squares sense of the distances between the
-rows of <span class="math inline">\(\mathbf{X}\)</span> (samples).
-Alternatively, the correlations between the variables (columns of <span class="math inline">\(\mathbf{X}\)</span>) can be optimally approximated
-by the cosines of the angles between the axes, leaving the approximation
-of the distances between the samples to be suboptimal. In this case
-<span class="math inline">\(\mathbf{G}=\mathbf{UJ}_2\)</span> and <span class="math inline">\(\mathbf{H}=\mathbf{VDJ}_2\)</span> and this biplot
-is obtained by setting the argument
+<p>It was mentioned in section 1 that the default choice
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐆</mi><mo>=</mo><msub><mrow><mi>𝐔</mi><mi>𝐃</mi><mi>𝐉</mi></mrow><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\mathbf{G}=\mathbf{UDJ}_2</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐇</mi><mo>=</mo><msub><mrow><mi>𝐕</mi><mi>𝐉</mi></mrow><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\mathbf{H}=\mathbf{VJ}_2</annotation></semantics></math>
+provides an exact representation of the distances between the rows of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><annotation encoding="application/x-tex">\mathbf{\hat{X}}</annotation></semantics></math>
+which is an optimal approximation in the least squares sense of the
+distances between the rows of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐗</mi><annotation encoding="application/x-tex">\mathbf{X}</annotation></semantics></math>
+(samples). Alternatively, the correlations between the variables
+(columns of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐗</mi><annotation encoding="application/x-tex">\mathbf{X}</annotation></semantics></math>)
+can be optimally approximated by the cosines of the angles between the
+axes, leaving the approximation of the distances between the samples to
+be suboptimal. In this case
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐆</mi><mo>=</mo><msub><mrow><mi>𝐔</mi><mi>𝐉</mi></mrow><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\mathbf{G}=\mathbf{UJ}_2</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐇</mi><mo>=</mo><msub><mrow><mi>𝐕</mi><mi>𝐃</mi><mi>𝐉</mi></mrow><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\mathbf{H}=\mathbf{VDJ}_2</annotation></semantics></math>
+and this biplot is obtained by setting the argument
 <code>correlation.biplot = TRUE</code>.</p>
-<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">state.region</span>, correlation.biplot <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>samples <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
@@ -433,7 +480,7 @@ <h2 id="the-function-samples">The function <code>samples()</code><a class="ancho
 <code>biplot</code> where the aesthetics should be applied. Let us first
 construct a PCA biplot of the <code>state.x77</code> data with samples
 coloured according to <code>state.division</code>.</p>
-<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">state.division</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/legend.type.html">legend.type</a></span><span class="op">(</span>samples <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
@@ -444,7 +491,7 @@ <h2 id="the-function-samples">The function <code>samples()</code><a class="ancho
 colours, other than the defaults, for the divisions. We can also change
 the opacity of the sample colours with the argument <code>opacity</code>
 that has default 1.</p>
-<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">state.division</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/samples.html">samples</a></span> <span class="op">(</span>col <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"red"</span>, <span class="st">"darkorange"</span>, <span class="st">"gold"</span>, <span class="st">"chartreuse4"</span>, </span>
@@ -453,7 +500,7 @@ <h2 id="the-function-samples">The function <code>samples()</code><a class="ancho
 <p><img src="biplotEZ_files/figure-html/unnamed-chunk-14-1.png" width="672"><img src="biplotEZ_files/figure-html/unnamed-chunk-14-2.png" width="672"></p>
 <p>Furthermore we want to use a different plotting character for the
 central regions.</p>
-<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/levels.html" class="external-link">levels</a></span> <span class="op">(</span><span class="va">state.division</span><span class="op">)</span></span>
 <span><span class="co">#&gt; [1] "New England"        "Middle Atlantic"    "South Atlantic"    </span></span>
 <span><span class="co">#&gt; [4] "East South Central" "West South Central" "East North Central"</span></span>
@@ -461,7 +508,7 @@ <h2 id="the-function-samples">The function <code>samples()</code><a class="ancho
 <p>We want to use <code>pch = 15</code> for the first three and final
 two divisions and <code>pch = 1</code> for the remaining four
 divisions.</p>
-<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">state.division</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/samples.html">samples</a></span> <span class="op">(</span>col <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"red"</span>, <span class="st">"darkorange"</span>, <span class="st">"gold"</span>, <span class="st">"chartreuse4"</span>, </span>
@@ -471,7 +518,7 @@ <h2 id="the-function-samples">The function <code>samples()</code><a class="ancho
 <p><img src="biplotEZ_files/figure-html/unnamed-chunk-16-1.png" width="672"><img src="biplotEZ_files/figure-html/unnamed-chunk-16-2.png" width="672"></p>
 <p>To increase the size of the plotting characters of the eastern
 states, we add the following:</p>
-<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">state.division</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/samples.html">samples</a></span> <span class="op">(</span>col <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"red"</span>, <span class="st">"darkorange"</span>, <span class="st">"gold"</span>, <span class="st">"chartreuse4"</span>, </span>
@@ -484,7 +531,7 @@ <h2 id="the-function-samples">The function <code>samples()</code><a class="ancho
 argument <code>which</code> is used either indicating the number(s) in
 the sequence of levels (<code>which = 4:7</code>), or as shown below,
 the levels themselves:</p>
-<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">state.division</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/samples.html">samples</a></span> <span class="op">(</span>col <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"red"</span>, <span class="st">"darkorange"</span>, <span class="st">"gold"</span>, <span class="st">"chartreuse4"</span>, </span>
@@ -505,14 +552,14 @@ <h2 id="the-function-samples">The function <code>samples()</code><a class="ancho
 label colours can be spesified with <code>label.col</code>, similar to
 <code>label.cex</code> as either a single value of a vector of length
 equal to the number of samples.</p>
-<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/samples.html">samples</a></span> <span class="op">(</span>label <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="biplotEZ_files/figure-html/unnamed-chunk-19-1.png" width="672"></p>
 <p>We can use the arguments <code>label.cex</code>,
 <code>label.side</code> and <code>label.offset</code> to make the plot
 more legible with a little effort.</p>
-<div class="sourceCode" id="cb37"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">state.x77</span><span class="op">)</span><span class="op">[</span><span class="fu"><a href="https://rdrr.io/r/base/match.html" class="external-link">match</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"Pennsylvania"</span>, <span class="st">"New Jersey"</span>, <span class="st">"Massachusetts"</span>,</span>
 <span>                            <span class="st">"Minnesota"</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">state.x77</span><span class="op">)</span><span class="op">)</span><span class="op">]</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"PA"</span>, <span class="st">"NJ"</span>, <span class="st">"MA"</span>, <span class="st">"MN"</span><span class="op">)</span></span>
 <span><span class="va">above</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/match.html" class="external-link">match</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"Alaska"</span>, <span class="st">"California"</span>, <span class="st">"Texas"</span>, <span class="st">"New York"</span>, <span class="st">"Nevada"</span>, <span class="st">"Georgia"</span>, <span class="st">"Alabama"</span>,</span>
@@ -534,7 +581,7 @@ <h2 id="the-function-samples">The function <code>samples()</code><a class="ancho
 <p><img src="biplotEZ_files/figure-html/unnamed-chunk-20-1.png" width="672"></p>
 <p>We can also make use of the functionality of the <code>ggrepel</code>
 package to place the labels.</p>
-<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/samples.html">samples</a></span> <span class="op">(</span>label <span class="op">=</span> <span class="st">"ggrepel"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span>
 <span><span class="co">#&gt; Warning: Use of `df$x` is discouraged.</span></span>
@@ -573,7 +620,7 @@ <h2 id="the-function-samples">The function <code>samples()</code><a class="ancho
 <span><span class="co">#&gt; <span style="color: #00BBBB;">ℹ</span> Use `y` instead.</span></span>
 <span><span class="co">#&gt; Warning: Use of `df$z` is discouraged.</span></span>
 <span><span class="co">#&gt; <span style="color: #00BBBB;">ℹ</span> Use `z` instead.</span></span></code></pre></div>
-<p><img src="biplotEZ_files/figure-html/unnamed-chunk-21-1.png" width="672"><img src="biplotEZ_files/figure-html/unnamed-chunk-21-2.png" width="672"></p>
+<p><img src="biplotEZ_files/figure-html/unnamed-chunk-21-1.png" width="672"></p>
 <p>Additionally, the user can add customised label names to the samples
 in the biplot. To do this, <code>label</code> must be set to
 <code>TRUE</code> (or <code>"ggrepel"</code>) and
@@ -581,7 +628,7 @@ <h2 id="the-function-samples">The function <code>samples()</code><a class="ancho
 specifying the label names of the samples. In this case, the label name
 is set to the first three characters of the state name (row names of the
 data).</p>
-<div class="sourceCode" id="cb39"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/samples.html">samples</a></span> <span class="op">(</span>label <span class="op">=</span> <span class="st">"TRUE"</span>,label.name<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/strtrim.html" class="external-link">strtrim</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/row.names.html" class="external-link">row.names</a></span><span class="op">(</span><span class="va">state.x77</span><span class="op">)</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="biplotEZ_files/figure-html/unnamed-chunk-22-1.png" width="672"></p>
@@ -589,7 +636,7 @@ <h2 id="the-function-samples">The function <code>samples()</code><a class="ancho
 can make sense to connect the data points in order. Let us consider the
 four quarters of the <code>UKgas</code> data set as four variables and
 we represent the years as sample points in a PCA biplot.</p>
-<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">gas.data</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">matrix</a></span> <span class="op">(</span><span class="va">UKgas</span>, ncol<span class="op">=</span><span class="fl">4</span>, byrow<span class="op">=</span><span class="cn">T</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">colnames</a></span><span class="op">(</span><span class="va">gas.data</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"Q"</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">4</span>, sep<span class="op">=</span><span class="st">""</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">gas.data</span><span class="op">)</span> <span class="op">&lt;-</span> <span class="fl">60</span><span class="op">:</span><span class="fl">86</span></span>
@@ -604,7 +651,7 @@ <h2 id="the-function-means">The function <code>means()</code><a class="anchor" a
 </h2>
 <p>The function <code><a href="../reference/means.html">means()</a></code> allow changing the aesthetics for
 group means specified by group.aes, when the argument
-<code>show.group.means = TRUE</code> in the call to the function
+<code>show.class.means = TRUE</code> in the call to the function
 <code><a href="../reference/PCA.html">PCA()</a></code>. The functionality of <code><a href="../reference/means.html">means()</a></code> mirrors
 that of <code><a href="../reference/samples.html">samples()</a></code> and is discussed in detail in the
 vignette <em>Class separation</em> where class means are more prominent
@@ -627,7 +674,7 @@ <h2 id="the-function-axes">The function <code>axes()</code><a class="anchor" ari
 <p>To construct a PCA biplot of the rock data, displaying only the axes
 for peri and shape with different colours for the two axes, different
 line widths and line type 2, we need to following code:</p>
-<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">rock</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>                               <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>which <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"shape"</span>,<span class="st">"peri"</span><span class="op">)</span>, </span>
 <span>                                    col<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"lightskyblue"</span>,<span class="st">"slategrey"</span><span class="op">)</span>,</span>
@@ -646,7 +693,7 @@ <h2 id="the-function-axes">The function <code>axes()</code><a class="anchor" ari
 colour and size 0.75. Note in for the illustration the in the code below
 the colour vector has only three components, so that recycling is
 applied.</p>
-<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">rock</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>                               <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"lightskyblue"</span>,<span class="st">"slategrey"</span>,<span class="st">"blue"</span><span class="op">)</span>,</span>
 <span>                                    label.dir<span class="op">=</span><span class="st">"Hor"</span>, label.line<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>,<span class="fl">0.5</span>,<span class="fl">1</span>,<span class="fl">1.5</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span></span>
@@ -664,7 +711,7 @@ <h2 id="the-function-axes">The function <code>axes()</code><a class="anchor" ari
 visible in the plot. If the user would like to specify alternative names
 for the axes, this can be done in the argument
 <code>ax.names</code>.</p>
-<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">rock</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>                               <span class="fu"><a href="../reference/axes.html">axes</a></span><span class="op">(</span>label.dir<span class="op">=</span><span class="st">"Paral"</span>,</span>
 <span>                                    ticks <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">3</span>, <span class="fl">5</span>, <span class="fl">5</span>, <span class="fl">10</span><span class="op">)</span>, tick.label<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="cn">F</span>, <span class="cn">F</span>, <span class="cn">T</span>, <span class="cn">T</span><span class="op">)</span>,</span>
@@ -679,18 +726,17 @@ <h2 id="the-functions-fit-measures-and-summary">The functions <code>fit.measures
 </h2>
 <p>The <code>print</code> method provides a short summary of the biplot
 object.</p>
-<div class="sourceCode" id="cb44"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span>  <span class="va">obj</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">airquality</span><span class="op">)</span></span>
-<span><span class="co">#&gt; Warning in biplot(airquality): 42 rows deleted due to missing values</span></span></code></pre></div>
-<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span>  <span class="va">obj</span></span>
+<span><span class="co">#&gt; Warning in biplot(airquality): 42 rows deleted due to missing values</span></span>
+<span>  <span class="va">obj</span></span>
 <span><span class="co">#&gt; Object of class biplot, based on 111 samples and 6 variables.</span></span>
 <span><span class="co">#&gt; 6 numeric variables.</span></span>
 <span><span class="co">#&gt; </span></span>
 <span><span class="co">#&gt; The following 42 sample-rows where removed due to missing values</span></span>
 <span><span class="co">#&gt;  5 6 10 11 25 26 27 32 33 34 35 36 37 39 42 43 45 46 52 53 54 55 56 57 58 59 60 61 65 72 75 83 84 96 97 98 102 103 107 115 119 150</span></span></code></pre></div>
 <p>The output from <code><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary()</a></code> will be very similar.</p>
-<div class="sourceCode" id="cb46"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span>  <span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">obj</span><span class="op">)</span></span>
 <span><span class="co">#&gt; Object of class biplot, based on 111 samples and 6 variables.</span></span>
 <span><span class="co">#&gt; 6 numeric variables.</span></span>
@@ -703,33 +749,35 @@ <h2 id="the-functions-fit-measures-and-summary">The functions <code>fit.measures
 <h3 id="quality-of-approximation">Quality of approximation<a class="anchor" aria-label="anchor" href="#quality-of-approximation"></a>
 </h3>
 <p>We start with the identity</p>
-<p><span class="math display">\[
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐗</mi><mo>=</mo><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mo>+</mo><mrow><mi>𝐗</mi><mo mathvariant="bold">−</mo><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover></mrow></mrow><annotation encoding="application/x-tex">
 \mathbf{X} = \mathbf{\hat{X}} + \mathbf{X-\hat{X}}
-\]</span> which decomposes <span class="math inline">\(\mathbf{X}\)</span> into a fitted part</p>
-<p><span class="math display">\[
-\mathbf{\hat{X}} = \mathbf{UJDJV'} =
-\mathbf{UDJ}_2(\mathbf{VJ}_2)' =
-\mathbf{UDV'VJ}_2(\mathbf{VJ}_2)' = \mathbf{XVJV'}
-\]</span></p>
-<p>and the residual part <span class="math inline">\(\mathbf{X-\hat{X}}\)</span>. The lack of fit is
-quantified by the quantity we are minimising</p>
-<p><span class="math display">\[
+</annotation></semantics></math> which decomposes
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐗</mi><annotation encoding="application/x-tex">\mathbf{X}</annotation></semantics></math>
+into a fitted part</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mo>=</mo><mrow><mi>𝐔</mi><mi>𝐉</mi><mi>𝐃</mi><mi>𝐉</mi><mi>𝐕</mi><mi mathvariant="bold">′</mi></mrow><mo>=</mo><msub><mrow><mi>𝐔</mi><mi>𝐃</mi><mi>𝐉</mi></mrow><mn>2</mn></msub><mrow><mo stretchy="true" form="prefix">(</mo><msub><mrow><mi>𝐕</mi><mi>𝐉</mi></mrow><mn>2</mn></msub><mo stretchy="true" form="postfix">)</mo></mrow><mi>′</mi><mo>=</mo><msub><mrow><mi>𝐔</mi><mi>𝐃</mi><mi>𝐕</mi><mi mathvariant="bold">′</mi><mi>𝐕</mi><mi>𝐉</mi></mrow><mn>2</mn></msub><mrow><mo stretchy="true" form="prefix">(</mo><msub><mrow><mi>𝐕</mi><mi>𝐉</mi></mrow><mn>2</mn></msub><mo stretchy="true" form="postfix">)</mo></mrow><mi>′</mi><mo>=</mo><mrow><mi>𝐗</mi><mi>𝐕</mi><mi>𝐉</mi><mi>𝐕</mi><mi mathvariant="bold">′</mi></mrow></mrow><annotation encoding="application/x-tex">
+\mathbf{\hat{X}} = \mathbf{UJDJV'} = \mathbf{UDJ}_2(\mathbf{VJ}_2)' = \mathbf{UDV'VJ}_2(\mathbf{VJ}_2)' = \mathbf{XVJV'}
+</annotation></semantics></math></p>
+<p>and the residual part
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐗</mi><mo mathvariant="bold">−</mo><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover></mrow><annotation encoding="application/x-tex">\mathbf{X-\hat{X}}</annotation></semantics></math>.
+The lack of fit is quantified by the quantity we are minimising</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="postfix">∥</mo><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mo>−</mo><mi>𝐗</mi><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">
 \| \hat{\mathbf{X}}-\mathbf{X} \|^2
-\]</span> where we have the orthogonal decomposition</p>
-<p><span class="math display">\[
-\|\mathbf{X}\|^2 = \|\hat{\mathbf{X}}\|^2 +
-\|\hat{\mathbf{X}}-\mathbf{X} \|^2.
-\]</span> The overall quality of fit is therefore defined as</p>
-<p><span class="math display">\[
+</annotation></semantics></math> where we have the orthogonal
+decomposition</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="postfix">∥</mo><mi>𝐗</mi><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup><mo>=</mo><mo stretchy="false" form="postfix">∥</mo><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup><mi>+</mi><mo stretchy="false" form="postfix">∥</mo><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mo>−</mo><mi>𝐗</mi><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup><mi>.</mi></mrow><annotation encoding="application/x-tex">
+\|\mathbf{X}\|^2 = \|\hat{\mathbf{X}}\|^2 + \|\hat{\mathbf{X}}-\mathbf{X} \|^2.
+</annotation></semantics></math> The overall quality of fit is therefore
+defined as</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi><mi>u</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo>=</mo><mfrac><mrow><mo stretchy="false" form="postfix">∥</mo><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup></mrow><mrow><mo stretchy="false" form="postfix">∥</mo><mi>𝐗</mi><msup><mo stretchy="false" form="postfix">∥</mo><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>t</mi><mi>r</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐗</mi><mi>𝐗</mi></mrow><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>t</mi><mi>r</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mi mathvariant="bold">′</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>t</mi><mi>r</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐗</mi><mi mathvariant="bold">′</mi><mi>𝐗</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>t</mi><mi>r</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mi mathvariant="bold">′</mi><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>t</mi><mi>r</mi><mrow><mo stretchy="true" form="prefix">(</mo><msup><mrow><mi>𝐕</mi><mi>𝐃</mi></mrow><mn>2</mn></msup><mrow><mi>𝐕</mi><mi mathvariant="bold">′</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>t</mi><mi>r</mi><mrow><mo stretchy="true" form="prefix">(</mo><msup><mrow><mi>𝐕</mi><mi>𝐃</mi></mrow><mn>2</mn></msup><mrow><mi>𝐉</mi><mi>𝐕</mi><mi mathvariant="bold">′</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow></mfrac><mi>.</mi></mrow><annotation encoding="application/x-tex">
 quality = \frac{\|\hat{\mathbf{X}}\|^2}{\|\mathbf{X}\|^2} =
 \frac{tr(\mathbf{XX}')}{tr(\mathbf{\hat{X}\hat{X}'})} =
 \frac{tr(\mathbf{X'X})}{tr(\mathbf{\hat{X}'\hat{X}})} =
 \frac{tr(\mathbf{VD}^2\mathbf{V'})}{tr(\mathbf{VD}^2\mathbf{JV'})}.
-\]</span> In <em>biplotEZ</em> the overall quality is displayed as a
-percentage:</p>
-<p><span class="math display">\[
+</annotation></semantics></math> In <em>biplotEZ</em> the overall
+quality is displayed as a percentage:</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi><mi>u</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo>=</mo><mfrac><mrow><msubsup><mi>d</mi><mn>1</mn><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>d</mi><mn>2</mn><mn>2</mn></msubsup></mrow><mrow><msubsup><mi>d</mi><mn>1</mn><mn>2</mn></msubsup><mo>+</mo><mi>…</mi><mo>+</mo><msubsup><mi>d</mi><mi>p</mi><mn>2</mn></msubsup></mrow></mfrac><mn>100</mn><mi>%</mi><mi>.</mi></mrow><annotation encoding="application/x-tex">
 quality =\frac{d_1^2+d_2^2}{d_1^2+\dots+d_p^2}100\%.
-\]</span></p>
+</annotation></semantics></math></p>
 </div>
 <div class="section level3">
 <h3 id="adequacy-of-representation-of-the-variables">Adequacy of representation of the variables<a class="anchor" aria-label="anchor" href="#adequacy-of-representation-of-the-variables"></a>
@@ -742,16 +790,16 @@ <h3 id="adequacy-of-representation-of-the-variables">Adequacy of representation
 <p>By fitting the biplot with calibrated axes, it is much easier to read
 off values for the variables, but the adequacy values can still be
 computed from</p>
-<p><span class="math display">\[
-\frac{diag(\mathbf{V}_r\mathbf{V}_r')}{diag(\mathbf{VV}')}=
-diag(\mathbf{V}_r\mathbf{V}_r')
-\]</span></p>
-<p>due to the orthogonality of the matrix <span class="math inline">\(\mathbf{V}:p \times p\)</span>.</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>𝐕</mi><mi>r</mi></msub><msub><mi>𝐕</mi><mi>r</mi></msub><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐕</mi><mi>𝐕</mi></mrow><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow></mfrac><mo>=</mo><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>𝐕</mi><mi>r</mi></msub><msub><mi>𝐕</mi><mi>r</mi></msub><mi>′</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">
+\frac{diag(\mathbf{V}_r\mathbf{V}_r')}{diag(\mathbf{VV}')}= diag(\mathbf{V}_r\mathbf{V}_r')
+</annotation></semantics></math></p>
+<p>due to the orthogonality of the matrix
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐕</mi><mo>:</mo><mi>p</mi><mo>×</mo><mi>p</mi></mrow><annotation encoding="application/x-tex">\mathbf{V}:p \times p</annotation></semantics></math>.</p>
 </div>
 <div class="section level3">
 <h3 id="predictivities">Predictivities<a class="anchor" aria-label="anchor" href="#predictivities"></a>
 </h3>
-<p>The predictivity provides a measure of who well the original values
+<p>The predictivity provides a measure of how well the original values
 are recovered from the biplot. An element that is well represented will
 have a predictivity close to one, indicating that the sample or variable
 values from prediction is close to the observed values. If an element is
@@ -760,45 +808,46 @@ <h3 id="predictivities">Predictivities<a class="anchor" aria-label="anchor" href
 <div class="section level4">
 <h4 id="axis-predictivity">Axis predictivity<a class="anchor" aria-label="anchor" href="#axis-predictivity"></a>
 </h4>
-<p>The predictivity for each of the <span class="math inline">\(p\)</span> variables is computed as the
-elementwise ratios</p>
-<p><span class="math display">\[
-axis \: predictivity =
-\frac{diag(\mathbf{\hat{X}'\hat{X}})}{diag(\mathbf{X'X})}
-\]</span></p>
+<p>The predictivity for each of the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>p</mi><annotation encoding="application/x-tex">p</annotation></semantics></math>
+variables is computed as the elementwise ratios</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mi>x</mi><mi>i</mi><mi>s</mi><mspace width="0.222em"></mspace><mi>p</mi><mi>r</mi><mi>e</mi><mi>d</mi><mi>i</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mi mathvariant="bold">′</mi><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐗</mi><mi mathvariant="bold">′</mi><mi>𝐗</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow></mfrac></mrow><annotation encoding="application/x-tex">
+axis \: predictivity = \frac{diag(\mathbf{\hat{X}'\hat{X}})}{diag(\mathbf{X'X})}
+</annotation></semantics></math></p>
 </div>
 <div class="section level4">
 <h4 id="sample-predictivity">Sample predictivity<a class="anchor" aria-label="anchor" href="#sample-predictivity"></a>
 </h4>
-<p>The predictivity for each of the <span class="math inline">\(n\)</span> samples is computed as the elementwise
-ratios</p>
-<p><span class="math display">\[
-sample \: predictivity =
-\frac{diag(\mathbf{\hat{X}\hat{X}'})}{diag(\mathbf{XX'})}
-\]</span> By calling the function <code><a href="../reference/fit.measures.html">fit.measures()</a></code> these
-quantities are computed for the specific biplot object. The values are
-displayed with the <code><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary()</a></code> function.</p>
-<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
+<p>The predictivity for each of the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>n</mi><annotation encoding="application/x-tex">n</annotation></semantics></math>
+samples is computed as the elementwise ratios</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi><mspace width="0.222em"></mspace><mi>p</mi><mi>r</mi><mi>e</mi><mi>d</mi><mi>i</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>v</mi><mi>i</mi><mi>t</mi><mi>y</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mover><mi>𝐗</mi><mo accent="true">̂</mo></mover><mi mathvariant="bold">′</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mrow><mi>𝐗</mi><mi>𝐗</mi><mi mathvariant="bold">′</mi></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow></mfrac></mrow><annotation encoding="application/x-tex">
+sample \: predictivity = \frac{diag(\mathbf{\hat{X}\hat{X}'})}{diag(\mathbf{XX'})}
+</annotation></semantics></math> By calling the function
+<code><a href="../reference/fit.measures.html">fit.measures()</a></code> these quantities are computed for the
+specific biplot object. The values are displayed with the
+<code><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary()</a></code> function.</p>
+<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">obj</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scale <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/fit.measures.html">fit.measures</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
 <p><img src="biplotEZ_files/figure-html/unnamed-chunk-29-1.png" width="672"></p>
-<div class="sourceCode" id="cb48"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span> <span class="op">(</span><span class="va">obj</span><span class="op">)</span></span>
 <span><span class="co">#&gt; Object of class biplot, based on 50 samples and 8 variables.</span></span>
 <span><span class="co">#&gt; 8 numeric variables.</span></span>
 <span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Quality of fit = 65.4% </span></span>
-<span><span class="co">#&gt; Adequacy of variables:</span></span>
+<span><span class="co">#&gt; Quality of fit in 2 dimension(s) = 65.4% </span></span>
+<span><span class="co">#&gt; Adequacy of variables in 2 dimension(s):</span></span>
 <span><span class="co">#&gt; Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost </span></span>
 <span><span class="co">#&gt;  0.1848016  0.3586383  0.2215201  0.1760908  0.2915819  0.2696184  0.1513317 </span></span>
 <span><span class="co">#&gt;       Area </span></span>
 <span><span class="co">#&gt;  0.3464170 </span></span>
-<span><span class="co">#&gt; Axis predictivity:</span></span>
+<span><span class="co">#&gt; Axis predictivity in 2 dimension(s):</span></span>
 <span><span class="co">#&gt; Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost </span></span>
 <span><span class="co">#&gt;  0.3330216  0.7609185  0.7917091  0.6206172  0.8640485  0.7947530  0.4982299 </span></span>
 <span><span class="co">#&gt;       Area </span></span>
 <span><span class="co">#&gt;  0.5675169 </span></span>
-<span><span class="co">#&gt; Sample predictivity:</span></span>
+<span><span class="co">#&gt; Sample predictivity in 2 dimension(s):</span></span>
 <span><span class="co">#&gt;        Alabama         Alaska        Arizona       Arkansas     California </span></span>
 <span><span class="co">#&gt;     0.95126856     0.61373919     0.26327256     0.86308539     0.57062754 </span></span>
 <span><span class="co">#&gt;       Colorado    Connecticut       Delaware        Florida        Georgia </span></span>
@@ -827,15 +876,15 @@ <h4 id="sample-predictivity">Sample predictivity<a class="anchor" aria-label="an
 there are many samples which result in a very long output, these can be
 set in the call to <code><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary()</a></code>. By default all measures are
 set to <code>TRUE</code>.</p>
-<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">obj</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scale <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/fit.measures.html">fit.measures</a></span><span class="op">(</span><span class="op">)</span> </span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span> <span class="op">(</span><span class="va">obj</span>, adequacy <span class="op">=</span> <span class="cn">FALSE</span>, sample.predictivity <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span>
 <span><span class="co">#&gt; Object of class biplot, based on 50 samples and 8 variables.</span></span>
 <span><span class="co">#&gt; 8 numeric variables.</span></span>
 <span><span class="co">#&gt; </span></span>
-<span><span class="co">#&gt; Quality of fit = 65.4% </span></span>
-<span><span class="co">#&gt; Axis predictivity:</span></span>
+<span><span class="co">#&gt; Quality of fit in 2 dimension(s) = 65.4% </span></span>
+<span><span class="co">#&gt; Axis predictivity in 2 dimension(s):</span></span>
 <span><span class="co">#&gt; Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost </span></span>
 <span><span class="co">#&gt;  0.3330216  0.7609185  0.7917091  0.6206172  0.8640485  0.7947530  0.4982299 </span></span>
 <span><span class="co">#&gt;       Area </span></span>
@@ -845,7 +894,7 @@ <h4 id="sample-predictivity">Sample predictivity<a class="anchor" aria-label="an
 and / or <code>sample.predictivity</code> to <code>TRUE</code>, applies
 shading for axes and shrinking for samples according to the predictivity
 values.</p>
-<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scale <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">state.region</span><span class="op">)</span> <span class="op">|&gt;</span></span>
 <span>  <span class="fu"><a href="../reference/samples.html">samples</a></span> <span class="op">(</span>which <span class="op">=</span> <span class="st">"South"</span>, pch <span class="op">=</span> <span class="fl">15</span>, label <span class="op">=</span> <span class="cn">T</span>, label.cex<span class="op">=</span><span class="fl">0.5</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/axes.html">axes</a></span> <span class="op">(</span>col <span class="op">=</span> <span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span></span>
@@ -861,6 +910,20 @@ <h4 id="sample-predictivity">Sample predictivity<a class="anchor" aria-label="an
 projected close to the origin and due to their orthogonality, very
 poorly represented.</p>
 </div>
+<div class="section level4">
+<h4 id="axes-represented-as-vectors">Axes represented as vectors<a class="anchor" aria-label="anchor" href="#axes-represented-as-vectors"></a>
+</h4>
+<p>If the user wishes to view the variables as arrows on the biplot to
+give information on the adequacy of the variables, this can be done with
+the <code><a href="../reference/axes.html">axes()</a></code> function, by setting <code>vectors = TRUE</code>
+and <code>unit.circle = TRUE</code>. The adequacy value is given by
+squared length of the arrow.</p>
+<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>, scale <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">state.region</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/axes.html">axes</a></span> <span class="op">(</span>vectors <span class="op">=</span> <span class="cn">TRUE</span>,unit.circle <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/fit.measures.html">fit.measures</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span> <span class="op">(</span><span class="op">)</span> </span></code></pre></div>
+<p><img src="biplotEZ_files/figure-html/unnamed-chunk-32-1.png" width="672"></p>
+</div>
 </div>
 </div>
 <div class="section level2">
@@ -878,35 +941,26 @@ <h2 class="unnumbered" id="references">References<a class="anchor" aria-label="a
 </div>
 </div>
 </div>
-  </div>
-
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-
-        <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
-    </nav>
-</div>
-
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside>
 </div>
 
 
 
-      <footer><div class="copyright">
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-<p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
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-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.</p>
+<div class="pkgdown-footer-right">
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diff --git a/docs/articles/biplotEZ_enhancements.html b/docs/articles/biplotEZ_enhancements.html
index 92ebc19..5645dee 100644
--- a/docs/articles/biplotEZ_enhancements.html
+++ b/docs/articles/biplotEZ_enhancements.html
@@ -4,101 +4,72 @@
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-      </header><div class="row">
-  <div class="col-md-9 contents">
-    <div class="page-header toc-ignore">
-      <h1 data-toc-skip>biplotEZ enhancements</h1>
+
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>biplotEZ enhancements</h1>
             
       
-      
-      <div class="hidden name"><code>biplotEZ_enhancements.Rmd</code></div>
 
+      <div class="d-none name"><code>biplotEZ_enhancements.Rmd</code></div>
     </div>
 
     
@@ -123,25 +94,37 @@ <h2 id="introduction">Introduction<a class="anchor" aria-label="anchor" href="#i
 <div class="section level2">
 <h2 id="the-function-alpha-bags">The function <code>alpha.bags()</code><a class="anchor" aria-label="anchor" href="#the-function-alpha-bags"></a>
 </h2>
-<p>An <span class="math inline">\(\alpha\)</span>-bag encloses the <span class="math inline">\(\alpha100\%\)</span> inner data points in a cloud
-of points. It is based on the concept of halfspace location depth as
-defined by <span class="citation">Tukey (1975)</span>. <span class="citation">Rousseeuw, Ruts, and Tukey (1999)</span> generalised a
-boxplot to a two-dimensional bagplot where the box is replaced by a bag
-containing the inner <span class="math inline">\(50\%\)</span> of the
-observations. <span class="citation">Gower, Lubbe, and Roux
-(2011)</span> replaces the <span class="math inline">\(50\%\)</span>-bag
-contour by a general <span class="math inline">\(\alpha100\%\)</span>
-contour referred to as an <span class="math inline">\(\alpha\)</span>-bag.</p>
+<p>An
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bag
+encloses the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi><mn>100</mn><mi>%</mi></mrow><annotation encoding="application/x-tex">\alpha100\%</annotation></semantics></math>
+inner data points in a cloud of points. It is based on the concept of
+halfspace location depth as defined by <span class="citation">Tukey
+(1975)</span>. <span class="citation">Rousseeuw, Ruts, and Tukey
+(1999)</span> generalised a boxplot to a two-dimensional bagplot where
+the box is replaced by a bag containing the inner
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mi>%</mi></mrow><annotation encoding="application/x-tex">50\%</annotation></semantics></math>
+of the observations. <span class="citation">Gower, Lubbe, and Roux
+(2011)</span> replaces the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mi>%</mi></mrow><annotation encoding="application/x-tex">50\%</annotation></semantics></math>-bag
+contour by a general
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi><mn>100</mn><mi>%</mi></mrow><annotation encoding="application/x-tex">\alpha100\%</annotation></semantics></math>
+contour referred to as an
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bag.</p>
 <p>When the number of samples in the biplot is larger, it becomes
 difficult to isolate individual observations. Often, when a grouping
 variable is present, the interest is not so much in the individual
 samples, but rather in the location and spread of the groups. In the
-plot below, we enclose each century’s number of sunspots by a <span class="math inline">\(95\%\)</span>-bag where the months are used as 12
-different variables for each year (sample point). Note that the legend
-displays the <span class="math inline">\(\alpha\)</span>-bags while
-<code>samples = FALSE</code> is left at the default. Both can be
-displayed, but since the <span class="math inline">\(\alpha\)</span>-bags’ colour defaults to the
-colour of the sample points, both are not necessary here.</p>
+plot below, we enclose each century’s number of sunspots by a
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>95</mn><mi>%</mi></mrow><annotation encoding="application/x-tex">95\%</annotation></semantics></math>-bag
+where the months are used as 12 different variables for each year
+(sample point). Note that the legend displays the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bags
+while <code>samples = FALSE</code> is left at the default. Both can be
+displayed, but since the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bags’
+colour defaults to the colour of the sample points, both are not
+necessary here.</p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">sunspots</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">matrix</a></span> <span class="op">(</span><span class="va">sunspot.month</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="op">(</span><span class="fl">264</span><span class="op">*</span><span class="fl">12</span><span class="op">)</span><span class="op">]</span>, ncol <span class="op">=</span> <span class="fl">12</span>, byrow <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span>
 <span><span class="va">years</span> <span class="op">&lt;-</span> <span class="fl">1749</span><span class="op">:</span><span class="fl">2012</span></span>
@@ -158,15 +141,20 @@ <h2 id="the-function-alpha-bags">The function <code>alpha.bags()</code><a class=
 <span><span class="co">#&gt; Computing 0.95 -bag for 20-th </span></span>
 <span><span class="co">#&gt; Computing 0.95 -bag for 21-st</span></span></code></pre></div>
 <p><img src="biplotEZ_enhancements_files/figure-html/unnamed-chunk-2-1.png" width="672"></p>
-<p>By default one <span class="math inline">\(95\%\)</span>-bag is
-constructed for each group. In general, the <code><a href="../reference/alpha.bags.html">alpha.bags()</a></code>
+<p>By default one
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>95</mn><mi>%</mi></mrow><annotation encoding="application/x-tex">95\%</annotation></semantics></math>-bag
+is constructed for each group. In general, the <code><a href="../reference/alpha.bags.html">alpha.bags()</a></code>
 function accepts an object of class biplot as first argument. The next
 argument <code>alpha</code> can be specified as a single value, or to
-construct a series of <span class="math inline">\(\alpha\)</span>-bags
+construct a series of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bags
 for a group, <code>alpha</code> can be a vector argument. The argument
-<code>which</code> specifies the groups to be fitted with <span class="math inline">\(\alpha\)</span>-bags. By default the
-<code>opacity</code> argument is set to <span class="math inline">\(0.25\)</span>, but by setting
-<code>opacity = 0</code> removes the fill of the <span class="math inline">\(\alpha\)</span>-bags.</p>
+<code>which</code> specifies the groups to be fitted with
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bags.
+By default the <code>opacity</code> argument is set to
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>0.25</mn><annotation encoding="application/x-tex">0.25</annotation></semantics></math>,
+but by setting <code>opacity = 0</code> removes the fill of the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bags.</p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">sunspots</span>, group.aes<span class="op">=</span><span class="va">century</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span></span>
 <span>        <span class="fu"><a href="../reference/axes.html">axes</a></span> <span class="op">(</span>label.dir <span class="op">=</span> <span class="st">"Hor"</span>, label.line <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.8</span>, <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="fl">0</span>,<span class="fl">10</span><span class="op">)</span>, <span class="fl">0.8</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span></span>
@@ -185,10 +173,14 @@ <h2 id="the-function-alpha-bags">The function <code>alpha.bags()</code><a class=
 arguments. Since we are mostly interested in the location and overlap of
 the clouds of points we can remove the indivdiual samples by setting
 <code>samples (which = NULL)</code>. The default colours will still be
-used for the <span class="math inline">\(\alpha\)</span>-bags and we
-chose to specify different line types for different <span class="math inline">\(\alpha\)</span> values. Here the
-<code>opacity</code> is set to <span class="math inline">\(0.05\)</span>
-which plots a lighter shade inside the <span class="math inline">\(\alpha\)</span>-bags.</p>
+used for the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bags
+and we chose to specify different line types for different
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>
+values. Here the <code>opacity</code> is set to
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>0.05</mn><annotation encoding="application/x-tex">0.05</annotation></semantics></math>
+which plots a lighter shade inside the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bags.</p>
 <div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">sunspots</span>, group.aes<span class="op">=</span><span class="va">century</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span></span>
 <span>        <span class="fu"><a href="../reference/axes.html">axes</a></span> <span class="op">(</span>label.dir <span class="op">=</span> <span class="st">"Hor"</span>, label.line <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.8</span>, <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="fl">0</span>,<span class="fl">10</span><span class="op">)</span>, <span class="fl">0.8</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span></span>
@@ -208,14 +200,18 @@ <h2 id="the-function-alpha-bags">The function <code>alpha.bags()</code><a class=
 <span><span class="co">#&gt; Computing 0.99 -bag for 20-th </span></span>
 <span><span class="co">#&gt; Computing 0.99 -bag for 21-st</span></span></code></pre></div>
 <p><img src="biplotEZ_enhancements_files/figure-html/unnamed-chunk-4-1.png" width="672"><img src="biplotEZ_enhancements_files/figure-html/unnamed-chunk-4-2.png" width="672"></p>
-<p>For a completely custom combination of <span class="math inline">\(\alpha\)</span>-bags, we do not rely on any
-recycling and specify each of the arguments <code>alpha</code>,
-<code>which</code>, <code>col</code>, <code>lty</code>, <code>lwd</code>
-as a vector. Since the calculation of halfspace location depth is very
-computationally intensive, a random sample of size 2500 is chosen for
-each group to construct the <span class="math inline">\(\alpha\)</span>-bag. This sample size can be
-changed with the argument <code>max</code>. Setting
-<code>trace = FALSE</code> will suppress the message “Computing <span class="math inline">\(\alpha\)</span>” -bag for groupX.”</p>
+<p>For a completely custom combination of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bags,
+we do not rely on any recycling and specify each of the arguments
+<code>alpha</code>, <code>which</code>, <code>col</code>,
+<code>lty</code>, <code>lwd</code> as a vector. Since the calculation of
+halfspace location depth is very computationally intensive, a random
+sample of size 2500 is chosen for each group to construct the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bag.
+This sample size can be changed with the argument <code>max</code>.
+Setting <code>trace = FALSE</code> will suppress the message “Computing
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>”
+-bag for groupX.”</p>
 <div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">sunspots</span>, group.aes<span class="op">=</span><span class="va">century</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span></span>
 <span>        <span class="fu"><a href="../reference/axes.html">axes</a></span> <span class="op">(</span>label.dir <span class="op">=</span> <span class="st">"Hor"</span>, label.line <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.8</span>, <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="fl">0</span>,<span class="fl">10</span><span class="op">)</span>, <span class="fl">0.8</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span></span>
@@ -234,12 +230,14 @@ <h2 id="the-function-alpha-bags">The function <code>alpha.bags()</code><a class=
 <span><span class="co">#&gt; Computing 0.7 -bag for 20-th</span></span></code></pre></div>
 <p><img src="biplotEZ_enhancements_files/figure-html/unnamed-chunk-5-1.png" width="672"></p>
 <p>The function <code>alpha.bags</code> provides the option to only plot
-the samples that sit outside the <span class="math inline">\(\alpha\)</span>-bags. This is done by setting the
-argument <code>outlying=TRUE</code>. Note the <code>which</code>
-argument may be overwritten when <code>outlying</code> is set to
-<code>TRUE</code>. This happens in particular when <code>which</code> in
-the <code><a href="../reference/samples.html">samples()</a></code> function differs from the <code>which</code>
-in the <code>alpha_bags()</code> function.</p>
+the samples that sit outside the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bags.
+This is done by setting the argument <code>outlying=TRUE</code>. Note
+the <code>which</code> argument may be overwritten when
+<code>outlying</code> is set to <code>TRUE</code>. This happens in
+particular when <code>which</code> in the <code><a href="../reference/samples.html">samples()</a></code>
+function differs from the <code>which</code> in the
+<code>alpha_bags()</code> function.</p>
 <div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">sunspots</span>, group.aes<span class="op">=</span><span class="va">century</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span></span>
 <span>        <span class="fu"><a href="../reference/alpha.bags.html">alpha.bags</a></span> <span class="op">(</span>col   <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"brown"</span>, <span class="st">"red"</span>, <span class="st">"gold"</span>,<span class="st">"deepskyblue2"</span><span class="op">)</span>,</span>
@@ -253,28 +251,48 @@ <h2 id="the-function-alpha-bags">The function <code>alpha.bags()</code><a class=
 <div class="section level2">
 <h2 id="the-function-ellipses">The function <code>ellipses()</code><a class="anchor" aria-label="anchor" href="#the-function-ellipses"></a>
 </h2>
-<p>If we observe a random sample from a <span class="math inline">\(p\)</span>-variate normal distribution with <span class="math inline">\(\bar{\mathbf{x}}\)</span> and <span class="math inline">\(\mathbf{S}\)</span> the usual unbaised estimates
-of the mean vector and covariance matrix, then</p>
-<p><span class="math display">\[
-(\mathbf{x} - \bar{\mathbf{x}})' \mathbf{S}^{-1} (\mathbf{x} -
-\bar{\mathbf{x}}) = \kappa^2
-\]</span></p>
-<p>traces an ellipsoid in <span class="math inline">\(p\)</span>
-dimensions. For <span class="math inline">\(p=2\)</span>, choosing <span class="math inline">\(\kappa =
-{(\chi^{2}_{2,1-\alpha})}^{\frac{1}{2}}\)</span> where <span class="math inline">\(\chi^{2}_{2,1-\alpha}\)</span> denotes the <span class="math inline">\((1-\alpha)100\)</span>-th percentage point of the
-<span class="math inline">\(\chi^2_2\)</span> distribution results in an
-ellipse covering approximately <span class="math inline">\(100\alpha\%\)</span> of the configuration of
-two-dimensional points. With default arguments <code>df = 2</code> and
-<code>alpha = 0.95</code>, the value of <span class="math inline">\(\kappa\)</span> is <span class="math inline">\(2.447747\)</span> and the ellipse function
-constructs an ellipse that would enclose approximately <span class="math inline">\(95\%\)</span> of the observations from a bivariate
-normal distribution. The argument <code>kappa</code> can be specified
-directly, and will take precedence over the specification of
-<code>alpha</code>. The other arguments of the <code><a href="../reference/ellipses.html">ellipses()</a></code>
-function operates identically to the corresponding arguments of the
-function <code><a href="../reference/alpha.bags.html">alpha.bags()</a></code>. Using <span class="math inline">\(\alpha\)</span>-bags, rather than ellipses is
-recommended in general, since the construction of the ellipses are based
-on the underlying assumption of a random sample observed from a normal
-distribution.</p>
+<p>If we observe a random sample from a
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>p</mi><annotation encoding="application/x-tex">p</annotation></semantics></math>-variate
+normal distribution with
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>𝐱</mi><mo accent="true">‾</mo></mover><annotation encoding="application/x-tex">\bar{\mathbf{x}}</annotation></semantics></math>
+and
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>𝐒</mi><annotation encoding="application/x-tex">\mathbf{S}</annotation></semantics></math>
+the usual unbaised estimates of the mean vector and covariance matrix,
+then</p>
+<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐱</mi><mo>−</mo><mover><mi>𝐱</mi><mo accent="true">‾</mo></mover><mo stretchy="true" form="postfix">)</mo></mrow><mi>′</mi><msup><mi>𝐒</mi><mrow><mi>−</mi><mn>1</mn></mrow></msup><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐱</mi><mo>−</mo><mover><mi>𝐱</mi><mo accent="true">‾</mo></mover><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><msup><mi>κ</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">
+(\mathbf{x} - \bar{\mathbf{x}})' \mathbf{S}^{-1} (\mathbf{x} - \bar{\mathbf{x}}) = \kappa^2
+</annotation></semantics></math></p>
+<p>traces an ellipsoid in
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>p</mi><annotation encoding="application/x-tex">p</annotation></semantics></math>
+dimensions. For
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo>=</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">p=2</annotation></semantics></math>,
+choosing
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>κ</mi><mo>=</mo><msup><mrow><mo stretchy="true" form="prefix">(</mo><msubsup><mi>χ</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>−</mo><mi>α</mi></mrow><mn>2</mn></msubsup><mo stretchy="true" form="postfix">)</mo></mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></mrow><annotation encoding="application/x-tex">\kappa = {(\chi^{2}_{2,1-\alpha})}^{\frac{1}{2}}</annotation></semantics></math>
+where
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msubsup><mi>χ</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>−</mo><mi>α</mi></mrow><mn>2</mn></msubsup><annotation encoding="application/x-tex">\chi^{2}_{2,1-\alpha}</annotation></semantics></math>
+denotes the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo stretchy="true" form="prefix">(</mo><mn>1</mn><mo>−</mo><mi>α</mi><mo stretchy="true" form="postfix">)</mo></mrow><mn>100</mn></mrow><annotation encoding="application/x-tex">(1-\alpha)100</annotation></semantics></math>-th
+percentage point of the
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msubsup><mi>χ</mi><mn>2</mn><mn>2</mn></msubsup><annotation encoding="application/x-tex">\chi^2_2</annotation></semantics></math>
+distribution results in an ellipse covering approximately
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>100</mn><mi>α</mi><mi>%</mi></mrow><annotation encoding="application/x-tex">100\alpha\%</annotation></semantics></math>
+of the configuration of two-dimensional points. With default arguments
+<code>df = 2</code> and <code>alpha = 0.95</code>, the value of
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>κ</mi><annotation encoding="application/x-tex">\kappa</annotation></semantics></math>
+is
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>2.447747</mn><annotation encoding="application/x-tex">2.447747</annotation></semantics></math>
+and the ellipse function constructs an ellipse that would enclose
+approximately
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>95</mn><mi>%</mi></mrow><annotation encoding="application/x-tex">95\%</annotation></semantics></math>
+of the observations from a bivariate normal distribution. The argument
+<code>kappa</code> can be specified directly, and will take precedence
+over the specification of <code>alpha</code>. The other arguments of the
+<code><a href="../reference/ellipses.html">ellipses()</a></code> function operates identically to the
+corresponding arguments of the function <code><a href="../reference/alpha.bags.html">alpha.bags()</a></code>. Using
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>-bags,
+rather than ellipses is recommended in general, since the construction
+of the ellipses are based on the underlying assumption of a random
+sample observed from a normal distribution.</p>
 <div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">sunspots</span>, group.aes<span class="op">=</span><span class="va">century</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span></span>
 <span>        <span class="fu"><a href="../reference/axes.html">axes</a></span> <span class="op">(</span>label.dir <span class="op">=</span> <span class="st">"Hor"</span>, label.line <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.8</span>, <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="fl">0</span>,<span class="fl">10</span><span class="op">)</span>, <span class="fl">0.8</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span></span>
@@ -340,19 +358,27 @@ <h2 id="the-functions-interpolate-with-newsamples-and-newaxes">The functions <co
 <code>newsamples()</code> and <code>newaxes()</code><a class="anchor" aria-label="anchor" href="#the-functions-interpolate-with-newsamples-and-newaxes"></a>
 </h2>
 <p>The process of interpolation is described by <span class="citation">Gower and Hand (1996)</span> as the process of finding
-the coordinates of a <span class="math inline">\(p\)</span>-dimensional
+the coordinates of a
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>p</mi><annotation encoding="application/x-tex">p</annotation></semantics></math>-dimensional
 sample in the lower dimensional biplot space. For PCA we showed in
 section 1 in the biplotEZ vignette that the sample points are
-represented by <span class="math inline">\(\mathbf{G}=\mathbf{UDJ}_2\)</span> which can be
-written as <span class="math inline">\(\mathbf{G}=\mathbf{UDV'VJ}_2=\mathbf{XVJ}_2\)</span>.
-Finding the position of a new sample <span class="math inline">\(\mathbf{x}^*:p \times 1\)</span> make use of the
-same transformation so that the 2D coordinates is given by <span class="math inline">\({\mathbf{z}^*}':2 \times 1
-={\mathbf{x}^*}' \mathbf{VJ}_2\)</span>. Similarly, the position of
-a new variable <span class="math inline">\(\mathbf{x}^*:n \times
-1\)</span> is added using a regression method that assumes that <span class="math inline">\(\mathbf{x}^*\)</span> is approximately a linear
-function <span class="math inline">\(\mathbf{x}^* =
-\mathbf{XV}_r\mathbf{b}_r\)</span> with solution <span class="math inline">\(\hat{\mathbf{b}}_r :r \times 1 =
-(\mathbf{V}'_r\mathbf{X}'\mathbf{XV}_r)^{-1}\mathbf{V}_r\mathbf{X}'\mathbf{x}^*\)</span>.</p>
+represented by
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐆</mi><mo>=</mo><msub><mrow><mi>𝐔</mi><mi>𝐃</mi><mi>𝐉</mi></mrow><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\mathbf{G}=\mathbf{UDJ}_2</annotation></semantics></math>
+which can be written as
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝐆</mi><mo>=</mo><msub><mrow><mi>𝐔</mi><mi>𝐃</mi><mi>𝐕</mi><mi mathvariant="bold">′</mi><mi>𝐕</mi><mi>𝐉</mi></mrow><mn>2</mn></msub><mo>=</mo><msub><mrow><mi>𝐗</mi><mi>𝐕</mi><mi>𝐉</mi></mrow><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\mathbf{G}=\mathbf{UDV'VJ}_2=\mathbf{XVJ}_2</annotation></semantics></math>.
+Finding the position of a new sample
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>𝐱</mi><mo>*</mo></msup><mo>:</mo><mi>p</mi><mo>×</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\mathbf{x}^*:p \times 1</annotation></semantics></math>
+make use of the same transformation so that the 2D coordinates is given
+by
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>𝐳</mi><mo>*</mo></msup><mi>′</mi><mo>:</mo><mn>2</mn><mo>×</mo><mn>1</mn><mo>=</mo><msup><mi>𝐱</mi><mo>*</mo></msup><mi>′</mi><msub><mrow><mi>𝐕</mi><mi>𝐉</mi></mrow><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">{\mathbf{z}^*}':2 \times 1 ={\mathbf{x}^*}' \mathbf{VJ}_2</annotation></semantics></math>.
+Similarly, the position of a new variable
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>𝐱</mi><mo>*</mo></msup><mo>:</mo><mi>n</mi><mo>×</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\mathbf{x}^*:n \times 1</annotation></semantics></math>
+is added using a regression method that assumes that
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>𝐱</mi><mo>*</mo></msup><annotation encoding="application/x-tex">\mathbf{x}^*</annotation></semantics></math>
+is approximately a linear function
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>𝐱</mi><mo>*</mo></msup><mo>=</mo><msub><mrow><mi>𝐗</mi><mi>𝐕</mi></mrow><mi>r</mi></msub><msub><mi>𝐛</mi><mi>r</mi></msub></mrow><annotation encoding="application/x-tex">\mathbf{x}^* = \mathbf{XV}_r\mathbf{b}_r</annotation></semantics></math>
+with solution
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover><mi>𝐛</mi><mo accent="true">̂</mo></mover><mi>r</mi></msub><mo>:</mo><mi>r</mi><mo>×</mo><mn>1</mn><mo>=</mo><msup><mrow><mo stretchy="true" form="prefix">(</mo><mi>𝐕</mi><msub><mi>′</mi><mi>r</mi></msub><mi>𝐗</mi><mi>′</mi><msub><mrow><mi>𝐗</mi><mi>𝐕</mi></mrow><mi>r</mi></msub><mo stretchy="true" form="postfix">)</mo></mrow><mrow><mi>−</mi><mn>1</mn></mrow></msup><msub><mi>𝐕</mi><mi>r</mi></msub><mi>𝐗</mi><mi>′</mi><msup><mi>𝐱</mi><mo>*</mo></msup></mrow><annotation encoding="application/x-tex">\hat{\mathbf{b}}_r :r \times 1 = (\mathbf{V}'_r\mathbf{X}'\mathbf{XV}_r)^{-1}\mathbf{V}_r\mathbf{X}'\mathbf{x}^*</annotation></semantics></math>.</p>
 <p>Adding samples and variables to the plot is facilitated by the
 function <code><a href="../reference/interpolate.html">interpolate()</a></code>. Note that the samples and variables
 to be interpolated did not contribute to the construction of the biplot.
@@ -368,9 +394,11 @@ <h2 id="the-functions-interpolate-with-newsamples-and-newaxes">The functions <co
 <code>newvariable</code> containing the new variables to be interpolated
 needs to have the same number of samples in the data sent to
 <code><a href="../reference/biplot.html">biplot()</a></code>.</p>
-<p>Suppose we construct a PCA biplot of the first <span class="math inline">\(40\)</span> samples in the data set
-<code>rock</code> and then <span class="math inline">\(8\)</span> new
-samples is to be interpolated the call will be:</p>
+<p>Suppose we construct a PCA biplot of the first
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>40</mn><annotation encoding="application/x-tex">40</annotation></semantics></math>
+samples in the data set <code>rock</code> and then
+<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>8</mn><annotation encoding="application/x-tex">8</annotation></semantics></math>
+new samples is to be interpolated the call will be:</p>
 <div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">rock</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">40</span>,<span class="op">]</span>, scale <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
 <span>  <span class="fu"><a href="../reference/interpolate.html">interpolate</a></span> <span class="op">(</span>newdata<span class="op">=</span><span class="va">rock</span><span class="op">[</span><span class="fl">41</span><span class="op">:</span><span class="fl">48</span>,<span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></code></pre></div>
@@ -546,6 +574,21 @@ <h2 id="zooming-in-on-the-biplot-with-zoom-true-in-plot">Zooming in on the biplo
 <p><img src="biplotEZ_enhancements_files/figure-html/unnamed-chunk-22-1.png" width="672">
 With the final plot then rendered as:</p>
 <p><img src="biplotEZ_enhancements_files/figure-html/unnamed-chunk-23-1.png" width="672"></p>
+</div>
+<div class="section level2">
+<h2 id="the-function-translate_axes">The function <code>translate_axes()</code><a class="anchor" aria-label="anchor" href="#the-function-translate_axes"></a>
+</h2>
+<p>This function implements the same algorithm as the
+<code>TDAbiplot()</code> in the <code>bipl5</code> package. It allows to
+translate the axes out of the plot center to the boundary using
+orthogonal parallel translation. The axes can be translated manually by
+setting the distance in the <code>distance</code> argument.</p>
+<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/biplot.html">biplot</a></span><span class="op">(</span><span class="va">state.x77</span>,scaled<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span>
+<span>  <span class="fu"><a href="../reference/PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="../reference/translate_axes.html">translate_axes</a></span><span class="op">(</span>delta <span class="op">=</span> <span class="fl">0.02</span><span class="op">)</span> <span class="op">|&gt;</span></span>
+<span>  <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span>exp.factor<span class="op">=</span><span class="fl">3</span><span class="op">)</span></span></code></pre></div>
+<p><img src="biplotEZ_enhancements_files/figure-html/unnamed-chunk-24-1.png" width="672"></p>
 <div id="refs" class="references csl-bib-body hanging-indent" entry-spacing="0">
 <div id="ref-GowerHand1996" class="csl-entry">
 Gower, J. C., and D. J. Hand. 1996. <em>Biplots.</em> Chapman &amp;
@@ -574,35 +617,26 @@ <h2 id="zooming-in-on-the-biplot-with-zoom-true-in-plot">Zooming in on the biplo
 </div>
 </div>
 </div>
-  </div>
-
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-
-        <nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
-    </nav>
-</div>
-
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside>
 </div>
 
 
 
-      <footer><div class="copyright">
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-<p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
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-      
 
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-  <div class="contents col-md-9">
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-      <div class="page-header">
-        <h1>Authors</h1>
-      </div>
+  </div>
+</nav><div class="container template-citation-authors">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="logo.png" class="logo" alt=""><h1>Authors and Citation</h1>
+    </div>
+
+    <div class="section level2">
+      <h2>Authors</h2>
 
-      
       <ul class="list-unstyled"><li>
           <p><strong>Sugnet Lubbe</strong>. Author, maintainer, copyright holder. <a href="https://orcid.org/0000-0003-2762-9944" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a>
           </p>
@@ -96,45 +71,40 @@ <h1>Authors</h1>
           </p>
         </li>
       </ul></div>
-    <div class="section level2 citation-section">
-    <div>
-      <h1 id="citation">Citation</h1>
-      
-    </div>
-    </div>
 
+    <div class="section level2">
+      <h2 id="citation">Citation</h2>
+      <p></p>
 
-    <p>Lubbe S, le Roux N, Nienkemper-Swanepoel J, Ganey R, Buys R, Adams Z, Manefeldt P (2024).
+      <p>Lubbe S, le Roux N, Nienkemper-Swanepoel J, Ganey R, Buys R, Adams Z, Manefeldt P (2025).
 <em>biplotEZ: EZ-to-Use Biplots</em>.
-R package version 2.1. 
+R package version 2.3.
 </p>
-    <pre>@Manual{,
+      <pre>@Manual{,
   title = {biplotEZ: EZ-to-Use Biplots},
   author = {Sugnet Lubbe and Niël {le Roux} and Johané Nienkemper-Swanepoel and Raeesa Ganey and Ruan Buys and Zoë-Mae Adams and Peter Manefeldt},
-  year = {2024},
-  note = {R package version 2.1},
+  year = {2025},
+  note = {R package version 2.3},
 }</pre>
+    </div>
 
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-  <p></p><p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p>
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.2.</p>
 </div>
 
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+
 
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diff --git a/docs/deps/bootstrap-5.3.1/bootstrap.bundle.min.js b/docs/deps/bootstrap-5.3.1/bootstrap.bundle.min.js
new file mode 100644
index 0000000..e8f21f7
--- /dev/null
+++ b/docs/deps/bootstrap-5.3.1/bootstrap.bundle.min.js
@@ -0,0 +1,7 @@
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vi=Object.freeze(Object.defineProperty({__proto__:null,afterMain:ae,afterRead:se,afterWrite:he,applyStyles:_e,arrow:je,auto:Kt,basePlacements:Qt,beforeMain:oe,beforeRead:ie,beforeWrite:le,bottom:Rt,clippingParents:Ut,computeStyles:Be,createPopper:bi,createPopperBase:gi,createPopperLite:_i,detectOverflow:ii,end:Yt,eventListeners:Re,flip:si,hide:ai,left:Vt,main:re,modifierPhases:de,offset:li,placements:ee,popper:Jt,popperGenerator:mi,popperOffsets:ci,preventOverflow:hi,read:ne,reference:Zt,right:qt,start:Xt,top:zt,variationPlacements:te,viewport:Gt,write:ce},Symbol.toStringTag,{value:"Module"})),yi="dropdown",wi=".bs.dropdown",Ai=".data-api",Ei="ArrowUp",Ti="ArrowDown",Ci=`hide${wi}`,Oi=`hidden${wi}`,xi=`show${wi}`,ki=`shown${wi}`,Li=`click${wi}${Ai}`,Si=`keydown${wi}${Ai}`,Di=`keyup${wi}${Ai}`,$i="show",Ii='[data-bs-toggle="dropdown"]:not(.disabled):not(:disabled)',Ni=`${Ii}.${$i}`,Pi=".dropdown-menu",Mi=p()?"top-end":"top-start",ji=p()?"top-start":"top-end",Fi=p()?"bottom-end":"bottom-start",Hi=p()?"bottom-start":"bottom-end",Wi=p()?"left-start":"right-start",Bi=p()?"right-start":"left-start",zi={autoClose:!0,boundary:"clippingParents",display:"dynamic",offset:[0,2],popperConfig:null,reference:"toggle"},Ri={autoClose:"(boolean|string)",boundary:"(string|element)",display:"string",offset:"(array|string|function)",popperConfig:"(null|object|function)",reference:"(string|element|object)"};class qi extends W{constructor(t,e){super(t,e),this._popper=null,this._parent=this._element.parentNode,this._menu=z.next(this._element,Pi)[0]||z.prev(this._element,Pi)[0]||z.findOne(Pi,this._parent),this._inNavbar=this._detectNavbar()}static get Default(){return zi}static get DefaultType(){return Ri}static get NAME(){return yi}toggle(){return this._isShown()?this.hide():this.show()}show(){if(l(this._element)||this._isShown())return;const t={relatedTarget:this._element};if(!N.trigger(this._element,xi,t).defaultPrevented){if(this._createPopper(),"ontouchstart"in document.documentElement&&!this._parent.closest(".navbar-nav"))for(const t of[].concat(...document.body.children))N.on(t,"mouseover",h);this._element.focus(),this._element.setAttribute("aria-expanded",!0),this._menu.classList.add($i),this._element.classList.add($i),N.trigger(this._element,ki,t)}}hide(){if(l(this._element)||!this._isShown())return;const t={relatedTarget:this._element};this._completeHide(t)}dispose(){this._popper&&this._popper.destroy(),super.dispose()}update(){this._inNavbar=this._detectNavbar(),this._popper&&this._popper.update()}_completeHide(t){if(!N.trigger(this._element,Ci,t).defaultPrevented){if("ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.off(t,"mouseover",h);this._popper&&this._popper.destroy(),this._menu.classList.remove($i),this._element.classList.remove($i),this._element.setAttribute("aria-expanded","false"),F.removeDataAttribute(this._menu,"popper"),N.trigger(this._element,Oi,t)}}_getConfig(t){if("object"==typeof(t=super._getConfig(t)).reference&&!o(t.reference)&&"function"!=typeof t.reference.getBoundingClientRect)throw new TypeError(`${yi.toUpperCase()}: Option "reference" provided type "object" without a required "getBoundingClientRect" method.`);return t}_createPopper(){if(void 0===vi)throw new TypeError("Bootstrap's dropdowns require Popper (https://popper.js.org)");let t=this._element;"parent"===this._config.reference?t=this._parent:o(this._config.reference)?t=r(this._config.reference):"object"==typeof this._config.reference&&(t=this._config.reference);const e=this._getPopperConfig();this._popper=bi(t,this._menu,e)}_isShown(){return this._menu.classList.contains($i)}_getPlacement(){const t=this._parent;if(t.classList.contains("dropend"))return Wi;if(t.classList.contains("dropstart"))return Bi;if(t.classList.contains("dropup-center"))return"top";if(t.classList.contains("dropdown-center"))return"bottom";const e="end"===getComputedStyle(this._menu).getPropertyValue("--bs-position").trim();return t.classList.contains("dropup")?e?ji:Mi:e?Hi:Fi}_detectNavbar(){return null!==this._element.closest(".navbar")}_getOffset(){const{offset:t}=this._config;return"string"==typeof t?t.split(",").map((t=>Number.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_getPopperConfig(){const t={placement:this._getPlacement(),modifiers:[{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"offset",options:{offset:this._getOffset()}}]};return(this._inNavbar||"static"===this._config.display)&&(F.setDataAttribute(this._menu,"popper","static"),t.modifiers=[{name:"applyStyles",enabled:!1}]),{...t,...g(this._config.popperConfig,[t])}}_selectMenuItem({key:t,target:e}){const i=z.find(".dropdown-menu .dropdown-item:not(.disabled):not(:disabled)",this._menu).filter((t=>a(t)));i.length&&b(i,e,t===Ti,!i.includes(e)).focus()}static jQueryInterface(t){return this.each((function(){const e=qi.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t]()}}))}static clearMenus(t){if(2===t.button||"keyup"===t.type&&"Tab"!==t.key)return;const e=z.find(Ni);for(const i of e){const e=qi.getInstance(i);if(!e||!1===e._config.autoClose)continue;const n=t.composedPath(),s=n.includes(e._menu);if(n.includes(e._element)||"inside"===e._config.autoClose&&!s||"outside"===e._config.autoClose&&s)continue;if(e._menu.contains(t.target)&&("keyup"===t.type&&"Tab"===t.key||/input|select|option|textarea|form/i.test(t.target.tagName)))continue;const o={relatedTarget:e._element};"click"===t.type&&(o.clickEvent=t),e._completeHide(o)}}static dataApiKeydownHandler(t){const e=/input|textarea/i.test(t.target.tagName),i="Escape"===t.key,n=[Ei,Ti].includes(t.key);if(!n&&!i)return;if(e&&!i)return;t.preventDefault();const s=this.matches(Ii)?this:z.prev(this,Ii)[0]||z.next(this,Ii)[0]||z.findOne(Ii,t.delegateTarget.parentNode),o=qi.getOrCreateInstance(s);if(n)return t.stopPropagation(),o.show(),void o._selectMenuItem(t);o._isShown()&&(t.stopPropagation(),o.hide(),s.focus())}}N.on(document,Si,Ii,qi.dataApiKeydownHandler),N.on(document,Si,Pi,qi.dataApiKeydownHandler),N.on(document,Li,qi.clearMenus),N.on(document,Di,qi.clearMenus),N.on(document,Li,Ii,(function(t){t.preventDefault(),qi.getOrCreateInstance(this).toggle()})),m(qi);const Vi="backdrop",Ki="show",Qi=`mousedown.bs.${Vi}`,Xi={className:"modal-backdrop",clickCallback:null,isAnimated:!1,isVisible:!0,rootElement:"body"},Yi={className:"string",clickCallback:"(function|null)",isAnimated:"boolean",isVisible:"boolean",rootElement:"(element|string)"};class Ui extends H{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Xi}static get DefaultType(){return Yi}static get NAME(){return Vi}show(t){if(!this._config.isVisible)return void g(t);this._append();const e=this._getElement();this._config.isAnimated&&d(e),e.classList.add(Ki),this._emulateAnimation((()=>{g(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ki),this._emulateAnimation((()=>{this.dispose(),g(t)}))):g(t)}dispose(){this._isAppended&&(N.off(this._element,Qi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement("div");t.className=this._config.className,this._config.isAnimated&&t.classList.add("fade"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=r(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),N.on(t,Qi,(()=>{g(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){_(t,this._getElement(),this._config.isAnimated)}}const Gi=".bs.focustrap",Ji=`focusin${Gi}`,Zi=`keydown.tab${Gi}`,tn="backward",en={autofocus:!0,trapElement:null},nn={autofocus:"boolean",trapElement:"element"};class sn extends H{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return en}static get DefaultType(){return nn}static get NAME(){return"focustrap"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),N.off(document,Gi),N.on(document,Ji,(t=>this._handleFocusin(t))),N.on(document,Zi,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,N.off(document,Gi))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=z.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===tn?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){"Tab"===t.key&&(this._lastTabNavDirection=t.shiftKey?tn:"forward")}}const on=".fixed-top, .fixed-bottom, .is-fixed, .sticky-top",rn=".sticky-top",an="padding-right",ln="margin-right";class cn{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,an,(e=>e+t)),this._setElementAttributes(on,an,(e=>e+t)),this._setElementAttributes(rn,ln,(e=>e-t))}reset(){this._resetElementAttributes(this._element,"overflow"),this._resetElementAttributes(this._element,an),this._resetElementAttributes(on,an),this._resetElementAttributes(rn,ln)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,"overflow"),this._element.style.overflow="hidden"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&F.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=F.getDataAttribute(t,e);null!==i?(F.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(o(t))e(t);else for(const i of z.find(t,this._element))e(i)}}const hn=".bs.modal",dn=`hide${hn}`,un=`hidePrevented${hn}`,fn=`hidden${hn}`,pn=`show${hn}`,mn=`shown${hn}`,gn=`resize${hn}`,_n=`click.dismiss${hn}`,bn=`mousedown.dismiss${hn}`,vn=`keydown.dismiss${hn}`,yn=`click${hn}.data-api`,wn="modal-open",An="show",En="modal-static",Tn={backdrop:!0,focus:!0,keyboard:!0},Cn={backdrop:"(boolean|string)",focus:"boolean",keyboard:"boolean"};class On extends W{constructor(t,e){super(t,e),this._dialog=z.findOne(".modal-dialog",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new cn,this._addEventListeners()}static get Default(){return Tn}static get DefaultType(){return Cn}static get NAME(){return"modal"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||N.trigger(this._element,pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(wn),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(N.trigger(this._element,dn).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(An),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){N.off(window,hn),N.off(this._dialog,hn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Ui({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display="block",this._element.removeAttribute("aria-hidden"),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.scrollTop=0;const e=z.findOne(".modal-body",this._dialog);e&&(e.scrollTop=0),d(this._element),this._element.classList.add(An),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,N.trigger(this._element,mn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){N.on(this._element,vn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),N.on(window,gn,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),N.on(this._element,bn,(t=>{N.one(this._element,_n,(e=>{this._element===t.target&&this._element===e.target&&("static"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(wn),this._resetAdjustments(),this._scrollBar.reset(),N.trigger(this._element,fn)}))}_isAnimated(){return this._element.classList.contains("fade")}_triggerBackdropTransition(){if(N.trigger(this._element,un).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;"hidden"===e||this._element.classList.contains(En)||(t||(this._element.style.overflowY="hidden"),this._element.classList.add(En),this._queueCallback((()=>{this._element.classList.remove(En),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=p()?"paddingLeft":"paddingRight";this._element.style[t]=`${e}px`}if(!i&&t){const t=p()?"paddingRight":"paddingLeft";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft="",this._element.style.paddingRight=""}static jQueryInterface(t,e){return this.each((function(){const i=On.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===i[t])throw new TypeError(`No method named "${t}"`);i[t](e)}}))}}N.on(document,yn,'[data-bs-toggle="modal"]',(function(t){const e=z.getElementFromSelector(this);["A","AREA"].includes(this.tagName)&&t.preventDefault(),N.one(e,pn,(t=>{t.defaultPrevented||N.one(e,fn,(()=>{a(this)&&this.focus()}))}));const i=z.findOne(".modal.show");i&&On.getInstance(i).hide(),On.getOrCreateInstance(e).toggle(this)})),R(On),m(On);const xn=".bs.offcanvas",kn=".data-api",Ln=`load${xn}${kn}`,Sn="show",Dn="showing",$n="hiding",In=".offcanvas.show",Nn=`show${xn}`,Pn=`shown${xn}`,Mn=`hide${xn}`,jn=`hidePrevented${xn}`,Fn=`hidden${xn}`,Hn=`resize${xn}`,Wn=`click${xn}${kn}`,Bn=`keydown.dismiss${xn}`,zn={backdrop:!0,keyboard:!0,scroll:!1},Rn={backdrop:"(boolean|string)",keyboard:"boolean",scroll:"boolean"};class qn extends W{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return zn}static get DefaultType(){return Rn}static get NAME(){return"offcanvas"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||N.trigger(this._element,Nn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new cn).hide(),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.classList.add(Dn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(Sn),this._element.classList.remove(Dn),N.trigger(this._element,Pn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(N.trigger(this._element,Mn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add($n),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(Sn,$n),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._config.scroll||(new cn).reset(),N.trigger(this._element,Fn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Ui({className:"offcanvas-backdrop",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{"static"!==this._config.backdrop?this.hide():N.trigger(this._element,jn)}:null})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_addEventListeners(){N.on(this._element,Bn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():N.trigger(this._element,jn))}))}static jQueryInterface(t){return this.each((function(){const e=qn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}N.on(document,Wn,'[data-bs-toggle="offcanvas"]',(function(t){const e=z.getElementFromSelector(this);if(["A","AREA"].includes(this.tagName)&&t.preventDefault(),l(this))return;N.one(e,Fn,(()=>{a(this)&&this.focus()}));const i=z.findOne(In);i&&i!==e&&qn.getInstance(i).hide(),qn.getOrCreateInstance(e).toggle(this)})),N.on(window,Ln,(()=>{for(const t of z.find(In))qn.getOrCreateInstance(t).show()})),N.on(window,Hn,(()=>{for(const t of z.find("[aria-modal][class*=show][class*=offcanvas-]"))"fixed"!==getComputedStyle(t).position&&qn.getOrCreateInstance(t).hide()})),R(qn),m(qn);const Vn={"*":["class","dir","id","lang","role",/^aria-[\w-]*$/i],a:["target","href","title","rel"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:["src","srcset","alt","title","width","height"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Kn=new Set(["background","cite","href","itemtype","longdesc","poster","src","xlink:href"]),Qn=/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Kn.has(i)||Boolean(Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Yn={allowList:Vn,content:{},extraClass:"",html:!1,sanitize:!0,sanitizeFn:null,template:"<div></div>"},Un={allowList:"object",content:"object",extraClass:"(string|function)",html:"boolean",sanitize:"boolean",sanitizeFn:"(null|function)",template:"string"},Gn={entry:"(string|element|function|null)",selector:"(string|element)"};class Jn extends H{constructor(t){super(),this._config=this._getConfig(t)}static get Default(){return Yn}static get DefaultType(){return Un}static get NAME(){return"TemplateFactory"}getContent(){return Object.values(this._config.content).map((t=>this._resolvePossibleFunction(t))).filter(Boolean)}hasContent(){return this.getContent().length>0}changeContent(t){return this._checkContent(t),this._config.content={...this._config.content,...t},this}toHtml(){const t=document.createElement("div");t.innerHTML=this._maybeSanitize(this._config.template);for(const[e,i]of Object.entries(this._config.content))this._setContent(t,i,e);const e=t.children[0],i=this._resolvePossibleFunction(this._config.extraClass);return i&&e.classList.add(...i.split(" ")),e}_typeCheckConfig(t){super._typeCheckConfig(t),this._checkContent(t.content)}_checkContent(t){for(const[e,i]of Object.entries(t))super._typeCheckConfig({selector:e,entry:i},Gn)}_setContent(t,e,i){const n=z.findOne(i,t);n&&((e=this._resolvePossibleFunction(e))?o(e)?this._putElementInTemplate(r(e),n):this._config.html?n.innerHTML=this._maybeSanitize(e):n.textContent=e:n.remove())}_maybeSanitize(t){return this._config.sanitize?function(t,e,i){if(!t.length)return t;if(i&&"function"==typeof i)return i(t);const n=(new window.DOMParser).parseFromString(t,"text/html"),s=[].concat(...n.body.querySelectorAll("*"));for(const t of s){const i=t.nodeName.toLowerCase();if(!Object.keys(e).includes(i)){t.remove();continue}const n=[].concat(...t.attributes),s=[].concat(e["*"]||[],e[i]||[]);for(const e of n)Xn(e,s)||t.removeAttribute(e.nodeName)}return n.body.innerHTML}(t,this._config.allowList,this._config.sanitizeFn):t}_resolvePossibleFunction(t){return g(t,[this])}_putElementInTemplate(t,e){if(this._config.html)return e.innerHTML="",void e.append(t);e.textContent=t.textContent}}const Zn=new Set(["sanitize","allowList","sanitizeFn"]),ts="fade",es="show",is=".modal",ns="hide.bs.modal",ss="hover",os="focus",rs={AUTO:"auto",TOP:"top",RIGHT:p()?"left":"right",BOTTOM:"bottom",LEFT:p()?"right":"left"},as={allowList:Vn,animation:!0,boundary:"clippingParents",container:!1,customClass:"",delay:0,fallbackPlacements:["top","right","bottom","left"],html:!1,offset:[0,6],placement:"top",popperConfig:null,sanitize:!0,sanitizeFn:null,selector:!1,template:'<div class="tooltip" role="tooltip"><div class="tooltip-arrow"></div><div class="tooltip-inner"></div></div>',title:"",trigger:"hover focus"},ls={allowList:"object",animation:"boolean",boundary:"(string|element)",container:"(string|element|boolean)",customClass:"(string|function)",delay:"(number|object)",fallbackPlacements:"array",html:"boolean",offset:"(array|string|function)",placement:"(string|function)",popperConfig:"(null|object|function)",sanitize:"boolean",sanitizeFn:"(null|function)",selector:"(string|boolean)",template:"string",title:"(string|element|function)",trigger:"string"};class cs extends W{constructor(t,e){if(void 0===vi)throw new TypeError("Bootstrap's tooltips require Popper (https://popper.js.org)");super(t,e),this._isEnabled=!0,this._timeout=0,this._isHovered=null,this._activeTrigger={},this._popper=null,this._templateFactory=null,this._newContent=null,this.tip=null,this._setListeners(),this._config.selector||this._fixTitle()}static get Default(){return as}static get DefaultType(){return ls}static get 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diff --git a/docs/deps/bootstrap-5.3.1/bootstrap.bundle.min.js.map b/docs/deps/bootstrap-5.3.1/bootstrap.bundle.min.js.map
new file mode 100644
index 0000000..3863da8
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object[0] : object\n  }\n\n  if (typeof object === 'string' && object.length > 0) {\n    return document.querySelector(parseSelector(object))\n  }\n\n  return null\n}\n\nconst isVisible = element => {\n  if (!isElement(element) || element.getClientRects().length === 0) {\n    return false\n  }\n\n  const elementIsVisible = getComputedStyle(element).getPropertyValue('visibility') === 'visible'\n  // Handle `details` element as its content may falsie appear visible when it is closed\n  const closedDetails = element.closest('details:not([open])')\n\n  if (!closedDetails) {\n    return elementIsVisible\n  }\n\n  if (closedDetails !== element) {\n    const summary = element.closest('summary')\n    if (summary && summary.parentNode !== closedDetails) {\n      return false\n    }\n\n    if (summary === null) {\n      return false\n    }\n  }\n\n  return elementIsVisible\n}\n\nconst isDisabled = element => {\n  if (!element || element.nodeType !== Node.ELEMENT_NODE) {\n    return true\n  }\n\n  if (element.classList.contains('disabled')) {\n    return true\n  }\n\n  if (typeof element.disabled !== 'undefined') {\n    return element.disabled\n  }\n\n  return element.hasAttribute('disabled') && element.getAttribute('disabled') !== 'false'\n}\n\nconst findShadowRoot = element => {\n  if (!document.documentElement.attachShadow) {\n    return null\n  }\n\n  // Can find the shadow root otherwise it'll return the document\n  if (typeof element.getRootNode === 'function') {\n    const root = element.getRootNode()\n    return root instanceof ShadowRoot ? root : null\n  }\n\n  if (element instanceof ShadowRoot) {\n    return element\n  }\n\n  // when we don't find a shadow root\n  if (!element.parentNode) {\n    return null\n  }\n\n  return findShadowRoot(element.parentNode)\n}\n\nconst noop = () => {}\n\n/**\n * Trick to restart an element's animation\n *\n * @param {HTMLElement} element\n * @return void\n *\n * @see https://www.charistheo.io/blog/2021/02/restart-a-css-animation-with-javascript/#restarting-a-css-animation\n */\nconst reflow = element => {\n  element.offsetHeight // eslint-disable-line no-unused-expressions\n}\n\nconst getjQuery = () => {\n  if (window.jQuery && !document.body.hasAttribute('data-bs-no-jquery')) {\n    return window.jQuery\n  }\n\n  return null\n}\n\nconst DOMContentLoadedCallbacks = []\n\nconst onDOMContentLoaded = callback => {\n  if (document.readyState === 'loading') {\n    // add listener on the first call when the document is in loading state\n    if (!DOMContentLoadedCallbacks.length) {\n      document.addEventListener('DOMContentLoaded', () => {\n        for (const callback of DOMContentLoadedCallbacks) {\n          callback()\n        }\n      })\n    }\n\n    DOMContentLoadedCallbacks.push(callback)\n  } else {\n    callback()\n  }\n}\n\nconst isRTL = () => document.documentElement.dir === 'rtl'\n\nconst defineJQueryPlugin = plugin => {\n  onDOMContentLoaded(() => {\n    const $ = getjQuery()\n    /* istanbul ignore if */\n    if ($) {\n      const name = plugin.NAME\n      const JQUERY_NO_CONFLICT = $.fn[name]\n      $.fn[name] = plugin.jQueryInterface\n      $.fn[name].Constructor = plugin\n      $.fn[name].noConflict = () => {\n        $.fn[name] = JQUERY_NO_CONFLICT\n        return plugin.jQueryInterface\n      }\n    }\n  })\n}\n\nconst execute = (possibleCallback, args = [], defaultValue = possibleCallback) => {\n  return typeof possibleCallback === 'function' ? possibleCallback(...args) : defaultValue\n}\n\nconst executeAfterTransition = (callback, transitionElement, waitForTransition = true) => {\n  if (!waitForTransition) {\n    execute(callback)\n    return\n  }\n\n  const durationPadding = 5\n  const emulatedDuration = getTransitionDurationFromElement(transitionElement) + durationPadding\n\n  let called = false\n\n  const handler = ({ target }) => {\n    if (target !== transitionElement) {\n      return\n    }\n\n    called = true\n    transitionElement.removeEventListener(TRANSITION_END, handler)\n    execute(callback)\n  }\n\n  transitionElement.addEventListener(TRANSITION_END, handler)\n  setTimeout(() => {\n    if (!called) {\n      triggerTransitionEnd(transitionElement)\n    }\n  }, emulatedDuration)\n}\n\n/**\n * Return the previous/next element of a list.\n *\n * @param {array} list    The list of elements\n * @param activeElement   The active element\n * @param shouldGetNext   Choose to get next or previous element\n * @param isCycleAllowed\n * @return {Element|elem} The proper element\n */\nconst getNextActiveElement = (list, activeElement, shouldGetNext, isCycleAllowed) => {\n  const listLength = list.length\n  let index = list.indexOf(activeElement)\n\n  // if the element does not exist in the list return an element\n  // depending on the direction and if cycle is allowed\n  if (index === -1) {\n    return !shouldGetNext && isCycleAllowed ? list[listLength - 1] : list[0]\n  }\n\n  index += shouldGetNext ? 1 : -1\n\n  if (isCycleAllowed) {\n    index = (index + listLength) % listLength\n  }\n\n  return list[Math.max(0, Math.min(index, listLength - 1))]\n}\n\nexport {\n  defineJQueryPlugin,\n  execute,\n  executeAfterTransition,\n  findShadowRoot,\n  getElement,\n  getjQuery,\n  getNextActiveElement,\n  getTransitionDurationFromElement,\n  getUID,\n  isDisabled,\n  isElement,\n  isRTL,\n  isVisible,\n  noop,\n  onDOMContentLoaded,\n  parseSelector,\n  reflow,\n  triggerTransitionEnd,\n  toType\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/event-handler.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport { getjQuery } from '../util/index.js'\n\n/**\n * Constants\n */\n\nconst namespaceRegex = /[^.]*(?=\\..*)\\.|.*/\nconst stripNameRegex = /\\..*/\nconst stripUidRegex = /::\\d+$/\nconst eventRegistry = {} // Events storage\nlet uidEvent = 1\nconst customEvents = {\n  mouseenter: 'mouseover',\n  mouseleave: 'mouseout'\n}\n\nconst nativeEvents = new Set([\n  'click',\n  'dblclick',\n  'mouseup',\n  'mousedown',\n  'contextmenu',\n  'mousewheel',\n  'DOMMouseScroll',\n  'mouseover',\n  'mouseout',\n  'mousemove',\n  'selectstart',\n  'selectend',\n  'keydown',\n  'keypress',\n  'keyup',\n  'orientationchange',\n  'touchstart',\n  'touchmove',\n  'touchend',\n  'touchcancel',\n  'pointerdown',\n  'pointermove',\n  'pointerup',\n  'pointerleave',\n  'pointercancel',\n  'gesturestart',\n  'gesturechange',\n  'gestureend',\n  'focus',\n  'blur',\n  'change',\n  'reset',\n  'select',\n  'submit',\n  'focusin',\n  'focusout',\n  'load',\n  'unload',\n  'beforeunload',\n  'resize',\n  'move',\n  'DOMContentLoaded',\n  'readystatechange',\n  'error',\n  'abort',\n  'scroll'\n])\n\n/**\n * Private methods\n */\n\nfunction makeEventUid(element, uid) {\n  return (uid && `${uid}::${uidEvent++}`) || element.uidEvent || uidEvent++\n}\n\nfunction getElementEvents(element) {\n  const uid = makeEventUid(element)\n\n  element.uidEvent = uid\n  eventRegistry[uid] = eventRegistry[uid] || {}\n\n  return eventRegistry[uid]\n}\n\nfunction bootstrapHandler(element, fn) {\n  return function handler(event) {\n    hydrateObj(event, { delegateTarget: element })\n\n    if (handler.oneOff) {\n      EventHandler.off(element, event.type, fn)\n    }\n\n    return fn.apply(element, [event])\n  }\n}\n\nfunction bootstrapDelegationHandler(element, selector, fn) {\n  return function handler(event) {\n    const domElements = element.querySelectorAll(selector)\n\n    for (let { target } = event; target && target !== this; target = target.parentNode) {\n      for (const domElement of domElements) {\n        if (domElement !== target) {\n          continue\n        }\n\n        hydrateObj(event, { delegateTarget: target })\n\n        if (handler.oneOff) {\n          EventHandler.off(element, event.type, selector, fn)\n        }\n\n        return fn.apply(target, [event])\n      }\n    }\n  }\n}\n\nfunction findHandler(events, callable, delegationSelector = null) {\n  return Object.values(events)\n    .find(event => event.callable === callable && event.delegationSelector === delegationSelector)\n}\n\nfunction normalizeParameters(originalTypeEvent, handler, delegationFunction) {\n  const isDelegated = typeof handler === 'string'\n  // TODO: tooltip passes `false` instead of selector, so we need to check\n  const callable = isDelegated ? delegationFunction : (handler || delegationFunction)\n  let typeEvent = getTypeEvent(originalTypeEvent)\n\n  if (!nativeEvents.has(typeEvent)) {\n    typeEvent = originalTypeEvent\n  }\n\n  return [isDelegated, callable, typeEvent]\n}\n\nfunction addHandler(element, originalTypeEvent, handler, delegationFunction, oneOff) {\n  if (typeof originalTypeEvent !== 'string' || !element) {\n    return\n  }\n\n  let [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction)\n\n  // in case of mouseenter or mouseleave wrap the handler within a function that checks for its DOM position\n  // this prevents the handler from being dispatched the same way as mouseover or mouseout does\n  if (originalTypeEvent in customEvents) {\n    const wrapFunction = fn => {\n      return function (event) {\n        if (!event.relatedTarget || (event.relatedTarget !== event.delegateTarget && !event.delegateTarget.contains(event.relatedTarget))) {\n          return fn.call(this, event)\n        }\n      }\n    }\n\n    callable = wrapFunction(callable)\n  }\n\n  const events = getElementEvents(element)\n  const handlers = events[typeEvent] || (events[typeEvent] = {})\n  const previousFunction = findHandler(handlers, callable, isDelegated ? handler : null)\n\n  if (previousFunction) {\n    previousFunction.oneOff = previousFunction.oneOff && oneOff\n\n    return\n  }\n\n  const uid = makeEventUid(callable, originalTypeEvent.replace(namespaceRegex, ''))\n  const fn = isDelegated ?\n    bootstrapDelegationHandler(element, handler, callable) :\n    bootstrapHandler(element, callable)\n\n  fn.delegationSelector = isDelegated ? handler : null\n  fn.callable = callable\n  fn.oneOff = oneOff\n  fn.uidEvent = uid\n  handlers[uid] = fn\n\n  element.addEventListener(typeEvent, fn, isDelegated)\n}\n\nfunction removeHandler(element, events, typeEvent, handler, delegationSelector) {\n  const fn = findHandler(events[typeEvent], handler, delegationSelector)\n\n  if (!fn) {\n    return\n  }\n\n  element.removeEventListener(typeEvent, fn, Boolean(delegationSelector))\n  delete events[typeEvent][fn.uidEvent]\n}\n\nfunction removeNamespacedHandlers(element, events, typeEvent, namespace) {\n  const storeElementEvent = events[typeEvent] || {}\n\n  for (const [handlerKey, event] of Object.entries(storeElementEvent)) {\n    if (handlerKey.includes(namespace)) {\n      removeHandler(element, events, typeEvent, event.callable, event.delegationSelector)\n    }\n  }\n}\n\nfunction getTypeEvent(event) {\n  // allow to get the native events from namespaced events ('click.bs.button' --> 'click')\n  event = event.replace(stripNameRegex, '')\n  return customEvents[event] || event\n}\n\nconst EventHandler = {\n  on(element, event, handler, delegationFunction) {\n    addHandler(element, event, handler, delegationFunction, false)\n  },\n\n  one(element, event, handler, delegationFunction) {\n    addHandler(element, event, handler, delegationFunction, true)\n  },\n\n  off(element, originalTypeEvent, handler, delegationFunction) {\n    if (typeof originalTypeEvent !== 'string' || !element) {\n      return\n    }\n\n    const [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction)\n    const inNamespace = typeEvent !== originalTypeEvent\n    const events = getElementEvents(element)\n    const storeElementEvent = events[typeEvent] || {}\n    const isNamespace = originalTypeEvent.startsWith('.')\n\n    if (typeof callable !== 'undefined') {\n      // Simplest case: handler is passed, remove that listener ONLY.\n      if (!Object.keys(storeElementEvent).length) {\n        return\n      }\n\n      removeHandler(element, events, typeEvent, callable, isDelegated ? handler : null)\n      return\n    }\n\n    if (isNamespace) {\n      for (const elementEvent of Object.keys(events)) {\n        removeNamespacedHandlers(element, events, elementEvent, originalTypeEvent.slice(1))\n      }\n    }\n\n    for (const [keyHandlers, event] of Object.entries(storeElementEvent)) {\n      const handlerKey = keyHandlers.replace(stripUidRegex, '')\n\n      if (!inNamespace || originalTypeEvent.includes(handlerKey)) {\n        removeHandler(element, events, typeEvent, event.callable, event.delegationSelector)\n      }\n    }\n  },\n\n  trigger(element, event, args) {\n    if (typeof event !== 'string' || !element) {\n      return null\n    }\n\n    const $ = getjQuery()\n    const typeEvent = getTypeEvent(event)\n    const inNamespace = event !== typeEvent\n\n    let jQueryEvent = null\n    let bubbles = true\n    let nativeDispatch = true\n    let defaultPrevented = false\n\n    if (inNamespace && $) {\n      jQueryEvent = $.Event(event, args)\n\n      $(element).trigger(jQueryEvent)\n      bubbles = !jQueryEvent.isPropagationStopped()\n      nativeDispatch = !jQueryEvent.isImmediatePropagationStopped()\n      defaultPrevented = jQueryEvent.isDefaultPrevented()\n    }\n\n    const evt = hydrateObj(new Event(event, { bubbles, cancelable: true }), args)\n\n    if (defaultPrevented) {\n      evt.preventDefault()\n    }\n\n    if (nativeDispatch) {\n      element.dispatchEvent(evt)\n    }\n\n    if (evt.defaultPrevented && jQueryEvent) {\n      jQueryEvent.preventDefault()\n    }\n\n    return evt\n  }\n}\n\nfunction hydrateObj(obj, meta = {}) {\n  for (const [key, value] of Object.entries(meta)) {\n    try {\n      obj[key] = value\n    } catch {\n      Object.defineProperty(obj, key, {\n        configurable: true,\n        get() {\n          return value\n        }\n      })\n    }\n  }\n\n  return obj\n}\n\nexport default EventHandler\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/manipulator.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nfunction normalizeData(value) {\n  if (value === 'true') {\n    return true\n  }\n\n  if (value === 'false') {\n    return false\n  }\n\n  if (value === Number(value).toString()) {\n    return Number(value)\n  }\n\n  if (value === '' || value === 'null') {\n    return null\n  }\n\n  if (typeof value !== 'string') {\n    return value\n  }\n\n  try {\n    return JSON.parse(decodeURIComponent(value))\n  } catch {\n    return value\n  }\n}\n\nfunction normalizeDataKey(key) {\n  return key.replace(/[A-Z]/g, chr => `-${chr.toLowerCase()}`)\n}\n\nconst Manipulator = {\n  setDataAttribute(element, key, value) {\n    element.setAttribute(`data-bs-${normalizeDataKey(key)}`, value)\n  },\n\n  removeDataAttribute(element, key) {\n    element.removeAttribute(`data-bs-${normalizeDataKey(key)}`)\n  },\n\n  getDataAttributes(element) {\n    if (!element) {\n      return {}\n    }\n\n    const attributes = {}\n    const bsKeys = Object.keys(element.dataset).filter(key => key.startsWith('bs') && !key.startsWith('bsConfig'))\n\n    for (const key of bsKeys) {\n      let pureKey = key.replace(/^bs/, '')\n      pureKey = pureKey.charAt(0).toLowerCase() + pureKey.slice(1, pureKey.length)\n      attributes[pureKey] = normalizeData(element.dataset[key])\n    }\n\n    return attributes\n  },\n\n  getDataAttribute(element, key) {\n    return normalizeData(element.getAttribute(`data-bs-${normalizeDataKey(key)}`))\n  }\n}\n\nexport default Manipulator\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/config.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Manipulator from '../dom/manipulator.js'\nimport { isElement, toType } from './index.js'\n\n/**\n * Class definition\n */\n\nclass Config {\n  // Getters\n  static get Default() {\n    return {}\n  }\n\n  static get DefaultType() {\n    return {}\n  }\n\n  static get NAME() {\n    throw new Error('You have to implement the static method \"NAME\", for each component!')\n  }\n\n  _getConfig(config) {\n    config = this._mergeConfigObj(config)\n    config = this._configAfterMerge(config)\n    this._typeCheckConfig(config)\n    return config\n  }\n\n  _configAfterMerge(config) {\n    return config\n  }\n\n  _mergeConfigObj(config, element) {\n    const jsonConfig = isElement(element) ? Manipulator.getDataAttribute(element, 'config') : {} // try to parse\n\n    return {\n      ...this.constructor.Default,\n      ...(typeof jsonConfig === 'object' ? jsonConfig : {}),\n      ...(isElement(element) ? Manipulator.getDataAttributes(element) : {}),\n      ...(typeof config === 'object' ? config : {})\n    }\n  }\n\n  _typeCheckConfig(config, configTypes = this.constructor.DefaultType) {\n    for (const [property, expectedTypes] of Object.entries(configTypes)) {\n      const value = config[property]\n      const valueType = isElement(value) ? 'element' : toType(value)\n\n      if (!new RegExp(expectedTypes).test(valueType)) {\n        throw new TypeError(\n          `${this.constructor.NAME.toUpperCase()}: Option \"${property}\" provided type \"${valueType}\" but expected type \"${expectedTypes}\".`\n        )\n      }\n    }\n  }\n}\n\nexport default Config\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap base-component.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Data from './dom/data.js'\nimport EventHandler from './dom/event-handler.js'\nimport Config from './util/config.js'\nimport { executeAfterTransition, getElement } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst VERSION = '5.3.1'\n\n/**\n * Class definition\n */\n\nclass BaseComponent extends Config {\n  constructor(element, config) {\n    super()\n\n    element = getElement(element)\n    if (!element) {\n      return\n    }\n\n    this._element = element\n    this._config = this._getConfig(config)\n\n    Data.set(this._element, this.constructor.DATA_KEY, this)\n  }\n\n  // Public\n  dispose() {\n    Data.remove(this._element, this.constructor.DATA_KEY)\n    EventHandler.off(this._element, this.constructor.EVENT_KEY)\n\n    for (const propertyName of Object.getOwnPropertyNames(this)) {\n      this[propertyName] = null\n    }\n  }\n\n  _queueCallback(callback, element, isAnimated = true) {\n    executeAfterTransition(callback, element, isAnimated)\n  }\n\n  _getConfig(config) {\n    config = this._mergeConfigObj(config, this._element)\n    config = this._configAfterMerge(config)\n    this._typeCheckConfig(config)\n    return config\n  }\n\n  // Static\n  static getInstance(element) {\n    return Data.get(getElement(element), this.DATA_KEY)\n  }\n\n  static getOrCreateInstance(element, config = {}) {\n    return this.getInstance(element) || new this(element, typeof config === 'object' ? config : null)\n  }\n\n  static get VERSION() {\n    return VERSION\n  }\n\n  static get DATA_KEY() {\n    return `bs.${this.NAME}`\n  }\n\n  static get EVENT_KEY() {\n    return `.${this.DATA_KEY}`\n  }\n\n  static eventName(name) {\n    return `${name}${this.EVENT_KEY}`\n  }\n}\n\nexport default BaseComponent\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/selector-engine.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport { isDisabled, isVisible, parseSelector } from '../util/index.js'\n\nconst getSelector = element => {\n  let selector = element.getAttribute('data-bs-target')\n\n  if (!selector || selector === '#') {\n    let hrefAttribute = element.getAttribute('href')\n\n    // The only valid content that could double as a selector are IDs or classes,\n    // so everything starting with `#` or `.`. If a \"real\" URL is used as the selector,\n    // `document.querySelector` will rightfully complain it is invalid.\n    // See https://github.com/twbs/bootstrap/issues/32273\n    if (!hrefAttribute || (!hrefAttribute.includes('#') && !hrefAttribute.startsWith('.'))) {\n      return null\n    }\n\n    // Just in case some CMS puts out a full URL with the anchor appended\n    if (hrefAttribute.includes('#') && !hrefAttribute.startsWith('#')) {\n      hrefAttribute = `#${hrefAttribute.split('#')[1]}`\n    }\n\n    selector = hrefAttribute && hrefAttribute !== '#' ? hrefAttribute.trim() : null\n  }\n\n  return parseSelector(selector)\n}\n\nconst SelectorEngine = {\n  find(selector, element = document.documentElement) {\n    return [].concat(...Element.prototype.querySelectorAll.call(element, selector))\n  },\n\n  findOne(selector, element = document.documentElement) {\n    return Element.prototype.querySelector.call(element, selector)\n  },\n\n  children(element, selector) {\n    return [].concat(...element.children).filter(child => child.matches(selector))\n  },\n\n  parents(element, selector) {\n    const parents = []\n    let ancestor = element.parentNode.closest(selector)\n\n    while (ancestor) {\n      parents.push(ancestor)\n      ancestor = ancestor.parentNode.closest(selector)\n    }\n\n    return parents\n  },\n\n  prev(element, selector) {\n    let previous = element.previousElementSibling\n\n    while (previous) {\n      if (previous.matches(selector)) {\n        return [previous]\n      }\n\n      previous = previous.previousElementSibling\n    }\n\n    return []\n  },\n  // TODO: this is now unused; remove later along with prev()\n  next(element, selector) {\n    let next = element.nextElementSibling\n\n    while (next) {\n      if (next.matches(selector)) {\n        return [next]\n      }\n\n      next = next.nextElementSibling\n    }\n\n    return []\n  },\n\n  focusableChildren(element) {\n    const focusables = [\n      'a',\n      'button',\n      'input',\n      'textarea',\n      'select',\n      'details',\n      '[tabindex]',\n      '[contenteditable=\"true\"]'\n    ].map(selector => `${selector}:not([tabindex^=\"-\"])`).join(',')\n\n    return this.find(focusables, element).filter(el => !isDisabled(el) && isVisible(el))\n  },\n\n  getSelectorFromElement(element) {\n    const selector = getSelector(element)\n\n    if (selector) {\n      return SelectorEngine.findOne(selector) ? selector : null\n    }\n\n    return null\n  },\n\n  getElementFromSelector(element) {\n    const selector = getSelector(element)\n\n    return selector ? SelectorEngine.findOne(selector) : null\n  },\n\n  getMultipleElementsFromSelector(element) {\n    const selector = getSelector(element)\n\n    return selector ? SelectorEngine.find(selector) : []\n  }\n}\n\nexport default SelectorEngine\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/component-functions.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport { isDisabled } from './index.js'\n\nconst enableDismissTrigger = (component, method = 'hide') => {\n  const clickEvent = `click.dismiss${component.EVENT_KEY}`\n  const name = component.NAME\n\n  EventHandler.on(document, clickEvent, `[data-bs-dismiss=\"${name}\"]`, function (event) {\n    if (['A', 'AREA'].includes(this.tagName)) {\n      event.preventDefault()\n    }\n\n    if (isDisabled(this)) {\n      return\n    }\n\n    const target = SelectorEngine.getElementFromSelector(this) || this.closest(`.${name}`)\n    const instance = component.getOrCreateInstance(target)\n\n    // Method argument is left, for Alert and only, as it doesn't implement the 'hide' method\n    instance[method]()\n  })\n}\n\nexport {\n  enableDismissTrigger\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap alert.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'alert'\nconst DATA_KEY = 'bs.alert'\nconst EVENT_KEY = `.${DATA_KEY}`\n\nconst EVENT_CLOSE = `close${EVENT_KEY}`\nconst EVENT_CLOSED = `closed${EVENT_KEY}`\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\n\n/**\n * Class definition\n */\n\nclass Alert extends BaseComponent {\n  // Getters\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  close() {\n    const closeEvent = EventHandler.trigger(this._element, EVENT_CLOSE)\n\n    if (closeEvent.defaultPrevented) {\n      return\n    }\n\n    this._element.classList.remove(CLASS_NAME_SHOW)\n\n    const isAnimated = this._element.classList.contains(CLASS_NAME_FADE)\n    this._queueCallback(() => this._destroyElement(), this._element, isAnimated)\n  }\n\n  // Private\n  _destroyElement() {\n    this._element.remove()\n    EventHandler.trigger(this._element, EVENT_CLOSED)\n    this.dispose()\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Alert.getOrCreateInstance(this)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config](this)\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nenableDismissTrigger(Alert, 'close')\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Alert)\n\nexport default Alert\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap button.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'button'\nconst DATA_KEY = 'bs.button'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst CLASS_NAME_ACTIVE = 'active'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"button\"]'\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\n/**\n * Class definition\n */\n\nclass Button extends BaseComponent {\n  // Getters\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle() {\n    // Toggle class and sync the `aria-pressed` attribute with the return value of the `.toggle()` method\n    this._element.setAttribute('aria-pressed', this._element.classList.toggle(CLASS_NAME_ACTIVE))\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Button.getOrCreateInstance(this)\n\n      if (config === 'toggle') {\n        data[config]()\n      }\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, event => {\n  event.preventDefault()\n\n  const button = event.target.closest(SELECTOR_DATA_TOGGLE)\n  const data = Button.getOrCreateInstance(button)\n\n  data.toggle()\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Button)\n\nexport default Button\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/swipe.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport Config from './config.js'\nimport { execute } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'swipe'\nconst EVENT_KEY = '.bs.swipe'\nconst EVENT_TOUCHSTART = `touchstart${EVENT_KEY}`\nconst EVENT_TOUCHMOVE = `touchmove${EVENT_KEY}`\nconst EVENT_TOUCHEND = `touchend${EVENT_KEY}`\nconst EVENT_POINTERDOWN = `pointerdown${EVENT_KEY}`\nconst EVENT_POINTERUP = `pointerup${EVENT_KEY}`\nconst POINTER_TYPE_TOUCH = 'touch'\nconst POINTER_TYPE_PEN = 'pen'\nconst CLASS_NAME_POINTER_EVENT = 'pointer-event'\nconst SWIPE_THRESHOLD = 40\n\nconst Default = {\n  endCallback: null,\n  leftCallback: null,\n  rightCallback: null\n}\n\nconst DefaultType = {\n  endCallback: '(function|null)',\n  leftCallback: '(function|null)',\n  rightCallback: '(function|null)'\n}\n\n/**\n * Class definition\n */\n\nclass Swipe extends Config {\n  constructor(element, config) {\n    super()\n    this._element = element\n\n    if (!element || !Swipe.isSupported()) {\n      return\n    }\n\n    this._config = this._getConfig(config)\n    this._deltaX = 0\n    this._supportPointerEvents = Boolean(window.PointerEvent)\n    this._initEvents()\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  dispose() {\n    EventHandler.off(this._element, EVENT_KEY)\n  }\n\n  // Private\n  _start(event) {\n    if (!this._supportPointerEvents) {\n      this._deltaX = event.touches[0].clientX\n\n      return\n    }\n\n    if (this._eventIsPointerPenTouch(event)) {\n      this._deltaX = event.clientX\n    }\n  }\n\n  _end(event) {\n    if (this._eventIsPointerPenTouch(event)) {\n      this._deltaX = event.clientX - this._deltaX\n    }\n\n    this._handleSwipe()\n    execute(this._config.endCallback)\n  }\n\n  _move(event) {\n    this._deltaX = event.touches && event.touches.length > 1 ?\n      0 :\n      event.touches[0].clientX - this._deltaX\n  }\n\n  _handleSwipe() {\n    const absDeltaX = Math.abs(this._deltaX)\n\n    if (absDeltaX <= SWIPE_THRESHOLD) {\n      return\n    }\n\n    const direction = absDeltaX / this._deltaX\n\n    this._deltaX = 0\n\n    if (!direction) {\n      return\n    }\n\n    execute(direction > 0 ? this._config.rightCallback : this._config.leftCallback)\n  }\n\n  _initEvents() {\n    if (this._supportPointerEvents) {\n      EventHandler.on(this._element, EVENT_POINTERDOWN, event => this._start(event))\n      EventHandler.on(this._element, EVENT_POINTERUP, event => this._end(event))\n\n      this._element.classList.add(CLASS_NAME_POINTER_EVENT)\n    } else {\n      EventHandler.on(this._element, EVENT_TOUCHSTART, event => this._start(event))\n      EventHandler.on(this._element, EVENT_TOUCHMOVE, event => this._move(event))\n      EventHandler.on(this._element, EVENT_TOUCHEND, event => this._end(event))\n    }\n  }\n\n  _eventIsPointerPenTouch(event) {\n    return this._supportPointerEvents && (event.pointerType === POINTER_TYPE_PEN || event.pointerType === POINTER_TYPE_TOUCH)\n  }\n\n  // Static\n  static isSupported() {\n    return 'ontouchstart' in document.documentElement || navigator.maxTouchPoints > 0\n  }\n}\n\nexport default Swipe\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap carousel.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n  defineJQueryPlugin,\n  getNextActiveElement,\n  isRTL,\n  isVisible,\n  reflow,\n  triggerTransitionEnd\n} from './util/index.js'\nimport Swipe from './util/swipe.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'carousel'\nconst DATA_KEY = 'bs.carousel'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst ARROW_LEFT_KEY = 'ArrowLeft'\nconst ARROW_RIGHT_KEY = 'ArrowRight'\nconst TOUCHEVENT_COMPAT_WAIT = 500 // Time for mouse compat events to fire after touch\n\nconst ORDER_NEXT = 'next'\nconst ORDER_PREV = 'prev'\nconst DIRECTION_LEFT = 'left'\nconst DIRECTION_RIGHT = 'right'\n\nconst EVENT_SLIDE = `slide${EVENT_KEY}`\nconst EVENT_SLID = `slid${EVENT_KEY}`\nconst EVENT_KEYDOWN = `keydown${EVENT_KEY}`\nconst EVENT_MOUSEENTER = `mouseenter${EVENT_KEY}`\nconst EVENT_MOUSELEAVE = `mouseleave${EVENT_KEY}`\nconst EVENT_DRAG_START = `dragstart${EVENT_KEY}`\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_CAROUSEL = 'carousel'\nconst CLASS_NAME_ACTIVE = 'active'\nconst CLASS_NAME_SLIDE = 'slide'\nconst CLASS_NAME_END = 'carousel-item-end'\nconst CLASS_NAME_START = 'carousel-item-start'\nconst CLASS_NAME_NEXT = 'carousel-item-next'\nconst CLASS_NAME_PREV = 'carousel-item-prev'\n\nconst SELECTOR_ACTIVE = '.active'\nconst SELECTOR_ITEM = '.carousel-item'\nconst SELECTOR_ACTIVE_ITEM = SELECTOR_ACTIVE + SELECTOR_ITEM\nconst SELECTOR_ITEM_IMG = '.carousel-item img'\nconst SELECTOR_INDICATORS = '.carousel-indicators'\nconst SELECTOR_DATA_SLIDE = '[data-bs-slide], [data-bs-slide-to]'\nconst SELECTOR_DATA_RIDE = '[data-bs-ride=\"carousel\"]'\n\nconst KEY_TO_DIRECTION = {\n  [ARROW_LEFT_KEY]: DIRECTION_RIGHT,\n  [ARROW_RIGHT_KEY]: DIRECTION_LEFT\n}\n\nconst Default = {\n  interval: 5000,\n  keyboard: true,\n  pause: 'hover',\n  ride: false,\n  touch: true,\n  wrap: true\n}\n\nconst DefaultType = {\n  interval: '(number|boolean)', // TODO:v6 remove boolean support\n  keyboard: 'boolean',\n  pause: '(string|boolean)',\n  ride: '(boolean|string)',\n  touch: 'boolean',\n  wrap: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Carousel extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._interval = null\n    this._activeElement = null\n    this._isSliding = false\n    this.touchTimeout = null\n    this._swipeHelper = null\n\n    this._indicatorsElement = SelectorEngine.findOne(SELECTOR_INDICATORS, this._element)\n    this._addEventListeners()\n\n    if (this._config.ride === CLASS_NAME_CAROUSEL) {\n      this.cycle()\n    }\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  next() {\n    this._slide(ORDER_NEXT)\n  }\n\n  nextWhenVisible() {\n    // FIXME TODO use `document.visibilityState`\n    // Don't call next when the page isn't visible\n    // or the carousel or its parent isn't visible\n    if (!document.hidden && isVisible(this._element)) {\n      this.next()\n    }\n  }\n\n  prev() {\n    this._slide(ORDER_PREV)\n  }\n\n  pause() {\n    if (this._isSliding) {\n      triggerTransitionEnd(this._element)\n    }\n\n    this._clearInterval()\n  }\n\n  cycle() {\n    this._clearInterval()\n    this._updateInterval()\n\n    this._interval = setInterval(() => this.nextWhenVisible(), this._config.interval)\n  }\n\n  _maybeEnableCycle() {\n    if (!this._config.ride) {\n      return\n    }\n\n    if (this._isSliding) {\n      EventHandler.one(this._element, EVENT_SLID, () => this.cycle())\n      return\n    }\n\n    this.cycle()\n  }\n\n  to(index) {\n    const items = this._getItems()\n    if (index > items.length - 1 || index < 0) {\n      return\n    }\n\n    if (this._isSliding) {\n      EventHandler.one(this._element, EVENT_SLID, () => this.to(index))\n      return\n    }\n\n    const activeIndex = this._getItemIndex(this._getActive())\n    if (activeIndex === index) {\n      return\n    }\n\n    const order = index > activeIndex ? ORDER_NEXT : ORDER_PREV\n\n    this._slide(order, items[index])\n  }\n\n  dispose() {\n    if (this._swipeHelper) {\n      this._swipeHelper.dispose()\n    }\n\n    super.dispose()\n  }\n\n  // Private\n  _configAfterMerge(config) {\n    config.defaultInterval = config.interval\n    return config\n  }\n\n  _addEventListeners() {\n    if (this._config.keyboard) {\n      EventHandler.on(this._element, EVENT_KEYDOWN, event => this._keydown(event))\n    }\n\n    if (this._config.pause === 'hover') {\n      EventHandler.on(this._element, EVENT_MOUSEENTER, () => this.pause())\n      EventHandler.on(this._element, EVENT_MOUSELEAVE, () => this._maybeEnableCycle())\n    }\n\n    if (this._config.touch && Swipe.isSupported()) {\n      this._addTouchEventListeners()\n    }\n  }\n\n  _addTouchEventListeners() {\n    for (const img of SelectorEngine.find(SELECTOR_ITEM_IMG, this._element)) {\n      EventHandler.on(img, EVENT_DRAG_START, event => event.preventDefault())\n    }\n\n    const endCallBack = () => {\n      if (this._config.pause !== 'hover') {\n        return\n      }\n\n      // If it's a touch-enabled device, mouseenter/leave are fired as\n      // part of the mouse compatibility events on first tap - the carousel\n      // would stop cycling until user tapped out of it;\n      // here, we listen for touchend, explicitly pause the carousel\n      // (as if it's the second time we tap on it, mouseenter compat event\n      // is NOT fired) and after a timeout (to allow for mouse compatibility\n      // events to fire) we explicitly restart cycling\n\n      this.pause()\n      if (this.touchTimeout) {\n        clearTimeout(this.touchTimeout)\n      }\n\n      this.touchTimeout = setTimeout(() => this._maybeEnableCycle(), TOUCHEVENT_COMPAT_WAIT + this._config.interval)\n    }\n\n    const swipeConfig = {\n      leftCallback: () => this._slide(this._directionToOrder(DIRECTION_LEFT)),\n      rightCallback: () => this._slide(this._directionToOrder(DIRECTION_RIGHT)),\n      endCallback: endCallBack\n    }\n\n    this._swipeHelper = new Swipe(this._element, swipeConfig)\n  }\n\n  _keydown(event) {\n    if (/input|textarea/i.test(event.target.tagName)) {\n      return\n    }\n\n    const direction = KEY_TO_DIRECTION[event.key]\n    if (direction) {\n      event.preventDefault()\n      this._slide(this._directionToOrder(direction))\n    }\n  }\n\n  _getItemIndex(element) {\n    return this._getItems().indexOf(element)\n  }\n\n  _setActiveIndicatorElement(index) {\n    if (!this._indicatorsElement) {\n      return\n    }\n\n    const activeIndicator = SelectorEngine.findOne(SELECTOR_ACTIVE, this._indicatorsElement)\n\n    activeIndicator.classList.remove(CLASS_NAME_ACTIVE)\n    activeIndicator.removeAttribute('aria-current')\n\n    const newActiveIndicator = SelectorEngine.findOne(`[data-bs-slide-to=\"${index}\"]`, this._indicatorsElement)\n\n    if (newActiveIndicator) {\n      newActiveIndicator.classList.add(CLASS_NAME_ACTIVE)\n      newActiveIndicator.setAttribute('aria-current', 'true')\n    }\n  }\n\n  _updateInterval() {\n    const element = this._activeElement || this._getActive()\n\n    if (!element) {\n      return\n    }\n\n    const elementInterval = Number.parseInt(element.getAttribute('data-bs-interval'), 10)\n\n    this._config.interval = elementInterval || this._config.defaultInterval\n  }\n\n  _slide(order, element = null) {\n    if (this._isSliding) {\n      return\n    }\n\n    const activeElement = this._getActive()\n    const isNext = order === ORDER_NEXT\n    const nextElement = element || getNextActiveElement(this._getItems(), activeElement, isNext, this._config.wrap)\n\n    if (nextElement === activeElement) {\n      return\n    }\n\n    const nextElementIndex = this._getItemIndex(nextElement)\n\n    const triggerEvent = eventName => {\n      return EventHandler.trigger(this._element, eventName, {\n        relatedTarget: nextElement,\n        direction: this._orderToDirection(order),\n        from: this._getItemIndex(activeElement),\n        to: nextElementIndex\n      })\n    }\n\n    const slideEvent = triggerEvent(EVENT_SLIDE)\n\n    if (slideEvent.defaultPrevented) {\n      return\n    }\n\n    if (!activeElement || !nextElement) {\n      // Some weirdness is happening, so we bail\n      // TODO: change tests that use empty divs to avoid this check\n      return\n    }\n\n    const isCycling = Boolean(this._interval)\n    this.pause()\n\n    this._isSliding = true\n\n    this._setActiveIndicatorElement(nextElementIndex)\n    this._activeElement = nextElement\n\n    const directionalClassName = isNext ? CLASS_NAME_START : CLASS_NAME_END\n    const orderClassName = isNext ? CLASS_NAME_NEXT : CLASS_NAME_PREV\n\n    nextElement.classList.add(orderClassName)\n\n    reflow(nextElement)\n\n    activeElement.classList.add(directionalClassName)\n    nextElement.classList.add(directionalClassName)\n\n    const completeCallBack = () => {\n      nextElement.classList.remove(directionalClassName, orderClassName)\n      nextElement.classList.add(CLASS_NAME_ACTIVE)\n\n      activeElement.classList.remove(CLASS_NAME_ACTIVE, orderClassName, directionalClassName)\n\n      this._isSliding = false\n\n      triggerEvent(EVENT_SLID)\n    }\n\n    this._queueCallback(completeCallBack, activeElement, this._isAnimated())\n\n    if (isCycling) {\n      this.cycle()\n    }\n  }\n\n  _isAnimated() {\n    return this._element.classList.contains(CLASS_NAME_SLIDE)\n  }\n\n  _getActive() {\n    return SelectorEngine.findOne(SELECTOR_ACTIVE_ITEM, this._element)\n  }\n\n  _getItems() {\n    return SelectorEngine.find(SELECTOR_ITEM, this._element)\n  }\n\n  _clearInterval() {\n    if (this._interval) {\n      clearInterval(this._interval)\n      this._interval = null\n    }\n  }\n\n  _directionToOrder(direction) {\n    if (isRTL()) {\n      return direction === DIRECTION_LEFT ? ORDER_PREV : ORDER_NEXT\n    }\n\n    return direction === DIRECTION_LEFT ? ORDER_NEXT : ORDER_PREV\n  }\n\n  _orderToDirection(order) {\n    if (isRTL()) {\n      return order === ORDER_PREV ? DIRECTION_LEFT : DIRECTION_RIGHT\n    }\n\n    return order === ORDER_PREV ? DIRECTION_RIGHT : DIRECTION_LEFT\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Carousel.getOrCreateInstance(this, config)\n\n      if (typeof config === 'number') {\n        data.to(config)\n        return\n      }\n\n      if (typeof config === 'string') {\n        if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n          throw new TypeError(`No method named \"${config}\"`)\n        }\n\n        data[config]()\n      }\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_SLIDE, function (event) {\n  const target = SelectorEngine.getElementFromSelector(this)\n\n  if (!target || !target.classList.contains(CLASS_NAME_CAROUSEL)) {\n    return\n  }\n\n  event.preventDefault()\n\n  const carousel = Carousel.getOrCreateInstance(target)\n  const slideIndex = this.getAttribute('data-bs-slide-to')\n\n  if (slideIndex) {\n    carousel.to(slideIndex)\n    carousel._maybeEnableCycle()\n    return\n  }\n\n  if (Manipulator.getDataAttribute(this, 'slide') === 'next') {\n    carousel.next()\n    carousel._maybeEnableCycle()\n    return\n  }\n\n  carousel.prev()\n  carousel._maybeEnableCycle()\n})\n\nEventHandler.on(window, EVENT_LOAD_DATA_API, () => {\n  const carousels = SelectorEngine.find(SELECTOR_DATA_RIDE)\n\n  for (const carousel of carousels) {\n    Carousel.getOrCreateInstance(carousel)\n  }\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Carousel)\n\nexport default Carousel\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap collapse.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n  defineJQueryPlugin,\n  getElement,\n  reflow\n} from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'collapse'\nconst DATA_KEY = 'bs.collapse'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_COLLAPSE = 'collapse'\nconst CLASS_NAME_COLLAPSING = 'collapsing'\nconst CLASS_NAME_COLLAPSED = 'collapsed'\nconst CLASS_NAME_DEEPER_CHILDREN = `:scope .${CLASS_NAME_COLLAPSE} .${CLASS_NAME_COLLAPSE}`\nconst CLASS_NAME_HORIZONTAL = 'collapse-horizontal'\n\nconst WIDTH = 'width'\nconst HEIGHT = 'height'\n\nconst SELECTOR_ACTIVES = '.collapse.show, .collapse.collapsing'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"collapse\"]'\n\nconst Default = {\n  parent: null,\n  toggle: true\n}\n\nconst DefaultType = {\n  parent: '(null|element)',\n  toggle: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Collapse extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._isTransitioning = false\n    this._triggerArray = []\n\n    const toggleList = SelectorEngine.find(SELECTOR_DATA_TOGGLE)\n\n    for (const elem of toggleList) {\n      const selector = SelectorEngine.getSelectorFromElement(elem)\n      const filterElement = SelectorEngine.find(selector)\n        .filter(foundElement => foundElement === this._element)\n\n      if (selector !== null && filterElement.length) {\n        this._triggerArray.push(elem)\n      }\n    }\n\n    this._initializeChildren()\n\n    if (!this._config.parent) {\n      this._addAriaAndCollapsedClass(this._triggerArray, this._isShown())\n    }\n\n    if (this._config.toggle) {\n      this.toggle()\n    }\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle() {\n    if (this._isShown()) {\n      this.hide()\n    } else {\n      this.show()\n    }\n  }\n\n  show() {\n    if (this._isTransitioning || this._isShown()) {\n      return\n    }\n\n    let activeChildren = []\n\n    // find active children\n    if (this._config.parent) {\n      activeChildren = this._getFirstLevelChildren(SELECTOR_ACTIVES)\n        .filter(element => element !== this._element)\n        .map(element => Collapse.getOrCreateInstance(element, { toggle: false }))\n    }\n\n    if (activeChildren.length && activeChildren[0]._isTransitioning) {\n      return\n    }\n\n    const startEvent = EventHandler.trigger(this._element, EVENT_SHOW)\n    if (startEvent.defaultPrevented) {\n      return\n    }\n\n    for (const activeInstance of activeChildren) {\n      activeInstance.hide()\n    }\n\n    const dimension = this._getDimension()\n\n    this._element.classList.remove(CLASS_NAME_COLLAPSE)\n    this._element.classList.add(CLASS_NAME_COLLAPSING)\n\n    this._element.style[dimension] = 0\n\n    this._addAriaAndCollapsedClass(this._triggerArray, true)\n    this._isTransitioning = true\n\n    const complete = () => {\n      this._isTransitioning = false\n\n      this._element.classList.remove(CLASS_NAME_COLLAPSING)\n      this._element.classList.add(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW)\n\n      this._element.style[dimension] = ''\n\n      EventHandler.trigger(this._element, EVENT_SHOWN)\n    }\n\n    const capitalizedDimension = dimension[0].toUpperCase() + dimension.slice(1)\n    const scrollSize = `scroll${capitalizedDimension}`\n\n    this._queueCallback(complete, this._element, true)\n    this._element.style[dimension] = `${this._element[scrollSize]}px`\n  }\n\n  hide() {\n    if (this._isTransitioning || !this._isShown()) {\n      return\n    }\n\n    const startEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n    if (startEvent.defaultPrevented) {\n      return\n    }\n\n    const dimension = this._getDimension()\n\n    this._element.style[dimension] = `${this._element.getBoundingClientRect()[dimension]}px`\n\n    reflow(this._element)\n\n    this._element.classList.add(CLASS_NAME_COLLAPSING)\n    this._element.classList.remove(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW)\n\n    for (const trigger of this._triggerArray) {\n      const element = SelectorEngine.getElementFromSelector(trigger)\n\n      if (element && !this._isShown(element)) {\n        this._addAriaAndCollapsedClass([trigger], false)\n      }\n    }\n\n    this._isTransitioning = true\n\n    const complete = () => {\n      this._isTransitioning = false\n      this._element.classList.remove(CLASS_NAME_COLLAPSING)\n      this._element.classList.add(CLASS_NAME_COLLAPSE)\n      EventHandler.trigger(this._element, EVENT_HIDDEN)\n    }\n\n    this._element.style[dimension] = ''\n\n    this._queueCallback(complete, this._element, true)\n  }\n\n  _isShown(element = this._element) {\n    return element.classList.contains(CLASS_NAME_SHOW)\n  }\n\n  // Private\n  _configAfterMerge(config) {\n    config.toggle = Boolean(config.toggle) // Coerce string values\n    config.parent = getElement(config.parent)\n    return config\n  }\n\n  _getDimension() {\n    return this._element.classList.contains(CLASS_NAME_HORIZONTAL) ? WIDTH : HEIGHT\n  }\n\n  _initializeChildren() {\n    if (!this._config.parent) {\n      return\n    }\n\n    const children = this._getFirstLevelChildren(SELECTOR_DATA_TOGGLE)\n\n    for (const element of children) {\n      const selected = SelectorEngine.getElementFromSelector(element)\n\n      if (selected) {\n        this._addAriaAndCollapsedClass([element], this._isShown(selected))\n      }\n    }\n  }\n\n  _getFirstLevelChildren(selector) {\n    const children = SelectorEngine.find(CLASS_NAME_DEEPER_CHILDREN, this._config.parent)\n    // remove children if greater depth\n    return SelectorEngine.find(selector, this._config.parent).filter(element => !children.includes(element))\n  }\n\n  _addAriaAndCollapsedClass(triggerArray, isOpen) {\n    if (!triggerArray.length) {\n      return\n    }\n\n    for (const element of triggerArray) {\n      element.classList.toggle(CLASS_NAME_COLLAPSED, !isOpen)\n      element.setAttribute('aria-expanded', isOpen)\n    }\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    const _config = {}\n    if (typeof config === 'string' && /show|hide/.test(config)) {\n      _config.toggle = false\n    }\n\n    return this.each(function () {\n      const data = Collapse.getOrCreateInstance(this, _config)\n\n      if (typeof config === 'string') {\n        if (typeof data[config] === 'undefined') {\n          throw new TypeError(`No method named \"${config}\"`)\n        }\n\n        data[config]()\n      }\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n  // preventDefault only for <a> elements (which change the URL) not inside the collapsible element\n  if (event.target.tagName === 'A' || (event.delegateTarget && event.delegateTarget.tagName === 'A')) {\n    event.preventDefault()\n  }\n\n  for (const element of SelectorEngine.getMultipleElementsFromSelector(this)) {\n    Collapse.getOrCreateInstance(element, { toggle: false }).toggle()\n  }\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Collapse)\n\nexport default Collapse\n","export var top = 'top';\nexport var bottom = 'bottom';\nexport var right = 'right';\nexport var left = 'left';\nexport var auto = 'auto';\nexport var basePlacements = [top, bottom, right, left];\nexport var start = 'start';\nexport var end = 'end';\nexport var clippingParents = 'clippingParents';\nexport var viewport = 'viewport';\nexport var popper = 'popper';\nexport var reference = 'reference';\nexport var variationPlacements = /*#__PURE__*/basePlacements.reduce(function (acc, placement) {\n  return acc.concat([placement + \"-\" + start, placement + \"-\" + end]);\n}, []);\nexport var placements = /*#__PURE__*/[].concat(basePlacements, [auto]).reduce(function (acc, placement) {\n  return acc.concat([placement, placement + \"-\" + start, placement + \"-\" + end]);\n}, []); // modifiers that need to read the DOM\n\nexport var beforeRead = 'beforeRead';\nexport var read = 'read';\nexport var afterRead = 'afterRead'; // pure-logic modifiers\n\nexport var beforeMain = 'beforeMain';\nexport var main = 'main';\nexport var afterMain = 'afterMain'; // modifier with the purpose to write to the DOM (or write into a framework state)\n\nexport var beforeWrite = 'beforeWrite';\nexport var write = 'write';\nexport var afterWrite = 'afterWrite';\nexport var modifierPhases = [beforeRead, read, afterRead, beforeMain, main, afterMain, beforeWrite, write, afterWrite];","export default function getNodeName(element) {\n  return element ? (element.nodeName || '').toLowerCase() : null;\n}","export default function getWindow(node) {\n  if (node == null) {\n    return window;\n  }\n\n  if (node.toString() !== '[object Window]') {\n    var ownerDocument = node.ownerDocument;\n    return ownerDocument ? ownerDocument.defaultView || window : window;\n  }\n\n  return node;\n}","import getWindow from \"./getWindow.js\";\n\nfunction isElement(node) {\n  var OwnElement = getWindow(node).Element;\n  return node instanceof OwnElement || node instanceof Element;\n}\n\nfunction isHTMLElement(node) {\n  var OwnElement = getWindow(node).HTMLElement;\n  return node instanceof OwnElement || node instanceof HTMLElement;\n}\n\nfunction isShadowRoot(node) {\n  // IE 11 has no ShadowRoot\n  if (typeof ShadowRoot === 'undefined') {\n    return false;\n  }\n\n  var OwnElement = getWindow(node).ShadowRoot;\n  return node instanceof OwnElement || node instanceof ShadowRoot;\n}\n\nexport { isElement, isHTMLElement, isShadowRoot };","import getNodeName from \"../dom-utils/getNodeName.js\";\nimport { isHTMLElement } from \"../dom-utils/instanceOf.js\"; // This modifier takes the styles prepared by the `computeStyles` modifier\n// and applies them to the HTMLElements such as popper and arrow\n\nfunction applyStyles(_ref) {\n  var state = _ref.state;\n  Object.keys(state.elements).forEach(function (name) {\n    var style = state.styles[name] || {};\n    var attributes = state.attributes[name] || {};\n    var element = state.elements[name]; // arrow is optional + virtual elements\n\n    if (!isHTMLElement(element) || !getNodeName(element)) {\n      return;\n    } // Flow doesn't support to extend this property, but it's the most\n    // effective way to apply styles to an HTMLElement\n    // $FlowFixMe[cannot-write]\n\n\n    Object.assign(element.style, style);\n    Object.keys(attributes).forEach(function (name) {\n      var value = attributes[name];\n\n      if (value === false) {\n        element.removeAttribute(name);\n      } else {\n        element.setAttribute(name, value === true ? '' : value);\n      }\n    });\n  });\n}\n\nfunction effect(_ref2) {\n  var state = _ref2.state;\n  var initialStyles = {\n    popper: {\n      position: state.options.strategy,\n      left: '0',\n      top: '0',\n      margin: '0'\n    },\n    arrow: {\n      position: 'absolute'\n    },\n    reference: {}\n  };\n  Object.assign(state.elements.popper.style, initialStyles.popper);\n  state.styles = initialStyles;\n\n  if (state.elements.arrow) {\n    Object.assign(state.elements.arrow.style, initialStyles.arrow);\n  }\n\n  return function () {\n    Object.keys(state.elements).forEach(function (name) {\n      var element = state.elements[name];\n      var attributes = state.attributes[name] || {};\n      var styleProperties = Object.keys(state.styles.hasOwnProperty(name) ? state.styles[name] : initialStyles[name]); // Set all values to an empty string to unset them\n\n      var style = styleProperties.reduce(function (style, property) {\n        style[property] = '';\n        return style;\n      }, {}); // arrow is optional + virtual elements\n\n      if (!isHTMLElement(element) || !getNodeName(element)) {\n        return;\n      }\n\n      Object.assign(element.style, style);\n      Object.keys(attributes).forEach(function (attribute) {\n        element.removeAttribute(attribute);\n      });\n    });\n  };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'applyStyles',\n  enabled: true,\n  phase: 'write',\n  fn: applyStyles,\n  effect: effect,\n  requires: ['computeStyles']\n};","import { auto } from \"../enums.js\";\nexport default function getBasePlacement(placement) {\n  return placement.split('-')[0];\n}","export var max = Math.max;\nexport var min = Math.min;\nexport var round = Math.round;","export default function getUAString() {\n  var uaData = navigator.userAgentData;\n\n  if (uaData != null && uaData.brands && Array.isArray(uaData.brands)) {\n    return uaData.brands.map(function (item) {\n      return item.brand + \"/\" + item.version;\n    }).join(' ');\n  }\n\n  return navigator.userAgent;\n}","import getUAString from \"../utils/userAgent.js\";\nexport default function isLayoutViewport() {\n  return !/^((?!chrome|android).)*safari/i.test(getUAString());\n}","import { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport { round } from \"../utils/math.js\";\nimport getWindow from \"./getWindow.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getBoundingClientRect(element, includeScale, isFixedStrategy) {\n  if (includeScale === void 0) {\n    includeScale = false;\n  }\n\n  if (isFixedStrategy === void 0) {\n    isFixedStrategy = false;\n  }\n\n  var clientRect = element.getBoundingClientRect();\n  var scaleX = 1;\n  var scaleY = 1;\n\n  if (includeScale && isHTMLElement(element)) {\n    scaleX = element.offsetWidth > 0 ? round(clientRect.width) / element.offsetWidth || 1 : 1;\n    scaleY = element.offsetHeight > 0 ? round(clientRect.height) / element.offsetHeight || 1 : 1;\n  }\n\n  var _ref = isElement(element) ? getWindow(element) : window,\n      visualViewport = _ref.visualViewport;\n\n  var addVisualOffsets = !isLayoutViewport() && isFixedStrategy;\n  var x = (clientRect.left + (addVisualOffsets && visualViewport ? visualViewport.offsetLeft : 0)) / scaleX;\n  var y = (clientRect.top + (addVisualOffsets && visualViewport ? visualViewport.offsetTop : 0)) / scaleY;\n  var width = clientRect.width / scaleX;\n  var height = clientRect.height / scaleY;\n  return {\n    width: width,\n    height: height,\n    top: y,\n    right: x + width,\n    bottom: y + height,\n    left: x,\n    x: x,\n    y: y\n  };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\"; // Returns the layout rect of an element relative to its offsetParent. Layout\n// means it doesn't take into account transforms.\n\nexport default function getLayoutRect(element) {\n  var clientRect = getBoundingClientRect(element); // Use the clientRect sizes if it's not been transformed.\n  // Fixes https://github.com/popperjs/popper-core/issues/1223\n\n  var width = element.offsetWidth;\n  var height = element.offsetHeight;\n\n  if (Math.abs(clientRect.width - width) <= 1) {\n    width = clientRect.width;\n  }\n\n  if (Math.abs(clientRect.height - height) <= 1) {\n    height = clientRect.height;\n  }\n\n  return {\n    x: element.offsetLeft,\n    y: element.offsetTop,\n    width: width,\n    height: height\n  };\n}","import { isShadowRoot } from \"./instanceOf.js\";\nexport default function contains(parent, child) {\n  var rootNode = child.getRootNode && child.getRootNode(); // First, attempt with faster native method\n\n  if (parent.contains(child)) {\n    return true;\n  } // then fallback to custom implementation with Shadow DOM support\n  else if (rootNode && isShadowRoot(rootNode)) {\n      var next = child;\n\n      do {\n        if (next && parent.isSameNode(next)) {\n          return true;\n        } // $FlowFixMe[prop-missing]: need a better way to handle this...\n\n\n        next = next.parentNode || next.host;\n      } while (next);\n    } // Give up, the result is false\n\n\n  return false;\n}","import getWindow from \"./getWindow.js\";\nexport default function getComputedStyle(element) {\n  return getWindow(element).getComputedStyle(element);\n}","import getNodeName from \"./getNodeName.js\";\nexport default function isTableElement(element) {\n  return ['table', 'td', 'th'].indexOf(getNodeName(element)) >= 0;\n}","import { isElement } from \"./instanceOf.js\";\nexport default function getDocumentElement(element) {\n  // $FlowFixMe[incompatible-return]: assume body is always available\n  return ((isElement(element) ? element.ownerDocument : // $FlowFixMe[prop-missing]\n  element.document) || window.document).documentElement;\n}","import getNodeName from \"./getNodeName.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport { isShadowRoot } from \"./instanceOf.js\";\nexport default function getParentNode(element) {\n  if (getNodeName(element) === 'html') {\n    return element;\n  }\n\n  return (// this is a quicker (but less type safe) way to save quite some bytes from the bundle\n    // $FlowFixMe[incompatible-return]\n    // $FlowFixMe[prop-missing]\n    element.assignedSlot || // step into the shadow DOM of the parent of a slotted node\n    element.parentNode || ( // DOM Element detected\n    isShadowRoot(element) ? element.host : null) || // ShadowRoot detected\n    // $FlowFixMe[incompatible-call]: HTMLElement is a Node\n    getDocumentElement(element) // fallback\n\n  );\n}","import getWindow from \"./getWindow.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isHTMLElement, isShadowRoot } from \"./instanceOf.js\";\nimport isTableElement from \"./isTableElement.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getUAString from \"../utils/userAgent.js\";\n\nfunction getTrueOffsetParent(element) {\n  if (!isHTMLElement(element) || // https://github.com/popperjs/popper-core/issues/837\n  getComputedStyle(element).position === 'fixed') {\n    return null;\n  }\n\n  return element.offsetParent;\n} // `.offsetParent` reports `null` for fixed elements, while absolute elements\n// return the containing block\n\n\nfunction getContainingBlock(element) {\n  var isFirefox = /firefox/i.test(getUAString());\n  var isIE = /Trident/i.test(getUAString());\n\n  if (isIE && isHTMLElement(element)) {\n    // In IE 9, 10 and 11 fixed elements containing block is always established by the viewport\n    var elementCss = getComputedStyle(element);\n\n    if (elementCss.position === 'fixed') {\n      return null;\n    }\n  }\n\n  var currentNode = getParentNode(element);\n\n  if (isShadowRoot(currentNode)) {\n    currentNode = currentNode.host;\n  }\n\n  while (isHTMLElement(currentNode) && ['html', 'body'].indexOf(getNodeName(currentNode)) < 0) {\n    var css = getComputedStyle(currentNode); // This is non-exhaustive but covers the most common CSS properties that\n    // create a containing block.\n    // https://developer.mozilla.org/en-US/docs/Web/CSS/Containing_block#identifying_the_containing_block\n\n    if (css.transform !== 'none' || css.perspective !== 'none' || css.contain === 'paint' || ['transform', 'perspective'].indexOf(css.willChange) !== -1 || isFirefox && css.willChange === 'filter' || isFirefox && css.filter && css.filter !== 'none') {\n      return currentNode;\n    } else {\n      currentNode = currentNode.parentNode;\n    }\n  }\n\n  return null;\n} // Gets the closest ancestor positioned element. Handles some edge cases,\n// such as table ancestors and cross browser bugs.\n\n\nexport default function getOffsetParent(element) {\n  var window = getWindow(element);\n  var offsetParent = getTrueOffsetParent(element);\n\n  while (offsetParent && isTableElement(offsetParent) && getComputedStyle(offsetParent).position === 'static') {\n    offsetParent = getTrueOffsetParent(offsetParent);\n  }\n\n  if (offsetParent && (getNodeName(offsetParent) === 'html' || getNodeName(offsetParent) === 'body' && getComputedStyle(offsetParent).position === 'static')) {\n    return window;\n  }\n\n  return offsetParent || getContainingBlock(element) || window;\n}","export default function getMainAxisFromPlacement(placement) {\n  return ['top', 'bottom'].indexOf(placement) >= 0 ? 'x' : 'y';\n}","import { max as mathMax, min as mathMin } from \"./math.js\";\nexport function within(min, value, max) {\n  return mathMax(min, mathMin(value, max));\n}\nexport function withinMaxClamp(min, value, max) {\n  var v = within(min, value, max);\n  return v > max ? max : v;\n}","import getFreshSideObject from \"./getFreshSideObject.js\";\nexport default function mergePaddingObject(paddingObject) {\n  return Object.assign({}, getFreshSideObject(), paddingObject);\n}","export default function getFreshSideObject() {\n  return {\n    top: 0,\n    right: 0,\n    bottom: 0,\n    left: 0\n  };\n}","export default function expandToHashMap(value, keys) {\n  return keys.reduce(function (hashMap, key) {\n    hashMap[key] = value;\n    return hashMap;\n  }, {});\n}","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport contains from \"../dom-utils/contains.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport { within } from \"../utils/within.js\";\nimport mergePaddingObject from \"../utils/mergePaddingObject.js\";\nimport expandToHashMap from \"../utils/expandToHashMap.js\";\nimport { left, right, basePlacements, top, bottom } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar toPaddingObject = function toPaddingObject(padding, state) {\n  padding = typeof padding === 'function' ? padding(Object.assign({}, state.rects, {\n    placement: state.placement\n  })) : padding;\n  return mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n};\n\nfunction arrow(_ref) {\n  var _state$modifiersData$;\n\n  var state = _ref.state,\n      name = _ref.name,\n      options = _ref.options;\n  var arrowElement = state.elements.arrow;\n  var popperOffsets = state.modifiersData.popperOffsets;\n  var basePlacement = getBasePlacement(state.placement);\n  var axis = getMainAxisFromPlacement(basePlacement);\n  var isVertical = [left, right].indexOf(basePlacement) >= 0;\n  var len = isVertical ? 'height' : 'width';\n\n  if (!arrowElement || !popperOffsets) {\n    return;\n  }\n\n  var paddingObject = toPaddingObject(options.padding, state);\n  var arrowRect = getLayoutRect(arrowElement);\n  var minProp = axis === 'y' ? top : left;\n  var maxProp = axis === 'y' ? bottom : right;\n  var endDiff = state.rects.reference[len] + state.rects.reference[axis] - popperOffsets[axis] - state.rects.popper[len];\n  var startDiff = popperOffsets[axis] - state.rects.reference[axis];\n  var arrowOffsetParent = getOffsetParent(arrowElement);\n  var clientSize = arrowOffsetParent ? axis === 'y' ? arrowOffsetParent.clientHeight || 0 : arrowOffsetParent.clientWidth || 0 : 0;\n  var centerToReference = endDiff / 2 - startDiff / 2; // Make sure the arrow doesn't overflow the popper if the center point is\n  // outside of the popper bounds\n\n  var min = paddingObject[minProp];\n  var max = clientSize - arrowRect[len] - paddingObject[maxProp];\n  var center = clientSize / 2 - arrowRect[len] / 2 + centerToReference;\n  var offset = within(min, center, max); // Prevents breaking syntax highlighting...\n\n  var axisProp = axis;\n  state.modifiersData[name] = (_state$modifiersData$ = {}, _state$modifiersData$[axisProp] = offset, _state$modifiersData$.centerOffset = offset - center, _state$modifiersData$);\n}\n\nfunction effect(_ref2) {\n  var state = _ref2.state,\n      options = _ref2.options;\n  var _options$element = options.element,\n      arrowElement = _options$element === void 0 ? '[data-popper-arrow]' : _options$element;\n\n  if (arrowElement == null) {\n    return;\n  } // CSS selector\n\n\n  if (typeof arrowElement === 'string') {\n    arrowElement = state.elements.popper.querySelector(arrowElement);\n\n    if (!arrowElement) {\n      return;\n    }\n  }\n\n  if (!contains(state.elements.popper, arrowElement)) {\n    return;\n  }\n\n  state.elements.arrow = arrowElement;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'arrow',\n  enabled: true,\n  phase: 'main',\n  fn: arrow,\n  effect: effect,\n  requires: ['popperOffsets'],\n  requiresIfExists: ['preventOverflow']\n};","export default function getVariation(placement) {\n  return placement.split('-')[1];\n}","import { top, left, right, bottom, end } from \"../enums.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getWindow from \"../dom-utils/getWindow.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getComputedStyle from \"../dom-utils/getComputedStyle.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport { round } from \"../utils/math.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar unsetSides = {\n  top: 'auto',\n  right: 'auto',\n  bottom: 'auto',\n  left: 'auto'\n}; // Round the offsets to the nearest suitable subpixel based on the DPR.\n// Zooming can change the DPR, but it seems to report a value that will\n// cleanly divide the values into the appropriate subpixels.\n\nfunction roundOffsetsByDPR(_ref, win) {\n  var x = _ref.x,\n      y = _ref.y;\n  var dpr = win.devicePixelRatio || 1;\n  return {\n    x: round(x * dpr) / dpr || 0,\n    y: round(y * dpr) / dpr || 0\n  };\n}\n\nexport function mapToStyles(_ref2) {\n  var _Object$assign2;\n\n  var popper = _ref2.popper,\n      popperRect = _ref2.popperRect,\n      placement = _ref2.placement,\n      variation = _ref2.variation,\n      offsets = _ref2.offsets,\n      position = _ref2.position,\n      gpuAcceleration = _ref2.gpuAcceleration,\n      adaptive = _ref2.adaptive,\n      roundOffsets = _ref2.roundOffsets,\n      isFixed = _ref2.isFixed;\n  var _offsets$x = offsets.x,\n      x = _offsets$x === void 0 ? 0 : _offsets$x,\n      _offsets$y = offsets.y,\n      y = _offsets$y === void 0 ? 0 : _offsets$y;\n\n  var _ref3 = typeof roundOffsets === 'function' ? roundOffsets({\n    x: x,\n    y: y\n  }) : {\n    x: x,\n    y: y\n  };\n\n  x = _ref3.x;\n  y = _ref3.y;\n  var hasX = offsets.hasOwnProperty('x');\n  var hasY = offsets.hasOwnProperty('y');\n  var sideX = left;\n  var sideY = top;\n  var win = window;\n\n  if (adaptive) {\n    var offsetParent = getOffsetParent(popper);\n    var heightProp = 'clientHeight';\n    var widthProp = 'clientWidth';\n\n    if (offsetParent === getWindow(popper)) {\n      offsetParent = getDocumentElement(popper);\n\n      if (getComputedStyle(offsetParent).position !== 'static' && position === 'absolute') {\n        heightProp = 'scrollHeight';\n        widthProp = 'scrollWidth';\n      }\n    } // $FlowFixMe[incompatible-cast]: force type refinement, we compare offsetParent with window above, but Flow doesn't detect it\n\n\n    offsetParent = offsetParent;\n\n    if (placement === top || (placement === left || placement === right) && variation === end) {\n      sideY = bottom;\n      var offsetY = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.height : // $FlowFixMe[prop-missing]\n      offsetParent[heightProp];\n      y -= offsetY - popperRect.height;\n      y *= gpuAcceleration ? 1 : -1;\n    }\n\n    if (placement === left || (placement === top || placement === bottom) && variation === end) {\n      sideX = right;\n      var offsetX = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.width : // $FlowFixMe[prop-missing]\n      offsetParent[widthProp];\n      x -= offsetX - popperRect.width;\n      x *= gpuAcceleration ? 1 : -1;\n    }\n  }\n\n  var commonStyles = Object.assign({\n    position: position\n  }, adaptive && unsetSides);\n\n  var _ref4 = roundOffsets === true ? roundOffsetsByDPR({\n    x: x,\n    y: y\n  }, getWindow(popper)) : {\n    x: x,\n    y: y\n  };\n\n  x = _ref4.x;\n  y = _ref4.y;\n\n  if (gpuAcceleration) {\n    var _Object$assign;\n\n    return Object.assign({}, commonStyles, (_Object$assign = {}, _Object$assign[sideY] = hasY ? '0' : '', _Object$assign[sideX] = hasX ? '0' : '', _Object$assign.transform = (win.devicePixelRatio || 1) <= 1 ? \"translate(\" + x + \"px, \" + y + \"px)\" : \"translate3d(\" + x + \"px, \" + y + \"px, 0)\", _Object$assign));\n  }\n\n  return Object.assign({}, commonStyles, (_Object$assign2 = {}, _Object$assign2[sideY] = hasY ? y + \"px\" : '', _Object$assign2[sideX] = hasX ? x + \"px\" : '', _Object$assign2.transform = '', _Object$assign2));\n}\n\nfunction computeStyles(_ref5) {\n  var state = _ref5.state,\n      options = _ref5.options;\n  var _options$gpuAccelerat = options.gpuAcceleration,\n      gpuAcceleration = _options$gpuAccelerat === void 0 ? true : _options$gpuAccelerat,\n      _options$adaptive = options.adaptive,\n      adaptive = _options$adaptive === void 0 ? true : _options$adaptive,\n      _options$roundOffsets = options.roundOffsets,\n      roundOffsets = _options$roundOffsets === void 0 ? true : _options$roundOffsets;\n  var commonStyles = {\n    placement: getBasePlacement(state.placement),\n    variation: getVariation(state.placement),\n    popper: state.elements.popper,\n    popperRect: state.rects.popper,\n    gpuAcceleration: gpuAcceleration,\n    isFixed: state.options.strategy === 'fixed'\n  };\n\n  if (state.modifiersData.popperOffsets != null) {\n    state.styles.popper = Object.assign({}, state.styles.popper, mapToStyles(Object.assign({}, commonStyles, {\n      offsets: state.modifiersData.popperOffsets,\n      position: state.options.strategy,\n      adaptive: adaptive,\n      roundOffsets: roundOffsets\n    })));\n  }\n\n  if (state.modifiersData.arrow != null) {\n    state.styles.arrow = Object.assign({}, state.styles.arrow, mapToStyles(Object.assign({}, commonStyles, {\n      offsets: state.modifiersData.arrow,\n      position: 'absolute',\n      adaptive: false,\n      roundOffsets: roundOffsets\n    })));\n  }\n\n  state.attributes.popper = Object.assign({}, state.attributes.popper, {\n    'data-popper-placement': state.placement\n  });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'computeStyles',\n  enabled: true,\n  phase: 'beforeWrite',\n  fn: computeStyles,\n  data: {}\n};","import getWindow from \"../dom-utils/getWindow.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar passive = {\n  passive: true\n};\n\nfunction effect(_ref) {\n  var state = _ref.state,\n      instance = _ref.instance,\n      options = _ref.options;\n  var _options$scroll = options.scroll,\n      scroll = _options$scroll === void 0 ? true : _options$scroll,\n      _options$resize = options.resize,\n      resize = _options$resize === void 0 ? true : _options$resize;\n  var window = getWindow(state.elements.popper);\n  var scrollParents = [].concat(state.scrollParents.reference, state.scrollParents.popper);\n\n  if (scroll) {\n    scrollParents.forEach(function (scrollParent) {\n      scrollParent.addEventListener('scroll', instance.update, passive);\n    });\n  }\n\n  if (resize) {\n    window.addEventListener('resize', instance.update, passive);\n  }\n\n  return function () {\n    if (scroll) {\n      scrollParents.forEach(function (scrollParent) {\n        scrollParent.removeEventListener('scroll', instance.update, passive);\n      });\n    }\n\n    if (resize) {\n      window.removeEventListener('resize', instance.update, passive);\n    }\n  };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'eventListeners',\n  enabled: true,\n  phase: 'write',\n  fn: function fn() {},\n  effect: effect,\n  data: {}\n};","var hash = {\n  left: 'right',\n  right: 'left',\n  bottom: 'top',\n  top: 'bottom'\n};\nexport default function getOppositePlacement(placement) {\n  return placement.replace(/left|right|bottom|top/g, function (matched) {\n    return hash[matched];\n  });\n}","var hash = {\n  start: 'end',\n  end: 'start'\n};\nexport default function getOppositeVariationPlacement(placement) {\n  return placement.replace(/start|end/g, function (matched) {\n    return hash[matched];\n  });\n}","import getWindow from \"./getWindow.js\";\nexport default function getWindowScroll(node) {\n  var win = getWindow(node);\n  var scrollLeft = win.pageXOffset;\n  var scrollTop = win.pageYOffset;\n  return {\n    scrollLeft: scrollLeft,\n    scrollTop: scrollTop\n  };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nexport default function getWindowScrollBarX(element) {\n  // If <html> has a CSS width greater than the viewport, then this will be\n  // incorrect for RTL.\n  // Popper 1 is broken in this case and never had a bug report so let's assume\n  // it's not an issue. I don't think anyone ever specifies width on <html>\n  // anyway.\n  // Browsers where the left scrollbar doesn't cause an issue report `0` for\n  // this (e.g. Edge 2019, IE11, Safari)\n  return getBoundingClientRect(getDocumentElement(element)).left + getWindowScroll(element).scrollLeft;\n}","import getComputedStyle from \"./getComputedStyle.js\";\nexport default function isScrollParent(element) {\n  // Firefox wants us to check `-x` and `-y` variations as well\n  var _getComputedStyle = getComputedStyle(element),\n      overflow = _getComputedStyle.overflow,\n      overflowX = _getComputedStyle.overflowX,\n      overflowY = _getComputedStyle.overflowY;\n\n  return /auto|scroll|overlay|hidden/.test(overflow + overflowY + overflowX);\n}","import getParentNode from \"./getParentNode.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nexport default function getScrollParent(node) {\n  if (['html', 'body', '#document'].indexOf(getNodeName(node)) >= 0) {\n    // $FlowFixMe[incompatible-return]: assume body is always available\n    return node.ownerDocument.body;\n  }\n\n  if (isHTMLElement(node) && isScrollParent(node)) {\n    return node;\n  }\n\n  return getScrollParent(getParentNode(node));\n}","import getScrollParent from \"./getScrollParent.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getWindow from \"./getWindow.js\";\nimport isScrollParent from \"./isScrollParent.js\";\n/*\ngiven a DOM element, return the list of all scroll parents, up the list of ancesors\nuntil we get to the top window object. This list is what we attach scroll listeners\nto, because if any of these parent elements scroll, we'll need to re-calculate the\nreference element's position.\n*/\n\nexport default function listScrollParents(element, list) {\n  var _element$ownerDocumen;\n\n  if (list === void 0) {\n    list = [];\n  }\n\n  var scrollParent = getScrollParent(element);\n  var isBody = scrollParent === ((_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body);\n  var win = getWindow(scrollParent);\n  var target = isBody ? [win].concat(win.visualViewport || [], isScrollParent(scrollParent) ? scrollParent : []) : scrollParent;\n  var updatedList = list.concat(target);\n  return isBody ? updatedList : // $FlowFixMe[incompatible-call]: isBody tells us target will be an HTMLElement here\n  updatedList.concat(listScrollParents(getParentNode(target)));\n}","export default function rectToClientRect(rect) {\n  return Object.assign({}, rect, {\n    left: rect.x,\n    top: rect.y,\n    right: rect.x + rect.width,\n    bottom: rect.y + rect.height\n  });\n}","import { viewport } from \"../enums.js\";\nimport getViewportRect from \"./getViewportRect.js\";\nimport getDocumentRect from \"./getDocumentRect.js\";\nimport listScrollParents from \"./listScrollParents.js\";\nimport getOffsetParent from \"./getOffsetParent.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport contains from \"./contains.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport rectToClientRect from \"../utils/rectToClientRect.js\";\nimport { max, min } from \"../utils/math.js\";\n\nfunction getInnerBoundingClientRect(element, strategy) {\n  var rect = getBoundingClientRect(element, false, strategy === 'fixed');\n  rect.top = rect.top + element.clientTop;\n  rect.left = rect.left + element.clientLeft;\n  rect.bottom = rect.top + element.clientHeight;\n  rect.right = rect.left + element.clientWidth;\n  rect.width = element.clientWidth;\n  rect.height = element.clientHeight;\n  rect.x = rect.left;\n  rect.y = rect.top;\n  return rect;\n}\n\nfunction getClientRectFromMixedType(element, clippingParent, strategy) {\n  return clippingParent === viewport ? rectToClientRect(getViewportRect(element, strategy)) : isElement(clippingParent) ? getInnerBoundingClientRect(clippingParent, strategy) : rectToClientRect(getDocumentRect(getDocumentElement(element)));\n} // A \"clipping parent\" is an overflowable container with the characteristic of\n// clipping (or hiding) overflowing elements with a position different from\n// `initial`\n\n\nfunction getClippingParents(element) {\n  var clippingParents = listScrollParents(getParentNode(element));\n  var canEscapeClipping = ['absolute', 'fixed'].indexOf(getComputedStyle(element).position) >= 0;\n  var clipperElement = canEscapeClipping && isHTMLElement(element) ? getOffsetParent(element) : element;\n\n  if (!isElement(clipperElement)) {\n    return [];\n  } // $FlowFixMe[incompatible-return]: https://github.com/facebook/flow/issues/1414\n\n\n  return clippingParents.filter(function (clippingParent) {\n    return isElement(clippingParent) && contains(clippingParent, clipperElement) && getNodeName(clippingParent) !== 'body';\n  });\n} // Gets the maximum area that the element is visible in due to any number of\n// clipping parents\n\n\nexport default function getClippingRect(element, boundary, rootBoundary, strategy) {\n  var mainClippingParents = boundary === 'clippingParents' ? getClippingParents(element) : [].concat(boundary);\n  var clippingParents = [].concat(mainClippingParents, [rootBoundary]);\n  var firstClippingParent = clippingParents[0];\n  var clippingRect = clippingParents.reduce(function (accRect, clippingParent) {\n    var rect = getClientRectFromMixedType(element, clippingParent, strategy);\n    accRect.top = max(rect.top, accRect.top);\n    accRect.right = min(rect.right, accRect.right);\n    accRect.bottom = min(rect.bottom, accRect.bottom);\n    accRect.left = max(rect.left, accRect.left);\n    return accRect;\n  }, getClientRectFromMixedType(element, firstClippingParent, strategy));\n  clippingRect.width = clippingRect.right - clippingRect.left;\n  clippingRect.height = clippingRect.bottom - clippingRect.top;\n  clippingRect.x = clippingRect.left;\n  clippingRect.y = clippingRect.top;\n  return clippingRect;\n}","import getWindow from \"./getWindow.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getViewportRect(element, strategy) {\n  var win = getWindow(element);\n  var html = getDocumentElement(element);\n  var visualViewport = win.visualViewport;\n  var width = html.clientWidth;\n  var height = html.clientHeight;\n  var x = 0;\n  var y = 0;\n\n  if (visualViewport) {\n    width = visualViewport.width;\n    height = visualViewport.height;\n    var layoutViewport = isLayoutViewport();\n\n    if (layoutViewport || !layoutViewport && strategy === 'fixed') {\n      x = visualViewport.offsetLeft;\n      y = visualViewport.offsetTop;\n    }\n  }\n\n  return {\n    width: width,\n    height: height,\n    x: x + getWindowScrollBarX(element),\n    y: y\n  };\n}","import getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nimport { max } from \"../utils/math.js\"; // Gets the entire size of the scrollable document area, even extending outside\n// of the `<html>` and `<body>` rect bounds if horizontally scrollable\n\nexport default function getDocumentRect(element) {\n  var _element$ownerDocumen;\n\n  var html = getDocumentElement(element);\n  var winScroll = getWindowScroll(element);\n  var body = (_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body;\n  var width = max(html.scrollWidth, html.clientWidth, body ? body.scrollWidth : 0, body ? body.clientWidth : 0);\n  var height = max(html.scrollHeight, html.clientHeight, body ? body.scrollHeight : 0, body ? body.clientHeight : 0);\n  var x = -winScroll.scrollLeft + getWindowScrollBarX(element);\n  var y = -winScroll.scrollTop;\n\n  if (getComputedStyle(body || html).direction === 'rtl') {\n    x += max(html.clientWidth, body ? body.clientWidth : 0) - width;\n  }\n\n  return {\n    width: width,\n    height: height,\n    x: x,\n    y: y\n  };\n}","import getBasePlacement from \"./getBasePlacement.js\";\nimport getVariation from \"./getVariation.js\";\nimport getMainAxisFromPlacement from \"./getMainAxisFromPlacement.js\";\nimport { top, right, bottom, left, start, end } from \"../enums.js\";\nexport default function computeOffsets(_ref) {\n  var reference = _ref.reference,\n      element = _ref.element,\n      placement = _ref.placement;\n  var basePlacement = placement ? getBasePlacement(placement) : null;\n  var variation = placement ? getVariation(placement) : null;\n  var commonX = reference.x + reference.width / 2 - element.width / 2;\n  var commonY = reference.y + reference.height / 2 - element.height / 2;\n  var offsets;\n\n  switch (basePlacement) {\n    case top:\n      offsets = {\n        x: commonX,\n        y: reference.y - element.height\n      };\n      break;\n\n    case bottom:\n      offsets = {\n        x: commonX,\n        y: reference.y + reference.height\n      };\n      break;\n\n    case right:\n      offsets = {\n        x: reference.x + reference.width,\n        y: commonY\n      };\n      break;\n\n    case left:\n      offsets = {\n        x: reference.x - element.width,\n        y: commonY\n      };\n      break;\n\n    default:\n      offsets = {\n        x: reference.x,\n        y: reference.y\n      };\n  }\n\n  var mainAxis = basePlacement ? getMainAxisFromPlacement(basePlacement) : null;\n\n  if (mainAxis != null) {\n    var len = mainAxis === 'y' ? 'height' : 'width';\n\n    switch (variation) {\n      case start:\n        offsets[mainAxis] = offsets[mainAxis] - (reference[len] / 2 - element[len] / 2);\n        break;\n\n      case end:\n        offsets[mainAxis] = offsets[mainAxis] + (reference[len] / 2 - element[len] / 2);\n        break;\n\n      default:\n    }\n  }\n\n  return offsets;\n}","import getClippingRect from \"../dom-utils/getClippingRect.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getBoundingClientRect from \"../dom-utils/getBoundingClientRect.js\";\nimport computeOffsets from \"./computeOffsets.js\";\nimport rectToClientRect from \"./rectToClientRect.js\";\nimport { clippingParents, reference, popper, bottom, top, right, basePlacements, viewport } from \"../enums.js\";\nimport { isElement } from \"../dom-utils/instanceOf.js\";\nimport mergePaddingObject from \"./mergePaddingObject.js\";\nimport expandToHashMap from \"./expandToHashMap.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport default function detectOverflow(state, options) {\n  if (options === void 0) {\n    options = {};\n  }\n\n  var _options = options,\n      _options$placement = _options.placement,\n      placement = _options$placement === void 0 ? state.placement : _options$placement,\n      _options$strategy = _options.strategy,\n      strategy = _options$strategy === void 0 ? state.strategy : _options$strategy,\n      _options$boundary = _options.boundary,\n      boundary = _options$boundary === void 0 ? clippingParents : _options$boundary,\n      _options$rootBoundary = _options.rootBoundary,\n      rootBoundary = _options$rootBoundary === void 0 ? viewport : _options$rootBoundary,\n      _options$elementConte = _options.elementContext,\n      elementContext = _options$elementConte === void 0 ? popper : _options$elementConte,\n      _options$altBoundary = _options.altBoundary,\n      altBoundary = _options$altBoundary === void 0 ? false : _options$altBoundary,\n      _options$padding = _options.padding,\n      padding = _options$padding === void 0 ? 0 : _options$padding;\n  var paddingObject = mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n  var altContext = elementContext === popper ? reference : popper;\n  var popperRect = state.rects.popper;\n  var element = state.elements[altBoundary ? altContext : elementContext];\n  var clippingClientRect = getClippingRect(isElement(element) ? element : element.contextElement || getDocumentElement(state.elements.popper), boundary, rootBoundary, strategy);\n  var referenceClientRect = getBoundingClientRect(state.elements.reference);\n  var popperOffsets = computeOffsets({\n    reference: referenceClientRect,\n    element: popperRect,\n    strategy: 'absolute',\n    placement: placement\n  });\n  var popperClientRect = rectToClientRect(Object.assign({}, popperRect, popperOffsets));\n  var elementClientRect = elementContext === popper ? popperClientRect : referenceClientRect; // positive = overflowing the clipping rect\n  // 0 or negative = within the clipping rect\n\n  var overflowOffsets = {\n    top: clippingClientRect.top - elementClientRect.top + paddingObject.top,\n    bottom: elementClientRect.bottom - clippingClientRect.bottom + paddingObject.bottom,\n    left: clippingClientRect.left - elementClientRect.left + paddingObject.left,\n    right: elementClientRect.right - clippingClientRect.right + paddingObject.right\n  };\n  var offsetData = state.modifiersData.offset; // Offsets can be applied only to the popper element\n\n  if (elementContext === popper && offsetData) {\n    var offset = offsetData[placement];\n    Object.keys(overflowOffsets).forEach(function (key) {\n      var multiply = [right, bottom].indexOf(key) >= 0 ? 1 : -1;\n      var axis = [top, bottom].indexOf(key) >= 0 ? 'y' : 'x';\n      overflowOffsets[key] += offset[axis] * multiply;\n    });\n  }\n\n  return overflowOffsets;\n}","import getVariation from \"./getVariation.js\";\nimport { variationPlacements, basePlacements, placements as allPlacements } from \"../enums.js\";\nimport detectOverflow from \"./detectOverflow.js\";\nimport getBasePlacement from \"./getBasePlacement.js\";\nexport default function computeAutoPlacement(state, options) {\n  if (options === void 0) {\n    options = {};\n  }\n\n  var _options = options,\n      placement = _options.placement,\n      boundary = _options.boundary,\n      rootBoundary = _options.rootBoundary,\n      padding = _options.padding,\n      flipVariations = _options.flipVariations,\n      _options$allowedAutoP = _options.allowedAutoPlacements,\n      allowedAutoPlacements = _options$allowedAutoP === void 0 ? allPlacements : _options$allowedAutoP;\n  var variation = getVariation(placement);\n  var placements = variation ? flipVariations ? variationPlacements : variationPlacements.filter(function (placement) {\n    return getVariation(placement) === variation;\n  }) : basePlacements;\n  var allowedPlacements = placements.filter(function (placement) {\n    return allowedAutoPlacements.indexOf(placement) >= 0;\n  });\n\n  if (allowedPlacements.length === 0) {\n    allowedPlacements = placements;\n  } // $FlowFixMe[incompatible-type]: Flow seems to have problems with two array unions...\n\n\n  var overflows = allowedPlacements.reduce(function (acc, placement) {\n    acc[placement] = detectOverflow(state, {\n      placement: placement,\n      boundary: boundary,\n      rootBoundary: rootBoundary,\n      padding: padding\n    })[getBasePlacement(placement)];\n    return acc;\n  }, {});\n  return Object.keys(overflows).sort(function (a, b) {\n    return overflows[a] - overflows[b];\n  });\n}","import getOppositePlacement from \"../utils/getOppositePlacement.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getOppositeVariationPlacement from \"../utils/getOppositeVariationPlacement.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport computeAutoPlacement from \"../utils/computeAutoPlacement.js\";\nimport { bottom, top, start, right, left, auto } from \"../enums.js\";\nimport getVariation from \"../utils/getVariation.js\"; // eslint-disable-next-line import/no-unused-modules\n\nfunction getExpandedFallbackPlacements(placement) {\n  if (getBasePlacement(placement) === auto) {\n    return [];\n  }\n\n  var oppositePlacement = getOppositePlacement(placement);\n  return [getOppositeVariationPlacement(placement), oppositePlacement, getOppositeVariationPlacement(oppositePlacement)];\n}\n\nfunction flip(_ref) {\n  var state = _ref.state,\n      options = _ref.options,\n      name = _ref.name;\n\n  if (state.modifiersData[name]._skip) {\n    return;\n  }\n\n  var _options$mainAxis = options.mainAxis,\n      checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n      _options$altAxis = options.altAxis,\n      checkAltAxis = _options$altAxis === void 0 ? true : _options$altAxis,\n      specifiedFallbackPlacements = options.fallbackPlacements,\n      padding = options.padding,\n      boundary = options.boundary,\n      rootBoundary = options.rootBoundary,\n      altBoundary = options.altBoundary,\n      _options$flipVariatio = options.flipVariations,\n      flipVariations = _options$flipVariatio === void 0 ? true : _options$flipVariatio,\n      allowedAutoPlacements = options.allowedAutoPlacements;\n  var preferredPlacement = state.options.placement;\n  var basePlacement = getBasePlacement(preferredPlacement);\n  var isBasePlacement = basePlacement === preferredPlacement;\n  var fallbackPlacements = specifiedFallbackPlacements || (isBasePlacement || !flipVariations ? [getOppositePlacement(preferredPlacement)] : getExpandedFallbackPlacements(preferredPlacement));\n  var placements = [preferredPlacement].concat(fallbackPlacements).reduce(function (acc, placement) {\n    return acc.concat(getBasePlacement(placement) === auto ? computeAutoPlacement(state, {\n      placement: placement,\n      boundary: boundary,\n      rootBoundary: rootBoundary,\n      padding: padding,\n      flipVariations: flipVariations,\n      allowedAutoPlacements: allowedAutoPlacements\n    }) : placement);\n  }, []);\n  var referenceRect = state.rects.reference;\n  var popperRect = state.rects.popper;\n  var checksMap = new Map();\n  var makeFallbackChecks = true;\n  var firstFittingPlacement = placements[0];\n\n  for (var i = 0; i < placements.length; i++) {\n    var placement = placements[i];\n\n    var _basePlacement = getBasePlacement(placement);\n\n    var isStartVariation = getVariation(placement) === start;\n    var isVertical = [top, bottom].indexOf(_basePlacement) >= 0;\n    var len = isVertical ? 'width' : 'height';\n    var overflow = detectOverflow(state, {\n      placement: placement,\n      boundary: boundary,\n      rootBoundary: rootBoundary,\n      altBoundary: altBoundary,\n      padding: padding\n    });\n    var mainVariationSide = isVertical ? isStartVariation ? right : left : isStartVariation ? bottom : top;\n\n    if (referenceRect[len] > popperRect[len]) {\n      mainVariationSide = getOppositePlacement(mainVariationSide);\n    }\n\n    var altVariationSide = getOppositePlacement(mainVariationSide);\n    var checks = [];\n\n    if (checkMainAxis) {\n      checks.push(overflow[_basePlacement] <= 0);\n    }\n\n    if (checkAltAxis) {\n      checks.push(overflow[mainVariationSide] <= 0, overflow[altVariationSide] <= 0);\n    }\n\n    if (checks.every(function (check) {\n      return check;\n    })) {\n      firstFittingPlacement = placement;\n      makeFallbackChecks = false;\n      break;\n    }\n\n    checksMap.set(placement, checks);\n  }\n\n  if (makeFallbackChecks) {\n    // `2` may be desired in some cases – research later\n    var numberOfChecks = flipVariations ? 3 : 1;\n\n    var _loop = function _loop(_i) {\n      var fittingPlacement = placements.find(function (placement) {\n        var checks = checksMap.get(placement);\n\n        if (checks) {\n          return checks.slice(0, _i).every(function (check) {\n            return check;\n          });\n        }\n      });\n\n      if (fittingPlacement) {\n        firstFittingPlacement = fittingPlacement;\n        return \"break\";\n      }\n    };\n\n    for (var _i = numberOfChecks; _i > 0; _i--) {\n      var _ret = _loop(_i);\n\n      if (_ret === \"break\") break;\n    }\n  }\n\n  if (state.placement !== firstFittingPlacement) {\n    state.modifiersData[name]._skip = true;\n    state.placement = firstFittingPlacement;\n    state.reset = true;\n  }\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'flip',\n  enabled: true,\n  phase: 'main',\n  fn: flip,\n  requiresIfExists: ['offset'],\n  data: {\n    _skip: false\n  }\n};","import { top, bottom, left, right } from \"../enums.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\n\nfunction getSideOffsets(overflow, rect, preventedOffsets) {\n  if (preventedOffsets === void 0) {\n    preventedOffsets = {\n      x: 0,\n      y: 0\n    };\n  }\n\n  return {\n    top: overflow.top - rect.height - preventedOffsets.y,\n    right: overflow.right - rect.width + preventedOffsets.x,\n    bottom: overflow.bottom - rect.height + preventedOffsets.y,\n    left: overflow.left - rect.width - preventedOffsets.x\n  };\n}\n\nfunction isAnySideFullyClipped(overflow) {\n  return [top, right, bottom, left].some(function (side) {\n    return overflow[side] >= 0;\n  });\n}\n\nfunction hide(_ref) {\n  var state = _ref.state,\n      name = _ref.name;\n  var referenceRect = state.rects.reference;\n  var popperRect = state.rects.popper;\n  var preventedOffsets = state.modifiersData.preventOverflow;\n  var referenceOverflow = detectOverflow(state, {\n    elementContext: 'reference'\n  });\n  var popperAltOverflow = detectOverflow(state, {\n    altBoundary: true\n  });\n  var referenceClippingOffsets = getSideOffsets(referenceOverflow, referenceRect);\n  var popperEscapeOffsets = getSideOffsets(popperAltOverflow, popperRect, preventedOffsets);\n  var isReferenceHidden = isAnySideFullyClipped(referenceClippingOffsets);\n  var hasPopperEscaped = isAnySideFullyClipped(popperEscapeOffsets);\n  state.modifiersData[name] = {\n    referenceClippingOffsets: referenceClippingOffsets,\n    popperEscapeOffsets: popperEscapeOffsets,\n    isReferenceHidden: isReferenceHidden,\n    hasPopperEscaped: hasPopperEscaped\n  };\n  state.attributes.popper = Object.assign({}, state.attributes.popper, {\n    'data-popper-reference-hidden': isReferenceHidden,\n    'data-popper-escaped': hasPopperEscaped\n  });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'hide',\n  enabled: true,\n  phase: 'main',\n  requiresIfExists: ['preventOverflow'],\n  fn: hide\n};","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport { top, left, right, placements } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport function distanceAndSkiddingToXY(placement, rects, offset) {\n  var basePlacement = getBasePlacement(placement);\n  var invertDistance = [left, top].indexOf(basePlacement) >= 0 ? -1 : 1;\n\n  var _ref = typeof offset === 'function' ? offset(Object.assign({}, rects, {\n    placement: placement\n  })) : offset,\n      skidding = _ref[0],\n      distance = _ref[1];\n\n  skidding = skidding || 0;\n  distance = (distance || 0) * invertDistance;\n  return [left, right].indexOf(basePlacement) >= 0 ? {\n    x: distance,\n    y: skidding\n  } : {\n    x: skidding,\n    y: distance\n  };\n}\n\nfunction offset(_ref2) {\n  var state = _ref2.state,\n      options = _ref2.options,\n      name = _ref2.name;\n  var _options$offset = options.offset,\n      offset = _options$offset === void 0 ? [0, 0] : _options$offset;\n  var data = placements.reduce(function (acc, placement) {\n    acc[placement] = distanceAndSkiddingToXY(placement, state.rects, offset);\n    return acc;\n  }, {});\n  var _data$state$placement = data[state.placement],\n      x = _data$state$placement.x,\n      y = _data$state$placement.y;\n\n  if (state.modifiersData.popperOffsets != null) {\n    state.modifiersData.popperOffsets.x += x;\n    state.modifiersData.popperOffsets.y += y;\n  }\n\n  state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'offset',\n  enabled: true,\n  phase: 'main',\n  requires: ['popperOffsets'],\n  fn: offset\n};","import computeOffsets from \"../utils/computeOffsets.js\";\n\nfunction popperOffsets(_ref) {\n  var state = _ref.state,\n      name = _ref.name;\n  // Offsets are the actual position the popper needs to have to be\n  // properly positioned near its reference element\n  // This is the most basic placement, and will be adjusted by\n  // the modifiers in the next step\n  state.modifiersData[name] = computeOffsets({\n    reference: state.rects.reference,\n    element: state.rects.popper,\n    strategy: 'absolute',\n    placement: state.placement\n  });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'popperOffsets',\n  enabled: true,\n  phase: 'read',\n  fn: popperOffsets,\n  data: {}\n};","import { top, left, right, bottom, start } from \"../enums.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport getAltAxis from \"../utils/getAltAxis.js\";\nimport { within, withinMaxClamp } from \"../utils/within.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport getFreshSideObject from \"../utils/getFreshSideObject.js\";\nimport { min as mathMin, max as mathMax } from \"../utils/math.js\";\n\nfunction preventOverflow(_ref) {\n  var state = _ref.state,\n      options = _ref.options,\n      name = _ref.name;\n  var _options$mainAxis = options.mainAxis,\n      checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n      _options$altAxis = options.altAxis,\n      checkAltAxis = _options$altAxis === void 0 ? false : _options$altAxis,\n      boundary = options.boundary,\n      rootBoundary = options.rootBoundary,\n      altBoundary = options.altBoundary,\n      padding = options.padding,\n      _options$tether = options.tether,\n      tether = _options$tether === void 0 ? true : _options$tether,\n      _options$tetherOffset = options.tetherOffset,\n      tetherOffset = _options$tetherOffset === void 0 ? 0 : _options$tetherOffset;\n  var overflow = detectOverflow(state, {\n    boundary: boundary,\n    rootBoundary: rootBoundary,\n    padding: padding,\n    altBoundary: altBoundary\n  });\n  var basePlacement = getBasePlacement(state.placement);\n  var variation = getVariation(state.placement);\n  var isBasePlacement = !variation;\n  var mainAxis = getMainAxisFromPlacement(basePlacement);\n  var altAxis = getAltAxis(mainAxis);\n  var popperOffsets = state.modifiersData.popperOffsets;\n  var referenceRect = state.rects.reference;\n  var popperRect = state.rects.popper;\n  var tetherOffsetValue = typeof tetherOffset === 'function' ? tetherOffset(Object.assign({}, state.rects, {\n    placement: state.placement\n  })) : tetherOffset;\n  var normalizedTetherOffsetValue = typeof tetherOffsetValue === 'number' ? {\n    mainAxis: tetherOffsetValue,\n    altAxis: tetherOffsetValue\n  } : Object.assign({\n    mainAxis: 0,\n    altAxis: 0\n  }, tetherOffsetValue);\n  var offsetModifierState = state.modifiersData.offset ? state.modifiersData.offset[state.placement] : null;\n  var data = {\n    x: 0,\n    y: 0\n  };\n\n  if (!popperOffsets) {\n    return;\n  }\n\n  if (checkMainAxis) {\n    var _offsetModifierState$;\n\n    var mainSide = mainAxis === 'y' ? top : left;\n    var altSide = mainAxis === 'y' ? bottom : right;\n    var len = mainAxis === 'y' ? 'height' : 'width';\n    var offset = popperOffsets[mainAxis];\n    var min = offset + overflow[mainSide];\n    var max = offset - overflow[altSide];\n    var additive = tether ? -popperRect[len] / 2 : 0;\n    var minLen = variation === start ? referenceRect[len] : popperRect[len];\n    var maxLen = variation === start ? -popperRect[len] : -referenceRect[len]; // We need to include the arrow in the calculation so the arrow doesn't go\n    // outside the reference bounds\n\n    var arrowElement = state.elements.arrow;\n    var arrowRect = tether && arrowElement ? getLayoutRect(arrowElement) : {\n      width: 0,\n      height: 0\n    };\n    var arrowPaddingObject = state.modifiersData['arrow#persistent'] ? state.modifiersData['arrow#persistent'].padding : getFreshSideObject();\n    var arrowPaddingMin = arrowPaddingObject[mainSide];\n    var arrowPaddingMax = arrowPaddingObject[altSide]; // If the reference length is smaller than the arrow length, we don't want\n    // to include its full size in the calculation. If the reference is small\n    // and near the edge of a boundary, the popper can overflow even if the\n    // reference is not overflowing as well (e.g. virtual elements with no\n    // width or height)\n\n    var arrowLen = within(0, referenceRect[len], arrowRect[len]);\n    var minOffset = isBasePlacement ? referenceRect[len] / 2 - additive - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis : minLen - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis;\n    var maxOffset = isBasePlacement ? -referenceRect[len] / 2 + additive + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis : maxLen + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis;\n    var arrowOffsetParent = state.elements.arrow && getOffsetParent(state.elements.arrow);\n    var clientOffset = arrowOffsetParent ? mainAxis === 'y' ? arrowOffsetParent.clientTop || 0 : arrowOffsetParent.clientLeft || 0 : 0;\n    var offsetModifierValue = (_offsetModifierState$ = offsetModifierState == null ? void 0 : offsetModifierState[mainAxis]) != null ? _offsetModifierState$ : 0;\n    var tetherMin = offset + minOffset - offsetModifierValue - clientOffset;\n    var tetherMax = offset + maxOffset - offsetModifierValue;\n    var preventedOffset = within(tether ? mathMin(min, tetherMin) : min, offset, tether ? mathMax(max, tetherMax) : max);\n    popperOffsets[mainAxis] = preventedOffset;\n    data[mainAxis] = preventedOffset - offset;\n  }\n\n  if (checkAltAxis) {\n    var _offsetModifierState$2;\n\n    var _mainSide = mainAxis === 'x' ? top : left;\n\n    var _altSide = mainAxis === 'x' ? bottom : right;\n\n    var _offset = popperOffsets[altAxis];\n\n    var _len = altAxis === 'y' ? 'height' : 'width';\n\n    var _min = _offset + overflow[_mainSide];\n\n    var _max = _offset - overflow[_altSide];\n\n    var isOriginSide = [top, left].indexOf(basePlacement) !== -1;\n\n    var _offsetModifierValue = (_offsetModifierState$2 = offsetModifierState == null ? void 0 : offsetModifierState[altAxis]) != null ? _offsetModifierState$2 : 0;\n\n    var _tetherMin = isOriginSide ? _min : _offset - referenceRect[_len] - popperRect[_len] - _offsetModifierValue + normalizedTetherOffsetValue.altAxis;\n\n    var _tetherMax = isOriginSide ? _offset + referenceRect[_len] + popperRect[_len] - _offsetModifierValue - normalizedTetherOffsetValue.altAxis : _max;\n\n    var _preventedOffset = tether && isOriginSide ? withinMaxClamp(_tetherMin, _offset, _tetherMax) : within(tether ? _tetherMin : _min, _offset, tether ? _tetherMax : _max);\n\n    popperOffsets[altAxis] = _preventedOffset;\n    data[altAxis] = _preventedOffset - _offset;\n  }\n\n  state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'preventOverflow',\n  enabled: true,\n  phase: 'main',\n  fn: preventOverflow,\n  requiresIfExists: ['offset']\n};","export default function getAltAxis(axis) {\n  return axis === 'x' ? 'y' : 'x';\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getNodeScroll from \"./getNodeScroll.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport { round } from \"../utils/math.js\";\n\nfunction isElementScaled(element) {\n  var rect = element.getBoundingClientRect();\n  var scaleX = round(rect.width) / element.offsetWidth || 1;\n  var scaleY = round(rect.height) / element.offsetHeight || 1;\n  return scaleX !== 1 || scaleY !== 1;\n} // Returns the composite rect of an element relative to its offsetParent.\n// Composite means it takes into account transforms as well as layout.\n\n\nexport default function getCompositeRect(elementOrVirtualElement, offsetParent, isFixed) {\n  if (isFixed === void 0) {\n    isFixed = false;\n  }\n\n  var isOffsetParentAnElement = isHTMLElement(offsetParent);\n  var offsetParentIsScaled = isHTMLElement(offsetParent) && isElementScaled(offsetParent);\n  var documentElement = getDocumentElement(offsetParent);\n  var rect = getBoundingClientRect(elementOrVirtualElement, offsetParentIsScaled, isFixed);\n  var scroll = {\n    scrollLeft: 0,\n    scrollTop: 0\n  };\n  var offsets = {\n    x: 0,\n    y: 0\n  };\n\n  if (isOffsetParentAnElement || !isOffsetParentAnElement && !isFixed) {\n    if (getNodeName(offsetParent) !== 'body' || // https://github.com/popperjs/popper-core/issues/1078\n    isScrollParent(documentElement)) {\n      scroll = getNodeScroll(offsetParent);\n    }\n\n    if (isHTMLElement(offsetParent)) {\n      offsets = getBoundingClientRect(offsetParent, true);\n      offsets.x += offsetParent.clientLeft;\n      offsets.y += offsetParent.clientTop;\n    } else if (documentElement) {\n      offsets.x = getWindowScrollBarX(documentElement);\n    }\n  }\n\n  return {\n    x: rect.left + scroll.scrollLeft - offsets.x,\n    y: rect.top + scroll.scrollTop - offsets.y,\n    width: rect.width,\n    height: rect.height\n  };\n}","import getWindowScroll from \"./getWindowScroll.js\";\nimport getWindow from \"./getWindow.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getHTMLElementScroll from \"./getHTMLElementScroll.js\";\nexport default function getNodeScroll(node) {\n  if (node === getWindow(node) || !isHTMLElement(node)) {\n    return getWindowScroll(node);\n  } else {\n    return getHTMLElementScroll(node);\n  }\n}","export default function getHTMLElementScroll(element) {\n  return {\n    scrollLeft: element.scrollLeft,\n    scrollTop: element.scrollTop\n  };\n}","import { modifierPhases } from \"../enums.js\"; // source: https://stackoverflow.com/questions/49875255\n\nfunction order(modifiers) {\n  var map = new Map();\n  var visited = new Set();\n  var result = [];\n  modifiers.forEach(function (modifier) {\n    map.set(modifier.name, modifier);\n  }); // On visiting object, check for its dependencies and visit them recursively\n\n  function sort(modifier) {\n    visited.add(modifier.name);\n    var requires = [].concat(modifier.requires || [], modifier.requiresIfExists || []);\n    requires.forEach(function (dep) {\n      if (!visited.has(dep)) {\n        var depModifier = map.get(dep);\n\n        if (depModifier) {\n          sort(depModifier);\n        }\n      }\n    });\n    result.push(modifier);\n  }\n\n  modifiers.forEach(function (modifier) {\n    if (!visited.has(modifier.name)) {\n      // check for visited object\n      sort(modifier);\n    }\n  });\n  return result;\n}\n\nexport default function orderModifiers(modifiers) {\n  // order based on dependencies\n  var orderedModifiers = order(modifiers); // order based on phase\n\n  return modifierPhases.reduce(function (acc, phase) {\n    return acc.concat(orderedModifiers.filter(function (modifier) {\n      return modifier.phase === phase;\n    }));\n  }, []);\n}","import getCompositeRect from \"./dom-utils/getCompositeRect.js\";\nimport getLayoutRect from \"./dom-utils/getLayoutRect.js\";\nimport listScrollParents from \"./dom-utils/listScrollParents.js\";\nimport getOffsetParent from \"./dom-utils/getOffsetParent.js\";\nimport orderModifiers from \"./utils/orderModifiers.js\";\nimport debounce from \"./utils/debounce.js\";\nimport mergeByName from \"./utils/mergeByName.js\";\nimport detectOverflow from \"./utils/detectOverflow.js\";\nimport { isElement } from \"./dom-utils/instanceOf.js\";\nvar DEFAULT_OPTIONS = {\n  placement: 'bottom',\n  modifiers: [],\n  strategy: 'absolute'\n};\n\nfunction areValidElements() {\n  for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {\n    args[_key] = arguments[_key];\n  }\n\n  return !args.some(function (element) {\n    return !(element && typeof element.getBoundingClientRect === 'function');\n  });\n}\n\nexport function popperGenerator(generatorOptions) {\n  if (generatorOptions === void 0) {\n    generatorOptions = {};\n  }\n\n  var _generatorOptions = generatorOptions,\n      _generatorOptions$def = _generatorOptions.defaultModifiers,\n      defaultModifiers = _generatorOptions$def === void 0 ? [] : _generatorOptions$def,\n      _generatorOptions$def2 = _generatorOptions.defaultOptions,\n      defaultOptions = _generatorOptions$def2 === void 0 ? DEFAULT_OPTIONS : _generatorOptions$def2;\n  return function createPopper(reference, popper, options) {\n    if (options === void 0) {\n      options = defaultOptions;\n    }\n\n    var state = {\n      placement: 'bottom',\n      orderedModifiers: [],\n      options: Object.assign({}, DEFAULT_OPTIONS, defaultOptions),\n      modifiersData: {},\n      elements: {\n        reference: reference,\n        popper: popper\n      },\n      attributes: {},\n      styles: {}\n    };\n    var effectCleanupFns = [];\n    var isDestroyed = false;\n    var instance = {\n      state: state,\n      setOptions: function setOptions(setOptionsAction) {\n        var options = typeof setOptionsAction === 'function' ? setOptionsAction(state.options) : setOptionsAction;\n        cleanupModifierEffects();\n        state.options = Object.assign({}, defaultOptions, state.options, options);\n        state.scrollParents = {\n          reference: isElement(reference) ? listScrollParents(reference) : reference.contextElement ? listScrollParents(reference.contextElement) : [],\n          popper: listScrollParents(popper)\n        }; // Orders the modifiers based on their dependencies and `phase`\n        // properties\n\n        var orderedModifiers = orderModifiers(mergeByName([].concat(defaultModifiers, state.options.modifiers))); // Strip out disabled modifiers\n\n        state.orderedModifiers = orderedModifiers.filter(function (m) {\n          return m.enabled;\n        });\n        runModifierEffects();\n        return instance.update();\n      },\n      // Sync update – it will always be executed, even if not necessary. This\n      // is useful for low frequency updates where sync behavior simplifies the\n      // logic.\n      // For high frequency updates (e.g. `resize` and `scroll` events), always\n      // prefer the async Popper#update method\n      forceUpdate: function forceUpdate() {\n        if (isDestroyed) {\n          return;\n        }\n\n        var _state$elements = state.elements,\n            reference = _state$elements.reference,\n            popper = _state$elements.popper; // Don't proceed if `reference` or `popper` are not valid elements\n        // anymore\n\n        if (!areValidElements(reference, popper)) {\n          return;\n        } // Store the reference and popper rects to be read by modifiers\n\n\n        state.rects = {\n          reference: getCompositeRect(reference, getOffsetParent(popper), state.options.strategy === 'fixed'),\n          popper: getLayoutRect(popper)\n        }; // Modifiers have the ability to reset the current update cycle. The\n        // most common use case for this is the `flip` modifier changing the\n        // placement, which then needs to re-run all the modifiers, because the\n        // logic was previously ran for the previous placement and is therefore\n        // stale/incorrect\n\n        state.reset = false;\n        state.placement = state.options.placement; // On each update cycle, the `modifiersData` property for each modifier\n        // is filled with the initial data specified by the modifier. This means\n        // it doesn't persist and is fresh on each update.\n        // To ensure persistent data, use `${name}#persistent`\n\n        state.orderedModifiers.forEach(function (modifier) {\n          return state.modifiersData[modifier.name] = Object.assign({}, modifier.data);\n        });\n\n        for (var index = 0; index < state.orderedModifiers.length; index++) {\n          if (state.reset === true) {\n            state.reset = false;\n            index = -1;\n            continue;\n          }\n\n          var _state$orderedModifie = state.orderedModifiers[index],\n              fn = _state$orderedModifie.fn,\n              _state$orderedModifie2 = _state$orderedModifie.options,\n              _options = _state$orderedModifie2 === void 0 ? {} : _state$orderedModifie2,\n              name = _state$orderedModifie.name;\n\n          if (typeof fn === 'function') {\n            state = fn({\n              state: state,\n              options: _options,\n              name: name,\n              instance: instance\n            }) || state;\n          }\n        }\n      },\n      // Async and optimistically optimized update – it will not be executed if\n      // not necessary (debounced to run at most once-per-tick)\n      update: debounce(function () {\n        return new Promise(function (resolve) {\n          instance.forceUpdate();\n          resolve(state);\n        });\n      }),\n      destroy: function destroy() {\n        cleanupModifierEffects();\n        isDestroyed = true;\n      }\n    };\n\n    if (!areValidElements(reference, popper)) {\n      return instance;\n    }\n\n    instance.setOptions(options).then(function (state) {\n      if (!isDestroyed && options.onFirstUpdate) {\n        options.onFirstUpdate(state);\n      }\n    }); // Modifiers have the ability to execute arbitrary code before the first\n    // update cycle runs. They will be executed in the same order as the update\n    // cycle. This is useful when a modifier adds some persistent data that\n    // other modifiers need to use, but the modifier is run after the dependent\n    // one.\n\n    function runModifierEffects() {\n      state.orderedModifiers.forEach(function (_ref) {\n        var name = _ref.name,\n            _ref$options = _ref.options,\n            options = _ref$options === void 0 ? {} : _ref$options,\n            effect = _ref.effect;\n\n        if (typeof effect === 'function') {\n          var cleanupFn = effect({\n            state: state,\n            name: name,\n            instance: instance,\n            options: options\n          });\n\n          var noopFn = function noopFn() {};\n\n          effectCleanupFns.push(cleanupFn || noopFn);\n        }\n      });\n    }\n\n    function cleanupModifierEffects() {\n      effectCleanupFns.forEach(function (fn) {\n        return fn();\n      });\n      effectCleanupFns = [];\n    }\n\n    return instance;\n  };\n}\nexport var createPopper = /*#__PURE__*/popperGenerator(); // eslint-disable-next-line import/no-unused-modules\n\nexport { detectOverflow };","export default function debounce(fn) {\n  var pending;\n  return function () {\n    if (!pending) {\n      pending = new Promise(function (resolve) {\n        Promise.resolve().then(function () {\n          pending = undefined;\n          resolve(fn());\n        });\n      });\n    }\n\n    return pending;\n  };\n}","export default function mergeByName(modifiers) {\n  var merged = modifiers.reduce(function (merged, current) {\n    var existing = merged[current.name];\n    merged[current.name] = existing ? Object.assign({}, existing, current, {\n      options: Object.assign({}, existing.options, current.options),\n      data: Object.assign({}, existing.data, current.data)\n    }) : current;\n    return merged;\n  }, {}); // IE11 does not support Object.values\n\n  return Object.keys(merged).map(function (key) {\n    return merged[key];\n  });\n}","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles];\nvar createPopper = /*#__PURE__*/popperGenerator({\n  defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow };","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nimport offset from \"./modifiers/offset.js\";\nimport flip from \"./modifiers/flip.js\";\nimport preventOverflow from \"./modifiers/preventOverflow.js\";\nimport arrow from \"./modifiers/arrow.js\";\nimport hide from \"./modifiers/hide.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles, offset, flip, preventOverflow, arrow, hide];\nvar createPopper = /*#__PURE__*/popperGenerator({\n  defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow }; // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper as createPopperLite } from \"./popper-lite.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport * from \"./modifiers/index.js\";","/**\n * --------------------------------------------------------------------------\n * Bootstrap dropdown.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport * as Popper from '@popperjs/core'\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n  defineJQueryPlugin,\n  execute,\n  getElement,\n  getNextActiveElement,\n  isDisabled,\n  isElement,\n  isRTL,\n  isVisible,\n  noop\n} from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'dropdown'\nconst DATA_KEY = 'bs.dropdown'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst ESCAPE_KEY = 'Escape'\nconst TAB_KEY = 'Tab'\nconst ARROW_UP_KEY = 'ArrowUp'\nconst ARROW_DOWN_KEY = 'ArrowDown'\nconst RIGHT_MOUSE_BUTTON = 2 // MouseEvent.button value for the secondary button, usually the right button\n\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYDOWN_DATA_API = `keydown${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYUP_DATA_API = `keyup${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_DROPUP = 'dropup'\nconst CLASS_NAME_DROPEND = 'dropend'\nconst CLASS_NAME_DROPSTART = 'dropstart'\nconst CLASS_NAME_DROPUP_CENTER = 'dropup-center'\nconst CLASS_NAME_DROPDOWN_CENTER = 'dropdown-center'\n\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"dropdown\"]:not(.disabled):not(:disabled)'\nconst SELECTOR_DATA_TOGGLE_SHOWN = `${SELECTOR_DATA_TOGGLE}.${CLASS_NAME_SHOW}`\nconst SELECTOR_MENU = '.dropdown-menu'\nconst SELECTOR_NAVBAR = '.navbar'\nconst SELECTOR_NAVBAR_NAV = '.navbar-nav'\nconst SELECTOR_VISIBLE_ITEMS = '.dropdown-menu .dropdown-item:not(.disabled):not(:disabled)'\n\nconst PLACEMENT_TOP = isRTL() ? 'top-end' : 'top-start'\nconst PLACEMENT_TOPEND = isRTL() ? 'top-start' : 'top-end'\nconst PLACEMENT_BOTTOM = isRTL() ? 'bottom-end' : 'bottom-start'\nconst PLACEMENT_BOTTOMEND = isRTL() ? 'bottom-start' : 'bottom-end'\nconst PLACEMENT_RIGHT = isRTL() ? 'left-start' : 'right-start'\nconst PLACEMENT_LEFT = isRTL() ? 'right-start' : 'left-start'\nconst PLACEMENT_TOPCENTER = 'top'\nconst PLACEMENT_BOTTOMCENTER = 'bottom'\n\nconst Default = {\n  autoClose: true,\n  boundary: 'clippingParents',\n  display: 'dynamic',\n  offset: [0, 2],\n  popperConfig: null,\n  reference: 'toggle'\n}\n\nconst DefaultType = {\n  autoClose: '(boolean|string)',\n  boundary: '(string|element)',\n  display: 'string',\n  offset: '(array|string|function)',\n  popperConfig: '(null|object|function)',\n  reference: '(string|element|object)'\n}\n\n/**\n * Class definition\n */\n\nclass Dropdown extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._popper = null\n    this._parent = this._element.parentNode // dropdown wrapper\n    // TODO: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.3/forms/input-group/\n    this._menu = SelectorEngine.next(this._element, SELECTOR_MENU)[0] ||\n      SelectorEngine.prev(this._element, SELECTOR_MENU)[0] ||\n      SelectorEngine.findOne(SELECTOR_MENU, this._parent)\n    this._inNavbar = this._detectNavbar()\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle() {\n    return this._isShown() ? this.hide() : this.show()\n  }\n\n  show() {\n    if (isDisabled(this._element) || this._isShown()) {\n      return\n    }\n\n    const relatedTarget = {\n      relatedTarget: this._element\n    }\n\n    const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, relatedTarget)\n\n    if (showEvent.defaultPrevented) {\n      return\n    }\n\n    this._createPopper()\n\n    // If this is a touch-enabled device we add extra\n    // empty mouseover listeners to the body's immediate children;\n    // only needed because of broken event delegation on iOS\n    // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n    if ('ontouchstart' in document.documentElement && !this._parent.closest(SELECTOR_NAVBAR_NAV)) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.on(element, 'mouseover', noop)\n      }\n    }\n\n    this._element.focus()\n    this._element.setAttribute('aria-expanded', true)\n\n    this._menu.classList.add(CLASS_NAME_SHOW)\n    this._element.classList.add(CLASS_NAME_SHOW)\n    EventHandler.trigger(this._element, EVENT_SHOWN, relatedTarget)\n  }\n\n  hide() {\n    if (isDisabled(this._element) || !this._isShown()) {\n      return\n    }\n\n    const relatedTarget = {\n      relatedTarget: this._element\n    }\n\n    this._completeHide(relatedTarget)\n  }\n\n  dispose() {\n    if (this._popper) {\n      this._popper.destroy()\n    }\n\n    super.dispose()\n  }\n\n  update() {\n    this._inNavbar = this._detectNavbar()\n    if (this._popper) {\n      this._popper.update()\n    }\n  }\n\n  // Private\n  _completeHide(relatedTarget) {\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE, relatedTarget)\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    // If this is a touch-enabled device we remove the extra\n    // empty mouseover listeners we added for iOS support\n    if ('ontouchstart' in document.documentElement) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.off(element, 'mouseover', noop)\n      }\n    }\n\n    if (this._popper) {\n      this._popper.destroy()\n    }\n\n    this._menu.classList.remove(CLASS_NAME_SHOW)\n    this._element.classList.remove(CLASS_NAME_SHOW)\n    this._element.setAttribute('aria-expanded', 'false')\n    Manipulator.removeDataAttribute(this._menu, 'popper')\n    EventHandler.trigger(this._element, EVENT_HIDDEN, relatedTarget)\n  }\n\n  _getConfig(config) {\n    config = super._getConfig(config)\n\n    if (typeof config.reference === 'object' && !isElement(config.reference) &&\n      typeof config.reference.getBoundingClientRect !== 'function'\n    ) {\n      // Popper virtual elements require a getBoundingClientRect method\n      throw new TypeError(`${NAME.toUpperCase()}: Option \"reference\" provided type \"object\" without a required \"getBoundingClientRect\" method.`)\n    }\n\n    return config\n  }\n\n  _createPopper() {\n    if (typeof Popper === 'undefined') {\n      throw new TypeError('Bootstrap\\'s dropdowns require Popper (https://popper.js.org)')\n    }\n\n    let referenceElement = this._element\n\n    if (this._config.reference === 'parent') {\n      referenceElement = this._parent\n    } else if (isElement(this._config.reference)) {\n      referenceElement = getElement(this._config.reference)\n    } else if (typeof this._config.reference === 'object') {\n      referenceElement = this._config.reference\n    }\n\n    const popperConfig = this._getPopperConfig()\n    this._popper = Popper.createPopper(referenceElement, this._menu, popperConfig)\n  }\n\n  _isShown() {\n    return this._menu.classList.contains(CLASS_NAME_SHOW)\n  }\n\n  _getPlacement() {\n    const parentDropdown = this._parent\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPEND)) {\n      return PLACEMENT_RIGHT\n    }\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPSTART)) {\n      return PLACEMENT_LEFT\n    }\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPUP_CENTER)) {\n      return PLACEMENT_TOPCENTER\n    }\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPDOWN_CENTER)) {\n      return PLACEMENT_BOTTOMCENTER\n    }\n\n    // We need to trim the value because custom properties can also include spaces\n    const isEnd = getComputedStyle(this._menu).getPropertyValue('--bs-position').trim() === 'end'\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPUP)) {\n      return isEnd ? PLACEMENT_TOPEND : PLACEMENT_TOP\n    }\n\n    return isEnd ? PLACEMENT_BOTTOMEND : PLACEMENT_BOTTOM\n  }\n\n  _detectNavbar() {\n    return this._element.closest(SELECTOR_NAVBAR) !== null\n  }\n\n  _getOffset() {\n    const { offset } = this._config\n\n    if (typeof offset === 'string') {\n      return offset.split(',').map(value => Number.parseInt(value, 10))\n    }\n\n    if (typeof offset === 'function') {\n      return popperData => offset(popperData, this._element)\n    }\n\n    return offset\n  }\n\n  _getPopperConfig() {\n    const defaultBsPopperConfig = {\n      placement: this._getPlacement(),\n      modifiers: [{\n        name: 'preventOverflow',\n        options: {\n          boundary: this._config.boundary\n        }\n      },\n      {\n        name: 'offset',\n        options: {\n          offset: this._getOffset()\n        }\n      }]\n    }\n\n    // Disable Popper if we have a static display or Dropdown is in Navbar\n    if (this._inNavbar || this._config.display === 'static') {\n      Manipulator.setDataAttribute(this._menu, 'popper', 'static') // TODO: v6 remove\n      defaultBsPopperConfig.modifiers = [{\n        name: 'applyStyles',\n        enabled: false\n      }]\n    }\n\n    return {\n      ...defaultBsPopperConfig,\n      ...execute(this._config.popperConfig, [defaultBsPopperConfig])\n    }\n  }\n\n  _selectMenuItem({ key, target }) {\n    const items = SelectorEngine.find(SELECTOR_VISIBLE_ITEMS, this._menu).filter(element => isVisible(element))\n\n    if (!items.length) {\n      return\n    }\n\n    // if target isn't included in items (e.g. when expanding the dropdown)\n    // allow cycling to get the last item in case key equals ARROW_UP_KEY\n    getNextActiveElement(items, target, key === ARROW_DOWN_KEY, !items.includes(target)).focus()\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Dropdown.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config]()\n    })\n  }\n\n  static clearMenus(event) {\n    if (event.button === RIGHT_MOUSE_BUTTON || (event.type === 'keyup' && event.key !== TAB_KEY)) {\n      return\n    }\n\n    const openToggles = SelectorEngine.find(SELECTOR_DATA_TOGGLE_SHOWN)\n\n    for (const toggle of openToggles) {\n      const context = Dropdown.getInstance(toggle)\n      if (!context || context._config.autoClose === false) {\n        continue\n      }\n\n      const composedPath = event.composedPath()\n      const isMenuTarget = composedPath.includes(context._menu)\n      if (\n        composedPath.includes(context._element) ||\n        (context._config.autoClose === 'inside' && !isMenuTarget) ||\n        (context._config.autoClose === 'outside' && isMenuTarget)\n      ) {\n        continue\n      }\n\n      // Tab navigation through the dropdown menu or events from contained inputs shouldn't close the menu\n      if (context._menu.contains(event.target) && ((event.type === 'keyup' && event.key === TAB_KEY) || /input|select|option|textarea|form/i.test(event.target.tagName))) {\n        continue\n      }\n\n      const relatedTarget = { relatedTarget: context._element }\n\n      if (event.type === 'click') {\n        relatedTarget.clickEvent = event\n      }\n\n      context._completeHide(relatedTarget)\n    }\n  }\n\n  static dataApiKeydownHandler(event) {\n    // If not an UP | DOWN | ESCAPE key => not a dropdown command\n    // If input/textarea && if key is other than ESCAPE => not a dropdown command\n\n    const isInput = /input|textarea/i.test(event.target.tagName)\n    const isEscapeEvent = event.key === ESCAPE_KEY\n    const isUpOrDownEvent = [ARROW_UP_KEY, ARROW_DOWN_KEY].includes(event.key)\n\n    if (!isUpOrDownEvent && !isEscapeEvent) {\n      return\n    }\n\n    if (isInput && !isEscapeEvent) {\n      return\n    }\n\n    event.preventDefault()\n\n    // TODO: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.3/forms/input-group/\n    const getToggleButton = this.matches(SELECTOR_DATA_TOGGLE) ?\n      this :\n      (SelectorEngine.prev(this, SELECTOR_DATA_TOGGLE)[0] ||\n        SelectorEngine.next(this, SELECTOR_DATA_TOGGLE)[0] ||\n        SelectorEngine.findOne(SELECTOR_DATA_TOGGLE, event.delegateTarget.parentNode))\n\n    const instance = Dropdown.getOrCreateInstance(getToggleButton)\n\n    if (isUpOrDownEvent) {\n      event.stopPropagation()\n      instance.show()\n      instance._selectMenuItem(event)\n      return\n    }\n\n    if (instance._isShown()) { // else is escape and we check if it is shown\n      event.stopPropagation()\n      instance.hide()\n      getToggleButton.focus()\n    }\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_DATA_TOGGLE, Dropdown.dataApiKeydownHandler)\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_MENU, Dropdown.dataApiKeydownHandler)\nEventHandler.on(document, EVENT_CLICK_DATA_API, Dropdown.clearMenus)\nEventHandler.on(document, EVENT_KEYUP_DATA_API, Dropdown.clearMenus)\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n  event.preventDefault()\n  Dropdown.getOrCreateInstance(this).toggle()\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Dropdown)\n\nexport default Dropdown\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/backdrop.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport Config from './config.js'\nimport { execute, executeAfterTransition, getElement, reflow } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'backdrop'\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\nconst EVENT_MOUSEDOWN = `mousedown.bs.${NAME}`\n\nconst Default = {\n  className: 'modal-backdrop',\n  clickCallback: null,\n  isAnimated: false,\n  isVisible: true, // if false, we use the backdrop helper without adding any element to the dom\n  rootElement: 'body' // give the choice to place backdrop under different elements\n}\n\nconst DefaultType = {\n  className: 'string',\n  clickCallback: '(function|null)',\n  isAnimated: 'boolean',\n  isVisible: 'boolean',\n  rootElement: '(element|string)'\n}\n\n/**\n * Class definition\n */\n\nclass Backdrop extends Config {\n  constructor(config) {\n    super()\n    this._config = this._getConfig(config)\n    this._isAppended = false\n    this._element = null\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  show(callback) {\n    if (!this._config.isVisible) {\n      execute(callback)\n      return\n    }\n\n    this._append()\n\n    const element = this._getElement()\n    if (this._config.isAnimated) {\n      reflow(element)\n    }\n\n    element.classList.add(CLASS_NAME_SHOW)\n\n    this._emulateAnimation(() => {\n      execute(callback)\n    })\n  }\n\n  hide(callback) {\n    if (!this._config.isVisible) {\n      execute(callback)\n      return\n    }\n\n    this._getElement().classList.remove(CLASS_NAME_SHOW)\n\n    this._emulateAnimation(() => {\n      this.dispose()\n      execute(callback)\n    })\n  }\n\n  dispose() {\n    if (!this._isAppended) {\n      return\n    }\n\n    EventHandler.off(this._element, EVENT_MOUSEDOWN)\n\n    this._element.remove()\n    this._isAppended = false\n  }\n\n  // Private\n  _getElement() {\n    if (!this._element) {\n      const backdrop = document.createElement('div')\n      backdrop.className = this._config.className\n      if (this._config.isAnimated) {\n        backdrop.classList.add(CLASS_NAME_FADE)\n      }\n\n      this._element = backdrop\n    }\n\n    return this._element\n  }\n\n  _configAfterMerge(config) {\n    // use getElement() with the default \"body\" to get a fresh Element on each instantiation\n    config.rootElement = getElement(config.rootElement)\n    return config\n  }\n\n  _append() {\n    if (this._isAppended) {\n      return\n    }\n\n    const element = this._getElement()\n    this._config.rootElement.append(element)\n\n    EventHandler.on(element, EVENT_MOUSEDOWN, () => {\n      execute(this._config.clickCallback)\n    })\n\n    this._isAppended = true\n  }\n\n  _emulateAnimation(callback) {\n    executeAfterTransition(callback, this._getElement(), this._config.isAnimated)\n  }\n}\n\nexport default Backdrop\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/focustrap.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport Config from './config.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'focustrap'\nconst DATA_KEY = 'bs.focustrap'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst EVENT_FOCUSIN = `focusin${EVENT_KEY}`\nconst EVENT_KEYDOWN_TAB = `keydown.tab${EVENT_KEY}`\n\nconst TAB_KEY = 'Tab'\nconst TAB_NAV_FORWARD = 'forward'\nconst TAB_NAV_BACKWARD = 'backward'\n\nconst Default = {\n  autofocus: true,\n  trapElement: null // The element to trap focus inside of\n}\n\nconst DefaultType = {\n  autofocus: 'boolean',\n  trapElement: 'element'\n}\n\n/**\n * Class definition\n */\n\nclass FocusTrap extends Config {\n  constructor(config) {\n    super()\n    this._config = this._getConfig(config)\n    this._isActive = false\n    this._lastTabNavDirection = null\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  activate() {\n    if (this._isActive) {\n      return\n    }\n\n    if (this._config.autofocus) {\n      this._config.trapElement.focus()\n    }\n\n    EventHandler.off(document, EVENT_KEY) // guard against infinite focus loop\n    EventHandler.on(document, EVENT_FOCUSIN, event => this._handleFocusin(event))\n    EventHandler.on(document, EVENT_KEYDOWN_TAB, event => this._handleKeydown(event))\n\n    this._isActive = true\n  }\n\n  deactivate() {\n    if (!this._isActive) {\n      return\n    }\n\n    this._isActive = false\n    EventHandler.off(document, EVENT_KEY)\n  }\n\n  // Private\n  _handleFocusin(event) {\n    const { trapElement } = this._config\n\n    if (event.target === document || event.target === trapElement || trapElement.contains(event.target)) {\n      return\n    }\n\n    const elements = SelectorEngine.focusableChildren(trapElement)\n\n    if (elements.length === 0) {\n      trapElement.focus()\n    } else if (this._lastTabNavDirection === TAB_NAV_BACKWARD) {\n      elements[elements.length - 1].focus()\n    } else {\n      elements[0].focus()\n    }\n  }\n\n  _handleKeydown(event) {\n    if (event.key !== TAB_KEY) {\n      return\n    }\n\n    this._lastTabNavDirection = event.shiftKey ? TAB_NAV_BACKWARD : TAB_NAV_FORWARD\n  }\n}\n\nexport default FocusTrap\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/scrollBar.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Manipulator from '../dom/manipulator.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport { isElement } from './index.js'\n\n/**\n * Constants\n */\n\nconst SELECTOR_FIXED_CONTENT = '.fixed-top, .fixed-bottom, .is-fixed, .sticky-top'\nconst SELECTOR_STICKY_CONTENT = '.sticky-top'\nconst PROPERTY_PADDING = 'padding-right'\nconst PROPERTY_MARGIN = 'margin-right'\n\n/**\n * Class definition\n */\n\nclass ScrollBarHelper {\n  constructor() {\n    this._element = document.body\n  }\n\n  // Public\n  getWidth() {\n    // https://developer.mozilla.org/en-US/docs/Web/API/Window/innerWidth#usage_notes\n    const documentWidth = document.documentElement.clientWidth\n    return Math.abs(window.innerWidth - documentWidth)\n  }\n\n  hide() {\n    const width = this.getWidth()\n    this._disableOverFlow()\n    // give padding to element to balance the hidden scrollbar width\n    this._setElementAttributes(this._element, PROPERTY_PADDING, calculatedValue => calculatedValue + width)\n    // trick: We adjust positive paddingRight and negative marginRight to sticky-top elements to keep showing fullwidth\n    this._setElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING, calculatedValue => calculatedValue + width)\n    this._setElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN, calculatedValue => calculatedValue - width)\n  }\n\n  reset() {\n    this._resetElementAttributes(this._element, 'overflow')\n    this._resetElementAttributes(this._element, PROPERTY_PADDING)\n    this._resetElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING)\n    this._resetElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN)\n  }\n\n  isOverflowing() {\n    return this.getWidth() > 0\n  }\n\n  // Private\n  _disableOverFlow() {\n    this._saveInitialAttribute(this._element, 'overflow')\n    this._element.style.overflow = 'hidden'\n  }\n\n  _setElementAttributes(selector, styleProperty, callback) {\n    const scrollbarWidth = this.getWidth()\n    const manipulationCallBack = element => {\n      if (element !== this._element && window.innerWidth > element.clientWidth + scrollbarWidth) {\n        return\n      }\n\n      this._saveInitialAttribute(element, styleProperty)\n      const calculatedValue = window.getComputedStyle(element).getPropertyValue(styleProperty)\n      element.style.setProperty(styleProperty, `${callback(Number.parseFloat(calculatedValue))}px`)\n    }\n\n    this._applyManipulationCallback(selector, manipulationCallBack)\n  }\n\n  _saveInitialAttribute(element, styleProperty) {\n    const actualValue = element.style.getPropertyValue(styleProperty)\n    if (actualValue) {\n      Manipulator.setDataAttribute(element, styleProperty, actualValue)\n    }\n  }\n\n  _resetElementAttributes(selector, styleProperty) {\n    const manipulationCallBack = element => {\n      const value = Manipulator.getDataAttribute(element, styleProperty)\n      // We only want to remove the property if the value is `null`; the value can also be zero\n      if (value === null) {\n        element.style.removeProperty(styleProperty)\n        return\n      }\n\n      Manipulator.removeDataAttribute(element, styleProperty)\n      element.style.setProperty(styleProperty, value)\n    }\n\n    this._applyManipulationCallback(selector, manipulationCallBack)\n  }\n\n  _applyManipulationCallback(selector, callBack) {\n    if (isElement(selector)) {\n      callBack(selector)\n      return\n    }\n\n    for (const sel of SelectorEngine.find(selector, this._element)) {\n      callBack(sel)\n    }\n  }\n}\n\nexport default ScrollBarHelper\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap modal.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport Backdrop from './util/backdrop.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport FocusTrap from './util/focustrap.js'\nimport { defineJQueryPlugin, isRTL, isVisible, reflow } from './util/index.js'\nimport ScrollBarHelper from './util/scrollbar.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'modal'\nconst DATA_KEY = 'bs.modal'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\nconst ESCAPE_KEY = 'Escape'\n\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDE_PREVENTED = `hidePrevented${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_RESIZE = `resize${EVENT_KEY}`\nconst EVENT_CLICK_DISMISS = `click.dismiss${EVENT_KEY}`\nconst EVENT_MOUSEDOWN_DISMISS = `mousedown.dismiss${EVENT_KEY}`\nconst EVENT_KEYDOWN_DISMISS = `keydown.dismiss${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_OPEN = 'modal-open'\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_STATIC = 'modal-static'\n\nconst OPEN_SELECTOR = '.modal.show'\nconst SELECTOR_DIALOG = '.modal-dialog'\nconst SELECTOR_MODAL_BODY = '.modal-body'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"modal\"]'\n\nconst Default = {\n  backdrop: true,\n  focus: true,\n  keyboard: true\n}\n\nconst DefaultType = {\n  backdrop: '(boolean|string)',\n  focus: 'boolean',\n  keyboard: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Modal extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._dialog = SelectorEngine.findOne(SELECTOR_DIALOG, this._element)\n    this._backdrop = this._initializeBackDrop()\n    this._focustrap = this._initializeFocusTrap()\n    this._isShown = false\n    this._isTransitioning = false\n    this._scrollBar = new ScrollBarHelper()\n\n    this._addEventListeners()\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle(relatedTarget) {\n    return this._isShown ? this.hide() : this.show(relatedTarget)\n  }\n\n  show(relatedTarget) {\n    if (this._isShown || this._isTransitioning) {\n      return\n    }\n\n    const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, {\n      relatedTarget\n    })\n\n    if (showEvent.defaultPrevented) {\n      return\n    }\n\n    this._isShown = true\n    this._isTransitioning = true\n\n    this._scrollBar.hide()\n\n    document.body.classList.add(CLASS_NAME_OPEN)\n\n    this._adjustDialog()\n\n    this._backdrop.show(() => this._showElement(relatedTarget))\n  }\n\n  hide() {\n    if (!this._isShown || this._isTransitioning) {\n      return\n    }\n\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    this._isShown = false\n    this._isTransitioning = true\n    this._focustrap.deactivate()\n\n    this._element.classList.remove(CLASS_NAME_SHOW)\n\n    this._queueCallback(() => this._hideModal(), this._element, this._isAnimated())\n  }\n\n  dispose() {\n    EventHandler.off(window, EVENT_KEY)\n    EventHandler.off(this._dialog, EVENT_KEY)\n\n    this._backdrop.dispose()\n    this._focustrap.deactivate()\n\n    super.dispose()\n  }\n\n  handleUpdate() {\n    this._adjustDialog()\n  }\n\n  // Private\n  _initializeBackDrop() {\n    return new Backdrop({\n      isVisible: Boolean(this._config.backdrop), // 'static' option will be translated to true, and booleans will keep their value,\n      isAnimated: this._isAnimated()\n    })\n  }\n\n  _initializeFocusTrap() {\n    return new FocusTrap({\n      trapElement: this._element\n    })\n  }\n\n  _showElement(relatedTarget) {\n    // try to append dynamic modal\n    if (!document.body.contains(this._element)) {\n      document.body.append(this._element)\n    }\n\n    this._element.style.display = 'block'\n    this._element.removeAttribute('aria-hidden')\n    this._element.setAttribute('aria-modal', true)\n    this._element.setAttribute('role', 'dialog')\n    this._element.scrollTop = 0\n\n    const modalBody = SelectorEngine.findOne(SELECTOR_MODAL_BODY, this._dialog)\n    if (modalBody) {\n      modalBody.scrollTop = 0\n    }\n\n    reflow(this._element)\n\n    this._element.classList.add(CLASS_NAME_SHOW)\n\n    const transitionComplete = () => {\n      if (this._config.focus) {\n        this._focustrap.activate()\n      }\n\n      this._isTransitioning = false\n      EventHandler.trigger(this._element, EVENT_SHOWN, {\n        relatedTarget\n      })\n    }\n\n    this._queueCallback(transitionComplete, this._dialog, this._isAnimated())\n  }\n\n  _addEventListeners() {\n    EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS, event => {\n      if (event.key !== ESCAPE_KEY) {\n        return\n      }\n\n      if (this._config.keyboard) {\n        this.hide()\n        return\n      }\n\n      this._triggerBackdropTransition()\n    })\n\n    EventHandler.on(window, EVENT_RESIZE, () => {\n      if (this._isShown && !this._isTransitioning) {\n        this._adjustDialog()\n      }\n    })\n\n    EventHandler.on(this._element, EVENT_MOUSEDOWN_DISMISS, event => {\n      // a bad trick to segregate clicks that may start inside dialog but end outside, and avoid listen to scrollbar clicks\n      EventHandler.one(this._element, EVENT_CLICK_DISMISS, event2 => {\n        if (this._element !== event.target || this._element !== event2.target) {\n          return\n        }\n\n        if (this._config.backdrop === 'static') {\n          this._triggerBackdropTransition()\n          return\n        }\n\n        if (this._config.backdrop) {\n          this.hide()\n        }\n      })\n    })\n  }\n\n  _hideModal() {\n    this._element.style.display = 'none'\n    this._element.setAttribute('aria-hidden', true)\n    this._element.removeAttribute('aria-modal')\n    this._element.removeAttribute('role')\n    this._isTransitioning = false\n\n    this._backdrop.hide(() => {\n      document.body.classList.remove(CLASS_NAME_OPEN)\n      this._resetAdjustments()\n      this._scrollBar.reset()\n      EventHandler.trigger(this._element, EVENT_HIDDEN)\n    })\n  }\n\n  _isAnimated() {\n    return this._element.classList.contains(CLASS_NAME_FADE)\n  }\n\n  _triggerBackdropTransition() {\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight\n    const initialOverflowY = this._element.style.overflowY\n    // return if the following background transition hasn't yet completed\n    if (initialOverflowY === 'hidden' || this._element.classList.contains(CLASS_NAME_STATIC)) {\n      return\n    }\n\n    if (!isModalOverflowing) {\n      this._element.style.overflowY = 'hidden'\n    }\n\n    this._element.classList.add(CLASS_NAME_STATIC)\n    this._queueCallback(() => {\n      this._element.classList.remove(CLASS_NAME_STATIC)\n      this._queueCallback(() => {\n        this._element.style.overflowY = initialOverflowY\n      }, this._dialog)\n    }, this._dialog)\n\n    this._element.focus()\n  }\n\n  /**\n   * The following methods are used to handle overflowing modals\n   */\n\n  _adjustDialog() {\n    const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight\n    const scrollbarWidth = this._scrollBar.getWidth()\n    const isBodyOverflowing = scrollbarWidth > 0\n\n    if (isBodyOverflowing && !isModalOverflowing) {\n      const property = isRTL() ? 'paddingLeft' : 'paddingRight'\n      this._element.style[property] = `${scrollbarWidth}px`\n    }\n\n    if (!isBodyOverflowing && isModalOverflowing) {\n      const property = isRTL() ? 'paddingRight' : 'paddingLeft'\n      this._element.style[property] = `${scrollbarWidth}px`\n    }\n  }\n\n  _resetAdjustments() {\n    this._element.style.paddingLeft = ''\n    this._element.style.paddingRight = ''\n  }\n\n  // Static\n  static jQueryInterface(config, relatedTarget) {\n    return this.each(function () {\n      const data = Modal.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config](relatedTarget)\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n  const target = SelectorEngine.getElementFromSelector(this)\n\n  if (['A', 'AREA'].includes(this.tagName)) {\n    event.preventDefault()\n  }\n\n  EventHandler.one(target, EVENT_SHOW, showEvent => {\n    if (showEvent.defaultPrevented) {\n      // only register focus restorer if modal will actually get shown\n      return\n    }\n\n    EventHandler.one(target, EVENT_HIDDEN, () => {\n      if (isVisible(this)) {\n        this.focus()\n      }\n    })\n  })\n\n  // avoid conflict when clicking modal toggler while another one is open\n  const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR)\n  if (alreadyOpen) {\n    Modal.getInstance(alreadyOpen).hide()\n  }\n\n  const data = Modal.getOrCreateInstance(target)\n\n  data.toggle(this)\n})\n\nenableDismissTrigger(Modal)\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Modal)\n\nexport default Modal\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap offcanvas.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport Backdrop from './util/backdrop.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport FocusTrap from './util/focustrap.js'\nimport {\n  defineJQueryPlugin,\n  isDisabled,\n  isVisible\n} from './util/index.js'\nimport ScrollBarHelper from './util/scrollbar.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'offcanvas'\nconst DATA_KEY = 'bs.offcanvas'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\nconst ESCAPE_KEY = 'Escape'\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_SHOWING = 'showing'\nconst CLASS_NAME_HIDING = 'hiding'\nconst CLASS_NAME_BACKDROP = 'offcanvas-backdrop'\nconst OPEN_SELECTOR = '.offcanvas.show'\n\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDE_PREVENTED = `hidePrevented${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_RESIZE = `resize${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYDOWN_DISMISS = `keydown.dismiss${EVENT_KEY}`\n\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"offcanvas\"]'\n\nconst Default = {\n  backdrop: true,\n  keyboard: true,\n  scroll: false\n}\n\nconst DefaultType = {\n  backdrop: '(boolean|string)',\n  keyboard: 'boolean',\n  scroll: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Offcanvas extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._isShown = false\n    this._backdrop = this._initializeBackDrop()\n    this._focustrap = this._initializeFocusTrap()\n    this._addEventListeners()\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle(relatedTarget) {\n    return this._isShown ? this.hide() : this.show(relatedTarget)\n  }\n\n  show(relatedTarget) {\n    if (this._isShown) {\n      return\n    }\n\n    const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, { relatedTarget })\n\n    if (showEvent.defaultPrevented) {\n      return\n    }\n\n    this._isShown = true\n    this._backdrop.show()\n\n    if (!this._config.scroll) {\n      new ScrollBarHelper().hide()\n    }\n\n    this._element.setAttribute('aria-modal', true)\n    this._element.setAttribute('role', 'dialog')\n    this._element.classList.add(CLASS_NAME_SHOWING)\n\n    const completeCallBack = () => {\n      if (!this._config.scroll || this._config.backdrop) {\n        this._focustrap.activate()\n      }\n\n      this._element.classList.add(CLASS_NAME_SHOW)\n      this._element.classList.remove(CLASS_NAME_SHOWING)\n      EventHandler.trigger(this._element, EVENT_SHOWN, { relatedTarget })\n    }\n\n    this._queueCallback(completeCallBack, this._element, true)\n  }\n\n  hide() {\n    if (!this._isShown) {\n      return\n    }\n\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    this._focustrap.deactivate()\n    this._element.blur()\n    this._isShown = false\n    this._element.classList.add(CLASS_NAME_HIDING)\n    this._backdrop.hide()\n\n    const completeCallback = () => {\n      this._element.classList.remove(CLASS_NAME_SHOW, CLASS_NAME_HIDING)\n      this._element.removeAttribute('aria-modal')\n      this._element.removeAttribute('role')\n\n      if (!this._config.scroll) {\n        new ScrollBarHelper().reset()\n      }\n\n      EventHandler.trigger(this._element, EVENT_HIDDEN)\n    }\n\n    this._queueCallback(completeCallback, this._element, true)\n  }\n\n  dispose() {\n    this._backdrop.dispose()\n    this._focustrap.deactivate()\n    super.dispose()\n  }\n\n  // Private\n  _initializeBackDrop() {\n    const clickCallback = () => {\n      if (this._config.backdrop === 'static') {\n        EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n        return\n      }\n\n      this.hide()\n    }\n\n    // 'static' option will be translated to true, and booleans will keep their value\n    const isVisible = Boolean(this._config.backdrop)\n\n    return new Backdrop({\n      className: CLASS_NAME_BACKDROP,\n      isVisible,\n      isAnimated: true,\n      rootElement: this._element.parentNode,\n      clickCallback: isVisible ? clickCallback : null\n    })\n  }\n\n  _initializeFocusTrap() {\n    return new FocusTrap({\n      trapElement: this._element\n    })\n  }\n\n  _addEventListeners() {\n    EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS, event => {\n      if (event.key !== ESCAPE_KEY) {\n        return\n      }\n\n      if (this._config.keyboard) {\n        this.hide()\n        return\n      }\n\n      EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n    })\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Offcanvas.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config](this)\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n  const target = SelectorEngine.getElementFromSelector(this)\n\n  if (['A', 'AREA'].includes(this.tagName)) {\n    event.preventDefault()\n  }\n\n  if (isDisabled(this)) {\n    return\n  }\n\n  EventHandler.one(target, EVENT_HIDDEN, () => {\n    // focus on trigger when it is closed\n    if (isVisible(this)) {\n      this.focus()\n    }\n  })\n\n  // avoid conflict when clicking a toggler of an offcanvas, while another is open\n  const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR)\n  if (alreadyOpen && alreadyOpen !== target) {\n    Offcanvas.getInstance(alreadyOpen).hide()\n  }\n\n  const data = Offcanvas.getOrCreateInstance(target)\n  data.toggle(this)\n})\n\nEventHandler.on(window, EVENT_LOAD_DATA_API, () => {\n  for (const selector of SelectorEngine.find(OPEN_SELECTOR)) {\n    Offcanvas.getOrCreateInstance(selector).show()\n  }\n})\n\nEventHandler.on(window, EVENT_RESIZE, () => {\n  for (const element of SelectorEngine.find('[aria-modal][class*=show][class*=offcanvas-]')) {\n    if (getComputedStyle(element).position !== 'fixed') {\n      Offcanvas.getOrCreateInstance(element).hide()\n    }\n  }\n})\n\nenableDismissTrigger(Offcanvas)\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Offcanvas)\n\nexport default Offcanvas\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/sanitizer.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n// js-docs-start allow-list\nconst ARIA_ATTRIBUTE_PATTERN = /^aria-[\\w-]*$/i\n\nexport const DefaultAllowlist = {\n  // Global attributes allowed on any supplied element below.\n  '*': ['class', 'dir', 'id', 'lang', 'role', ARIA_ATTRIBUTE_PATTERN],\n  a: ['target', 'href', 'title', 'rel'],\n  area: [],\n  b: [],\n  br: [],\n  col: [],\n  code: [],\n  div: [],\n  em: [],\n  hr: [],\n  h1: [],\n  h2: [],\n  h3: [],\n  h4: [],\n  h5: [],\n  h6: [],\n  i: [],\n  img: ['src', 'srcset', 'alt', 'title', 'width', 'height'],\n  li: [],\n  ol: [],\n  p: [],\n  pre: [],\n  s: [],\n  small: [],\n  span: [],\n  sub: [],\n  sup: [],\n  strong: [],\n  u: [],\n  ul: []\n}\n// js-docs-end allow-list\n\nconst uriAttributes = new Set([\n  'background',\n  'cite',\n  'href',\n  'itemtype',\n  'longdesc',\n  'poster',\n  'src',\n  'xlink:href'\n])\n\n/**\n * A pattern that recognizes URLs that are safe wrt. XSS in URL navigation\n * contexts.\n *\n * Shout-out to Angular https://github.com/angular/angular/blob/15.2.8/packages/core/src/sanitization/url_sanitizer.ts#L38\n */\n// eslint-disable-next-line unicorn/better-regex\nconst SAFE_URL_PATTERN = /^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i\n\nconst allowedAttribute = (attribute, allowedAttributeList) => {\n  const attributeName = attribute.nodeName.toLowerCase()\n\n  if (allowedAttributeList.includes(attributeName)) {\n    if (uriAttributes.has(attributeName)) {\n      return Boolean(SAFE_URL_PATTERN.test(attribute.nodeValue))\n    }\n\n    return true\n  }\n\n  // Check if a regular expression validates the attribute.\n  return allowedAttributeList.filter(attributeRegex => attributeRegex instanceof RegExp)\n    .some(regex => regex.test(attributeName))\n}\n\nexport function sanitizeHtml(unsafeHtml, allowList, sanitizeFunction) {\n  if (!unsafeHtml.length) {\n    return unsafeHtml\n  }\n\n  if (sanitizeFunction && typeof sanitizeFunction === 'function') {\n    return sanitizeFunction(unsafeHtml)\n  }\n\n  const domParser = new window.DOMParser()\n  const createdDocument = domParser.parseFromString(unsafeHtml, 'text/html')\n  const elements = [].concat(...createdDocument.body.querySelectorAll('*'))\n\n  for (const element of elements) {\n    const elementName = element.nodeName.toLowerCase()\n\n    if (!Object.keys(allowList).includes(elementName)) {\n      element.remove()\n      continue\n    }\n\n    const attributeList = [].concat(...element.attributes)\n    const allowedAttributes = [].concat(allowList['*'] || [], allowList[elementName] || [])\n\n    for (const attribute of attributeList) {\n      if (!allowedAttribute(attribute, allowedAttributes)) {\n        element.removeAttribute(attribute.nodeName)\n      }\n    }\n  }\n\n  return createdDocument.body.innerHTML\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/template-factory.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport SelectorEngine from '../dom/selector-engine.js'\nimport Config from './config.js'\nimport { DefaultAllowlist, sanitizeHtml } from './sanitizer.js'\nimport { execute, getElement, isElement } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'TemplateFactory'\n\nconst Default = {\n  allowList: DefaultAllowlist,\n  content: {}, // { selector : text ,  selector2 : text2 , }\n  extraClass: '',\n  html: false,\n  sanitize: true,\n  sanitizeFn: null,\n  template: '<div></div>'\n}\n\nconst DefaultType = {\n  allowList: 'object',\n  content: 'object',\n  extraClass: '(string|function)',\n  html: 'boolean',\n  sanitize: 'boolean',\n  sanitizeFn: '(null|function)',\n  template: 'string'\n}\n\nconst DefaultContentType = {\n  entry: '(string|element|function|null)',\n  selector: '(string|element)'\n}\n\n/**\n * Class definition\n */\n\nclass TemplateFactory extends Config {\n  constructor(config) {\n    super()\n    this._config = this._getConfig(config)\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  getContent() {\n    return Object.values(this._config.content)\n      .map(config => this._resolvePossibleFunction(config))\n      .filter(Boolean)\n  }\n\n  hasContent() {\n    return this.getContent().length > 0\n  }\n\n  changeContent(content) {\n    this._checkContent(content)\n    this._config.content = { ...this._config.content, ...content }\n    return this\n  }\n\n  toHtml() {\n    const templateWrapper = document.createElement('div')\n    templateWrapper.innerHTML = this._maybeSanitize(this._config.template)\n\n    for (const [selector, text] of Object.entries(this._config.content)) {\n      this._setContent(templateWrapper, text, selector)\n    }\n\n    const template = templateWrapper.children[0]\n    const extraClass = this._resolvePossibleFunction(this._config.extraClass)\n\n    if (extraClass) {\n      template.classList.add(...extraClass.split(' '))\n    }\n\n    return template\n  }\n\n  // Private\n  _typeCheckConfig(config) {\n    super._typeCheckConfig(config)\n    this._checkContent(config.content)\n  }\n\n  _checkContent(arg) {\n    for (const [selector, content] of Object.entries(arg)) {\n      super._typeCheckConfig({ selector, entry: content }, DefaultContentType)\n    }\n  }\n\n  _setContent(template, content, selector) {\n    const templateElement = SelectorEngine.findOne(selector, template)\n\n    if (!templateElement) {\n      return\n    }\n\n    content = this._resolvePossibleFunction(content)\n\n    if (!content) {\n      templateElement.remove()\n      return\n    }\n\n    if (isElement(content)) {\n      this._putElementInTemplate(getElement(content), templateElement)\n      return\n    }\n\n    if (this._config.html) {\n      templateElement.innerHTML = this._maybeSanitize(content)\n      return\n    }\n\n    templateElement.textContent = content\n  }\n\n  _maybeSanitize(arg) {\n    return this._config.sanitize ? sanitizeHtml(arg, this._config.allowList, this._config.sanitizeFn) : arg\n  }\n\n  _resolvePossibleFunction(arg) {\n    return execute(arg, [this])\n  }\n\n  _putElementInTemplate(element, templateElement) {\n    if (this._config.html) {\n      templateElement.innerHTML = ''\n      templateElement.append(element)\n      return\n    }\n\n    templateElement.textContent = element.textContent\n  }\n}\n\nexport default TemplateFactory\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap tooltip.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport * as Popper from '@popperjs/core'\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport { defineJQueryPlugin, execute, findShadowRoot, getElement, getUID, isRTL, noop } from './util/index.js'\nimport { DefaultAllowlist } from './util/sanitizer.js'\nimport TemplateFactory from './util/template-factory.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'tooltip'\nconst DISALLOWED_ATTRIBUTES = new Set(['sanitize', 'allowList', 'sanitizeFn'])\n\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_MODAL = 'modal'\nconst CLASS_NAME_SHOW = 'show'\n\nconst SELECTOR_TOOLTIP_INNER = '.tooltip-inner'\nconst SELECTOR_MODAL = `.${CLASS_NAME_MODAL}`\n\nconst EVENT_MODAL_HIDE = 'hide.bs.modal'\n\nconst TRIGGER_HOVER = 'hover'\nconst TRIGGER_FOCUS = 'focus'\nconst TRIGGER_CLICK = 'click'\nconst TRIGGER_MANUAL = 'manual'\n\nconst EVENT_HIDE = 'hide'\nconst EVENT_HIDDEN = 'hidden'\nconst EVENT_SHOW = 'show'\nconst EVENT_SHOWN = 'shown'\nconst EVENT_INSERTED = 'inserted'\nconst EVENT_CLICK = 'click'\nconst EVENT_FOCUSIN = 'focusin'\nconst EVENT_FOCUSOUT = 'focusout'\nconst EVENT_MOUSEENTER = 'mouseenter'\nconst EVENT_MOUSELEAVE = 'mouseleave'\n\nconst AttachmentMap = {\n  AUTO: 'auto',\n  TOP: 'top',\n  RIGHT: isRTL() ? 'left' : 'right',\n  BOTTOM: 'bottom',\n  LEFT: isRTL() ? 'right' : 'left'\n}\n\nconst Default = {\n  allowList: DefaultAllowlist,\n  animation: true,\n  boundary: 'clippingParents',\n  container: false,\n  customClass: '',\n  delay: 0,\n  fallbackPlacements: ['top', 'right', 'bottom', 'left'],\n  html: false,\n  offset: [0, 6],\n  placement: 'top',\n  popperConfig: null,\n  sanitize: true,\n  sanitizeFn: null,\n  selector: false,\n  template: '<div class=\"tooltip\" role=\"tooltip\">' +\n            '<div class=\"tooltip-arrow\"></div>' +\n            '<div class=\"tooltip-inner\"></div>' +\n            '</div>',\n  title: '',\n  trigger: 'hover focus'\n}\n\nconst DefaultType = {\n  allowList: 'object',\n  animation: 'boolean',\n  boundary: '(string|element)',\n  container: '(string|element|boolean)',\n  customClass: '(string|function)',\n  delay: '(number|object)',\n  fallbackPlacements: 'array',\n  html: 'boolean',\n  offset: '(array|string|function)',\n  placement: '(string|function)',\n  popperConfig: '(null|object|function)',\n  sanitize: 'boolean',\n  sanitizeFn: '(null|function)',\n  selector: '(string|boolean)',\n  template: 'string',\n  title: '(string|element|function)',\n  trigger: 'string'\n}\n\n/**\n * Class definition\n */\n\nclass Tooltip extends BaseComponent {\n  constructor(element, config) {\n    if (typeof Popper === 'undefined') {\n      throw new TypeError('Bootstrap\\'s tooltips require Popper (https://popper.js.org)')\n    }\n\n    super(element, config)\n\n    // Private\n    this._isEnabled = true\n    this._timeout = 0\n    this._isHovered = null\n    this._activeTrigger = {}\n    this._popper = null\n    this._templateFactory = null\n    this._newContent = null\n\n    // Protected\n    this.tip = null\n\n    this._setListeners()\n\n    if (!this._config.selector) {\n      this._fixTitle()\n    }\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  enable() {\n    this._isEnabled = true\n  }\n\n  disable() {\n    this._isEnabled = false\n  }\n\n  toggleEnabled() {\n    this._isEnabled = !this._isEnabled\n  }\n\n  toggle() {\n    if (!this._isEnabled) {\n      return\n    }\n\n    this._activeTrigger.click = !this._activeTrigger.click\n    if (this._isShown()) {\n      this._leave()\n      return\n    }\n\n    this._enter()\n  }\n\n  dispose() {\n    clearTimeout(this._timeout)\n\n    EventHandler.off(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler)\n\n    if (this._element.getAttribute('data-bs-original-title')) {\n      this._element.setAttribute('title', this._element.getAttribute('data-bs-original-title'))\n    }\n\n    this._disposePopper()\n    super.dispose()\n  }\n\n  show() {\n    if (this._element.style.display === 'none') {\n      throw new Error('Please use show on visible elements')\n    }\n\n    if (!(this._isWithContent() && this._isEnabled)) {\n      return\n    }\n\n    const showEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOW))\n    const shadowRoot = findShadowRoot(this._element)\n    const isInTheDom = (shadowRoot || this._element.ownerDocument.documentElement).contains(this._element)\n\n    if (showEvent.defaultPrevented || !isInTheDom) {\n      return\n    }\n\n    // TODO: v6 remove this or make it optional\n    this._disposePopper()\n\n    const tip = this._getTipElement()\n\n    this._element.setAttribute('aria-describedby', tip.getAttribute('id'))\n\n    const { container } = this._config\n\n    if (!this._element.ownerDocument.documentElement.contains(this.tip)) {\n      container.append(tip)\n      EventHandler.trigger(this._element, this.constructor.eventName(EVENT_INSERTED))\n    }\n\n    this._popper = this._createPopper(tip)\n\n    tip.classList.add(CLASS_NAME_SHOW)\n\n    // If this is a touch-enabled device we add extra\n    // empty mouseover listeners to the body's immediate children;\n    // only needed because of broken event delegation on iOS\n    // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n    if ('ontouchstart' in document.documentElement) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.on(element, 'mouseover', noop)\n      }\n    }\n\n    const complete = () => {\n      EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOWN))\n\n      if (this._isHovered === false) {\n        this._leave()\n      }\n\n      this._isHovered = false\n    }\n\n    this._queueCallback(complete, this.tip, this._isAnimated())\n  }\n\n  hide() {\n    if (!this._isShown()) {\n      return\n    }\n\n    const hideEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDE))\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    const tip = this._getTipElement()\n    tip.classList.remove(CLASS_NAME_SHOW)\n\n    // If this is a touch-enabled device we remove the extra\n    // empty mouseover listeners we added for iOS support\n    if ('ontouchstart' in document.documentElement) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.off(element, 'mouseover', noop)\n      }\n    }\n\n    this._activeTrigger[TRIGGER_CLICK] = false\n    this._activeTrigger[TRIGGER_FOCUS] = false\n    this._activeTrigger[TRIGGER_HOVER] = false\n    this._isHovered = null // it is a trick to support manual triggering\n\n    const complete = () => {\n      if (this._isWithActiveTrigger()) {\n        return\n      }\n\n      if (!this._isHovered) {\n        this._disposePopper()\n      }\n\n      this._element.removeAttribute('aria-describedby')\n      EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDDEN))\n    }\n\n    this._queueCallback(complete, this.tip, this._isAnimated())\n  }\n\n  update() {\n    if (this._popper) {\n      this._popper.update()\n    }\n  }\n\n  // Protected\n  _isWithContent() {\n    return Boolean(this._getTitle())\n  }\n\n  _getTipElement() {\n    if (!this.tip) {\n      this.tip = this._createTipElement(this._newContent || this._getContentForTemplate())\n    }\n\n    return this.tip\n  }\n\n  _createTipElement(content) {\n    const tip = this._getTemplateFactory(content).toHtml()\n\n    // TODO: remove this check in v6\n    if (!tip) {\n      return null\n    }\n\n    tip.classList.remove(CLASS_NAME_FADE, CLASS_NAME_SHOW)\n    // TODO: v6 the following can be achieved with CSS only\n    tip.classList.add(`bs-${this.constructor.NAME}-auto`)\n\n    const tipId = getUID(this.constructor.NAME).toString()\n\n    tip.setAttribute('id', tipId)\n\n    if (this._isAnimated()) {\n      tip.classList.add(CLASS_NAME_FADE)\n    }\n\n    return tip\n  }\n\n  setContent(content) {\n    this._newContent = content\n    if (this._isShown()) {\n      this._disposePopper()\n      this.show()\n    }\n  }\n\n  _getTemplateFactory(content) {\n    if (this._templateFactory) {\n      this._templateFactory.changeContent(content)\n    } else {\n      this._templateFactory = new TemplateFactory({\n        ...this._config,\n        // the `content` var has to be after `this._config`\n        // to override config.content in case of popover\n        content,\n        extraClass: this._resolvePossibleFunction(this._config.customClass)\n      })\n    }\n\n    return this._templateFactory\n  }\n\n  _getContentForTemplate() {\n    return {\n      [SELECTOR_TOOLTIP_INNER]: this._getTitle()\n    }\n  }\n\n  _getTitle() {\n    return this._resolvePossibleFunction(this._config.title) || this._element.getAttribute('data-bs-original-title')\n  }\n\n  // Private\n  _initializeOnDelegatedTarget(event) {\n    return this.constructor.getOrCreateInstance(event.delegateTarget, this._getDelegateConfig())\n  }\n\n  _isAnimated() {\n    return this._config.animation || (this.tip && this.tip.classList.contains(CLASS_NAME_FADE))\n  }\n\n  _isShown() {\n    return this.tip && this.tip.classList.contains(CLASS_NAME_SHOW)\n  }\n\n  _createPopper(tip) {\n    const placement = execute(this._config.placement, [this, tip, this._element])\n    const attachment = AttachmentMap[placement.toUpperCase()]\n    return Popper.createPopper(this._element, tip, this._getPopperConfig(attachment))\n  }\n\n  _getOffset() {\n    const { offset } = this._config\n\n    if (typeof offset === 'string') {\n      return offset.split(',').map(value => Number.parseInt(value, 10))\n    }\n\n    if (typeof offset === 'function') {\n      return popperData => offset(popperData, this._element)\n    }\n\n    return offset\n  }\n\n  _resolvePossibleFunction(arg) {\n    return execute(arg, [this._element])\n  }\n\n  _getPopperConfig(attachment) {\n    const defaultBsPopperConfig = {\n      placement: attachment,\n      modifiers: [\n        {\n          name: 'flip',\n          options: {\n            fallbackPlacements: this._config.fallbackPlacements\n          }\n        },\n        {\n          name: 'offset',\n          options: {\n            offset: this._getOffset()\n          }\n        },\n        {\n          name: 'preventOverflow',\n          options: {\n            boundary: this._config.boundary\n          }\n        },\n        {\n          name: 'arrow',\n          options: {\n            element: `.${this.constructor.NAME}-arrow`\n          }\n        },\n        {\n          name: 'preSetPlacement',\n          enabled: true,\n          phase: 'beforeMain',\n          fn: data => {\n            // Pre-set Popper's placement attribute in order to read the arrow sizes properly.\n            // Otherwise, Popper mixes up the width and height dimensions since the initial arrow style is for top placement\n            this._getTipElement().setAttribute('data-popper-placement', data.state.placement)\n          }\n        }\n      ]\n    }\n\n    return {\n      ...defaultBsPopperConfig,\n      ...execute(this._config.popperConfig, [defaultBsPopperConfig])\n    }\n  }\n\n  _setListeners() {\n    const triggers = this._config.trigger.split(' ')\n\n    for (const trigger of triggers) {\n      if (trigger === 'click') {\n        EventHandler.on(this._element, this.constructor.eventName(EVENT_CLICK), this._config.selector, event => {\n          const context = this._initializeOnDelegatedTarget(event)\n          context.toggle()\n        })\n      } else if (trigger !== TRIGGER_MANUAL) {\n        const eventIn = trigger === TRIGGER_HOVER ?\n          this.constructor.eventName(EVENT_MOUSEENTER) :\n          this.constructor.eventName(EVENT_FOCUSIN)\n        const eventOut = trigger === TRIGGER_HOVER ?\n          this.constructor.eventName(EVENT_MOUSELEAVE) :\n          this.constructor.eventName(EVENT_FOCUSOUT)\n\n        EventHandler.on(this._element, eventIn, this._config.selector, event => {\n          const context = this._initializeOnDelegatedTarget(event)\n          context._activeTrigger[event.type === 'focusin' ? TRIGGER_FOCUS : TRIGGER_HOVER] = true\n          context._enter()\n        })\n        EventHandler.on(this._element, eventOut, this._config.selector, event => {\n          const context = this._initializeOnDelegatedTarget(event)\n          context._activeTrigger[event.type === 'focusout' ? TRIGGER_FOCUS : TRIGGER_HOVER] =\n            context._element.contains(event.relatedTarget)\n\n          context._leave()\n        })\n      }\n    }\n\n    this._hideModalHandler = () => {\n      if (this._element) {\n        this.hide()\n      }\n    }\n\n    EventHandler.on(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler)\n  }\n\n  _fixTitle() {\n    const title = this._element.getAttribute('title')\n\n    if (!title) {\n      return\n    }\n\n    if (!this._element.getAttribute('aria-label') && !this._element.textContent.trim()) {\n      this._element.setAttribute('aria-label', title)\n    }\n\n    this._element.setAttribute('data-bs-original-title', title) // DO NOT USE IT. Is only for backwards compatibility\n    this._element.removeAttribute('title')\n  }\n\n  _enter() {\n    if (this._isShown() || this._isHovered) {\n      this._isHovered = true\n      return\n    }\n\n    this._isHovered = true\n\n    this._setTimeout(() => {\n      if (this._isHovered) {\n        this.show()\n      }\n    }, this._config.delay.show)\n  }\n\n  _leave() {\n    if (this._isWithActiveTrigger()) {\n      return\n    }\n\n    this._isHovered = false\n\n    this._setTimeout(() => {\n      if (!this._isHovered) {\n        this.hide()\n      }\n    }, this._config.delay.hide)\n  }\n\n  _setTimeout(handler, timeout) {\n    clearTimeout(this._timeout)\n    this._timeout = setTimeout(handler, timeout)\n  }\n\n  _isWithActiveTrigger() {\n    return Object.values(this._activeTrigger).includes(true)\n  }\n\n  _getConfig(config) {\n    const dataAttributes = Manipulator.getDataAttributes(this._element)\n\n    for (const dataAttribute of Object.keys(dataAttributes)) {\n      if (DISALLOWED_ATTRIBUTES.has(dataAttribute)) {\n        delete dataAttributes[dataAttribute]\n      }\n    }\n\n    config = {\n      ...dataAttributes,\n      ...(typeof config === 'object' && config ? config : {})\n    }\n    config = this._mergeConfigObj(config)\n    config = this._configAfterMerge(config)\n    this._typeCheckConfig(config)\n    return config\n  }\n\n  _configAfterMerge(config) {\n    config.container = config.container === false ? document.body : getElement(config.container)\n\n    if (typeof config.delay === 'number') {\n      config.delay = {\n        show: config.delay,\n        hide: config.delay\n      }\n    }\n\n    if (typeof config.title === 'number') {\n      config.title = config.title.toString()\n    }\n\n    if (typeof config.content === 'number') {\n      config.content = config.content.toString()\n    }\n\n    return config\n  }\n\n  _getDelegateConfig() {\n    const config = {}\n\n    for (const [key, value] of Object.entries(this._config)) {\n      if (this.constructor.Default[key] !== value) {\n        config[key] = value\n      }\n    }\n\n    config.selector = false\n    config.trigger = 'manual'\n\n    // In the future can be replaced with:\n    // const keysWithDifferentValues = Object.entries(this._config).filter(entry => this.constructor.Default[entry[0]] !== this._config[entry[0]])\n    // `Object.fromEntries(keysWithDifferentValues)`\n    return config\n  }\n\n  _disposePopper() {\n    if (this._popper) {\n      this._popper.destroy()\n      this._popper = null\n    }\n\n    if (this.tip) {\n      this.tip.remove()\n      this.tip = null\n    }\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Tooltip.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config]()\n    })\n  }\n}\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Tooltip)\n\nexport default Tooltip\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap popover.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Tooltip from './tooltip.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'popover'\n\nconst SELECTOR_TITLE = '.popover-header'\nconst SELECTOR_CONTENT = '.popover-body'\n\nconst Default = {\n  ...Tooltip.Default,\n  content: '',\n  offset: [0, 8],\n  placement: 'right',\n  template: '<div class=\"popover\" role=\"tooltip\">' +\n    '<div class=\"popover-arrow\"></div>' +\n    '<h3 class=\"popover-header\"></h3>' +\n    '<div class=\"popover-body\"></div>' +\n    '</div>',\n  trigger: 'click'\n}\n\nconst DefaultType = {\n  ...Tooltip.DefaultType,\n  content: '(null|string|element|function)'\n}\n\n/**\n * Class definition\n */\n\nclass Popover extends Tooltip {\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Overrides\n  _isWithContent() {\n    return this._getTitle() || this._getContent()\n  }\n\n  // Private\n  _getContentForTemplate() {\n    return {\n      [SELECTOR_TITLE]: this._getTitle(),\n      [SELECTOR_CONTENT]: this._getContent()\n    }\n  }\n\n  _getContent() {\n    return this._resolvePossibleFunction(this._config.content)\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Popover.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config]()\n    })\n  }\n}\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Popover)\n\nexport default Popover\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap scrollspy.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport { defineJQueryPlugin, getElement, isDisabled, isVisible } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'scrollspy'\nconst DATA_KEY = 'bs.scrollspy'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst EVENT_ACTIVATE = `activate${EVENT_KEY}`\nconst EVENT_CLICK = `click${EVENT_KEY}`\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_DROPDOWN_ITEM = 'dropdown-item'\nconst CLASS_NAME_ACTIVE = 'active'\n\nconst SELECTOR_DATA_SPY = '[data-bs-spy=\"scroll\"]'\nconst SELECTOR_TARGET_LINKS = '[href]'\nconst SELECTOR_NAV_LIST_GROUP = '.nav, .list-group'\nconst SELECTOR_NAV_LINKS = '.nav-link'\nconst SELECTOR_NAV_ITEMS = '.nav-item'\nconst SELECTOR_LIST_ITEMS = '.list-group-item'\nconst SELECTOR_LINK_ITEMS = `${SELECTOR_NAV_LINKS}, ${SELECTOR_NAV_ITEMS} > ${SELECTOR_NAV_LINKS}, ${SELECTOR_LIST_ITEMS}`\nconst SELECTOR_DROPDOWN = '.dropdown'\nconst SELECTOR_DROPDOWN_TOGGLE = '.dropdown-toggle'\n\nconst Default = {\n  offset: null, // TODO: v6 @deprecated, keep it for backwards compatibility reasons\n  rootMargin: '0px 0px -25%',\n  smoothScroll: false,\n  target: null,\n  threshold: [0.1, 0.5, 1]\n}\n\nconst DefaultType = {\n  offset: '(number|null)', // TODO v6 @deprecated, keep it for backwards compatibility reasons\n  rootMargin: 'string',\n  smoothScroll: 'boolean',\n  target: 'element',\n  threshold: 'array'\n}\n\n/**\n * Class definition\n */\n\nclass ScrollSpy extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    // this._element is the observablesContainer and config.target the menu links wrapper\n    this._targetLinks = new Map()\n    this._observableSections = new Map()\n    this._rootElement = getComputedStyle(this._element).overflowY === 'visible' ? null : this._element\n    this._activeTarget = null\n    this._observer = null\n    this._previousScrollData = {\n      visibleEntryTop: 0,\n      parentScrollTop: 0\n    }\n    this.refresh() // initialize\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  refresh() {\n    this._initializeTargetsAndObservables()\n    this._maybeEnableSmoothScroll()\n\n    if (this._observer) {\n      this._observer.disconnect()\n    } else {\n      this._observer = this._getNewObserver()\n    }\n\n    for (const section of this._observableSections.values()) {\n      this._observer.observe(section)\n    }\n  }\n\n  dispose() {\n    this._observer.disconnect()\n    super.dispose()\n  }\n\n  // Private\n  _configAfterMerge(config) {\n    // TODO: on v6 target should be given explicitly & remove the {target: 'ss-target'} case\n    config.target = getElement(config.target) || document.body\n\n    // TODO: v6 Only for backwards compatibility reasons. Use rootMargin only\n    config.rootMargin = config.offset ? `${config.offset}px 0px -30%` : config.rootMargin\n\n    if (typeof config.threshold === 'string') {\n      config.threshold = config.threshold.split(',').map(value => Number.parseFloat(value))\n    }\n\n    return config\n  }\n\n  _maybeEnableSmoothScroll() {\n    if (!this._config.smoothScroll) {\n      return\n    }\n\n    // unregister any previous listeners\n    EventHandler.off(this._config.target, EVENT_CLICK)\n\n    EventHandler.on(this._config.target, EVENT_CLICK, SELECTOR_TARGET_LINKS, event => {\n      const observableSection = this._observableSections.get(event.target.hash)\n      if (observableSection) {\n        event.preventDefault()\n        const root = this._rootElement || window\n        const height = observableSection.offsetTop - this._element.offsetTop\n        if (root.scrollTo) {\n          root.scrollTo({ top: height, behavior: 'smooth' })\n          return\n        }\n\n        // Chrome 60 doesn't support `scrollTo`\n        root.scrollTop = height\n      }\n    })\n  }\n\n  _getNewObserver() {\n    const options = {\n      root: this._rootElement,\n      threshold: this._config.threshold,\n      rootMargin: this._config.rootMargin\n    }\n\n    return new IntersectionObserver(entries => this._observerCallback(entries), options)\n  }\n\n  // The logic of selection\n  _observerCallback(entries) {\n    const targetElement = entry => this._targetLinks.get(`#${entry.target.id}`)\n    const activate = entry => {\n      this._previousScrollData.visibleEntryTop = entry.target.offsetTop\n      this._process(targetElement(entry))\n    }\n\n    const parentScrollTop = (this._rootElement || document.documentElement).scrollTop\n    const userScrollsDown = parentScrollTop >= this._previousScrollData.parentScrollTop\n    this._previousScrollData.parentScrollTop = parentScrollTop\n\n    for (const entry of entries) {\n      if (!entry.isIntersecting) {\n        this._activeTarget = null\n        this._clearActiveClass(targetElement(entry))\n\n        continue\n      }\n\n      const entryIsLowerThanPrevious = entry.target.offsetTop >= this._previousScrollData.visibleEntryTop\n      // if we are scrolling down, pick the bigger offsetTop\n      if (userScrollsDown && entryIsLowerThanPrevious) {\n        activate(entry)\n        // if parent isn't scrolled, let's keep the first visible item, breaking the iteration\n        if (!parentScrollTop) {\n          return\n        }\n\n        continue\n      }\n\n      // if we are scrolling up, pick the smallest offsetTop\n      if (!userScrollsDown && !entryIsLowerThanPrevious) {\n        activate(entry)\n      }\n    }\n  }\n\n  _initializeTargetsAndObservables() {\n    this._targetLinks = new Map()\n    this._observableSections = new Map()\n\n    const targetLinks = SelectorEngine.find(SELECTOR_TARGET_LINKS, this._config.target)\n\n    for (const anchor of targetLinks) {\n      // ensure that the anchor has an id and is not disabled\n      if (!anchor.hash || isDisabled(anchor)) {\n        continue\n      }\n\n      const observableSection = SelectorEngine.findOne(decodeURI(anchor.hash), this._element)\n\n      // ensure that the observableSection exists & is visible\n      if (isVisible(observableSection)) {\n        this._targetLinks.set(decodeURI(anchor.hash), anchor)\n        this._observableSections.set(anchor.hash, observableSection)\n      }\n    }\n  }\n\n  _process(target) {\n    if (this._activeTarget === target) {\n      return\n    }\n\n    this._clearActiveClass(this._config.target)\n    this._activeTarget = target\n    target.classList.add(CLASS_NAME_ACTIVE)\n    this._activateParents(target)\n\n    EventHandler.trigger(this._element, EVENT_ACTIVATE, { relatedTarget: target })\n  }\n\n  _activateParents(target) {\n    // Activate dropdown parents\n    if (target.classList.contains(CLASS_NAME_DROPDOWN_ITEM)) {\n      SelectorEngine.findOne(SELECTOR_DROPDOWN_TOGGLE, target.closest(SELECTOR_DROPDOWN))\n        .classList.add(CLASS_NAME_ACTIVE)\n      return\n    }\n\n    for (const listGroup of SelectorEngine.parents(target, SELECTOR_NAV_LIST_GROUP)) {\n      // Set triggered links parents as active\n      // With both <ul> and <nav> markup a parent is the previous sibling of any nav ancestor\n      for (const item of SelectorEngine.prev(listGroup, SELECTOR_LINK_ITEMS)) {\n        item.classList.add(CLASS_NAME_ACTIVE)\n      }\n    }\n  }\n\n  _clearActiveClass(parent) {\n    parent.classList.remove(CLASS_NAME_ACTIVE)\n\n    const activeNodes = SelectorEngine.find(`${SELECTOR_TARGET_LINKS}.${CLASS_NAME_ACTIVE}`, parent)\n    for (const node of activeNodes) {\n      node.classList.remove(CLASS_NAME_ACTIVE)\n    }\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = ScrollSpy.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config]()\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(window, EVENT_LOAD_DATA_API, () => {\n  for (const spy of SelectorEngine.find(SELECTOR_DATA_SPY)) {\n    ScrollSpy.getOrCreateInstance(spy)\n  }\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(ScrollSpy)\n\nexport default ScrollSpy\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap tab.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport { defineJQueryPlugin, getNextActiveElement, isDisabled } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'tab'\nconst DATA_KEY = 'bs.tab'\nconst EVENT_KEY = `.${DATA_KEY}`\n\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}`\nconst EVENT_KEYDOWN = `keydown${EVENT_KEY}`\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}`\n\nconst ARROW_LEFT_KEY = 'ArrowLeft'\nconst ARROW_RIGHT_KEY = 'ArrowRight'\nconst ARROW_UP_KEY = 'ArrowUp'\nconst ARROW_DOWN_KEY = 'ArrowDown'\nconst HOME_KEY = 'Home'\nconst END_KEY = 'End'\n\nconst CLASS_NAME_ACTIVE = 'active'\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_DROPDOWN = 'dropdown'\n\nconst SELECTOR_DROPDOWN_TOGGLE = '.dropdown-toggle'\nconst SELECTOR_DROPDOWN_MENU = '.dropdown-menu'\nconst NOT_SELECTOR_DROPDOWN_TOGGLE = ':not(.dropdown-toggle)'\n\nconst SELECTOR_TAB_PANEL = '.list-group, .nav, [role=\"tablist\"]'\nconst SELECTOR_OUTER = '.nav-item, .list-group-item'\nconst SELECTOR_INNER = `.nav-link${NOT_SELECTOR_DROPDOWN_TOGGLE}, .list-group-item${NOT_SELECTOR_DROPDOWN_TOGGLE}, [role=\"tab\"]${NOT_SELECTOR_DROPDOWN_TOGGLE}`\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"tab\"], [data-bs-toggle=\"pill\"], [data-bs-toggle=\"list\"]' // TODO: could only be `tab` in v6\nconst SELECTOR_INNER_ELEM = `${SELECTOR_INNER}, ${SELECTOR_DATA_TOGGLE}`\n\nconst SELECTOR_DATA_TOGGLE_ACTIVE = `.${CLASS_NAME_ACTIVE}[data-bs-toggle=\"tab\"], .${CLASS_NAME_ACTIVE}[data-bs-toggle=\"pill\"], .${CLASS_NAME_ACTIVE}[data-bs-toggle=\"list\"]`\n\n/**\n * Class definition\n */\n\nclass Tab extends BaseComponent {\n  constructor(element) {\n    super(element)\n    this._parent = this._element.closest(SELECTOR_TAB_PANEL)\n\n    if (!this._parent) {\n      return\n      // TODO: should throw exception in v6\n      // throw new TypeError(`${element.outerHTML} has not a valid parent ${SELECTOR_INNER_ELEM}`)\n    }\n\n    // Set up initial aria attributes\n    this._setInitialAttributes(this._parent, this._getChildren())\n\n    EventHandler.on(this._element, EVENT_KEYDOWN, event => this._keydown(event))\n  }\n\n  // Getters\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  show() { // Shows this elem and deactivate the active sibling if exists\n    const innerElem = this._element\n    if (this._elemIsActive(innerElem)) {\n      return\n    }\n\n    // Search for active tab on same parent to deactivate it\n    const active = this._getActiveElem()\n\n    const hideEvent = active ?\n      EventHandler.trigger(active, EVENT_HIDE, { relatedTarget: innerElem }) :\n      null\n\n    const showEvent = EventHandler.trigger(innerElem, EVENT_SHOW, { relatedTarget: active })\n\n    if (showEvent.defaultPrevented || (hideEvent && hideEvent.defaultPrevented)) {\n      return\n    }\n\n    this._deactivate(active, innerElem)\n    this._activate(innerElem, active)\n  }\n\n  // Private\n  _activate(element, relatedElem) {\n    if (!element) {\n      return\n    }\n\n    element.classList.add(CLASS_NAME_ACTIVE)\n\n    this._activate(SelectorEngine.getElementFromSelector(element)) // Search and activate/show the proper section\n\n    const complete = () => {\n      if (element.getAttribute('role') !== 'tab') {\n        element.classList.add(CLASS_NAME_SHOW)\n        return\n      }\n\n      element.removeAttribute('tabindex')\n      element.setAttribute('aria-selected', true)\n      this._toggleDropDown(element, true)\n      EventHandler.trigger(element, EVENT_SHOWN, {\n        relatedTarget: relatedElem\n      })\n    }\n\n    this._queueCallback(complete, element, element.classList.contains(CLASS_NAME_FADE))\n  }\n\n  _deactivate(element, relatedElem) {\n    if (!element) {\n      return\n    }\n\n    element.classList.remove(CLASS_NAME_ACTIVE)\n    element.blur()\n\n    this._deactivate(SelectorEngine.getElementFromSelector(element)) // Search and deactivate the shown section too\n\n    const complete = () => {\n      if (element.getAttribute('role') !== 'tab') {\n        element.classList.remove(CLASS_NAME_SHOW)\n        return\n      }\n\n      element.setAttribute('aria-selected', false)\n      element.setAttribute('tabindex', '-1')\n      this._toggleDropDown(element, false)\n      EventHandler.trigger(element, EVENT_HIDDEN, { relatedTarget: relatedElem })\n    }\n\n    this._queueCallback(complete, element, element.classList.contains(CLASS_NAME_FADE))\n  }\n\n  _keydown(event) {\n    if (!([ARROW_LEFT_KEY, ARROW_RIGHT_KEY, ARROW_UP_KEY, ARROW_DOWN_KEY, HOME_KEY, END_KEY].includes(event.key))) {\n      return\n    }\n\n    event.stopPropagation()// stopPropagation/preventDefault both added to support up/down keys without scrolling the page\n    event.preventDefault()\n\n    const children = this._getChildren().filter(element => !isDisabled(element))\n    let nextActiveElement\n\n    if ([HOME_KEY, END_KEY].includes(event.key)) {\n      nextActiveElement = children[event.key === HOME_KEY ? 0 : children.length - 1]\n    } else {\n      const isNext = [ARROW_RIGHT_KEY, ARROW_DOWN_KEY].includes(event.key)\n      nextActiveElement = getNextActiveElement(children, event.target, isNext, true)\n    }\n\n    if (nextActiveElement) {\n      nextActiveElement.focus({ preventScroll: true })\n      Tab.getOrCreateInstance(nextActiveElement).show()\n    }\n  }\n\n  _getChildren() { // collection of inner elements\n    return SelectorEngine.find(SELECTOR_INNER_ELEM, this._parent)\n  }\n\n  _getActiveElem() {\n    return this._getChildren().find(child => this._elemIsActive(child)) || null\n  }\n\n  _setInitialAttributes(parent, children) {\n    this._setAttributeIfNotExists(parent, 'role', 'tablist')\n\n    for (const child of children) {\n      this._setInitialAttributesOnChild(child)\n    }\n  }\n\n  _setInitialAttributesOnChild(child) {\n    child = this._getInnerElement(child)\n    const isActive = this._elemIsActive(child)\n    const outerElem = this._getOuterElement(child)\n    child.setAttribute('aria-selected', isActive)\n\n    if (outerElem !== child) {\n      this._setAttributeIfNotExists(outerElem, 'role', 'presentation')\n    }\n\n    if (!isActive) {\n      child.setAttribute('tabindex', '-1')\n    }\n\n    this._setAttributeIfNotExists(child, 'role', 'tab')\n\n    // set attributes to the related panel too\n    this._setInitialAttributesOnTargetPanel(child)\n  }\n\n  _setInitialAttributesOnTargetPanel(child) {\n    const target = SelectorEngine.getElementFromSelector(child)\n\n    if (!target) {\n      return\n    }\n\n    this._setAttributeIfNotExists(target, 'role', 'tabpanel')\n\n    if (child.id) {\n      this._setAttributeIfNotExists(target, 'aria-labelledby', `${child.id}`)\n    }\n  }\n\n  _toggleDropDown(element, open) {\n    const outerElem = this._getOuterElement(element)\n    if (!outerElem.classList.contains(CLASS_DROPDOWN)) {\n      return\n    }\n\n    const toggle = (selector, className) => {\n      const element = SelectorEngine.findOne(selector, outerElem)\n      if (element) {\n        element.classList.toggle(className, open)\n      }\n    }\n\n    toggle(SELECTOR_DROPDOWN_TOGGLE, CLASS_NAME_ACTIVE)\n    toggle(SELECTOR_DROPDOWN_MENU, CLASS_NAME_SHOW)\n    outerElem.setAttribute('aria-expanded', open)\n  }\n\n  _setAttributeIfNotExists(element, attribute, value) {\n    if (!element.hasAttribute(attribute)) {\n      element.setAttribute(attribute, value)\n    }\n  }\n\n  _elemIsActive(elem) {\n    return elem.classList.contains(CLASS_NAME_ACTIVE)\n  }\n\n  // Try to get the inner element (usually the .nav-link)\n  _getInnerElement(elem) {\n    return elem.matches(SELECTOR_INNER_ELEM) ? elem : SelectorEngine.findOne(SELECTOR_INNER_ELEM, elem)\n  }\n\n  // Try to get the outer element (usually the .nav-item)\n  _getOuterElement(elem) {\n    return elem.closest(SELECTOR_OUTER) || elem\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Tab.getOrCreateInstance(this)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config]()\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n  if (['A', 'AREA'].includes(this.tagName)) {\n    event.preventDefault()\n  }\n\n  if (isDisabled(this)) {\n    return\n  }\n\n  Tab.getOrCreateInstance(this).show()\n})\n\n/**\n * Initialize on focus\n */\nEventHandler.on(window, EVENT_LOAD_DATA_API, () => {\n  for (const element of SelectorEngine.find(SELECTOR_DATA_TOGGLE_ACTIVE)) {\n    Tab.getOrCreateInstance(element)\n  }\n})\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Tab)\n\nexport default Tab\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap toast.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport { defineJQueryPlugin, reflow } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'toast'\nconst DATA_KEY = 'bs.toast'\nconst EVENT_KEY = `.${DATA_KEY}`\n\nconst EVENT_MOUSEOVER = `mouseover${EVENT_KEY}`\nconst EVENT_MOUSEOUT = `mouseout${EVENT_KEY}`\nconst EVENT_FOCUSIN = `focusin${EVENT_KEY}`\nconst EVENT_FOCUSOUT = `focusout${EVENT_KEY}`\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\n\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_HIDE = 'hide' // @deprecated - kept here only for backwards compatibility\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_SHOWING = 'showing'\n\nconst DefaultType = {\n  animation: 'boolean',\n  autohide: 'boolean',\n  delay: 'number'\n}\n\nconst Default = {\n  animation: true,\n  autohide: true,\n  delay: 5000\n}\n\n/**\n * Class definition\n */\n\nclass Toast extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._timeout = null\n    this._hasMouseInteraction = false\n    this._hasKeyboardInteraction = false\n    this._setListeners()\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  show() {\n    const showEvent = EventHandler.trigger(this._element, EVENT_SHOW)\n\n    if (showEvent.defaultPrevented) {\n      return\n    }\n\n    this._clearTimeout()\n\n    if (this._config.animation) {\n      this._element.classList.add(CLASS_NAME_FADE)\n    }\n\n    const complete = () => {\n      this._element.classList.remove(CLASS_NAME_SHOWING)\n      EventHandler.trigger(this._element, EVENT_SHOWN)\n\n      this._maybeScheduleHide()\n    }\n\n    this._element.classList.remove(CLASS_NAME_HIDE) // @deprecated\n    reflow(this._element)\n    this._element.classList.add(CLASS_NAME_SHOW, CLASS_NAME_SHOWING)\n\n    this._queueCallback(complete, this._element, this._config.animation)\n  }\n\n  hide() {\n    if (!this.isShown()) {\n      return\n    }\n\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    const complete = () => {\n      this._element.classList.add(CLASS_NAME_HIDE) // @deprecated\n      this._element.classList.remove(CLASS_NAME_SHOWING, CLASS_NAME_SHOW)\n      EventHandler.trigger(this._element, EVENT_HIDDEN)\n    }\n\n    this._element.classList.add(CLASS_NAME_SHOWING)\n    this._queueCallback(complete, this._element, this._config.animation)\n  }\n\n  dispose() {\n    this._clearTimeout()\n\n    if (this.isShown()) {\n      this._element.classList.remove(CLASS_NAME_SHOW)\n    }\n\n    super.dispose()\n  }\n\n  isShown() {\n    return this._element.classList.contains(CLASS_NAME_SHOW)\n  }\n\n  // Private\n\n  _maybeScheduleHide() {\n    if (!this._config.autohide) {\n      return\n    }\n\n    if (this._hasMouseInteraction || this._hasKeyboardInteraction) {\n      return\n    }\n\n    this._timeout = setTimeout(() => {\n      this.hide()\n    }, this._config.delay)\n  }\n\n  _onInteraction(event, isInteracting) {\n    switch (event.type) {\n      case 'mouseover':\n      case 'mouseout': {\n        this._hasMouseInteraction = isInteracting\n        break\n      }\n\n      case 'focusin':\n      case 'focusout': {\n        this._hasKeyboardInteraction = isInteracting\n        break\n      }\n\n      default: {\n        break\n      }\n    }\n\n    if (isInteracting) {\n      this._clearTimeout()\n      return\n    }\n\n    const nextElement = event.relatedTarget\n    if (this._element === nextElement || this._element.contains(nextElement)) {\n      return\n    }\n\n    this._maybeScheduleHide()\n  }\n\n  _setListeners() {\n    EventHandler.on(this._element, EVENT_MOUSEOVER, event => this._onInteraction(event, true))\n    EventHandler.on(this._element, EVENT_MOUSEOUT, event => this._onInteraction(event, false))\n    EventHandler.on(this._element, EVENT_FOCUSIN, event => this._onInteraction(event, true))\n    EventHandler.on(this._element, EVENT_FOCUSOUT, event => this._onInteraction(event, false))\n  }\n\n  _clearTimeout() {\n    clearTimeout(this._timeout)\n    this._timeout = null\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Toast.getOrCreateInstance(this, config)\n\n      if (typeof config === 'string') {\n        if (typeof data[config] === 'undefined') {\n          throw new TypeError(`No method named \"${config}\"`)\n        }\n\n        data[config](this)\n      }\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nenableDismissTrigger(Toast)\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Toast)\n\nexport default Toast\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap index.umd.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Alert from './src/alert.js'\nimport Button from './src/button.js'\nimport Carousel from './src/carousel.js'\nimport Collapse from './src/collapse.js'\nimport Dropdown from './src/dropdown.js'\nimport Modal from './src/modal.js'\nimport Offcanvas from './src/offcanvas.js'\nimport Popover from './src/popover.js'\nimport ScrollSpy from './src/scrollspy.js'\nimport Tab from './src/tab.js'\nimport Toast from './src/toast.js'\nimport Tooltip from 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\ No newline at end of file
diff --git a/docs/deps/bootstrap-5.3.1/bootstrap.min.css b/docs/deps/bootstrap-5.3.1/bootstrap.min.css
new file mode 100644
index 0000000..3363cb2
--- /dev/null
+++ b/docs/deps/bootstrap-5.3.1/bootstrap.min.css
@@ -0,0 +1,5 @@
+:root{--bslib-bootstrap-version: 5;--bslib-preset-name: ;--bslib-preset-type: }/*!
+   * Bootstrap  v5.3.1 (https://getbootstrap.com/)
+   * Copyright 2011-2023 The Bootstrap Authors
+   * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)
+   */:root,[data-bs-theme="light"]{--bs-blue: #0d6efd;--bs-indigo: #6610f2;--bs-purple: #6f42c1;--bs-pink: #d63384;--bs-red: #dc3545;--bs-orange: #fd7e14;--bs-yellow: #ffc107;--bs-green: #198754;--bs-teal: #20c997;--bs-cyan: #0dcaf0;--bs-black: #000;--bs-white: #fff;--bs-gray: #6c757d;--bs-gray-dark: #343a40;--bs-gray-100: #f8f9fa;--bs-gray-200: #e9ecef;--bs-gray-300: #dee2e6;--bs-gray-400: #ced4da;--bs-gray-500: #adb5bd;--bs-gray-600: #6c757d;--bs-gray-700: #495057;--bs-gray-800: #343a40;--bs-gray-900: #212529;--bs-default: #dee2e6;--bs-primary: #0d6efd;--bs-secondary: #6c757d;--bs-success: #198754;--bs-info: #0dcaf0;--bs-warning: #ffc107;--bs-danger: #dc3545;--bs-light: #f8f9fa;--bs-dark: #212529;--bs-default-rgb: 222,226,230;--bs-primary-rgb: 13,110,253;--bs-secondary-rgb: 108,117,125;--bs-success-rgb: 25,135,84;--bs-info-rgb: 13,202,240;--bs-warning-rgb: 255,193,7;--bs-danger-rgb: 220,53,69;--bs-light-rgb: 248,249,250;--bs-dark-rgb: 33,37,41;--bs-primary-text-emphasis: 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#198754;--bs-btn-border-color: #198754;--bs-btn-hover-color: #fff;--bs-btn-hover-bg: #198754;--bs-btn-hover-border-color: #198754;--bs-btn-focus-shadow-rgb: 25,135,84;--bs-btn-active-color: #fff;--bs-btn-active-bg: #198754;--bs-btn-active-border-color: #198754;--bs-btn-active-shadow: inset 0 3px 5px rgba(0,0,0,0.125);--bs-btn-disabled-color: #198754;--bs-btn-disabled-bg: transparent;--bs-btn-disabled-border-color: #198754;--bs-btn-bg: transparent;--bs-gradient: none}.btn-outline-info{--bs-btn-color: #0dcaf0;--bs-btn-border-color: #0dcaf0;--bs-btn-hover-color: #000;--bs-btn-hover-bg: #0dcaf0;--bs-btn-hover-border-color: #0dcaf0;--bs-btn-focus-shadow-rgb: 13,202,240;--bs-btn-active-color: #000;--bs-btn-active-bg: #0dcaf0;--bs-btn-active-border-color: #0dcaf0;--bs-btn-active-shadow: inset 0 3px 5px rgba(0,0,0,0.125);--bs-btn-disabled-color: #0dcaf0;--bs-btn-disabled-bg: transparent;--bs-btn-disabled-border-color: #0dcaf0;--bs-btn-bg: transparent;--bs-gradient: none}.btn-outline-warning{--bs-btn-color: #ffc107;--bs-btn-border-color: #ffc107;--bs-btn-hover-color: #000;--bs-btn-hover-bg: #ffc107;--bs-btn-hover-border-color: #ffc107;--bs-btn-focus-shadow-rgb: 255,193,7;--bs-btn-active-color: #000;--bs-btn-active-bg: #ffc107;--bs-btn-active-border-color: #ffc107;--bs-btn-active-shadow: inset 0 3px 5px rgba(0,0,0,0.125);--bs-btn-disabled-color: #ffc107;--bs-btn-disabled-bg: transparent;--bs-btn-disabled-border-color: #ffc107;--bs-btn-bg: transparent;--bs-gradient: none}.btn-outline-danger{--bs-btn-color: #dc3545;--bs-btn-border-color: #dc3545;--bs-btn-hover-color: #fff;--bs-btn-hover-bg: #dc3545;--bs-btn-hover-border-color: #dc3545;--bs-btn-focus-shadow-rgb: 220,53,69;--bs-btn-active-color: #fff;--bs-btn-active-bg: #dc3545;--bs-btn-active-border-color: #dc3545;--bs-btn-active-shadow: inset 0 3px 5px rgba(0,0,0,0.125);--bs-btn-disabled-color: #dc3545;--bs-btn-disabled-bg: transparent;--bs-btn-disabled-border-color: #dc3545;--bs-btn-bg: transparent;--bs-gradient: none}.btn-outline-light{--bs-btn-color: #f8f9fa;--bs-btn-border-color: #f8f9fa;--bs-btn-hover-color: #000;--bs-btn-hover-bg: #f8f9fa;--bs-btn-hover-border-color: #f8f9fa;--bs-btn-focus-shadow-rgb: 248,249,250;--bs-btn-active-color: #000;--bs-btn-active-bg: #f8f9fa;--bs-btn-active-border-color: #f8f9fa;--bs-btn-active-shadow: inset 0 3px 5px rgba(0,0,0,0.125);--bs-btn-disabled-color: #f8f9fa;--bs-btn-disabled-bg: transparent;--bs-btn-disabled-border-color: #f8f9fa;--bs-btn-bg: transparent;--bs-gradient: none}.btn-outline-dark{--bs-btn-color: #212529;--bs-btn-border-color: #212529;--bs-btn-hover-color: #fff;--bs-btn-hover-bg: #212529;--bs-btn-hover-border-color: #212529;--bs-btn-focus-shadow-rgb: 33,37,41;--bs-btn-active-color: #fff;--bs-btn-active-bg: #212529;--bs-btn-active-border-color: #212529;--bs-btn-active-shadow: inset 0 3px 5px rgba(0,0,0,0.125);--bs-btn-disabled-color: #212529;--bs-btn-disabled-bg: transparent;--bs-btn-disabled-border-color: #212529;--bs-btn-bg: transparent;--bs-gradient: none}.btn-link{--bs-btn-font-weight: 400;--bs-btn-color: var(--bs-link-color);--bs-btn-bg: transparent;--bs-btn-border-color: transparent;--bs-btn-hover-color: var(--bs-link-hover-color);--bs-btn-hover-border-color: transparent;--bs-btn-active-color: var(--bs-link-hover-color);--bs-btn-active-border-color: transparent;--bs-btn-disabled-color: #6c757d;--bs-btn-disabled-border-color: transparent;--bs-btn-box-shadow: 0 0 0 #000;--bs-btn-focus-shadow-rgb: 49,132,253;text-decoration:underline;-webkit-text-decoration:underline;-moz-text-decoration:underline;-ms-text-decoration:underline;-o-text-decoration:underline}.btn-link:focus-visible{color:var(--bs-btn-color)}.btn-link:hover{color:var(--bs-btn-hover-color)}.btn-lg,.btn-group-lg>.btn{--bs-btn-padding-y: .5rem;--bs-btn-padding-x: 1rem;--bs-btn-font-size:1.25rem;--bs-btn-border-radius: var(--bs-border-radius-lg)}.btn-sm,.btn-group-sm>.btn{--bs-btn-padding-y: .25rem;--bs-btn-padding-x: .5rem;--bs-btn-font-size:.875rem;--bs-btn-border-radius: var(--bs-border-radius-sm)}.fade{transition:opacity 0.15s linear}@media (prefers-reduced-motion: reduce){.fade{transition:none}}.fade:not(.show){opacity:0}.collapse:not(.show){display:none}.collapsing{height:0;overflow:hidden;transition:height 0.35s ease}@media (prefers-reduced-motion: reduce){.collapsing{transition:none}}.collapsing.collapse-horizontal{width:0;height:auto;transition:width 0.35s ease}@media (prefers-reduced-motion: reduce){.collapsing.collapse-horizontal{transition:none}}.dropup,.dropend,.dropdown,.dropstart,.dropup-center,.dropdown-center{position:relative}.dropdown-toggle{white-space:nowrap}.dropdown-toggle::after{display:inline-block;margin-left:.255em;vertical-align:.255em;content:"";border-top:.3em solid;border-right:.3em solid transparent;border-bottom:0;border-left:.3em solid transparent}.dropdown-toggle:empty::after{margin-left:0}.dropdown-menu{--bs-dropdown-zindex: 1000;--bs-dropdown-min-width: 10rem;--bs-dropdown-padding-x: 0;--bs-dropdown-padding-y: .5rem;--bs-dropdown-spacer: .125rem;--bs-dropdown-font-size:1rem;--bs-dropdown-color: var(--bs-body-color);--bs-dropdown-bg: var(--bs-body-bg);--bs-dropdown-border-color: var(--bs-border-color-translucent);--bs-dropdown-border-radius: var(--bs-border-radius);--bs-dropdown-border-width: var(--bs-border-width);--bs-dropdown-inner-border-radius: calc(var(--bs-border-radius) - var(--bs-border-width));--bs-dropdown-divider-bg: var(--bs-border-color-translucent);--bs-dropdown-divider-margin-y: .5rem;--bs-dropdown-box-shadow: 0 0.5rem 1rem rgba(0,0,0,0.15);--bs-dropdown-link-color: var(--bs-body-color);--bs-dropdown-link-hover-color: var(--bs-body-color);--bs-dropdown-link-hover-bg: var(--bs-tertiary-bg);--bs-dropdown-link-active-color: #fff;--bs-dropdown-link-active-bg: #0d6efd;--bs-dropdown-link-disabled-color: var(--bs-tertiary-color);--bs-dropdown-item-padding-x: 1rem;--bs-dropdown-item-padding-y: .25rem;--bs-dropdown-header-color: #6c757d;--bs-dropdown-header-padding-x: 1rem;--bs-dropdown-header-padding-y: .5rem;position:absolute;z-index:var(--bs-dropdown-zindex);display:none;min-width:var(--bs-dropdown-min-width);padding:var(--bs-dropdown-padding-y) var(--bs-dropdown-padding-x);margin:0;font-size:var(--bs-dropdown-font-size);color:var(--bs-dropdown-color);text-align:left;list-style:none;background-color:var(--bs-dropdown-bg);background-clip:padding-box;border:var(--bs-dropdown-border-width) solid var(--bs-dropdown-border-color);border-radius:var(--bs-dropdown-border-radius)}.dropdown-menu[data-bs-popper]{top:100%;left:0;margin-top:var(--bs-dropdown-spacer)}.dropdown-menu-start{--bs-position: start}.dropdown-menu-start[data-bs-popper]{right:auto;left:0}.dropdown-menu-end{--bs-position: end}.dropdown-menu-end[data-bs-popper]{right:0;left:auto}@media (min-width: 576px){.dropdown-menu-sm-start{--bs-position: start}.dropdown-menu-sm-start[data-bs-popper]{right:auto;left:0}.dropdown-menu-sm-end{--bs-position: 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.dropdown-toggle::after{display:inline-block;margin-left:.255em;vertical-align:.255em;content:""}.dropstart .dropdown-toggle::after{display:none}.dropstart .dropdown-toggle::before{display:inline-block;margin-right:.255em;vertical-align:.255em;content:"";border-top:.3em solid transparent;border-right:.3em solid;border-bottom:.3em solid transparent}.dropstart .dropdown-toggle:empty::after{margin-left:0}.dropstart .dropdown-toggle::before{vertical-align:0}.dropdown-divider{height:0;margin:var(--bs-dropdown-divider-margin-y) 0;overflow:hidden;border-top:1px solid var(--bs-dropdown-divider-bg);opacity:1}.dropdown-item{display:block;width:100%;padding:var(--bs-dropdown-item-padding-y) 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var(--bs-dropdown-header-padding-x);margin-bottom:0;font-size:.875rem;color:var(--bs-dropdown-header-color);white-space:nowrap}.dropdown-item-text{display:block;padding:var(--bs-dropdown-item-padding-y) var(--bs-dropdown-item-padding-x);color:var(--bs-dropdown-link-color)}.dropdown-menu-dark{--bs-dropdown-color: #dee2e6;--bs-dropdown-bg: #343a40;--bs-dropdown-border-color: var(--bs-border-color-translucent);--bs-dropdown-box-shadow: ;--bs-dropdown-link-color: #dee2e6;--bs-dropdown-link-hover-color: #fff;--bs-dropdown-divider-bg: var(--bs-border-color-translucent);--bs-dropdown-link-hover-bg: rgba(255,255,255,0.15);--bs-dropdown-link-active-color: #fff;--bs-dropdown-link-active-bg: #0d6efd;--bs-dropdown-link-disabled-color: #adb5bd;--bs-dropdown-header-color: #adb5bd}.btn-group,.btn-group-vertical{position:relative;display:inline-flex;vertical-align:middle}.btn-group>.btn,.btn-group-vertical>.btn{position:relative;flex:1 1 auto;-webkit-flex:1 1 auto}.btn-group>.btn-check:checked+.btn,.btn-group>.btn-check:focus+.btn,.btn-group>.btn:hover,.btn-group>.btn:focus,.btn-group>.btn:active,.btn-group>.btn.active,.btn-group-vertical>.btn-check:checked+.btn,.btn-group-vertical>.btn-check:focus+.btn,.btn-group-vertical>.btn:hover,.btn-group-vertical>.btn:focus,.btn-group-vertical>.btn:active,.btn-group-vertical>.btn.active{z-index:1}.btn-toolbar{display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;justify-content:flex-start;-webkit-justify-content:flex-start}.btn-toolbar .input-group{width:auto}.btn-group{border-radius:var(--bs-border-radius)}.btn-group>:not(.btn-check:first-child)+.btn,.btn-group>.btn-group:not(:first-child){margin-left:calc(var(--bs-border-width) * -1)}.btn-group>.btn:not(:last-child):not(.dropdown-toggle),.btn-group>.btn.dropdown-toggle-split:first-child,.btn-group>.btn-group:not(:last-child)>.btn{border-top-right-radius:0;border-bottom-right-radius:0}.btn-group>.btn:nth-child(n + 3),.btn-group>:not(.btn-check)+.btn,.btn-group>.btn-group:not(:first-child)>.btn{border-top-left-radius:0;border-bottom-left-radius:0}.dropdown-toggle-split{padding-right:.5625rem;padding-left:.5625rem}.dropdown-toggle-split::after,.dropup .dropdown-toggle-split::after,.dropend .dropdown-toggle-split::after{margin-left:0}.dropstart .dropdown-toggle-split::before{margin-right:0}.btn-sm+.dropdown-toggle-split,.btn-group-sm>.btn+.dropdown-toggle-split{padding-right:.375rem;padding-left:.375rem}.btn-lg+.dropdown-toggle-split,.btn-group-lg>.btn+.dropdown-toggle-split{padding-right:.75rem;padding-left:.75rem}.btn-group-vertical{flex-direction:column;-webkit-flex-direction:column;align-items:flex-start;-webkit-align-items:flex-start;justify-content:center;-webkit-justify-content:center}.btn-group-vertical>.btn,.btn-group-vertical>.btn-group{width:100%}.btn-group-vertical>.btn:not(:first-child),.btn-group-vertical>.btn-group:not(:first-child){margin-top:calc(var(--bs-border-width) * -1)}.btn-group-vertical>.btn:not(:last-child):not(.dropdown-toggle),.btn-group-vertical>.btn-group:not(:last-child)>.btn{border-bottom-right-radius:0;border-bottom-left-radius:0}.btn-group-vertical>.btn~.btn,.btn-group-vertical>.btn-group:not(:first-child)>.btn{border-top-left-radius:0;border-top-right-radius:0}.nav{--bs-nav-link-padding-x: 1rem;--bs-nav-link-padding-y: .5rem;--bs-nav-link-font-weight: ;--bs-nav-link-color: var(--bs-link-color);--bs-nav-link-hover-color: var(--bs-link-hover-color);--bs-nav-link-disabled-color: var(--bs-secondary-color);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding-left:0;margin-bottom:0;list-style:none}.nav-link{display:block;padding:var(--bs-nav-link-padding-y) var(--bs-nav-link-padding-x);font-size:var(--bs-nav-link-font-size);font-weight:var(--bs-nav-link-font-weight);color:var(--bs-nav-link-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background:none;border:0;transition:color 0.15s ease-in-out,background-color 0.15s ease-in-out,border-color 0.15s ease-in-out}@media (prefers-reduced-motion: reduce){.nav-link{transition:none}}.nav-link:hover,.nav-link:focus{color:var(--bs-nav-link-hover-color)}.nav-link:focus-visible{outline:0;box-shadow:0 0 0 .25rem rgba(13,110,253,0.25)}.nav-link.disabled,.nav-link:disabled{color:var(--bs-nav-link-disabled-color);pointer-events:none;cursor:default}.nav-tabs{--bs-nav-tabs-border-width: var(--bs-border-width);--bs-nav-tabs-border-color: var(--bs-border-color);--bs-nav-tabs-border-radius: var(--bs-border-radius);--bs-nav-tabs-link-hover-border-color: var(--bs-secondary-bg) var(--bs-secondary-bg) var(--bs-border-color);--bs-nav-tabs-link-active-color: var(--bs-emphasis-color);--bs-nav-tabs-link-active-bg: var(--bs-body-bg);--bs-nav-tabs-link-active-border-color: var(--bs-border-color) var(--bs-border-color) var(--bs-body-bg);border-bottom:var(--bs-nav-tabs-border-width) solid var(--bs-nav-tabs-border-color)}.nav-tabs .nav-link{margin-bottom:calc(-1 * var(--bs-nav-tabs-border-width));border:var(--bs-nav-tabs-border-width) solid transparent;border-top-left-radius:var(--bs-nav-tabs-border-radius);border-top-right-radius:var(--bs-nav-tabs-border-radius)}.nav-tabs .nav-link:hover,.nav-tabs .nav-link:focus{isolation:isolate;border-color:var(--bs-nav-tabs-link-hover-border-color)}.nav-tabs .nav-link.active,.nav-tabs .nav-item.show .nav-link{color:var(--bs-nav-tabs-link-active-color);background-color:var(--bs-nav-tabs-link-active-bg);border-color:var(--bs-nav-tabs-link-active-border-color)}.nav-tabs .dropdown-menu{margin-top:calc(-1 * var(--bs-nav-tabs-border-width));border-top-left-radius:0;border-top-right-radius:0}.nav-pills{--bs-nav-pills-border-radius: var(--bs-border-radius);--bs-nav-pills-link-active-color: #fff;--bs-nav-pills-link-active-bg: #0d6efd}.nav-pills .nav-link{border-radius:var(--bs-nav-pills-border-radius)}.nav-pills .nav-link.active,.nav-pills .show>.nav-link{color:var(--bs-nav-pills-link-active-color);background-color:var(--bs-nav-pills-link-active-bg)}.nav-underline{--bs-nav-underline-gap: 1rem;--bs-nav-underline-border-width: .125rem;--bs-nav-underline-link-active-color: var(--bs-emphasis-color);gap:var(--bs-nav-underline-gap)}.nav-underline .nav-link{padding-right:0;padding-left:0;border-bottom:var(--bs-nav-underline-border-width) solid transparent}.nav-underline .nav-link:hover,.nav-underline .nav-link:focus{border-bottom-color:currentcolor}.nav-underline .nav-link.active,.nav-underline .show>.nav-link{font-weight:700;color:var(--bs-nav-underline-link-active-color);border-bottom-color:currentcolor}.nav-fill>.nav-link,.nav-fill .nav-item{flex:1 1 auto;-webkit-flex:1 1 auto;text-align:center}.nav-justified>.nav-link,.nav-justified .nav-item{flex-basis:0;-webkit-flex-basis:0;flex-grow:1;-webkit-flex-grow:1;text-align:center}.nav-fill .nav-item .nav-link,.nav-justified .nav-item .nav-link{width:100%}.tab-content>.tab-pane{display:none}.tab-content>.active{display:block}.navbar,:where([data-bs-theme="light"]) .navbar{--bs-navbar-padding-x: 0;--bs-navbar-padding-y: .5rem;--bs-navbar-color: rgba(var(--bs-emphasis-color-rgb), 0.65);--bs-navbar-hover-color: rgba(var(--bs-emphasis-color-rgb), 0.8);--bs-navbar-disabled-color: rgba(var(--bs-emphasis-color-rgb), 0.3);--bs-navbar-active-color: rgba(var(--bs-emphasis-color-rgb), 1);--bs-navbar-brand-padding-y: .3125rem;--bs-navbar-brand-margin-end: 1rem;--bs-navbar-brand-font-size: 1.25rem;--bs-navbar-brand-color: 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url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23052c65'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-focus-border-color: #86b7fe;--bs-accordion-btn-focus-box-shadow: 0 0 0 .25rem rgba(13,110,253,0.25);--bs-accordion-body-padding-x: 1.25rem;--bs-accordion-body-padding-y: 1rem;--bs-accordion-active-color: var(--bs-primary-text-emphasis);--bs-accordion-active-bg: var(--bs-primary-bg-subtle)}.accordion-button{position:relative;display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;width:100%;padding:var(--bs-accordion-btn-padding-y) var(--bs-accordion-btn-padding-x);font-size:1rem;color:var(--bs-accordion-btn-color);text-align:left;background-color:var(--bs-accordion-btn-bg);border:0;border-radius:0;overflow-anchor:none;transition:var(--bs-accordion-transition)}@media 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reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme="dark"] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: var(--bs-secondary-color);--bs-breadcrumb-item-padding-x: .5rem;--bs-breadcrumb-item-active-color: var(--bs-secondary-color);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, "/") /* rtl: var(--bs-breadcrumb-divider, "/") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: .75rem;--bs-pagination-padding-y: .375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: var(--bs-link-color);--bs-pagination-bg: var(--bs-body-bg);--bs-pagination-border-width: var(--bs-border-width);--bs-pagination-border-color: var(--bs-border-color);--bs-pagination-border-radius: var(--bs-border-radius);--bs-pagination-hover-color: var(--bs-link-hover-color);--bs-pagination-hover-bg: var(--bs-tertiary-bg);--bs-pagination-hover-border-color: var(--bs-border-color);--bs-pagination-focus-color: var(--bs-link-hover-color);--bs-pagination-focus-bg: var(--bs-secondary-bg);--bs-pagination-focus-box-shadow: 0 0 0 .25rem rgba(13,110,253,0.25);--bs-pagination-active-color: #fff;--bs-pagination-active-bg: #0d6efd;--bs-pagination-active-border-color: #0d6efd;--bs-pagination-disabled-color: var(--bs-secondary-color);--bs-pagination-disabled-bg: var(--bs-secondary-bg);--bs-pagination-disabled-border-color: var(--bs-border-color);display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color 0.15s ease-in-out,background-color 0.15s ease-in-out,border-color 0.15s ease-in-out,box-shadow 0.15s ease-in-out}@media (prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(var(--bs-border-width) * -1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: .75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: var(--bs-border-radius-lg)}.pagination-sm{--bs-pagination-padding-x: .5rem;--bs-pagination-padding-y: .25rem;--bs-pagination-font-size:.875rem;--bs-pagination-border-radius: var(--bs-border-radius-sm)}.badge{--bs-badge-padding-x: .65em;--bs-badge-padding-y: .35em;--bs-badge-font-size:.75em;--bs-badge-font-weight: 700;--bs-badge-color: #fff;--bs-badge-border-radius: var(--bs-border-radius);display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: var(--bs-border-width) solid var(--bs-alert-border-color);--bs-alert-border-radius: var(--bs-border-radius);--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:.75rem;--bs-progress-bg: var(--bs-secondary-bg);--bs-progress-border-radius: var(--bs-border-radius);--bs-progress-box-shadow: var(--bs-box-shadow-inset);--bs-progress-bar-color: #fff;--bs-progress-bar-bg: #0d6efd;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media (prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media (prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: var(--bs-body-color);--bs-list-group-bg: var(--bs-body-bg);--bs-list-group-border-color: var(--bs-border-color);--bs-list-group-border-width: var(--bs-border-width);--bs-list-group-border-radius: var(--bs-border-radius);--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: .5rem;--bs-list-group-action-color: var(--bs-secondary-color);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-tertiary-bg);--bs-list-group-action-active-color: var(--bs-body-color);--bs-list-group-action-active-bg: var(--bs-secondary-bg);--bs-list-group-disabled-color: var(--bs-secondary-color);--bs-list-group-disabled-bg: var(--bs-body-bg);--bs-list-group-active-color: #fff;--bs-list-group-active-bg: #0d6efd;--bs-list-group-active-border-color: #0d6efd;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") ". ";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1 * var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media (min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xxl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-primary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-primary-border-subtle);--bs-list-group-active-color: var(--bs-primary-bg-subtle);--bs-list-group-active-bg: var(--bs-primary-text-emphasis);--bs-list-group-active-border-color: var(--bs-primary-text-emphasis)}.list-group-item-secondary{--bs-list-group-color: var(--bs-secondary-text-emphasis);--bs-list-group-bg: var(--bs-secondary-bg-subtle);--bs-list-group-border-color: var(--bs-secondary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-secondary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-secondary-border-subtle);--bs-list-group-active-color: var(--bs-secondary-bg-subtle);--bs-list-group-active-bg: var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23000'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e");--bs-btn-close-opacity: .5;--bs-btn-close-hover-opacity: .75;--bs-btn-close-focus-shadow: 0 0 0 .25rem rgba(13,110,253,0.25);--bs-btn-close-focus-opacity: 1;--bs-btn-close-disabled-opacity: .25;--bs-btn-close-white-filter: invert(1) grayscale(100%) brightness(200%);box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:var(--bs-btn-close-color);background:transparent var(--bs-btn-close-bg) center/1em auto no-repeat;border:0;border-radius:.375rem;opacity:var(--bs-btn-close-opacity)}.btn-close:hover{color:var(--bs-btn-close-color);text-decoration:none;opacity:var(--bs-btn-close-hover-opacity)}.btn-close:focus{outline:0;box-shadow:var(--bs-btn-close-focus-shadow);opacity:var(--bs-btn-close-focus-opacity)}.btn-close:disabled,.btn-close.disabled{pointer-events:none;user-select:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;-o-user-select:none;opacity:var(--bs-btn-close-disabled-opacity)}.btn-close-white{filter:var(--bs-btn-close-white-filter)}[data-bs-theme="dark"] .btn-close{filter:var(--bs-btn-close-white-filter)}.toast{--bs-toast-zindex: 1090;--bs-toast-padding-x: .75rem;--bs-toast-padding-y: .5rem;--bs-toast-spacing: 1.5rem;--bs-toast-max-width: 350px;--bs-toast-font-size:.875rem;--bs-toast-color: ;--bs-toast-bg: rgba(var(--bs-body-bg-rgb), 0.85);--bs-toast-border-width: var(--bs-border-width);--bs-toast-border-color: var(--bs-border-color-translucent);--bs-toast-border-radius: var(--bs-border-radius);--bs-toast-box-shadow: var(--bs-box-shadow);--bs-toast-header-color: var(--bs-secondary-color);--bs-toast-header-bg: rgba(var(--bs-body-bg-rgb), 0.85);--bs-toast-header-border-color: var(--bs-border-color-translucent);width:var(--bs-toast-max-width);max-width:100%;font-size:var(--bs-toast-font-size);color:var(--bs-toast-color);pointer-events:auto;background-color:var(--bs-toast-bg);background-clip:padding-box;border:var(--bs-toast-border-width) solid var(--bs-toast-border-color);box-shadow:var(--bs-toast-box-shadow);border-radius:var(--bs-toast-border-radius)}.toast.showing{opacity:0}.toast:not(.show){display:none}.toast-container{--bs-toast-zindex: 1090;position:absolute;z-index:var(--bs-toast-zindex);width:max-content;width:-webkit-max-content;width:-moz-max-content;width:-ms-max-content;width:-o-max-content;max-width:100%;pointer-events:none}.toast-container>:not(:last-child){margin-bottom:var(--bs-toast-spacing)}.toast-header{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;padding:var(--bs-toast-padding-y) var(--bs-toast-padding-x);color:var(--bs-toast-header-color);background-color:var(--bs-toast-header-bg);background-clip:padding-box;border-bottom:var(--bs-toast-border-width) solid var(--bs-toast-header-border-color);border-top-left-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width));border-top-right-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width))}.toast-header .btn-close{margin-right:calc(-.5 * var(--bs-toast-padding-x));margin-left:var(--bs-toast-padding-x)}.toast-body{padding:var(--bs-toast-padding-x);word-wrap:break-word}.modal{--bs-modal-zindex: 1055;--bs-modal-width: 500px;--bs-modal-padding: 1rem;--bs-modal-margin: .5rem;--bs-modal-color: ;--bs-modal-bg: var(--bs-body-bg);--bs-modal-border-color: var(--bs-border-color-translucent);--bs-modal-border-width: var(--bs-border-width);--bs-modal-border-radius: var(--bs-border-radius-lg);--bs-modal-box-shadow: 0 0.125rem 0.25rem rgba(0,0,0,0.075);--bs-modal-inner-border-radius: calc(var(--bs-border-radius-lg) - (var(--bs-border-width)));--bs-modal-header-padding-x: 1rem;--bs-modal-header-padding-y: 1rem;--bs-modal-header-padding: 1rem 1rem;--bs-modal-header-border-color: var(--bs-border-color);--bs-modal-header-border-width: var(--bs-border-width);--bs-modal-title-line-height: 1.5;--bs-modal-footer-gap: .5rem;--bs-modal-footer-bg: ;--bs-modal-footer-border-color: var(--bs-border-color);--bs-modal-footer-border-width: var(--bs-border-width);position:fixed;top:0;left:0;z-index:var(--bs-modal-zindex);display:none;width:100%;height:100%;overflow-x:hidden;overflow-y:auto;outline:0}.modal-dialog{position:relative;width:auto;margin:var(--bs-modal-margin);pointer-events:none}.modal.fade .modal-dialog{transition:transform 0.3s ease-out;transform:translate(0, -50px)}@media (prefers-reduced-motion: reduce){.modal.fade .modal-dialog{transition:none}}.modal.show .modal-dialog{transform:none}.modal.modal-static .modal-dialog{transform:scale(1.02)}.modal-dialog-scrollable{height:calc(100% - var(--bs-modal-margin) * 2)}.modal-dialog-scrollable .modal-content{max-height:100%;overflow:hidden}.modal-dialog-scrollable .modal-body{overflow-y:auto}.modal-dialog-centered{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;min-height:calc(100% - var(--bs-modal-margin) * 2)}.modal-content{position:relative;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;width:100%;color:var(--bs-modal-color);pointer-events:auto;background-color:var(--bs-modal-bg);background-clip:padding-box;border:var(--bs-modal-border-width) solid var(--bs-modal-border-color);border-radius:var(--bs-modal-border-radius);outline:0}.modal-backdrop{--bs-backdrop-zindex: 1050;--bs-backdrop-bg: #000;--bs-backdrop-opacity: .5;position:fixed;top:0;left:0;z-index:var(--bs-backdrop-zindex);width:100vw;height:100vh;background-color:var(--bs-backdrop-bg)}.modal-backdrop.fade{opacity:0}.modal-backdrop.show{opacity:var(--bs-backdrop-opacity)}.modal-header{display:flex;display:-webkit-flex;flex-shrink:0;-webkit-flex-shrink:0;align-items:center;-webkit-align-items:center;justify-content:space-between;-webkit-justify-content:space-between;padding:var(--bs-modal-header-padding);border-bottom:var(--bs-modal-header-border-width) solid 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.modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-sm-down .modal-header,.modal-fullscreen-sm-down .modal-footer{border-radius:0}.modal-fullscreen-sm-down .modal-body{overflow-y:auto}}@media (max-width: 767.98px){.modal-fullscreen-md-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-md-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-md-down .modal-header,.modal-fullscreen-md-down .modal-footer{border-radius:0}.modal-fullscreen-md-down .modal-body{overflow-y:auto}}@media (max-width: 991.98px){.modal-fullscreen-lg-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-lg-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-lg-down .modal-header,.modal-fullscreen-lg-down .modal-footer{border-radius:0}.modal-fullscreen-lg-down .modal-body{overflow-y:auto}}@media (max-width: 1199.98px){.modal-fullscreen-xl-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-xl-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-xl-down .modal-header,.modal-fullscreen-xl-down .modal-footer{border-radius:0}.modal-fullscreen-xl-down .modal-body{overflow-y:auto}}@media (max-width: 1399.98px){.modal-fullscreen-xxl-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-xxl-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-xxl-down .modal-header,.modal-fullscreen-xxl-down .modal-footer{border-radius:0}.modal-fullscreen-xxl-down .modal-body{overflow-y:auto}}.tooltip{--bs-tooltip-zindex: 1080;--bs-tooltip-max-width: 200px;--bs-tooltip-padding-x: .5rem;--bs-tooltip-padding-y: .25rem;--bs-tooltip-margin: ;--bs-tooltip-font-size:.875rem;--bs-tooltip-color: var(--bs-body-bg);--bs-tooltip-bg: var(--bs-emphasis-color);--bs-tooltip-border-radius: var(--bs-border-radius);--bs-tooltip-opacity: .9;--bs-tooltip-arrow-width: .8rem;--bs-tooltip-arrow-height: .4rem;z-index:var(--bs-tooltip-zindex);display:block;margin:var(--bs-tooltip-margin);font-family:var(--bs-font-sans-serif);font-style:normal;font-weight:400;line-height:1.5;text-align:left;text-align:start;text-decoration:none;text-shadow:none;text-transform:none;letter-spacing:normal;word-break:normal;white-space:normal;word-spacing:normal;line-break:auto;font-size:var(--bs-tooltip-font-size);word-wrap:break-word;opacity:0}.tooltip.show{opacity:var(--bs-tooltip-opacity)}.tooltip .tooltip-arrow{display:block;width:var(--bs-tooltip-arrow-width);height:var(--bs-tooltip-arrow-height)}.tooltip .tooltip-arrow::before{position:absolute;content:"";border-color:transparent;border-style:solid}.bs-tooltip-top .tooltip-arrow,.bs-tooltip-auto[data-popper-placement^="top"] .tooltip-arrow{bottom:calc(-1 * var(--bs-tooltip-arrow-height))}.bs-tooltip-top .tooltip-arrow::before,.bs-tooltip-auto[data-popper-placement^="top"] .tooltip-arrow::before{top:-1px;border-width:var(--bs-tooltip-arrow-height) 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var(--bs-border-width);--bs-popover-border-color: var(--bs-border-color-translucent);--bs-popover-border-radius: var(--bs-border-radius-lg);--bs-popover-inner-border-radius: calc(var(--bs-border-radius-lg) - var(--bs-border-width));--bs-popover-box-shadow: 0 0.5rem 1rem rgba(0,0,0,0.15);--bs-popover-header-padding-x: 1rem;--bs-popover-header-padding-y: .5rem;--bs-popover-header-font-size:1rem;--bs-popover-header-color: inherit;--bs-popover-header-bg: var(--bs-secondary-bg);--bs-popover-body-padding-x: 1rem;--bs-popover-body-padding-y: 1rem;--bs-popover-body-color: var(--bs-body-color);--bs-popover-arrow-width: 1rem;--bs-popover-arrow-height: .5rem;--bs-popover-arrow-border: 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diff --git a/docs/deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js b/docs/deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js
new file mode 100644
index 0000000..c628326
--- /dev/null
+++ b/docs/deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js
@@ -0,0 +1,5 @@
+/*!
+ * Bootstrap Table of Contents v1.0.1 (http://afeld.github.io/bootstrap-toc/)
+ * Copyright 2015 Aidan Feldman
+ * Licensed under MIT (https://github.com/afeld/bootstrap-toc/blob/gh-pages/LICENSE.md) */
+!function(a){"use strict";window.Toc={helpers:{findOrFilter:function(e,t){var n=e.find(t);return e.filter(t).add(n).filter(":not([data-toc-skip])")},generateUniqueIdBase:function(e){return a(e).text().trim().replace(/\'/gi,"").replace(/[& +$,:;=?@"#{}|^~[`%!'<>\]\.\/\(\)\*\\\n\t\b\v]/g,"-").replace(/-{2,}/g,"-").substring(0,64).replace(/^-+|-+$/gm,"").toLowerCase()||e.tagName.toLowerCase()},generateUniqueId:function(e){for(var t=this.generateUniqueIdBase(e),n=0;;n++){var r=t;if(0<n&&(r+="-"+n),!document.getElementById(r))return r}},generateAnchor:function(e){if(e.id)return e.id;var t=this.generateUniqueId(e);return e.id=t},createNavList:function(){return a('<ul class="nav navbar-nav"></ul>')},createChildNavList:function(e){var t=this.createNavList();return e.append(t),t},generateNavEl:function(e,t){var n=a('<a class="nav-link"></a>');n.attr("href","#"+e),n.text(t);var r=a("<li></li>");return r.append(n),r},generateNavItem:function(e){var t=this.generateAnchor(e),n=a(e),r=n.data("toc-text")||n.text();return this.generateNavEl(t,r)},getTopLevel:function(e){for(var t=1;t<=6;t++){if(1<this.findOrFilter(e,"h"+t).length)return t}return 1},getHeadings:function(e,t){var n="h"+t,r="h"+(t+1);return this.findOrFilter(e,n+","+r)},getNavLevel:function(e){return parseInt(e.tagName.charAt(1),10)},populateNav:function(r,a,e){var i,s=r,c=this;e.each(function(e,t){var n=c.generateNavItem(t);c.getNavLevel(t)===a?s=r:i&&s===r&&(s=c.createChildNavList(i)),s.append(n),i=n})},parseOps:function(e){var t;return(t=e.jquery?{$nav:e}:e).$scope=t.$scope||a(document.body),t}},init:function(e){(e=this.helpers.parseOps(e)).$nav.attr("data-toggle","toc");var t=this.helpers.createChildNavList(e.$nav),n=this.helpers.getTopLevel(e.$scope),r=this.helpers.getHeadings(e.$scope,n);this.helpers.populateNav(t,n,r)}},a(function(){a('nav[data-toggle="toc"]').each(function(e,t){var n=a(t);Toc.init(n)})})}(jQuery);
\ No newline at end of file
diff --git a/docs/deps/clipboard.js-2.0.11/clipboard.min.js b/docs/deps/clipboard.js-2.0.11/clipboard.min.js
new file mode 100644
index 0000000..1103f81
--- /dev/null
+++ b/docs/deps/clipboard.js-2.0.11/clipboard.min.js
@@ -0,0 +1,7 @@
+/*!
+ * clipboard.js v2.0.11
+ * https://clipboardjs.com/
+ *
+ * Licensed MIT © Zeno Rocha
+ */
+!function(t,e){"object"==typeof exports&&"object"==typeof module?module.exports=e():"function"==typeof define&&define.amd?define([],e):"object"==typeof exports?exports.ClipboardJS=e():t.ClipboardJS=e()}(this,function(){return n={686:function(t,e,n){"use strict";n.d(e,{default:function(){return b}});var e=n(279),i=n.n(e),e=n(370),u=n.n(e),e=n(817),r=n.n(e);function c(t){try{return document.execCommand(t)}catch(t){return}}var a=function(t){t=r()(t);return c("cut"),t};function o(t,e){var n,o,t=(n=t,o="rtl"===document.documentElement.getAttribute("dir"),(t=document.createElement("textarea")).style.fontSize="12pt",t.style.border="0",t.style.padding="0",t.style.margin="0",t.style.position="absolute",t.style[o?"right":"left"]="-9999px",o=window.pageYOffset||document.documentElement.scrollTop,t.style.top="".concat(o,"px"),t.setAttribute("readonly",""),t.value=n,t);return e.container.appendChild(t),e=r()(t),c("copy"),t.remove(),e}var f=function(t){var e=1<arguments.length&&void 0!==arguments[1]?arguments[1]:{container:document.body},n="";return"string"==typeof t?n=o(t,e):t instanceof HTMLInputElement&&!["text","search","url","tel","password"].includes(null==t?void 0:t.type)?n=o(t.value,e):(n=r()(t),c("copy")),n};function l(t){return(l="function"==typeof Symbol&&"symbol"==typeof Symbol.iterator?function(t){return typeof t}:function(t){return t&&"function"==typeof Symbol&&t.constructor===Symbol&&t!==Symbol.prototype?"symbol":typeof t})(t)}var s=function(){var t=0<arguments.length&&void 0!==arguments[0]?arguments[0]:{},e=t.action,n=void 0===e?"copy":e,o=t.container,e=t.target,t=t.text;if("copy"!==n&&"cut"!==n)throw new Error('Invalid "action" value, use either "copy" or "cut"');if(void 0!==e){if(!e||"object"!==l(e)||1!==e.nodeType)throw new Error('Invalid "target" value, use a valid Element');if("copy"===n&&e.hasAttribute("disabled"))throw new Error('Invalid "target" attribute. 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\ No newline at end of file
diff --git a/docs/deps/data-deps.txt b/docs/deps/data-deps.txt
index 21592b5..ca4dfd9 100644
--- a/docs/deps/data-deps.txt
+++ b/docs/deps/data-deps.txt
@@ -1,4 +1,13 @@
 <script src="deps/jquery-3.6.0/jquery-3.6.0.min.js"></script>
 <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no" />
-<link href="deps/bootstrap-5.2.2/bootstrap.min.css" rel="stylesheet" />
-<script src="deps/bootstrap-5.2.2/bootstrap.bundle.min.js"></script>
+<link href="deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet" />
+<script src="deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script>
+<link href="deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet" />
+<link href="deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet" />
+<script src="deps/headroom-0.11.0/headroom.min.js"></script>
+<script src="deps/headroom-0.11.0/jQuery.headroom.min.js"></script>
+<script src="deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script>
+<script src="deps/clipboard.js-2.0.11/clipboard.min.js"></script>
+<script src="deps/search-1.0.0/autocomplete.jquery.min.js"></script>
+<script src="deps/search-1.0.0/fuse.min.js"></script>
+<script src="deps/search-1.0.0/mark.min.js"></script>
diff --git a/docs/deps/font-awesome-6.5.2/css/all.css b/docs/deps/font-awesome-6.5.2/css/all.css
new file mode 100644
index 0000000..151dd57
--- /dev/null
+++ b/docs/deps/font-awesome-6.5.2/css/all.css
@@ -0,0 +1,8028 @@
+/*!
+ * Font Awesome Free 6.5.2 by @fontawesome - https://fontawesome.com
+ * License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License)
+ * Copyright 2024 Fonticons, Inc.
+ */
+.fa {
+  font-family: var(--fa-style-family, "Font Awesome 6 Free");
+  font-weight: var(--fa-style, 900); }
+
+.fa,
+.fa-classic,
+.fa-sharp,
+.fas,
+.fa-solid,
+.far,
+.fa-regular,
+.fab,
+.fa-brands {
+  -moz-osx-font-smoothing: grayscale;
+  -webkit-font-smoothing: antialiased;
+  display: var(--fa-display, inline-block);
+  font-style: normal;
+  font-variant: normal;
+  line-height: 1;
+  text-rendering: auto; }
+
+.fas,
+.fa-classic,
+.fa-solid,
+.far,
+.fa-regular {
+  font-family: 'Font Awesome 6 Free'; }
+
+.fab,
+.fa-brands {
+  font-family: 'Font Awesome 6 Brands'; }
+
+.fa-1x {
+  font-size: 1em; }
+
+.fa-2x {
+  font-size: 2em; }
+
+.fa-3x {
+  font-size: 3em; }
+
+.fa-4x {
+  font-size: 4em; }
+
+.fa-5x {
+  font-size: 5em; }
+
+.fa-6x {
+  font-size: 6em; }
+
+.fa-7x {
+  font-size: 7em; }
+
+.fa-8x {
+  font-size: 8em; }
+
+.fa-9x {
+  font-size: 9em; }
+
+.fa-10x {
+  font-size: 10em; }
+
+.fa-2xs {
+  font-size: 0.625em;
+  line-height: 0.1em;
+  vertical-align: 0.225em; }
+
+.fa-xs {
+  font-size: 0.75em;
+  line-height: 0.08333em;
+  vertical-align: 0.125em; }
+
+.fa-sm {
+  font-size: 0.875em;
+  line-height: 0.07143em;
+  vertical-align: 0.05357em; }
+
+.fa-lg {
+  font-size: 1.25em;
+  line-height: 0.05em;
+  vertical-align: -0.075em; }
+
+.fa-xl {
+  font-size: 1.5em;
+  line-height: 0.04167em;
+  vertical-align: -0.125em; }
+
+.fa-2xl {
+  font-size: 2em;
+  line-height: 0.03125em;
+  vertical-align: -0.1875em; }
+
+.fa-fw {
+  text-align: center;
+  width: 1.25em; }
+
+.fa-ul {
+  list-style-type: none;
+  margin-left: var(--fa-li-margin, 2.5em);
+  padding-left: 0; }
+  .fa-ul > li {
+    position: relative; }
+
+.fa-li {
+  left: calc(var(--fa-li-width, 2em) * -1);
+  position: absolute;
+  text-align: center;
+  width: var(--fa-li-width, 2em);
+  line-height: inherit; }
+
+.fa-border {
+  border-color: var(--fa-border-color, #eee);
+  border-radius: var(--fa-border-radius, 0.1em);
+  border-style: var(--fa-border-style, solid);
+  border-width: var(--fa-border-width, 0.08em);
+  padding: var(--fa-border-padding, 0.2em 0.25em 0.15em); }
+
+.fa-pull-left {
+  float: left;
+  margin-right: var(--fa-pull-margin, 0.3em); }
+
+.fa-pull-right {
+  float: right;
+  margin-left: var(--fa-pull-margin, 0.3em); }
+
+.fa-beat {
+  -webkit-animation-name: fa-beat;
+          animation-name: fa-beat;
+  -webkit-animation-delay: var(--fa-animation-delay, 0s);
+          animation-delay: var(--fa-animation-delay, 0s);
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 1s);
+          animation-duration: var(--fa-animation-duration, 1s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, ease-in-out);
+          animation-timing-function: var(--fa-animation-timing, ease-in-out); }
+
+.fa-bounce {
+  -webkit-animation-name: fa-bounce;
+          animation-name: fa-bounce;
+  -webkit-animation-delay: var(--fa-animation-delay, 0s);
+          animation-delay: var(--fa-animation-delay, 0s);
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 1s);
+          animation-duration: var(--fa-animation-duration, 1s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.28, 0.84, 0.42, 1));
+          animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.28, 0.84, 0.42, 1)); }
+
+.fa-fade {
+  -webkit-animation-name: fa-fade;
+          animation-name: fa-fade;
+  -webkit-animation-delay: var(--fa-animation-delay, 0s);
+          animation-delay: var(--fa-animation-delay, 0s);
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 1s);
+          animation-duration: var(--fa-animation-duration, 1s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.4, 0, 0.6, 1));
+          animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.4, 0, 0.6, 1)); }
+
+.fa-beat-fade {
+  -webkit-animation-name: fa-beat-fade;
+          animation-name: fa-beat-fade;
+  -webkit-animation-delay: var(--fa-animation-delay, 0s);
+          animation-delay: var(--fa-animation-delay, 0s);
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 1s);
+          animation-duration: var(--fa-animation-duration, 1s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.4, 0, 0.6, 1));
+          animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.4, 0, 0.6, 1)); }
+
+.fa-flip {
+  -webkit-animation-name: fa-flip;
+          animation-name: fa-flip;
+  -webkit-animation-delay: var(--fa-animation-delay, 0s);
+          animation-delay: var(--fa-animation-delay, 0s);
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 1s);
+          animation-duration: var(--fa-animation-duration, 1s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, ease-in-out);
+          animation-timing-function: var(--fa-animation-timing, ease-in-out); }
+
+.fa-shake {
+  -webkit-animation-name: fa-shake;
+          animation-name: fa-shake;
+  -webkit-animation-delay: var(--fa-animation-delay, 0s);
+          animation-delay: var(--fa-animation-delay, 0s);
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 1s);
+          animation-duration: var(--fa-animation-duration, 1s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, linear);
+          animation-timing-function: var(--fa-animation-timing, linear); }
+
+.fa-spin {
+  -webkit-animation-name: fa-spin;
+          animation-name: fa-spin;
+  -webkit-animation-delay: var(--fa-animation-delay, 0s);
+          animation-delay: var(--fa-animation-delay, 0s);
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 2s);
+          animation-duration: var(--fa-animation-duration, 2s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, linear);
+          animation-timing-function: var(--fa-animation-timing, linear); }
+
+.fa-spin-reverse {
+  --fa-animation-direction: reverse; }
+
+.fa-pulse,
+.fa-spin-pulse {
+  -webkit-animation-name: fa-spin;
+          animation-name: fa-spin;
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 1s);
+          animation-duration: var(--fa-animation-duration, 1s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, steps(8));
+          animation-timing-function: var(--fa-animation-timing, steps(8)); }
+
+@media (prefers-reduced-motion: reduce) {
+  .fa-beat,
+  .fa-bounce,
+  .fa-fade,
+  .fa-beat-fade,
+  .fa-flip,
+  .fa-pulse,
+  .fa-shake,
+  .fa-spin,
+  .fa-spin-pulse {
+    -webkit-animation-delay: -1ms;
+            animation-delay: -1ms;
+    -webkit-animation-duration: 1ms;
+            animation-duration: 1ms;
+    -webkit-animation-iteration-count: 1;
+            animation-iteration-count: 1;
+    -webkit-transition-delay: 0s;
+            transition-delay: 0s;
+    -webkit-transition-duration: 0s;
+            transition-duration: 0s; } }
+
+@-webkit-keyframes fa-beat {
+  0%, 90% {
+    -webkit-transform: scale(1);
+            transform: scale(1); }
+  45% {
+    -webkit-transform: scale(var(--fa-beat-scale, 1.25));
+            transform: scale(var(--fa-beat-scale, 1.25)); } }
+
+@keyframes fa-beat {
+  0%, 90% {
+    -webkit-transform: scale(1);
+            transform: scale(1); }
+  45% {
+    -webkit-transform: scale(var(--fa-beat-scale, 1.25));
+            transform: scale(var(--fa-beat-scale, 1.25)); } }
+
+@-webkit-keyframes fa-bounce {
+  0% {
+    -webkit-transform: scale(1, 1) translateY(0);
+            transform: scale(1, 1) translateY(0); }
+  10% {
+    -webkit-transform: scale(var(--fa-bounce-start-scale-x, 1.1), var(--fa-bounce-start-scale-y, 0.9)) translateY(0);
+            transform: scale(var(--fa-bounce-start-scale-x, 1.1), var(--fa-bounce-start-scale-y, 0.9)) translateY(0); }
+  30% {
+    -webkit-transform: scale(var(--fa-bounce-jump-scale-x, 0.9), var(--fa-bounce-jump-scale-y, 1.1)) translateY(var(--fa-bounce-height, -0.5em));
+            transform: scale(var(--fa-bounce-jump-scale-x, 0.9), var(--fa-bounce-jump-scale-y, 1.1)) translateY(var(--fa-bounce-height, -0.5em)); }
+  50% {
+    -webkit-transform: scale(var(--fa-bounce-land-scale-x, 1.05), var(--fa-bounce-land-scale-y, 0.95)) translateY(0);
+            transform: scale(var(--fa-bounce-land-scale-x, 1.05), var(--fa-bounce-land-scale-y, 0.95)) translateY(0); }
+  57% {
+    -webkit-transform: scale(1, 1) translateY(var(--fa-bounce-rebound, -0.125em));
+            transform: scale(1, 1) translateY(var(--fa-bounce-rebound, -0.125em)); }
+  64% {
+    -webkit-transform: scale(1, 1) translateY(0);
+            transform: scale(1, 1) translateY(0); }
+  100% {
+    -webkit-transform: scale(1, 1) translateY(0);
+            transform: scale(1, 1) translateY(0); } }
+
+@keyframes fa-bounce {
+  0% {
+    -webkit-transform: scale(1, 1) translateY(0);
+            transform: scale(1, 1) translateY(0); }
+  10% {
+    -webkit-transform: scale(var(--fa-bounce-start-scale-x, 1.1), var(--fa-bounce-start-scale-y, 0.9)) translateY(0);
+            transform: scale(var(--fa-bounce-start-scale-x, 1.1), var(--fa-bounce-start-scale-y, 0.9)) translateY(0); }
+  30% {
+    -webkit-transform: scale(var(--fa-bounce-jump-scale-x, 0.9), var(--fa-bounce-jump-scale-y, 1.1)) translateY(var(--fa-bounce-height, -0.5em));
+            transform: scale(var(--fa-bounce-jump-scale-x, 0.9), var(--fa-bounce-jump-scale-y, 1.1)) translateY(var(--fa-bounce-height, -0.5em)); }
+  50% {
+    -webkit-transform: scale(var(--fa-bounce-land-scale-x, 1.05), var(--fa-bounce-land-scale-y, 0.95)) translateY(0);
+            transform: scale(var(--fa-bounce-land-scale-x, 1.05), var(--fa-bounce-land-scale-y, 0.95)) translateY(0); }
+  57% {
+    -webkit-transform: scale(1, 1) translateY(var(--fa-bounce-rebound, -0.125em));
+            transform: scale(1, 1) translateY(var(--fa-bounce-rebound, -0.125em)); }
+  64% {
+    -webkit-transform: scale(1, 1) translateY(0);
+            transform: scale(1, 1) translateY(0); }
+  100% {
+    -webkit-transform: scale(1, 1) translateY(0);
+            transform: scale(1, 1) translateY(0); } }
+
+@-webkit-keyframes fa-fade {
+  50% {
+    opacity: var(--fa-fade-opacity, 0.4); } }
+
+@keyframes fa-fade {
+  50% {
+    opacity: var(--fa-fade-opacity, 0.4); } }
+
+@-webkit-keyframes fa-beat-fade {
+  0%, 100% {
+    opacity: var(--fa-beat-fade-opacity, 0.4);
+    -webkit-transform: scale(1);
+            transform: scale(1); }
+  50% {
+    opacity: 1;
+    -webkit-transform: scale(var(--fa-beat-fade-scale, 1.125));
+            transform: scale(var(--fa-beat-fade-scale, 1.125)); } }
+
+@keyframes fa-beat-fade {
+  0%, 100% {
+    opacity: var(--fa-beat-fade-opacity, 0.4);
+    -webkit-transform: scale(1);
+            transform: scale(1); }
+  50% {
+    opacity: 1;
+    -webkit-transform: scale(var(--fa-beat-fade-scale, 1.125));
+            transform: scale(var(--fa-beat-fade-scale, 1.125)); } }
+
+@-webkit-keyframes fa-flip {
+  50% {
+    -webkit-transform: rotate3d(var(--fa-flip-x, 0), var(--fa-flip-y, 1), var(--fa-flip-z, 0), var(--fa-flip-angle, -180deg));
+            transform: rotate3d(var(--fa-flip-x, 0), var(--fa-flip-y, 1), var(--fa-flip-z, 0), var(--fa-flip-angle, -180deg)); } }
+
+@keyframes fa-flip {
+  50% {
+    -webkit-transform: rotate3d(var(--fa-flip-x, 0), var(--fa-flip-y, 1), var(--fa-flip-z, 0), var(--fa-flip-angle, -180deg));
+            transform: rotate3d(var(--fa-flip-x, 0), var(--fa-flip-y, 1), var(--fa-flip-z, 0), var(--fa-flip-angle, -180deg)); } }
+
+@-webkit-keyframes fa-shake {
+  0% {
+    -webkit-transform: rotate(-15deg);
+            transform: rotate(-15deg); }
+  4% {
+    -webkit-transform: rotate(15deg);
+            transform: rotate(15deg); }
+  8%, 24% {
+    -webkit-transform: rotate(-18deg);
+            transform: rotate(-18deg); }
+  12%, 28% {
+    -webkit-transform: rotate(18deg);
+            transform: rotate(18deg); }
+  16% {
+    -webkit-transform: rotate(-22deg);
+            transform: rotate(-22deg); }
+  20% {
+    -webkit-transform: rotate(22deg);
+            transform: rotate(22deg); }
+  32% {
+    -webkit-transform: rotate(-12deg);
+            transform: rotate(-12deg); }
+  36% {
+    -webkit-transform: rotate(12deg);
+            transform: rotate(12deg); }
+  40%, 100% {
+    -webkit-transform: rotate(0deg);
+            transform: rotate(0deg); } }
+
+@keyframes fa-shake {
+  0% {
+    -webkit-transform: rotate(-15deg);
+            transform: rotate(-15deg); }
+  4% {
+    -webkit-transform: rotate(15deg);
+            transform: rotate(15deg); }
+  8%, 24% {
+    -webkit-transform: rotate(-18deg);
+            transform: rotate(-18deg); }
+  12%, 28% {
+    -webkit-transform: rotate(18deg);
+            transform: rotate(18deg); }
+  16% {
+    -webkit-transform: rotate(-22deg);
+            transform: rotate(-22deg); }
+  20% {
+    -webkit-transform: rotate(22deg);
+            transform: rotate(22deg); }
+  32% {
+    -webkit-transform: rotate(-12deg);
+            transform: rotate(-12deg); }
+  36% {
+    -webkit-transform: rotate(12deg);
+            transform: rotate(12deg); }
+  40%, 100% {
+    -webkit-transform: rotate(0deg);
+            transform: rotate(0deg); } }
+
+@-webkit-keyframes fa-spin {
+  0% {
+    -webkit-transform: rotate(0deg);
+            transform: rotate(0deg); }
+  100% {
+    -webkit-transform: rotate(360deg);
+            transform: rotate(360deg); } }
+
+@keyframes fa-spin {
+  0% {
+    -webkit-transform: rotate(0deg);
+            transform: rotate(0deg); }
+  100% {
+    -webkit-transform: rotate(360deg);
+            transform: rotate(360deg); } }
+
+.fa-rotate-90 {
+  -webkit-transform: rotate(90deg);
+          transform: rotate(90deg); }
+
+.fa-rotate-180 {
+  -webkit-transform: rotate(180deg);
+          transform: rotate(180deg); }
+
+.fa-rotate-270 {
+  -webkit-transform: rotate(270deg);
+          transform: rotate(270deg); }
+
+.fa-flip-horizontal {
+  -webkit-transform: scale(-1, 1);
+          transform: scale(-1, 1); }
+
+.fa-flip-vertical {
+  -webkit-transform: scale(1, -1);
+          transform: scale(1, -1); }
+
+.fa-flip-both,
+.fa-flip-horizontal.fa-flip-vertical {
+  -webkit-transform: scale(-1, -1);
+          transform: scale(-1, -1); }
+
+.fa-rotate-by {
+  -webkit-transform: rotate(var(--fa-rotate-angle, 0));
+          transform: rotate(var(--fa-rotate-angle, 0)); }
+
+.fa-stack {
+  display: inline-block;
+  height: 2em;
+  line-height: 2em;
+  position: relative;
+  vertical-align: middle;
+  width: 2.5em; }
+
+.fa-stack-1x,
+.fa-stack-2x {
+  left: 0;
+  position: absolute;
+  text-align: center;
+  width: 100%;
+  z-index: var(--fa-stack-z-index, auto); }
+
+.fa-stack-1x {
+  line-height: inherit; }
+
+.fa-stack-2x {
+  font-size: 2em; }
+
+.fa-inverse {
+  color: var(--fa-inverse, #fff); }
+
+/* Font Awesome uses the Unicode Private Use Area (PUA) to ensure screen
+readers do not read off random characters that represent icons */
+
+.fa-0::before {
+  content: "\30"; }
+
+.fa-1::before {
+  content: "\31"; }
+
+.fa-2::before {
+  content: "\32"; }
+
+.fa-3::before {
+  content: "\33"; }
+
+.fa-4::before {
+  content: "\34"; }
+
+.fa-5::before {
+  content: "\35"; }
+
+.fa-6::before {
+  content: "\36"; }
+
+.fa-7::before {
+  content: "\37"; }
+
+.fa-8::before {
+  content: "\38"; }
+
+.fa-9::before {
+  content: "\39"; }
+
+.fa-fill-drip::before {
+  content: "\f576"; }
+
+.fa-arrows-to-circle::before {
+  content: "\e4bd"; }
+
+.fa-circle-chevron-right::before {
+  content: "\f138"; }
+
+.fa-chevron-circle-right::before {
+  content: "\f138"; }
+
+.fa-at::before {
+  content: "\40"; }
+
+.fa-trash-can::before {
+  content: "\f2ed"; }
+
+.fa-trash-alt::before {
+  content: "\f2ed"; }
+
+.fa-text-height::before {
+  content: "\f034"; }
+
+.fa-user-xmark::before {
+  content: "\f235"; }
+
+.fa-user-times::before {
+  content: "\f235"; }
+
+.fa-stethoscope::before {
+  content: "\f0f1"; }
+
+.fa-message::before {
+  content: "\f27a"; }
+
+.fa-comment-alt::before {
+  content: "\f27a"; }
+
+.fa-info::before {
+  content: "\f129"; }
+
+.fa-down-left-and-up-right-to-center::before {
+  content: "\f422"; }
+
+.fa-compress-alt::before {
+  content: "\f422"; }
+
+.fa-explosion::before {
+  content: "\e4e9"; }
+
+.fa-file-lines::before {
+  content: "\f15c"; }
+
+.fa-file-alt::before {
+  content: "\f15c"; }
+
+.fa-file-text::before {
+  content: "\f15c"; }
+
+.fa-wave-square::before {
+  content: "\f83e"; }
+
+.fa-ring::before {
+  content: "\f70b"; }
+
+.fa-building-un::before {
+  content: "\e4d9"; }
+
+.fa-dice-three::before {
+  content: "\f527"; }
+
+.fa-calendar-days::before {
+  content: "\f073"; }
+
+.fa-calendar-alt::before {
+  content: "\f073"; }
+
+.fa-anchor-circle-check::before {
+  content: "\e4aa"; }
+
+.fa-building-circle-arrow-right::before {
+  content: "\e4d1"; }
+
+.fa-volleyball::before {
+  content: "\f45f"; }
+
+.fa-volleyball-ball::before {
+  content: "\f45f"; }
+
+.fa-arrows-up-to-line::before {
+  content: "\e4c2"; }
+
+.fa-sort-down::before {
+  content: "\f0dd"; }
+
+.fa-sort-desc::before {
+  content: "\f0dd"; }
+
+.fa-circle-minus::before {
+  content: "\f056"; }
+
+.fa-minus-circle::before {
+  content: "\f056"; }
+
+.fa-door-open::before {
+  content: "\f52b"; }
+
+.fa-right-from-bracket::before {
+  content: "\f2f5"; }
+
+.fa-sign-out-alt::before {
+  content: "\f2f5"; }
+
+.fa-atom::before {
+  content: "\f5d2"; }
+
+.fa-soap::before {
+  content: "\e06e"; }
+
+.fa-icons::before {
+  content: "\f86d"; }
+
+.fa-heart-music-camera-bolt::before {
+  content: "\f86d"; }
+
+.fa-microphone-lines-slash::before {
+  content: "\f539"; }
+
+.fa-microphone-alt-slash::before {
+  content: "\f539"; }
+
+.fa-bridge-circle-check::before {
+  content: "\e4c9"; }
+
+.fa-pump-medical::before {
+  content: "\e06a"; }
+
+.fa-fingerprint::before {
+  content: "\f577"; }
+
+.fa-hand-point-right::before {
+  content: "\f0a4"; }
+
+.fa-magnifying-glass-location::before {
+  content: "\f689"; }
+
+.fa-search-location::before {
+  content: "\f689"; }
+
+.fa-forward-step::before {
+  content: "\f051"; }
+
+.fa-step-forward::before {
+  content: "\f051"; }
+
+.fa-face-smile-beam::before {
+  content: "\f5b8"; }
+
+.fa-smile-beam::before {
+  content: "\f5b8"; }
+
+.fa-flag-checkered::before {
+  content: "\f11e"; }
+
+.fa-football::before {
+  content: "\f44e"; }
+
+.fa-football-ball::before {
+  content: "\f44e"; }
+
+.fa-school-circle-exclamation::before {
+  content: "\e56c"; }
+
+.fa-crop::before {
+  content: "\f125"; }
+
+.fa-angles-down::before {
+  content: "\f103"; }
+
+.fa-angle-double-down::before {
+  content: "\f103"; }
+
+.fa-users-rectangle::before {
+  content: "\e594"; }
+
+.fa-people-roof::before {
+  content: "\e537"; }
+
+.fa-people-line::before {
+  content: "\e534"; }
+
+.fa-beer-mug-empty::before {
+  content: "\f0fc"; }
+
+.fa-beer::before {
+  content: "\f0fc"; }
+
+.fa-diagram-predecessor::before {
+  content: "\e477"; }
+
+.fa-arrow-up-long::before {
+  content: "\f176"; }
+
+.fa-long-arrow-up::before {
+  content: "\f176"; }
+
+.fa-fire-flame-simple::before {
+  content: "\f46a"; }
+
+.fa-burn::before {
+  content: "\f46a"; }
+
+.fa-person::before {
+  content: "\f183"; }
+
+.fa-male::before {
+  content: "\f183"; }
+
+.fa-laptop::before {
+  content: "\f109"; }
+
+.fa-file-csv::before {
+  content: "\f6dd"; }
+
+.fa-menorah::before {
+  content: "\f676"; }
+
+.fa-truck-plane::before {
+  content: "\e58f"; }
+
+.fa-record-vinyl::before {
+  content: "\f8d9"; }
+
+.fa-face-grin-stars::before {
+  content: "\f587"; }
+
+.fa-grin-stars::before {
+  content: "\f587"; }
+
+.fa-bong::before {
+  content: "\f55c"; }
+
+.fa-spaghetti-monster-flying::before {
+  content: "\f67b"; }
+
+.fa-pastafarianism::before {
+  content: "\f67b"; }
+
+.fa-arrow-down-up-across-line::before {
+  content: "\e4af"; }
+
+.fa-spoon::before {
+  content: "\f2e5"; }
+
+.fa-utensil-spoon::before {
+  content: "\f2e5"; }
+
+.fa-jar-wheat::before {
+  content: "\e517"; }
+
+.fa-envelopes-bulk::before {
+  content: "\f674"; }
+
+.fa-mail-bulk::before {
+  content: "\f674"; }
+
+.fa-file-circle-exclamation::before {
+  content: "\e4eb"; }
+
+.fa-circle-h::before {
+  content: "\f47e"; }
+
+.fa-hospital-symbol::before {
+  content: "\f47e"; }
+
+.fa-pager::before {
+  content: "\f815"; }
+
+.fa-address-book::before {
+  content: "\f2b9"; }
+
+.fa-contact-book::before {
+  content: "\f2b9"; }
+
+.fa-strikethrough::before {
+  content: "\f0cc"; }
+
+.fa-k::before {
+  content: "\4b"; }
+
+.fa-landmark-flag::before {
+  content: "\e51c"; }
+
+.fa-pencil::before {
+  content: "\f303"; }
+
+.fa-pencil-alt::before {
+  content: "\f303"; }
+
+.fa-backward::before {
+  content: "\f04a"; }
+
+.fa-caret-right::before {
+  content: "\f0da"; }
+
+.fa-comments::before {
+  content: "\f086"; }
+
+.fa-paste::before {
+  content: "\f0ea"; }
+
+.fa-file-clipboard::before {
+  content: "\f0ea"; }
+
+.fa-code-pull-request::before {
+  content: "\e13c"; }
+
+.fa-clipboard-list::before {
+  content: "\f46d"; }
+
+.fa-truck-ramp-box::before {
+  content: "\f4de"; }
+
+.fa-truck-loading::before {
+  content: "\f4de"; }
+
+.fa-user-check::before {
+  content: "\f4fc"; }
+
+.fa-vial-virus::before {
+  content: "\e597"; }
+
+.fa-sheet-plastic::before {
+  content: "\e571"; }
+
+.fa-blog::before {
+  content: "\f781"; }
+
+.fa-user-ninja::before {
+  content: "\f504"; }
+
+.fa-person-arrow-up-from-line::before {
+  content: "\e539"; }
+
+.fa-scroll-torah::before {
+  content: "\f6a0"; }
+
+.fa-torah::before {
+  content: "\f6a0"; }
+
+.fa-broom-ball::before {
+  content: "\f458"; }
+
+.fa-quidditch::before {
+  content: "\f458"; }
+
+.fa-quidditch-broom-ball::before {
+  content: "\f458"; }
+
+.fa-toggle-off::before {
+  content: "\f204"; }
+
+.fa-box-archive::before {
+  content: "\f187"; }
+
+.fa-archive::before {
+  content: "\f187"; }
+
+.fa-person-drowning::before {
+  content: "\e545"; }
+
+.fa-arrow-down-9-1::before {
+  content: "\f886"; }
+
+.fa-sort-numeric-desc::before {
+  content: "\f886"; }
+
+.fa-sort-numeric-down-alt::before {
+  content: "\f886"; }
+
+.fa-face-grin-tongue-squint::before {
+  content: "\f58a"; }
+
+.fa-grin-tongue-squint::before {
+  content: "\f58a"; }
+
+.fa-spray-can::before {
+  content: "\f5bd"; }
+
+.fa-truck-monster::before {
+  content: "\f63b"; }
+
+.fa-w::before {
+  content: "\57"; }
+
+.fa-earth-africa::before {
+  content: "\f57c"; }
+
+.fa-globe-africa::before {
+  content: "\f57c"; }
+
+.fa-rainbow::before {
+  content: "\f75b"; }
+
+.fa-circle-notch::before {
+  content: "\f1ce"; }
+
+.fa-tablet-screen-button::before {
+  content: "\f3fa"; }
+
+.fa-tablet-alt::before {
+  content: "\f3fa"; }
+
+.fa-paw::before {
+  content: "\f1b0"; }
+
+.fa-cloud::before {
+  content: "\f0c2"; }
+
+.fa-trowel-bricks::before {
+  content: "\e58a"; }
+
+.fa-face-flushed::before {
+  content: "\f579"; }
+
+.fa-flushed::before {
+  content: "\f579"; }
+
+.fa-hospital-user::before {
+  content: "\f80d"; }
+
+.fa-tent-arrow-left-right::before {
+  content: "\e57f"; }
+
+.fa-gavel::before {
+  content: "\f0e3"; }
+
+.fa-legal::before {
+  content: "\f0e3"; }
+
+.fa-binoculars::before {
+  content: "\f1e5"; }
+
+.fa-microphone-slash::before {
+  content: "\f131"; }
+
+.fa-box-tissue::before {
+  content: "\e05b"; }
+
+.fa-motorcycle::before {
+  content: "\f21c"; }
+
+.fa-bell-concierge::before {
+  content: "\f562"; }
+
+.fa-concierge-bell::before {
+  content: "\f562"; }
+
+.fa-pen-ruler::before {
+  content: "\f5ae"; }
+
+.fa-pencil-ruler::before {
+  content: "\f5ae"; }
+
+.fa-people-arrows::before {
+  content: "\e068"; }
+
+.fa-people-arrows-left-right::before {
+  content: "\e068"; }
+
+.fa-mars-and-venus-burst::before {
+  content: "\e523"; }
+
+.fa-square-caret-right::before {
+  content: "\f152"; }
+
+.fa-caret-square-right::before {
+  content: "\f152"; }
+
+.fa-scissors::before {
+  content: "\f0c4"; }
+
+.fa-cut::before {
+  content: "\f0c4"; }
+
+.fa-sun-plant-wilt::before {
+  content: "\e57a"; }
+
+.fa-toilets-portable::before {
+  content: "\e584"; }
+
+.fa-hockey-puck::before {
+  content: "\f453"; }
+
+.fa-table::before {
+  content: "\f0ce"; }
+
+.fa-magnifying-glass-arrow-right::before {
+  content: "\e521"; }
+
+.fa-tachograph-digital::before {
+  content: "\f566"; }
+
+.fa-digital-tachograph::before {
+  content: "\f566"; }
+
+.fa-users-slash::before {
+  content: "\e073"; }
+
+.fa-clover::before {
+  content: "\e139"; }
+
+.fa-reply::before {
+  content: "\f3e5"; }
+
+.fa-mail-reply::before {
+  content: "\f3e5"; }
+
+.fa-star-and-crescent::before {
+  content: "\f699"; }
+
+.fa-house-fire::before {
+  content: "\e50c"; }
+
+.fa-square-minus::before {
+  content: "\f146"; }
+
+.fa-minus-square::before {
+  content: "\f146"; }
+
+.fa-helicopter::before {
+  content: "\f533"; }
+
+.fa-compass::before {
+  content: "\f14e"; }
+
+.fa-square-caret-down::before {
+  content: "\f150"; }
+
+.fa-caret-square-down::before {
+  content: "\f150"; }
+
+.fa-file-circle-question::before {
+  content: "\e4ef"; }
+
+.fa-laptop-code::before {
+  content: "\f5fc"; }
+
+.fa-swatchbook::before {
+  content: "\f5c3"; }
+
+.fa-prescription-bottle::before {
+  content: "\f485"; }
+
+.fa-bars::before {
+  content: "\f0c9"; }
+
+.fa-navicon::before {
+  content: "\f0c9"; }
+
+.fa-people-group::before {
+  content: "\e533"; }
+
+.fa-hourglass-end::before {
+  content: "\f253"; }
+
+.fa-hourglass-3::before {
+  content: "\f253"; }
+
+.fa-heart-crack::before {
+  content: "\f7a9"; }
+
+.fa-heart-broken::before {
+  content: "\f7a9"; }
+
+.fa-square-up-right::before {
+  content: "\f360"; }
+
+.fa-external-link-square-alt::before {
+  content: "\f360"; }
+
+.fa-face-kiss-beam::before {
+  content: "\f597"; }
+
+.fa-kiss-beam::before {
+  content: "\f597"; }
+
+.fa-film::before {
+  content: "\f008"; }
+
+.fa-ruler-horizontal::before {
+  content: "\f547"; }
+
+.fa-people-robbery::before {
+  content: "\e536"; }
+
+.fa-lightbulb::before {
+  content: "\f0eb"; }
+
+.fa-caret-left::before {
+  content: "\f0d9"; }
+
+.fa-circle-exclamation::before {
+  content: "\f06a"; }
+
+.fa-exclamation-circle::before {
+  content: "\f06a"; }
+
+.fa-school-circle-xmark::before {
+  content: "\e56d"; }
+
+.fa-arrow-right-from-bracket::before {
+  content: "\f08b"; }
+
+.fa-sign-out::before {
+  content: "\f08b"; }
+
+.fa-circle-chevron-down::before {
+  content: "\f13a"; }
+
+.fa-chevron-circle-down::before {
+  content: "\f13a"; }
+
+.fa-unlock-keyhole::before {
+  content: "\f13e"; }
+
+.fa-unlock-alt::before {
+  content: "\f13e"; }
+
+.fa-cloud-showers-heavy::before {
+  content: "\f740"; }
+
+.fa-headphones-simple::before {
+  content: "\f58f"; }
+
+.fa-headphones-alt::before {
+  content: "\f58f"; }
+
+.fa-sitemap::before {
+  content: "\f0e8"; }
+
+.fa-circle-dollar-to-slot::before {
+  content: "\f4b9"; }
+
+.fa-donate::before {
+  content: "\f4b9"; }
+
+.fa-memory::before {
+  content: "\f538"; }
+
+.fa-road-spikes::before {
+  content: "\e568"; }
+
+.fa-fire-burner::before {
+  content: "\e4f1"; }
+
+.fa-flag::before {
+  content: "\f024"; }
+
+.fa-hanukiah::before {
+  content: "\f6e6"; }
+
+.fa-feather::before {
+  content: "\f52d"; }
+
+.fa-volume-low::before {
+  content: "\f027"; }
+
+.fa-volume-down::before {
+  content: "\f027"; }
+
+.fa-comment-slash::before {
+  content: "\f4b3"; }
+
+.fa-cloud-sun-rain::before {
+  content: "\f743"; }
+
+.fa-compress::before {
+  content: "\f066"; }
+
+.fa-wheat-awn::before {
+  content: "\e2cd"; }
+
+.fa-wheat-alt::before {
+  content: "\e2cd"; }
+
+.fa-ankh::before {
+  content: "\f644"; }
+
+.fa-hands-holding-child::before {
+  content: "\e4fa"; }
+
+.fa-asterisk::before {
+  content: "\2a"; }
+
+.fa-square-check::before {
+  content: "\f14a"; }
+
+.fa-check-square::before {
+  content: "\f14a"; }
+
+.fa-peseta-sign::before {
+  content: "\e221"; }
+
+.fa-heading::before {
+  content: "\f1dc"; }
+
+.fa-header::before {
+  content: "\f1dc"; }
+
+.fa-ghost::before {
+  content: "\f6e2"; }
+
+.fa-list::before {
+  content: "\f03a"; }
+
+.fa-list-squares::before {
+  content: "\f03a"; }
+
+.fa-square-phone-flip::before {
+  content: "\f87b"; }
+
+.fa-phone-square-alt::before {
+  content: "\f87b"; }
+
+.fa-cart-plus::before {
+  content: "\f217"; }
+
+.fa-gamepad::before {
+  content: "\f11b"; }
+
+.fa-circle-dot::before {
+  content: "\f192"; }
+
+.fa-dot-circle::before {
+  content: "\f192"; }
+
+.fa-face-dizzy::before {
+  content: "\f567"; }
+
+.fa-dizzy::before {
+  content: "\f567"; }
+
+.fa-egg::before {
+  content: "\f7fb"; }
+
+.fa-house-medical-circle-xmark::before {
+  content: "\e513"; }
+
+.fa-campground::before {
+  content: "\f6bb"; }
+
+.fa-folder-plus::before {
+  content: "\f65e"; }
+
+.fa-futbol::before {
+  content: "\f1e3"; }
+
+.fa-futbol-ball::before {
+  content: "\f1e3"; }
+
+.fa-soccer-ball::before {
+  content: "\f1e3"; }
+
+.fa-paintbrush::before {
+  content: "\f1fc"; }
+
+.fa-paint-brush::before {
+  content: "\f1fc"; }
+
+.fa-lock::before {
+  content: "\f023"; }
+
+.fa-gas-pump::before {
+  content: "\f52f"; }
+
+.fa-hot-tub-person::before {
+  content: "\f593"; }
+
+.fa-hot-tub::before {
+  content: "\f593"; }
+
+.fa-map-location::before {
+  content: "\f59f"; }
+
+.fa-map-marked::before {
+  content: "\f59f"; }
+
+.fa-house-flood-water::before {
+  content: "\e50e"; }
+
+.fa-tree::before {
+  content: "\f1bb"; }
+
+.fa-bridge-lock::before {
+  content: "\e4cc"; }
+
+.fa-sack-dollar::before {
+  content: "\f81d"; }
+
+.fa-pen-to-square::before {
+  content: "\f044"; }
+
+.fa-edit::before {
+  content: "\f044"; }
+
+.fa-car-side::before {
+  content: "\f5e4"; }
+
+.fa-share-nodes::before {
+  content: "\f1e0"; }
+
+.fa-share-alt::before {
+  content: "\f1e0"; }
+
+.fa-heart-circle-minus::before {
+  content: "\e4ff"; }
+
+.fa-hourglass-half::before {
+  content: "\f252"; }
+
+.fa-hourglass-2::before {
+  content: "\f252"; }
+
+.fa-microscope::before {
+  content: "\f610"; }
+
+.fa-sink::before {
+  content: "\e06d"; }
+
+.fa-bag-shopping::before {
+  content: "\f290"; }
+
+.fa-shopping-bag::before {
+  content: "\f290"; }
+
+.fa-arrow-down-z-a::before {
+  content: "\f881"; }
+
+.fa-sort-alpha-desc::before {
+  content: "\f881"; }
+
+.fa-sort-alpha-down-alt::before {
+  content: "\f881"; }
+
+.fa-mitten::before {
+  content: "\f7b5"; }
+
+.fa-person-rays::before {
+  content: "\e54d"; }
+
+.fa-users::before {
+  content: "\f0c0"; }
+
+.fa-eye-slash::before {
+  content: "\f070"; }
+
+.fa-flask-vial::before {
+  content: "\e4f3"; }
+
+.fa-hand::before {
+  content: "\f256"; }
+
+.fa-hand-paper::before {
+  content: "\f256"; }
+
+.fa-om::before {
+  content: "\f679"; }
+
+.fa-worm::before {
+  content: "\e599"; }
+
+.fa-house-circle-xmark::before {
+  content: "\e50b"; }
+
+.fa-plug::before {
+  content: "\f1e6"; }
+
+.fa-chevron-up::before {
+  content: "\f077"; }
+
+.fa-hand-spock::before {
+  content: "\f259"; }
+
+.fa-stopwatch::before {
+  content: "\f2f2"; }
+
+.fa-face-kiss::before {
+  content: "\f596"; }
+
+.fa-kiss::before {
+  content: "\f596"; }
+
+.fa-bridge-circle-xmark::before {
+  content: "\e4cb"; }
+
+.fa-face-grin-tongue::before {
+  content: "\f589"; }
+
+.fa-grin-tongue::before {
+  content: "\f589"; }
+
+.fa-chess-bishop::before {
+  content: "\f43a"; }
+
+.fa-face-grin-wink::before {
+  content: "\f58c"; }
+
+.fa-grin-wink::before {
+  content: "\f58c"; }
+
+.fa-ear-deaf::before {
+  content: "\f2a4"; }
+
+.fa-deaf::before {
+  content: "\f2a4"; }
+
+.fa-deafness::before {
+  content: "\f2a4"; }
+
+.fa-hard-of-hearing::before {
+  content: "\f2a4"; }
+
+.fa-road-circle-check::before {
+  content: "\e564"; }
+
+.fa-dice-five::before {
+  content: "\f523"; }
+
+.fa-square-rss::before {
+  content: "\f143"; }
+
+.fa-rss-square::before {
+  content: "\f143"; }
+
+.fa-land-mine-on::before {
+  content: "\e51b"; }
+
+.fa-i-cursor::before {
+  content: "\f246"; }
+
+.fa-stamp::before {
+  content: "\f5bf"; }
+
+.fa-stairs::before {
+  content: "\e289"; }
+
+.fa-i::before {
+  content: "\49"; }
+
+.fa-hryvnia-sign::before {
+  content: "\f6f2"; }
+
+.fa-hryvnia::before {
+  content: "\f6f2"; }
+
+.fa-pills::before {
+  content: "\f484"; }
+
+.fa-face-grin-wide::before {
+  content: "\f581"; }
+
+.fa-grin-alt::before {
+  content: "\f581"; }
+
+.fa-tooth::before {
+  content: "\f5c9"; }
+
+.fa-v::before {
+  content: "\56"; }
+
+.fa-bangladeshi-taka-sign::before {
+  content: "\e2e6"; }
+
+.fa-bicycle::before {
+  content: "\f206"; }
+
+.fa-staff-snake::before {
+  content: "\e579"; }
+
+.fa-rod-asclepius::before {
+  content: "\e579"; }
+
+.fa-rod-snake::before {
+  content: "\e579"; }
+
+.fa-staff-aesculapius::before {
+  content: "\e579"; }
+
+.fa-head-side-cough-slash::before {
+  content: "\e062"; }
+
+.fa-truck-medical::before {
+  content: "\f0f9"; }
+
+.fa-ambulance::before {
+  content: "\f0f9"; }
+
+.fa-wheat-awn-circle-exclamation::before {
+  content: "\e598"; }
+
+.fa-snowman::before {
+  content: "\f7d0"; }
+
+.fa-mortar-pestle::before {
+  content: "\f5a7"; }
+
+.fa-road-barrier::before {
+  content: "\e562"; }
+
+.fa-school::before {
+  content: "\f549"; }
+
+.fa-igloo::before {
+  content: "\f7ae"; }
+
+.fa-joint::before {
+  content: "\f595"; }
+
+.fa-angle-right::before {
+  content: "\f105"; }
+
+.fa-horse::before {
+  content: "\f6f0"; }
+
+.fa-q::before {
+  content: "\51"; }
+
+.fa-g::before {
+  content: "\47"; }
+
+.fa-notes-medical::before {
+  content: "\f481"; }
+
+.fa-temperature-half::before {
+  content: "\f2c9"; }
+
+.fa-temperature-2::before {
+  content: "\f2c9"; }
+
+.fa-thermometer-2::before {
+  content: "\f2c9"; }
+
+.fa-thermometer-half::before {
+  content: "\f2c9"; }
+
+.fa-dong-sign::before {
+  content: "\e169"; }
+
+.fa-capsules::before {
+  content: "\f46b"; }
+
+.fa-poo-storm::before {
+  content: "\f75a"; }
+
+.fa-poo-bolt::before {
+  content: "\f75a"; }
+
+.fa-face-frown-open::before {
+  content: "\f57a"; }
+
+.fa-frown-open::before {
+  content: "\f57a"; }
+
+.fa-hand-point-up::before {
+  content: "\f0a6"; }
+
+.fa-money-bill::before {
+  content: "\f0d6"; }
+
+.fa-bookmark::before {
+  content: "\f02e"; }
+
+.fa-align-justify::before {
+  content: "\f039"; }
+
+.fa-umbrella-beach::before {
+  content: "\f5ca"; }
+
+.fa-helmet-un::before {
+  content: "\e503"; }
+
+.fa-bullseye::before {
+  content: "\f140"; }
+
+.fa-bacon::before {
+  content: "\f7e5"; }
+
+.fa-hand-point-down::before {
+  content: "\f0a7"; }
+
+.fa-arrow-up-from-bracket::before {
+  content: "\e09a"; }
+
+.fa-folder::before {
+  content: "\f07b"; }
+
+.fa-folder-blank::before {
+  content: "\f07b"; }
+
+.fa-file-waveform::before {
+  content: "\f478"; }
+
+.fa-file-medical-alt::before {
+  content: "\f478"; }
+
+.fa-radiation::before {
+  content: "\f7b9"; }
+
+.fa-chart-simple::before {
+  content: "\e473"; }
+
+.fa-mars-stroke::before {
+  content: "\f229"; }
+
+.fa-vial::before {
+  content: "\f492"; }
+
+.fa-gauge::before {
+  content: "\f624"; }
+
+.fa-dashboard::before {
+  content: "\f624"; }
+
+.fa-gauge-med::before {
+  content: "\f624"; }
+
+.fa-tachometer-alt-average::before {
+  content: "\f624"; }
+
+.fa-wand-magic-sparkles::before {
+  content: "\e2ca"; }
+
+.fa-magic-wand-sparkles::before {
+  content: "\e2ca"; }
+
+.fa-e::before {
+  content: "\45"; }
+
+.fa-pen-clip::before {
+  content: "\f305"; }
+
+.fa-pen-alt::before {
+  content: "\f305"; }
+
+.fa-bridge-circle-exclamation::before {
+  content: "\e4ca"; }
+
+.fa-user::before {
+  content: "\f007"; }
+
+.fa-school-circle-check::before {
+  content: "\e56b"; }
+
+.fa-dumpster::before {
+  content: "\f793"; }
+
+.fa-van-shuttle::before {
+  content: "\f5b6"; }
+
+.fa-shuttle-van::before {
+  content: "\f5b6"; }
+
+.fa-building-user::before {
+  content: "\e4da"; }
+
+.fa-square-caret-left::before {
+  content: "\f191"; }
+
+.fa-caret-square-left::before {
+  content: "\f191"; }
+
+.fa-highlighter::before {
+  content: "\f591"; }
+
+.fa-key::before {
+  content: "\f084"; }
+
+.fa-bullhorn::before {
+  content: "\f0a1"; }
+
+.fa-globe::before {
+  content: "\f0ac"; }
+
+.fa-synagogue::before {
+  content: "\f69b"; }
+
+.fa-person-half-dress::before {
+  content: "\e548"; }
+
+.fa-road-bridge::before {
+  content: "\e563"; }
+
+.fa-location-arrow::before {
+  content: "\f124"; }
+
+.fa-c::before {
+  content: "\43"; }
+
+.fa-tablet-button::before {
+  content: "\f10a"; }
+
+.fa-building-lock::before {
+  content: "\e4d6"; }
+
+.fa-pizza-slice::before {
+  content: "\f818"; }
+
+.fa-money-bill-wave::before {
+  content: "\f53a"; }
+
+.fa-chart-area::before {
+  content: "\f1fe"; }
+
+.fa-area-chart::before {
+  content: "\f1fe"; }
+
+.fa-house-flag::before {
+  content: "\e50d"; }
+
+.fa-person-circle-minus::before {
+  content: "\e540"; }
+
+.fa-ban::before {
+  content: "\f05e"; }
+
+.fa-cancel::before {
+  content: "\f05e"; }
+
+.fa-camera-rotate::before {
+  content: "\e0d8"; }
+
+.fa-spray-can-sparkles::before {
+  content: "\f5d0"; }
+
+.fa-air-freshener::before {
+  content: "\f5d0"; }
+
+.fa-star::before {
+  content: "\f005"; }
+
+.fa-repeat::before {
+  content: "\f363"; }
+
+.fa-cross::before {
+  content: "\f654"; }
+
+.fa-box::before {
+  content: "\f466"; }
+
+.fa-venus-mars::before {
+  content: "\f228"; }
+
+.fa-arrow-pointer::before {
+  content: "\f245"; }
+
+.fa-mouse-pointer::before {
+  content: "\f245"; }
+
+.fa-maximize::before {
+  content: "\f31e"; }
+
+.fa-expand-arrows-alt::before {
+  content: "\f31e"; }
+
+.fa-charging-station::before {
+  content: "\f5e7"; }
+
+.fa-shapes::before {
+  content: "\f61f"; }
+
+.fa-triangle-circle-square::before {
+  content: "\f61f"; }
+
+.fa-shuffle::before {
+  content: "\f074"; }
+
+.fa-random::before {
+  content: "\f074"; }
+
+.fa-person-running::before {
+  content: "\f70c"; }
+
+.fa-running::before {
+  content: "\f70c"; }
+
+.fa-mobile-retro::before {
+  content: "\e527"; }
+
+.fa-grip-lines-vertical::before {
+  content: "\f7a5"; }
+
+.fa-spider::before {
+  content: "\f717"; }
+
+.fa-hands-bound::before {
+  content: "\e4f9"; }
+
+.fa-file-invoice-dollar::before {
+  content: "\f571"; }
+
+.fa-plane-circle-exclamation::before {
+  content: "\e556"; }
+
+.fa-x-ray::before {
+  content: "\f497"; }
+
+.fa-spell-check::before {
+  content: "\f891"; }
+
+.fa-slash::before {
+  content: "\f715"; }
+
+.fa-computer-mouse::before {
+  content: "\f8cc"; }
+
+.fa-mouse::before {
+  content: "\f8cc"; }
+
+.fa-arrow-right-to-bracket::before {
+  content: "\f090"; }
+
+.fa-sign-in::before {
+  content: "\f090"; }
+
+.fa-shop-slash::before {
+  content: "\e070"; }
+
+.fa-store-alt-slash::before {
+  content: "\e070"; }
+
+.fa-server::before {
+  content: "\f233"; }
+
+.fa-virus-covid-slash::before {
+  content: "\e4a9"; }
+
+.fa-shop-lock::before {
+  content: "\e4a5"; }
+
+.fa-hourglass-start::before {
+  content: "\f251"; }
+
+.fa-hourglass-1::before {
+  content: "\f251"; }
+
+.fa-blender-phone::before {
+  content: "\f6b6"; }
+
+.fa-building-wheat::before {
+  content: "\e4db"; }
+
+.fa-person-breastfeeding::before {
+  content: "\e53a"; }
+
+.fa-right-to-bracket::before {
+  content: "\f2f6"; }
+
+.fa-sign-in-alt::before {
+  content: "\f2f6"; }
+
+.fa-venus::before {
+  content: "\f221"; }
+
+.fa-passport::before {
+  content: "\f5ab"; }
+
+.fa-heart-pulse::before {
+  content: "\f21e"; }
+
+.fa-heartbeat::before {
+  content: "\f21e"; }
+
+.fa-people-carry-box::before {
+  content: "\f4ce"; }
+
+.fa-people-carry::before {
+  content: "\f4ce"; }
+
+.fa-temperature-high::before {
+  content: "\f769"; }
+
+.fa-microchip::before {
+  content: "\f2db"; }
+
+.fa-crown::before {
+  content: "\f521"; }
+
+.fa-weight-hanging::before {
+  content: "\f5cd"; }
+
+.fa-xmarks-lines::before {
+  content: "\e59a"; }
+
+.fa-file-prescription::before {
+  content: "\f572"; }
+
+.fa-weight-scale::before {
+  content: "\f496"; }
+
+.fa-weight::before {
+  content: "\f496"; }
+
+.fa-user-group::before {
+  content: "\f500"; }
+
+.fa-user-friends::before {
+  content: "\f500"; }
+
+.fa-arrow-up-a-z::before {
+  content: "\f15e"; }
+
+.fa-sort-alpha-up::before {
+  content: "\f15e"; }
+
+.fa-chess-knight::before {
+  content: "\f441"; }
+
+.fa-face-laugh-squint::before {
+  content: "\f59b"; }
+
+.fa-laugh-squint::before {
+  content: "\f59b"; }
+
+.fa-wheelchair::before {
+  content: "\f193"; }
+
+.fa-circle-arrow-up::before {
+  content: "\f0aa"; }
+
+.fa-arrow-circle-up::before {
+  content: "\f0aa"; }
+
+.fa-toggle-on::before {
+  content: "\f205"; }
+
+.fa-person-walking::before {
+  content: "\f554"; }
+
+.fa-walking::before {
+  content: "\f554"; }
+
+.fa-l::before {
+  content: "\4c"; }
+
+.fa-fire::before {
+  content: "\f06d"; }
+
+.fa-bed-pulse::before {
+  content: "\f487"; }
+
+.fa-procedures::before {
+  content: "\f487"; }
+
+.fa-shuttle-space::before {
+  content: "\f197"; }
+
+.fa-space-shuttle::before {
+  content: "\f197"; }
+
+.fa-face-laugh::before {
+  content: "\f599"; }
+
+.fa-laugh::before {
+  content: "\f599"; }
+
+.fa-folder-open::before {
+  content: "\f07c"; }
+
+.fa-heart-circle-plus::before {
+  content: "\e500"; }
+
+.fa-code-fork::before {
+  content: "\e13b"; }
+
+.fa-city::before {
+  content: "\f64f"; }
+
+.fa-microphone-lines::before {
+  content: "\f3c9"; }
+
+.fa-microphone-alt::before {
+  content: "\f3c9"; }
+
+.fa-pepper-hot::before {
+  content: "\f816"; }
+
+.fa-unlock::before {
+  content: "\f09c"; }
+
+.fa-colon-sign::before {
+  content: "\e140"; }
+
+.fa-headset::before {
+  content: "\f590"; }
+
+.fa-store-slash::before {
+  content: "\e071"; }
+
+.fa-road-circle-xmark::before {
+  content: "\e566"; }
+
+.fa-user-minus::before {
+  content: "\f503"; }
+
+.fa-mars-stroke-up::before {
+  content: "\f22a"; }
+
+.fa-mars-stroke-v::before {
+  content: "\f22a"; }
+
+.fa-champagne-glasses::before {
+  content: "\f79f"; }
+
+.fa-glass-cheers::before {
+  content: "\f79f"; }
+
+.fa-clipboard::before {
+  content: "\f328"; }
+
+.fa-house-circle-exclamation::before {
+  content: "\e50a"; }
+
+.fa-file-arrow-up::before {
+  content: "\f574"; }
+
+.fa-file-upload::before {
+  content: "\f574"; }
+
+.fa-wifi::before {
+  content: "\f1eb"; }
+
+.fa-wifi-3::before {
+  content: "\f1eb"; }
+
+.fa-wifi-strong::before {
+  content: "\f1eb"; }
+
+.fa-bath::before {
+  content: "\f2cd"; }
+
+.fa-bathtub::before {
+  content: "\f2cd"; }
+
+.fa-underline::before {
+  content: "\f0cd"; }
+
+.fa-user-pen::before {
+  content: "\f4ff"; }
+
+.fa-user-edit::before {
+  content: "\f4ff"; }
+
+.fa-signature::before {
+  content: "\f5b7"; }
+
+.fa-stroopwafel::before {
+  content: "\f551"; }
+
+.fa-bold::before {
+  content: "\f032"; }
+
+.fa-anchor-lock::before {
+  content: "\e4ad"; }
+
+.fa-building-ngo::before {
+  content: "\e4d7"; }
+
+.fa-manat-sign::before {
+  content: "\e1d5"; }
+
+.fa-not-equal::before {
+  content: "\f53e"; }
+
+.fa-border-top-left::before {
+  content: "\f853"; }
+
+.fa-border-style::before {
+  content: "\f853"; }
+
+.fa-map-location-dot::before {
+  content: "\f5a0"; }
+
+.fa-map-marked-alt::before {
+  content: "\f5a0"; }
+
+.fa-jedi::before {
+  content: "\f669"; }
+
+.fa-square-poll-vertical::before {
+  content: "\f681"; }
+
+.fa-poll::before {
+  content: "\f681"; }
+
+.fa-mug-hot::before {
+  content: "\f7b6"; }
+
+.fa-car-battery::before {
+  content: "\f5df"; }
+
+.fa-battery-car::before {
+  content: "\f5df"; }
+
+.fa-gift::before {
+  content: "\f06b"; }
+
+.fa-dice-two::before {
+  content: "\f528"; }
+
+.fa-chess-queen::before {
+  content: "\f445"; }
+
+.fa-glasses::before {
+  content: "\f530"; }
+
+.fa-chess-board::before {
+  content: "\f43c"; }
+
+.fa-building-circle-check::before {
+  content: "\e4d2"; }
+
+.fa-person-chalkboard::before {
+  content: "\e53d"; }
+
+.fa-mars-stroke-right::before {
+  content: "\f22b"; }
+
+.fa-mars-stroke-h::before {
+  content: "\f22b"; }
+
+.fa-hand-back-fist::before {
+  content: "\f255"; }
+
+.fa-hand-rock::before {
+  content: "\f255"; }
+
+.fa-square-caret-up::before {
+  content: "\f151"; }
+
+.fa-caret-square-up::before {
+  content: "\f151"; }
+
+.fa-cloud-showers-water::before {
+  content: "\e4e4"; }
+
+.fa-chart-bar::before {
+  content: "\f080"; }
+
+.fa-bar-chart::before {
+  content: "\f080"; }
+
+.fa-hands-bubbles::before {
+  content: "\e05e"; }
+
+.fa-hands-wash::before {
+  content: "\e05e"; }
+
+.fa-less-than-equal::before {
+  content: "\f537"; }
+
+.fa-train::before {
+  content: "\f238"; }
+
+.fa-eye-low-vision::before {
+  content: "\f2a8"; }
+
+.fa-low-vision::before {
+  content: "\f2a8"; }
+
+.fa-crow::before {
+  content: "\f520"; }
+
+.fa-sailboat::before {
+  content: "\e445"; }
+
+.fa-window-restore::before {
+  content: "\f2d2"; }
+
+.fa-square-plus::before {
+  content: "\f0fe"; }
+
+.fa-plus-square::before {
+  content: "\f0fe"; }
+
+.fa-torii-gate::before {
+  content: "\f6a1"; }
+
+.fa-frog::before {
+  content: "\f52e"; }
+
+.fa-bucket::before {
+  content: "\e4cf"; }
+
+.fa-image::before {
+  content: "\f03e"; }
+
+.fa-microphone::before {
+  content: "\f130"; }
+
+.fa-cow::before {
+  content: "\f6c8"; }
+
+.fa-caret-up::before {
+  content: "\f0d8"; }
+
+.fa-screwdriver::before {
+  content: "\f54a"; }
+
+.fa-folder-closed::before {
+  content: "\e185"; }
+
+.fa-house-tsunami::before {
+  content: "\e515"; }
+
+.fa-square-nfi::before {
+  content: "\e576"; }
+
+.fa-arrow-up-from-ground-water::before {
+  content: "\e4b5"; }
+
+.fa-martini-glass::before {
+  content: "\f57b"; }
+
+.fa-glass-martini-alt::before {
+  content: "\f57b"; }
+
+.fa-rotate-left::before {
+  content: "\f2ea"; }
+
+.fa-rotate-back::before {
+  content: "\f2ea"; }
+
+.fa-rotate-backward::before {
+  content: "\f2ea"; }
+
+.fa-undo-alt::before {
+  content: "\f2ea"; }
+
+.fa-table-columns::before {
+  content: "\f0db"; }
+
+.fa-columns::before {
+  content: "\f0db"; }
+
+.fa-lemon::before {
+  content: "\f094"; }
+
+.fa-head-side-mask::before {
+  content: "\e063"; }
+
+.fa-handshake::before {
+  content: "\f2b5"; }
+
+.fa-gem::before {
+  content: "\f3a5"; }
+
+.fa-dolly::before {
+  content: "\f472"; }
+
+.fa-dolly-box::before {
+  content: "\f472"; }
+
+.fa-smoking::before {
+  content: "\f48d"; }
+
+.fa-minimize::before {
+  content: "\f78c"; }
+
+.fa-compress-arrows-alt::before {
+  content: "\f78c"; }
+
+.fa-monument::before {
+  content: "\f5a6"; }
+
+.fa-snowplow::before {
+  content: "\f7d2"; }
+
+.fa-angles-right::before {
+  content: "\f101"; }
+
+.fa-angle-double-right::before {
+  content: "\f101"; }
+
+.fa-cannabis::before {
+  content: "\f55f"; }
+
+.fa-circle-play::before {
+  content: "\f144"; }
+
+.fa-play-circle::before {
+  content: "\f144"; }
+
+.fa-tablets::before {
+  content: "\f490"; }
+
+.fa-ethernet::before {
+  content: "\f796"; }
+
+.fa-euro-sign::before {
+  content: "\f153"; }
+
+.fa-eur::before {
+  content: "\f153"; }
+
+.fa-euro::before {
+  content: "\f153"; }
+
+.fa-chair::before {
+  content: "\f6c0"; }
+
+.fa-circle-check::before {
+  content: "\f058"; }
+
+.fa-check-circle::before {
+  content: "\f058"; }
+
+.fa-circle-stop::before {
+  content: "\f28d"; }
+
+.fa-stop-circle::before {
+  content: "\f28d"; }
+
+.fa-compass-drafting::before {
+  content: "\f568"; }
+
+.fa-drafting-compass::before {
+  content: "\f568"; }
+
+.fa-plate-wheat::before {
+  content: "\e55a"; }
+
+.fa-icicles::before {
+  content: "\f7ad"; }
+
+.fa-person-shelter::before {
+  content: "\e54f"; }
+
+.fa-neuter::before {
+  content: "\f22c"; }
+
+.fa-id-badge::before {
+  content: "\f2c1"; }
+
+.fa-marker::before {
+  content: "\f5a1"; }
+
+.fa-face-laugh-beam::before {
+  content: "\f59a"; }
+
+.fa-laugh-beam::before {
+  content: "\f59a"; }
+
+.fa-helicopter-symbol::before {
+  content: "\e502"; }
+
+.fa-universal-access::before {
+  content: "\f29a"; }
+
+.fa-circle-chevron-up::before {
+  content: "\f139"; }
+
+.fa-chevron-circle-up::before {
+  content: "\f139"; }
+
+.fa-lari-sign::before {
+  content: "\e1c8"; }
+
+.fa-volcano::before {
+  content: "\f770"; }
+
+.fa-person-walking-dashed-line-arrow-right::before {
+  content: "\e553"; }
+
+.fa-sterling-sign::before {
+  content: "\f154"; }
+
+.fa-gbp::before {
+  content: "\f154"; }
+
+.fa-pound-sign::before {
+  content: "\f154"; }
+
+.fa-viruses::before {
+  content: "\e076"; }
+
+.fa-square-person-confined::before {
+  content: "\e577"; }
+
+.fa-user-tie::before {
+  content: "\f508"; }
+
+.fa-arrow-down-long::before {
+  content: "\f175"; }
+
+.fa-long-arrow-down::before {
+  content: "\f175"; }
+
+.fa-tent-arrow-down-to-line::before {
+  content: "\e57e"; }
+
+.fa-certificate::before {
+  content: "\f0a3"; }
+
+.fa-reply-all::before {
+  content: "\f122"; }
+
+.fa-mail-reply-all::before {
+  content: "\f122"; }
+
+.fa-suitcase::before {
+  content: "\f0f2"; }
+
+.fa-person-skating::before {
+  content: "\f7c5"; }
+
+.fa-skating::before {
+  content: "\f7c5"; }
+
+.fa-filter-circle-dollar::before {
+  content: "\f662"; }
+
+.fa-funnel-dollar::before {
+  content: "\f662"; }
+
+.fa-camera-retro::before {
+  content: "\f083"; }
+
+.fa-circle-arrow-down::before {
+  content: "\f0ab"; }
+
+.fa-arrow-circle-down::before {
+  content: "\f0ab"; }
+
+.fa-file-import::before {
+  content: "\f56f"; }
+
+.fa-arrow-right-to-file::before {
+  content: "\f56f"; }
+
+.fa-square-arrow-up-right::before {
+  content: "\f14c"; }
+
+.fa-external-link-square::before {
+  content: "\f14c"; }
+
+.fa-box-open::before {
+  content: "\f49e"; }
+
+.fa-scroll::before {
+  content: "\f70e"; }
+
+.fa-spa::before {
+  content: "\f5bb"; }
+
+.fa-location-pin-lock::before {
+  content: "\e51f"; }
+
+.fa-pause::before {
+  content: "\f04c"; }
+
+.fa-hill-avalanche::before {
+  content: "\e507"; }
+
+.fa-temperature-empty::before {
+  content: "\f2cb"; }
+
+.fa-temperature-0::before {
+  content: "\f2cb"; }
+
+.fa-thermometer-0::before {
+  content: "\f2cb"; }
+
+.fa-thermometer-empty::before {
+  content: "\f2cb"; }
+
+.fa-bomb::before {
+  content: "\f1e2"; }
+
+.fa-registered::before {
+  content: "\f25d"; }
+
+.fa-address-card::before {
+  content: "\f2bb"; }
+
+.fa-contact-card::before {
+  content: "\f2bb"; }
+
+.fa-vcard::before {
+  content: "\f2bb"; }
+
+.fa-scale-unbalanced-flip::before {
+  content: "\f516"; }
+
+.fa-balance-scale-right::before {
+  content: "\f516"; }
+
+.fa-subscript::before {
+  content: "\f12c"; }
+
+.fa-diamond-turn-right::before {
+  content: "\f5eb"; }
+
+.fa-directions::before {
+  content: "\f5eb"; }
+
+.fa-burst::before {
+  content: "\e4dc"; }
+
+.fa-house-laptop::before {
+  content: "\e066"; }
+
+.fa-laptop-house::before {
+  content: "\e066"; }
+
+.fa-face-tired::before {
+  content: "\f5c8"; }
+
+.fa-tired::before {
+  content: "\f5c8"; }
+
+.fa-money-bills::before {
+  content: "\e1f3"; }
+
+.fa-smog::before {
+  content: "\f75f"; }
+
+.fa-crutch::before {
+  content: "\f7f7"; }
+
+.fa-cloud-arrow-up::before {
+  content: "\f0ee"; }
+
+.fa-cloud-upload::before {
+  content: "\f0ee"; }
+
+.fa-cloud-upload-alt::before {
+  content: "\f0ee"; }
+
+.fa-palette::before {
+  content: "\f53f"; }
+
+.fa-arrows-turn-right::before {
+  content: "\e4c0"; }
+
+.fa-vest::before {
+  content: "\e085"; }
+
+.fa-ferry::before {
+  content: "\e4ea"; }
+
+.fa-arrows-down-to-people::before {
+  content: "\e4b9"; }
+
+.fa-seedling::before {
+  content: "\f4d8"; }
+
+.fa-sprout::before {
+  content: "\f4d8"; }
+
+.fa-left-right::before {
+  content: "\f337"; }
+
+.fa-arrows-alt-h::before {
+  content: "\f337"; }
+
+.fa-boxes-packing::before {
+  content: "\e4c7"; }
+
+.fa-circle-arrow-left::before {
+  content: "\f0a8"; }
+
+.fa-arrow-circle-left::before {
+  content: "\f0a8"; }
+
+.fa-group-arrows-rotate::before {
+  content: "\e4f6"; }
+
+.fa-bowl-food::before {
+  content: "\e4c6"; }
+
+.fa-candy-cane::before {
+  content: "\f786"; }
+
+.fa-arrow-down-wide-short::before {
+  content: "\f160"; }
+
+.fa-sort-amount-asc::before {
+  content: "\f160"; }
+
+.fa-sort-amount-down::before {
+  content: "\f160"; }
+
+.fa-cloud-bolt::before {
+  content: "\f76c"; }
+
+.fa-thunderstorm::before {
+  content: "\f76c"; }
+
+.fa-text-slash::before {
+  content: "\f87d"; }
+
+.fa-remove-format::before {
+  content: "\f87d"; }
+
+.fa-face-smile-wink::before {
+  content: "\f4da"; }
+
+.fa-smile-wink::before {
+  content: "\f4da"; }
+
+.fa-file-word::before {
+  content: "\f1c2"; }
+
+.fa-file-powerpoint::before {
+  content: "\f1c4"; }
+
+.fa-arrows-left-right::before {
+  content: "\f07e"; }
+
+.fa-arrows-h::before {
+  content: "\f07e"; }
+
+.fa-house-lock::before {
+  content: "\e510"; }
+
+.fa-cloud-arrow-down::before {
+  content: "\f0ed"; }
+
+.fa-cloud-download::before {
+  content: "\f0ed"; }
+
+.fa-cloud-download-alt::before {
+  content: "\f0ed"; }
+
+.fa-children::before {
+  content: "\e4e1"; }
+
+.fa-chalkboard::before {
+  content: "\f51b"; }
+
+.fa-blackboard::before {
+  content: "\f51b"; }
+
+.fa-user-large-slash::before {
+  content: "\f4fa"; }
+
+.fa-user-alt-slash::before {
+  content: "\f4fa"; }
+
+.fa-envelope-open::before {
+  content: "\f2b6"; }
+
+.fa-handshake-simple-slash::before {
+  content: "\e05f"; }
+
+.fa-handshake-alt-slash::before {
+  content: "\e05f"; }
+
+.fa-mattress-pillow::before {
+  content: "\e525"; }
+
+.fa-guarani-sign::before {
+  content: "\e19a"; }
+
+.fa-arrows-rotate::before {
+  content: "\f021"; }
+
+.fa-refresh::before {
+  content: "\f021"; }
+
+.fa-sync::before {
+  content: "\f021"; }
+
+.fa-fire-extinguisher::before {
+  content: "\f134"; }
+
+.fa-cruzeiro-sign::before {
+  content: "\e152"; }
+
+.fa-greater-than-equal::before {
+  content: "\f532"; }
+
+.fa-shield-halved::before {
+  content: "\f3ed"; }
+
+.fa-shield-alt::before {
+  content: "\f3ed"; }
+
+.fa-book-atlas::before {
+  content: "\f558"; }
+
+.fa-atlas::before {
+  content: "\f558"; }
+
+.fa-virus::before {
+  content: "\e074"; }
+
+.fa-envelope-circle-check::before {
+  content: "\e4e8"; }
+
+.fa-layer-group::before {
+  content: "\f5fd"; }
+
+.fa-arrows-to-dot::before {
+  content: "\e4be"; }
+
+.fa-archway::before {
+  content: "\f557"; }
+
+.fa-heart-circle-check::before {
+  content: "\e4fd"; }
+
+.fa-house-chimney-crack::before {
+  content: "\f6f1"; }
+
+.fa-house-damage::before {
+  content: "\f6f1"; }
+
+.fa-file-zipper::before {
+  content: "\f1c6"; }
+
+.fa-file-archive::before {
+  content: "\f1c6"; }
+
+.fa-square::before {
+  content: "\f0c8"; }
+
+.fa-martini-glass-empty::before {
+  content: "\f000"; }
+
+.fa-glass-martini::before {
+  content: "\f000"; }
+
+.fa-couch::before {
+  content: "\f4b8"; }
+
+.fa-cedi-sign::before {
+  content: "\e0df"; }
+
+.fa-italic::before {
+  content: "\f033"; }
+
+.fa-table-cells-column-lock::before {
+  content: "\e678"; }
+
+.fa-church::before {
+  content: "\f51d"; }
+
+.fa-comments-dollar::before {
+  content: "\f653"; }
+
+.fa-democrat::before {
+  content: "\f747"; }
+
+.fa-z::before {
+  content: "\5a"; }
+
+.fa-person-skiing::before {
+  content: "\f7c9"; }
+
+.fa-skiing::before {
+  content: "\f7c9"; }
+
+.fa-road-lock::before {
+  content: "\e567"; }
+
+.fa-a::before {
+  content: "\41"; }
+
+.fa-temperature-arrow-down::before {
+  content: "\e03f"; }
+
+.fa-temperature-down::before {
+  content: "\e03f"; }
+
+.fa-feather-pointed::before {
+  content: "\f56b"; }
+
+.fa-feather-alt::before {
+  content: "\f56b"; }
+
+.fa-p::before {
+  content: "\50"; }
+
+.fa-snowflake::before {
+  content: "\f2dc"; }
+
+.fa-newspaper::before {
+  content: "\f1ea"; }
+
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+  content: "\f641"; }
+
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+  content: "\f641"; }
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+  content: "\f0a9"; }
+
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+  content: "\f0a9"; }
+
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+  content: "\e17b"; }
+
+.fa-locust::before {
+  content: "\e520"; }
+
+.fa-sort::before {
+  content: "\f0dc"; }
+
+.fa-unsorted::before {
+  content: "\f0dc"; }
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+.fa-list-ol::before {
+  content: "\f0cb"; }
+
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+  content: "\f0cb"; }
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+  content: "\f0cb"; }
+
+.fa-person-dress-burst::before {
+  content: "\e544"; }
+
+.fa-money-check-dollar::before {
+  content: "\f53d"; }
+
+.fa-money-check-alt::before {
+  content: "\f53d"; }
+
+.fa-vector-square::before {
+  content: "\f5cb"; }
+
+.fa-bread-slice::before {
+  content: "\f7ec"; }
+
+.fa-language::before {
+  content: "\f1ab"; }
+
+.fa-face-kiss-wink-heart::before {
+  content: "\f598"; }
+
+.fa-kiss-wink-heart::before {
+  content: "\f598"; }
+
+.fa-filter::before {
+  content: "\f0b0"; }
+
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+  content: "\3f"; }
+
+.fa-file-signature::before {
+  content: "\f573"; }
+
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+  content: "\f0b2"; }
+
+.fa-arrows-alt::before {
+  content: "\f0b2"; }
+
+.fa-house-chimney-user::before {
+  content: "\e065"; }
+
+.fa-hand-holding-heart::before {
+  content: "\f4be"; }
+
+.fa-puzzle-piece::before {
+  content: "\f12e"; }
+
+.fa-money-check::before {
+  content: "\f53c"; }
+
+.fa-star-half-stroke::before {
+  content: "\f5c0"; }
+
+.fa-star-half-alt::before {
+  content: "\f5c0"; }
+
+.fa-code::before {
+  content: "\f121"; }
+
+.fa-whiskey-glass::before {
+  content: "\f7a0"; }
+
+.fa-glass-whiskey::before {
+  content: "\f7a0"; }
+
+.fa-building-circle-exclamation::before {
+  content: "\e4d3"; }
+
+.fa-magnifying-glass-chart::before {
+  content: "\e522"; }
+
+.fa-arrow-up-right-from-square::before {
+  content: "\f08e"; }
+
+.fa-external-link::before {
+  content: "\f08e"; }
+
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+  content: "\e4e6"; }
+
+.fa-won-sign::before {
+  content: "\f159"; }
+
+.fa-krw::before {
+  content: "\f159"; }
+
+.fa-won::before {
+  content: "\f159"; }
+
+.fa-virus-covid::before {
+  content: "\e4a8"; }
+
+.fa-austral-sign::before {
+  content: "\e0a9"; }
+
+.fa-f::before {
+  content: "\46"; }
+
+.fa-leaf::before {
+  content: "\f06c"; }
+
+.fa-road::before {
+  content: "\f018"; }
+
+.fa-taxi::before {
+  content: "\f1ba"; }
+
+.fa-cab::before {
+  content: "\f1ba"; }
+
+.fa-person-circle-plus::before {
+  content: "\e541"; }
+
+.fa-chart-pie::before {
+  content: "\f200"; }
+
+.fa-pie-chart::before {
+  content: "\f200"; }
+
+.fa-bolt-lightning::before {
+  content: "\e0b7"; }
+
+.fa-sack-xmark::before {
+  content: "\e56a"; }
+
+.fa-file-excel::before {
+  content: "\f1c3"; }
+
+.fa-file-contract::before {
+  content: "\f56c"; }
+
+.fa-fish-fins::before {
+  content: "\e4f2"; }
+
+.fa-building-flag::before {
+  content: "\e4d5"; }
+
+.fa-face-grin-beam::before {
+  content: "\f582"; }
+
+.fa-grin-beam::before {
+  content: "\f582"; }
+
+.fa-object-ungroup::before {
+  content: "\f248"; }
+
+.fa-poop::before {
+  content: "\f619"; }
+
+.fa-location-pin::before {
+  content: "\f041"; }
+
+.fa-map-marker::before {
+  content: "\f041"; }
+
+.fa-kaaba::before {
+  content: "\f66b"; }
+
+.fa-toilet-paper::before {
+  content: "\f71e"; }
+
+.fa-helmet-safety::before {
+  content: "\f807"; }
+
+.fa-hard-hat::before {
+  content: "\f807"; }
+
+.fa-hat-hard::before {
+  content: "\f807"; }
+
+.fa-eject::before {
+  content: "\f052"; }
+
+.fa-circle-right::before {
+  content: "\f35a"; }
+
+.fa-arrow-alt-circle-right::before {
+  content: "\f35a"; }
+
+.fa-plane-circle-check::before {
+  content: "\e555"; }
+
+.fa-face-rolling-eyes::before {
+  content: "\f5a5"; }
+
+.fa-meh-rolling-eyes::before {
+  content: "\f5a5"; }
+
+.fa-object-group::before {
+  content: "\f247"; }
+
+.fa-chart-line::before {
+  content: "\f201"; }
+
+.fa-line-chart::before {
+  content: "\f201"; }
+
+.fa-mask-ventilator::before {
+  content: "\e524"; }
+
+.fa-arrow-right::before {
+  content: "\f061"; }
+
+.fa-signs-post::before {
+  content: "\f277"; }
+
+.fa-map-signs::before {
+  content: "\f277"; }
+
+.fa-cash-register::before {
+  content: "\f788"; }
+
+.fa-person-circle-question::before {
+  content: "\e542"; }
+
+.fa-h::before {
+  content: "\48"; }
+
+.fa-tarp::before {
+  content: "\e57b"; }
+
+.fa-screwdriver-wrench::before {
+  content: "\f7d9"; }
+
+.fa-tools::before {
+  content: "\f7d9"; }
+
+.fa-arrows-to-eye::before {
+  content: "\e4bf"; }
+
+.fa-plug-circle-bolt::before {
+  content: "\e55b"; }
+
+.fa-heart::before {
+  content: "\f004"; }
+
+.fa-mars-and-venus::before {
+  content: "\f224"; }
+
+.fa-house-user::before {
+  content: "\e1b0"; }
+
+.fa-home-user::before {
+  content: "\e1b0"; }
+
+.fa-dumpster-fire::before {
+  content: "\f794"; }
+
+.fa-house-crack::before {
+  content: "\e3b1"; }
+
+.fa-martini-glass-citrus::before {
+  content: "\f561"; }
+
+.fa-cocktail::before {
+  content: "\f561"; }
+
+.fa-face-surprise::before {
+  content: "\f5c2"; }
+
+.fa-surprise::before {
+  content: "\f5c2"; }
+
+.fa-bottle-water::before {
+  content: "\e4c5"; }
+
+.fa-circle-pause::before {
+  content: "\f28b"; }
+
+.fa-pause-circle::before {
+  content: "\f28b"; }
+
+.fa-toilet-paper-slash::before {
+  content: "\e072"; }
+
+.fa-apple-whole::before {
+  content: "\f5d1"; }
+
+.fa-apple-alt::before {
+  content: "\f5d1"; }
+
+.fa-kitchen-set::before {
+  content: "\e51a"; }
+
+.fa-r::before {
+  content: "\52"; }
+
+.fa-temperature-quarter::before {
+  content: "\f2ca"; }
+
+.fa-temperature-1::before {
+  content: "\f2ca"; }
+
+.fa-thermometer-1::before {
+  content: "\f2ca"; }
+
+.fa-thermometer-quarter::before {
+  content: "\f2ca"; }
+
+.fa-cube::before {
+  content: "\f1b2"; }
+
+.fa-bitcoin-sign::before {
+  content: "\e0b4"; }
+
+.fa-shield-dog::before {
+  content: "\e573"; }
+
+.fa-solar-panel::before {
+  content: "\f5ba"; }
+
+.fa-lock-open::before {
+  content: "\f3c1"; }
+
+.fa-elevator::before {
+  content: "\e16d"; }
+
+.fa-money-bill-transfer::before {
+  content: "\e528"; }
+
+.fa-money-bill-trend-up::before {
+  content: "\e529"; }
+
+.fa-house-flood-water-circle-arrow-right::before {
+  content: "\e50f"; }
+
+.fa-square-poll-horizontal::before {
+  content: "\f682"; }
+
+.fa-poll-h::before {
+  content: "\f682"; }
+
+.fa-circle::before {
+  content: "\f111"; }
+
+.fa-backward-fast::before {
+  content: "\f049"; }
+
+.fa-fast-backward::before {
+  content: "\f049"; }
+
+.fa-recycle::before {
+  content: "\f1b8"; }
+
+.fa-user-astronaut::before {
+  content: "\f4fb"; }
+
+.fa-plane-slash::before {
+  content: "\e069"; }
+
+.fa-trademark::before {
+  content: "\f25c"; }
+
+.fa-basketball::before {
+  content: "\f434"; }
+
+.fa-basketball-ball::before {
+  content: "\f434"; }
+
+.fa-satellite-dish::before {
+  content: "\f7c0"; }
+
+.fa-circle-up::before {
+  content: "\f35b"; }
+
+.fa-arrow-alt-circle-up::before {
+  content: "\f35b"; }
+
+.fa-mobile-screen-button::before {
+  content: "\f3cd"; }
+
+.fa-mobile-alt::before {
+  content: "\f3cd"; }
+
+.fa-volume-high::before {
+  content: "\f028"; }
+
+.fa-volume-up::before {
+  content: "\f028"; }
+
+.fa-users-rays::before {
+  content: "\e593"; }
+
+.fa-wallet::before {
+  content: "\f555"; }
+
+.fa-clipboard-check::before {
+  content: "\f46c"; }
+
+.fa-file-audio::before {
+  content: "\f1c7"; }
+
+.fa-burger::before {
+  content: "\f805"; }
+
+.fa-hamburger::before {
+  content: "\f805"; }
+
+.fa-wrench::before {
+  content: "\f0ad"; }
+
+.fa-bugs::before {
+  content: "\e4d0"; }
+
+.fa-rupee-sign::before {
+  content: "\f156"; }
+
+.fa-rupee::before {
+  content: "\f156"; }
+
+.fa-file-image::before {
+  content: "\f1c5"; }
+
+.fa-circle-question::before {
+  content: "\f059"; }
+
+.fa-question-circle::before {
+  content: "\f059"; }
+
+.fa-plane-departure::before {
+  content: "\f5b0"; }
+
+.fa-handshake-slash::before {
+  content: "\e060"; }
+
+.fa-book-bookmark::before {
+  content: "\e0bb"; }
+
+.fa-code-branch::before {
+  content: "\f126"; }
+
+.fa-hat-cowboy::before {
+  content: "\f8c0"; }
+
+.fa-bridge::before {
+  content: "\e4c8"; }
+
+.fa-phone-flip::before {
+  content: "\f879"; }
+
+.fa-phone-alt::before {
+  content: "\f879"; }
+
+.fa-truck-front::before {
+  content: "\e2b7"; }
+
+.fa-cat::before {
+  content: "\f6be"; }
+
+.fa-anchor-circle-exclamation::before {
+  content: "\e4ab"; }
+
+.fa-truck-field::before {
+  content: "\e58d"; }
+
+.fa-route::before {
+  content: "\f4d7"; }
+
+.fa-clipboard-question::before {
+  content: "\e4e3"; }
+
+.fa-panorama::before {
+  content: "\e209"; }
+
+.fa-comment-medical::before {
+  content: "\f7f5"; }
+
+.fa-teeth-open::before {
+  content: "\f62f"; }
+
+.fa-file-circle-minus::before {
+  content: "\e4ed"; }
+
+.fa-tags::before {
+  content: "\f02c"; }
+
+.fa-wine-glass::before {
+  content: "\f4e3"; }
+
+.fa-forward-fast::before {
+  content: "\f050"; }
+
+.fa-fast-forward::before {
+  content: "\f050"; }
+
+.fa-face-meh-blank::before {
+  content: "\f5a4"; }
+
+.fa-meh-blank::before {
+  content: "\f5a4"; }
+
+.fa-square-parking::before {
+  content: "\f540"; }
+
+.fa-parking::before {
+  content: "\f540"; }
+
+.fa-house-signal::before {
+  content: "\e012"; }
+
+.fa-bars-progress::before {
+  content: "\f828"; }
+
+.fa-tasks-alt::before {
+  content: "\f828"; }
+
+.fa-faucet-drip::before {
+  content: "\e006"; }
+
+.fa-cart-flatbed::before {
+  content: "\f474"; }
+
+.fa-dolly-flatbed::before {
+  content: "\f474"; }
+
+.fa-ban-smoking::before {
+  content: "\f54d"; }
+
+.fa-smoking-ban::before {
+  content: "\f54d"; }
+
+.fa-terminal::before {
+  content: "\f120"; }
+
+.fa-mobile-button::before {
+  content: "\f10b"; }
+
+.fa-house-medical-flag::before {
+  content: "\e514"; }
+
+.fa-basket-shopping::before {
+  content: "\f291"; }
+
+.fa-shopping-basket::before {
+  content: "\f291"; }
+
+.fa-tape::before {
+  content: "\f4db"; }
+
+.fa-bus-simple::before {
+  content: "\f55e"; }
+
+.fa-bus-alt::before {
+  content: "\f55e"; }
+
+.fa-eye::before {
+  content: "\f06e"; }
+
+.fa-face-sad-cry::before {
+  content: "\f5b3"; }
+
+.fa-sad-cry::before {
+  content: "\f5b3"; }
+
+.fa-audio-description::before {
+  content: "\f29e"; }
+
+.fa-person-military-to-person::before {
+  content: "\e54c"; }
+
+.fa-file-shield::before {
+  content: "\e4f0"; }
+
+.fa-user-slash::before {
+  content: "\f506"; }
+
+.fa-pen::before {
+  content: "\f304"; }
+
+.fa-tower-observation::before {
+  content: "\e586"; }
+
+.fa-file-code::before {
+  content: "\f1c9"; }
+
+.fa-signal::before {
+  content: "\f012"; }
+
+.fa-signal-5::before {
+  content: "\f012"; }
+
+.fa-signal-perfect::before {
+  content: "\f012"; }
+
+.fa-bus::before {
+  content: "\f207"; }
+
+.fa-heart-circle-xmark::before {
+  content: "\e501"; }
+
+.fa-house-chimney::before {
+  content: "\e3af"; }
+
+.fa-home-lg::before {
+  content: "\e3af"; }
+
+.fa-window-maximize::before {
+  content: "\f2d0"; }
+
+.fa-face-frown::before {
+  content: "\f119"; }
+
+.fa-frown::before {
+  content: "\f119"; }
+
+.fa-prescription::before {
+  content: "\f5b1"; }
+
+.fa-shop::before {
+  content: "\f54f"; }
+
+.fa-store-alt::before {
+  content: "\f54f"; }
+
+.fa-floppy-disk::before {
+  content: "\f0c7"; }
+
+.fa-save::before {
+  content: "\f0c7"; }
+
+.fa-vihara::before {
+  content: "\f6a7"; }
+
+.fa-scale-unbalanced::before {
+  content: "\f515"; }
+
+.fa-balance-scale-left::before {
+  content: "\f515"; }
+
+.fa-sort-up::before {
+  content: "\f0de"; }
+
+.fa-sort-asc::before {
+  content: "\f0de"; }
+
+.fa-comment-dots::before {
+  content: "\f4ad"; }
+
+.fa-commenting::before {
+  content: "\f4ad"; }
+
+.fa-plant-wilt::before {
+  content: "\e5aa"; }
+
+.fa-diamond::before {
+  content: "\f219"; }
+
+.fa-face-grin-squint::before {
+  content: "\f585"; }
+
+.fa-grin-squint::before {
+  content: "\f585"; }
+
+.fa-hand-holding-dollar::before {
+  content: "\f4c0"; }
+
+.fa-hand-holding-usd::before {
+  content: "\f4c0"; }
+
+.fa-bacterium::before {
+  content: "\e05a"; }
+
+.fa-hand-pointer::before {
+  content: "\f25a"; }
+
+.fa-drum-steelpan::before {
+  content: "\f56a"; }
+
+.fa-hand-scissors::before {
+  content: "\f257"; }
+
+.fa-hands-praying::before {
+  content: "\f684"; }
+
+.fa-praying-hands::before {
+  content: "\f684"; }
+
+.fa-arrow-rotate-right::before {
+  content: "\f01e"; }
+
+.fa-arrow-right-rotate::before {
+  content: "\f01e"; }
+
+.fa-arrow-rotate-forward::before {
+  content: "\f01e"; }
+
+.fa-redo::before {
+  content: "\f01e"; }
+
+.fa-biohazard::before {
+  content: "\f780"; }
+
+.fa-location-crosshairs::before {
+  content: "\f601"; }
+
+.fa-location::before {
+  content: "\f601"; }
+
+.fa-mars-double::before {
+  content: "\f227"; }
+
+.fa-child-dress::before {
+  content: "\e59c"; }
+
+.fa-users-between-lines::before {
+  content: "\e591"; }
+
+.fa-lungs-virus::before {
+  content: "\e067"; }
+
+.fa-face-grin-tears::before {
+  content: "\f588"; }
+
+.fa-grin-tears::before {
+  content: "\f588"; }
+
+.fa-phone::before {
+  content: "\f095"; }
+
+.fa-calendar-xmark::before {
+  content: "\f273"; }
+
+.fa-calendar-times::before {
+  content: "\f273"; }
+
+.fa-child-reaching::before {
+  content: "\e59d"; }
+
+.fa-head-side-virus::before {
+  content: "\e064"; }
+
+.fa-user-gear::before {
+  content: "\f4fe"; }
+
+.fa-user-cog::before {
+  content: "\f4fe"; }
+
+.fa-arrow-up-1-9::before {
+  content: "\f163"; }
+
+.fa-sort-numeric-up::before {
+  content: "\f163"; }
+
+.fa-door-closed::before {
+  content: "\f52a"; }
+
+.fa-shield-virus::before {
+  content: "\e06c"; }
+
+.fa-dice-six::before {
+  content: "\f526"; }
+
+.fa-mosquito-net::before {
+  content: "\e52c"; }
+
+.fa-bridge-water::before {
+  content: "\e4ce"; }
+
+.fa-person-booth::before {
+  content: "\f756"; }
+
+.fa-text-width::before {
+  content: "\f035"; }
+
+.fa-hat-wizard::before {
+  content: "\f6e8"; }
+
+.fa-pen-fancy::before {
+  content: "\f5ac"; }
+
+.fa-person-digging::before {
+  content: "\f85e"; }
+
+.fa-digging::before {
+  content: "\f85e"; }
+
+.fa-trash::before {
+  content: "\f1f8"; }
+
+.fa-gauge-simple::before {
+  content: "\f629"; }
+
+.fa-gauge-simple-med::before {
+  content: "\f629"; }
+
+.fa-tachometer-average::before {
+  content: "\f629"; }
+
+.fa-book-medical::before {
+  content: "\f7e6"; }
+
+.fa-poo::before {
+  content: "\f2fe"; }
+
+.fa-quote-right::before {
+  content: "\f10e"; }
+
+.fa-quote-right-alt::before {
+  content: "\f10e"; }
+
+.fa-shirt::before {
+  content: "\f553"; }
+
+.fa-t-shirt::before {
+  content: "\f553"; }
+
+.fa-tshirt::before {
+  content: "\f553"; }
+
+.fa-cubes::before {
+  content: "\f1b3"; }
+
+.fa-divide::before {
+  content: "\f529"; }
+
+.fa-tenge-sign::before {
+  content: "\f7d7"; }
+
+.fa-tenge::before {
+  content: "\f7d7"; }
+
+.fa-headphones::before {
+  content: "\f025"; }
+
+.fa-hands-holding::before {
+  content: "\f4c2"; }
+
+.fa-hands-clapping::before {
+  content: "\e1a8"; }
+
+.fa-republican::before {
+  content: "\f75e"; }
+
+.fa-arrow-left::before {
+  content: "\f060"; }
+
+.fa-person-circle-xmark::before {
+  content: "\e543"; }
+
+.fa-ruler::before {
+  content: "\f545"; }
+
+.fa-align-left::before {
+  content: "\f036"; }
+
+.fa-dice-d6::before {
+  content: "\f6d1"; }
+
+.fa-restroom::before {
+  content: "\f7bd"; }
+
+.fa-j::before {
+  content: "\4a"; }
+
+.fa-users-viewfinder::before {
+  content: "\e595"; }
+
+.fa-file-video::before {
+  content: "\f1c8"; }
+
+.fa-up-right-from-square::before {
+  content: "\f35d"; }
+
+.fa-external-link-alt::before {
+  content: "\f35d"; }
+
+.fa-table-cells::before {
+  content: "\f00a"; }
+
+.fa-th::before {
+  content: "\f00a"; }
+
+.fa-file-pdf::before {
+  content: "\f1c1"; }
+
+.fa-book-bible::before {
+  content: "\f647"; }
+
+.fa-bible::before {
+  content: "\f647"; }
+
+.fa-o::before {
+  content: "\4f"; }
+
+.fa-suitcase-medical::before {
+  content: "\f0fa"; }
+
+.fa-medkit::before {
+  content: "\f0fa"; }
+
+.fa-user-secret::before {
+  content: "\f21b"; }
+
+.fa-otter::before {
+  content: "\f700"; }
+
+.fa-person-dress::before {
+  content: "\f182"; }
+
+.fa-female::before {
+  content: "\f182"; }
+
+.fa-comment-dollar::before {
+  content: "\f651"; }
+
+.fa-business-time::before {
+  content: "\f64a"; }
+
+.fa-briefcase-clock::before {
+  content: "\f64a"; }
+
+.fa-table-cells-large::before {
+  content: "\f009"; }
+
+.fa-th-large::before {
+  content: "\f009"; }
+
+.fa-book-tanakh::before {
+  content: "\f827"; }
+
+.fa-tanakh::before {
+  content: "\f827"; }
+
+.fa-phone-volume::before {
+  content: "\f2a0"; }
+
+.fa-volume-control-phone::before {
+  content: "\f2a0"; }
+
+.fa-hat-cowboy-side::before {
+  content: "\f8c1"; }
+
+.fa-clipboard-user::before {
+  content: "\f7f3"; }
+
+.fa-child::before {
+  content: "\f1ae"; }
+
+.fa-lira-sign::before {
+  content: "\f195"; }
+
+.fa-satellite::before {
+  content: "\f7bf"; }
+
+.fa-plane-lock::before {
+  content: "\e558"; }
+
+.fa-tag::before {
+  content: "\f02b"; }
+
+.fa-comment::before {
+  content: "\f075"; }
+
+.fa-cake-candles::before {
+  content: "\f1fd"; }
+
+.fa-birthday-cake::before {
+  content: "\f1fd"; }
+
+.fa-cake::before {
+  content: "\f1fd"; }
+
+.fa-envelope::before {
+  content: "\f0e0"; }
+
+.fa-angles-up::before {
+  content: "\f102"; }
+
+.fa-angle-double-up::before {
+  content: "\f102"; }
+
+.fa-paperclip::before {
+  content: "\f0c6"; }
+
+.fa-arrow-right-to-city::before {
+  content: "\e4b3"; }
+
+.fa-ribbon::before {
+  content: "\f4d6"; }
+
+.fa-lungs::before {
+  content: "\f604"; }
+
+.fa-arrow-up-9-1::before {
+  content: "\f887"; }
+
+.fa-sort-numeric-up-alt::before {
+  content: "\f887"; }
+
+.fa-litecoin-sign::before {
+  content: "\e1d3"; }
+
+.fa-border-none::before {
+  content: "\f850"; }
+
+.fa-circle-nodes::before {
+  content: "\e4e2"; }
+
+.fa-parachute-box::before {
+  content: "\f4cd"; }
+
+.fa-indent::before {
+  content: "\f03c"; }
+
+.fa-truck-field-un::before {
+  content: "\e58e"; }
+
+.fa-hourglass::before {
+  content: "\f254"; }
+
+.fa-hourglass-empty::before {
+  content: "\f254"; }
+
+.fa-mountain::before {
+  content: "\f6fc"; }
+
+.fa-user-doctor::before {
+  content: "\f0f0"; }
+
+.fa-user-md::before {
+  content: "\f0f0"; }
+
+.fa-circle-info::before {
+  content: "\f05a"; }
+
+.fa-info-circle::before {
+  content: "\f05a"; }
+
+.fa-cloud-meatball::before {
+  content: "\f73b"; }
+
+.fa-camera::before {
+  content: "\f030"; }
+
+.fa-camera-alt::before {
+  content: "\f030"; }
+
+.fa-square-virus::before {
+  content: "\e578"; }
+
+.fa-meteor::before {
+  content: "\f753"; }
+
+.fa-car-on::before {
+  content: "\e4dd"; }
+
+.fa-sleigh::before {
+  content: "\f7cc"; }
+
+.fa-arrow-down-1-9::before {
+  content: "\f162"; }
+
+.fa-sort-numeric-asc::before {
+  content: "\f162"; }
+
+.fa-sort-numeric-down::before {
+  content: "\f162"; }
+
+.fa-hand-holding-droplet::before {
+  content: "\f4c1"; }
+
+.fa-hand-holding-water::before {
+  content: "\f4c1"; }
+
+.fa-water::before {
+  content: "\f773"; }
+
+.fa-calendar-check::before {
+  content: "\f274"; }
+
+.fa-braille::before {
+  content: "\f2a1"; }
+
+.fa-prescription-bottle-medical::before {
+  content: "\f486"; }
+
+.fa-prescription-bottle-alt::before {
+  content: "\f486"; }
+
+.fa-landmark::before {
+  content: "\f66f"; }
+
+.fa-truck::before {
+  content: "\f0d1"; }
+
+.fa-crosshairs::before {
+  content: "\f05b"; }
+
+.fa-person-cane::before {
+  content: "\e53c"; }
+
+.fa-tent::before {
+  content: "\e57d"; }
+
+.fa-vest-patches::before {
+  content: "\e086"; }
+
+.fa-check-double::before {
+  content: "\f560"; }
+
+.fa-arrow-down-a-z::before {
+  content: "\f15d"; }
+
+.fa-sort-alpha-asc::before {
+  content: "\f15d"; }
+
+.fa-sort-alpha-down::before {
+  content: "\f15d"; }
+
+.fa-money-bill-wheat::before {
+  content: "\e52a"; }
+
+.fa-cookie::before {
+  content: "\f563"; }
+
+.fa-arrow-rotate-left::before {
+  content: "\f0e2"; }
+
+.fa-arrow-left-rotate::before {
+  content: "\f0e2"; }
+
+.fa-arrow-rotate-back::before {
+  content: "\f0e2"; }
+
+.fa-arrow-rotate-backward::before {
+  content: "\f0e2"; }
+
+.fa-undo::before {
+  content: "\f0e2"; }
+
+.fa-hard-drive::before {
+  content: "\f0a0"; }
+
+.fa-hdd::before {
+  content: "\f0a0"; }
+
+.fa-face-grin-squint-tears::before {
+  content: "\f586"; }
+
+.fa-grin-squint-tears::before {
+  content: "\f586"; }
+
+.fa-dumbbell::before {
+  content: "\f44b"; }
+
+.fa-rectangle-list::before {
+  content: "\f022"; }
+
+.fa-list-alt::before {
+  content: "\f022"; }
+
+.fa-tarp-droplet::before {
+  content: "\e57c"; }
+
+.fa-house-medical-circle-check::before {
+  content: "\e511"; }
+
+.fa-person-skiing-nordic::before {
+  content: "\f7ca"; }
+
+.fa-skiing-nordic::before {
+  content: "\f7ca"; }
+
+.fa-calendar-plus::before {
+  content: "\f271"; }
+
+.fa-plane-arrival::before {
+  content: "\f5af"; }
+
+.fa-circle-left::before {
+  content: "\f359"; }
+
+.fa-arrow-alt-circle-left::before {
+  content: "\f359"; }
+
+.fa-train-subway::before {
+  content: "\f239"; }
+
+.fa-subway::before {
+  content: "\f239"; }
+
+.fa-chart-gantt::before {
+  content: "\e0e4"; }
+
+.fa-indian-rupee-sign::before {
+  content: "\e1bc"; }
+
+.fa-indian-rupee::before {
+  content: "\e1bc"; }
+
+.fa-inr::before {
+  content: "\e1bc"; }
+
+.fa-crop-simple::before {
+  content: "\f565"; }
+
+.fa-crop-alt::before {
+  content: "\f565"; }
+
+.fa-money-bill-1::before {
+  content: "\f3d1"; }
+
+.fa-money-bill-alt::before {
+  content: "\f3d1"; }
+
+.fa-left-long::before {
+  content: "\f30a"; }
+
+.fa-long-arrow-alt-left::before {
+  content: "\f30a"; }
+
+.fa-dna::before {
+  content: "\f471"; }
+
+.fa-virus-slash::before {
+  content: "\e075"; }
+
+.fa-minus::before {
+  content: "\f068"; }
+
+.fa-subtract::before {
+  content: "\f068"; }
+
+.fa-chess::before {
+  content: "\f439"; }
+
+.fa-arrow-left-long::before {
+  content: "\f177"; }
+
+.fa-long-arrow-left::before {
+  content: "\f177"; }
+
+.fa-plug-circle-check::before {
+  content: "\e55c"; }
+
+.fa-street-view::before {
+  content: "\f21d"; }
+
+.fa-franc-sign::before {
+  content: "\e18f"; }
+
+.fa-volume-off::before {
+  content: "\f026"; }
+
+.fa-hands-asl-interpreting::before {
+  content: "\f2a3"; }
+
+.fa-american-sign-language-interpreting::before {
+  content: "\f2a3"; }
+
+.fa-asl-interpreting::before {
+  content: "\f2a3"; }
+
+.fa-hands-american-sign-language-interpreting::before {
+  content: "\f2a3"; }
+
+.fa-gear::before {
+  content: "\f013"; }
+
+.fa-cog::before {
+  content: "\f013"; }
+
+.fa-droplet-slash::before {
+  content: "\f5c7"; }
+
+.fa-tint-slash::before {
+  content: "\f5c7"; }
+
+.fa-mosque::before {
+  content: "\f678"; }
+
+.fa-mosquito::before {
+  content: "\e52b"; }
+
+.fa-star-of-david::before {
+  content: "\f69a"; }
+
+.fa-person-military-rifle::before {
+  content: "\e54b"; }
+
+.fa-cart-shopping::before {
+  content: "\f07a"; }
+
+.fa-shopping-cart::before {
+  content: "\f07a"; }
+
+.fa-vials::before {
+  content: "\f493"; }
+
+.fa-plug-circle-plus::before {
+  content: "\e55f"; }
+
+.fa-place-of-worship::before {
+  content: "\f67f"; }
+
+.fa-grip-vertical::before {
+  content: "\f58e"; }
+
+.fa-arrow-turn-up::before {
+  content: "\f148"; }
+
+.fa-level-up::before {
+  content: "\f148"; }
+
+.fa-u::before {
+  content: "\55"; }
+
+.fa-square-root-variable::before {
+  content: "\f698"; }
+
+.fa-square-root-alt::before {
+  content: "\f698"; }
+
+.fa-clock::before {
+  content: "\f017"; }
+
+.fa-clock-four::before {
+  content: "\f017"; }
+
+.fa-backward-step::before {
+  content: "\f048"; }
+
+.fa-step-backward::before {
+  content: "\f048"; }
+
+.fa-pallet::before {
+  content: "\f482"; }
+
+.fa-faucet::before {
+  content: "\e005"; }
+
+.fa-baseball-bat-ball::before {
+  content: "\f432"; }
+
+.fa-s::before {
+  content: "\53"; }
+
+.fa-timeline::before {
+  content: "\e29c"; }
+
+.fa-keyboard::before {
+  content: "\f11c"; }
+
+.fa-caret-down::before {
+  content: "\f0d7"; }
+
+.fa-house-chimney-medical::before {
+  content: "\f7f2"; }
+
+.fa-clinic-medical::before {
+  content: "\f7f2"; }
+
+.fa-temperature-three-quarters::before {
+  content: "\f2c8"; }
+
+.fa-temperature-3::before {
+  content: "\f2c8"; }
+
+.fa-thermometer-3::before {
+  content: "\f2c8"; }
+
+.fa-thermometer-three-quarters::before {
+  content: "\f2c8"; }
+
+.fa-mobile-screen::before {
+  content: "\f3cf"; }
+
+.fa-mobile-android-alt::before {
+  content: "\f3cf"; }
+
+.fa-plane-up::before {
+  content: "\e22d"; }
+
+.fa-piggy-bank::before {
+  content: "\f4d3"; }
+
+.fa-battery-half::before {
+  content: "\f242"; }
+
+.fa-battery-3::before {
+  content: "\f242"; }
+
+.fa-mountain-city::before {
+  content: "\e52e"; }
+
+.fa-coins::before {
+  content: "\f51e"; }
+
+.fa-khanda::before {
+  content: "\f66d"; }
+
+.fa-sliders::before {
+  content: "\f1de"; }
+
+.fa-sliders-h::before {
+  content: "\f1de"; }
+
+.fa-folder-tree::before {
+  content: "\f802"; }
+
+.fa-network-wired::before {
+  content: "\f6ff"; }
+
+.fa-map-pin::before {
+  content: "\f276"; }
+
+.fa-hamsa::before {
+  content: "\f665"; }
+
+.fa-cent-sign::before {
+  content: "\e3f5"; }
+
+.fa-flask::before {
+  content: "\f0c3"; }
+
+.fa-person-pregnant::before {
+  content: "\e31e"; }
+
+.fa-wand-sparkles::before {
+  content: "\f72b"; }
+
+.fa-ellipsis-vertical::before {
+  content: "\f142"; }
+
+.fa-ellipsis-v::before {
+  content: "\f142"; }
+
+.fa-ticket::before {
+  content: "\f145"; }
+
+.fa-power-off::before {
+  content: "\f011"; }
+
+.fa-right-long::before {
+  content: "\f30b"; }
+
+.fa-long-arrow-alt-right::before {
+  content: "\f30b"; }
+
+.fa-flag-usa::before {
+  content: "\f74d"; }
+
+.fa-laptop-file::before {
+  content: "\e51d"; }
+
+.fa-tty::before {
+  content: "\f1e4"; }
+
+.fa-teletype::before {
+  content: "\f1e4"; }
+
+.fa-diagram-next::before {
+  content: "\e476"; }
+
+.fa-person-rifle::before {
+  content: "\e54e"; }
+
+.fa-house-medical-circle-exclamation::before {
+  content: "\e512"; }
+
+.fa-closed-captioning::before {
+  content: "\f20a"; }
+
+.fa-person-hiking::before {
+  content: "\f6ec"; }
+
+.fa-hiking::before {
+  content: "\f6ec"; }
+
+.fa-venus-double::before {
+  content: "\f226"; }
+
+.fa-images::before {
+  content: "\f302"; }
+
+.fa-calculator::before {
+  content: "\f1ec"; }
+
+.fa-people-pulling::before {
+  content: "\e535"; }
+
+.fa-n::before {
+  content: "\4e"; }
+
+.fa-cable-car::before {
+  content: "\f7da"; }
+
+.fa-tram::before {
+  content: "\f7da"; }
+
+.fa-cloud-rain::before {
+  content: "\f73d"; }
+
+.fa-building-circle-xmark::before {
+  content: "\e4d4"; }
+
+.fa-ship::before {
+  content: "\f21a"; }
+
+.fa-arrows-down-to-line::before {
+  content: "\e4b8"; }
+
+.fa-download::before {
+  content: "\f019"; }
+
+.fa-face-grin::before {
+  content: "\f580"; }
+
+.fa-grin::before {
+  content: "\f580"; }
+
+.fa-delete-left::before {
+  content: "\f55a"; }
+
+.fa-backspace::before {
+  content: "\f55a"; }
+
+.fa-eye-dropper::before {
+  content: "\f1fb"; }
+
+.fa-eye-dropper-empty::before {
+  content: "\f1fb"; }
+
+.fa-eyedropper::before {
+  content: "\f1fb"; }
+
+.fa-file-circle-check::before {
+  content: "\e5a0"; }
+
+.fa-forward::before {
+  content: "\f04e"; }
+
+.fa-mobile::before {
+  content: "\f3ce"; }
+
+.fa-mobile-android::before {
+  content: "\f3ce"; }
+
+.fa-mobile-phone::before {
+  content: "\f3ce"; }
+
+.fa-face-meh::before {
+  content: "\f11a"; }
+
+.fa-meh::before {
+  content: "\f11a"; }
+
+.fa-align-center::before {
+  content: "\f037"; }
+
+.fa-book-skull::before {
+  content: "\f6b7"; }
+
+.fa-book-dead::before {
+  content: "\f6b7"; }
+
+.fa-id-card::before {
+  content: "\f2c2"; }
+
+.fa-drivers-license::before {
+  content: "\f2c2"; }
+
+.fa-outdent::before {
+  content: "\f03b"; }
+
+.fa-dedent::before {
+  content: "\f03b"; }
+
+.fa-heart-circle-exclamation::before {
+  content: "\e4fe"; }
+
+.fa-house::before {
+  content: "\f015"; }
+
+.fa-home::before {
+  content: "\f015"; }
+
+.fa-home-alt::before {
+  content: "\f015"; }
+
+.fa-home-lg-alt::before {
+  content: "\f015"; }
+
+.fa-calendar-week::before {
+  content: "\f784"; }
+
+.fa-laptop-medical::before {
+  content: "\f812"; }
+
+.fa-b::before {
+  content: "\42"; }
+
+.fa-file-medical::before {
+  content: "\f477"; }
+
+.fa-dice-one::before {
+  content: "\f525"; }
+
+.fa-kiwi-bird::before {
+  content: "\f535"; }
+
+.fa-arrow-right-arrow-left::before {
+  content: "\f0ec"; }
+
+.fa-exchange::before {
+  content: "\f0ec"; }
+
+.fa-rotate-right::before {
+  content: "\f2f9"; }
+
+.fa-redo-alt::before {
+  content: "\f2f9"; }
+
+.fa-rotate-forward::before {
+  content: "\f2f9"; }
+
+.fa-utensils::before {
+  content: "\f2e7"; }
+
+.fa-cutlery::before {
+  content: "\f2e7"; }
+
+.fa-arrow-up-wide-short::before {
+  content: "\f161"; }
+
+.fa-sort-amount-up::before {
+  content: "\f161"; }
+
+.fa-mill-sign::before {
+  content: "\e1ed"; }
+
+.fa-bowl-rice::before {
+  content: "\e2eb"; }
+
+.fa-skull::before {
+  content: "\f54c"; }
+
+.fa-tower-broadcast::before {
+  content: "\f519"; }
+
+.fa-broadcast-tower::before {
+  content: "\f519"; }
+
+.fa-truck-pickup::before {
+  content: "\f63c"; }
+
+.fa-up-long::before {
+  content: "\f30c"; }
+
+.fa-long-arrow-alt-up::before {
+  content: "\f30c"; }
+
+.fa-stop::before {
+  content: "\f04d"; }
+
+.fa-code-merge::before {
+  content: "\f387"; }
+
+.fa-upload::before {
+  content: "\f093"; }
+
+.fa-hurricane::before {
+  content: "\f751"; }
+
+.fa-mound::before {
+  content: "\e52d"; }
+
+.fa-toilet-portable::before {
+  content: "\e583"; }
+
+.fa-compact-disc::before {
+  content: "\f51f"; }
+
+.fa-file-arrow-down::before {
+  content: "\f56d"; }
+
+.fa-file-download::before {
+  content: "\f56d"; }
+
+.fa-caravan::before {
+  content: "\f8ff"; }
+
+.fa-shield-cat::before {
+  content: "\e572"; }
+
+.fa-bolt::before {
+  content: "\f0e7"; }
+
+.fa-zap::before {
+  content: "\f0e7"; }
+
+.fa-glass-water::before {
+  content: "\e4f4"; }
+
+.fa-oil-well::before {
+  content: "\e532"; }
+
+.fa-vault::before {
+  content: "\e2c5"; }
+
+.fa-mars::before {
+  content: "\f222"; }
+
+.fa-toilet::before {
+  content: "\f7d8"; }
+
+.fa-plane-circle-xmark::before {
+  content: "\e557"; }
+
+.fa-yen-sign::before {
+  content: "\f157"; }
+
+.fa-cny::before {
+  content: "\f157"; }
+
+.fa-jpy::before {
+  content: "\f157"; }
+
+.fa-rmb::before {
+  content: "\f157"; }
+
+.fa-yen::before {
+  content: "\f157"; }
+
+.fa-ruble-sign::before {
+  content: "\f158"; }
+
+.fa-rouble::before {
+  content: "\f158"; }
+
+.fa-rub::before {
+  content: "\f158"; }
+
+.fa-ruble::before {
+  content: "\f158"; }
+
+.fa-sun::before {
+  content: "\f185"; }
+
+.fa-guitar::before {
+  content: "\f7a6"; }
+
+.fa-face-laugh-wink::before {
+  content: "\f59c"; }
+
+.fa-laugh-wink::before {
+  content: "\f59c"; }
+
+.fa-horse-head::before {
+  content: "\f7ab"; }
+
+.fa-bore-hole::before {
+  content: "\e4c3"; }
+
+.fa-industry::before {
+  content: "\f275"; }
+
+.fa-circle-down::before {
+  content: "\f358"; }
+
+.fa-arrow-alt-circle-down::before {
+  content: "\f358"; }
+
+.fa-arrows-turn-to-dots::before {
+  content: "\e4c1"; }
+
+.fa-florin-sign::before {
+  content: "\e184"; }
+
+.fa-arrow-down-short-wide::before {
+  content: "\f884"; }
+
+.fa-sort-amount-desc::before {
+  content: "\f884"; }
+
+.fa-sort-amount-down-alt::before {
+  content: "\f884"; }
+
+.fa-less-than::before {
+  content: "\3c"; }
+
+.fa-angle-down::before {
+  content: "\f107"; }
+
+.fa-car-tunnel::before {
+  content: "\e4de"; }
+
+.fa-head-side-cough::before {
+  content: "\e061"; }
+
+.fa-grip-lines::before {
+  content: "\f7a4"; }
+
+.fa-thumbs-down::before {
+  content: "\f165"; }
+
+.fa-user-lock::before {
+  content: "\f502"; }
+
+.fa-arrow-right-long::before {
+  content: "\f178"; }
+
+.fa-long-arrow-right::before {
+  content: "\f178"; }
+
+.fa-anchor-circle-xmark::before {
+  content: "\e4ac"; }
+
+.fa-ellipsis::before {
+  content: "\f141"; }
+
+.fa-ellipsis-h::before {
+  content: "\f141"; }
+
+.fa-chess-pawn::before {
+  content: "\f443"; }
+
+.fa-kit-medical::before {
+  content: "\f479"; }
+
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+  content: "\f479"; }
+
+.fa-person-through-window::before {
+  content: "\e5a9"; }
+
+.fa-toolbox::before {
+  content: "\f552"; }
+
+.fa-hands-holding-circle::before {
+  content: "\e4fb"; }
+
+.fa-bug::before {
+  content: "\f188"; }
+
+.fa-credit-card::before {
+  content: "\f09d"; }
+
+.fa-credit-card-alt::before {
+  content: "\f09d"; }
+
+.fa-car::before {
+  content: "\f1b9"; }
+
+.fa-automobile::before {
+  content: "\f1b9"; }
+
+.fa-hand-holding-hand::before {
+  content: "\e4f7"; }
+
+.fa-book-open-reader::before {
+  content: "\f5da"; }
+
+.fa-book-reader::before {
+  content: "\f5da"; }
+
+.fa-mountain-sun::before {
+  content: "\e52f"; }
+
+.fa-arrows-left-right-to-line::before {
+  content: "\e4ba"; }
+
+.fa-dice-d20::before {
+  content: "\f6cf"; }
+
+.fa-truck-droplet::before {
+  content: "\e58c"; }
+
+.fa-file-circle-xmark::before {
+  content: "\e5a1"; }
+
+.fa-temperature-arrow-up::before {
+  content: "\e040"; }
+
+.fa-temperature-up::before {
+  content: "\e040"; }
+
+.fa-medal::before {
+  content: "\f5a2"; }
+
+.fa-bed::before {
+  content: "\f236"; }
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+.fa-square-h::before {
+  content: "\f0fd"; }
+
+.fa-h-square::before {
+  content: "\f0fd"; }
+
+.fa-podcast::before {
+  content: "\f2ce"; }
+
+.fa-temperature-full::before {
+  content: "\f2c7"; }
+
+.fa-temperature-4::before {
+  content: "\f2c7"; }
+
+.fa-thermometer-4::before {
+  content: "\f2c7"; }
+
+.fa-thermometer-full::before {
+  content: "\f2c7"; }
+
+.fa-bell::before {
+  content: "\f0f3"; }
+
+.fa-superscript::before {
+  content: "\f12b"; }
+
+.fa-plug-circle-xmark::before {
+  content: "\e560"; }
+
+.fa-star-of-life::before {
+  content: "\f621"; }
+
+.fa-phone-slash::before {
+  content: "\f3dd"; }
+
+.fa-paint-roller::before {
+  content: "\f5aa"; }
+
+.fa-handshake-angle::before {
+  content: "\f4c4"; }
+
+.fa-hands-helping::before {
+  content: "\f4c4"; }
+
+.fa-location-dot::before {
+  content: "\f3c5"; }
+
+.fa-map-marker-alt::before {
+  content: "\f3c5"; }
+
+.fa-file::before {
+  content: "\f15b"; }
+
+.fa-greater-than::before {
+  content: "\3e"; }
+
+.fa-person-swimming::before {
+  content: "\f5c4"; }
+
+.fa-swimmer::before {
+  content: "\f5c4"; }
+
+.fa-arrow-down::before {
+  content: "\f063"; }
+
+.fa-droplet::before {
+  content: "\f043"; }
+
+.fa-tint::before {
+  content: "\f043"; }
+
+.fa-eraser::before {
+  content: "\f12d"; }
+
+.fa-earth-americas::before {
+  content: "\f57d"; }
+
+.fa-earth::before {
+  content: "\f57d"; }
+
+.fa-earth-america::before {
+  content: "\f57d"; }
+
+.fa-globe-americas::before {
+  content: "\f57d"; }
+
+.fa-person-burst::before {
+  content: "\e53b"; }
+
+.fa-dove::before {
+  content: "\f4ba"; }
+
+.fa-battery-empty::before {
+  content: "\f244"; }
+
+.fa-battery-0::before {
+  content: "\f244"; }
+
+.fa-socks::before {
+  content: "\f696"; }
+
+.fa-inbox::before {
+  content: "\f01c"; }
+
+.fa-section::before {
+  content: "\e447"; }
+
+.fa-gauge-high::before {
+  content: "\f625"; }
+
+.fa-tachometer-alt::before {
+  content: "\f625"; }
+
+.fa-tachometer-alt-fast::before {
+  content: "\f625"; }
+
+.fa-envelope-open-text::before {
+  content: "\f658"; }
+
+.fa-hospital::before {
+  content: "\f0f8"; }
+
+.fa-hospital-alt::before {
+  content: "\f0f8"; }
+
+.fa-hospital-wide::before {
+  content: "\f0f8"; }
+
+.fa-wine-bottle::before {
+  content: "\f72f"; }
+
+.fa-chess-rook::before {
+  content: "\f447"; }
+
+.fa-bars-staggered::before {
+  content: "\f550"; }
+
+.fa-reorder::before {
+  content: "\f550"; }
+
+.fa-stream::before {
+  content: "\f550"; }
+
+.fa-dharmachakra::before {
+  content: "\f655"; }
+
+.fa-hotdog::before {
+  content: "\f80f"; }
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+.fa-person-walking-with-cane::before {
+  content: "\f29d"; }
+
+.fa-blind::before {
+  content: "\f29d"; }
+
+.fa-drum::before {
+  content: "\f569"; }
+
+.fa-ice-cream::before {
+  content: "\f810"; }
+
+.fa-heart-circle-bolt::before {
+  content: "\e4fc"; }
+
+.fa-fax::before {
+  content: "\f1ac"; }
+
+.fa-paragraph::before {
+  content: "\f1dd"; }
+
+.fa-check-to-slot::before {
+  content: "\f772"; }
+
+.fa-vote-yea::before {
+  content: "\f772"; }
+
+.fa-star-half::before {
+  content: "\f089"; }
+
+.fa-boxes-stacked::before {
+  content: "\f468"; }
+
+.fa-boxes::before {
+  content: "\f468"; }
+
+.fa-boxes-alt::before {
+  content: "\f468"; }
+
+.fa-link::before {
+  content: "\f0c1"; }
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+.fa-chain::before {
+  content: "\f0c1"; }
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+.fa-ear-listen::before {
+  content: "\f2a2"; }
+
+.fa-assistive-listening-systems::before {
+  content: "\f2a2"; }
+
+.fa-tree-city::before {
+  content: "\e587"; }
+
+.fa-play::before {
+  content: "\f04b"; }
+
+.fa-font::before {
+  content: "\f031"; }
+
+.fa-table-cells-row-lock::before {
+  content: "\e67a"; }
+
+.fa-rupiah-sign::before {
+  content: "\e23d"; }
+
+.fa-magnifying-glass::before {
+  content: "\f002"; }
+
+.fa-search::before {
+  content: "\f002"; }
+
+.fa-table-tennis-paddle-ball::before {
+  content: "\f45d"; }
+
+.fa-ping-pong-paddle-ball::before {
+  content: "\f45d"; }
+
+.fa-table-tennis::before {
+  content: "\f45d"; }
+
+.fa-person-dots-from-line::before {
+  content: "\f470"; }
+
+.fa-diagnoses::before {
+  content: "\f470"; }
+
+.fa-trash-can-arrow-up::before {
+  content: "\f82a"; }
+
+.fa-trash-restore-alt::before {
+  content: "\f82a"; }
+
+.fa-naira-sign::before {
+  content: "\e1f6"; }
+
+.fa-cart-arrow-down::before {
+  content: "\f218"; }
+
+.fa-walkie-talkie::before {
+  content: "\f8ef"; }
+
+.fa-file-pen::before {
+  content: "\f31c"; }
+
+.fa-file-edit::before {
+  content: "\f31c"; }
+
+.fa-receipt::before {
+  content: "\f543"; }
+
+.fa-square-pen::before {
+  content: "\f14b"; }
+
+.fa-pen-square::before {
+  content: "\f14b"; }
+
+.fa-pencil-square::before {
+  content: "\f14b"; }
+
+.fa-suitcase-rolling::before {
+  content: "\f5c1"; }
+
+.fa-person-circle-exclamation::before {
+  content: "\e53f"; }
+
+.fa-chevron-down::before {
+  content: "\f078"; }
+
+.fa-battery-full::before {
+  content: "\f240"; }
+
+.fa-battery::before {
+  content: "\f240"; }
+
+.fa-battery-5::before {
+  content: "\f240"; }
+
+.fa-skull-crossbones::before {
+  content: "\f714"; }
+
+.fa-code-compare::before {
+  content: "\e13a"; }
+
+.fa-list-ul::before {
+  content: "\f0ca"; }
+
+.fa-list-dots::before {
+  content: "\f0ca"; }
+
+.fa-school-lock::before {
+  content: "\e56f"; }
+
+.fa-tower-cell::before {
+  content: "\e585"; }
+
+.fa-down-long::before {
+  content: "\f309"; }
+
+.fa-long-arrow-alt-down::before {
+  content: "\f309"; }
+
+.fa-ranking-star::before {
+  content: "\e561"; }
+
+.fa-chess-king::before {
+  content: "\f43f"; }
+
+.fa-person-harassing::before {
+  content: "\e549"; }
+
+.fa-brazilian-real-sign::before {
+  content: "\e46c"; }
+
+.fa-landmark-dome::before {
+  content: "\f752"; }
+
+.fa-landmark-alt::before {
+  content: "\f752"; }
+
+.fa-arrow-up::before {
+  content: "\f062"; }
+
+.fa-tv::before {
+  content: "\f26c"; }
+
+.fa-television::before {
+  content: "\f26c"; }
+
+.fa-tv-alt::before {
+  content: "\f26c"; }
+
+.fa-shrimp::before {
+  content: "\e448"; }
+
+.fa-list-check::before {
+  content: "\f0ae"; }
+
+.fa-tasks::before {
+  content: "\f0ae"; }
+
+.fa-jug-detergent::before {
+  content: "\e519"; }
+
+.fa-circle-user::before {
+  content: "\f2bd"; }
+
+.fa-user-circle::before {
+  content: "\f2bd"; }
+
+.fa-user-shield::before {
+  content: "\f505"; }
+
+.fa-wind::before {
+  content: "\f72e"; }
+
+.fa-car-burst::before {
+  content: "\f5e1"; }
+
+.fa-car-crash::before {
+  content: "\f5e1"; }
+
+.fa-y::before {
+  content: "\59"; }
+
+.fa-person-snowboarding::before {
+  content: "\f7ce"; }
+
+.fa-snowboarding::before {
+  content: "\f7ce"; }
+
+.fa-truck-fast::before {
+  content: "\f48b"; }
+
+.fa-shipping-fast::before {
+  content: "\f48b"; }
+
+.fa-fish::before {
+  content: "\f578"; }
+
+.fa-user-graduate::before {
+  content: "\f501"; }
+
+.fa-circle-half-stroke::before {
+  content: "\f042"; }
+
+.fa-adjust::before {
+  content: "\f042"; }
+
+.fa-clapperboard::before {
+  content: "\e131"; }
+
+.fa-circle-radiation::before {
+  content: "\f7ba"; }
+
+.fa-radiation-alt::before {
+  content: "\f7ba"; }
+
+.fa-baseball::before {
+  content: "\f433"; }
+
+.fa-baseball-ball::before {
+  content: "\f433"; }
+
+.fa-jet-fighter-up::before {
+  content: "\e518"; }
+
+.fa-diagram-project::before {
+  content: "\f542"; }
+
+.fa-project-diagram::before {
+  content: "\f542"; }
+
+.fa-copy::before {
+  content: "\f0c5"; }
+
+.fa-volume-xmark::before {
+  content: "\f6a9"; }
+
+.fa-volume-mute::before {
+  content: "\f6a9"; }
+
+.fa-volume-times::before {
+  content: "\f6a9"; }
+
+.fa-hand-sparkles::before {
+  content: "\e05d"; }
+
+.fa-grip::before {
+  content: "\f58d"; }
+
+.fa-grip-horizontal::before {
+  content: "\f58d"; }
+
+.fa-share-from-square::before {
+  content: "\f14d"; }
+
+.fa-share-square::before {
+  content: "\f14d"; }
+
+.fa-child-combatant::before {
+  content: "\e4e0"; }
+
+.fa-child-rifle::before {
+  content: "\e4e0"; }
+
+.fa-gun::before {
+  content: "\e19b"; }
+
+.fa-square-phone::before {
+  content: "\f098"; }
+
+.fa-phone-square::before {
+  content: "\f098"; }
+
+.fa-plus::before {
+  content: "\2b"; }
+
+.fa-add::before {
+  content: "\2b"; }
+
+.fa-expand::before {
+  content: "\f065"; }
+
+.fa-computer::before {
+  content: "\e4e5"; }
+
+.fa-xmark::before {
+  content: "\f00d"; }
+
+.fa-close::before {
+  content: "\f00d"; }
+
+.fa-multiply::before {
+  content: "\f00d"; }
+
+.fa-remove::before {
+  content: "\f00d"; }
+
+.fa-times::before {
+  content: "\f00d"; }
+
+.fa-arrows-up-down-left-right::before {
+  content: "\f047"; }
+
+.fa-arrows::before {
+  content: "\f047"; }
+
+.fa-chalkboard-user::before {
+  content: "\f51c"; }
+
+.fa-chalkboard-teacher::before {
+  content: "\f51c"; }
+
+.fa-peso-sign::before {
+  content: "\e222"; }
+
+.fa-building-shield::before {
+  content: "\e4d8"; }
+
+.fa-baby::before {
+  content: "\f77c"; }
+
+.fa-users-line::before {
+  content: "\e592"; }
+
+.fa-quote-left::before {
+  content: "\f10d"; }
+
+.fa-quote-left-alt::before {
+  content: "\f10d"; }
+
+.fa-tractor::before {
+  content: "\f722"; }
+
+.fa-trash-arrow-up::before {
+  content: "\f829"; }
+
+.fa-trash-restore::before {
+  content: "\f829"; }
+
+.fa-arrow-down-up-lock::before {
+  content: "\e4b0"; }
+
+.fa-lines-leaning::before {
+  content: "\e51e"; }
+
+.fa-ruler-combined::before {
+  content: "\f546"; }
+
+.fa-copyright::before {
+  content: "\f1f9"; }
+
+.fa-equals::before {
+  content: "\3d"; }
+
+.fa-blender::before {
+  content: "\f517"; }
+
+.fa-teeth::before {
+  content: "\f62e"; }
+
+.fa-shekel-sign::before {
+  content: "\f20b"; }
+
+.fa-ils::before {
+  content: "\f20b"; }
+
+.fa-shekel::before {
+  content: "\f20b"; }
+
+.fa-sheqel::before {
+  content: "\f20b"; }
+
+.fa-sheqel-sign::before {
+  content: "\f20b"; }
+
+.fa-map::before {
+  content: "\f279"; }
+
+.fa-rocket::before {
+  content: "\f135"; }
+
+.fa-photo-film::before {
+  content: "\f87c"; }
+
+.fa-photo-video::before {
+  content: "\f87c"; }
+
+.fa-folder-minus::before {
+  content: "\f65d"; }
+
+.fa-store::before {
+  content: "\f54e"; }
+
+.fa-arrow-trend-up::before {
+  content: "\e098"; }
+
+.fa-plug-circle-minus::before {
+  content: "\e55e"; }
+
+.fa-sign-hanging::before {
+  content: "\f4d9"; }
+
+.fa-sign::before {
+  content: "\f4d9"; }
+
+.fa-bezier-curve::before {
+  content: "\f55b"; }
+
+.fa-bell-slash::before {
+  content: "\f1f6"; }
+
+.fa-tablet::before {
+  content: "\f3fb"; }
+
+.fa-tablet-android::before {
+  content: "\f3fb"; }
+
+.fa-school-flag::before {
+  content: "\e56e"; }
+
+.fa-fill::before {
+  content: "\f575"; }
+
+.fa-angle-up::before {
+  content: "\f106"; }
+
+.fa-drumstick-bite::before {
+  content: "\f6d7"; }
+
+.fa-holly-berry::before {
+  content: "\f7aa"; }
+
+.fa-chevron-left::before {
+  content: "\f053"; }
+
+.fa-bacteria::before {
+  content: "\e059"; }
+
+.fa-hand-lizard::before {
+  content: "\f258"; }
+
+.fa-notdef::before {
+  content: "\e1fe"; }
+
+.fa-disease::before {
+  content: "\f7fa"; }
+
+.fa-briefcase-medical::before {
+  content: "\f469"; }
+
+.fa-genderless::before {
+  content: "\f22d"; }
+
+.fa-chevron-right::before {
+  content: "\f054"; }
+
+.fa-retweet::before {
+  content: "\f079"; }
+
+.fa-car-rear::before {
+  content: "\f5de"; }
+
+.fa-car-alt::before {
+  content: "\f5de"; }
+
+.fa-pump-soap::before {
+  content: "\e06b"; }
+
+.fa-video-slash::before {
+  content: "\f4e2"; }
+
+.fa-battery-quarter::before {
+  content: "\f243"; }
+
+.fa-battery-2::before {
+  content: "\f243"; }
+
+.fa-radio::before {
+  content: "\f8d7"; }
+
+.fa-baby-carriage::before {
+  content: "\f77d"; }
+
+.fa-carriage-baby::before {
+  content: "\f77d"; }
+
+.fa-traffic-light::before {
+  content: "\f637"; }
+
+.fa-thermometer::before {
+  content: "\f491"; }
+
+.fa-vr-cardboard::before {
+  content: "\f729"; }
+
+.fa-hand-middle-finger::before {
+  content: "\f806"; }
+
+.fa-percent::before {
+  content: "\25"; }
+
+.fa-percentage::before {
+  content: "\25"; }
+
+.fa-truck-moving::before {
+  content: "\f4df"; }
+
+.fa-glass-water-droplet::before {
+  content: "\e4f5"; }
+
+.fa-display::before {
+  content: "\e163"; }
+
+.fa-face-smile::before {
+  content: "\f118"; }
+
+.fa-smile::before {
+  content: "\f118"; }
+
+.fa-thumbtack::before {
+  content: "\f08d"; }
+
+.fa-thumb-tack::before {
+  content: "\f08d"; }
+
+.fa-trophy::before {
+  content: "\f091"; }
+
+.fa-person-praying::before {
+  content: "\f683"; }
+
+.fa-pray::before {
+  content: "\f683"; }
+
+.fa-hammer::before {
+  content: "\f6e3"; }
+
+.fa-hand-peace::before {
+  content: "\f25b"; }
+
+.fa-rotate::before {
+  content: "\f2f1"; }
+
+.fa-sync-alt::before {
+  content: "\f2f1"; }
+
+.fa-spinner::before {
+  content: "\f110"; }
+
+.fa-robot::before {
+  content: "\f544"; }
+
+.fa-peace::before {
+  content: "\f67c"; }
+
+.fa-gears::before {
+  content: "\f085"; }
+
+.fa-cogs::before {
+  content: "\f085"; }
+
+.fa-warehouse::before {
+  content: "\f494"; }
+
+.fa-arrow-up-right-dots::before {
+  content: "\e4b7"; }
+
+.fa-splotch::before {
+  content: "\f5bc"; }
+
+.fa-face-grin-hearts::before {
+  content: "\f584"; }
+
+.fa-grin-hearts::before {
+  content: "\f584"; }
+
+.fa-dice-four::before {
+  content: "\f524"; }
+
+.fa-sim-card::before {
+  content: "\f7c4"; }
+
+.fa-transgender::before {
+  content: "\f225"; }
+
+.fa-transgender-alt::before {
+  content: "\f225"; }
+
+.fa-mercury::before {
+  content: "\f223"; }
+
+.fa-arrow-turn-down::before {
+  content: "\f149"; }
+
+.fa-level-down::before {
+  content: "\f149"; }
+
+.fa-person-falling-burst::before {
+  content: "\e547"; }
+
+.fa-award::before {
+  content: "\f559"; }
+
+.fa-ticket-simple::before {
+  content: "\f3ff"; }
+
+.fa-ticket-alt::before {
+  content: "\f3ff"; }
+
+.fa-building::before {
+  content: "\f1ad"; }
+
+.fa-angles-left::before {
+  content: "\f100"; }
+
+.fa-angle-double-left::before {
+  content: "\f100"; }
+
+.fa-qrcode::before {
+  content: "\f029"; }
+
+.fa-clock-rotate-left::before {
+  content: "\f1da"; }
+
+.fa-history::before {
+  content: "\f1da"; }
+
+.fa-face-grin-beam-sweat::before {
+  content: "\f583"; }
+
+.fa-grin-beam-sweat::before {
+  content: "\f583"; }
+
+.fa-file-export::before {
+  content: "\f56e"; }
+
+.fa-arrow-right-from-file::before {
+  content: "\f56e"; }
+
+.fa-shield::before {
+  content: "\f132"; }
+
+.fa-shield-blank::before {
+  content: "\f132"; }
+
+.fa-arrow-up-short-wide::before {
+  content: "\f885"; }
+
+.fa-sort-amount-up-alt::before {
+  content: "\f885"; }
+
+.fa-house-medical::before {
+  content: "\e3b2"; }
+
+.fa-golf-ball-tee::before {
+  content: "\f450"; }
+
+.fa-golf-ball::before {
+  content: "\f450"; }
+
+.fa-circle-chevron-left::before {
+  content: "\f137"; }
+
+.fa-chevron-circle-left::before {
+  content: "\f137"; }
+
+.fa-house-chimney-window::before {
+  content: "\e00d"; }
+
+.fa-pen-nib::before {
+  content: "\f5ad"; }
+
+.fa-tent-arrow-turn-left::before {
+  content: "\e580"; }
+
+.fa-tents::before {
+  content: "\e582"; }
+
+.fa-wand-magic::before {
+  content: "\f0d0"; }
+
+.fa-magic::before {
+  content: "\f0d0"; }
+
+.fa-dog::before {
+  content: "\f6d3"; }
+
+.fa-carrot::before {
+  content: "\f787"; }
+
+.fa-moon::before {
+  content: "\f186"; }
+
+.fa-wine-glass-empty::before {
+  content: "\f5ce"; }
+
+.fa-wine-glass-alt::before {
+  content: "\f5ce"; }
+
+.fa-cheese::before {
+  content: "\f7ef"; }
+
+.fa-yin-yang::before {
+  content: "\f6ad"; }
+
+.fa-music::before {
+  content: "\f001"; }
+
+.fa-code-commit::before {
+  content: "\f386"; }
+
+.fa-temperature-low::before {
+  content: "\f76b"; }
+
+.fa-person-biking::before {
+  content: "\f84a"; }
+
+.fa-biking::before {
+  content: "\f84a"; }
+
+.fa-broom::before {
+  content: "\f51a"; }
+
+.fa-shield-heart::before {
+  content: "\e574"; }
+
+.fa-gopuram::before {
+  content: "\f664"; }
+
+.fa-earth-oceania::before {
+  content: "\e47b"; }
+
+.fa-globe-oceania::before {
+  content: "\e47b"; }
+
+.fa-square-xmark::before {
+  content: "\f2d3"; }
+
+.fa-times-square::before {
+  content: "\f2d3"; }
+
+.fa-xmark-square::before {
+  content: "\f2d3"; }
+
+.fa-hashtag::before {
+  content: "\23"; }
+
+.fa-up-right-and-down-left-from-center::before {
+  content: "\f424"; }
+
+.fa-expand-alt::before {
+  content: "\f424"; }
+
+.fa-oil-can::before {
+  content: "\f613"; }
+
+.fa-t::before {
+  content: "\54"; }
+
+.fa-hippo::before {
+  content: "\f6ed"; }
+
+.fa-chart-column::before {
+  content: "\e0e3"; }
+
+.fa-infinity::before {
+  content: "\f534"; }
+
+.fa-vial-circle-check::before {
+  content: "\e596"; }
+
+.fa-person-arrow-down-to-line::before {
+  content: "\e538"; }
+
+.fa-voicemail::before {
+  content: "\f897"; }
+
+.fa-fan::before {
+  content: "\f863"; }
+
+.fa-person-walking-luggage::before {
+  content: "\e554"; }
+
+.fa-up-down::before {
+  content: "\f338"; }
+
+.fa-arrows-alt-v::before {
+  content: "\f338"; }
+
+.fa-cloud-moon-rain::before {
+  content: "\f73c"; }
+
+.fa-calendar::before {
+  content: "\f133"; }
+
+.fa-trailer::before {
+  content: "\e041"; }
+
+.fa-bahai::before {
+  content: "\f666"; }
+
+.fa-haykal::before {
+  content: "\f666"; }
+
+.fa-sd-card::before {
+  content: "\f7c2"; }
+
+.fa-dragon::before {
+  content: "\f6d5"; }
+
+.fa-shoe-prints::before {
+  content: "\f54b"; }
+
+.fa-circle-plus::before {
+  content: "\f055"; }
+
+.fa-plus-circle::before {
+  content: "\f055"; }
+
+.fa-face-grin-tongue-wink::before {
+  content: "\f58b"; }
+
+.fa-grin-tongue-wink::before {
+  content: "\f58b"; }
+
+.fa-hand-holding::before {
+  content: "\f4bd"; }
+
+.fa-plug-circle-exclamation::before {
+  content: "\e55d"; }
+
+.fa-link-slash::before {
+  content: "\f127"; }
+
+.fa-chain-broken::before {
+  content: "\f127"; }
+
+.fa-chain-slash::before {
+  content: "\f127"; }
+
+.fa-unlink::before {
+  content: "\f127"; }
+
+.fa-clone::before {
+  content: "\f24d"; }
+
+.fa-person-walking-arrow-loop-left::before {
+  content: "\e551"; }
+
+.fa-arrow-up-z-a::before {
+  content: "\f882"; }
+
+.fa-sort-alpha-up-alt::before {
+  content: "\f882"; }
+
+.fa-fire-flame-curved::before {
+  content: "\f7e4"; }
+
+.fa-fire-alt::before {
+  content: "\f7e4"; }
+
+.fa-tornado::before {
+  content: "\f76f"; }
+
+.fa-file-circle-plus::before {
+  content: "\e494"; }
+
+.fa-book-quran::before {
+  content: "\f687"; }
+
+.fa-quran::before {
+  content: "\f687"; }
+
+.fa-anchor::before {
+  content: "\f13d"; }
+
+.fa-border-all::before {
+  content: "\f84c"; }
+
+.fa-face-angry::before {
+  content: "\f556"; }
+
+.fa-angry::before {
+  content: "\f556"; }
+
+.fa-cookie-bite::before {
+  content: "\f564"; }
+
+.fa-arrow-trend-down::before {
+  content: "\e097"; }
+
+.fa-rss::before {
+  content: "\f09e"; }
+
+.fa-feed::before {
+  content: "\f09e"; }
+
+.fa-draw-polygon::before {
+  content: "\f5ee"; }
+
+.fa-scale-balanced::before {
+  content: "\f24e"; }
+
+.fa-balance-scale::before {
+  content: "\f24e"; }
+
+.fa-gauge-simple-high::before {
+  content: "\f62a"; }
+
+.fa-tachometer::before {
+  content: "\f62a"; }
+
+.fa-tachometer-fast::before {
+  content: "\f62a"; }
+
+.fa-shower::before {
+  content: "\f2cc"; }
+
+.fa-desktop::before {
+  content: "\f390"; }
+
+.fa-desktop-alt::before {
+  content: "\f390"; }
+
+.fa-m::before {
+  content: "\4d"; }
+
+.fa-table-list::before {
+  content: "\f00b"; }
+
+.fa-th-list::before {
+  content: "\f00b"; }
+
+.fa-comment-sms::before {
+  content: "\f7cd"; }
+
+.fa-sms::before {
+  content: "\f7cd"; }
+
+.fa-book::before {
+  content: "\f02d"; }
+
+.fa-user-plus::before {
+  content: "\f234"; }
+
+.fa-check::before {
+  content: "\f00c"; }
+
+.fa-battery-three-quarters::before {
+  content: "\f241"; }
+
+.fa-battery-4::before {
+  content: "\f241"; }
+
+.fa-house-circle-check::before {
+  content: "\e509"; }
+
+.fa-angle-left::before {
+  content: "\f104"; }
+
+.fa-diagram-successor::before {
+  content: "\e47a"; }
+
+.fa-truck-arrow-right::before {
+  content: "\e58b"; }
+
+.fa-arrows-split-up-and-left::before {
+  content: "\e4bc"; }
+
+.fa-hand-fist::before {
+  content: "\f6de"; }
+
+.fa-fist-raised::before {
+  content: "\f6de"; }
+
+.fa-cloud-moon::before {
+  content: "\f6c3"; }
+
+.fa-briefcase::before {
+  content: "\f0b1"; }
+
+.fa-person-falling::before {
+  content: "\e546"; }
+
+.fa-image-portrait::before {
+  content: "\f3e0"; }
+
+.fa-portrait::before {
+  content: "\f3e0"; }
+
+.fa-user-tag::before {
+  content: "\f507"; }
+
+.fa-rug::before {
+  content: "\e569"; }
+
+.fa-earth-europe::before {
+  content: "\f7a2"; }
+
+.fa-globe-europe::before {
+  content: "\f7a2"; }
+
+.fa-cart-flatbed-suitcase::before {
+  content: "\f59d"; }
+
+.fa-luggage-cart::before {
+  content: "\f59d"; }
+
+.fa-rectangle-xmark::before {
+  content: "\f410"; }
+
+.fa-rectangle-times::before {
+  content: "\f410"; }
+
+.fa-times-rectangle::before {
+  content: "\f410"; }
+
+.fa-window-close::before {
+  content: "\f410"; }
+
+.fa-baht-sign::before {
+  content: "\e0ac"; }
+
+.fa-book-open::before {
+  content: "\f518"; }
+
+.fa-book-journal-whills::before {
+  content: "\f66a"; }
+
+.fa-journal-whills::before {
+  content: "\f66a"; }
+
+.fa-handcuffs::before {
+  content: "\e4f8"; }
+
+.fa-triangle-exclamation::before {
+  content: "\f071"; }
+
+.fa-exclamation-triangle::before {
+  content: "\f071"; }
+
+.fa-warning::before {
+  content: "\f071"; }
+
+.fa-database::before {
+  content: "\f1c0"; }
+
+.fa-share::before {
+  content: "\f064"; }
+
+.fa-mail-forward::before {
+  content: "\f064"; }
+
+.fa-bottle-droplet::before {
+  content: "\e4c4"; }
+
+.fa-mask-face::before {
+  content: "\e1d7"; }
+
+.fa-hill-rockslide::before {
+  content: "\e508"; }
+
+.fa-right-left::before {
+  content: "\f362"; }
+
+.fa-exchange-alt::before {
+  content: "\f362"; }
+
+.fa-paper-plane::before {
+  content: "\f1d8"; }
+
+.fa-road-circle-exclamation::before {
+  content: "\e565"; }
+
+.fa-dungeon::before {
+  content: "\f6d9"; }
+
+.fa-align-right::before {
+  content: "\f038"; }
+
+.fa-money-bill-1-wave::before {
+  content: "\f53b"; }
+
+.fa-money-bill-wave-alt::before {
+  content: "\f53b"; }
+
+.fa-life-ring::before {
+  content: "\f1cd"; }
+
+.fa-hands::before {
+  content: "\f2a7"; }
+
+.fa-sign-language::before {
+  content: "\f2a7"; }
+
+.fa-signing::before {
+  content: "\f2a7"; }
+
+.fa-calendar-day::before {
+  content: "\f783"; }
+
+.fa-water-ladder::before {
+  content: "\f5c5"; }
+
+.fa-ladder-water::before {
+  content: "\f5c5"; }
+
+.fa-swimming-pool::before {
+  content: "\f5c5"; }
+
+.fa-arrows-up-down::before {
+  content: "\f07d"; }
+
+.fa-arrows-v::before {
+  content: "\f07d"; }
+
+.fa-face-grimace::before {
+  content: "\f57f"; }
+
+.fa-grimace::before {
+  content: "\f57f"; }
+
+.fa-wheelchair-move::before {
+  content: "\e2ce"; }
+
+.fa-wheelchair-alt::before {
+  content: "\e2ce"; }
+
+.fa-turn-down::before {
+  content: "\f3be"; }
+
+.fa-level-down-alt::before {
+  content: "\f3be"; }
+
+.fa-person-walking-arrow-right::before {
+  content: "\e552"; }
+
+.fa-square-envelope::before {
+  content: "\f199"; }
+
+.fa-envelope-square::before {
+  content: "\f199"; }
+
+.fa-dice::before {
+  content: "\f522"; }
+
+.fa-bowling-ball::before {
+  content: "\f436"; }
+
+.fa-brain::before {
+  content: "\f5dc"; }
+
+.fa-bandage::before {
+  content: "\f462"; }
+
+.fa-band-aid::before {
+  content: "\f462"; }
+
+.fa-calendar-minus::before {
+  content: "\f272"; }
+
+.fa-circle-xmark::before {
+  content: "\f057"; }
+
+.fa-times-circle::before {
+  content: "\f057"; }
+
+.fa-xmark-circle::before {
+  content: "\f057"; }
+
+.fa-gifts::before {
+  content: "\f79c"; }
+
+.fa-hotel::before {
+  content: "\f594"; }
+
+.fa-earth-asia::before {
+  content: "\f57e"; }
+
+.fa-globe-asia::before {
+  content: "\f57e"; }
+
+.fa-id-card-clip::before {
+  content: "\f47f"; }
+
+.fa-id-card-alt::before {
+  content: "\f47f"; }
+
+.fa-magnifying-glass-plus::before {
+  content: "\f00e"; }
+
+.fa-search-plus::before {
+  content: "\f00e"; }
+
+.fa-thumbs-up::before {
+  content: "\f164"; }
+
+.fa-user-clock::before {
+  content: "\f4fd"; }
+
+.fa-hand-dots::before {
+  content: "\f461"; }
+
+.fa-allergies::before {
+  content: "\f461"; }
+
+.fa-file-invoice::before {
+  content: "\f570"; }
+
+.fa-window-minimize::before {
+  content: "\f2d1"; }
+
+.fa-mug-saucer::before {
+  content: "\f0f4"; }
+
+.fa-coffee::before {
+  content: "\f0f4"; }
+
+.fa-brush::before {
+  content: "\f55d"; }
+
+.fa-mask::before {
+  content: "\f6fa"; }
+
+.fa-magnifying-glass-minus::before {
+  content: "\f010"; }
+
+.fa-search-minus::before {
+  content: "\f010"; }
+
+.fa-ruler-vertical::before {
+  content: "\f548"; }
+
+.fa-user-large::before {
+  content: "\f406"; }
+
+.fa-user-alt::before {
+  content: "\f406"; }
+
+.fa-train-tram::before {
+  content: "\e5b4"; }
+
+.fa-user-nurse::before {
+  content: "\f82f"; }
+
+.fa-syringe::before {
+  content: "\f48e"; }
+
+.fa-cloud-sun::before {
+  content: "\f6c4"; }
+
+.fa-stopwatch-20::before {
+  content: "\e06f"; }
+
+.fa-square-full::before {
+  content: "\f45c"; }
+
+.fa-magnet::before {
+  content: "\f076"; }
+
+.fa-jar::before {
+  content: "\e516"; }
+
+.fa-note-sticky::before {
+  content: "\f249"; }
+
+.fa-sticky-note::before {
+  content: "\f249"; }
+
+.fa-bug-slash::before {
+  content: "\e490"; }
+
+.fa-arrow-up-from-water-pump::before {
+  content: "\e4b6"; }
+
+.fa-bone::before {
+  content: "\f5d7"; }
+
+.fa-user-injured::before {
+  content: "\f728"; }
+
+.fa-face-sad-tear::before {
+  content: "\f5b4"; }
+
+.fa-sad-tear::before {
+  content: "\f5b4"; }
+
+.fa-plane::before {
+  content: "\f072"; }
+
+.fa-tent-arrows-down::before {
+  content: "\e581"; }
+
+.fa-exclamation::before {
+  content: "\21"; }
+
+.fa-arrows-spin::before {
+  content: "\e4bb"; }
+
+.fa-print::before {
+  content: "\f02f"; }
+
+.fa-turkish-lira-sign::before {
+  content: "\e2bb"; }
+
+.fa-try::before {
+  content: "\e2bb"; }
+
+.fa-turkish-lira::before {
+  content: "\e2bb"; }
+
+.fa-dollar-sign::before {
+  content: "\24"; }
+
+.fa-dollar::before {
+  content: "\24"; }
+
+.fa-usd::before {
+  content: "\24"; }
+
+.fa-x::before {
+  content: "\58"; }
+
+.fa-magnifying-glass-dollar::before {
+  content: "\f688"; }
+
+.fa-search-dollar::before {
+  content: "\f688"; }
+
+.fa-users-gear::before {
+  content: "\f509"; }
+
+.fa-users-cog::before {
+  content: "\f509"; }
+
+.fa-person-military-pointing::before {
+  content: "\e54a"; }
+
+.fa-building-columns::before {
+  content: "\f19c"; }
+
+.fa-bank::before {
+  content: "\f19c"; }
+
+.fa-institution::before {
+  content: "\f19c"; }
+
+.fa-museum::before {
+  content: "\f19c"; }
+
+.fa-university::before {
+  content: "\f19c"; }
+
+.fa-umbrella::before {
+  content: "\f0e9"; }
+
+.fa-trowel::before {
+  content: "\e589"; }
+
+.fa-d::before {
+  content: "\44"; }
+
+.fa-stapler::before {
+  content: "\e5af"; }
+
+.fa-masks-theater::before {
+  content: "\f630"; }
+
+.fa-theater-masks::before {
+  content: "\f630"; }
+
+.fa-kip-sign::before {
+  content: "\e1c4"; }
+
+.fa-hand-point-left::before {
+  content: "\f0a5"; }
+
+.fa-handshake-simple::before {
+  content: "\f4c6"; }
+
+.fa-handshake-alt::before {
+  content: "\f4c6"; }
+
+.fa-jet-fighter::before {
+  content: "\f0fb"; }
+
+.fa-fighter-jet::before {
+  content: "\f0fb"; }
+
+.fa-square-share-nodes::before {
+  content: "\f1e1"; }
+
+.fa-share-alt-square::before {
+  content: "\f1e1"; }
+
+.fa-barcode::before {
+  content: "\f02a"; }
+
+.fa-plus-minus::before {
+  content: "\e43c"; }
+
+.fa-video::before {
+  content: "\f03d"; }
+
+.fa-video-camera::before {
+  content: "\f03d"; }
+
+.fa-graduation-cap::before {
+  content: "\f19d"; }
+
+.fa-mortar-board::before {
+  content: "\f19d"; }
+
+.fa-hand-holding-medical::before {
+  content: "\e05c"; }
+
+.fa-person-circle-check::before {
+  content: "\e53e"; }
+
+.fa-turn-up::before {
+  content: "\f3bf"; }
+
+.fa-level-up-alt::before {
+  content: "\f3bf"; }
+
+.sr-only,
+.fa-sr-only {
+  position: absolute;
+  width: 1px;
+  height: 1px;
+  padding: 0;
+  margin: -1px;
+  overflow: hidden;
+  clip: rect(0, 0, 0, 0);
+  white-space: nowrap;
+  border-width: 0; }
+
+.sr-only-focusable:not(:focus),
+.fa-sr-only-focusable:not(:focus) {
+  position: absolute;
+  width: 1px;
+  height: 1px;
+  padding: 0;
+  margin: -1px;
+  overflow: hidden;
+  clip: rect(0, 0, 0, 0);
+  white-space: nowrap;
+  border-width: 0; }
+:root, :host {
+  --fa-style-family-brands: 'Font Awesome 6 Brands';
+  --fa-font-brands: normal 400 1em/1 'Font Awesome 6 Brands'; }
+
+@font-face {
+  font-family: 'Font Awesome 6 Brands';
+  font-style: normal;
+  font-weight: 400;
+  font-display: block;
+  src: url("../webfonts/fa-brands-400.woff2") format("woff2"), url("../webfonts/fa-brands-400.ttf") format("truetype"); }
+
+.fab,
+.fa-brands {
+  font-weight: 400; }
+
+.fa-monero:before {
+  content: "\f3d0"; }
+
+.fa-hooli:before {
+  content: "\f427"; }
+
+.fa-yelp:before {
+  content: "\f1e9"; }
+
+.fa-cc-visa:before {
+  content: "\f1f0"; }
+
+.fa-lastfm:before {
+  content: "\f202"; }
+
+.fa-shopware:before {
+  content: "\f5b5"; }
+
+.fa-creative-commons-nc:before {
+  content: "\f4e8"; }
+
+.fa-aws:before {
+  content: "\f375"; }
+
+.fa-redhat:before {
+  content: "\f7bc"; }
+
+.fa-yoast:before {
+  content: "\f2b1"; }
+
+.fa-cloudflare:before {
+  content: "\e07d"; }
+
+.fa-ups:before {
+  content: "\f7e0"; }
+
+.fa-pixiv:before {
+  content: "\e640"; }
+
+.fa-wpexplorer:before {
+  content: "\f2de"; }
+
+.fa-dyalog:before {
+  content: "\f399"; }
+
+.fa-bity:before {
+  content: "\f37a"; }
+
+.fa-stackpath:before {
+  content: "\f842"; }
+
+.fa-buysellads:before {
+  content: "\f20d"; }
+
+.fa-first-order:before {
+  content: "\f2b0"; }
+
+.fa-modx:before {
+  content: "\f285"; }
+
+.fa-guilded:before {
+  content: "\e07e"; }
+
+.fa-vnv:before {
+  content: "\f40b"; }
+
+.fa-square-js:before {
+  content: "\f3b9"; }
+
+.fa-js-square:before {
+  content: "\f3b9"; }
+
+.fa-microsoft:before {
+  content: "\f3ca"; }
+
+.fa-qq:before {
+  content: "\f1d6"; }
+
+.fa-orcid:before {
+  content: "\f8d2"; }
+
+.fa-java:before {
+  content: "\f4e4"; }
+
+.fa-invision:before {
+  content: "\f7b0"; }
+
+.fa-creative-commons-pd-alt:before {
+  content: "\f4ed"; }
+
+.fa-centercode:before {
+  content: "\f380"; }
+
+.fa-glide-g:before {
+  content: "\f2a6"; }
+
+.fa-drupal:before {
+  content: "\f1a9"; }
+
+.fa-jxl:before {
+  content: "\e67b"; }
+
+.fa-hire-a-helper:before {
+  content: "\f3b0"; }
+
+.fa-creative-commons-by:before {
+  content: "\f4e7"; }
+
+.fa-unity:before {
+  content: "\e049"; }
+
+.fa-whmcs:before {
+  content: "\f40d"; }
+
+.fa-rocketchat:before {
+  content: "\f3e8"; }
+
+.fa-vk:before {
+  content: "\f189"; }
+
+.fa-untappd:before {
+  content: "\f405"; }
+
+.fa-mailchimp:before {
+  content: "\f59e"; }
+
+.fa-css3-alt:before {
+  content: "\f38b"; }
+
+.fa-square-reddit:before {
+  content: "\f1a2"; }
+
+.fa-reddit-square:before {
+  content: "\f1a2"; }
+
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+.fa-cmplid:before {
+  content: "\e360"; }
+
+.fa-upwork:before {
+  content: "\e641"; }
+
+.fa-facebook:before {
+  content: "\f09a"; }
+
+.fa-gripfire:before {
+  content: "\f3ac"; }
+
+.fa-jedi-order:before {
+  content: "\f50e"; }
+
+.fa-uikit:before {
+  content: "\f403"; }
+
+.fa-fort-awesome-alt:before {
+  content: "\f3a3"; }
+
+.fa-phabricator:before {
+  content: "\f3db"; }
+
+.fa-ussunnah:before {
+  content: "\f407"; }
+
+.fa-earlybirds:before {
+  content: "\f39a"; }
+
+.fa-trade-federation:before {
+  content: "\f513"; }
+
+.fa-autoprefixer:before {
+  content: "\f41c"; }
+
+.fa-whatsapp:before {
+  content: "\f232"; }
+
+.fa-square-upwork:before {
+  content: "\e67c"; }
+
+.fa-slideshare:before {
+  content: "\f1e7"; }
+
+.fa-google-play:before {
+  content: "\f3ab"; }
+
+.fa-viadeo:before {
+  content: "\f2a9"; }
+
+.fa-line:before {
+  content: "\f3c0"; }
+
+.fa-google-drive:before {
+  content: "\f3aa"; }
+
+.fa-servicestack:before {
+  content: "\f3ec"; }
+
+.fa-simplybuilt:before {
+  content: "\f215"; }
+
+.fa-bitbucket:before {
+  content: "\f171"; }
+
+.fa-imdb:before {
+  content: "\f2d8"; }
+
+.fa-deezer:before {
+  content: "\e077"; }
+
+.fa-raspberry-pi:before {
+  content: "\f7bb"; }
+
+.fa-jira:before {
+  content: "\f7b1"; }
+
+.fa-docker:before {
+  content: "\f395"; }
+
+.fa-screenpal:before {
+  content: "\e570"; }
+
+.fa-bluetooth:before {
+  content: "\f293"; }
+
+.fa-gitter:before {
+  content: "\f426"; }
+
+.fa-d-and-d:before {
+  content: "\f38d"; }
+
+.fa-microblog:before {
+  content: "\e01a"; }
+
+.fa-cc-diners-club:before {
+  content: "\f24c"; }
+
+.fa-gg-circle:before {
+  content: "\f261"; }
+
+.fa-pied-piper-hat:before {
+  content: "\f4e5"; }
+
+.fa-kickstarter-k:before {
+  content: "\f3bc"; }
+
+.fa-yandex:before {
+  content: "\f413"; }
+
+.fa-readme:before {
+  content: "\f4d5"; }
+
+.fa-html5:before {
+  content: "\f13b"; }
+
+.fa-sellsy:before {
+  content: "\f213"; }
+
+.fa-square-web-awesome:before {
+  content: "\e683"; }
+
+.fa-sass:before {
+  content: "\f41e"; }
+
+.fa-wirsindhandwerk:before {
+  content: "\e2d0"; }
+
+.fa-wsh:before {
+  content: "\e2d0"; }
+
+.fa-buromobelexperte:before {
+  content: "\f37f"; }
+
+.fa-salesforce:before {
+  content: "\f83b"; }
+
+.fa-octopus-deploy:before {
+  content: "\e082"; }
+
+.fa-medapps:before {
+  content: "\f3c6"; }
+
+.fa-ns8:before {
+  content: "\f3d5"; }
+
+.fa-pinterest-p:before {
+  content: "\f231"; }
+
+.fa-apper:before {
+  content: "\f371"; }
+
+.fa-fort-awesome:before {
+  content: "\f286"; }
+
+.fa-waze:before {
+  content: "\f83f"; }
+
+.fa-bluesky:before {
+  content: "\e671"; }
+
+.fa-cc-jcb:before {
+  content: "\f24b"; }
+
+.fa-snapchat:before {
+  content: "\f2ab"; }
+
+.fa-snapchat-ghost:before {
+  content: "\f2ab"; }
+
+.fa-fantasy-flight-games:before {
+  content: "\f6dc"; }
+
+.fa-rust:before {
+  content: "\e07a"; }
+
+.fa-wix:before {
+  content: "\f5cf"; }
+
+.fa-square-behance:before {
+  content: "\f1b5"; }
+
+.fa-behance-square:before {
+  content: "\f1b5"; }
+
+.fa-supple:before {
+  content: "\f3f9"; }
+
+.fa-webflow:before {
+  content: "\e65c"; }
+
+.fa-rebel:before {
+  content: "\f1d0"; }
+
+.fa-css3:before {
+  content: "\f13c"; }
+
+.fa-staylinked:before {
+  content: "\f3f5"; }
+
+.fa-kaggle:before {
+  content: "\f5fa"; }
+
+.fa-space-awesome:before {
+  content: "\e5ac"; }
+
+.fa-deviantart:before {
+  content: "\f1bd"; }
+
+.fa-cpanel:before {
+  content: "\f388"; }
+
+.fa-goodreads-g:before {
+  content: "\f3a9"; }
+
+.fa-square-git:before {
+  content: "\f1d2"; }
+
+.fa-git-square:before {
+  content: "\f1d2"; }
+
+.fa-square-tumblr:before {
+  content: "\f174"; }
+
+.fa-tumblr-square:before {
+  content: "\f174"; }
+
+.fa-trello:before {
+  content: "\f181"; }
+
+.fa-creative-commons-nc-jp:before {
+  content: "\f4ea"; }
+
+.fa-get-pocket:before {
+  content: "\f265"; }
+
+.fa-perbyte:before {
+  content: "\e083"; }
+
+.fa-grunt:before {
+  content: "\f3ad"; }
+
+.fa-weebly:before {
+  content: "\f5cc"; }
+
+.fa-connectdevelop:before {
+  content: "\f20e"; }
+
+.fa-leanpub:before {
+  content: "\f212"; }
+
+.fa-black-tie:before {
+  content: "\f27e"; }
+
+.fa-themeco:before {
+  content: "\f5c6"; }
+
+.fa-python:before {
+  content: "\f3e2"; }
+
+.fa-android:before {
+  content: "\f17b"; }
+
+.fa-bots:before {
+  content: "\e340"; }
+
+.fa-free-code-camp:before {
+  content: "\f2c5"; }
+
+.fa-hornbill:before {
+  content: "\f592"; }
+
+.fa-js:before {
+  content: "\f3b8"; }
+
+.fa-ideal:before {
+  content: "\e013"; }
+
+.fa-git:before {
+  content: "\f1d3"; }
+
+.fa-dev:before {
+  content: "\f6cc"; }
+
+.fa-sketch:before {
+  content: "\f7c6"; }
+
+.fa-yandex-international:before {
+  content: "\f414"; }
+
+.fa-cc-amex:before {
+  content: "\f1f3"; }
+
+.fa-uber:before {
+  content: "\f402"; }
+
+.fa-github:before {
+  content: "\f09b"; }
+
+.fa-php:before {
+  content: "\f457"; }
+
+.fa-alipay:before {
+  content: "\f642"; }
+
+.fa-youtube:before {
+  content: "\f167"; }
+
+.fa-skyatlas:before {
+  content: "\f216"; }
+
+.fa-firefox-browser:before {
+  content: "\e007"; }
+
+.fa-replyd:before {
+  content: "\f3e6"; }
+
+.fa-suse:before {
+  content: "\f7d6"; }
+
+.fa-jenkins:before {
+  content: "\f3b6"; }
+
+.fa-twitter:before {
+  content: "\f099"; }
+
+.fa-rockrms:before {
+  content: "\f3e9"; }
+
+.fa-pinterest:before {
+  content: "\f0d2"; }
+
+.fa-buffer:before {
+  content: "\f837"; }
+
+.fa-npm:before {
+  content: "\f3d4"; }
+
+.fa-yammer:before {
+  content: "\f840"; }
+
+.fa-btc:before {
+  content: "\f15a"; }
+
+.fa-dribbble:before {
+  content: "\f17d"; }
+
+.fa-stumbleupon-circle:before {
+  content: "\f1a3"; }
+
+.fa-internet-explorer:before {
+  content: "\f26b"; }
+
+.fa-stubber:before {
+  content: "\e5c7"; }
+
+.fa-telegram:before {
+  content: "\f2c6"; }
+
+.fa-telegram-plane:before {
+  content: "\f2c6"; }
+
+.fa-old-republic:before {
+  content: "\f510"; }
+
+.fa-odysee:before {
+  content: "\e5c6"; }
+
+.fa-square-whatsapp:before {
+  content: "\f40c"; }
+
+.fa-whatsapp-square:before {
+  content: "\f40c"; }
+
+.fa-node-js:before {
+  content: "\f3d3"; }
+
+.fa-edge-legacy:before {
+  content: "\e078"; }
+
+.fa-slack:before {
+  content: "\f198"; }
+
+.fa-slack-hash:before {
+  content: "\f198"; }
+
+.fa-medrt:before {
+  content: "\f3c8"; }
+
+.fa-usb:before {
+  content: "\f287"; }
+
+.fa-tumblr:before {
+  content: "\f173"; }
+
+.fa-vaadin:before {
+  content: "\f408"; }
+
+.fa-quora:before {
+  content: "\f2c4"; }
+
+.fa-square-x-twitter:before {
+  content: "\e61a"; }
+
+.fa-reacteurope:before {
+  content: "\f75d"; }
+
+.fa-medium:before {
+  content: "\f23a"; }
+
+.fa-medium-m:before {
+  content: "\f23a"; }
+
+.fa-amilia:before {
+  content: "\f36d"; }
+
+.fa-mixcloud:before {
+  content: "\f289"; }
+
+.fa-flipboard:before {
+  content: "\f44d"; }
+
+.fa-viacoin:before {
+  content: "\f237"; }
+
+.fa-critical-role:before {
+  content: "\f6c9"; }
+
+.fa-sitrox:before {
+  content: "\e44a"; }
+
+.fa-discourse:before {
+  content: "\f393"; }
+
+.fa-joomla:before {
+  content: "\f1aa"; }
+
+.fa-mastodon:before {
+  content: "\f4f6"; }
+
+.fa-airbnb:before {
+  content: "\f834"; }
+
+.fa-wolf-pack-battalion:before {
+  content: "\f514"; }
+
+.fa-buy-n-large:before {
+  content: "\f8a6"; }
+
+.fa-gulp:before {
+  content: "\f3ae"; }
+
+.fa-creative-commons-sampling-plus:before {
+  content: "\f4f1"; }
+
+.fa-strava:before {
+  content: "\f428"; }
+
+.fa-ember:before {
+  content: "\f423"; }
+
+.fa-canadian-maple-leaf:before {
+  content: "\f785"; }
+
+.fa-teamspeak:before {
+  content: "\f4f9"; }
+
+.fa-pushed:before {
+  content: "\f3e1"; }
+
+.fa-wordpress-simple:before {
+  content: "\f411"; }
+
+.fa-nutritionix:before {
+  content: "\f3d6"; }
+
+.fa-wodu:before {
+  content: "\e088"; }
+
+.fa-google-pay:before {
+  content: "\e079"; }
+
+.fa-intercom:before {
+  content: "\f7af"; }
+
+.fa-zhihu:before {
+  content: "\f63f"; }
+
+.fa-korvue:before {
+  content: "\f42f"; }
+
+.fa-pix:before {
+  content: "\e43a"; }
+
+.fa-steam-symbol:before {
+  content: "\f3f6"; }
+:root, :host {
+  --fa-style-family-classic: 'Font Awesome 6 Free';
+  --fa-font-regular: normal 400 1em/1 'Font Awesome 6 Free'; }
+
+@font-face {
+  font-family: 'Font Awesome 6 Free';
+  font-style: normal;
+  font-weight: 400;
+  font-display: block;
+  src: url("../webfonts/fa-regular-400.woff2") format("woff2"), url("../webfonts/fa-regular-400.ttf") format("truetype"); }
+
+.far,
+.fa-regular {
+  font-weight: 400; }
+:root, :host {
+  --fa-style-family-classic: 'Font Awesome 6 Free';
+  --fa-font-solid: normal 900 1em/1 'Font Awesome 6 Free'; }
+
+@font-face {
+  font-family: 'Font Awesome 6 Free';
+  font-style: normal;
+  font-weight: 900;
+  font-display: block;
+  src: url("../webfonts/fa-solid-900.woff2") format("woff2"), url("../webfonts/fa-solid-900.ttf") format("truetype"); }
+
+.fas,
+.fa-solid {
+  font-weight: 900; }
+@font-face {
+  font-family: 'Font Awesome 5 Brands';
+  font-display: block;
+  font-weight: 400;
+  src: url("../webfonts/fa-brands-400.woff2") format("woff2"), url("../webfonts/fa-brands-400.ttf") format("truetype"); }
+
+@font-face {
+  font-family: 'Font Awesome 5 Free';
+  font-display: block;
+  font-weight: 900;
+  src: url("../webfonts/fa-solid-900.woff2") format("woff2"), url("../webfonts/fa-solid-900.ttf") format("truetype"); }
+
+@font-face {
+  font-family: 'Font Awesome 5 Free';
+  font-display: block;
+  font-weight: 400;
+  src: url("../webfonts/fa-regular-400.woff2") format("woff2"), url("../webfonts/fa-regular-400.ttf") format("truetype"); }
+@font-face {
+  font-family: 'FontAwesome';
+  font-display: block;
+  src: url("../webfonts/fa-solid-900.woff2") format("woff2"), url("../webfonts/fa-solid-900.ttf") format("truetype"); }
+
+@font-face {
+  font-family: 'FontAwesome';
+  font-display: block;
+  src: url("../webfonts/fa-brands-400.woff2") format("woff2"), url("../webfonts/fa-brands-400.ttf") format("truetype"); }
+
+@font-face {
+  font-family: 'FontAwesome';
+  font-display: block;
+  src: url("../webfonts/fa-regular-400.woff2") format("woff2"), url("../webfonts/fa-regular-400.ttf") format("truetype"); }
+
+@font-face {
+  font-family: 'FontAwesome';
+  font-display: block;
+  src: url("../webfonts/fa-v4compatibility.woff2") format("woff2"), url("../webfonts/fa-v4compatibility.ttf") format("truetype"); }
diff --git a/docs/deps/font-awesome-6.5.2/css/all.min.css b/docs/deps/font-awesome-6.5.2/css/all.min.css
new file mode 100644
index 0000000..269bcee
--- /dev/null
+++ b/docs/deps/font-awesome-6.5.2/css/all.min.css
@@ -0,0 +1,9 @@
+/*!
+ * Font Awesome Free 6.5.2 by @fontawesome - https://fontawesome.com
+ * License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License)
+ * Copyright 2024 Fonticons, Inc.
+ */
+.fa{font-family:var(--fa-style-family,"Font Awesome 6 Free");font-weight:var(--fa-style,900)}.fa,.fa-brands,.fa-classic,.fa-regular,.fa-sharp,.fa-solid,.fab,.far,.fas{-moz-osx-font-smoothing:grayscale;-webkit-font-smoothing:antialiased;display:var(--fa-display,inline-block);font-style:normal;font-variant:normal;line-height:1;text-rendering:auto}.fa-classic,.fa-regular,.fa-solid,.far,.fas{font-family:"Font Awesome 6 Free"}.fa-brands,.fab{font-family:"Font Awesome 6 Brands"}.fa-1x{font-size:1em}.fa-2x{font-size:2em}.fa-3x{font-size:3em}.fa-4x{font-size:4em}.fa-5x{font-size:5em}.fa-6x{font-size:6em}.fa-7x{font-size:7em}.fa-8x{font-size:8em}.fa-9x{font-size:9em}.fa-10x{font-size:10em}.fa-2xs{font-size:.625em;line-height:.1em;vertical-align:.225em}.fa-xs{font-size:.75em;line-height:.08333em;vertical-align:.125em}.fa-sm{font-size:.875em;line-height:.07143em;vertical-align:.05357em}.fa-lg{font-size:1.25em;line-height:.05em;vertical-align:-.075em}.fa-xl{font-size:1.5em;line-height:.04167em;vertical-align:-.125em}.fa-2xl{font-size:2em;line-height:.03125em;vertical-align:-.1875em}.fa-fw{text-align:center;width:1.25em}.fa-ul{list-style-type:none;margin-left:var(--fa-li-margin,2.5em);padding-left:0}.fa-ul>li{position:relative}.fa-li{left:calc(var(--fa-li-width, 2em)*-1);position:absolute;text-align:center;width:var(--fa-li-width,2em);line-height:inherit}.fa-border{border-radius:var(--fa-border-radius,.1em);border:var(--fa-border-width,.08em) var(--fa-border-style,solid) var(--fa-border-color,#eee);padding:var(--fa-border-padding,.2em .25em 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diff --git a/docs/deps/font-awesome-6.5.2/css/v4-shims.css b/docs/deps/font-awesome-6.5.2/css/v4-shims.css
new file mode 100644
index 0000000..ea60ea4
--- /dev/null
+++ b/docs/deps/font-awesome-6.5.2/css/v4-shims.css
@@ -0,0 +1,2194 @@
+/*!
+ * Font Awesome Free 6.5.2 by @fontawesome - https://fontawesome.com
+ * License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License)
+ * Copyright 2024 Fonticons, Inc.
+ */
+.fa.fa-glass:before {
+  content: "\f000"; }
+
+.fa.fa-envelope-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-envelope-o:before {
+  content: "\f0e0"; }
+
+.fa.fa-star-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-star-o:before {
+  content: "\f005"; }
+
+.fa.fa-remove:before {
+  content: "\f00d"; }
+
+.fa.fa-close:before {
+  content: "\f00d"; }
+
+.fa.fa-gear:before {
+  content: "\f013"; }
+
+.fa.fa-trash-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-trash-o:before {
+  content: "\f2ed"; }
+
+.fa.fa-home:before {
+  content: "\f015"; }
+
+.fa.fa-file-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-file-o:before {
+  content: "\f15b"; }
+
+.fa.fa-clock-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-clock-o:before {
+  content: "\f017"; }
+
+.fa.fa-arrow-circle-o-down {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-arrow-circle-o-down:before {
+  content: "\f358"; }
+
+.fa.fa-arrow-circle-o-up {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-arrow-circle-o-up:before {
+  content: "\f35b"; }
+
+.fa.fa-play-circle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-play-circle-o:before {
+  content: "\f144"; }
+
+.fa.fa-repeat:before {
+  content: "\f01e"; }
+
+.fa.fa-rotate-right:before {
+  content: "\f01e"; }
+
+.fa.fa-refresh:before {
+  content: "\f021"; }
+
+.fa.fa-list-alt {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-list-alt:before {
+  content: "\f022"; }
+
+.fa.fa-dedent:before {
+  content: "\f03b"; }
+
+.fa.fa-video-camera:before {
+  content: "\f03d"; }
+
+.fa.fa-picture-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-picture-o:before {
+  content: "\f03e"; }
+
+.fa.fa-photo {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-photo:before {
+  content: "\f03e"; }
+
+.fa.fa-image {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-image:before {
+  content: "\f03e"; }
+
+.fa.fa-map-marker:before {
+  content: "\f3c5"; }
+
+.fa.fa-pencil-square-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-pencil-square-o:before {
+  content: "\f044"; }
+
+.fa.fa-edit {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-edit:before {
+  content: "\f044"; }
+
+.fa.fa-share-square-o:before {
+  content: "\f14d"; }
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+.fa.fa-check-square-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-check-square-o:before {
+  content: "\f14a"; }
+
+.fa.fa-arrows:before {
+  content: "\f0b2"; }
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+.fa.fa-times-circle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
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+.fa.fa-times-circle-o:before {
+  content: "\f057"; }
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+.fa.fa-check-circle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
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+.fa.fa-check-circle-o:before {
+  content: "\f058"; }
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+.fa.fa-mail-forward:before {
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+  font-weight: 400; }
+
+.fa.fa-modx {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-fort-awesome {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-usb {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-product-hunt {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-mixcloud {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-scribd {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-pause-circle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-pause-circle-o:before {
+  content: "\f28b"; }
+
+.fa.fa-stop-circle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-stop-circle-o:before {
+  content: "\f28d"; }
+
+.fa.fa-bluetooth {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-bluetooth-b {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-gitlab {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-wpbeginner {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-wpforms {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-envira {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-wheelchair-alt {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-wheelchair-alt:before {
+  content: "\f368"; }
+
+.fa.fa-question-circle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-question-circle-o:before {
+  content: "\f059"; }
+
+.fa.fa-volume-control-phone:before {
+  content: "\f2a0"; }
+
+.fa.fa-asl-interpreting:before {
+  content: "\f2a3"; }
+
+.fa.fa-deafness:before {
+  content: "\f2a4"; }
+
+.fa.fa-hard-of-hearing:before {
+  content: "\f2a4"; }
+
+.fa.fa-glide {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-glide-g {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-signing:before {
+  content: "\f2a7"; }
+
+.fa.fa-viadeo {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-viadeo-square {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-viadeo-square:before {
+  content: "\f2aa"; }
+
+.fa.fa-snapchat {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-snapchat-ghost {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-snapchat-ghost:before {
+  content: "\f2ab"; }
+
+.fa.fa-snapchat-square {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-snapchat-square:before {
+  content: "\f2ad"; }
+
+.fa.fa-pied-piper {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-first-order {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-yoast {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-themeisle {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-google-plus-official {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-google-plus-official:before {
+  content: "\f2b3"; }
+
+.fa.fa-google-plus-circle {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-google-plus-circle:before {
+  content: "\f2b3"; }
+
+.fa.fa-font-awesome {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-fa {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-fa:before {
+  content: "\f2b4"; }
+
+.fa.fa-handshake-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-handshake-o:before {
+  content: "\f2b5"; }
+
+.fa.fa-envelope-open-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-envelope-open-o:before {
+  content: "\f2b6"; }
+
+.fa.fa-linode {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-address-book-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-address-book-o:before {
+  content: "\f2b9"; }
+
+.fa.fa-vcard:before {
+  content: "\f2bb"; }
+
+.fa.fa-address-card-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-address-card-o:before {
+  content: "\f2bb"; }
+
+.fa.fa-vcard-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-vcard-o:before {
+  content: "\f2bb"; }
+
+.fa.fa-user-circle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-user-circle-o:before {
+  content: "\f2bd"; }
+
+.fa.fa-user-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-user-o:before {
+  content: "\f007"; }
+
+.fa.fa-id-badge {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-drivers-license:before {
+  content: "\f2c2"; }
+
+.fa.fa-id-card-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-id-card-o:before {
+  content: "\f2c2"; }
+
+.fa.fa-drivers-license-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-drivers-license-o:before {
+  content: "\f2c2"; }
+
+.fa.fa-quora {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-free-code-camp {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-telegram {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-thermometer-4:before {
+  content: "\f2c7"; }
+
+.fa.fa-thermometer:before {
+  content: "\f2c7"; }
+
+.fa.fa-thermometer-3:before {
+  content: "\f2c8"; }
+
+.fa.fa-thermometer-2:before {
+  content: "\f2c9"; }
+
+.fa.fa-thermometer-1:before {
+  content: "\f2ca"; }
+
+.fa.fa-thermometer-0:before {
+  content: "\f2cb"; }
+
+.fa.fa-bathtub:before {
+  content: "\f2cd"; }
+
+.fa.fa-s15:before {
+  content: "\f2cd"; }
+
+.fa.fa-window-maximize {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-window-restore {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-times-rectangle:before {
+  content: "\f410"; }
+
+.fa.fa-window-close-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-window-close-o:before {
+  content: "\f410"; }
+
+.fa.fa-times-rectangle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-times-rectangle-o:before {
+  content: "\f410"; }
+
+.fa.fa-bandcamp {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-grav {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-etsy {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-imdb {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-ravelry {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-eercast {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-eercast:before {
+  content: "\f2da"; }
+
+.fa.fa-snowflake-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-snowflake-o:before {
+  content: "\f2dc"; }
+
+.fa.fa-superpowers {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-wpexplorer {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-meetup {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
diff --git a/docs/deps/font-awesome-6.5.2/css/v4-shims.min.css b/docs/deps/font-awesome-6.5.2/css/v4-shims.min.css
new file mode 100644
index 0000000..09baf5f
--- /dev/null
+++ b/docs/deps/font-awesome-6.5.2/css/v4-shims.min.css
@@ -0,0 +1,6 @@
+/*!
+ * Font Awesome Free 6.5.2 by @fontawesome - https://fontawesome.com
+ * License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License)
+ * Copyright 2024 Fonticons, Inc.
+ */
+.fa.fa-glass:before{content:"\f000"}.fa.fa-envelope-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-envelope-o:before{content:"\f0e0"}.fa.fa-star-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-star-o:before{content:"\f005"}.fa.fa-close:before,.fa.fa-remove:before{content:"\f00d"}.fa.fa-gear:before{content:"\f013"}.fa.fa-trash-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-trash-o:before{content:"\f2ed"}.fa.fa-home:before{content:"\f015"}.fa.fa-file-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-file-o:before{content:"\f15b"}.fa.fa-clock-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-clock-o:before{content:"\f017"}.fa.fa-arrow-circle-o-down{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-arrow-circle-o-down:before{content:"\f358"}.fa.fa-arrow-circle-o-up{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-arrow-circle-o-up:before{content:"\f35b"}.fa.fa-play-circle-o{font-family:"Font Awesome 6 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Awesome 6 Free";font-weight:400}.fa.fa-check-square-o:before{content:"\f14a"}.fa.fa-arrows:before{content:"\f0b2"}.fa.fa-times-circle-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-times-circle-o:before{content:"\f057"}.fa.fa-check-circle-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-check-circle-o:before{content:"\f058"}.fa.fa-mail-forward:before{content:"\f064"}.fa.fa-expand:before{content:"\f424"}.fa.fa-compress:before{content:"\f422"}.fa.fa-eye,.fa.fa-eye-slash{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-warning:before{content:"\f071"}.fa.fa-calendar:before{content:"\f073"}.fa.fa-arrows-v:before{content:"\f338"}.fa.fa-arrows-h:before{content:"\f337"}.fa.fa-bar-chart-o:before,.fa.fa-bar-chart:before{content:"\e0e3"}.fa.fa-twitter-square{font-family:"Font Awesome 6 Brands";font-weight:400}.fa.fa-twitter-square:before{content:"\f081"}.fa.fa-facebook-square{font-family:"Font Awesome 6 Brands";font-weight:400}.fa.fa-facebook-square:before{content:"\f082"}.fa.fa-gears:before{content:"\f085"}.fa.fa-thumbs-o-up{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-thumbs-o-up:before{content:"\f164"}.fa.fa-thumbs-o-down{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-thumbs-o-down:before{content:"\f165"}.fa.fa-heart-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-heart-o:before{content:"\f004"}.fa.fa-sign-out:before{content:"\f2f5"}.fa.fa-linkedin-square{font-family:"Font Awesome 6 Brands";font-weight:400}.fa.fa-linkedin-square:before{content:"\f08c"}.fa.fa-thumb-tack:before{content:"\f08d"}.fa.fa-external-link:before{content:"\f35d"}.fa.fa-sign-in:before{content:"\f2f6"}.fa.fa-github-square{font-family:"Font Awesome 6 Brands";font-weight:400}.fa.fa-github-square:before{content:"\f092"}.fa.fa-lemon-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-lemon-o:before{content:"\f094"}.fa.fa-square-o{font-family:"Font Awesome 6 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--- /dev/null
+++ b/docs/deps/headroom-0.11.0/headroom.min.js
@@ -0,0 +1,7 @@
+/*!
+ * headroom.js v0.11.0 - Give your page some headroom. Hide your header until you need it
+ * Copyright (c) 2020 Nick Williams - http://wicky.nillia.ms/headroom.js
+ * License: MIT
+ */
+
+!function(t,n){"object"==typeof exports&&"undefined"!=typeof module?module.exports=n():"function"==typeof define&&define.amd?define(n):(t=t||self).Headroom=n()}(this,function(){"use strict";function t(){return"undefined"!=typeof window}function d(t){return function(t){return t&&t.document&&function(t){return 9===t.nodeType}(t.document)}(t)?function(t){var n=t.document,o=n.body,s=n.documentElement;return{scrollHeight:function(){return Math.max(o.scrollHeight,s.scrollHeight,o.offsetHeight,s.offsetHeight,o.clientHeight,s.clientHeight)},height:function(){return t.innerHeight||s.clientHeight||o.clientHeight},scrollY:function(){return void 0!==t.pageYOffset?t.pageYOffset:(s||o.parentNode||o).scrollTop}}}(t):function(t){return{scrollHeight:function(){return Math.max(t.scrollHeight,t.offsetHeight,t.clientHeight)},height:function(){return Math.max(t.offsetHeight,t.clientHeight)},scrollY:function(){return t.scrollTop}}}(t)}function n(t,s,e){var n,o=function(){var n=!1;try{var t={get passive(){n=!0}};window.addEventListener("test",t,t),window.removeEventListener("test",t,t)}catch(t){n=!1}return n}(),i=!1,r=d(t),l=r.scrollY(),a={};function c(){var t=Math.round(r.scrollY()),n=r.height(),o=r.scrollHeight();a.scrollY=t,a.lastScrollY=l,a.direction=l<t?"down":"up",a.distance=Math.abs(t-l),a.isOutOfBounds=t<0||o<t+n,a.top=t<=s.offset,a.bottom=o<=t+n,a.toleranceExceeded=a.distance>s.tolerance[a.direction],e(a),l=t,i=!1}function h(){i||(i=!0,n=requestAnimationFrame(c))}var u=!!o&&{passive:!0,capture:!1};return t.addEventListener("scroll",h,u),c(),{destroy:function(){cancelAnimationFrame(n),t.removeEventListener("scroll",h,u)}}}function o(t,n){n=n||{},Object.assign(this,o.options,n),this.classes=Object.assign({},o.options.classes,n.classes),this.elem=t,this.tolerance=function(t){return t===Object(t)?t:{down:t,up:t}}(this.tolerance),this.initialised=!1,this.frozen=!1}return o.prototype={constructor:o,init:function(){return o.cutsTheMustard&&!this.initialised&&(this.addClass("initial"),this.initialised=!0,setTimeout(function(t){t.scrollTracker=n(t.scroller,{offset:t.offset,tolerance:t.tolerance},t.update.bind(t))},100,this)),this},destroy:function(){this.initialised=!1,Object.keys(this.classes).forEach(this.removeClass,this),this.scrollTracker.destroy()},unpin:function(){!this.hasClass("pinned")&&this.hasClass("unpinned")||(this.addClass("unpinned"),this.removeClass("pinned"),this.onUnpin&&this.onUnpin.call(this))},pin:function(){this.hasClass("unpinned")&&(this.addClass("pinned"),this.removeClass("unpinned"),this.onPin&&this.onPin.call(this))},freeze:function(){this.frozen=!0,this.addClass("frozen")},unfreeze:function(){this.frozen=!1,this.removeClass("frozen")},top:function(){this.hasClass("top")||(this.addClass("top"),this.removeClass("notTop"),this.onTop&&this.onTop.call(this))},notTop:function(){this.hasClass("notTop")||(this.addClass("notTop"),this.removeClass("top"),this.onNotTop&&this.onNotTop.call(this))},bottom:function(){this.hasClass("bottom")||(this.addClass("bottom"),this.removeClass("notBottom"),this.onBottom&&this.onBottom.call(this))},notBottom:function(){this.hasClass("notBottom")||(this.addClass("notBottom"),this.removeClass("bottom"),this.onNotBottom&&this.onNotBottom.call(this))},shouldUnpin:function(t){return"down"===t.direction&&!t.top&&t.toleranceExceeded},shouldPin:function(t){return"up"===t.direction&&t.toleranceExceeded||t.top},addClass:function(t){this.elem.classList.add.apply(this.elem.classList,this.classes[t].split(" "))},removeClass:function(t){this.elem.classList.remove.apply(this.elem.classList,this.classes[t].split(" "))},hasClass:function(t){return this.classes[t].split(" ").every(function(t){return this.classList.contains(t)},this.elem)},update:function(t){t.isOutOfBounds||!0!==this.frozen&&(t.top?this.top():this.notTop(),t.bottom?this.bottom():this.notBottom(),this.shouldUnpin(t)?this.unpin():this.shouldPin(t)&&this.pin())}},o.options={tolerance:{up:0,down:0},offset:0,scroller:t()?window:null,classes:{frozen:"headroom--frozen",pinned:"headroom--pinned",unpinned:"headroom--unpinned",top:"headroom--top",notTop:"headroom--not-top",bottom:"headroom--bottom",notBottom:"headroom--not-bottom",initial:"headroom"}},o.cutsTheMustard=!!(t()&&function(){}.bind&&"classList"in document.documentElement&&Object.assign&&Object.keys&&requestAnimationFrame),o});
\ No newline at end of file
diff --git a/docs/deps/headroom-0.11.0/jQuery.headroom.min.js b/docs/deps/headroom-0.11.0/jQuery.headroom.min.js
new file mode 100644
index 0000000..17f70c9
--- /dev/null
+++ b/docs/deps/headroom-0.11.0/jQuery.headroom.min.js
@@ -0,0 +1,7 @@
+/*!
+ * headroom.js v0.9.4 - Give your page some headroom. Hide your header until you need it
+ * Copyright (c) 2017 Nick Williams - http://wicky.nillia.ms/headroom.js
+ * License: MIT
+ */
+
+!function(a){a&&(a.fn.headroom=function(b){return this.each(function(){var c=a(this),d=c.data("headroom"),e="object"==typeof b&&b;e=a.extend(!0,{},Headroom.options,e),d||(d=new Headroom(this,e),d.init(),c.data("headroom",d)),"string"==typeof b&&(d[b](),"destroy"===b&&c.removeData("headroom"))})},a("[data-headroom]").each(function(){var b=a(this);b.headroom(b.data())}))}(window.Zepto||window.jQuery);
\ No newline at end of file
diff --git a/docs/deps/search-1.0.0/autocomplete.jquery.min.js b/docs/deps/search-1.0.0/autocomplete.jquery.min.js
new file mode 100644
index 0000000..fb63a6a
--- /dev/null
+++ b/docs/deps/search-1.0.0/autocomplete.jquery.min.js
@@ -0,0 +1,7 @@
+/*!
+ * autocomplete.js 0.38.0
+ * https://github.com/algolia/autocomplete.js
+ * Copyright 2020 Algolia, Inc. and other contributors; Licensed MIT
+ */
+!function(a){function b(d){if(c[d])return c[d].exports;var e=c[d]={exports:{},id:d,loaded:!1};return a[d].call(e.exports,e,e.exports,b),e.loaded=!0,e.exports}var c={};b.m=a,b.c=c,b.p="",b(0)}([function(a,b,c){"use strict";a.exports=c(1)},function(a,b,c){"use strict";var d=c(2),e=c(3);d.element=e;var f=c(4);f.isArray=e.isArray,f.isFunction=e.isFunction,f.isObject=e.isPlainObject,f.bind=e.proxy,f.each=function(a,b){function c(a,c){return b(c,a)}e.each(a,c)},f.map=e.map,f.mixin=e.extend,f.Event=e.Event;var g,h,i,j=c(5),k=c(6);g=e.fn.autocomplete,h="aaAutocomplete",i={initialize:function(a,b){function c(){var c,d=e(this),f=new k({el:d});c=new j({input:d,eventBus:f,dropdownMenuContainer:a.dropdownMenuContainer,hint:void 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i[a]&&"initialize"!==a?(b=this.filter(function(){return!!e(this).data(h)}),i[a].apply(b,[].slice.call(arguments,1))):i.initialize.apply(this,arguments)},e.fn.autocomplete.noConflict=function(){return e.fn.autocomplete=g,this},e.fn.autocomplete.sources=j.sources,e.fn.autocomplete.escapeHighlightedString=f.escapeHighlightedString,a.exports=e.fn.autocomplete},function(a,b){"use strict";a.exports={element:null}},function(a,b){a.exports=jQuery},function(a,b,c){"use strict";function d(a){return a.replace(/[\-\[\]\/\{\}\(\)\*\+\?\.\\\^\$\|]/g,"\\$&")}var e=c(2);a.exports={isArray:null,isFunction:null,isObject:null,bind:null,each:null,map:null,mixin:null,isMsie:function(a){if(void 0===a&&(a=navigator.userAgent),/(msie|trident)/i.test(a)){var b=a.match(/(msie |rv:)(\d+(.\d+)?)/i);if(b)return b[2]}return!1},escapeRegExChars:function(a){return a.replace(/[\-\[\]\/\{\}\(\)\*\+\?\.\\\^\$\|]/g,"\\$&")},isNumber:function(a){return"number"==typeof a},toStr:function(a){return void 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d.Dropdown({appendTo:a.appendTo,wrapper:this.$node,menu:b,datasets:a.datasets,templates:a.templates,cssClasses:a.cssClasses,minLength:this.minLength}).onSync("suggestionClicked",this._onSuggestionClicked,this).onSync("cursorMoved",this._onCursorMoved,this).onSync("cursorRemoved",this._onCursorRemoved,this).onSync("opened",this._onOpened,this).onSync("closed",this._onClosed,this).onSync("shown",this._onShown,this).onSync("empty",this._onEmpty,this).onSync("redrawn",this._onRedrawn,this).onAsync("datasetRendered",this._onDatasetRendered,this),this.input=new 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required").prop("readonly",!0).attr({"aria-hidden":"true",autocomplete:"off",spellcheck:"false",tabindex:-1}),e.removeData&&e.removeData(),b.data(h,{"aria-autocomplete":b.attr("aria-autocomplete"),"aria-expanded":b.attr("aria-expanded"),"aria-owns":b.attr("aria-owns"),autocomplete:b.attr("autocomplete"),dir:b.attr("dir"),role:b.attr("role"),spellcheck:b.attr("spellcheck"),style:b.attr("style"),type:b.attr("type")}),b.addClass(i.className(a.cssClasses.prefix,a.cssClasses.input,!0)).attr({autocomplete:"off",spellcheck:!1,role:"combobox","aria-autocomplete":a.datasets&&a.datasets[0]&&a.datasets[0].displayKey?"both":"list","aria-expanded":"false","aria-label":a.ariaLabel,"aria-owns":a.listboxId}).css(a.hint?a.css.input:a.css.inputWithNoHint);try{b.attr("dir")||b.attr("dir","auto")}catch(a){}return c=a.appendTo?c.appendTo(j.element(a.appendTo).eq(0)).eq(0):b.wrap(c).parent(),c.prepend(a.hint?e:null).append(d),{wrapper:c,input:b,hint:e,menu:d}}function 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+var c=[].slice.call(arguments,1);this.cacheSuggestions(a,b,c),this._render.apply(this,[a,b].concat(c))}}if(this.query=a,this.canceled=!1,this.shouldFetchFromCache(a))b.apply(this,[this.cachedSuggestions].concat(this.cachedRenderExtraArgs));else{var c=this,d=function(){c.canceled||c.source(a,b.bind(c))};if(this.debounce){var e=function(){c.debounceTimeout=null,d()};clearTimeout(this.debounceTimeout),this.debounceTimeout=setTimeout(e,this.debounce)}else d()}},cacheSuggestions:function(a,b,c){this.cachedQuery=a,this.cachedSuggestions=b,this.cachedRenderExtraArgs=c},shouldFetchFromCache:function(a){return this.cache&&this.cachedQuery===a&&this.cachedSuggestions&&this.cachedSuggestions.length},clearCachedSuggestions:function(){delete this.cachedQuery,delete this.cachedSuggestions,delete this.cachedRenderExtraArgs},cancel:function(){this.canceled=!0},clear:function(){this.$el&&(this.cancel(),this.$el.empty(),this.trigger("rendered",""))},isEmpty:function(){return this._isEmpty},destroy:function(){this.clearCachedSuggestions(),this.$el=null}}),a.exports=d},function(a,b){"use strict";a.exports={wrapper:'<span class="%ROOT%"></span>',dropdown:'<span class="%PREFIX%%DROPDOWN_MENU%"></span>',dataset:'<div class="%PREFIX%%DATASET%-%CLASS%"></div>',suggestions:'<span class="%PREFIX%%SUGGESTIONS%"></span>',suggestion:'<div class="%PREFIX%%SUGGESTION%"></div>'}},function(a,b,c){"use strict";var d=c(4),e={wrapper:{position:"relative",display:"inline-block"},hint:{position:"absolute",top:"0",left:"0",borderColor:"transparent",boxShadow:"none",opacity:"1"},input:{position:"relative",verticalAlign:"top",backgroundColor:"transparent"},inputWithNoHint:{position:"relative",verticalAlign:"top"},dropdown:{position:"absolute",top:"100%",left:"0",zIndex:"100",display:"none"},suggestions:{display:"block"},suggestion:{whiteSpace:"nowrap",cursor:"pointer"},suggestionChild:{whiteSpace:"normal"},ltr:{left:"0",right:"auto"},rtl:{left:"auto",right:"0"},defaultClasses:{root:"algolia-autocomplete",prefix:"aa",noPrefix:!1,dropdownMenu:"dropdown-menu",input:"input",hint:"hint",suggestions:"suggestions",suggestion:"suggestion",cursor:"cursor",dataset:"dataset",empty:"empty"},appendTo:{wrapper:{position:"absolute",zIndex:"100",display:"none"},input:{},inputWithNoHint:{},dropdown:{display:"block"}}};d.isMsie()&&d.mixin(e.input,{backgroundImage:"url(data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)"}),d.isMsie()&&d.isMsie()<=7&&d.mixin(e.input,{marginTop:"-1px"}),a.exports=e},function(a,b,c){"use strict";a.exports={hits:c(21),popularIn:c(24)}},function(a,b,c){"use strict";var d=c(4),e=c(22),f=c(23),g=function(){function a(a,d){return window.Promise.resolve().then(function(){return b.length&&(e=a.search(b),b=[]),e}).then(function(a){if(a)return c=a.results,c[d]})}var b=[],c=[],e=window.Promise.resolve();return function(c,e){return function(f,g){a(c.as,b.push({indexName:c.indexName,query:f,params:e})-1).then(function(a){a&&g(a.hits,a)}).catch(function(a){d.error(a.message)})}}}();a.exports=function(a,b){var c=f(a.as._ua);if(c&&c[0]>=3&&c[1]>20){var d="autocomplete.js "+e;a.as._ua.indexOf(d)===-1&&(a.as._ua+="; "+d)}return g(a,b)}},function(a,b){a.exports="0.38.0"},function(a,b){"use strict";a.exports=function(a){var b=a.match(/Algolia for JavaScript \((\d+\.)(\d+\.)(\d+)\)/)||a.match(/Algolia for vanilla JavaScript (\d+\.)(\d+\.)(\d+)/);if(b)return[b[1],b[2],b[3]]}},function(a,b,c){"use strict";var d=c(4),e=c(22),f=c(23);a.exports=function(a,b,c,g){function h(h,i){a.search(h,b,function(a,h){if(a)return void d.error(a.message);if(h.hits.length>0){var l=h.hits[0],m=d.mixin({hitsPerPage:0},c);delete m.source,delete m.index;var n=f(k.as._ua);return n&&n[0]>=3&&n[1]>20&&(b.additionalUA="autocomplete.js "+e),void k.search(j(l),m,function(a,b){if(a)return void d.error(a.message);var c=[];if(g.includeAll){var e=g.allTitle||"All departments";c.push(d.mixin({facet:{value:e,count:b.nbHits}},d.cloneDeep(l)))}d.each(b.facets,function(a,b){d.each(a,function(a,e){c.push(d.mixin({facet:{facet:b,value:e,count:a}},d.cloneDeep(l)))})});for(var f=1;f<h.hits.length;++f)c.push(h.hits[f]);i(c,h)})}i([])})}var i=f(a.as._ua);if(i&&i[0]>=3&&i[1]>20&&(b=b||{},b.additionalUA="autocomplete.js "+e),!c.source)return d.error("Missing 'source' key");var j=d.isFunction(c.source)?c.source:function(a){return a[c.source]};if(!c.index)return d.error("Missing 'index' key");var k=c.index;return g=g||{},h}}]);
\ No newline at end of file
diff --git a/docs/deps/search-1.0.0/fuse.min.js b/docs/deps/search-1.0.0/fuse.min.js
new file mode 100644
index 0000000..7def598
--- /dev/null
+++ b/docs/deps/search-1.0.0/fuse.min.js
@@ -0,0 +1,9 @@
+/**
+ * Fuse.js v6.4.6 - Lightweight fuzzy-search (http://fusejs.io)
+ *
+ * Copyright (c) 2021 Kiro Risk (http://kiro.me)
+ * All Rights Reserved. Apache Software License 2.0
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ */
+var e,t;e=this,t=function(){"use strict";function e(t){return(e="function"==typeof Symbol&&"symbol"==typeof Symbol.iterator?function(e){return typeof e}:function(e){return e&&"function"==typeof Symbol&&e.constructor===Symbol&&e!==Symbol.prototype?"symbol":typeof e})(t)}function t(e,t){if(!(e instanceof t))throw new TypeError("Cannot call a class as a function")}function n(e,t){for(var n=0;n<t.length;n++){var r=t[n];r.enumerable=r.enumerable||!1,r.configurable=!0,"value"in r&&(r.writable=!0),Object.defineProperty(e,r.key,r)}}function r(e,t,r){return t&&n(e.prototype,t),r&&n(e,r),e}function i(e,t,n){return t in e?Object.defineProperty(e,t,{value:n,enumerable:!0,configurable:!0,writable:!0}):e[t]=n,e}function o(e,t){var n=Object.keys(e);if(Object.getOwnPropertySymbols){var r=Object.getOwnPropertySymbols(e);t&&(r=r.filter((function(t){return Object.getOwnPropertyDescriptor(e,t).enumerable}))),n.push.apply(n,r)}return n}function c(e){for(var t=1;t<arguments.length;t++){var n=null!=arguments[t]?arguments[t]:{};t%2?o(Object(n),!0).forEach((function(t){i(e,t,n[t])})):Object.getOwnPropertyDescriptors?Object.defineProperties(e,Object.getOwnPropertyDescriptors(n)):o(Object(n)).forEach((function(t){Object.defineProperty(e,t,Object.getOwnPropertyDescriptor(n,t))}))}return e}function a(e,t){if("function"!=typeof t&&null!==t)throw new TypeError("Super expression must either be null or a function");e.prototype=Object.create(t&&t.prototype,{constructor:{value:e,writable:!0,configurable:!0}}),t&&u(e,t)}function s(e){return(s=Object.setPrototypeOf?Object.getPrototypeOf:function(e){return e.__proto__||Object.getPrototypeOf(e)})(e)}function u(e,t){return(u=Object.setPrototypeOf||function(e,t){return e.__proto__=t,e})(e,t)}function h(e,t){return!t||"object"!=typeof t&&"function"!=typeof t?function(e){if(void 0===e)throw new ReferenceError("this hasn't been initialised - super() hasn't been called");return e}(e):t}function f(e){var t=function(){if("undefined"==typeof 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diff --git a/docs/deps/search-1.0.0/mark.min.js b/docs/deps/search-1.0.0/mark.min.js
new file mode 100644
index 0000000..1eea053
--- /dev/null
+++ b/docs/deps/search-1.0.0/mark.min.js
@@ -0,0 +1,7 @@
+/*!***************************************************
+* mark.js v8.11.1
+* https://markjs.io/
+* Copyright (c) 2014–2018, Julian Kühnel
+* Released under the MIT license https://git.io/vwTVl
+*****************************************************/
+!function(e,t){"object"==typeof exports&&"undefined"!=typeof module?module.exports=t():"function"==typeof define&&define.amd?define(t):e.Mark=t()}(this,function(){"use strict";var e="function"==typeof Symbol&&"symbol"==typeof Symbol.iterator?function(e){return typeof e}:function(e){return e&&"function"==typeof Symbol&&e.constructor===Symbol&&e!==Symbol.prototype?"symbol":typeof e},t=function(e,t){if(!(e instanceof t))throw new TypeError("Cannot call a class as a function")},n=function(){function e(e,t){for(var n=0;n<t.length;n++){var r=t[n];r.enumerable=r.enumerable||!1,r.configurable=!0,"value"in r&&(r.writable=!0),Object.defineProperty(e,r.key,r)}}return function(t,n,r){return n&&e(t.prototype,n),r&&e(t,r),t}}(),r=Object.assign||function(e){for(var t=1;t<arguments.length;t++){var n=arguments[t];for(var r in n)Object.prototype.hasOwnProperty.call(n,r)&&(e[r]=n[r])}return e},i=function(){function e(n){var r=!(arguments.length>1&&void 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diff --git a/docs/index.html b/docs/index.html
index 7648abb..1cfad6c 100644
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-  <a href="reference/index.html">Reference</a>
-</li>
-<li class="dropdown">
-  <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
-    Articles
-     
-    <span class="caret"></span>
-  </a>
-  <ul class="dropdown-menu" role="menu">
-<li>
-      <a href="articles/biplotEZ_enhancements.html">biplotEZ enhancements</a>
-    </li>
-    <li>
-      <a href="articles/Biplots_in_1D.html">Biplots in 1D</a>
-    </li>
-    <li>
-      <a href="articles/Biplots_in_3D.html">Biplots in 3D</a>
-    </li>
-    <li>
-      <a href="articles/CA_in_biplotEZ.html">CA in biplotEZ</a>
-    </li>
-    <li>
-      <a href="articles/Class_separation.html">Class separation</a>
-    </li>
-    <li>
-      <a href="articles/MDS.html">MDS</a>
-    </li>
+<body>
+    <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
+
+
+    <nav class="navbar navbar-expand-lg fixed-top bg-light" data-bs-theme="light" aria-label="Site navigation"><div class="container">
+
+    <a class="navbar-brand me-2" href="index.html">biplotEZ</a>
+
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.3</small>
+
+
+    <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
+      <span class="navbar-toggler-icon"></span>
+    </button>
+
+    <div id="navbar" class="collapse navbar-collapse ms-3">
+      <ul class="navbar-nav me-auto">
+<li class="nav-item"><a class="nav-link" href="articles/biplotEZ.html">Get started</a></li>
+<li class="nav-item"><a class="nav-link" href="reference/index.html">Reference</a></li>
+<li class="nav-item dropdown">
+  <button class="nav-link dropdown-toggle" type="button" id="dropdown-articles" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true">Articles</button>
+  <ul class="dropdown-menu" aria-labelledby="dropdown-articles">
+<li><a class="dropdown-item" href="articles/biplotEZ.html">biplotEZ</a></li>
+    <li><a class="dropdown-item" href="articles/biplotEZ_enhancements.html">biplotEZ enhancements</a></li>
+    <li><a class="dropdown-item" href="articles/MDS.html">Multi-dimensional scaling</a></li>
+    <li><a class="dropdown-item" href="articles/Class_separation.html">Biplots for separating classes</a></li>
+    <li><a class="dropdown-item" href="articles/CA_in_biplotEZ.html">Categorical biplots</a></li>
+    <li><a class="dropdown-item" href="articles/Biplots_in_1D.html">One dimensional biplots</a></li>
+    <li><a class="dropdown-item" href="articles/Biplots_in_3D.html">Three dimensional biplots</a></li>
   </ul>
 </li>
       </ul>
-<ul class="nav navbar-nav navbar-right"></ul>
-</div>
-<!--/.nav-collapse -->
-  </div>
-<!--/.container -->
+<ul class="navbar-nav">
+<li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="search.json">
+</form></li>
+      </ul>
 </div>
-<!--/.navbar -->
 
-      
 
-      </header><div class="row">
-  <div class="contents col-md-9">
-<div class="section level1">
-<div class="page-header"><h1 id="biplotez">biplotEZ<a class="anchor" aria-label="anchor" href="#biplotez"></a>
-</h1></div>
+  </div>
+</nav><div class="container template-home">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="section level1">
+<div class="page-header">
+<img src="logo.png" class="logo" alt=""><h1 id="biplotez">biplotEZ<a class="anchor" aria-label="anchor" href="#biplotez"></a>
+</h1>
+</div>
 <!-- badges: start -->
 <!-- badges: end -->
 <p>The goal of biplotEZ is to provide users an EZ-to-use platform for visually representing their data with biplots. Currently, this package includes principal component analysis (PCA) and canonical variate analysis (CVA) biplots. This is accompanied by various formatting options for the samples and axes. Alpha-bags and concentration ellipses are included for visual enhancements and interpretation.</p>
@@ -175,10 +141,7 @@ <h2 id="report-bugs-and-support">Report Bugs and Support<a class="anchor" aria-l
 <p>If you encounter any issues or have questions, please open an issue on the GitHub repository.</p>
 </div>
 </div>
-  </div>
-
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-    <div class="links">
+  </main><aside class="col-md-3"><div class="links">
 <h2 data-toc-skip>Links</h2>
 <ul class="list-unstyled">
 <li><a href="https://cloud.r-project.org/package=biplotEZ" class="external-link">View on CRAN</a></li>
@@ -204,39 +167,36 @@ <h2 data-toc-skip>Citation</h2>
 <div class="developers">
 <h2 data-toc-skip>Developers</h2>
 <ul class="list-unstyled">
-<li>Sugnet Lubbe <br><small class="roles"> Author, maintainer, copyright holder </small> <a href="https://orcid.org/0000-0003-2762-9944" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a> </li>
-<li>Niël le Roux <br><small class="roles"> Author </small> <a href="https://orcid.org/0000-0002-1791-746X" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a> </li>
-<li>Johané Nienkemper-Swanepoel <br><small class="roles"> Author </small> <a href="https://orcid.org/0000-0001-6086-8272" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a> </li>
-<li>Raeesa Ganey <br><small class="roles"> Author </small> <a href="https://orcid.org/0009-0008-6973-0999" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a> </li>
-<li>Ruan Buys <br><small class="roles"> Author </small> <a href="https://orcid.org/0000-0001-8527-8631" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a> </li>
-<li>Zoë-Mae Adams <br><small class="roles"> Author </small> <a href="https://orcid.org/0000-0003-3730-4887" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a> </li>
-<li>Peter Manefeldt <br><small class="roles"> Author </small> <a href="https://orcid.org/0000-0002-8604-843X" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a> </li>
+<li>Sugnet Lubbe <br><small class="roles"> Author, maintainer, copyright holder </small> <a href="https://orcid.org/0000-0003-2762-9944" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a>  </li>
+<li>Niël le Roux <br><small class="roles"> Author </small> <a href="https://orcid.org/0000-0002-1791-746X" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a>  </li>
+<li>Johané Nienkemper-Swanepoel <br><small class="roles"> Author </small> <a href="https://orcid.org/0000-0001-6086-8272" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a>  </li>
+<li>Raeesa Ganey <br><small class="roles"> Author </small> <a href="https://orcid.org/0009-0008-6973-0999" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a>  </li>
+<li>Ruan Buys <br><small class="roles"> Author </small> <a href="https://orcid.org/0000-0001-8527-8631" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a>  </li>
+<li>Zoë-Mae Adams <br><small class="roles"> Author </small> <a href="https://orcid.org/0000-0003-3730-4887" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a>  </li>
+<li>Peter Manefeldt <br><small class="roles"> Author </small> <a href="https://orcid.org/0000-0002-8604-843X" target="orcid.widget" aria-label="ORCID" class="external-link"><span class="fab fa-orcid orcid" aria-hidden="true"></span></a>  </li>
 </ul>
 </div>
 
 
 
-  </div>
+  </aside>
 </div>
 
 
-      <footer><div class="copyright">
-  <p></p>
-<p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
-  <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p>
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.2.</p>
 </div>
 
-      </footer>
+    </footer>
 </div>
 
-  
 
 
-  
+
 
   </body>
 </html>
diff --git a/docs/katex-auto.js b/docs/katex-auto.js
new file mode 100644
index 0000000..20651d9
--- /dev/null
+++ b/docs/katex-auto.js
@@ -0,0 +1,14 @@
+// https://github.com/jgm/pandoc/blob/29fa97ab96b8e2d62d48326e1b949a71dc41f47a/src/Text/Pandoc/Writers/HTML.hs#L332-L345
+document.addEventListener("DOMContentLoaded", function () {
+  var mathElements = document.getElementsByClassName("math");
+  var macros = [];
+  for (var i = 0; i < mathElements.length; i++) {
+    var texText = mathElements[i].firstChild;
+    if (mathElements[i].tagName == "SPAN") {
+      katex.render(texText.data, mathElements[i], {
+        displayMode: mathElements[i].classList.contains("display"),
+        throwOnError: false,
+        macros: macros,
+        fleqn: false
+      });
+    }}});
diff --git a/docs/lightswitch.js b/docs/lightswitch.js
new file mode 100644
index 0000000..9467125
--- /dev/null
+++ b/docs/lightswitch.js
@@ -0,0 +1,85 @@
+
+/*!
+ * Color mode toggler for Bootstrap's docs (https://getbootstrap.com/)
+ * Copyright 2011-2023 The Bootstrap Authors
+ * Licensed under the Creative Commons Attribution 3.0 Unported License.
+ * Updates for {pkgdown} by the {bslib} authors, also licensed under CC-BY-3.0.
+ */
+
+const getStoredTheme = () => localStorage.getItem('theme')
+const setStoredTheme = theme => localStorage.setItem('theme', theme)
+
+const getPreferredTheme = () => {
+  const storedTheme = getStoredTheme()
+  if (storedTheme) {
+    return storedTheme
+  }
+
+  return window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'
+}
+
+const setTheme = theme => {
+  if (theme === 'auto') {
+    document.documentElement.setAttribute('data-bs-theme', (window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'))
+  } else {
+    document.documentElement.setAttribute('data-bs-theme', theme)
+  }
+}
+
+function bsSetupThemeToggle () {
+  'use strict'
+
+  const showActiveTheme = (theme, focus = false) => {
+    var activeLabel, activeIcon;
+
+    document.querySelectorAll('[data-bs-theme-value]').forEach(element => {
+      const buttonTheme = element.getAttribute('data-bs-theme-value')
+      const isActive = buttonTheme == theme
+      
+      element.classList.toggle('active', isActive)
+      element.setAttribute('aria-pressed', isActive)
+
+      if (isActive) {
+        activeLabel = element.textContent;
+        activeIcon = element.querySelector('span').classList.value;
+      }
+    })
+
+    const themeSwitcher = document.querySelector('#dropdown-lightswitch')
+    if (!themeSwitcher) {
+      return
+    }
+
+    themeSwitcher.setAttribute('aria-label', activeLabel)
+    themeSwitcher.querySelector('span').classList.value = activeIcon;
+
+    if (focus) {
+      themeSwitcher.focus()
+    }
+  }
+
+  window.matchMedia('(prefers-color-scheme: dark)').addEventListener('change', () => {
+    const storedTheme = getStoredTheme()
+    if (storedTheme !== 'light' && storedTheme !== 'dark') {
+      setTheme(getPreferredTheme())
+    }
+  })
+
+  window.addEventListener('DOMContentLoaded', () => {
+    showActiveTheme(getPreferredTheme())
+
+    document
+      .querySelectorAll('[data-bs-theme-value]')
+      .forEach(toggle => {
+        toggle.addEventListener('click', () => {
+          const theme = toggle.getAttribute('data-bs-theme-value')
+          setTheme(theme)
+          setStoredTheme(theme)
+          showActiveTheme(theme, true)
+        })
+      })
+  })
+}
+
+setTheme(getPreferredTheme());
+bsSetupThemeToggle();
diff --git a/docs/pkgdown.js b/docs/pkgdown.js
index 6f0eee4..1a99c65 100644
--- a/docs/pkgdown.js
+++ b/docs/pkgdown.js
@@ -2,83 +2,43 @@
 (function($) {
   $(function() {
 
-    $('.navbar-fixed-top').headroom();
+    $('nav.navbar').headroom();
 
-    $('body').css('padding-top', $('.navbar').height() + 10);
-    $(window).resize(function(){
-      $('body').css('padding-top', $('.navbar').height() + 10);
+    Toc.init({
+      $nav: $("#toc"),
+      $scope: $("main h2, main h3, main h4, main h5, main h6")
     });
 
-    $('[data-toggle="tooltip"]').tooltip();
-
-    var cur_path = paths(location.pathname);
-    var links = $("#navbar ul li a");
-    var max_length = -1;
-    var pos = -1;
-    for (var i = 0; i < links.length; i++) {
-      if (links[i].getAttribute("href") === "#")
-        continue;
-      // Ignore external links
-      if (links[i].host !== location.host)
-        continue;
-
-      var nav_path = paths(links[i].pathname);
-
-      var length = prefix_length(nav_path, cur_path);
-      if (length > max_length) {
-        max_length = length;
-        pos = i;
-      }
-    }
-
-    // Add class to parent <li>, and enclosing <li> if in dropdown
-    if (pos >= 0) {
-      var menu_anchor = $(links[pos]);
-      menu_anchor.parent().addClass("active");
-      menu_anchor.closest("li.dropdown").addClass("active");
-    }
-  });
-
-  function paths(pathname) {
-    var pieces = pathname.split("/");
-    pieces.shift(); // always starts with /
-
-    var end = pieces[pieces.length - 1];
-    if (end === "index.html" || end === "")
-      pieces.pop();
-    return(pieces);
-  }
-
-  // Returns -1 if not found
-  function prefix_length(needle, haystack) {
-    if (needle.length > haystack.length)
-      return(-1);
-
-    // Special case for length-0 haystack, since for loop won't run
-    if (haystack.length === 0) {
-      return(needle.length === 0 ? 0 : -1);
+    if ($('#toc').length) {
+      $('body').scrollspy({
+        target: '#toc',
+        offset: $("nav.navbar").outerHeight() + 1
+      });
     }
 
-    for (var i = 0; i < haystack.length; i++) {
-      if (needle[i] != haystack[i])
-        return(i);
-    }
+    // Activate popovers
+    $('[data-bs-toggle="popover"]').popover({
+      container: 'body',
+      html: true,
+      trigger: 'focus',
+      placement: "top",
+      sanitize: false,
+    });
 
-    return(haystack.length);
-  }
+    $('[data-bs-toggle="tooltip"]').tooltip();
 
   /* Clipboard --------------------------*/
 
   function changeTooltipMessage(element, msg) {
-    var tooltipOriginalTitle=element.getAttribute('data-original-title');
-    element.setAttribute('data-original-title', msg);
+    var tooltipOriginalTitle=element.getAttribute('data-bs-original-title');
+    element.setAttribute('data-bs-original-title', msg);
     $(element).tooltip('show');
-    element.setAttribute('data-original-title', tooltipOriginalTitle);
+    element.setAttribute('data-bs-original-title', tooltipOriginalTitle);
   }
 
   if(ClipboardJS.isSupported()) {
     $(document).ready(function() {
-      var copyButton = "<button type='button' class='btn btn-primary btn-copy-ex' type = 'submit' title='Copy to clipboard' aria-label='Copy to clipboard' data-toggle='tooltip' data-placement='left auto' data-trigger='hover' data-clipboard-copy><i class='fa fa-copy'></i></button>";
+      var copyButton = "<button type='button' class='btn btn-primary btn-copy-ex' title='Copy to clipboard' aria-label='Copy to clipboard' data-toggle='tooltip' data-placement='left' data-trigger='hover' data-clipboard-copy><i class='fa fa-copy'></i></button>";
 
       $("div.sourceCode").addClass("hasCopyButton");
 
@@ -89,20 +49,114 @@
       $('.btn-copy-ex').tooltip({container: 'body'});
 
       // Initialize clipboard:
-      var clipboardBtnCopies = new ClipboardJS('[data-clipboard-copy]', {
+      var clipboard = new ClipboardJS('[data-clipboard-copy]', {
         text: function(trigger) {
           return trigger.parentNode.textContent.replace(/\n#>[^\n]*/g, "");
         }
       });
 
-      clipboardBtnCopies.on('success', function(e) {
+      clipboard.on('success', function(e) {
         changeTooltipMessage(e.trigger, 'Copied!');
         e.clearSelection();
       });
 
-      clipboardBtnCopies.on('error', function() {
+      clipboard.on('error', function(e) {
         changeTooltipMessage(e.trigger,'Press Ctrl+C or Command+C to copy');
       });
+
     });
   }
+
+    /* Search marking --------------------------*/
+    var url = new URL(window.location.href);
+    var toMark = url.searchParams.get("q");
+    var mark = new Mark("main#main");
+    if (toMark) {
+      mark.mark(toMark, {
+        accuracy: {
+          value: "complementary",
+          limiters: [",", ".", ":", "/"],
+        }
+      });
+    }
+
+  /* Search --------------------------*/
+  /* Adapted from https://github.com/rstudio/bookdown/blob/2d692ba4b61f1e466c92e78fd712b0ab08c11d31/inst/resources/bs4_book/bs4_book.js#L25 */
+    // Initialise search index on focus
+  var fuse;
+  $("#search-input").focus(async function(e) {
+    if (fuse) {
+      return;
+    }
+
+    $(e.target).addClass("loading");
+    var response = await fetch($("#search-input").data("search-index"));
+    var data = await response.json();
+
+    var options = {
+      keys: ["what", "text", "code"],
+      ignoreLocation: true,
+      threshold: 0.1,
+      includeMatches: true,
+      includeScore: true,
+    };
+    fuse = new Fuse(data, options);
+
+    $(e.target).removeClass("loading");
+  });
+
+  // Use algolia autocomplete
+  var options = {
+    autoselect: true,
+    debug: true,
+    hint: false,
+    minLength: 2,
+  };
+  var q;
+async function searchFuse(query, callback) {
+  await fuse;
+
+  var items;
+  if (!fuse) {
+    items = [];
+  } else {
+    q = query;
+    var results = fuse.search(query, { limit: 20 });
+    items = results
+      .filter((x) => x.score <= 0.75)
+      .map((x) => x.item);
+    if (items.length === 0) {
+      items = [{dir:"Sorry 😿",previous_headings:"",title:"No results found.",what:"No results found.",path:window.location.href}];
+    }
+  }
+  callback(items);
+}
+  $("#search-input").autocomplete(options, [
+    {
+      name: "content",
+      source: searchFuse,
+      templates: {
+        suggestion: (s) => {
+          if (s.title == s.what) {
+            return `${s.dir} >	<div class="search-details"> ${s.title}</div>`;
+          } else if (s.previous_headings == "") {
+            return `${s.dir} >	<div class="search-details"> ${s.title}</div> > ${s.what}`;
+          } else {
+            return `${s.dir} >	<div class="search-details"> ${s.title}</div> > ${s.previous_headings} > ${s.what}`;
+          }
+        },
+      },
+    },
+  ]).on('autocomplete:selected', function(event, s) {
+    window.location.href = s.path + "?q=" + q + "#" + s.id;
+  });
+  });
 })(window.jQuery || window.$)
+
+document.addEventListener('keydown', function(event) {
+  // Check if the pressed key is '/'
+  if (event.key === '/') {
+    event.preventDefault();  // Prevent any default action associated with the '/' key
+    document.getElementById('search-input').focus();  // Set focus to the search input
+  }
+});
diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml
index 35100f9..2ee246b 100644
--- a/docs/pkgdown.yml
+++ b/docs/pkgdown.yml
@@ -1,5 +1,5 @@
-pandoc: 3.2.1
-pkgdown: 2.0.7
+pandoc: '3.4'
+pkgdown: 2.1.2
 pkgdown_sha: ~
 articles:
   biplotEZ: biplotEZ.html
@@ -9,5 +9,4 @@ articles:
   CA_in_biplotEZ: CA_in_biplotEZ.html
   Class_separation: Class_separation.html
   MDS: MDS.html
-last_built: 2024-10-28T08:29Z
-
+last_built: 2025-05-27T00:15Z
diff --git a/docs/reference/AoD-1.png b/docs/reference/AoD-1.png
index 41f83cd..ba4bb69 100644
Binary files a/docs/reference/AoD-1.png and b/docs/reference/AoD-1.png differ
diff --git a/docs/reference/AoD.biplot-1.png b/docs/reference/AoD.biplot-1.png
index 41f83cd..ba4bb69 100644
Binary files a/docs/reference/AoD.biplot-1.png and b/docs/reference/AoD.biplot-1.png differ
diff --git a/docs/reference/AoD.biplot.html b/docs/reference/AoD.biplot.html
index b6c01ac..377dfe7 100644
--- a/docs/reference/AoD.biplot.html
+++ b/docs/reference/AoD.biplot.html
@@ -1,85 +1,60 @@
 <!DOCTYPE html>
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-    <h1>AoD biplot</h1>
-    
-    <div class="hidden name"><code>AoD.biplot.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Calculate elements for the Analysis of Distance (AoD) biplot</h1>
+
+      <div class="d-none name"><code>AoD.biplot.Rd</code></div>
     </div>
 
-    <div class="ref-description">
-    <p>Computes Analysis of Distance biplot</p>
+    <div class="ref-description section level2">
+    <p>This function is used to construct the AoD biplot</p>
     </div>
 
-    <div id="ref-usage">
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for biplot</span></span>
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'biplot'</span></span>
 <span><span class="fu"><a href="AoD.html">AoD</a></span><span class="op">(</span></span>
 <span>  <span class="va">bp</span>,</span>
-<span>  Dmat <span class="op">=</span> <span class="cn">NULL</span>,</span>
+<span>  classes <span class="op">=</span> <span class="va">bp</span><span class="op">$</span><span class="va">classes</span>,</span>
 <span>  dist.func <span class="op">=</span> <span class="cn">NULL</span>,</span>
+<span>  dist.func.cat <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>  dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>, <span class="fl">1</span>, <span class="fl">3</span><span class="op">)</span>,</span>
 <span>  e.vects <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>,</span>
-<span>  classes <span class="op">=</span> <span class="va">bp</span><span class="op">$</span><span class="va">classes</span>,</span>
 <span>  weighted <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"unweighted"</span>, <span class="st">"weighted"</span><span class="op">)</span>,</span>
 <span>  show.class.means <span class="op">=</span> <span class="cn">TRUE</span>,</span>
 <span>  axes <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"regression"</span>, <span class="st">"splines"</span><span class="op">)</span>,</span>
@@ -87,85 +62,79 @@ <h1>AoD biplot</h1>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
 
 
-<dt>Dmat</dt>
-<dd><p>nxn matrix of Euclidean embeddable distances between samples</p></dd>
+<dt id="arg-classes">classes<a class="anchor" aria-label="anchor" href="#arg-classes"></a></dt>
+<dd><p>a vector of the same length as the number of rows in the data matrix with the class indicator for the samples.</p></dd>
 
 
-<dt>dist.func</dt>
-<dd><p>function to compute Euclidean embeddable distances between samples. The
-default NULL computes Euclidean distance.</p></dd>
+<dt id="arg-dist-func">dist.func<a class="anchor" aria-label="anchor" href="#arg-dist-func"></a></dt>
+<dd><p>a character string indicating which distance function is used to compute the Euclidean embeddable distances between samples. One of <code>NULL</code> (default) which computes the Euclidean distance or other functions that can be used for the <code><a href="https://rdrr.io/r/stats/dist.html" class="external-link">dist()</a></code> function.</p></dd>
 
 
-<dt>dim.biplot</dt>
-<dd><p>dimension of the biplot. Only values 1, 2 and 3 are accepted, with default <code>2</code>.</p></dd>
+<dt id="arg-dist-func-cat">dist.func.cat<a class="anchor" aria-label="anchor" href="#arg-dist-func-cat"></a></dt>
+<dd><p>a character string indicating which distance function is used to compute the Euclidean embeddable distances between samples. One of <code>NULL</code> (default) which computes the extended matching coefficient or other functions.</p></dd>
 
 
-<dt>e.vects</dt>
-<dd><p>e.vects which eigenvectors (canonical variates) to extract, with default <code>1:dim.biplot</code>.</p></dd>
+<dt id="arg-dim-biplot">dim.biplot<a class="anchor" aria-label="anchor" href="#arg-dim-biplot"></a></dt>
+<dd><p>the dimension of the biplot. Only values <code>1</code>, <code>2</code> and <code>3</code> are accepted, with default <code>2</code>.</p></dd>
 
 
-<dt>classes</dt>
-<dd><p>classes vector of the same length as the number of rows in the data matrix
-with the class indicator for the samples.</p></dd>
+<dt id="arg-e-vects">e.vects<a class="anchor" aria-label="anchor" href="#arg-e-vects"></a></dt>
+<dd><p>the vector indicating which eigenvectors (canonical variates) should be plotted in the biplot, with default <code>1:dim.biplot</code>.</p></dd>
 
 
-<dt>weighted</dt>
-<dd><p>the default is "unweighted" where each class receives equal weight, alternatively "weighted" use class sizes as weights.</p></dd>
+<dt id="arg-weighted">weighted<a class="anchor" aria-label="anchor" href="#arg-weighted"></a></dt>
+<dd><p>a character string indicating the weighting of the classes. One of "<code>unweighted</code>" for each class to receive equal weighting or "<code>weighted</code>" for each class to receive their class sizes as weights.</p></dd>
 
 
-<dt>show.class.means</dt>
-<dd><p>logical, indicating whether to plot the class means on the biplot.</p></dd>
+<dt id="arg-show-class-means">show.class.means<a class="anchor" aria-label="anchor" href="#arg-show-class-means"></a></dt>
+<dd><p>a logical value indicating whether to plot the class means on the biplot.</p></dd>
 
 
-<dt>axes</dt>
-<dd><p>type of biplot axes, currently only regression axes are implemented</p></dd>
+<dt id="arg-axes">axes<a class="anchor" aria-label="anchor" href="#arg-axes"></a></dt>
+<dd><p>a character string indicating the type of biplot axes to be used in the biplot. One of <code>"regression"</code> or <code>"splines"</code>.</p></dd>
 
 
-<dt>...</dt>
-<dd><p>more arguments to <code>dist.func</code></p></dd>
+<dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
+<dd><p>more arguments to <code>dist.func</code>.</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>an object of class biplot.</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>an object of class <code>biplot</code>.</p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="AoD.html">AoD</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="AoD.biplot-1.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span></span></span>
 </code></pre></div>
     </div>
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diff --git a/docs/reference/AoD.html b/docs/reference/AoD.html
index d301dab..61a471c 100644
--- a/docs/reference/AoD.html
+++ b/docs/reference/AoD.html
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-    <h1>Analysis of Distance biplot method</h1>
-    
-    <div class="hidden name"><code>AoD.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Use the Analysis of Distance (AoD) method to construct the biplot</h1>
+
+      <div class="d-none name"><code>AoD.Rd</code></div>
     </div>
 
-    <div class="ref-description">
-    <p>Analysis of Distance biplot method</p>
+    <div class="ref-description section level2">
+    <p>This function appends the <code>biplot</code> object with elements resulting from using the AoD method.</p>
     </div>
 
-    <div id="ref-usage">
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">AoD</span><span class="op">(</span><span class="va">bp</span>, Dmat<span class="op">=</span><span class="cn">NULL</span>, dist.func<span class="op">=</span><span class="st">"Euclidean"</span>, dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>,<span class="fl">1</span>,<span class="fl">3</span><span class="op">)</span>, </span>
-<span>e.vects <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>, classes<span class="op">=</span><span class="va">bp</span><span class="op">$</span><span class="va">classes</span>, weighted <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"unweighted"</span>,<span class="st">"weighted"</span><span class="op">)</span>, </span>
-<span>show.class.means <span class="op">=</span> <span class="cn">TRUE</span>, axes <span class="op">=</span> <span class="st">"regression"</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">AoD</span><span class="op">(</span><span class="va">bp</span>, classes<span class="op">=</span><span class="va">bp</span><span class="op">$</span><span class="va">classes</span>, dist.func<span class="op">=</span><span class="cn">NULL</span>, dist.func.cat<span class="op">=</span><span class="cn">NULL</span>,</span>
+<span>dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>,<span class="fl">1</span>,<span class="fl">3</span><span class="op">)</span>, e.vects <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>, </span>
+<span>weighted <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"unweighted"</span>,<span class="st">"weighted"</span><span class="op">)</span>, show.class.means <span class="op">=</span> <span class="cn">TRUE</span>, </span>
+<span>axes <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"regression"</span>,<span class="st">"splines"</span><span class="op">)</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
 
 
-<dt>Dmat</dt>
-<dd><p>nxn matrix of Euclidean embeddable distances between samples</p></dd>
+<dt id="arg-classes">classes<a class="anchor" aria-label="anchor" href="#arg-classes"></a></dt>
+<dd><p>a vector of the same length as the number of rows in the data matrix with the class indicator for the samples.</p></dd>
 
 
-<dt>dist.func</dt>
-<dd><p>function to compute Euclidean embeddable distances between samples. The
-default NULL computes Euclidean distance.</p></dd>
+<dt id="arg-dist-func">dist.func<a class="anchor" aria-label="anchor" href="#arg-dist-func"></a></dt>
+<dd><p>a character string indicating which distance function is used to compute the Euclidean embeddable distances between samples. One of <code>NULL</code> (default) which computes the Euclidean distance or other functions that can be used for the <code><a href="https://rdrr.io/r/stats/dist.html" class="external-link">dist()</a></code> function.</p></dd>
 
 
-<dt>dim.biplot</dt>
-<dd><p>dimension of the biplot. Only values 1, 2 and 3 are accepted, with default <code>2</code>.</p></dd>
+<dt id="arg-dist-func-cat">dist.func.cat<a class="anchor" aria-label="anchor" href="#arg-dist-func-cat"></a></dt>
+<dd><p>a character string indicating which distance function is used to compute the Euclidean embeddable distances between samples. One of <code>NULL</code> (default) which computes the extended matching coefficient or other functions.</p></dd>
 
 
-<dt>e.vects</dt>
-<dd><p>e.vects which eigenvectors (canonical variates) to extract, with default <code>1:dim.biplot</code>.</p></dd>
+<dt id="arg-dim-biplot">dim.biplot<a class="anchor" aria-label="anchor" href="#arg-dim-biplot"></a></dt>
+<dd><p>the dimension of the biplot. Only values <code>1</code>, <code>2</code> and <code>3</code> are accepted, with default <code>2</code>.</p></dd>
 
 
-<dt>classes</dt>
-<dd><p>classes vector of the same length as the number of rows in the data matrix
-with the class indicator for the samples.</p></dd>
+<dt id="arg-e-vects">e.vects<a class="anchor" aria-label="anchor" href="#arg-e-vects"></a></dt>
+<dd><p>the vector indicating which eigenvectors (canonical variates) should be plotted in the biplot, with default <code>1:dim.biplot</code>.</p></dd>
 
 
-<dt>weighted</dt>
-<dd><p>the default is "unweighted" where each class receives equal weight, alternatively "weighted" use class sizes as weights.</p></dd>
+<dt id="arg-weighted">weighted<a class="anchor" aria-label="anchor" href="#arg-weighted"></a></dt>
+<dd><p>a character string indicating the weighting of the classes. One of "<code>unweighted</code>" for each class to receive equal weighting or "<code>weighted</code>" for each class to receive their class sizes as weights.</p></dd>
 
 
-<dt>show.class.means</dt>
-<dd><p>logical, indicating whether to plot the class means on the biplot.</p></dd>
+<dt id="arg-show-class-means">show.class.means<a class="anchor" aria-label="anchor" href="#arg-show-class-means"></a></dt>
+<dd><p>a logical value indicating whether to plot the class means on the biplot.</p></dd>
 
 
-<dt>axes</dt>
-<dd><p>type of biplot axes, currently only regression axes are implemented</p></dd>
+<dt id="arg-axes">axes<a class="anchor" aria-label="anchor" href="#arg-axes"></a></dt>
+<dd><p>a character string indicating the type of biplot axes to be used in the biplot. One of <code>"regression"</code> or <code>"splines"</code>.</p></dd>
 
 
-<dt>...</dt>
-<dd><p>more arguments to <code>dist.func</code></p></dd>
+<dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
+<dd><p>more arguments to <code>dist.func</code>.</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>Object of class biplot</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>Object of class <code>biplot</code></p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">AoD</span><span class="op">(</span>classes<span class="op">=</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Object of class biplot, based on 150 samples and 4 variables.</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 4 numeric variables.</span>
@@ -137,29 +111,26 @@ <h2>Examples</h2>
 <span class="r-in"><span><span class="co"># create a CVA biplot</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">AoD</span><span class="op">(</span>classes<span class="op">=</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="AoD-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span></span></span>
 </code></pre></div>
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+++ b/docs/reference/CA.biplot.html
@@ -0,0 +1,119 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>CA biplot — CA.biplot • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="CA biplot — CA.biplot"><meta name="description" content="Performs calculations for a CA biplot."><meta property="og:description" content="Performs calculations for a CA biplot."><meta property="og:image" content="/logo.png"></head><body>
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>CA biplot</h1>
+
+      <div class="d-none name"><code>CA.biplot.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>Performs calculations for a CA biplot.</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'biplot'</span></span>
+<span><span class="fu"><a href="CA.html">CA</a></span><span class="op">(</span></span>
+<span>  <span class="va">bp</span>,</span>
+<span>  dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>, <span class="fl">1</span>, <span class="fl">3</span><span class="op">)</span>,</span>
+<span>  e.vects <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>,</span>
+<span>  variant <span class="op">=</span> <span class="st">"Princ"</span>,</span>
+<span>  lambda.scal <span class="op">=</span> <span class="cn">FALSE</span></span>
+<span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>object of class <code>biplot</code> obtained from preceding function <code>biplot(center = FALSE)</code>. In order to maintain the frequency table, the input should not be centered or scaled. For <code>CA</code>, <code>bp</code> should be a contingency table.</p></dd>
+
+
+<dt id="arg-dim-biplot">dim.biplot<a class="anchor" aria-label="anchor" href="#arg-dim-biplot"></a></dt>
+<dd><p>dimension of the biplot. Only values 1, 2 and 3 are accepted, with default <code>2</code>.</p></dd>
+
+
+<dt id="arg-e-vects">e.vects<a class="anchor" aria-label="anchor" href="#arg-e-vects"></a></dt>
+<dd><p>which eigenvectors (canonical variates) to extract, with default <code>1:dim.biplot</code>.</p></dd>
+
+
+<dt id="arg-variant">variant<a class="anchor" aria-label="anchor" href="#arg-variant"></a></dt>
+<dd><p>which correspondence analysis variant, with default "Princ", presents a biplot with rows in principal coordinates
+and columns in standard coordinates. <code>variant = "Stand"</code>, presents a biplot with rows in standard coordinates and columns in
+principal coordinates. <code>variant = "symmetric"</code>, presents a symmetric biplot with row and column standard coordinates scaled
+equally by the singular values.</p></dd>
+
+
+<dt id="arg-lambda-scal">lambda.scal<a class="anchor" aria-label="anchor" href="#arg-lambda-scal"></a></dt>
+<dd><p>logical value to request lambda-scaling, default is <code>FALSE</code>. Controls stretching or shrinking of
+column and row distances.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>an object of class CA, inherits from class biplot.</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="CA.html">CA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="CA.biplot-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span></span></span>
+</code></pre></div>
+    </div>
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+    </nav></aside></div>
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+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
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diff --git a/docs/reference/CA.html b/docs/reference/CA.html
index d0cdc0c..310db0b 100644
--- a/docs/reference/CA.html
+++ b/docs/reference/CA.html
@@ -1,106 +1,87 @@
 <!DOCTYPE html>
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-    <div class="page-header">
-    <h1>Correspondence Analysis (CA) method</h1>
-    
-    <div class="hidden name"><code>CA.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+      </ul></div>
+
+
+  </div>
+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Correspondence Analysis (CA) method</h1>
+
+      <div class="d-none name"><code>CA.Rd</code></div>
     </div>
 
-    <div class="ref-description">
+    <div class="ref-description section level2">
     <p>This function produces a list of elements to be used for CA biplot construction by approximation of the Pearson residuals.</p>
     </div>
 
-    <div id="ref-usage">
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">CA</span><span class="op">(</span><span class="va">bp</span>, dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>,<span class="fl">1</span>,<span class="fl">3</span><span class="op">)</span>, e.vects <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>, variant <span class="op">=</span> <span class="st">"Princ"</span><span class="op">)</span></span></code></pre></div>
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">CA</span><span class="op">(</span><span class="va">bp</span>, dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>,<span class="fl">1</span>,<span class="fl">3</span><span class="op">)</span>, e.vects <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>, variant <span class="op">=</span> <span class="st">"Princ"</span>, </span>
+<span>lambda.scal <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>object of class <code>biplot</code> obtained from preceding function <code>biplot(center = FALSE)</code>. In order to maintain the frequency table, the input should not be centered or scaled. For <code>CA</code>, <code>bp</code> should be a contingency table.</p></dd>
 
 
-<dt>dim.biplot</dt>
+<dt id="arg-dim-biplot">dim.biplot<a class="anchor" aria-label="anchor" href="#arg-dim-biplot"></a></dt>
 <dd><p>dimension of the biplot. Only values 1, 2 and 3 are accepted, with default <code>2</code>.</p></dd>
 
 
-<dt>e.vects</dt>
+<dt id="arg-e-vects">e.vects<a class="anchor" aria-label="anchor" href="#arg-e-vects"></a></dt>
 <dd><p>which eigenvectors (canonical variates) to extract, with default <code>1:dim.biplot</code>.</p></dd>
 
 
-<dt>variant</dt>
+<dt id="arg-variant">variant<a class="anchor" aria-label="anchor" href="#arg-variant"></a></dt>
 <dd><p>which correspondence analysis variant, with default "Princ", presents a biplot with rows in principal coordinates
 and columns in standard coordinates. <code>variant = "Stand"</code>, presents a biplot with rows in standard coordinates and columns in
-principal coordinates. <code>variant = "symmetric"</code>, presents a symmtric biplot with row and column standard coordinates scaled
+principal coordinates. <code>variant = "symmetric"</code>, presents a symmetric biplot with row and column standard coordinates scaled
 equally by the singular values.</p></dd>
 
-</dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
 
-<p>A list with the following components is available:</p>
+<dt id="arg-lambda-scal">lambda.scal<a class="anchor" aria-label="anchor" href="#arg-lambda-scal"></a></dt>
+<dd><p>logical value to request lambda-scaling, default is <code>FALSE</code>. Controls stretching or shrinking of
+column and row distances.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>A list with the following components is available:</p>
 <dl><dt>Z</dt>
 <dd><p>Combined data frame of the row and column coordinates.</p></dd>
 
@@ -110,6 +91,18 @@ <h2>Value</h2>
 <dt>c</dt>
 <dd><p>Numer of levels in the column factor.</p></dd>
 
+<dt>Dr</dt>
+<dd><p>Diagonal matrix of row profiles.</p></dd>
+
+<dt>Dc</dt>
+<dd><p>Diagonal matrix of column profiles.</p></dd>
+
+<dt>Drh</dt>
+<dd><p>Weighted row profiles.</p></dd>
+
+<dt>Dch</dt>
+<dd><p>Weighted column profiles.</p></dd>
+
 <dt>rowcoor</dt>
 <dd><p>Row coordinates based on the selected <code>variant</code>.</p></dd>
 
@@ -117,7 +110,7 @@ <h2>Value</h2>
 <dd><p>Column coordinates based on the selected <code>variant</code>.</p></dd>
 
 <dt>P</dt>
-<dd><p>Correspondence Matrix</p></dd>
+<dd><p>Correspondence Matrix.</p></dd>
 
 <dt>Smat</dt>
 <dd><p>Standardised Pearson residuals.</p></dd>
@@ -125,47 +118,56 @@ <h2>Value</h2>
 <dt>SVD</dt>
 <dd><p>Singular value decomposition solution: <code>d, u, v</code>.</p></dd>
 
-<dt>qual</dt>
-<dd><p>Quality of the approximation.</p></dd>
+<dt>e.vects</dt>
+<dd><p>Depending on what was specified in <code>CA</code> argument.</p></dd>
+
+<dt>dim.biplot</dt>
+<dd><p>The dimension of the biplot.</p></dd>
+
+<dt>lambda.val</dt>
+<dd><p>The computed lambda value if lambda-scaling is requested.</p></dd>
+
+<dt>gamma</dt>
+<dd><p>Contribution of the singular values, based on the CA variant.</p></dd>
 
 </dl></div>
+    <div class="section level2">
+    <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
+    <div class="dont-index"><p><code><a href="biplot.html">biplot()</a></code></p></div>
+    </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># Creating a CA biplot with rows in principal coordinates:</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">CA</span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="CA-1.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span><span class="co"># Creating a CA biplot with rows in standard coordinates:</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">CA</span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Stand"</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
-<span class="r-in"><span><span class="fu"><a href="samples.html">samples</a></span><span class="op">(</span>col<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"magenta"</span>,<span class="st">"purple"</span><span class="op">)</span>, pch<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">15</span>,<span class="fl">17</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="samples.html">samples</a></span><span class="op">(</span>col<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"magenta"</span>,<span class="st">"purple"</span><span class="op">)</span>, pch <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">15</span>,<span class="fl">17</span><span class="op">)</span>, label.col <span class="op">=</span> <span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="CA-2.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span><span class="co"># Creating a CA biplot with rows and columns scaled equally:</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">CA</span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Symmetric"</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
-<span class="r-in"><span><span class="fu"><a href="samples.html">samples</a></span><span class="op">(</span>col<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"magenta"</span>,<span class="st">"purple"</span><span class="op">)</span>, pch<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">15</span>,<span class="fl">17</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="samples.html">samples</a></span><span class="op">(</span>col <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"magenta"</span>,<span class="st">"purple"</span><span class="op">)</span>, pch <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">15</span>,<span class="fl">17</span><span class="op">)</span>, label.col <span class="op">=</span> <span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="CA-3.png" alt="" width="700" height="433"></span>
 </code></pre></div>
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index 605a4db..023d6d4 100644
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@@ -1,139 +1,108 @@
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-    <div class="hidden name"><code>CATPCA.Rd</code></div>
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+      <div class="d-none name"><code>CATPCA.Rd</code></div>
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-    <div class="ref-description">
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     <p>Categorical Principal Component Analysis</p>
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+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">CATPCA</span><span class="op">(</span><span class="va">bp</span>, dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>, <span class="fl">1</span>, <span class="fl">3</span><span class="op">)</span>, e.vects <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>,</span>
 <span>group.aes <span class="op">=</span> <span class="cn">NULL</span>, show.class.means <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
 
 
-<dt>dim.biplot</dt>
+<dt id="arg-dim-biplot">dim.biplot<a class="anchor" aria-label="anchor" href="#arg-dim-biplot"></a></dt>
 <dd><p>dimension of the biplot. Only values 1, 2 and 3 are accepted, with default <code>2</code>.</p></dd>
 
 
-<dt>e.vects</dt>
+<dt id="arg-e-vects">e.vects<a class="anchor" aria-label="anchor" href="#arg-e-vects"></a></dt>
 <dd><p>which eigenvectors (principal components) to extract, with default <code>1:dim.biplot</code>.</p></dd>
 
 
-<dt>group.aes</dt>
+<dt id="arg-group-aes">group.aes<a class="anchor" aria-label="anchor" href="#arg-group-aes"></a></dt>
 <dd><p>vector of the same length as the number of rows in the data matrix
 for differentiated aesthetics for samples.</p></dd>
 
 
-<dt>show.class.means</dt>
+<dt id="arg-show-class-means">show.class.means<a class="anchor" aria-label="anchor" href="#arg-show-class-means"></a></dt>
 <dd><p>logical, indicating whether group means should be plotted in the biplot.</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>an object of class <code>biplot</code></p>
-
-
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>an object of class <code>biplot</code></p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu">CATPCA</span> <span class="op">(</span><span class="va">iris</span><span class="op">)</span></span></span>
 </code></pre></div>
     </div>
-  </div>
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
-    </nav></div>
-</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
 
 
-      <footer><div class="copyright">
-  <p></p><p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.</p>
+<div class="pkgdown-footer-right">
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 </div>
 
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   </body></html>
 
diff --git a/docs/reference/CLPs-1.png b/docs/reference/CLPs-1.png
new file mode 100644
index 0000000..65b5a84
Binary files /dev/null and b/docs/reference/CLPs-1.png differ
diff --git a/docs/reference/CLPs.html b/docs/reference/CLPs.html
new file mode 100644
index 0000000..10118a8
--- /dev/null
+++ b/docs/reference/CLPs.html
@@ -0,0 +1,127 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Format aesthetics for the category level points — CLPs • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Format aesthetics for the category level points — CLPs"><meta name="description" content="This function allows the user to format the aesthetics for the category level points (CLPs)."><meta property="og:description" content="This function allows the user to format the aesthetics for the category level points (CLPs)."><meta property="og:image" content="/logo.png"></head><body>
+    <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
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+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Format aesthetics for the category level points</h1>
+
+      <div class="d-none name"><code>CLPs.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>This function allows the user to format the aesthetics for the category level points (CLPs).</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">CLPs</span> <span class="op">(</span><span class="va">bp</span>,  which <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">Xcat</span><span class="op">)</span>, col <span class="op">=</span> <span class="st">"black"</span>, cex <span class="op">=</span> <span class="fl">0.6</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code>.</p></dd>
+
+
+<dt id="arg-which">which<a class="anchor" aria-label="anchor" href="#arg-which"></a></dt>
+<dd><p>a vector containing the columns or variables for which the CLPs should be displayed,
+with default <code>1:ncol(Xcat)</code>.</p></dd>
+
+
+<dt id="arg-col">col<a class="anchor" aria-label="anchor" href="#arg-col"></a></dt>
+<dd><p>the colour(s) for the CLPs, with default <code>black</code>.</p></dd>
+
+
+<dt id="arg-cex">cex<a class="anchor" aria-label="anchor" href="#arg-cex"></a></dt>
+<dd><p>the character expansion(s) for the CLPs, with default <code>0.6</code>.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>The object of class <code>biplot</code> will be appended with a list called <code>CLP.aes</code> containing the following elements  A list with the following components is available:</p>
+<dl><dt>which</dt>
+<dd><p>a vector containing the columns or variables for which the CLPs are displayed.</p></dd>
+
+<dt>col</dt>
+<dd><p>the colour(s) of the CLPs.</p></dd>
+
+<dt>cex</dt>
+<dd><p>the character expansion(s) of the plotting characters of the CLPs.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
+    <div class="dont-index"><p><code><a href="biplot.html">biplot</a></code>, <code><a href="CA.html">CA</a></code>, <code><a href="AoD.html">AoD</a></code></p></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="va">mtdf</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/as.data.frame.html" class="external-link">as.data.frame</a></span><span class="op">(</span><span class="va">mtcars</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">cyl</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">cyl</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">vs</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">vs</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">am</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">am</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">gear</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">gear</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">carb</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">carb</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">[</span>,<span class="op">-</span><span class="fl">11</span><span class="op">]</span>, scaled <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="AoD.html">AoD</a></span><span class="op">(</span>classes <span class="op">=</span> <span class="va">mtdf</span><span class="op">[</span>,<span class="fl">11</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
+<span class="r-in"><span><span class="fu">CLPs</span><span class="op">(</span>col <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="st">"olivedrab"</span>,<span class="fl">3</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="st">"orange"</span>,<span class="fl">2</span><span class="op">)</span>,</span></span>
+<span class="r-in"><span>                <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="st">"coral"</span>,<span class="fl">2</span><span class="op">)</span>, <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="st">"brown"</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="CLPs-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span></span></span>
+</code></pre></div>
+    </div>
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+    </nav></aside></div>
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diff --git a/docs/reference/CLRs.html b/docs/reference/CLRs.html
new file mode 100644
index 0000000..b357096
--- /dev/null
+++ b/docs/reference/CLRs.html
@@ -0,0 +1,117 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Format aesthetics for the category level regions — CLRs • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Format aesthetics for the category level regions — CLRs"><meta name="description" content="This function allows the user to format the aesthetics for the category level points (CLRs)."><meta property="og:description" content="This function allows the user to format the aesthetics for the category level points (CLRs)."><meta property="og:image" content="/logo.png"></head><body>
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Format aesthetics for the category level regions</h1>
+
+      <div class="d-none name"><code>CLRs.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>This function allows the user to format the aesthetics for the category level points (CLRs).</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">CLRs</span> <span class="op">(</span><span class="va">bp</span>,  which <span class="op">=</span> <span class="fl">1</span>, col <span class="op">=</span> <span class="st">"black"</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code>.</p></dd>
+
+
+<dt id="arg-which">which<a class="anchor" aria-label="anchor" href="#arg-which"></a></dt>
+<dd><p>the column name or number for which the CLRs should be displayed, with default <code>1</code>. Only
+one variable can be selected at a time.</p></dd>
+
+
+<dt id="arg-col">col<a class="anchor" aria-label="anchor" href="#arg-col"></a></dt>
+<dd><p>the colours for the CLRs, with default <code>colorRampPalette(c("black","white"))</code>.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>The object of class <code>biplot</code> will be appended with a list called <code>CLP.aes</code> containing the following elements  A list with the following components is available:</p>
+<dl><dt>which</dt>
+<dd><p>the variable number for which the CLRs are displayed.</p></dd>
+
+<dt>col</dt>
+<dd><p>the colours of the CLRs.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
+    <div class="dont-index"><p><code><a href="biplot.html">biplot</a></code>, <code><a href="PCO.html">PCO</a></code>, <code><a href="AoD.html">AoD</a></code></p></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="va">mtdf</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/as.data.frame.html" class="external-link">as.data.frame</a></span><span class="op">(</span><span class="va">mtcars</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">cyl</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">cyl</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">vs</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">vs</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">am</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">am</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">gear</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">gear</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">carb</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">carb</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="co">#biplot(mtdf[,-11], scaled = TRUE) |&gt; PCO(group.aes = mtdf[,11]) |&gt; </span></span></span>
+<span class="r-in"><span><span class="co">#CLRs(which = 10, col = "coral") |&gt; plot()</span></span></span>
+<span class="r-in"><span></span></span>
+</code></pre></div>
+    </div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
+
+
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+</div>
+
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.2.</p>
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diff --git a/docs/reference/CVA-1.png b/docs/reference/CVA-1.png
new file mode 100644
index 0000000..127e285
Binary files /dev/null and b/docs/reference/CVA-1.png differ
diff --git a/docs/reference/CVA.biplot.html b/docs/reference/CVA.biplot.html
index ca12b95..54b5df3 100644
--- a/docs/reference/CVA.biplot.html
+++ b/docs/reference/CVA.biplot.html
@@ -1,78 +1,53 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>CVA biplot — CVA.biplot • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.1/jquery.min.js" integrity="sha512-v2CJ7UaYy4JwqLDIrZUI/4hqeoQieOmAZNXBeQyjo21dadnwR+8ZaIJVT8EE2iyI61OV8e6M8PP2/4hpQINQ/g==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="CVA biplot — CVA.biplot"><meta property="og:description" content="Performs calculations for a CVA biplot."><meta property="og:image" content="/logo.png"><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate elements for the CVA biplot — CVA.biplot • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate elements for the CVA biplot — CVA.biplot"><meta name="description" content="This function performs calculations for the construction of a CVA biplot."><meta property="og:description" content="This function performs calculations for the construction of a CVA biplot."><meta property="og:image" content="/logo.png"></head><body>
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-    <div class="page-header">
-    <h1>CVA biplot</h1>
-    
-    <div class="hidden name"><code>CVA.biplot.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+      </ul></div>
+
+
+  </div>
+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Calculate elements for the CVA biplot</h1>
+
+      <div class="d-none name"><code>CVA.biplot.Rd</code></div>
     </div>
 
-    <div class="ref-description">
-    <p>Performs calculations for a CVA biplot.</p>
+    <div class="ref-description section level2">
+    <p>This function performs calculations for the construction of a CVA biplot.</p>
     </div>
 
-    <div id="ref-usage">
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for biplot</span></span>
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'biplot'</span></span>
 <span><span class="fu"><a href="CVA.html">CVA</a></span><span class="op">(</span></span>
 <span>  <span class="va">bp</span>,</span>
 <span>  classes <span class="op">=</span> <span class="va">bp</span><span class="op">$</span><span class="va">classes</span>,</span>
@@ -84,50 +59,45 @@ <h1>CVA biplot</h1>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
-<dd><p>object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
 
 
-<dt>classes</dt>
-<dd><p>vector of the same length as the number of rows in the data matrix
-with the class indicator for the samples.</p></dd>
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
 
 
-<dt>dim.biplot</dt>
-<dd><p>dimension of the biplot. Only values 1, 2 and 3 are accepted, with default <code>2</code>.</p></dd>
+<dt id="arg-classes">classes<a class="anchor" aria-label="anchor" href="#arg-classes"></a></dt>
+<dd><p>a vector of the same length as the number of rows in the data matrix with the class indicator for the samples.</p></dd>
 
 
-<dt>e.vects</dt>
-<dd><p>which eigenvectors (canonical variates) to extract, with default <code>1:dim.biplot</code>.</p></dd>
+<dt id="arg-dim-biplot">dim.biplot<a class="anchor" aria-label="anchor" href="#arg-dim-biplot"></a></dt>
+<dd><p>the dimension of the biplot. Only values <code>1</code>, <code>2</code> and <code>3</code> are accepted, with default <code>2</code>.</p></dd>
 
 
-<dt>weightedCVA</dt>
-<dd><p>the default is "weighted", specifying a weighted CVA to be performed. Other possible values are "unweightedI" and "unweightedCent".</p></dd>
+<dt id="arg-e-vects">e.vects<a class="anchor" aria-label="anchor" href="#arg-e-vects"></a></dt>
+<dd><p>the vector indicating which eigenvectors (canonical variates) should be plotted in the biplot, with default <code>1:dim.biplot</code>.</p></dd>
 
 
-<dt>show.class.means</dt>
-<dd><p>logical, indicating whether to plot the class means on the biplot.</p></dd>
+<dt id="arg-weightedcva">weightedCVA<a class="anchor" aria-label="anchor" href="#arg-weightedcva"></a></dt>
+<dd><p>a character string indicating which type of CVA to perform. One of "<code>weighted</code>" (default) for a weighted CVA to be performed (The centring matrix will be a diagonal matrix with the class sizes (\(\mathbf{C} = \mathbf{N}\)), "<code>unweightedCent</code>" for unweighted CVA to be performed (The centring matrix is the usual centring matrix (\(\mathbf{C} = \mathbf{I}_{G} - G^{-1}\mathbf{1}_{G}\mathbf{1}_{G}'\))) or "<code>unweightedI</code>" for unweighted CVA to be performed while retaining the weighted centroid (The centring matrix is an indicator matrix (\(\mathbf{C} = \mathbf{I}_{G}\))).</p></dd>
 
 
-<dt>low.dim</dt>
-<dd><p>if the dimension of the canonical space is smaller than <code>dim.biplot</code>, the method to use to construct
-additional dimension(s). Currently two options are implemented: <code>sample.opt</code> maximises the sample predictivity
-of the individual samples in the biplot and <code>Bhattacharyya.dist</code> is based on the decomposition of the
-Bhattacharyya distance into a component for the sample means and a component for the dissimilarity
-between the sample covariance matrices.</p></dd>
+<dt id="arg-show-class-means">show.class.means<a class="anchor" aria-label="anchor" href="#arg-show-class-means"></a></dt>
+<dd><p>a logical value indicating whether to plot the class means on the biplot.</p></dd>
 
-</dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
 
-<p>an object of class CVA, inherits from class biplot.</p>
+<dt id="arg-low-dim">low.dim<a class="anchor" aria-label="anchor" href="#arg-low-dim"></a></dt>
+<dd><p>a character string indicating which method to use to construct additional dimension(s) if the dimension of the canonical space is smaller than <code>dim.biplot</code>. One of "<code>sample.opt</code>" (default) for maximising the sample predictivity of the individual samples in the biplot or "<code>Bhattacharyya.dist</code>" which is based on the decomposition of the Bhattacharyya distance into a component for the sample means and a component for the dissimilarity between the sample covariance matrices.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>an object of class <code>CVA</code>, inherits from class <code>biplot</code>.</p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="CVA.html">CVA</a></span><span class="op">(</span>classes<span class="op">=</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Object of class biplot, based on 150 samples and 4 variables.</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 4 numeric variables.</span>
@@ -135,27 +105,23 @@ <h2>Examples</h2>
 <span class="r-in"><span></span></span>
 </code></pre></div>
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diff --git a/docs/reference/CVA.html b/docs/reference/CVA.html
index e6f9ce4..6584389 100644
--- a/docs/reference/CVA.html
+++ b/docs/reference/CVA.html
@@ -1,211 +1,202 @@
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-    <h1>Canonical Variate Analysis (CVA) method</h1>
-    
-    <div class="hidden name"><code>CVA.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Perform Canonical Variate Analysis (CVA)</h1>
+
+      <div class="d-none name"><code>CVA.Rd</code></div>
     </div>
 
-    <div class="ref-description">
-    <p>This function produces a list of elements to be used for CVA biplot construction.</p>
+    <div class="ref-description section level2">
+    <p>This function appends the <code>biplot</code> object with elements resulting from performing CVA.</p>
     </div>
 
-    <div id="ref-usage">
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">CVA</span><span class="op">(</span><span class="va">bp</span>, classes<span class="op">=</span><span class="va">bp</span><span class="op">$</span><span class="va">classes</span>, dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>, <span class="fl">1</span>, <span class="fl">3</span><span class="op">)</span>, </span>
-<span>           e.vects <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>,weightedCVA <span class="op">=</span> <span class="st">"weighted"</span>, </span>
-<span>           show.class.means <span class="op">=</span> <span class="cn">TRUE</span>, low.dim <span class="op">=</span> <span class="st">"sample.opt"</span><span class="op">)</span></span></code></pre></div>
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">CVA</span><span class="op">(</span><span class="va">bp</span>, classes<span class="op">=</span><span class="va">bp</span><span class="op">$</span><span class="va">classes</span>, dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>, <span class="fl">1</span>, <span class="fl">3</span><span class="op">)</span>, e.vects <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>,</span>
+<span>           weightedCVA <span class="op">=</span> <span class="st">"weighted"</span>, show.class.means <span class="op">=</span> <span class="cn">TRUE</span>,</span>
+<span>           low.dim <span class="op">=</span> <span class="st">"sample.opt"</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
-<dd><p>object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
 
 
-<dt>classes</dt>
-<dd><p>vector of the same length as the number of rows in the data matrix
-with the class indicator for the samples.</p></dd>
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
 
 
-<dt>dim.biplot</dt>
-<dd><p>dimension of the biplot. Only values 1, 2 and 3 are accepted, with default <code>2</code>.</p></dd>
+<dt id="arg-classes">classes<a class="anchor" aria-label="anchor" href="#arg-classes"></a></dt>
+<dd><p>a vector of the same length as the number of rows in the data matrix with the class indicator for the samples.</p></dd>
 
 
-<dt>e.vects</dt>
-<dd><p>which eigenvectors (canonical variates) to extract, with default <code>1:dim.biplot</code>.</p></dd>
+<dt id="arg-dim-biplot">dim.biplot<a class="anchor" aria-label="anchor" href="#arg-dim-biplot"></a></dt>
+<dd><p>the dimension of the biplot. Only values <code>1</code>, <code>2</code> and <code>3</code> are accepted, with default <code>2</code>.</p></dd>
 
 
-<dt>weightedCVA</dt>
-<dd><p>the default is "weighted", specifying a weighted CVA to be performed. Other possible values are "unweightedI" and "unweightedCent".</p></dd>
+<dt id="arg-e-vects">e.vects<a class="anchor" aria-label="anchor" href="#arg-e-vects"></a></dt>
+<dd><p>the vector indicating which eigenvectors (canonical variates) should be plotted in the biplot, with default <code>1:dim.biplot</code>.</p></dd>
 
 
-<dt>show.class.means</dt>
-<dd><p>logical, indicating whether to plot the class means on the biplot.</p></dd>
+<dt id="arg-weightedcva">weightedCVA<a class="anchor" aria-label="anchor" href="#arg-weightedcva"></a></dt>
+<dd><p>a character string indicating which type of CVA to perform. One of "<code>weighted</code>" (default) for a weighted CVA to be performed (The centring matrix will be a diagonal matrix with the class sizes (\(\mathbf{C} = \mathbf{N}\)), "<code>unweightedCent</code>" for unweighted CVA to be performed (The centring matrix is the usual centring matrix (\(\mathbf{C} = \mathbf{I}_{G} - G^{-1}\mathbf{1}_{G}\mathbf{1}_{G}'\))) or "<code>unweightedI</code>" for unweighted CVA to be performed while retaining the weighted centroid (The centring matrix is an indicator matrix (\(\mathbf{C} = \mathbf{I}_{G}\))).</p></dd>
 
 
-<dt>low.dim</dt>
-<dd><p>if the dimension of the canonical space is smaller than <code>dim.biplot</code>, the method to use to construct
-additional dimension(s). Currently two options are implemented: <code>sample.opt</code> maximises the sample predictivity
-of the individual samples in the biplot and <code>Bhattacharyya.dist</code> is based on the decomposition of the
-Bhattacharyya distance into a component for the sample means and a component for the dissimilarity
-between the sample covariance matrices.</p></dd>
+<dt id="arg-show-class-means">show.class.means<a class="anchor" aria-label="anchor" href="#arg-show-class-means"></a></dt>
+<dd><p>a logical value indicating whether to plot the class means on the biplot.</p></dd>
 
-</dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
 
-<p>Object of class CVA with the following elements:</p>
+<dt id="arg-low-dim">low.dim<a class="anchor" aria-label="anchor" href="#arg-low-dim"></a></dt>
+<dd><p>a character string indicating which method to use to construct additional dimension(s) if the dimension of the canonical space is smaller than <code>dim.biplot</code>. One of "<code>sample.opt</code>" (default) for maximising the sample predictivity of the individual samples in the biplot or "<code>Bhattacharyya.dist</code>" which is based on the decomposition of the Bhattacharyya distance into a component for the sample means and a component for the dissimilarity between the sample covariance matrices.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>Object of class CVA with the following elements:</p>
 <dl><dt>X</dt>
-<dd><p>matrix of the centered and scaled numeric variables.</p></dd>
+<dd><p>the matrix of the centered and scaled numeric variables.</p></dd>
 
 <dt>Xcat</dt>
-<dd><p>matrix of the categorical variables.</p></dd>
+<dd><p>the data frame of the categorical variables.</p></dd>
 
 <dt>raw.X</dt>
-<dd><p>original data.</p></dd>
+<dd><p>the original data.</p></dd>
+
+<dt>classes</dt>
+<dd><p>the vector of category levels for the class variable. This is to be used for <code>colour</code>, <code>pch</code> and <code>cex</code> specifications.</p></dd>
 
 <dt>na.action</dt>
-<dd><p>vector of observations that have been removed.</p></dd>
+<dd><p>the vector of observations that have been removed.</p></dd>
 
 <dt>center</dt>
-<dd><p>TRUE or FALSE, whether X is centred.</p></dd>
+<dd><p>a logical value indicating whether \(\mathbf{X}\) is centered.</p></dd>
 
 <dt>scaled</dt>
-<dd><p>TRUE or FALSE, whether X is scaled.</p></dd>
+<dd><p>a logical value indicating whether \(\mathbf{X}\) is scaled.</p></dd>
 
 <dt>means</dt>
-<dd><p>mean of each numerical variable.</p></dd>
+<dd><p>the vector of means for each numerical variable.</p></dd>
 
 <dt>sd</dt>
-<dd><p>standard deviation of each numerical variable.</p></dd>
+<dd><p>the vector of standard deviations for each numerical variable.</p></dd>
 
 <dt>n</dt>
-<dd><p>number of observations.</p></dd>
+<dd><p>the number of observations.</p></dd>
 
 <dt>p</dt>
-<dd><p>number of variables.</p></dd>
+<dd><p>the number of variables.</p></dd>
 
 <dt>group.aes</dt>
-<dd><p>vector of the same length as the number of rows in the data matrix for differentiated aesthetics for samples.</p></dd>
+<dd><p>the vector of category levels for the grouping variable. This is to be used for <code>colour</code>, <code>pch</code> and <code>cex</code> specifications.</p></dd>
 
 <dt>g.names</dt>
-<dd><p>descriptive name to be used for group labels.</p></dd>
+<dd><p>the descriptive names to be used for group labels.</p></dd>
 
 <dt>g</dt>
-<dd><p>number of groups.</p></dd>
+<dd><p>the number of groups.</p></dd>
 
 <dt>Title</dt>
-<dd><p>title of the biplot to be rendered.</p></dd>
+<dd><p>the title of the biplot rendered.</p></dd>
 
-<dt>Gmat</dt>
-<dd><p>indicator matrix for class membership.</p></dd>
+<dt>Lmat</dt>
+<dd><p>the matrix for transformation to the canonical space.</p></dd>
 
-<dt>Xmeans</dt>
-<dd><p>matrix of class means.</p></dd>
+<dt>Linv</dt>
+<dd><p>the inverse of \(\mathbf{L}\).</p></dd>
+
+<dt>eigenvalues</dt>
+<dd><p>the vector of eigenvalues of the two-sided eigenvalue problem.</p></dd>
 
 <dt>Z</dt>
-<dd><p>matrix with each row containing the details of the point to be plotted (i.e. coordinates).</p></dd>
+<dd><p>the matrix with each row containing the details of the points to be plotted (i.e. coordinates).</p></dd>
 
-<dt>Zmeans</dt>
-<dd><p>matrix of canonical means.</p></dd>
+<dt>ax.one.unit</dt>
+<dd><p>one unit in the positive direction of each biplot axis.</p></dd>
 
-<dt>Lmat</dt>
-<dd><p>matrix for transformation to the canonical space.</p></dd>
+<dt>Gmat</dt>
+<dd><p>the indicator matrix defining membership of the classes.</p></dd>
 
-<dt>eigenvalues</dt>
-<dd><p>vector of eigenvalues of the two-sided eigenvalue problem.</p></dd>
+<dt>Xmeans</dt>
+<dd><p>the matrix of the class means.</p></dd>
+
+<dt>Zmeans</dt>
+<dd><p>the matrix of the class mean coordinates that are plotted in the biplot.</p></dd>
+
+<dt>e.vects</dt>
+<dd><p>the vector indicating which canonical variates are plotted in the biplot.</p></dd>
 
 <dt>Cmat</dt>
-<dd><p>Centring matrix based on different choices of weighting.
-For <code>"weighted"</code>, <code>Cmat</code> is a diagonal matrix with
-the class sizes, for <code>"unweightedI"</code>, <code>Cmat</code> is an
-indicator matrix and for
-<code>"unweightedCent"</code>, <code>Cmat</code> is the usual centring matrix.</p></dd>
+<dd><p>the centring matrix based on different choices of weighting described in arguments.</p></dd>
 
 <dt>Bmat</dt>
-<dd><p>Between class sums of squares and cross products matrix.</p></dd>
+<dd><p>the between class sums of squares and cross products matrix.</p></dd>
 
 <dt>Wmat</dt>
-<dd><p>Within class sums of squares and corss products matrix.</p></dd>
+<dd><p>the within class sums of squares and cross products matrix.</p></dd>
 
-<dt>e.vects</dt>
-<dd><p>vector indicating which canonical variates are plotted in the biplot.</p></dd>
+<dt>Mrr</dt>
+<dd><p>the matrix used for prediction from the canonical space (the inverse of \(\mathbf{M}=\mathbf{LV})\).</p></dd>
 
-<dt>ax.one.unit</dt>
-<dd><p>one unit in the positive direction of each biplot axis.</p></dd>
+<dt>Mr</dt>
+<dd><p>the first r dimensions of the solution to be plotted.</p></dd>
+
+<dt>Nmat</dt>
+<dd><p>the matrix with the class sizes on the diagonal.</p></dd>
+
+<dt>lambda.mat</dt>
+<dd><p>the matrix with the eigenvalues of \(\mathbf{W}^{-1/2}\mathbf{BW}^{-1/2}\) on the diagonal.</p></dd>
 
 <dt>class.means</dt>
-<dd><p>logical value, indicating whether the class means should be plotted in the biplot.</p></dd>
+<dd><p>a logical value indicating whether the class means should be plotted in the biplot.</p></dd>
 
-<dt>Zmeans</dt>
-<dd><p>matrix of the class mean coordinates to be plotted in the biplot.</p></dd>
+<dt>dim.biplot</dt>
+<dd><p>the dimension of the biplot.</p></dd>
+
+<dt>low.dim</dt>
+<dd><p>the method used to construct additional dimension(s).</p></dd>
 
 </dl></div>
+    <div class="section level2">
+    <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
+    <div class="dont-index"><p><code><a href="biplot.html">biplot()</a></code></p></div>
+    </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">CVA</span><span class="op">(</span>classes<span class="op">=</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Object of class biplot, based on 150 samples and 4 variables.</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 4 numeric variables.</span>
@@ -213,29 +204,26 @@ <h2>Examples</h2>
 <span class="r-in"><span><span class="co"># create a CVA biplot</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">CVA</span><span class="op">(</span>classes<span class="op">=</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="CVA-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span></span></span>
 </code></pre></div>
     </div>
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-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
-    </nav></div>
-</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
 
 
-      <footer><div class="copyright">
-  <p></p><p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
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diff --git a/docs/reference/CVAlowdim.html b/docs/reference/CVAlowdim.html
new file mode 100644
index 0000000..30f8fc9
--- /dev/null
+++ b/docs/reference/CVAlowdim.html
@@ -0,0 +1,118 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Construct additional dimensions when the dimension of the canonical space is smaller than the dimension of the biplot — CVAlowdim • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Construct additional dimensions when the dimension of the canonical space is smaller than the dimension of the biplot — CVAlowdim"><meta name="description" content="This function is used to add dimensions to the CVA biplot when the dimension of the canonical space \(K\) is smaller than the dimension of the biplot (dim.biplot). This function is already used in the CVA calculations, and will therefore not have to be used in isolation."><meta property="og:description" content="This function is used to add dimensions to the CVA biplot when the dimension of the canonical space \(K\) is smaller than the dimension of the biplot (dim.biplot). This function is already used in the CVA calculations, and will therefore not have to be used in isolation."><meta property="og:image" content="/logo.png"></head><body>
+    <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
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+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Construct additional dimensions when the dimension of the canonical space is smaller than the dimension of the biplot</h1>
+
+      <div class="d-none name"><code>CVAlowdim.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>This function is used to add dimensions to the CVA biplot when the dimension of the canonical space \(K\) is smaller than the dimension of the biplot (<code>dim.biplot</code>). This function is already used in the CVA calculations, and will therefore not have to be used in isolation.</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">CVAlowdim</span><span class="op">(</span><span class="va">bp</span>, <span class="va">G</span>, <span class="va">W</span>, <span class="va">Mmat</span>, <span class="va">low.dim</span>, <span class="va">K</span>, <span class="va">e.vects</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code>.</p></dd>
+
+
+<dt id="arg-g">G<a class="anchor" aria-label="anchor" href="#arg-g"></a></dt>
+<dd><p>the indicator matrix defining membership of the classes.</p></dd>
+
+
+<dt id="arg-w">W<a class="anchor" aria-label="anchor" href="#arg-w"></a></dt>
+<dd><p>the within class sums of squares and cross products matrix.</p></dd>
+
+
+<dt id="arg-mmat">Mmat<a class="anchor" aria-label="anchor" href="#arg-mmat"></a></dt>
+<dd><p>the eigenvector matrix from CVA.</p></dd>
+
+
+<dt id="arg-low-dim">low.dim<a class="anchor" aria-label="anchor" href="#arg-low-dim"></a></dt>
+<dd><p>a character string indicating which method to use to construct additional dimension(s) if the dimension of the canonical space is smaller than <code>dim.biplot</code>. One of "<code>sample.opt</code>" (default) for maximising the sample predictivity of the individual samples in the biplot or <code>Bhattacharyya.dist</code> which is based on the decomposition of the Bhattacharyya distance into a component for the sample means and a component for the dissimilarity between the sample covariance matrices.</p></dd>
+
+
+<dt id="arg-k">K<a class="anchor" aria-label="anchor" href="#arg-k"></a></dt>
+<dd><p>the dimension of the canonical space.</p></dd>
+
+
+<dt id="arg-e-vects">e.vects<a class="anchor" aria-label="anchor" href="#arg-e-vects"></a></dt>
+<dd><p>the vector indicating which canonical variates are plotted in the biplot, with default <code>1:dim.biplot</code></p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>A list with three components:</p>
+<dl><dt>Mr</dt>
+<dd><p>the first r dimensions of the solution to be plotted.</p></dd>
+
+<dt>Mrr</dt>
+<dd><p>the matrix used for prediction from the canonical space.</p></dd>
+
+<dt>Lmat</dt>
+<dd><p>the matrix for transformation to the canonical space.</p></dd>
+
+</dl></div>
+
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
+
+
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+</div>
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+<div class="pkgdown-footer-right">
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+
diff --git a/docs/reference/PCA-1.png b/docs/reference/PCA-1.png
index 308f5f3..bf2eb47 100644
Binary files a/docs/reference/PCA-1.png and b/docs/reference/PCA-1.png differ
diff --git a/docs/reference/PCA.biplot-1.png b/docs/reference/PCA.biplot-1.png
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diff --git a/docs/reference/PCA.biplot.html b/docs/reference/PCA.biplot.html
new file mode 100644
index 0000000..3a679db
--- /dev/null
+++ b/docs/reference/PCA.biplot.html
@@ -0,0 +1,128 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calculate elements for the PCA biplot — PCA.biplot • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calculate elements for the PCA biplot — PCA.biplot"><meta name="description" content="This function performs calculations for the construction of a PCA biplot."><meta property="og:description" content="This function performs calculations for the construction of a PCA biplot."><meta property="og:image" content="/logo.png"></head><body>
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+    <li><a class="dropdown-item" href="../articles/Biplots_in_3D.html">Three dimensional biplots</a></li>
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+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+      </ul></div>
+
+
+  </div>
+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Calculate elements for the PCA biplot</h1>
+
+      <div class="d-none name"><code>PCA.biplot.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>This function performs calculations for the construction of a PCA biplot.</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'biplot'</span></span>
+<span><span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span></span>
+<span>  <span class="va">bp</span>,</span>
+<span>  dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>, <span class="fl">1</span>, <span class="fl">3</span><span class="op">)</span>,</span>
+<span>  e.vects <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>,</span>
+<span>  group.aes <span class="op">=</span> <span class="cn">NULL</span>,</span>
+<span>  show.class.means <span class="op">=</span> <span class="cn">FALSE</span>,</span>
+<span>  correlation.biplot <span class="op">=</span> <span class="cn">FALSE</span></span>
+<span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
+
+
+<dt id="arg-dim-biplot">dim.biplot<a class="anchor" aria-label="anchor" href="#arg-dim-biplot"></a></dt>
+<dd><p>the dimension of the biplot. Only values <code>1</code>, <code>2</code> and <code>3</code> are accepted, with default <code>2</code>.</p></dd>
+
+
+<dt id="arg-e-vects">e.vects<a class="anchor" aria-label="anchor" href="#arg-e-vects"></a></dt>
+<dd><p>the vector indicating which eigenvectors (principal components) should be plotted in the biplot, with default <code>1:dim.biplot</code>.</p></dd>
+
+
+<dt id="arg-group-aes">group.aes<a class="anchor" aria-label="anchor" href="#arg-group-aes"></a></dt>
+<dd><p>a vector of the same length as the number of rows in the data matrix
+for differentiated aesthetics for samples.</p></dd>
+
+
+<dt id="arg-show-class-means">show.class.means<a class="anchor" aria-label="anchor" href="#arg-show-class-means"></a></dt>
+<dd><p>a logical value indicating whether group means should be plotted in the biplot.</p></dd>
+
+
+<dt id="arg-correlation-biplot">correlation.biplot<a class="anchor" aria-label="anchor" href="#arg-correlation-biplot"></a></dt>
+<dd><p>a logical value. If <code>FALSE</code>, the distances between sample points are
+optimally approximated in the biplot. If <code>TRUE</code>, the correlations between
+variables are optimally approximated by the cosine of the angles between
+axes. Default is <code>FALSE</code>.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>an object of class <code>PCA</code>, inherits from class <code>biplot</code>.</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Object of class biplot, based on 150 samples and 4 variables.</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 4 numeric variables.</span>
+<span class="r-in"><span><span class="co"># create a PCA biplot</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span>data <span class="op">=</span> <span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="PCA.biplot-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span></span></span>
+</code></pre></div>
+    </div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
+
+
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+</div>
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+<div class="pkgdown-footer-right">
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diff --git a/docs/reference/PCA.html b/docs/reference/PCA.html
new file mode 100644
index 0000000..78c4ed6
--- /dev/null
+++ b/docs/reference/PCA.html
@@ -0,0 +1,204 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Perform Principal Components Analysis (PCA) — PCA • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Perform Principal Components Analysis (PCA) — PCA"><meta name="description" content="This function appends the biplot object with elements resulting from performing PCA."><meta property="og:description" content="This function appends the biplot object with elements resulting from performing PCA."><meta property="og:image" content="/logo.png"></head><body>
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Perform Principal Components Analysis (PCA)</h1>
+
+      <div class="d-none name"><code>PCA.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>This function appends the <code>biplot</code> object with elements resulting from performing PCA.</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">PCA</span><span class="op">(</span><span class="va">bp</span>, dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>, <span class="fl">1</span>, <span class="fl">3</span><span class="op">)</span>, e.vects <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>,</span>
+<span>group.aes <span class="op">=</span> <span class="cn">NULL</span>, show.class.means <span class="op">=</span> <span class="cn">FALSE</span>, correlation.biplot <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
+
+
+<dt id="arg-dim-biplot">dim.biplot<a class="anchor" aria-label="anchor" href="#arg-dim-biplot"></a></dt>
+<dd><p>the dimension of the biplot. Only values <code>1</code>, <code>2</code> and <code>3</code> are accepted, with default <code>2</code>.</p></dd>
+
+
+<dt id="arg-e-vects">e.vects<a class="anchor" aria-label="anchor" href="#arg-e-vects"></a></dt>
+<dd><p>the vector indicating which eigenvectors (principal components) should be plotted in the biplot, with default <code>1:dim.biplot</code>.</p></dd>
+
+
+<dt id="arg-group-aes">group.aes<a class="anchor" aria-label="anchor" href="#arg-group-aes"></a></dt>
+<dd><p>a vector of the same length as the number of rows in the data matrix
+for differentiated aesthetics for samples.</p></dd>
+
+
+<dt id="arg-show-class-means">show.class.means<a class="anchor" aria-label="anchor" href="#arg-show-class-means"></a></dt>
+<dd><p>a logical value indicating whether group means should be plotted in the biplot.</p></dd>
+
+
+<dt id="arg-correlation-biplot">correlation.biplot<a class="anchor" aria-label="anchor" href="#arg-correlation-biplot"></a></dt>
+<dd><p>a logical value. If <code>FALSE</code>, the distances between sample points are
+optimally approximated in the biplot. If <code>TRUE</code>, the correlations between
+variables are optimally approximated by the cosine of the angles between
+axes. Default is <code>FALSE</code>.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>An object of class PCA with the following elements:</p>
+<dl><dt>X</dt>
+<dd><p>the matrix of the centered and scaled numeric variables.</p></dd>
+
+<dt>Xcat</dt>
+<dd><p>the data frame of the categorical variables.</p></dd>
+
+<dt>raw.X</dt>
+<dd><p>the original data.</p></dd>
+
+<dt>classes</dt>
+<dd><p>the vector of category levels for the class variable. This is to be used for <code>colour</code>, <code>pch</code> and <code>cex</code> specifications.</p></dd>
+
+<dt>na.action</dt>
+<dd><p>the vector of observations that have been removed.</p></dd>
+
+<dt>center</dt>
+<dd><p>a logical value indicating whether \(\mathbf{X}\) is centered.</p></dd>
+
+<dt>scaled</dt>
+<dd><p>a logical value indicating whether \(\mathbf{X}\) is scaled.</p></dd>
+
+<dt>means</dt>
+<dd><p>the vector of means for each numerical variable.</p></dd>
+
+<dt>sd</dt>
+<dd><p>the vector of standard deviations for each numerical variable.</p></dd>
+
+<dt>n</dt>
+<dd><p>the number of observations.</p></dd>
+
+<dt>p</dt>
+<dd><p>the number of variables.</p></dd>
+
+<dt>group.aes</dt>
+<dd><p>the vector of category levels for the grouping variable. This is to be used for <code>colour</code>, <code>pch</code> and <code>cex</code> specification.</p></dd>
+
+<dt>g.names</dt>
+<dd><p>the descriptive names to be used for group labels.</p></dd>
+
+<dt>g</dt>
+<dd><p>the number of groups.</p></dd>
+
+<dt>Title</dt>
+<dd><p>the title of the biplot rendered.</p></dd>
+
+<dt>Z</dt>
+<dd><p>the matrix with each row containing the details of the points that are plotted (i.e. coordinates).</p></dd>
+
+<dt>Lmat</dt>
+<dd><p>the matrix for transformation to the principal components.</p></dd>
+
+<dt>Linv</dt>
+<dd><p>the inverse of \(\mathbf{L}\).</p></dd>
+
+<dt>eigenvalues</dt>
+<dd><p>the vector of eigenvalues of the covariance matrix of \(\mathbf{X}\).</p></dd>
+
+<dt>ax.one.unit</dt>
+<dd><p>one unit in the positive direction of each biplot axis.</p></dd>
+
+<dt>e.vects</dt>
+<dd><p>the vector indicating which principal components are plotted in the biplot.</p></dd>
+
+<dt>Vr</dt>
+<dd><p>the <code>1:dim.biplot</code> columns of \(\mathbf{V}\).</p></dd>
+
+<dt>dim.biplot</dt>
+<dd><p>the dimension of the biplot.</p></dd>
+
+<dt>class.means</dt>
+<dd><p>a logical value indicating whether group means are plotted in the biplot.</p></dd>
+
+<dt>Zmeans</dt>
+<dd><p>the matrix of class mean coordinates that are plotted in the biplot.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a></h2>
+    <p>Gabriel, K.R. (1971) The biplot graphic display of matrices with application to principal component analysis. <em>Biometrika.</em> 58(3):453–467.</p>
+    </div>
+    <div class="section level2">
+    <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
+    <div class="dont-index"><p><code><a href="biplot.html">biplot()</a></code></p></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">PCA</span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Object of class biplot, based on 150 samples and 4 variables.</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 4 numeric variables.</span>
+<span class="r-in"><span><span class="co"># create a PCA biplot</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span>data <span class="op">=</span> <span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">PCA</span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="PCA-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span></span></span>
+</code></pre></div>
+    </div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
+
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+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+</div>
+
+<div class="pkgdown-footer-right">
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-
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-  <div class="col-md-9 contents">
-    <div class="page-header">
-    <h1>PCO biplot</h1>
-    
-    <div class="hidden name"><code>PCO.biplot.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+      </ul></div>
+
+
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+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>PCO biplot</h1>
+
+      <div class="d-none name"><code>PCO.biplot.Rd</code></div>
     </div>
 
-    <div class="ref-description">
+    <div class="ref-description section level2">
     <p>Computes Principal Coordinate Analysis biplot</p>
     </div>
 
-    <div id="ref-usage">
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for biplot</span></span>
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'biplot'</span></span>
 <span><span class="fu"><a href="PCO.html">PCO</a></span><span class="op">(</span></span>
 <span>  <span class="va">bp</span>,</span>
 <span>  Dmat <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>  dist.func <span class="op">=</span> <span class="cn">NULL</span>,</span>
+<span>  dist.func.cat <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>  dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>, <span class="fl">1</span>, <span class="fl">3</span><span class="op">)</span>,</span>
-<span>  e.vects <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>,</span>
+<span>  e.vects <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>  group.aes <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>  show.class.means <span class="op">=</span> <span class="cn">FALSE</span>,</span>
 <span>  axes <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"regression"</span>, <span class="st">"splines"</span><span class="op">)</span>,</span>
@@ -86,81 +62,83 @@ <h1>PCO biplot</h1>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
 
 
-<dt>Dmat</dt>
+<dt id="arg-dmat">Dmat<a class="anchor" aria-label="anchor" href="#arg-dmat"></a></dt>
 <dd><p>nxn matrix of Euclidean embeddable distances between samples</p></dd>
 
 
-<dt>dist.func</dt>
+<dt id="arg-dist-func">dist.func<a class="anchor" aria-label="anchor" href="#arg-dist-func"></a></dt>
 <dd><p>function to compute Euclidean embeddable distances between samples. The
 default NULL computes Euclidean distance.</p></dd>
 
 
-<dt>dim.biplot</dt>
+<dt id="arg-dist-func-cat">dist.func.cat<a class="anchor" aria-label="anchor" href="#arg-dist-func-cat"></a></dt>
+<dd><p>function to compute Euclidean embeddable distance between categorical
+variables for the samples. The default NULL computes the extended
+matching coefficient.</p></dd>
+
+
+<dt id="arg-dim-biplot">dim.biplot<a class="anchor" aria-label="anchor" href="#arg-dim-biplot"></a></dt>
 <dd><p>dimension of the biplot. Only values 1, 2 and 3 are accepted, with default <code>2</code>.</p></dd>
 
 
-<dt>e.vects</dt>
+<dt id="arg-e-vects">e.vects<a class="anchor" aria-label="anchor" href="#arg-e-vects"></a></dt>
 <dd><p>e.vects which eigenvectors (canonical variates) to extract, with default <code>1:dim.biplot</code>.</p></dd>
 
 
-<dt>group.aes</dt>
+<dt id="arg-group-aes">group.aes<a class="anchor" aria-label="anchor" href="#arg-group-aes"></a></dt>
 <dd><p>vector of the same length as the number of rows in the data matrix
 for differentiated aesthetics for samples.</p></dd>
 
 
-<dt>show.class.means</dt>
+<dt id="arg-show-class-means">show.class.means<a class="anchor" aria-label="anchor" href="#arg-show-class-means"></a></dt>
 <dd><p>logical, indicating whether to plot the class means on the biplot.</p></dd>
 
 
-<dt>axes</dt>
+<dt id="arg-axes">axes<a class="anchor" aria-label="anchor" href="#arg-axes"></a></dt>
 <dd><p>type of biplot axes, currently only regression axes are implemented</p></dd>
 
 
-<dt>...</dt>
+<dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
 <dd><p>more arguments to <code>dist.func</code></p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>an object of class biplot.</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>an object of class biplot.</p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCO.html">PCO</a></span><span class="op">(</span>dist.func<span class="op">=</span><span class="va">sqrtManhattan</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="PCO.biplot-1.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span></span></span>
 </code></pre></div>
     </div>
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-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
-    </nav></div>
-</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
 
 
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-  <p></p><p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
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diff --git a/docs/reference/PCO.html b/docs/reference/PCO.html
new file mode 100644
index 0000000..8d37410
--- /dev/null
+++ b/docs/reference/PCO.html
@@ -0,0 +1,137 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Principal Coordinate Analysis (PCO) biplot method — PCO • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Principal Coordinate Analysis (PCO) biplot method — PCO"><meta name="description" content="Principal Coordinate Analysis (PCO) biplot method"><meta property="og:description" content="Principal Coordinate Analysis (PCO) biplot method"><meta property="og:image" content="/logo.png"></head><body>
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+  </ul></li>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+      </ul></div>
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+  </div>
+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Principal Coordinate Analysis (PCO) biplot method</h1>
+
+      <div class="d-none name"><code>PCO.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>Principal Coordinate Analysis (PCO) biplot method</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">PCO</span><span class="op">(</span><span class="va">bp</span>, Dmat<span class="op">=</span><span class="cn">NULL</span>, dist.func<span class="op">=</span><span class="cn">NULL</span>, dist.func.cat<span class="op">=</span><span class="cn">NULL</span>,</span>
+<span>           dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>,<span class="fl">1</span>,<span class="fl">3</span><span class="op">)</span>, e.vects <span class="op">=</span> <span class="cn">NULL</span>, group.aes<span class="op">=</span><span class="cn">NULL</span>,</span>
+<span>           show.class.means <span class="op">=</span> <span class="cn">FALSE</span>, axes <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"regression"</span>,<span class="st">"splines"</span><span class="op">)</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
+
+
+<dt id="arg-dmat">Dmat<a class="anchor" aria-label="anchor" href="#arg-dmat"></a></dt>
+<dd><p>nxn matrix of Euclidean embeddable distances between samples</p></dd>
+
+
+<dt id="arg-dist-func">dist.func<a class="anchor" aria-label="anchor" href="#arg-dist-func"></a></dt>
+<dd><p>function to compute Euclidean embeddable distances between samples. The
+default NULL computes Euclidean distance.</p></dd>
+
+
+<dt id="arg-dist-func-cat">dist.func.cat<a class="anchor" aria-label="anchor" href="#arg-dist-func-cat"></a></dt>
+<dd><p>function to compute Euclidean embeddable distance between categorical
+variables for the samples. The default NULL computes the extended
+matching coefficient.</p></dd>
+
+
+<dt id="arg-dim-biplot">dim.biplot<a class="anchor" aria-label="anchor" href="#arg-dim-biplot"></a></dt>
+<dd><p>dimension of the biplot. Only values 1, 2 and 3 are accepted, with default <code>2</code>.</p></dd>
+
+
+<dt id="arg-e-vects">e.vects<a class="anchor" aria-label="anchor" href="#arg-e-vects"></a></dt>
+<dd><p>e.vects which eigenvectors (canonical variates) to extract, with default <code>1:dim.biplot</code>.</p></dd>
+
+
+<dt id="arg-group-aes">group.aes<a class="anchor" aria-label="anchor" href="#arg-group-aes"></a></dt>
+<dd><p>vector of the same length as the number of rows in the data matrix
+for differentiated aesthetics for samples.</p></dd>
+
+
+<dt id="arg-show-class-means">show.class.means<a class="anchor" aria-label="anchor" href="#arg-show-class-means"></a></dt>
+<dd><p>logical, indicating whether to plot the class means on the biplot.</p></dd>
+
+
+<dt id="arg-axes">axes<a class="anchor" aria-label="anchor" href="#arg-axes"></a></dt>
+<dd><p>type of biplot axes, currently only regression axes are implemented</p></dd>
+
+
+<dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
+<dd><p>more arguments to <code>dist.func</code></p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>Object of class biplot</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">PCO</span><span class="op">(</span>dist.func <span class="op">=</span> <span class="va">sqrtManhattan</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Object of class biplot, based on 150 samples and 4 variables.</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 4 numeric variables.</span>
+<span class="r-in"><span><span class="co"># create a CVA biplot</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">PCO</span><span class="op">(</span>dist.func <span class="op">=</span> <span class="va">sqrtManhattan</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="PCO-1.png" alt="" width="700" height="433"></span>
+</code></pre></div>
+    </div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
+
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+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
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diff --git a/docs/reference/alpha.bags.html b/docs/reference/alpha.bags.html
index 182442a..709f507 100644
--- a/docs/reference/alpha.bags.html
+++ b/docs/reference/alpha.bags.html
@@ -1,131 +1,107 @@
 <!DOCTYPE html>
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+scatter plot. The alpha-bag refers to a contour which contains \(\alpha\)% of the observations."><meta property="og:description" content="This function produces \(\alpha\)-bags, which is a useful graphical summary of the
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-    <div class="page-header">
-    <h1>Create alpha bags</h1>
-    
-    <div class="hidden name"><code>alpha.bags.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+      </ul></div>
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+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Create alpha bags</h1>
+
+      <div class="d-none name"><code>alpha.bags.Rd</code></div>
     </div>
 
-    <div class="ref-description">
+    <div class="ref-description section level2">
     <p>This function produces \(\alpha\)-bags, which is a useful graphical summary of the
 scatter plot. The alpha-bag refers to a contour which contains \(\alpha\)% of the observations.</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">alpha.bags</span><span class="op">(</span><span class="va">bp</span>, alpha <span class="op">=</span> <span class="fl">0.95</span>, which <span class="op">=</span> <span class="cn">NULL</span>, col <span class="op">=</span> <span class="va">ez.col</span><span class="op">[</span><span class="va">which</span><span class="op">]</span>, lty <span class="op">=</span> <span class="fl">1</span>,</span>
 <span>lwd <span class="op">=</span> <span class="fl">1</span>, max <span class="op">=</span> <span class="fl">2500</span>, trace <span class="op">=</span> <span class="cn">TRUE</span>, opacity <span class="op">=</span> <span class="fl">0.25</span>, outlying<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>an object of class <code>biplot</code>.</p></dd>
 
 
-<dt>alpha</dt>
+<dt id="arg-alpha">alpha<a class="anchor" aria-label="anchor" href="#arg-alpha"></a></dt>
 <dd><p>numeric vector between 0 and 1 to determine coverage of the bag (\(\alpha\)), with default <code>0.95</code>.</p></dd>
 
 
-<dt>which</dt>
+<dt id="arg-which">which<a class="anchor" aria-label="anchor" href="#arg-which"></a></dt>
 <dd><p>numeric vector indicating the selection of groups or classes to be fitted with \(\alpha\)-bags.</p></dd>
 
 
-<dt>col</dt>
+<dt id="arg-col">col<a class="anchor" aria-label="anchor" href="#arg-col"></a></dt>
 <dd><p>vector of colours for the \(\alpha\)-bags. Multiple \(\alpha\) bags for one group will be displayed in the same colour.</p></dd>
 
 
-<dt>lty</dt>
+<dt id="arg-lty">lty<a class="anchor" aria-label="anchor" href="#arg-lty"></a></dt>
 <dd><p>vector of line types for the \(\alpha\)-bags. The same line type will be used per value of \(\alpha\).</p></dd>
 
 
-<dt>lwd</dt>
+<dt id="arg-lwd">lwd<a class="anchor" aria-label="anchor" href="#arg-lwd"></a></dt>
 <dd><p>vector of line widths for the \(\alpha\)-bags. The same line width will be used per value of \(\alpha\).</p></dd>
 
 
-<dt>max</dt>
+<dt id="arg-max">max<a class="anchor" aria-label="anchor" href="#arg-max"></a></dt>
 <dd><p>maximum number of samples to include in \(\alpha\)-bag calculations, with default 2500. If
 more samples are in the group, a random sample of size max is taken for the computations.</p></dd>
 
 
-<dt>trace</dt>
+<dt id="arg-trace">trace<a class="anchor" aria-label="anchor" href="#arg-trace"></a></dt>
 <dd><p>logical, indicating progress of computation.</p></dd>
 
 
-<dt>opacity</dt>
+<dt id="arg-opacity">opacity<a class="anchor" aria-label="anchor" href="#arg-opacity"></a></dt>
 <dd><p>level of opacity, with default <code>0.5</code>.</p></dd>
 
 
-<dt>outlying</dt>
+<dt id="arg-outlying">outlying<a class="anchor" aria-label="anchor" href="#arg-outlying"></a></dt>
 <dd><p>logical indicating whether only outlying points should be plotted. Note the <code>which</code> argument may be overwritten when <code>TRUE</code></p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>A list with the following components is available:</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>A list with the following components is available:</p>
 <dl><dt>alpha.bags</dt>
 <dd><p>list of coordinates for the \(\alpha\)-bags for each group.</p></dd>
 
@@ -139,46 +115,42 @@ <h2>Value</h2>
 <dd><p>vector of line widths for the \(\alpha\)-bags.</p></dd>
 
 </dl></div>
-    <div id="references">
-    <h2>References</h2>
-    <p>Gower, J., Gardner-Lubbe, S. &amp; Le Roux, N. (2011, ISBN: 978-0-470-01255-0) <em>Understanding Biplots.</em> Chichester, England: John Wiley &amp; Sons Ltd.<br><br></p>
+    <div class="section level2">
+    <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a></h2>
+    <p>Gower, J., Gardner-Lubbe, S. &amp; Le Roux, N. (2011, ISBN: 978-0-470-01255-0) <em>Understanding Biplots.</em> Chichester, England: John Wiley &amp; Sons Ltd.</p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span> <span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span>group.aes<span class="op">=</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">alpha.bags</span><span class="op">(</span>alpha<span class="op">=</span><span class="fl">0.95</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Computing 0.95 -bag for setosa </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Computing 0.95 -bag for versicolor </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Computing 0.95 -bag for virginica </span>
+<span class="r-plt img"><img src="alpha.bags-1.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span> <span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span>,group.aes<span class="op">=</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">alpha.bags</span><span class="op">(</span>alpha<span class="op">=</span><span class="fl">0.95</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Computing 0.95 -bag for setosa </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Computing 0.95 -bag for versicolor </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Computing 0.95 -bag for virginica </span>
-<span class="r-plt img"><img src="alpha.bags-1.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span></span></span>
 </code></pre></div>
     </div>
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-    <h1>Aesthetics for biplot axes</h1>
-    
-    <div class="hidden name"><code>axes.Rd</code></div>
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+      <img src="../logo.png" class="logo" alt=""><h1>Format aesthetics for the biplot axes</h1>
+
+      <div class="d-none name"><code>axes.Rd</code></div>
     </div>
 
-    <div class="ref-description">
-    <p>This function allows formatting changes to axes.</p>
+    <div class="ref-description section level2">
+    <p>This function allows the user to format the aesthetics for the biplot axes.</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">axes</span><span class="op">(</span><span class="va">bp</span>, X.names<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">colnames</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>, which <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="va">bp</span><span class="op">$</span><span class="va">p</span>, col <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/grDevices/gray.html" class="external-link">grey</a></span><span class="op">(</span><span class="fl">0.7</span><span class="op">)</span>, lwd <span class="op">=</span> <span class="fl">1</span>, lty <span class="op">=</span> <span class="fl">1</span>,</span>
 <span>label.dir <span class="op">=</span> <span class="st">"Orthog"</span>, label.col <span class="op">=</span> <span class="va">col</span>, label.cex <span class="op">=</span> <span class="fl">0.75</span>, label.line <span class="op">=</span> <span class="fl">0.1</span>, </span>
 <span>label.offset<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="fl">0</span>,<span class="fl">4</span><span class="op">)</span>, ticks <span class="op">=</span> <span class="fl">5</span>, tick.col <span class="op">=</span> <span class="va">col</span>, tick.size <span class="op">=</span> <span class="fl">1</span>, tick.label <span class="op">=</span> <span class="cn">TRUE</span>, </span>
@@ -80,197 +55,191 @@ <h1>Aesthetics for biplot axes</h1>
 <span>orthogx <span class="op">=</span> <span class="fl">0</span>, orthogy <span class="op">=</span> <span class="fl">0</span>, vectors <span class="op">=</span> <span class="cn">FALSE</span>, unit.circle<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>an object of class <code>biplot</code>.</p></dd>
 
 
-<dt>X.names</dt>
-<dd><p>refers to the column names of <code>bp</code> to specify which axes to label.</p></dd>
+<dt id="arg-x-names">X.names<a class="anchor" aria-label="anchor" href="#arg-x-names"></a></dt>
+<dd><p>a vector of column names of <code>bp</code> to specify which axes should be labelled.</p></dd>
 
 
-<dt>which</dt>
-<dd><p>integer-valued vector specifying which biplot axes are shown
-in a biplot. By default all p biplot axes are shown.</p></dd>
+<dt id="arg-which">which<a class="anchor" aria-label="anchor" href="#arg-which"></a></dt>
+<dd><p>a vector containing the columns or variables for which the axes should be displayed, with default <code>1:p</code>.</p></dd>
 
 
-<dt>col</dt>
-<dd><p>vector of size p specifying colours of labels of biplot axes. The default is <code>grey(0.7)</code>.</p></dd>
+<dt id="arg-col">col<a class="anchor" aria-label="anchor" href="#arg-col"></a></dt>
+<dd><p>the colour(s) for the axes, with default <code>grey(0.7)</code>. Alternatively, provide a vector of colours corresponding to <code>X.names</code>.</p></dd>
 
 
-<dt>lwd</dt>
-<dd><p>axis line width, with default <code>1</code>.</p></dd>
+<dt id="arg-lwd">lwd<a class="anchor" aria-label="anchor" href="#arg-lwd"></a></dt>
+<dd><p>the line width(s) for the axes, with default <code>1</code>.</p></dd>
 
 
-<dt>lty</dt>
-<dd><p>axis line type, with default <code>1</code>.</p></dd>
+<dt id="arg-lty">lty<a class="anchor" aria-label="anchor" href="#arg-lty"></a></dt>
+<dd><p>the line type(s) for the axes, with default <code>1</code>.</p></dd>
 
 
-<dt>label.dir</dt>
-<dd><p>One of "Orthog" (default), "Hor" or "Paral" specifying titles of
-axes to appear orthogonal to the side of the figure; always
-horizontally or always parallel to the side of the figure.</p></dd>
+<dt id="arg-label-dir">label.dir<a class="anchor" aria-label="anchor" href="#arg-label-dir"></a></dt>
+<dd><p>a character string indicating the placement of the axis titles to the side of the figure. One of "<code>Orthog</code>" for axis titles to appear orthogonal to the side of the figure (default) , "<code>Hor</code>" for axis titles to appear horizontally or "<code>Paral</code>" for axis titles to appear parallel to the side of the figure.</p></dd>
 
 
-<dt>label.col</dt>
-<dd><p>axis label colour, with default, <code>col</code>.</p></dd>
+<dt id="arg-label-col">label.col<a class="anchor" aria-label="anchor" href="#arg-label-col"></a></dt>
+<dd><p>the colour(s) for the axis labels, with default, <code>col</code>.</p></dd>
 
 
-<dt>label.cex</dt>
-<dd><p>axis label expansion, with default <code>0.75</code>.</p></dd>
+<dt id="arg-label-cex">label.cex<a class="anchor" aria-label="anchor" href="#arg-label-cex"></a></dt>
+<dd><p>the label expansion for the axis labels, with default <code>0.75</code>.</p></dd>
 
 
-<dt>label.line</dt>
-<dd><p>axis label written on which margin line, with default <code>0.1</code>.</p></dd>
+<dt id="arg-label-line">label.line<a class="anchor" aria-label="anchor" href="#arg-label-line"></a></dt>
+<dd><p>the distance of the axis title from the side of the figure, with default <code>0.1</code>.</p></dd>
 
 
-<dt>label.offset</dt>
-<dd><p>A four-component numeric vector controlling the distance a
-biplot axis title is printed from the side of the figure. Sides are
-numbered 1 to 4 according to R conventions clockwise starting
-from the bottom horizontal side. Default is rep(0,4)</p></dd>
+<dt id="arg-label-offset">label.offset<a class="anchor" aria-label="anchor" href="#arg-label-offset"></a></dt>
+<dd><p>a four-component numeric vector controlling the distances axis titles are displayed from the side of the figure, with default <code>rep(0,4)</code>. Sides are numbered <code>1</code> to <code>4</code> according to <code>R</code> conventions.</p></dd>
 
 
-<dt>ticks</dt>
-<dd><p>integer-valued vector of size equal to the number of biplot axes
-to control the number of tickmarks on each individual biplot
-axis. Default is 5 for each axis.</p></dd>
+<dt id="arg-ticks">ticks<a class="anchor" aria-label="anchor" href="#arg-ticks"></a></dt>
+<dd><p>an integer-valued vector indicating the number of tickmarks for each axis, with default <code>5</code> for each axis.</p></dd>
 
 
-<dt>tick.col</dt>
-<dd><p>tick mark colour, with default <code>col</code>.</p></dd>
+<dt id="arg-tick-col">tick.col<a class="anchor" aria-label="anchor" href="#arg-tick-col"></a></dt>
+<dd><p>the colour(s) for the tick marks, with default <code>col</code>.</p></dd>
 
 
-<dt>tick.size</dt>
-<dd><p>positive integer-valued vector with specifying tick mark sizes, with default <code>1</code>.</p></dd>
+<dt id="arg-tick-size">tick.size<a class="anchor" aria-label="anchor" href="#arg-tick-size"></a></dt>
+<dd><p>a vector specifying the sizes of tick marks for each axis, with default <code>1</code> for each .</p></dd>
 
 
-<dt>tick.label</dt>
-<dd><p>logical, whether axes should be labelled or not, with default <code>TRUE</code>.</p></dd>
+<dt id="arg-tick-label">tick.label<a class="anchor" aria-label="anchor" href="#arg-tick-label"></a></dt>
+<dd><p>a logical value indicating whether the axes should be labelled, with default <code>TRUE</code>.</p></dd>
 
 
-<dt>tick.label.side</dt>
-<dd><p>character vector specifying position of the tick label "below" or "above" the axis.</p></dd>
+<dt id="arg-tick-label-side">tick.label.side<a class="anchor" aria-label="anchor" href="#arg-tick-label-side"></a></dt>
+<dd><p>a character string indicating the position of the tick label. One of "<code>below</code>" for the label to appear below the tick mark (default) or "<code>above</code>" for the label to appear above the tick mark.</p></dd>
 
 
-<dt>tick.label.col</dt>
-<dd><p>tick mark label colour, with default <code>tick.col</code>.</p></dd>
+<dt id="arg-tick-label-col">tick.label.col<a class="anchor" aria-label="anchor" href="#arg-tick-label-col"></a></dt>
+<dd><p>the colour(s) for the tick mark labels, with default <code>tick.col</code>.</p></dd>
 
 
-<dt>tick.label.cex</dt>
-<dd><p>tick mark label expansion, with default <code>0.6</code>.</p></dd>
+<dt id="arg-tick-label-cex">tick.label.cex<a class="anchor" aria-label="anchor" href="#arg-tick-label-cex"></a></dt>
+<dd><p>the label expansion for the tick mark labels, with default <code>0.6</code>.</p></dd>
 
 
-<dt>predict.col</dt>
-<dd><p>predicted samples colour, with default <code>col</code>.</p></dd>
+<dt id="arg-predict-col">predict.col<a class="anchor" aria-label="anchor" href="#arg-predict-col"></a></dt>
+<dd><p>the colour(s) for the predicted samples, with default <code>col</code>.</p></dd>
 
 
-<dt>predict.lwd</dt>
-<dd><p>predicted samples line width, with default <code>lwd</code>.</p></dd>
+<dt id="arg-predict-lwd">predict.lwd<a class="anchor" aria-label="anchor" href="#arg-predict-lwd"></a></dt>
+<dd><p>the line width(s) for the predicted samples, with default <code>lwd</code>.</p></dd>
 
 
-<dt>predict.lty</dt>
-<dd><p>predicted samples line type, with default <code>lty</code>.</p></dd>
+<dt id="arg-predict-lty">predict.lty<a class="anchor" aria-label="anchor" href="#arg-predict-lty"></a></dt>
+<dd><p>the line type(s) for the predicted samples, with default <code>lty</code>.</p></dd>
 
 
-<dt>ax.names</dt>
-<dd><p>vector of size <code>p</code> containing user defined names for the variables.</p></dd>
+<dt id="arg-ax-names">ax.names<a class="anchor" aria-label="anchor" href="#arg-ax-names"></a></dt>
+<dd><p>a vector of size <code>p</code> containing user defined titles for the axes.</p></dd>
 
 
-<dt>orthogx</dt>
-<dd><p>numeric vector of size p specifying the x-coordinate of the parallel transformation of each axis.
-Defaults to zero for each axis. Only used when the dimension of the biplot is two.</p></dd>
+<dt id="arg-orthogx">orthogx<a class="anchor" aria-label="anchor" href="#arg-orthogx"></a></dt>
+<dd><p>a numeric vector of size <code>p</code> specifying the x-coordinate of the parallel transformation of each axis, with default <code>0</code> for each axis. This is only used when <code>dim.biplot = 2</code>.</p></dd>
 
 
-<dt>orthogy</dt>
-<dd><p>numeric vector of size p specifying the y-coordinate of the parallel transformation of each axis.
-Defaults to zero for each axis. Only used when the dimension of the biplot is two.</p></dd>
+<dt id="arg-orthogy">orthogy<a class="anchor" aria-label="anchor" href="#arg-orthogy"></a></dt>
+<dd><p>a numeric vector of size <code>p</code> specifying the y-coordinate of the parallel transformation of each axis, with default <code>0</code> for each axis. This is only used when <code>dim.biplot = 2</code>.</p></dd>
 
 
-<dt>vectors</dt>
-<dd><p>logical, whether calibrated axes should be displayed on the biplot</p></dd>
+<dt id="arg-vectors">vectors<a class="anchor" aria-label="anchor" href="#arg-vectors"></a></dt>
+<dd><p>a logical value indicating whether vector representation (calibrated axes) should be displayed on the biplot. This is only used when a PCA biplot is produced.</p></dd>
 
 
-<dt>unit.circle</dt>
-<dd><p>logical, whether a unit circle should be displayed on the biplot</p></dd>
+<dt id="arg-unit-circle">unit.circle<a class="anchor" aria-label="anchor" href="#arg-unit-circle"></a></dt>
+<dd><p>a logical value indicating whether a unit circle should be displayed on the biplot.</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>A list with the following components is available:</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>The object of class <code>biplot</code> will be appended with a list called <code>axes</code> containing the following elements:</p>
 <dl><dt>which</dt>
-<dd><p>vector of the columns displayed as axes.</p></dd>
+<dd><p>a vector containing the columns for which the axes are displayed.</p></dd>
 
 <dt>col</dt>
-<dd><p>vector of axis colours.</p></dd>
+<dd><p>the colour(s) of the axes.</p></dd>
 
 <dt>lwd</dt>
-<dd><p>vector of axis line widths.</p></dd>
+<dd><p>the line width(s) of the axes.</p></dd>
 
 <dt>lty</dt>
-<dd><p>vector of axis line types.</p></dd>
+<dd><p>the line type(s) of the axes.</p></dd>
 
 <dt>label.dir</dt>
-<dd><p>direction of the axis labels.</p></dd>
+<dd><p>the placement of the axis titles to the side of the figure.</p></dd>
 
 <dt>label.col</dt>
-<dd><p>vector of axis label colours.</p></dd>
+<dd><p>the colour(s) of the axis titles.</p></dd>
 
 <dt>label.cex</dt>
-<dd><p>vector of axis labels expansions.</p></dd>
+<dd><p>the label expansion(s) of the axis titles.</p></dd>
 
 <dt>label.line</dt>
-<dd><p>vector of axis label margin lines from axes.</p></dd>
+<dd><p>the distance(s) of the axis titles from the side of the figure.</p></dd>
 
 <dt>ticks</dt>
-<dd><p>vector representing the number of tick marks per axis.</p></dd>
+<dd><p>the number of tick marks per axis.</p></dd>
 
 <dt>tick.col</dt>
-<dd><p>vector of tick mark colours.</p></dd>
+<dd><p>the colour(s) of the tick marks.</p></dd>
 
 <dt>tick.size</dt>
-<dd><p>vector of tick mark sizes.</p></dd>
+<dd><p>the size(s) of the tick marks.</p></dd>
 
 <dt>tick.label</dt>
-<dd><p>vector of logical values indicating whether axes are labelled.</p></dd>
+<dd><p>logical value(s) indicating whether axes are labelled.</p></dd>
 
 <dt>tick.label.side</dt>
-<dd><p>vector specifying position of the tick label "below" or "above" the axis.</p></dd>
+<dd><p>the position of the tick mark labels.</p></dd>
 
 <dt>tick.label.col</dt>
-<dd><p>vector of tick mark label colours.</p></dd>
+<dd><p>the colour(s) of the tick mark labels.</p></dd>
 
 <dt>tick.label.cex</dt>
-<dd><p>vector of tick mark label expansions.</p></dd>
+<dd><p>the expansion(s) of the tick mark labels.</p></dd>
 
 <dt>predict.col</dt>
-<dd><p>vector of colours for the predicted samples.</p></dd>
+<dd><p>the colour(s) of the predicted samples.</p></dd>
 
 <dt>predict.lty</dt>
-<dd><p>vector of line types for the predicted samples.</p></dd>
+<dd><p>the line type(s) of the predicted samples.</p></dd>
 
 <dt>predict.lwd</dt>
-<dd><p>vector of line widths for the predicted samples.</p></dd>
+<dd><p>the line width(s) of the predicted samples.</p></dd>
 
 <dt>names</dt>
-<dd><p>vector of variable names defined by the user.</p></dd>
+<dd><p>the user defined axis titles.</p></dd>
 
 <dt>orthogx</dt>
-<dd><p>vector of the horisontal translations for each axis.</p></dd>
+<dd><p>the horizontal translations for each axis.</p></dd>
 
 <dt>orthogy</dt>
-<dd><p>vector of the vertical translations for each axis.</p></dd>
+<dd><p>the vertical translations for each axis.</p></dd>
 
-<dt>calibrated.axis</dt>
-<dd><p>whether to plot calibrated axis</p></dd>
+<dt>vectors</dt>
+<dd><p>a logical value indicating whether calibrated axes are plotted.</p></dd>
 
 </dl></div>
+    <div class="section level2">
+    <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
+    <div class="dont-index"><p><code><a href="biplot.html">biplot()</a></code></p></div>
+    </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">axes</span><span class="op">(</span>col<span class="op">=</span><span class="st">"purple"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="axes-1.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="samples.html">samples</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"purple"</span>,pch<span class="op">=</span><span class="fl">15</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">axes</span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
@@ -278,27 +247,23 @@ <h2>Examples</h2>
 <span class="r-in"><span></span></span>
 </code></pre></div>
     </div>
-  </div>
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
-    </nav></div>
-</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
 
 
-      <footer><div class="copyright">
-  <p></p><p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.</p>
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.2.</p>
 </div>
 
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diff --git a/docs/reference/axes_coordinates.html b/docs/reference/axes_coordinates.html
new file mode 100644
index 0000000..99a1073
--- /dev/null
+++ b/docs/reference/axes_coordinates.html
@@ -0,0 +1,91 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Calibrate Biplot Axes — axes_coordinates • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Calibrate Biplot Axes — axes_coordinates"><meta name="description" content="Convenience function to obtain the coordinates of the calibrated ticks marks on the biplot"><meta property="og:description" content="Convenience function to obtain the coordinates of the calibrated ticks marks on the biplot"><meta property="og:image" content="/logo.png"></head><body>
+    <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Calibrate Biplot Axes</h1>
+
+      <div class="d-none name"><code>axes_coordinates.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>Convenience function to obtain the coordinates of the calibrated ticks marks on the biplot</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">axes_coordinates</span><span class="op">(</span><span class="va">x</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
+<dd><p>an object of class <code>biplot</code></p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>An ordered list containing the coordinates the of tick marks to plotted on the biplot</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="va">x</span><span class="op">&lt;-</span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">coordinates</span><span class="op">&lt;-</span><span class="fu">axes_coordinates</span><span class="op">(</span><span class="va">x</span><span class="op">)</span></span></span>
+</code></pre></div>
+    </div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
+
+
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+</div>
+
+<div class="pkgdown-footer-right">
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+
diff --git a/docs/reference/biplot-1.png b/docs/reference/biplot-1.png
index 308f5f3..bf2eb47 100644
Binary files a/docs/reference/biplot-1.png and b/docs/reference/biplot-1.png differ
diff --git a/docs/reference/biplot.html b/docs/reference/biplot.html
index b4ccc33..fa5fc8d 100644
--- a/docs/reference/biplot.html
+++ b/docs/reference/biplot.html
@@ -1,78 +1,57 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>First step to create a new biplot with biplotEZ — biplot • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.1/jquery.min.js" integrity="sha512-v2CJ7UaYy4JwqLDIrZUI/4hqeoQieOmAZNXBeQyjo21dadnwR+8ZaIJVT8EE2iyI61OV8e6M8PP2/4hpQINQ/g==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="First step to create a new biplot with biplotEZ — biplot"><meta property="og:description" content="This function produces a list of elements to be used when producing a biplot,
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>First step to create a new biplot with biplotEZ — biplot • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="First step to create a new biplot with biplotEZ — biplot"><meta name="description" content="This function produces a list of elements to be used when producing a biplot,
 which provides a useful data analysis tool and allows the visual appraisal
 of the structure of large data matrices. Biplots are the
 multivariate analogue of scatter plots. They approximate the multivariate
 distribution of a sample in a few dimensions and they superimpose on this
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+display representations of the variables on which the samples are measured."><meta property="og:description" content="This function produces a list of elements to be used when producing a biplot,
+which provides a useful data analysis tool and allows the visual appraisal
+of the structure of large data matrices. Biplots are the
+multivariate analogue of scatter plots. They approximate the multivariate
+distribution of a sample in a few dimensions and they superimpose on this
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+    <li><a class="dropdown-item" href="../articles/MDS.html">Multi-dimensional scaling</a></li>
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-    <div class="page-header">
-    <h1>First step to create a new biplot with <span class="pkg">biplotEZ</span></h1>
-    
-    <div class="hidden name"><code>biplot.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+      </ul></div>
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>First step to create a new biplot with <span class="pkg">biplotEZ</span></h1>
+
+      <div class="d-none name"><code>biplot.Rd</code></div>
     </div>
 
-    <div class="ref-description">
+    <div class="ref-description section level2">
     <p>This function produces a list of elements to be used when producing a biplot,
 which provides a useful data analysis tool and allows the visual appraisal
 of the structure of large data matrices. Biplots are the
@@ -81,79 +60,136 @@ <h1>First step to create a new biplot with <span class="pkg">biplotEZ</span></h1
 display representations of the variables on which the samples are measured.</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">biplot</span><span class="op">(</span><span class="va">data</span>, classes <span class="op">=</span> <span class="cn">NULL</span>, group.aes <span class="op">=</span> <span class="cn">NULL</span>, center <span class="op">=</span> <span class="cn">TRUE</span>, scaled <span class="op">=</span> <span class="cn">FALSE</span>,</span>
 <span>Title <span class="op">=</span> <span class="cn">NULL</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>data</dt>
-<dd><p>a dataframe or matrix containing all variables the user wants to analyse.</p></dd>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
 
 
-<dt>classes</dt>
-<dd><p>vector identifying class membership.</p></dd>
+<dl><dt id="arg-data">data<a class="anchor" aria-label="anchor" href="#arg-data"></a></dt>
+<dd><p>a data frame or numeric matrix containing all variables the user wants to analyse.</p></dd>
 
 
-<dt>group.aes</dt>
-<dd><p>vector identifying groups for aesthetic formatting.</p></dd>
+<dt id="arg-classes">classes<a class="anchor" aria-label="anchor" href="#arg-classes"></a></dt>
+<dd><p>a vector identifying class membership.</p></dd>
 
 
-<dt>center</dt>
-<dd><p>logical, indicating whether <code>data</code> should be column centered, with default <code>TRUE</code>.</p></dd>
+<dt id="arg-group-aes">group.aes<a class="anchor" aria-label="anchor" href="#arg-group-aes"></a></dt>
+<dd><p>a vector identifying groups for aesthetic formatting.</p></dd>
 
 
-<dt>scaled</dt>
-<dd><p>logical, indicating whether <code>data</code> should be standardized to unit column variances, with default <code>FALSE</code>.</p></dd>
+<dt id="arg-center">center<a class="anchor" aria-label="anchor" href="#arg-center"></a></dt>
+<dd><p>a logical value indicating whether <code>data</code> should be column centered, with default <code>TRUE</code>.</p></dd>
 
 
-<dt>Title</dt>
-<dd><p>title of the biplot to be rendered, enter text in "  ".</p></dd>
+<dt id="arg-scaled">scaled<a class="anchor" aria-label="anchor" href="#arg-scaled"></a></dt>
+<dd><p>a logical value indicating whether <code>data</code> should be standardised to unit column variances, with default <code>FALSE</code>.</p></dd>
 
-</dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
 
-<p>A list with the following components is available:</p>
+<dt id="arg-title">Title<a class="anchor" aria-label="anchor" href="#arg-title"></a></dt>
+<dd><p>the title of the biplot to be rendered, enter text in "  ".</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>A list with the following components is available:</p>
 <dl><dt>X</dt>
-<dd><p>matrix of the centered and scaled numeric variables.</p></dd>
+<dd><p>the matrix of the centered and scaled numeric variables.</p></dd>
 
 <dt>Xcat</dt>
-<dd><p>data frame of the categorical variables.</p></dd>
+<dd><p>the data frame of the categorical variables.</p></dd>
 
 <dt>raw.X</dt>
-<dd><p>original data.</p></dd>
+<dd><p>the original data.</p></dd>
+
+<dt>classes</dt>
+<dd><p>the vector of category levels for the class variable. This is to be used for <code>colour</code>, <code>pch</code> and <code>cex</code> specifications.</p></dd>
+
+<dt>na.action</dt>
+<dd><p>the vector of observations that have been removed.</p></dd>
 
 <dt>center</dt>
-<dd><p>TRUE or FALSE, whether X is centered.</p></dd>
+<dd><p>a logical value indicating whether \(\mathbf{X}\) is centered.</p></dd>
 
 <dt>scaled</dt>
-<dd><p>TRUE or FALSE, wether X is scaled.</p></dd>
+<dd><p>a logical value indicating whether \(\mathbf{X}\) is scaled.</p></dd>
 
 <dt>means</dt>
-<dd><p>vector of means for each numeric variable.</p></dd>
+<dd><p>the vector of means for each numeric variable.</p></dd>
 
 <dt>sd</dt>
-<dd><p>vector of standard deviations for each numeric variable.</p></dd>
+<dd><p>the vector of standard deviations for each numeric variable.</p></dd>
+
+<dt>n</dt>
+<dd><p>the number of observations.</p></dd>
+
+<dt>p</dt>
+<dd><p>the number of variables.</p></dd>
 
 <dt>group.aes</dt>
-<dd><p>vector of category levels for the grouping variable. This is to be used for colour, pch and cex specifications.</p></dd>
+<dd><p>the vector of category levels for the grouping variable. This is to be used for <code>colour</code>, <code>pch</code> and <code>cex</code> specifications.</p></dd>
+
+<dt>g.names</dt>
+<dd><p>the descriptive names to be used for group labels.</p></dd>
+
+<dt>g</dt>
+<dd><p>the number of groups.</p></dd>
 
 <dt>Title</dt>
-<dd><p>title of the biplot to be rendered</p></dd>
+<dd><p>the title of the biplot rendered</p></dd>
 
 </dl></div>
-    <div id="references">
-    <h2>References</h2>
-    <p>Gabriel, K.R. (1971) The biplot graphic display of matrices with application to principal component analysis. <em>Biometrika.</em> 58(3):453–467.<br><br>
-Gower, J., Gardner-Lubbe, S. &amp; Le Roux, N. (2011, ISBN: 978-0-470-01255-0) <em>Understanding Biplots.</em> Chichester, England: John Wiley &amp; Sons Ltd.<br><br>
-Gower, J.C. &amp; Hand, D.J.(1996, ISBN: 0-412-71630-5) <em>Biplots.</em> London: Chapman &amp; Hall.</p>
+    <div class="section level2">
+    <h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></a></h2>
+    <p>This function is the entry-level function in <code>biplotEZ</code> to construct a biplot display.
+It initialises an object of class <code>biplot</code> which can then be piped to various other functions
+to build up the biplot display.</p>
+    </div>
+    <div class="section level2">
+    <h2 id="useful-links">Useful links<a class="anchor" aria-label="anchor" href="#useful-links"></a></h2>
+
+
+
+<p>The biplot display can be built up in four broad steps depending on the needs for the display.
+Firstly, choose an appropriate method to construct the display;
+Secondly, change the aesthetics of the display;
+Thirdly, append the display with supplementary features such as axes, samples and means;
+Finally, superimpose shapes, characters or elements onto the display.</p>
+<p><strong>1. Different types of biplots:</strong></p><ul><li><p><code><a href="PCA.html">PCA()</a></code>: Principal Component Analysis biplot of various dimensions</p></li>
+<li><p><code><a href="CVA.html">CVA()</a></code>: Canonical Variate Analysis biplot</p></li>
+<li><p><code><a href="PCO.html">PCO()</a></code>: Principal Coordinate Analysis biplot</p></li>
+<li><p><code><a href="CA.html">CA()</a></code>: Correspondence Analysis biplot</p></li>
+<li><p><code><a href="regress.html">regress()</a></code>: Regression biplot method</p></li>
+</ul><p><strong>2. Customise the biplot display with aesthetic functions:</strong></p><ul><li><p><code><a href="samples.html">samples()</a></code>: Change the formatting of sample points on the biplot display</p></li>
+<li><p><code><a href="axes.html">axes()</a></code>: Change the formatting of the biplot axes</p></li>
+</ul><p><strong>3. Supplement the existing biplot with additional axes, samples and group means:</strong></p><ul><li><p><code><a href="newsamples.html">newsamples()</a></code>: Add and change formatting of additional samples</p></li>
+<li><p><code><a href="newaxes.html">newaxes()</a></code>: Add and change formatting of additional axes</p></li>
+<li><p><code><a href="means.html">means()</a></code>: Insert class means to the display, and format appropriately</p></li>
+</ul><p><strong>4. Append the biplot display:</strong></p><ul><li><p><code><a href="alpha.bags.html">alpha.bags()</a></code>: Add \(\alpha\)-bags</p></li>
+<li><p><code><a href="ellipses.html">ellipses()</a></code>: Add ellipses</p></li>
+<li><p><code><a href="density2D.html">density2D()</a></code>: Add 2D density regions</p></li>
+</ul><p><strong>Other useful links:</strong></p><ul><li><p><code><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot()</a></code></p></li>
+<li><p><code><a href="fit.measures.html">fit.measures()</a></code></p></li>
+<li><p><code><a href="legend.type.html">legend.type()</a></code></p></li>
+<li><p><code><a href="interpolate.html">interpolate()</a></code></p></li>
+<li><p><code><a href="prediction.html">prediction()</a></code></p></li>
+<li><p><code><a href="classify.html">classify()</a></code></p></li>
+<li><p><code><a href="reflect.html">reflect()</a></code></p></li>
+<li><p><code><a href="rotate.html">rotate()</a></code></p></li>
+</ul></div>
+    <div class="section level2">
+    <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a></h2>
+    <p>Gabriel, K.R. (1971) The biplot graphic display of matrices with application to principal component analysis. <em>Biometrika.</em> 58(3):453–467.</p>
+<p>Gower, J., Gardner-Lubbe, S. &amp; Le Roux, N. (2011, ISBN: 978-0-470-01255-0) <em>Understanding Biplots.</em> Chichester, England: John Wiley &amp; Sons Ltd.</p>
+<p>Gower, J.C. &amp; Hand, D.J.(1996, ISBN: 0-412-71630-5) <em>Biplots.</em> London: Chapman &amp; Hall.</p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu">biplot</span><span class="op">(</span>data <span class="op">=</span> <span class="va">iris</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Object of class biplot, based on 150 samples and 5 variables.</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 4 numeric variables.</span>
@@ -161,29 +197,26 @@ <h2>Examples</h2>
 <span class="r-in"><span><span class="co"># create a PCA biplot</span></span></span>
 <span class="r-in"><span><span class="fu">biplot</span><span class="op">(</span>data <span class="op">=</span> <span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="biplot-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span></span></span>
 </code></pre></div>
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-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
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+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
 
 
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-  <p></p><p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
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diff --git a/docs/reference/biplotEZ.html b/docs/reference/biplotEZ.html
index e35d0ce..0b31588 100644
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+++ b/docs/reference/biplotEZ.html
@@ -1,94 +1,68 @@
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+      <img src="../logo.png" class="logo" alt=""><h1>biplotEZ: EZ-to-Use Biplots</h1>
+
+      <div class="d-none name"><code>biplotEZ.Rd</code></div>
     </div>
 
-    <div class="ref-description">
+    <div class="ref-description section level2">
     <p></p>
     </div>
 
 
-    <div id="details">
-    <h2>Details</h2>
+    <div class="section level2">
+    <h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></a></h2>
     <p>The goal of biplotEZ is to provide users an EZ-to-use platform for visually representing
 their data with biplots. Currently, this package includes principal component analysis
 (PCA) and canonical variate analysis (CVA) biplots. This is accompanied by various
 formatting options for the samples and axes. Alpha-bags and concentration ellipses are
 included for visual enhancements and interpretation.</p>
     </div>
-    <div id="details">
-    <h2>Details</h2>
-    
+    <div class="section level2">
+    <h2 id="details-1">Details<a class="anchor" aria-label="anchor" href="#details-1"></a></h2>
+
 
 
 <table class="table table"><tr><td>Package:</td><td>biplotEZ</td></tr><tr><td>Type:</td><td>Package</td></tr><tr><td>Version:</td><td>2.0</td></tr><tr><td>Date:</td><td>05-04-2024</td></tr><tr><td>License:</td><td>MIT</td></tr><tr><td>LazyLoad:</td><td>TRUE</td></tr></table></div>
-    <div id="author-s-">
-    <h2>Author(s)</h2>
-    
+    <div class="section level2">
+    <h2 id="author-s-">Author(s)<a class="anchor" aria-label="anchor" href="#author-s-"></a></h2>
+
 
 
 <ul><li><p>Sugnet Lubbe (Maintainer, muvisu@sun.ac.za)</p></li>
@@ -99,45 +73,41 @@ <h2>Author(s)</h2>
 <li><p>Zoë-Mae Adams</p></li>
 <li><p>Peter Manefeldt</p></li>
 </ul></div>
-    <div id="core-functions">
-    <h2>Core Functions</h2>
-    
+    <div class="section level2">
+    <h2 id="core-functions">Core Functions<a class="anchor" aria-label="anchor" href="#core-functions"></a></h2>
+
 
 <ul><li><p><a href="biplot.html">biplot</a></p></li>
 <li><p><a href="PCA.html">PCA</a></p></li>
 <li><p><a href="CVA.html">CVA</a></p></li>
 <li><p><a href="CA.html">CA</a></p></li>
 </ul></div>
-    <div id="code-availability">
-    <h2>Code Availability</h2>
-    
+    <div class="section level2">
+    <h2 id="code-availability">Code Availability<a class="anchor" aria-label="anchor" href="#code-availability"></a></h2>
+
 
 
 <p>The newest version of the package can be obtained on
 GitHub: <a href="https://github.com/MuViSU/biplotEZ" class="external-link">https://github.com/MuViSU/biplotEZ</a></p>
     </div>
 
-  </div>
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
-    </nav></div>
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+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
 
 
-      <footer><div class="copyright">
-  <p></p><p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
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diff --git a/docs/reference/classification-1.png b/docs/reference/classification-1.png
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diff --git a/docs/reference/classification.biplot.html b/docs/reference/classification.biplot.html
new file mode 100644
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--- /dev/null
+++ b/docs/reference/classification.biplot.html
@@ -0,0 +1,129 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>classification biplot — classification.biplot • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="classification biplot — classification.biplot"><meta name="description" content="Performs calculations for a classification biplot."><meta property="og:description" content="Performs calculations for a classification biplot."><meta property="og:image" content="/logo.png"></head><body>
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+    <li><a class="dropdown-item" href="../articles/Class_separation.html">Biplots for separating classes</a></li>
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+    <li><a class="dropdown-item" href="../articles/Biplots_in_1D.html">One dimensional biplots</a></li>
+    <li><a class="dropdown-item" href="../articles/Biplots_in_3D.html">Three dimensional biplots</a></li>
+  </ul></li>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+      </ul></div>
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+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>classification biplot</h1>
+
+      <div class="d-none name"><code>classification.biplot.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>Performs calculations for a classification biplot.</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'biplot'</span></span>
+<span><span class="fu"><a href="classification.html">classification</a></span><span class="op">(</span></span>
+<span>  <span class="va">bp</span>,</span>
+<span>  <span class="va">Pmat</span>,</span>
+<span>  dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>, <span class="fl">1</span>, <span class="fl">3</span><span class="op">)</span>,</span>
+<span>  e.vects <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>,</span>
+<span>  group.aes <span class="op">=</span> <span class="cn">NULL</span>,</span>
+<span>  axes <span class="op">=</span> <span class="st">"regression"</span>,</span>
+<span>  col <span class="op">=</span> <span class="va">ez.col</span>,</span>
+<span>  opacity <span class="op">=</span> <span class="fl">0.4</span>,</span>
+<span>  borders <span class="op">=</span> <span class="cn">FALSE</span></span>
+<span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
+
+
+<dt id="arg-pmat">Pmat<a class="anchor" aria-label="anchor" href="#arg-pmat"></a></dt>
+<dd><p>a matrix containing the posterior probability for the classes</p></dd>
+
+
+<dt id="arg-dim-biplot">dim.biplot<a class="anchor" aria-label="anchor" href="#arg-dim-biplot"></a></dt>
+<dd><p>dimension of the biplot. Only values 1, 2 and 3 are accepted, with default <code>2</code>.</p></dd>
+
+
+<dt id="arg-e-vects">e.vects<a class="anchor" aria-label="anchor" href="#arg-e-vects"></a></dt>
+<dd><p>which eigenvectors (principal components) to extract, with default <code>1:dim.biplot</code>.</p></dd>
+
+
+<dt id="arg-group-aes">group.aes<a class="anchor" aria-label="anchor" href="#arg-group-aes"></a></dt>
+<dd><p>vector of the same length as the number of rows in the data matrix
+for differentiated aesthetics for samples.</p></dd>
+
+
+<dt id="arg-axes">axes<a class="anchor" aria-label="anchor" href="#arg-axes"></a></dt>
+<dd><p>type of axes, defaults to "regression"</p></dd>
+
+
+<dt id="arg-col">col<a class="anchor" aria-label="anchor" href="#arg-col"></a></dt>
+<dd><p>colour of the classification regions</p></dd>
+
+
+<dt id="arg-opacity">opacity<a class="anchor" aria-label="anchor" href="#arg-opacity"></a></dt>
+<dd><p>opacity of classification regions</p></dd>
+
+
+<dt id="arg-borders">borders<a class="anchor" aria-label="anchor" href="#arg-borders"></a></dt>
+<dd><p>logical, indicating whether borders should be added to classification regions</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>an object of class biplot.</p>
+    </div>
+
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
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+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
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+<div class="pkgdown-footer-right">
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index 26d652b..cdf3933 100644
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-    <div class="page-header">
-    <h1>Classification biplot method</h1>
-    
-    <div class="hidden name"><code>classification.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Classification biplot method</h1>
+
+      <div class="d-none name"><code>classification.Rd</code></div>
     </div>
 
-    <div class="ref-description">
+    <div class="ref-description section level2">
     <p>This function produces a list of elements to be used for constructing a classification biplot.</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">classification</span><span class="op">(</span><span class="va">bp</span>, <span class="va">Pmat</span>, dim.biplot <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>, <span class="fl">1</span>, <span class="fl">3</span><span class="op">)</span>, e.vects <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">ncol</a></span><span class="op">(</span><span class="va">bp</span><span class="op">$</span><span class="va">X</span><span class="op">)</span>,</span>
 <span>group.aes<span class="op">=</span><span class="cn">NULL</span>, axes <span class="op">=</span> <span class="st">"regression"</span>, col<span class="op">=</span><span class="va">ez.col</span>, opacity<span class="op">=</span><span class="fl">0.4</span>, borders <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
 
 
-<dt>Pmat</dt>
+<dt id="arg-pmat">Pmat<a class="anchor" aria-label="anchor" href="#arg-pmat"></a></dt>
 <dd><p>a matrix containing the posterior probability for the classes</p></dd>
 
 
-<dt>dim.biplot</dt>
+<dt id="arg-dim-biplot">dim.biplot<a class="anchor" aria-label="anchor" href="#arg-dim-biplot"></a></dt>
 <dd><p>dimension of the biplot. Only values 1, 2 and 3 are accepted, with default <code>2</code>.</p></dd>
 
 
-<dt>e.vects</dt>
+<dt id="arg-e-vects">e.vects<a class="anchor" aria-label="anchor" href="#arg-e-vects"></a></dt>
 <dd><p>which eigenvectors (principal components) to extract, with default <code>1:dim.biplot</code>.</p></dd>
 
 
-<dt>group.aes</dt>
+<dt id="arg-group-aes">group.aes<a class="anchor" aria-label="anchor" href="#arg-group-aes"></a></dt>
 <dd><p>vector of the same length as the number of rows in the data matrix
 for differentiated aesthetics for samples.</p></dd>
 
 
-<dt>axes</dt>
+<dt id="arg-axes">axes<a class="anchor" aria-label="anchor" href="#arg-axes"></a></dt>
 <dd><p>type of axes, defaults to "regression"</p></dd>
 
 
-<dt>col</dt>
+<dt id="arg-col">col<a class="anchor" aria-label="anchor" href="#arg-col"></a></dt>
 <dd><p>colour of the classification regions</p></dd>
 
 
-<dt>opacity</dt>
+<dt id="arg-opacity">opacity<a class="anchor" aria-label="anchor" href="#arg-opacity"></a></dt>
 <dd><p>opacity of classification regions</p></dd>
 
 
-<dt>borders</dt>
+<dt id="arg-borders">borders<a class="anchor" aria-label="anchor" href="#arg-borders"></a></dt>
 <dd><p>logical, indicating whether borders should be added to classification regions</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>Object of class biplot with the following elements:</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>Object of class biplot with the following elements:</p>
     </div>
-    <div id="references">
-    <h2>References</h2>
+    <div class="section level2">
+    <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a></h2>
     <p>Gardner-Lubbe, S., 2016. A triplot for multiclass classification visualisation. <em>Computational Statistics &amp; Data Analysis</em>, 94, pp.20-32.</p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
 <span class="r-in"><span><span class="fu">classification</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/predict.html" class="external-link">predict</a></span><span class="op">(</span><span class="fu">MASS</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/MASS/man/lda.html" class="external-link">lda</a></span><span class="op">(</span><span class="va">Species</span> <span class="op">~</span> <span class="va">.</span>, data <span class="op">=</span> <span class="va">iris</span><span class="op">)</span><span class="op">)</span><span class="op">$</span><span class="va">posterior</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Object of class biplot, based on 150 samples and 4 variables.</span>
@@ -136,31 +111,26 @@ <h2>Examples</h2>
 <span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
 <span class="r-in"><span><span class="fu">classification</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/predict.html" class="external-link">predict</a></span><span class="op">(</span><span class="fu">MASS</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/MASS/man/lda.html" class="external-link">lda</a></span><span class="op">(</span><span class="va">Species</span> <span class="op">~</span> <span class="va">.</span>, data <span class="op">=</span> <span class="va">iris</span><span class="op">)</span><span class="op">)</span><span class="op">$</span><span class="va">posterior</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
-<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>no non-missing arguments to min; returning Inf</span>
 <span class="r-plt img"><img src="classification-1.png" alt="" width="700" height="433"></span>
 </code></pre></div>
     </div>
-  </div>
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
-    </nav></div>
-</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
 
 
-      <footer><div class="copyright">
-  <p></p><p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.</p>
+<div class="pkgdown-footer-right">
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diff --git a/docs/reference/classify-1.png b/docs/reference/classify-1.png
index 980c430..d797625 100644
Binary files a/docs/reference/classify-1.png and b/docs/reference/classify-1.png differ
diff --git a/docs/reference/classify.html b/docs/reference/classify.html
index 115f915..f4a90f8 100644
--- a/docs/reference/classify.html
+++ b/docs/reference/classify.html
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-    <div class="page-header">
-    <h1>Classification of samples into classes</h1>
-    
-    <div class="hidden name"><code>classify.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
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+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Classify samples into classes</h1>
+
+      <div class="d-none name"><code>classify.Rd</code></div>
     </div>
 
-    <div class="ref-description">
-    <p>Classification of samples into classes</p>
+    <div class="ref-description section level2">
+    <p>Classify samples into classes</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">classify</span><span class="op">(</span></span>
 <span>  <span class="va">bp</span>,</span>
 <span>  classify.regions <span class="op">=</span> <span class="cn">TRUE</span>,</span>
@@ -81,66 +56,72 @@ <h1>Classification of samples into classes</h1>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
-<dd><p>object of class <code>biplot</code></p></dd>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
 
 
-<dt>classify.regions</dt>
-<dd><p>logical indicating whether classifications regions are
-shown in the biplot</p></dd>
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code></p></dd>
+
+
+<dt id="arg-classify-regions">classify.regions<a class="anchor" aria-label="anchor" href="#arg-classify-regions"></a></dt>
+<dd><p>a logical value indicating whether classifications regions should be
+shown in the biplot, with default <code>TRUE</code>.</p></dd>
 
 
-<dt>col</dt>
-<dd><p>color of classification regions</p></dd>
+<dt id="arg-col">col<a class="anchor" aria-label="anchor" href="#arg-col"></a></dt>
+<dd><p>the colours of the classification regions</p></dd>
 
 
-<dt>opacity</dt>
-<dd><p>opacity of classification regions</p></dd>
+<dt id="arg-opacity">opacity<a class="anchor" aria-label="anchor" href="#arg-opacity"></a></dt>
+<dd><p>the opacity levels of the classification regions</p></dd>
 
 
-<dt>borders</dt>
-<dd><p>border colour of classification regions</p></dd>
+<dt id="arg-borders">borders<a class="anchor" aria-label="anchor" href="#arg-borders"></a></dt>
+<dd><p>the border colours of the classification regions</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>A list object called <code>classify</code> appended to the object of class <code>biplot</code> with the following elements:</p>
+<dl><dt>table</dt>
+<dd><p>the confusion matrix resulting from the classification into classes.</p></dd>
 
-<p>An object of class <code>biplot</code></p>
+<dt>rate</dt>
+<dd><p>the classification accuracy rate.</p></dd>
 
+<dt>classify.regions</dt>
+<dd><p>a logical value indicating whether classification regions are shown in the biplot.</p></dd>
 
-    </div>
+<dt>aes</dt>
+<dd><p>a list of chosen aesthetics for the colours, opacity levels and border colours of the classification regions.</p></dd>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
-    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span>,classes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="CVA.html">CVA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="axes.html">axes</a></span><span class="op">(</span>col <span class="op">=</span> <span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
-<span class="r-in"><span>  <span class="fu">classify</span><span class="op">(</span>col <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"red"</span>,<span class="st">"blue"</span>,<span class="st">"orange"</span><span class="op">)</span>, opacity <span class="op">=</span> <span class="fl">0.1</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+</dl></div>
+
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span>,classes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="CVA.html">CVA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="axes.html">axes</a></span><span class="op">(</span>col<span class="op">=</span><span class="st">"black"</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
+<span class="r-in"><span>  <span class="fu">classify</span><span class="op">(</span>col<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"red"</span>,<span class="st">"blue"</span>,<span class="st">"orange"</span><span class="op">)</span>,opacity<span class="op">=</span><span class="fl">0.1</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="classify-1.png" alt="" width="700" height="433"></span>
 </code></pre></div>
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diff --git a/docs/reference/density1D-1.png b/docs/reference/density1D-1.png
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+++ b/docs/reference/density1D.html
@@ -0,0 +1,123 @@
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+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Creates a kernel density in 1-dimension</h1>
+
+      <div class="d-none name"><code>density1D.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>Creates a kernel density in 1-dimension</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">density1D</span><span class="op">(</span></span>
+<span>  <span class="va">bp</span>,</span>
+<span>  which <span class="op">=</span> <span class="cn">NULL</span>,</span>
+<span>  h <span class="op">=</span> <span class="st">"nrd0"</span>,</span>
+<span>  kernel <span class="op">=</span> <span class="st">"gaussian"</span>,</span>
+<span>  col <span class="op">=</span> <span class="va">ez.col</span>,</span>
+<span>  lwd <span class="op">=</span> <span class="fl">1.5</span>,</span>
+<span>  legend.mar <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">2</span>, <span class="fl">5</span>, <span class="fl">0</span>, <span class="fl">5</span><span class="op">)</span></span>
+<span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>object of class <code>biplot</code></p></dd>
+
+
+<dt id="arg-which">which<a class="anchor" aria-label="anchor" href="#arg-which"></a></dt>
+<dd><p>which group.</p></dd>
+
+
+<dt id="arg-h">h<a class="anchor" aria-label="anchor" href="#arg-h"></a></dt>
+<dd><p>bandwidth.</p></dd>
+
+
+<dt id="arg-kernel">kernel<a class="anchor" aria-label="anchor" href="#arg-kernel"></a></dt>
+<dd><p>character string giving the smoothing kernel to be used.</p></dd>
+
+
+<dt id="arg-col">col<a class="anchor" aria-label="anchor" href="#arg-col"></a></dt>
+<dd><p>colours to be used for each of the density curves.</p></dd>
+
+
+<dt id="arg-lwd">lwd<a class="anchor" aria-label="anchor" href="#arg-lwd"></a></dt>
+<dd><p>linewidth of density curve.</p></dd>
+
+
+<dt id="arg-legend-mar">legend.mar<a class="anchor" aria-label="anchor" href="#arg-legend-mar"></a></dt>
+<dd><p>The margin line of the legend.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>An object of class <code>biplot</code>.</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span> <span class="op">(</span><span class="va">iris</span>,classes<span class="op">=</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="CVA.html">CVA</a></span><span class="op">(</span>dim<span class="op">=</span><span class="fl">1</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">density1D</span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="density1D-1.png" alt="" width="700" height="433"></span>
+</code></pre></div>
+    </div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
+
+
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+</div>
+
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.2.</p>
+</div>
+
+    </footer></div>
+
+
+
+
+
+  </body></html>
+
diff --git a/docs/reference/density2D-1.png b/docs/reference/density2D-1.png
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diff --git a/docs/reference/density2D.html b/docs/reference/density2D.html
index efe0f9e..4a1df47 100644
--- a/docs/reference/density2D.html
+++ b/docs/reference/density2D.html
@@ -1,77 +1,52 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Create a density in 2-dimensions — density2D • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.1/jquery.min.js" integrity="sha512-v2CJ7UaYy4JwqLDIrZUI/4hqeoQieOmAZNXBeQyjo21dadnwR+8ZaIJVT8EE2iyI61OV8e6M8PP2/4hpQINQ/g==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Create a density in 2-dimensions — density2D"><meta property="og:description" content="Create a density in 2-dimensions"><meta property="og:image" content="/logo.png"><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Create a density in 2-dimensions — density2D • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Create a density in 2-dimensions — density2D"><meta name="description" content="Create a density in 2-dimensions"><meta property="og:description" content="Create a density in 2-dimensions"><meta property="og:image" content="/logo.png"></head><body>
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-  <div class="col-md-9 contents">
-    <div class="page-header">
-    <h1>Create a density in 2-dimensions</h1>
-    
-    <div class="hidden name"><code>density2D.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+      </ul></div>
+
+
+  </div>
+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Create a density in 2-dimensions</h1>
+
+      <div class="d-none name"><code>density2D.Rd</code></div>
     </div>
 
-    <div class="ref-description">
+    <div class="ref-description section level2">
     <p>Create a density in 2-dimensions</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">density2D</span><span class="op">(</span></span>
 <span>  <span class="va">bp</span>,</span>
 <span>  which <span class="op">=</span> <span class="cn">NULL</span>,</span>
@@ -89,70 +64,71 @@ <h1>Create a density in 2-dimensions</h1>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>object of class <code>biplot</code></p></dd>
 
 
-<dt>which</dt>
-<dd><p>which group.</p></dd>
+<dt id="arg-which">which<a class="anchor" aria-label="anchor" href="#arg-which"></a></dt>
+<dd><p>which group to create a density; limited to only a single group at a time.
+If NULL, density drawn over all data points.</p></dd>
 
 
-<dt>contours</dt>
+<dt id="arg-contours">contours<a class="anchor" aria-label="anchor" href="#arg-contours"></a></dt>
 <dd><p>logical indicating whether contours are added to the density plot</p></dd>
 
 
-<dt>h</dt>
+<dt id="arg-h">h<a class="anchor" aria-label="anchor" href="#arg-h"></a></dt>
 <dd><p>vector of bandwidths for x and y directions, see <code><a href="https://rdrr.io/pkg/MASS/man/kde2d.html" class="external-link">kde2d</a></code>.</p></dd>
 
 
-<dt>n</dt>
+<dt id="arg-n">n<a class="anchor" aria-label="anchor" href="#arg-n"></a></dt>
 <dd><p>number of grid points in each direction. Can be scalar or a length-2 integer
 vector.</p></dd>
 
 
-<dt>col</dt>
+<dt id="arg-col">col<a class="anchor" aria-label="anchor" href="#arg-col"></a></dt>
 <dd><p>vector of colours to use to form a 'continuous' sequence of colours.</p></dd>
 
 
-<dt>contour.col</dt>
+<dt id="arg-contour-col">contour.col<a class="anchor" aria-label="anchor" href="#arg-contour-col"></a></dt>
 <dd><p>colour of the contours.</p></dd>
 
 
-<dt>cuts</dt>
+<dt id="arg-cuts">cuts<a class="anchor" aria-label="anchor" href="#arg-cuts"></a></dt>
 <dd><p>number of colours in <code>col</code>.</p></dd>
 
 
-<dt>cex</dt>
+<dt id="arg-cex">cex<a class="anchor" aria-label="anchor" href="#arg-cex"></a></dt>
 <dd><p>character expansion.</p></dd>
 
 
-<dt>tcl</dt>
+<dt id="arg-tcl">tcl<a class="anchor" aria-label="anchor" href="#arg-tcl"></a></dt>
 <dd><p>The length of tick marks as a fraction of the height of a line of text.</p></dd>
 
 
-<dt>mgp</dt>
+<dt id="arg-mgp">mgp<a class="anchor" aria-label="anchor" href="#arg-mgp"></a></dt>
 <dd><p>The margin line.</p></dd>
 
 
-<dt>layout.heights</dt>
+<dt id="arg-layout-heights">layout.heights<a class="anchor" aria-label="anchor" href="#arg-layout-heights"></a></dt>
 <dd><p>A vector of values for the heights of rows.</p></dd>
 
 
-<dt>legend.mar</dt>
+<dt id="arg-legend-mar">legend.mar<a class="anchor" aria-label="anchor" href="#arg-legend-mar"></a></dt>
 <dd><p>The margin line of the legend.</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>An object of class <code>biplot</code>.</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>An object of class <code>biplot</code>.</p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span>,group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
 <span class="r-in"><span>  <span class="fu">density2D</span><span class="op">(</span>which<span class="op">=</span><span class="fl">3</span>,col<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"white"</span>,<span class="st">"purple"</span>,<span class="st">"cyan"</span>,<span class="st">"blue"</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="density2D-1.png" alt="" width="700" height="433"></span>
@@ -162,27 +138,23 @@ <h2>Examples</h2>
 <span class="r-plt img"><img src="density2D-2.png" alt="" width="700" height="433"></span>
 </code></pre></div>
     </div>
-  </div>
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
-    </nav></div>
-</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
 
 
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diff --git a/docs/reference/ellipses-1.png b/docs/reference/ellipses-1.png
index 4d62532..cd00227 100644
Binary files a/docs/reference/ellipses-1.png and b/docs/reference/ellipses-1.png differ
diff --git a/docs/reference/ellipses.html b/docs/reference/ellipses.html
index fdba0ed..4a7a1b6 100644
--- a/docs/reference/ellipses.html
+++ b/docs/reference/ellipses.html
@@ -1,131 +1,107 @@
 <!DOCTYPE html>
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-    <div class="page-header">
-    <h1>Concentration ellipses (\(\kappa\)-ellipses)</h1>
-    
-    <div class="hidden name"><code>ellipses.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Concentration ellipses (\(\kappa\)-ellipses)</h1>
+
+      <div class="d-none name"><code>ellipses.Rd</code></div>
     </div>
 
-    <div class="ref-description">
+    <div class="ref-description section level2">
     <p>This function produces \(\kappa\)-ellipses, which is a useful geometrical description of the
 data points about the sample mean.</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">ellipses</span><span class="op">(</span><span class="va">bp</span>, df<span class="op">=</span><span class="fl">2</span>, kappa <span class="op">=</span> <span class="cn">NULL</span>, which <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>alpha <span class="op">=</span> <span class="fl">0.95</span>, col <span class="op">=</span> <span class="va">bp</span><span class="op">$</span><span class="va">sample</span><span class="op">$</span><span class="va">col</span><span class="op">[</span><span class="va">which</span><span class="op">]</span>, lty <span class="op">=</span> <span class="fl">1</span>, lwd <span class="op">=</span> <span class="fl">1</span>,</span>
 <span>opacity <span class="op">=</span> <span class="fl">0.25</span>, trace <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>an object of class <code>biplot</code>.</p></dd>
 
 
-<dt>df</dt>
+<dt id="arg-df">df<a class="anchor" aria-label="anchor" href="#arg-df"></a></dt>
 <dd><p>degrees of freedom, with default <code>2</code>.</p></dd>
 
 
-<dt>kappa</dt>
+<dt id="arg-kappa">kappa<a class="anchor" aria-label="anchor" href="#arg-kappa"></a></dt>
 <dd><p>value to construct \(\kappa\)-ellipse (the value of \(\kappa\)).</p></dd>
 
 
-<dt>which</dt>
+<dt id="arg-which">which<a class="anchor" aria-label="anchor" href="#arg-which"></a></dt>
 <dd><p>the selection of the group for ellipse construction.</p></dd>
 
 
-<dt>alpha</dt>
+<dt id="arg-alpha">alpha<a class="anchor" aria-label="anchor" href="#arg-alpha"></a></dt>
 <dd><p>size of \(\alpha\)-bag, with default <code>0.95</code>.</p></dd>
 
 
-<dt>col</dt>
+<dt id="arg-col">col<a class="anchor" aria-label="anchor" href="#arg-col"></a></dt>
 <dd><p>colour of ellipse. Multiple \(\kappa\)-ellipse for one group will be displayed in the same colour.</p></dd>
 
 
-<dt>lty</dt>
+<dt id="arg-lty">lty<a class="anchor" aria-label="anchor" href="#arg-lty"></a></dt>
 <dd><p>line type of ellipse. The same line type will be used per value of \(\kappa\).</p></dd>
 
 
-<dt>lwd</dt>
+<dt id="arg-lwd">lwd<a class="anchor" aria-label="anchor" href="#arg-lwd"></a></dt>
 <dd><p>line width of ellipse. The same line width will be used per value of \(\kappa\).</p></dd>
 
 
-<dt>opacity</dt>
+<dt id="arg-opacity">opacity<a class="anchor" aria-label="anchor" href="#arg-opacity"></a></dt>
 <dd><p>level of opacity, with default <code>0.25</code>.</p></dd>
 
 
-<dt>trace</dt>
+<dt id="arg-trace">trace<a class="anchor" aria-label="anchor" href="#arg-trace"></a></dt>
 <dd><p>logical, indicating progress of computation.</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>A list with the following components is available:</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>A list with the following components is available:</p>
 <dl><dt>conc.ellipses</dt>
 <dd><p>list of coordinates for the \(\kappa\)-ellipses for each group.</p></dd>
 
@@ -142,13 +118,13 @@ <h2>Value</h2>
 <dd><p>vector of \(\alpha\) values.</p></dd>
 
 </dl></div>
-    <div id="references">
-    <h2>References</h2>
+    <div class="section level2">
+    <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a></h2>
     <p>Gower, J., Gardner-Lubbe, S. &amp; Le Roux, N. (2011, ISBN: 978-0-470-01255-0) <em>Understanding Biplots.</em> Chichester, England: John Wiley &amp; Sons Ltd.<br><br></p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span> <span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span>group.aes<span class="op">=</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">ellipses</span><span class="op">(</span>kappa<span class="op">=</span><span class="fl">2</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Computing 2 -ellipse for setosa </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Computing 2 -ellipse for versicolor </span>
@@ -157,27 +133,23 @@ <h2>Examples</h2>
 <span class="r-in"><span></span></span>
 </code></pre></div>
     </div>
-  </div>
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
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-</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
 
 
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+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
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+<div class="pkgdown-footer-right">
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diff --git a/docs/reference/extended.matching.coefficient.html b/docs/reference/extended.matching.coefficient.html
new file mode 100644
index 0000000..2d48181
--- /dev/null
+++ b/docs/reference/extended.matching.coefficient.html
@@ -0,0 +1,225 @@
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Extended matching coefficient</h1>
+
+      <div class="d-none name"><code>extended.matching.coefficient.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>Extended matching coefficient</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">extended.matching.coefficient</span><span class="op">(</span><span class="va">X</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-x">X<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
+<dd><p>a data frame containing the categorical variables used for computing the EMC distance</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>a dist object</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="va">mtdf</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/as.data.frame.html" class="external-link">as.data.frame</a></span><span class="op">(</span><span class="va">mtcars</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">cyl</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">cyl</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">vs</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">vs</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">am</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">am</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">gear</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">gear</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">mtdf</span><span class="op">$</span><span class="va">carb</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">factor</a></span><span class="op">(</span><span class="va">mtdf</span><span class="op">$</span><span class="va">carb</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu">extended.matching.coefficient</span><span class="op">(</span><span class="va">mtdf</span><span class="op">[</span>,<span class="fl">8</span><span class="op">:</span><span class="fl">11</span><span class="op">]</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>           1        2        3        4        5        6        7        8</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2  0.000000                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 3  1.414214 1.414214                                                      </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 4  2.000000 2.000000 1.414214                                             </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 5  1.732051 1.732051 2.000000 1.414214                                    </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 6  2.000000 2.000000 1.414214 0.000000 1.414214                           </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 7  1.414214 1.414214 2.000000 1.414214 1.000000 1.414214                  </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 8  1.732051 1.732051 1.414214 1.414214 1.414214 1.414214 1.732051         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 9  1.732051 1.732051 1.414214 1.414214 1.414214 1.414214 1.732051 0.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 10 1.414214 1.414214 1.414214 1.414214 1.732051 1.414214 1.414214 1.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 11 1.414214 1.414214 1.414214 1.414214 1.732051 1.414214 1.414214 1.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 12 1.732051 1.732051 2.000000 1.414214 1.000000 1.414214 1.000000 1.732051</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 13 1.732051 1.732051 2.000000 1.414214 1.000000 1.414214 1.000000 1.732051</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 14 1.732051 1.732051 2.000000 1.414214 1.000000 1.414214 1.000000 1.732051</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 15 1.414214 1.414214 2.000000 1.414214 1.000000 1.414214 0.000000 1.732051</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 16 1.414214 1.414214 2.000000 1.414214 1.000000 1.414214 0.000000 1.732051</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 17 1.414214 1.414214 2.000000 1.414214 1.000000 1.414214 0.000000 1.732051</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 18 1.414214 1.414214 0.000000 1.414214 2.000000 1.414214 2.000000 1.414214</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 19 1.414214 1.414214 1.000000 1.732051 1.732051 1.732051 2.000000 1.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 20 1.414214 1.414214 0.000000 1.414214 2.000000 1.414214 2.000000 1.414214</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 21 2.000000 2.000000 1.414214 0.000000 1.414214 0.000000 1.414214 1.414214</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 22 1.732051 1.732051 2.000000 1.414214 0.000000 1.414214 1.000000 1.414214</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 23 1.732051 1.732051 2.000000 1.414214 0.000000 1.414214 1.000000 1.414214</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 24 1.414214 1.414214 2.000000 1.414214 1.000000 1.414214 0.000000 1.732051</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 25 1.732051 1.732051 2.000000 1.414214 0.000000 1.414214 1.000000 1.414214</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 26 1.414214 1.414214 0.000000 1.414214 2.000000 1.414214 2.000000 1.414214</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 27 1.414214 1.414214 1.732051 2.000000 1.414214 2.000000 1.732051 1.732051</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 28 1.732051 1.732051 1.414214 1.732051 1.732051 1.732051 2.000000 1.414214</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 29 1.000000 1.000000 1.732051 2.000000 1.732051 2.000000 1.414214 2.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 30 1.414214 1.414214 1.732051 2.000000 1.732051 2.000000 1.732051 2.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 31 1.414214 1.414214 1.732051 2.000000 1.732051 2.000000 1.732051 2.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 32 1.414214 1.414214 1.000000 1.732051 1.732051 1.732051 2.000000 1.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>           9       10       11       12       13       14       15       16</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 3                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 4                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 5                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 6                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 7                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 8                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 9                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 10 1.000000                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 11 1.000000 0.000000                                                      </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 12 1.732051 1.732051 1.732051                                             </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 13 1.732051 1.732051 1.732051 0.000000                                    </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 14 1.732051 1.732051 1.732051 0.000000 0.000000                           </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 15 1.732051 1.414214 1.414214 1.000000 1.000000 1.000000                  </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 16 1.732051 1.414214 1.414214 1.000000 1.000000 1.000000 0.000000         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 17 1.732051 1.414214 1.414214 1.000000 1.000000 1.000000 0.000000 0.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 18 1.414214 1.414214 1.414214 2.000000 2.000000 2.000000 2.000000 2.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 19 1.000000 1.414214 1.414214 2.000000 2.000000 2.000000 2.000000 2.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 20 1.414214 1.414214 1.414214 2.000000 2.000000 2.000000 2.000000 2.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 21 1.414214 1.414214 1.414214 1.414214 1.414214 1.414214 1.414214 1.414214</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 22 1.414214 1.732051 1.732051 1.000000 1.000000 1.000000 1.000000 1.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 23 1.414214 1.732051 1.732051 1.000000 1.000000 1.000000 1.000000 1.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 24 1.732051 1.414214 1.414214 1.000000 1.000000 1.000000 0.000000 0.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 25 1.414214 1.732051 1.732051 1.000000 1.000000 1.000000 1.000000 1.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 26 1.414214 1.414214 1.414214 2.000000 2.000000 2.000000 2.000000 2.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 27 1.732051 2.000000 2.000000 1.732051 1.732051 1.732051 1.732051 1.732051</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 28 1.414214 1.732051 1.732051 2.000000 2.000000 2.000000 2.000000 2.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 29 2.000000 1.732051 1.732051 1.732051 1.732051 1.732051 1.414214 1.414214</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 30 2.000000 2.000000 2.000000 1.732051 1.732051 1.732051 1.732051 1.732051</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 31 2.000000 2.000000 2.000000 1.732051 1.732051 1.732051 1.732051 1.732051</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 32 1.000000 1.414214 1.414214 2.000000 2.000000 2.000000 2.000000 2.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>          17       18       19       20       21       22       23       24</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 3                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 4                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 5                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 6                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 7                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 8                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 9                                                                         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 10                                                                        </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 11                                                                        </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 12                                                                        </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 13                                                                        </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 14                                                                        </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 15                                                                        </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 16                                                                        </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 17                                                                        </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 18 2.000000                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 19 2.000000 1.000000                                                      </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 20 2.000000 0.000000 1.000000                                             </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 21 1.414214 1.414214 1.732051 1.414214                                    </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 22 1.000000 2.000000 1.732051 2.000000 1.414214                           </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 23 1.000000 2.000000 1.732051 2.000000 1.414214 0.000000                  </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 24 0.000000 2.000000 2.000000 2.000000 1.414214 1.000000 1.000000         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 25 1.000000 2.000000 1.732051 2.000000 1.414214 0.000000 0.000000 1.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 26 2.000000 0.000000 1.000000 0.000000 1.414214 2.000000 2.000000 2.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 27 1.732051 1.732051 1.414214 1.732051 2.000000 1.414214 1.414214 1.732051</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 28 2.000000 1.414214 1.000000 1.414214 1.732051 1.732051 1.732051 2.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 29 1.414214 1.732051 1.732051 1.732051 2.000000 1.732051 1.732051 1.414214</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 30 1.732051 1.732051 1.732051 1.732051 2.000000 1.732051 1.732051 1.732051</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 31 1.732051 1.732051 1.732051 1.732051 2.000000 1.732051 1.732051 1.732051</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 32 2.000000 1.000000 0.000000 1.000000 1.732051 1.732051 1.732051 2.000000</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span>          25       26       27       28       29       30       31</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2                                                                </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 3                                                                </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 4                                                                </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 5                                                                </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 6                                                                </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 7                                                                </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 8                                                                </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 9                                                                </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 10                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 11                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 12                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 13                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 14                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 15                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 16                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 17                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 18                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 19                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 20                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 21                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 22                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 23                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 24                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 25                                                               </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 26 2.000000                                                      </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 27 1.414214 1.732051                                             </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 28 1.732051 1.414214 1.000000                                    </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 29 1.732051 1.732051 1.000000 1.414214                           </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 30 1.732051 1.732051 1.000000 1.414214 1.000000                  </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 31 1.732051 1.732051 1.000000 1.414214 1.000000 1.000000         </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 32 1.732051 1.000000 1.414214 1.000000 1.732051 1.732051 1.732051</span>
+<span class="r-in"><span></span></span>
+</code></pre></div>
+    </div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
+
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+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
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-    <div class="page-header">
-    <h1>Compute measures of fit for biplot.</h1>
-    
-    <div class="hidden name"><code>fit.measures.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Compute measures of fit for the biplot.</h1>
+
+      <div class="d-none name"><code>fit.measures.Rd</code></div>
     </div>
 
-    <div class="ref-description">
-    <p>Compute measures of fit for biplot.</p>
+    <div class="ref-description section level2">
+    <p>This function computes the measures of fit for the biplot. The biplot object is augmented with additional items, which can differ depending on the type of biplot. The measures provide information on the overall quality of fit and the adequacy of representation of variables.</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">fit.measures</span><span class="op">(</span><span class="va">bp</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>an object of class <code>biplot</code>.</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>An object of class <code>biplot</code>. The object is augmented with
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>An object of class <code>biplot</code>. The object is augmented with
 additional items, depending on the type of biplot object.</p>
 <dl><dt>quality</dt>
-<dd><p>overall quality of fit.</p></dd>
+<dd><p>the overall quality of fit.</p></dd>
 
 <dt>adequacy</dt>
-<dd><p>adequacy of representation of variables.</p></dd>
+<dd><p>the adequacy of representation of variables.</p></dd>
 
 
 </dl><p>For an object of class <code>PCA</code>:</p>
 <dl><dt>axis.predictivity</dt>
-<dd><p>fit measure of each individual axis.</p></dd>
+<dd><p>the fit measure of each individual axis.</p></dd>
 
 <dt>sample.predictivity</dt>
-<dd><p>fit measure for each individual sample.</p></dd>
+<dd><p>the fit measure for each individual sample.</p></dd>
 
 </dl><p>For an object of class <code>CVA</code>:</p>
 <dl><dt>axis.predictivity</dt>
-<dd><p>fit measure of each individual axis.</p></dd>
+<dd><p>the fit measure of each individual axis.</p></dd>
 
 <dt>class.predictivity</dt>
-<dd><p>fit measure for each class mean.</p></dd>
+<dd><p>the fit measure for each class mean.</p></dd>
 
 <dt>within.class.axis.predictivity</dt>
-<dd><p>fit measure for each axis based on values
+<dd><p>the fit measure for each axis based on values
 expressed as deviations from their class means.</p></dd>
 
 <dt>within.class.sample.predictivity</dt>
-<dd><p>fit measure for each sample expressed as
+<dd><p>the fit measure for each sample expressed as
 deviation from its class mean.</p></dd>
 
+
+</dl><p>For an object of class <code>CA</code>:</p>
+<dl><dt>row.predictivity</dt>
+<dd><p>the fit measure for each row of the input matrix individual sample.</p></dd>
+
+<dt>col.predictivity</dt>
+<dd><p>the fit measure for each column of the input matrix individual sample.</p></dd>
+
+<dt>Xhat</dt>
+<dd><p>predicted matrix per row profile</p></dd>
+
 </dl></div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="va">out</span> <span class="op">&lt;-</span> <span class="fu"><a href="biplot.html">biplot</a></span> <span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">fit.measures</span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">out</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Object of class biplot, based on 150 samples and 4 variables.</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 4 numeric variables.</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Quality of fit = 97.8% </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Adequacy of variables:</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Quality of fit in 2 dimension(s) = 97.8% </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Adequacy of variables in 2 dimension(s):</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Sepal.Length  Sepal.Width Petal.Length  Petal.Width </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    0.5617091    0.5402798    0.7639426    0.1340685 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Axis predictivity:</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Axis predictivity in 2 dimension(s):</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Sepal.Length  Sepal.Width Petal.Length  Petal.Width </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    0.9579017    0.8400028    0.9980931    0.9365937 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Sample predictivity:</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Sample predictivity in 2 dimension(s):</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>         1         2         3         4         5         6         7         8 </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 0.9998927 0.9927400 0.9999141 0.9991226 0.9984312 0.9949770 0.9914313 0.9996346 </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>         9        10        11        12        13        14        15        16 </span>
@@ -171,29 +157,26 @@ <h2>Examples</h2>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 0.8947527 0.9797055 0.9458421 0.9902488 0.9674660 0.9350646 0.9636413 0.9867931 </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>       145       146       147       148       149       150 </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 0.9500265 0.9470544 0.9688318 0.9886543 0.8735433 0.9281727 </span>
+<span class="r-in"><span></span></span>
 </code></pre></div>
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+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Package index • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Package index"><meta property="og:image" content="/logo.png"></head><body>
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-      
 
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Package index</h1>
     </div>
 
-    <table class="ref-index"><colgroup><col class="alias"><col class="title"></colgroup><tbody><tr><th colspan="2">
-          <h2 id="all-functions">All functions <a href="#all-functions" class="anchor" aria-hidden="true"></a></h2>
-          <p class="section-desc"></p>
-        </th>
-      </tr></tbody><tbody><tr><td>
-          <p><code><a href="alpha.bags.html">alpha.bags()</a></code> </p>
-        </td>
-        <td><p>Create alpha bags</p></td>
-      </tr><tr><td>
-          <p><code><a href="AoD.biplot.html">AoD(<i>&lt;biplot&gt;</i>)</a></code> </p>
-        </td>
-        <td><p>Calculate elements for the Analysis of Distance (AoD) biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="AoD.html">AoD()</a></code> </p>
-        </td>
-        <td><p>Use the Analysis of Distance (AoD) method to construct the biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="axes.html">axes()</a></code> </p>
-        </td>
-        <td><p>Format aesthetics for the biplot axes</p></td>
-      </tr><tr><td>
-          <p><code><a href="axes_coordinates.html">axes_coordinates()</a></code> </p>
-        </td>
-        <td><p>Calibrate Biplot Axes</p></td>
-      </tr><tr><td>
-          <p><code><a href="biplot.html">biplot()</a></code> </p>
-        </td>
-        <td><p>First step to create a new biplot with <span class="pkg">biplotEZ</span></p></td>
-      </tr><tr><td>
-          <p><code><a href="biplotEZ.html">biplotEZ</a></code> </p>
-        </td>
-        <td><p>biplotEZ: EZ-to-Use Biplots</p></td>
-      </tr><tr><td>
-          <p><code><a href="CA.biplot.html">CA(<i>&lt;biplot&gt;</i>)</a></code> </p>
-        </td>
-        <td><p>CA biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="CA.html">CA()</a></code> </p>
-        </td>
-        <td><p>Correspondence Analysis (CA) method</p></td>
-      </tr><tr><td>
-          <p><code><a href="CATPCA.html">CATPCA()</a></code> </p>
-        </td>
-        <td><p>Categorical Principal Component Analysis</p></td>
-      </tr><tr><td>
-          <p><code><a href="classification.biplot.html">classification(<i>&lt;biplot&gt;</i>)</a></code> </p>
-        </td>
-        <td><p>classification biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="classification.html">classification()</a></code> </p>
-        </td>
-        <td><p>Classification biplot method</p></td>
-      </tr><tr><td>
-          <p><code><a href="classify.html">classify()</a></code> </p>
-        </td>
-        <td><p>Classify samples into classes</p></td>
-      </tr><tr><td>
-          <p><code><a href="CLPs.html">CLPs()</a></code> </p>
-        </td>
-        <td><p>Format aesthetics for the category level points</p></td>
-      </tr><tr><td>
-          <p><code><a href="CLRs.html">CLRs()</a></code> </p>
-        </td>
-        <td><p>Format aesthetics for the category level regions</p></td>
-      </tr><tr><td>
-          <p><code><a href="CVA.biplot.html">CVA(<i>&lt;biplot&gt;</i>)</a></code> </p>
-        </td>
-        <td><p>Calculate elements for the CVA biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="CVA.html">CVA()</a></code> </p>
-        </td>
-        <td><p>Perform Canonical Variate Analysis (CVA)</p></td>
-      </tr><tr><td>
-          <p><code><a href="CVAlowdim.html">CVAlowdim()</a></code> </p>
-        </td>
-        <td><p>Construct additional dimensions when the dimension of the canonical space is smaller than the dimension of the biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="density1D.html">density1D()</a></code> </p>
-        </td>
-        <td><p>Creates a kernel density in 1-dimension</p></td>
-      </tr><tr><td>
-          <p><code><a href="density2D.html">density2D()</a></code> </p>
-        </td>
-        <td><p>Create a density in 2-dimensions</p></td>
-      </tr><tr><td>
-          <p><code><a href="ellipses.html">ellipses()</a></code> </p>
-        </td>
-        <td><p>Concentration ellipses (\(\kappa\)-ellipses)</p></td>
-      </tr><tr><td>
-          <p><code><a href="extended.matching.coefficient.html">extended.matching.coefficient()</a></code> </p>
-        </td>
-        <td><p>Extended matching coefficient</p></td>
-      </tr><tr><td>
-          <p><code><a href="fit.measures.html">fit.measures()</a></code> </p>
-        </td>
-        <td><p>Compute measures of fit for the biplot.</p></td>
-      </tr><tr><td>
-          <p><code><a href="interpolate.html">interpolate()</a></code> </p>
-        </td>
-        <td><p>Interpolate supplementary points and variables to add to the biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="legend.type.html">legend.type()</a></code> </p>
-        </td>
-        <td><p>Format the legend for the biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="means.html">means()</a></code> </p>
-        </td>
-        <td><p>Format aesthetics for the class or group means</p></td>
-      </tr><tr><td>
-          <p><code><a href="newaxes.html">newaxes()</a></code> </p>
-        </td>
-        <td><p>Format aesthetics for the supplementary (new) biplot axes</p></td>
-      </tr><tr><td>
-          <p><code><a href="newsamples.html">newsamples()</a></code> </p>
-        </td>
-        <td><p>Format aesthetics for the supplementary (new) biplot samples</p></td>
-      </tr><tr><td>
-          <p><code><a href="PCA.biplot.html">PCA(<i>&lt;biplot&gt;</i>)</a></code> </p>
-        </td>
-        <td><p>Calculate elements for the PCA biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="PCA.html">PCA()</a></code> </p>
-        </td>
-        <td><p>Perform Principal Components Analysis (PCA)</p></td>
-      </tr><tr><td>
-          <p><code><a href="PCO.biplot.html">PCO(<i>&lt;biplot&gt;</i>)</a></code> </p>
-        </td>
-        <td><p>PCO biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="PCO.html">PCO()</a></code> </p>
-        </td>
-        <td><p>Principal Coordinate Analysis (PCO) biplot method</p></td>
-      </tr><tr><td>
-          <p><code><a href="plot.biplot.html">plot(<i>&lt;biplot&gt;</i>)</a></code> </p>
-        </td>
-        <td><p>Generic Plotting function of objects of class biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="prediction.html">prediction()</a></code> </p>
-        </td>
-        <td><p>Predict samples to display on the biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="print.biplot.html">print(<i>&lt;biplot&gt;</i>)</a></code> </p>
-        </td>
-        <td><p>Generic print function for objects of class biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="print.CA.html">print(<i>&lt;CA&gt;</i>)</a></code> </p>
-        </td>
-        <td><p>Generic print function of objects of class CA</p></td>
-      </tr><tr><td>
-          <p><code><a href="reflect.html">reflect()</a></code> </p>
-        </td>
-        <td><p>Reflect the biplot about a chosen axis</p></td>
-      </tr><tr><td>
-          <p><code><a href="regress.biplot.html">regress(<i>&lt;biplot&gt;</i>)</a></code> </p>
-        </td>
-        <td><p>Regression biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="regress.html">regress()</a></code> </p>
-        </td>
-        <td><p>Regression biplot method</p></td>
-      </tr><tr><td>
-          <p><code><a href="rotate.html">rotate()</a></code> </p>
-        </td>
-        <td><p>Rotate the biplot a chosen amount of degrees</p></td>
-      </tr><tr><td>
-          <p><code><a href="samples.html">samples()</a></code> </p>
-        </td>
-        <td><p>Format aesthetics for the biplot samples</p></td>
-      </tr><tr><td>
-          <p><code><a href="sqrtManhattan.html">sqrtManhattan()</a></code> </p>
-        </td>
-        <td><p>Computes the square root of the Manhattan distance
-An example of a Euclidean embeddable distance metric</p></td>
-      </tr><tr><td>
-          <p><code><a href="summary.biplot.html">summary(<i>&lt;biplot&gt;</i>)</a></code> </p>
-        </td>
-        <td><p>Generic summary function for objects of class biplot</p></td>
-      </tr><tr><td>
-          <p><code><a href="translate_axes.html">translate_axes()</a></code> </p>
-        </td>
-        <td><p>Translate biplot axes</p></td>
-      </tr></tbody></table></div>
-
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
-    </nav></div>
-</div>
+    <div class="section level2">
+      <h2 id="all-functions">All functions<a class="anchor" aria-label="anchor" href="#all-functions"></a></h2>
+
+
+
+
+    </div><div class="section level2">
+
+
+
+
+      <dl><dt>
+
+          <code><a href="alpha.bags.html">alpha.bags()</a></code>
+
+        </dt>
+        <dd>Create alpha bags</dd>
+      </dl><dl><dt>
+
+          <code><a href="AoD.biplot.html">AoD(<i>&lt;biplot&gt;</i>)</a></code>
+
+        </dt>
+        <dd>Calculate elements for the Analysis of Distance (AoD) biplot</dd>
+      </dl><dl><dt>
+
+          <code><a href="AoD.html">AoD()</a></code>
+
+        </dt>
+        <dd>Use the Analysis of Distance (AoD) method to construct the biplot</dd>
+      </dl><dl><dt>
+
+          <code><a href="axes.html">axes()</a></code>
+
+        </dt>
+        <dd>Format aesthetics for the biplot axes</dd>
+      </dl><dl><dt>
+
+          <code><a href="axes_coordinates.html">axes_coordinates()</a></code>
+
+        </dt>
+        <dd>Calibrate Biplot Axes</dd>
+      </dl><dl><dt>
+
+          <code><a href="biplot.html">biplot()</a></code>
+
+        </dt>
+        <dd>First step to create a new biplot with <span class="pkg">biplotEZ</span></dd>
+      </dl><dl><dt>
+
+          <code><a href="biplotEZ.html">biplotEZ</a></code>
+
+        </dt>
+        <dd>biplotEZ: EZ-to-Use Biplots</dd>
+      </dl><dl><dt>
+
+          <code><a href="CA.biplot.html">CA(<i>&lt;biplot&gt;</i>)</a></code>
+
+        </dt>
+        <dd>CA biplot</dd>
+      </dl><dl><dt>
+
+          <code><a href="CA.html">CA()</a></code>
+
+        </dt>
+        <dd>Correspondence Analysis (CA) method</dd>
+      </dl><dl><dt>
+
+          <code><a href="CATPCA.html">CATPCA()</a></code>
+
+        </dt>
+        <dd>Categorical Principal Component Analysis</dd>
+      </dl><dl><dt>
+
+          <code><a href="classification.biplot.html">classification(<i>&lt;biplot&gt;</i>)</a></code>
+
+        </dt>
+        <dd>classification biplot</dd>
+      </dl><dl><dt>
+
+          <code><a href="classification.html">classification()</a></code>
+
+        </dt>
+        <dd>Classification biplot method</dd>
+      </dl><dl><dt>
+
+          <code><a href="classify.html">classify()</a></code>
+
+        </dt>
+        <dd>Classify samples into classes</dd>
+      </dl><dl><dt>
+
+          <code><a href="CLPs.html">CLPs()</a></code>
+
+        </dt>
+        <dd>Format aesthetics for the category level points</dd>
+      </dl><dl><dt>
+
+          <code><a href="CLRs.html">CLRs()</a></code>
+
+        </dt>
+        <dd>Format aesthetics for the category level regions</dd>
+      </dl><dl><dt>
+
+          <code><a href="CVA.biplot.html">CVA(<i>&lt;biplot&gt;</i>)</a></code>
+
+        </dt>
+        <dd>Calculate elements for the CVA biplot</dd>
+      </dl><dl><dt>
+
+          <code><a href="CVA.html">CVA()</a></code>
+
+        </dt>
+        <dd>Perform Canonical Variate Analysis (CVA)</dd>
+      </dl><dl><dt>
+
+          <code><a href="CVAlowdim.html">CVAlowdim()</a></code>
+
+        </dt>
+        <dd>Construct additional dimensions when the dimension of the canonical space is smaller than the dimension of the biplot</dd>
+      </dl><dl><dt>
 
+          <code><a href="density1D.html">density1D()</a></code>
 
-      <footer><div class="copyright">
-  <p></p><p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+        </dt>
+        <dd>Creates a kernel density in 1-dimension</dd>
+      </dl><dl><dt>
+
+          <code><a href="density2D.html">density2D()</a></code>
+
+        </dt>
+        <dd>Create a density in 2-dimensions</dd>
+      </dl><dl><dt>
+
+          <code><a href="ellipses.html">ellipses()</a></code>
+
+        </dt>
+        <dd>Concentration ellipses (\(\kappa\)-ellipses)</dd>
+      </dl><dl><dt>
+
+          <code><a href="extended.matching.coefficient.html">extended.matching.coefficient()</a></code>
+
+        </dt>
+        <dd>Extended matching coefficient</dd>
+      </dl><dl><dt>
+
+          <code><a href="fit.measures.html">fit.measures()</a></code>
+
+        </dt>
+        <dd>Compute measures of fit for the biplot.</dd>
+      </dl><dl><dt>
+
+          <code><a href="interpolate.html">interpolate()</a></code>
+
+        </dt>
+        <dd>Interpolate supplementary points and variables to add to the biplot</dd>
+      </dl><dl><dt>
+
+          <code><a href="legend.type.html">legend.type()</a></code>
+
+        </dt>
+        <dd>Format the legend for the biplot</dd>
+      </dl><dl><dt>
+
+          <code><a href="means.html">means()</a></code>
+
+        </dt>
+        <dd>Format aesthetics for the class or group means</dd>
+      </dl><dl><dt>
+
+          <code><a href="newaxes.html">newaxes()</a></code>
+
+        </dt>
+        <dd>Format aesthetics for the supplementary (new) biplot axes</dd>
+      </dl><dl><dt>
+
+          <code><a href="newsamples.html">newsamples()</a></code>
+
+        </dt>
+        <dd>Format aesthetics for the supplementary (new) biplot samples</dd>
+      </dl><dl><dt>
+
+          <code><a href="PCA.biplot.html">PCA(<i>&lt;biplot&gt;</i>)</a></code>
+
+        </dt>
+        <dd>Calculate elements for the PCA biplot</dd>
+      </dl><dl><dt>
+
+          <code><a href="PCA.html">PCA()</a></code>
+
+        </dt>
+        <dd>Perform Principal Components Analysis (PCA)</dd>
+      </dl><dl><dt>
+
+          <code><a href="PCO.biplot.html">PCO(<i>&lt;biplot&gt;</i>)</a></code>
+
+        </dt>
+        <dd>PCO biplot</dd>
+      </dl><dl><dt>
+
+          <code><a href="PCO.html">PCO()</a></code>
+
+        </dt>
+        <dd>Principal Coordinate Analysis (PCO) biplot method</dd>
+      </dl><dl><dt>
+
+          <code><a href="plot.biplot.html">plot(<i>&lt;biplot&gt;</i>)</a></code>
+
+        </dt>
+        <dd>Generic Plotting function of objects of class biplot</dd>
+      </dl><dl><dt>
+
+          <code><a href="prediction.html">prediction()</a></code>
+
+        </dt>
+        <dd>Predict samples to display on the biplot</dd>
+      </dl><dl><dt>
+
+          <code><a href="print.biplot.html">print(<i>&lt;biplot&gt;</i>)</a></code>
+
+        </dt>
+        <dd>Generic print function for objects of class biplot</dd>
+      </dl><dl><dt>
+
+          <code><a href="reflect.html">reflect()</a></code>
+
+        </dt>
+        <dd>Reflect the biplot about a chosen axis</dd>
+      </dl><dl><dt>
+
+          <code><a href="regress.biplot.html">regress(<i>&lt;biplot&gt;</i>)</a></code>
+
+        </dt>
+        <dd>Regression biplot</dd>
+      </dl><dl><dt>
+
+          <code><a href="regress.html">regress()</a></code>
+
+        </dt>
+        <dd>Regression biplot method</dd>
+      </dl><dl><dt>
+
+          <code><a href="rotate.html">rotate()</a></code>
+
+        </dt>
+        <dd>Rotate the biplot a chosen amount of degrees</dd>
+      </dl><dl><dt>
+
+          <code><a href="samples.html">samples()</a></code>
+
+        </dt>
+        <dd>Format aesthetics for the biplot samples</dd>
+      </dl><dl><dt>
+
+          <code><a href="sqrtManhattan.html">sqrtManhattan()</a></code>
+
+        </dt>
+        <dd>Computes the square root of the Manhattan distance An example of a Euclidean embeddable distance metric</dd>
+      </dl><dl><dt>
+
+          <code><a href="summary.biplot.html">summary(<i>&lt;biplot&gt;</i>)</a></code>
+
+        </dt>
+        <dd>Generic summary function for objects of class biplot</dd>
+      </dl><dl><dt>
+
+          <code><a href="translate_axes.html">translate_axes()</a></code>
+
+        </dt>
+        <dd>Translate biplot axes</dd>
+      </dl></div>
+  </main></div>
+
+
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p>
+<div class="pkgdown-footer-right">
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-    <div class="page-header">
-    <h1>Interpolation of new samples</h1>
-    
-    <div class="hidden name"><code>interpolate.Rd</code></div>
-    </div>
-
-    <div class="ref-description">
-    <p>Interpolation of new samples</p>
-    </div>
-
-    <div id="ref-usage">
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">interpolate</span><span class="op">(</span><span class="va">bp</span>, newdata <span class="op">=</span> <span class="cn">NULL</span>, newvariable <span class="op">=</span> <span class="cn">NULL</span><span class="op">)</span></span></code></pre></div>
-    </div>
-
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
-<dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
-
-
-<dt>newdata</dt>
-<dd><p>a new data set, similar in structure to the data set supplied to <code><a href="biplot.html">biplot()</a></code>
-containing supplementary data points to be added on the biplot.</p></dd>
-
-
-<dt>newvariable</dt>
-<dd><p>a new data set, similar in structure to the data set supplied to <code><a href="biplot.html">biplot()</a></code>
-containing supplementary variables to be added on the biplot.</p></dd>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Interpolate supplementary points and variables to add to the biplot — interpolate • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Interpolate supplementary points and variables to add to the biplot — interpolate"><meta name="description" content="This function adds supplementary points and variables to the plot from a new data set."><meta property="og:description" content="This function adds supplementary points and variables to the plot from a new data set."><meta property="og:image" content="/logo.png"></head><body>
+    <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
 
-</dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
 
-<p>Object of class PCA with the following elements:</p>
-<dl><dt>X</dt>
-<dd><p>matrix of the centered and scaled numeric variables.</p></dd>
+    <nav class="navbar navbar-expand-lg fixed-top bg-light" data-bs-theme="light" aria-label="Site navigation"><div class="container">
 
-<dt>Xcat</dt>
-<dd><p>matrix of the categorical variables.</p></dd>
+    <a class="navbar-brand me-2" href="../index.html">biplotEZ</a>
 
-<dt>raw.X</dt>
-<dd><p>original data.</p></dd>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">2.3</small>
 
-<dt>na.action</dt>
-<dd><p>vector of observations that have been removed.</p></dd>
 
-<dt>center</dt>
-<dd><p>TRUE or FALSE, whether X is centred.</p></dd>
+    <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
+      <span class="navbar-toggler-icon"></span>
+    </button>
 
-<dt>scaled</dt>
-<dd><p>TRUE or FALSE, whether X is scaled.</p></dd>
+    <div id="navbar" class="collapse navbar-collapse ms-3">
+      <ul class="navbar-nav me-auto"><li class="nav-item"><a class="nav-link" href="../articles/biplotEZ.html">Get started</a></li>
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+    <li><a class="dropdown-item" href="../articles/biplotEZ_enhancements.html">biplotEZ enhancements</a></li>
+    <li><a class="dropdown-item" href="../articles/MDS.html">Multi-dimensional scaling</a></li>
+    <li><a class="dropdown-item" href="../articles/Class_separation.html">Biplots for separating classes</a></li>
+    <li><a class="dropdown-item" href="../articles/CA_in_biplotEZ.html">Categorical biplots</a></li>
+    <li><a class="dropdown-item" href="../articles/Biplots_in_1D.html">One dimensional biplots</a></li>
+    <li><a class="dropdown-item" href="../articles/Biplots_in_3D.html">Three dimensional biplots</a></li>
+  </ul></li>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+      </ul></div>
 
-<dt>means</dt>
-<dd><p>mean of each numerical variable.</p></dd>
 
-<dt>sd</dt>
-<dd><p>standard deviation of each numerical variable.</p></dd>
+  </div>
+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Interpolate supplementary points and variables to add to the biplot</h1>
 
-<dt>n</dt>
-<dd><p>number of observations.</p></dd>
+      <div class="d-none name"><code>interpolate.Rd</code></div>
+    </div>
 
-<dt>p</dt>
-<dd><p>number of variables.</p></dd>
+    <div class="ref-description section level2">
+    <p>This function adds supplementary points and variables to the plot from a new data set.</p>
+    </div>
 
-<dt>group.aes</dt>
-<dd><p>vector of the same length as the number of rows in the data matrix for differentiated aesthetics for samples.</p></dd>
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">interpolate</span><span class="op">(</span><span class="va">bp</span>, newdata <span class="op">=</span> <span class="cn">NULL</span>, newvariable <span class="op">=</span> <span class="cn">NULL</span><span class="op">)</span></span></code></pre></div>
+    </div>
 
-<dt>g.names</dt>
-<dd><p>descriptive name to be used for group labels.</p></dd>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
 
-<dt>g</dt>
-<dd><p>number of groups.</p></dd>
 
-<dt>Title</dt>
-<dd><p>title of the biplot to be rendered</p></dd>
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
 
-<dt>Z</dt>
-<dd><p>matrix with each row containing the details of the point to be plotted (i.e. coordinates).</p></dd>
 
-<dt>Lmat</dt>
-<dd><p>matrix for transformation to the principal components.</p></dd>
+<dt id="arg-newdata">newdata<a class="anchor" aria-label="anchor" href="#arg-newdata"></a></dt>
+<dd><p>a new data set, similar in structure to the data set supplied to <code><a href="biplot.html">biplot()</a></code>
+containing supplementary data points to be added onto the biplot.</p></dd>
 
-<dt>e.vects</dt>
-<dd><p>vector indicating which principal components are plotted in the biplot.</p></dd>
 
-<dt>ax.one.unit</dt>
-<dd><p>one unit in the positive direction of each biplot axis.</p></dd>
+<dt id="arg-newvariable">newvariable<a class="anchor" aria-label="anchor" href="#arg-newvariable"></a></dt>
+<dd><p>a new data set, similar in structure to the data set supplied to <code><a href="biplot.html">biplot()</a></code>
+containing supplementary variables to be added onto the biplot.</p></dd>
 
-<dt>Xnew.raw</dt>
-<dd><p>newdata numerical variables.</p></dd>
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>The object of class <code>biplot</code> will be appended with the following elements:</p>
+<dl><dt>Xnew.raw</dt>
+<dd><p>the new data.</p></dd>
 
 <dt>Xnew</dt>
-<dd><p>matrix of the centered and scaled new numeric variables.</p></dd>
+<dd><p>the matrix of the centered and scaled new numeric variables of new data.</p></dd>
 
 <dt>Xnew.cat</dt>
-<dd><p>matrix of the new categorical variables.</p></dd>
+<dd><p>the matrix of the categorical variables of new data.</p></dd>
 
 <dt>Znew</dt>
-<dd><p>matrix of the coordinates of the newdata in the biplot.</p></dd>
+<dd><p>the matrix of the coordinates of the new data in the biplot.</p></dd>
+
+
+</dl><p>For an object of class <code>CA</code> the following additional elements will be appended:</p>
+<dl><dt>newrowcoor</dt>
+<dd><p>the matrix of row coordinates of the new data in the biplot.</p></dd>
+
+<dt>newcolcoor</dt>
+<dd><p>the matrix of column coordinates of the new data in the biplot.</p></dd>
 
 </dl></div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span>data <span class="op">=</span> <span class="va">iris</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">145</span>,<span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">interpolate</span><span class="op">(</span>newdata <span class="op">=</span> <span class="va">iris</span><span class="op">[</span><span class="fl">146</span><span class="op">:</span><span class="fl">150</span>,<span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="interpolate-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">2</span><span class="op">]</span>, center <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="CA.html">CA</a></span><span class="op">(</span>variant <span class="op">=</span> <span class="st">"Symmetric"</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
+<span class="r-in"><span>     <span class="fu">interpolate</span><span class="op">(</span>newdata <span class="op">=</span> <span class="va">HairEyeColor</span><span class="op">[</span>,,<span class="fl">1</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="interpolate-2.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span></span></span>
 </code></pre></div>
     </div>
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-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
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+    </nav></aside></div>
 
 
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-  <p></p><p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
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diff --git a/docs/reference/legend.type-1.png b/docs/reference/legend.type-1.png
new file mode 100644
index 0000000..bb3e06e
Binary files /dev/null and b/docs/reference/legend.type-1.png differ
diff --git a/docs/reference/legend.type.html b/docs/reference/legend.type.html
new file mode 100644
index 0000000..9b375d0
--- /dev/null
+++ b/docs/reference/legend.type.html
@@ -0,0 +1,140 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Format the legend for the biplot — legend.type • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Format the legend for the biplot — legend.type"><meta name="description" content="This function enables the user to format the legend and make a required selection to display."><meta property="og:description" content="This function enables the user to format the legend and make a required selection to display."><meta property="og:image" content="/logo.png"></head><body>
+    <a href="#main" class="visually-hidden-focusable">Skip to contents</a>
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+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Format the legend for the biplot</h1>
+
+      <div class="d-none name"><code>legend.type.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>This function enables the user to format the legend and make a required selection to display.</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">legend.type</span><span class="op">(</span><span class="va">bp</span>, samples <span class="op">=</span> <span class="cn">FALSE</span>, means <span class="op">=</span> <span class="cn">FALSE</span>, bags <span class="op">=</span> <span class="cn">FALSE</span>,</span>
+<span>                   ellipses<span class="op">=</span><span class="cn">FALSE</span>,regions<span class="op">=</span><span class="cn">FALSE</span>, new<span class="op">=</span><span class="cn">FALSE</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code>.</p></dd>
+
+
+<dt id="arg-samples">samples<a class="anchor" aria-label="anchor" href="#arg-samples"></a></dt>
+<dd><p>a logical value indicating whether a legend should be printed for samples, with default <code>FALSE</code>.</p></dd>
+
+
+<dt id="arg-means">means<a class="anchor" aria-label="anchor" href="#arg-means"></a></dt>
+<dd><p>a logical value indicating whether a legend should be printed for means, with default <code>FALSE</code>.</p></dd>
+
+
+<dt id="arg-bags">bags<a class="anchor" aria-label="anchor" href="#arg-bags"></a></dt>
+<dd><p>a logical value indicating whether a legend should be printed for bags, with default <code>FALSE</code>.</p></dd>
+
+
+<dt id="arg-ellipses">ellipses<a class="anchor" aria-label="anchor" href="#arg-ellipses"></a></dt>
+<dd><p>a logical value indicating whether a legend should be printed for concentration ellipses, with default <code>FALSE</code>.</p></dd>
+
+
+<dt id="arg-regions">regions<a class="anchor" aria-label="anchor" href="#arg-regions"></a></dt>
+<dd><p>a logical value indicating whether a legend should be printed for classification regions, with default <code>FALSE</code>.</p></dd>
+
+
+<dt id="arg-new">new<a class="anchor" aria-label="anchor" href="#arg-new"></a></dt>
+<dd><p>a logical value indicating whether the legend should appear in a new window, with default <code>FALSE</code>.</p></dd>
+
+
+<dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
+<dd><p>additional arguments to be sent to <code><a href="https://rdrr.io/r/graphics/legend.html" class="external-link">legend()</a></code>.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>A list with the following components is available:</p>
+<dl><dt>samples</dt>
+<dd><p>a logical value indicating whether a legend for samples are provided.</p></dd>
+
+<dt>means</dt>
+<dd><p>a logical value indicating whether a legend for class means are provided.</p></dd>
+
+<dt>bags</dt>
+<dd><p>a logical value indicating whether a legend for \(\alpha\)-bags are provided.</p></dd>
+
+<dt>ellipses</dt>
+<dd><p>a logical value indicating whether a legend for \(\kappa\)-ellipses are provided.</p></dd>
+
+<dt>regions</dt>
+<dd><p>a logical value indicating whether a legend for classification regions are provided.</p></dd>
+
+<dt>new</dt>
+<dd><p>a logical value indicating whether the legend appears on new plot.</p></dd>
+
+</dl></div>
+
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span> <span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span>, Title<span class="op">=</span><span class="st">"Test biplot"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span>group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span></span></span>
+<span class="r-in"><span>    <span class="fu">legend.type</span><span class="op">(</span>samples<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="legend.type-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span>    </span></span>
+</code></pre></div>
+    </div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
+
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+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+</div>
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+<div class="pkgdown-footer-right">
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diff --git a/docs/reference/means-1.png b/docs/reference/means-1.png
index 308f5f3..bf2eb47 100644
Binary files a/docs/reference/means-1.png and b/docs/reference/means-1.png differ
diff --git a/docs/reference/means.html b/docs/reference/means.html
index b88c226..bca09ed 100644
--- a/docs/reference/means.html
+++ b/docs/reference/means.html
@@ -1,205 +1,177 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Aesthetics for biplot class / group means — means • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.1/jquery.min.js" integrity="sha512-v2CJ7UaYy4JwqLDIrZUI/4hqeoQieOmAZNXBeQyjo21dadnwR+8ZaIJVT8EE2iyI61OV8e6M8PP2/4hpQINQ/g==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Aesthetics for biplot class / group means — means"><meta property="og:description" content="This function allows formatting changes to class means or group means."><meta property="og:image" content="/logo.png"><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Format aesthetics for the class or group means — means • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Format aesthetics for the class or group means — means"><meta name="description" content="This function allows the user to format the aesthetics for the class means or group means."><meta property="og:description" content="This function allows the user to format the aesthetics for the class means or group means."><meta property="og:image" content="/logo.png"></head><body>
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-    <h1>Aesthetics for biplot class / group means</h1>
-    
-    <div class="hidden name"><code>means.Rd</code></div>
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+      <img src="../logo.png" class="logo" alt=""><h1>Format aesthetics for the class or group means</h1>
+
+      <div class="d-none name"><code>means.Rd</code></div>
     </div>
 
-    <div class="ref-description">
-    <p>This function allows formatting changes to class means or group means.</p>
+    <div class="ref-description section level2">
+    <p>This function allows the user to format the aesthetics for the class means or group means.</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">means</span> <span class="op">(</span><span class="va">bp</span>,  which <span class="op">=</span> <span class="cn">NULL</span>, col <span class="op">=</span> <span class="cn">NULL</span>, pch <span class="op">=</span> <span class="fl">15</span>, cex <span class="op">=</span> <span class="fl">1</span>, label <span class="op">=</span> <span class="cn">FALSE</span>,</span>
 <span>label.col <span class="op">=</span> <span class="cn">NULL</span>,label.cex <span class="op">=</span> <span class="fl">0.75</span>, label.side <span class="op">=</span> <span class="st">"bottom"</span>, label.offset <span class="op">=</span> <span class="fl">0.5</span>,</span>
 <span>opacity <span class="op">=</span> <span class="fl">1</span>, shade.darker <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>an object of class <code>biplot</code>.</p></dd>
 
 
-<dt>which</dt>
-<dd><p>vector of which means to display, with default <code>bp$g</code>.</p></dd>
+<dt id="arg-which">which<a class="anchor" aria-label="anchor" href="#arg-which"></a></dt>
+<dd><p>a vector containing the groups or classes for which the means should be displayed, with default <code>bp$g</code>.</p></dd>
 
 
-<dt>col</dt>
-<dd><p>mean colour, with default to sample colour.</p></dd>
+<dt id="arg-col">col<a class="anchor" aria-label="anchor" href="#arg-col"></a></dt>
+<dd><p>the colour(s) for the means, with default as the colour of the samples.</p></dd>
 
 
-<dt>pch</dt>
-<dd><p>mean plotting character, with default <code>o</code>.</p></dd>
+<dt id="arg-pch">pch<a class="anchor" aria-label="anchor" href="#arg-pch"></a></dt>
+<dd><p>the plotting character(s) for the means, with default <code>15</code>.</p></dd>
 
 
-<dt>cex</dt>
-<dd><p>mean character expansion, with default <code>1</code>.</p></dd>
+<dt id="arg-cex">cex<a class="anchor" aria-label="anchor" href="#arg-cex"></a></dt>
+<dd><p>the character expansion(s) for the means, with default <code>1</code>.</p></dd>
 
 
-<dt>label</dt>
-<dd><p>logical, whether means should be labelled or not, with default <code>TRUE</code>.</p></dd>
+<dt id="arg-label">label<a class="anchor" aria-label="anchor" href="#arg-label"></a></dt>
+<dd><p>a logical value indicating whether the means should be labelled, with default <code>TRUE</code>.</p></dd>
 
 
-<dt>label.col</dt>
-<dd><p>vector of length g with the colour of the labels, defaulting to the
-colour of the means.</p></dd>
+<dt id="arg-label-col">label.col<a class="anchor" aria-label="anchor" href="#arg-label-col"></a></dt>
+<dd><p>a vector of the same length as <code>which</code> with label colours for the means, with default as the colour of the means.</p></dd>
 
 
-<dt>label.cex</dt>
-<dd><p>label text expansion, with default <code>0.75</code>.</p></dd>
+<dt id="arg-label-cex">label.cex<a class="anchor" aria-label="anchor" href="#arg-label-cex"></a></dt>
+<dd><p>a vector of the same length as <code>which</code> with label text expansions for the means, with default <code>0.75</code>.</p></dd>
 
 
-<dt>label.side</dt>
-<dd><p>side of the plotting character where label appears, with default <code>bottom</code>. Note that unlike
-the argument <code>pos</code> in <code><a href="https://rdrr.io/r/graphics/text.html" class="external-link">text()</a></code>, options are "bottom", "left", "top", "right" and not 1, 2, 3, 4.</p></dd>
+<dt id="arg-label-side">label.side<a class="anchor" aria-label="anchor" href="#arg-label-side"></a></dt>
+<dd><p>the side at which the label of the plotted mean point appears, with default <code>bottom</code>. Note that unlike the argument <code>pos</code> in <code><a href="https://rdrr.io/r/graphics/text.html" class="external-link">text()</a></code>, options are "<code>bottom</code>", "<code>left</code>", "<code>top</code>", "<code>right</code>" and not <code>1</code>, <code>2</code>, <code>3</code>, <code>4</code>.</p></dd>
 
 
-<dt>label.offset</dt>
-<dd><p>offset of the label from the mean point. See ?text for a detailed explanation of the
-argument <code>offset</code>.</p></dd>
+<dt id="arg-label-offset">label.offset<a class="anchor" aria-label="anchor" href="#arg-label-offset"></a></dt>
+<dd><p>the offset of the label from the plotted mean point. See <code><a href="https://rdrr.io/r/graphics/text.html" class="external-link">?text</a></code> for a detailed explanation of the argument <code>offset</code>.</p></dd>
 
 
-<dt>opacity</dt>
+<dt id="arg-opacity">opacity<a class="anchor" aria-label="anchor" href="#arg-opacity"></a></dt>
 <dd><p>transparency of means.</p></dd>
 
 
-<dt>shade.darker</dt>
-<dd><p>automatically makes the colour of the means a darker shade than the default (or specified) colour</p></dd>
+<dt id="arg-shade-darker">shade.darker<a class="anchor" aria-label="anchor" href="#arg-shade-darker"></a></dt>
+<dd><p>a logical value indicating whether the colour of the mean points should be made a shade darker than the default or specified colour, with default <code>TRUE</code>.</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>A list with the following components is available:</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>The object of class <code>biplot</code> will be appended with a list called <code>means</code> containing the following elements:</p>
 <dl><dt>which</dt>
-<dd><p>which means to display.</p></dd>
+<dd><p>a vector containing the groups or classes for which the means are displayed.</p></dd>
 
 <dt>col</dt>
-<dd><p>colour of the means.</p></dd>
+<dd><p>the colour(s) of the means.</p></dd>
 
 <dt>pch</dt>
-<dd><p>plotting character of the means.</p></dd>
+<dd><p>the plotting character(s) of the means.</p></dd>
 
 <dt>cex</dt>
-<dd><p>expansion of the plotting character of the means.</p></dd>
+<dd><p>the character expansion(s) of the plotting character(s) of the means.</p></dd>
 
 <dt>label</dt>
-<dd><p>logical, whether means should be labelled.</p></dd>
+<dd><p>a logical value indicating whether means are labelled.</p></dd>
 
 <dt>label.col</dt>
-<dd><p>colour of the label.</p></dd>
+<dd><p>the label colours of the means.</p></dd>
 
 <dt>label.cex</dt>
-<dd><p>expansion of the label.</p></dd>
+<dd><p>the label text expansions of the samples.</p></dd>
 
 <dt>label.side</dt>
-<dd><p>side at which to plot the label of means.</p></dd>
+<dd><p>the side at which the label of the plotted mean point appears.</p></dd>
 
 <dt>label.offset</dt>
-<dd><p>offset of the label from the mean point.</p></dd>
+<dd><p>the offset of the label from the plotted mean point.</p></dd>
 
 <dt>opacity</dt>
-<dd><p>transparency of means</p></dd>
+<dd><p>the opacity level of the plotted points.</p></dd>
 
 </dl></div>
-    <div id="details">
-    <h2>Details</h2>
+    <div class="section level2">
+    <h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></a></h2>
     <p>The number of classes or groups (defined by group.aes) is indicated as <code>g</code>. If an argument is not of length <code>g</code>,
 recycling is used.</p>
     </div>
+    <div class="section level2">
+    <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
+    <div class="dont-index"><p><code><a href="biplot.html">biplot()</a></code></p></div>
+    </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span></span></span>
 <span class="r-in"><span>          <span class="fu">means</span><span class="op">(</span>col <span class="op">=</span> <span class="st">"purple"</span>, pch <span class="op">=</span> <span class="fl">15</span>, cex <span class="op">=</span> <span class="fl">2</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="means-1.png" alt="" width="700" height="433"></span>
 </code></pre></div>
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-    <div class="page-header">
-    <h1>Aesthetics for supplementary (new) biplot axes</h1>
-    
-    <div class="hidden name"><code>newaxes.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Format aesthetics for the supplementary (new) biplot axes</h1>
+
+      <div class="d-none name"><code>newaxes.Rd</code></div>
     </div>
 
-    <div class="ref-description">
-    <p>Aesthetics for supplementary (new) biplot axes</p>
+    <div class="ref-description section level2">
+    <p>This function allows the user to format the aesthetics for the supplementary (new) biplot axes.</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">newaxes</span><span class="op">(</span><span class="va">bp</span>, X.new.names<span class="op">=</span><span class="va">bp</span><span class="op">$</span><span class="va">var.names</span>, which <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="va">bp</span><span class="op">$</span><span class="va">num.vars</span>, col <span class="op">=</span> <span class="st">"orange"</span>, lwd <span class="op">=</span> <span class="fl">1</span>, </span>
 <span>lty <span class="op">=</span> <span class="fl">1</span>, label.dir <span class="op">=</span> <span class="st">"Orthog"</span>, label.col <span class="op">=</span> <span class="va">col</span>, label.cex <span class="op">=</span> <span class="fl">0.75</span>, label.line <span class="op">=</span> <span class="fl">0.1</span>, </span>
 <span>ticks <span class="op">=</span> <span class="fl">5</span>, tick.col <span class="op">=</span> <span class="va">col</span>, tick.size <span class="op">=</span> <span class="fl">1</span>, tick.label <span class="op">=</span> <span class="cn">TRUE</span>, tick.label.col <span class="op">=</span> <span class="va">tick.col</span>, </span>
@@ -79,143 +54,135 @@ <h1>Aesthetics for supplementary (new) biplot axes</h1>
 <span>predict.lty <span class="op">=</span> <span class="va">lty</span>, ax.names <span class="op">=</span> <span class="va">X.new.names</span>, orthogx <span class="op">=</span> <span class="fl">0</span>, orthogy <span class="op">=</span> <span class="fl">0</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
-<dd><p>object of class <code>biplot</code></p></dd>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
 
 
-<dt>X.new.names</dt>
-<dd><p>refers to the new column names of <code>bp</code> to specify which axes to label.</p></dd>
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code>.</p></dd>
 
 
-<dt>which</dt>
-<dd><p>vector of new columns to be displayed in the biplot.</p></dd>
+<dt id="arg-x-new-names">X.new.names<a class="anchor" aria-label="anchor" href="#arg-x-new-names"></a></dt>
+<dd><p>a vector of the new column names of <code>bp</code> to specify which axes should be labelled.</p></dd>
 
 
-<dt>col</dt>
-<dd><p>vector of size p specifying colours of labels of biplot axes. The default is <code>grey(0.7)</code>.</p></dd>
+<dt id="arg-which">which<a class="anchor" aria-label="anchor" href="#arg-which"></a></dt>
+<dd><p>a vector containing the new columns or variables for which the axes should be displayed, with default <code>1:num.vars</code>.</p></dd>
 
 
-<dt>lwd</dt>
-<dd><p>axis line width, with default <code>1</code>.</p></dd>
+<dt id="arg-col">col<a class="anchor" aria-label="anchor" href="#arg-col"></a></dt>
+<dd><p>the colour(s) for the axes, with default <code>grey(0.7)</code>. Alternatively, provide a vector of colours corresponding to <code>X.names</code>.</p></dd>
 
 
-<dt>lty</dt>
-<dd><p>axis line type, with default <code>1</code>.</p></dd>
+<dt id="arg-lwd">lwd<a class="anchor" aria-label="anchor" href="#arg-lwd"></a></dt>
+<dd><p>the line width(s) for the axes, with default <code>1</code>.</p></dd>
 
 
-<dt>label.dir</dt>
-<dd><p>One of "Orthog" (default), "Hor" or "Paral" specifying titles of
-axes to appear orthogonal to the side of the figure; always
-horizontally or always parallel to the side of the figure.</p></dd>
+<dt id="arg-lty">lty<a class="anchor" aria-label="anchor" href="#arg-lty"></a></dt>
+<dd><p>the line type(s) for the axes, with default <code>1</code>.</p></dd>
 
 
-<dt>label.col</dt>
-<dd><p>axis label colour, with default, <code>col</code>.</p></dd>
+<dt id="arg-label-dir">label.dir<a class="anchor" aria-label="anchor" href="#arg-label-dir"></a></dt>
+<dd><p>a character string indicating the placement of the axis titles to the side of the figure. One of "<code>Orthog</code>" for axis titles to appear orthogonal to the side of the figure (default) , "<code>Hor</code>" for axis titles to appear horizontally or "<code>Paral</code>" for axis titles to appear parallel to the side of the figure.</p></dd>
 
 
-<dt>label.cex</dt>
-<dd><p>axis label expansion, with default <code>0.75</code>.</p></dd>
+<dt id="arg-label-col">label.col<a class="anchor" aria-label="anchor" href="#arg-label-col"></a></dt>
+<dd><p>the colour(s) for the axis labels, with default, <code>col</code>.</p></dd>
 
 
-<dt>label.line</dt>
-<dd><p>axis label written on which margin line, with default <code>0.1</code>.</p></dd>
+<dt id="arg-label-cex">label.cex<a class="anchor" aria-label="anchor" href="#arg-label-cex"></a></dt>
+<dd><p>the label expansion for the axis labels, with default <code>0.75</code>.</p></dd>
 
 
-<dt>ticks</dt>
-<dd><p>integer-valued vector of size equal to the number of biplot axes
-to control the number of tickmarks on each individual biplot
-axis. Default is 5 for each axis.</p></dd>
+<dt id="arg-label-line">label.line<a class="anchor" aria-label="anchor" href="#arg-label-line"></a></dt>
+<dd><p>the distance of the axis title from the side of the figure, with default <code>0.1</code>.</p></dd>
 
 
-<dt>tick.col</dt>
-<dd><p>tick mark colour, with default <code>col</code>.</p></dd>
+<dt id="arg-ticks">ticks<a class="anchor" aria-label="anchor" href="#arg-ticks"></a></dt>
+<dd><p>an integer-valued vector indicating the number of tickmarks for each axis, with default <code>5</code> for each axis.</p></dd>
 
 
-<dt>tick.size</dt>
-<dd><p>positive integer-valued vector with specifying tick mark sizes, with default <code>1</code>.</p></dd>
+<dt id="arg-tick-col">tick.col<a class="anchor" aria-label="anchor" href="#arg-tick-col"></a></dt>
+<dd><p>the colour(s) for the tick marks, with default <code>col</code>.</p></dd>
 
 
-<dt>tick.label</dt>
-<dd><p>logical, whether axes should be labelled or not, with default <code>TRUE</code>.</p></dd>
+<dt id="arg-tick-size">tick.size<a class="anchor" aria-label="anchor" href="#arg-tick-size"></a></dt>
+<dd><p>a vector specifying the sizes of tick marks for each axis, with default <code>1</code> for each .</p></dd>
 
 
-<dt>tick.label.col</dt>
-<dd><p>tick mark label colour, with default <code>tick.col</code>.</p></dd>
+<dt id="arg-tick-label">tick.label<a class="anchor" aria-label="anchor" href="#arg-tick-label"></a></dt>
+<dd><p>a logical value indicating whether the axes should be labelled, with default <code>TRUE</code>.</p></dd>
 
 
-<dt>tick.label.cex</dt>
-<dd><p>tick mark label expansion, with default <code>0.6</code>.</p></dd>
+<dt id="arg-tick-label-col">tick.label.col<a class="anchor" aria-label="anchor" href="#arg-tick-label-col"></a></dt>
+<dd><p>the colour(s) for the tick mark labels, with default <code>tick.col</code>.</p></dd>
 
 
-<dt>tick.label.side</dt>
-<dd><p>character vector specifying position of the tick label "below" or "above" the axis.</p></dd>
+<dt id="arg-tick-label-cex">tick.label.cex<a class="anchor" aria-label="anchor" href="#arg-tick-label-cex"></a></dt>
+<dd><p>the label expansion for the tick mark labels, with default <code>0.6</code>.</p></dd>
 
 
-<dt>predict.col</dt>
-<dd><p>predicted samples colour, with default <code>col</code>.</p></dd>
+<dt id="arg-tick-label-side">tick.label.side<a class="anchor" aria-label="anchor" href="#arg-tick-label-side"></a></dt>
+<dd><p>a character string indicating the position of the tick label. One of "<code>below</code>" for the label to appear below the tick mark (default) or "<code>above</code>" for the label to appear above the tick mark.</p></dd>
 
 
-<dt>predict.lwd</dt>
-<dd><p>predicted samples line width, with default <code>lwd</code>.</p></dd>
+<dt id="arg-predict-col">predict.col<a class="anchor" aria-label="anchor" href="#arg-predict-col"></a></dt>
+<dd><p>the colour(s) for the predicted samples, with default <code>col</code>.</p></dd>
 
 
-<dt>predict.lty</dt>
-<dd><p>predicted samples line type, with default <code>lty</code>.</p></dd>
+<dt id="arg-predict-lwd">predict.lwd<a class="anchor" aria-label="anchor" href="#arg-predict-lwd"></a></dt>
+<dd><p>the line width(s) for the predicted samples, with default <code>lwd</code>.</p></dd>
 
 
-<dt>ax.names</dt>
-<dd><p>vector of size <code>p</code> containing user defined names for the variables.</p></dd>
+<dt id="arg-predict-lty">predict.lty<a class="anchor" aria-label="anchor" href="#arg-predict-lty"></a></dt>
+<dd><p>the line type(s) for the predicted samples, with default <code>lty</code>.</p></dd>
 
 
-<dt>orthogx</dt>
-<dd><p>numeric vector of size p specifying the x-coordinate of the parallel transformation of each axis.
-Defaults to zero for each axis. Only used when the dimension of the biplot is two.</p></dd>
+<dt id="arg-ax-names">ax.names<a class="anchor" aria-label="anchor" href="#arg-ax-names"></a></dt>
+<dd><p>a vector of size <code>p</code> containing user defined titles for the axes.</p></dd>
 
 
-<dt>orthogy</dt>
-<dd><p>numeric vector of size p specifying the y-coordinate of the parallel transformation of each axis.
-Defaults to zero for each axis. Only used when the dimension of the biplot is two.</p></dd>
+<dt id="arg-orthogx">orthogx<a class="anchor" aria-label="anchor" href="#arg-orthogx"></a></dt>
+<dd><p>a numeric vector of size <code>p</code> specifying the x-coordinate of the parallel transformation of each axis, with default <code>0</code> for each axis. This is only used when <code>dim.biplot = 2</code>.</p></dd>
 
-</dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>an object of class <code>biplot</code></p>
 
+<dt id="arg-orthogy">orthogy<a class="anchor" aria-label="anchor" href="#arg-orthogy"></a></dt>
+<dd><p>a numeric vector of size <code>p</code> specifying the y-coordinate of the parallel transformation of each axis, with default <code>0</code> for each axis. This is only used when <code>dim.biplot = 2</code>.</p></dd>
 
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>The object of class <code>biplot</code> will be appended with a list called <code>newaxes</code> containing elements similar to that of <code>axes</code>.</p>
+    </div>
+    <div class="section level2">
+    <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
+    <div class="dont-index"><p><code><a href="biplot.html">biplot</a></code>, <code><a href="axes.html">axes</a></code></p></div>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span>data <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="interpolate.html">interpolate</a></span><span class="op">(</span>newvariable <span class="op">=</span> <span class="va">iris</span><span class="op">[</span><span class="fl">3</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
 <span class="r-in"><span>  <span class="fu">newaxes</span><span class="op">(</span>col<span class="op">=</span><span class="st">"gold"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="newaxes-1.png" alt="" width="700" height="433"></span>
 </code></pre></div>
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diff --git a/docs/reference/newsamples-1.png b/docs/reference/newsamples-1.png
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diff --git a/docs/reference/newsamples.html b/docs/reference/newsamples.html
new file mode 100644
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--- /dev/null
+++ b/docs/reference/newsamples.html
@@ -0,0 +1,188 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Format aesthetics for the supplementary (new) biplot samples — newsamples • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Format aesthetics for the supplementary (new) biplot samples — newsamples"><meta name="description" content="This function allows formatting changes to new samples."><meta property="og:description" content="This function allows formatting changes to new samples."><meta property="og:image" content="/logo.png"></head><body>
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+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Format aesthetics for the supplementary (new) biplot samples</h1>
+
+      <div class="d-none name"><code>newsamples.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>This function allows formatting changes to new samples.</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">newsamples</span> <span class="op">(</span><span class="va">bp</span>,  col <span class="op">=</span> <span class="st">"darkorange1"</span>, pch <span class="op">=</span> <span class="fl">1</span>, cex <span class="op">=</span> <span class="fl">1</span>, label <span class="op">=</span> <span class="cn">FALSE</span>,</span>
+<span>label.name <span class="op">=</span> <span class="cn">NULL</span>, label.col <span class="op">=</span> <span class="cn">NULL</span>,label.cex <span class="op">=</span> <span class="fl">0.75</span>, label.side <span class="op">=</span> <span class="st">"bottom"</span>, </span>
+<span>label.offset <span class="op">=</span> <span class="fl">0.5</span>, connected <span class="op">=</span> <span class="cn">FALSE</span>, connect.col <span class="op">=</span> <span class="st">"black"</span>, connect.lty<span class="op">=</span><span class="fl">1</span>, </span>
+<span>connect.lwd<span class="op">=</span><span class="fl">1</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code>.</p></dd>
+
+
+<dt id="arg-col">col<a class="anchor" aria-label="anchor" href="#arg-col"></a></dt>
+<dd><p>the colour(s) for the new samples, with default <code>darkorange1</code>.</p></dd>
+
+
+<dt id="arg-pch">pch<a class="anchor" aria-label="anchor" href="#arg-pch"></a></dt>
+<dd><p>the plotting character(s) for the new samples, with default <code>1</code>.</p></dd>
+
+
+<dt id="arg-cex">cex<a class="anchor" aria-label="anchor" href="#arg-cex"></a></dt>
+<dd><p>the character expansion(s) for the new samples, with default <code>1</code>.</p></dd>
+
+
+<dt id="arg-label">label<a class="anchor" aria-label="anchor" href="#arg-label"></a></dt>
+<dd><p>a logical value indicating whether new samples should be labelled or not, with default <code>FALSE</code>.</p></dd>
+
+
+<dt id="arg-label-name">label.name<a class="anchor" aria-label="anchor" href="#arg-label-name"></a></dt>
+<dd><p>the label names for the new samples.</p></dd>
+
+
+<dt id="arg-label-col">label.col<a class="anchor" aria-label="anchor" href="#arg-label-col"></a></dt>
+<dd><p>a vector of the same length as the number of new samples containing the colour(s) for the labels of the new samples, with default the colour of the sample points.</p></dd>
+
+
+<dt id="arg-label-cex">label.cex<a class="anchor" aria-label="anchor" href="#arg-label-cex"></a></dt>
+<dd><p>the label text expansion(s) for the new samples, with default <code>0.75</code>.</p></dd>
+
+
+<dt id="arg-label-side">label.side<a class="anchor" aria-label="anchor" href="#arg-label-side"></a></dt>
+<dd><p>the side at which the label of the plotted point appears, with default <code>bottom</code>. Note that unlike the argument <code>pos</code> in <code><a href="https://rdrr.io/r/graphics/text.html" class="external-link">text()</a></code>, options are "<code>bottom</code>", "<code>left</code>", "<code>top</code>","<code>right</code>" and not <code>1</code>, <code>2</code>, <code>3</code>, <code>4</code>.</p></dd>
+
+
+<dt id="arg-label-offset">label.offset<a class="anchor" aria-label="anchor" href="#arg-label-offset"></a></dt>
+<dd><p>the offset of the label from the plotted point. See <code><a href="https://rdrr.io/r/graphics/text.html" class="external-link">?text</a></code> for a detailed explanation of the argument <code>offset</code>.</p></dd>
+
+
+<dt id="arg-connected">connected<a class="anchor" aria-label="anchor" href="#arg-connected"></a></dt>
+<dd><p>a logical value indicating whether samples are connected in order of rows of the data matrix, with default <code>FALSE</code>.</p></dd>
+
+
+<dt id="arg-connect-col">connect.col<a class="anchor" aria-label="anchor" href="#arg-connect-col"></a></dt>
+<dd><p>the colour of the connecting line, with default <code>black</code>.</p></dd>
+
+
+<dt id="arg-connect-lty">connect.lty<a class="anchor" aria-label="anchor" href="#arg-connect-lty"></a></dt>
+<dd><p>the line type of the connecting line, with default <code>1</code>.</p></dd>
+
+
+<dt id="arg-connect-lwd">connect.lwd<a class="anchor" aria-label="anchor" href="#arg-connect-lwd"></a></dt>
+<dd><p>the line width of the connecting line, with default <code>1</code>.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>The object of class <code>biplot</code> will be appended with a list called <code>newsamples</code> containing the following elements:</p>
+<dl><dt>col</dt>
+<dd><p>the colour(s) of the new samples.</p></dd>
+
+<dt>pch</dt>
+<dd><p>the plotting character(s) of the new samples.</p></dd>
+
+<dt>cex</dt>
+<dd><p>the character expansion(s) of the plotting character(s) of the new samples.</p></dd>
+
+<dt>label</dt>
+<dd><p>a logical value indicating whether new samples are labelled.</p></dd>
+
+<dt>label.col</dt>
+<dd><p>the label colours of the new samples.</p></dd>
+
+<dt>label.cex</dt>
+<dd><p>the label text expansions of the new samples.</p></dd>
+
+<dt>label.side</dt>
+<dd><p>the side at which the label of the plotted point appears.</p></dd>
+
+<dt>label.offset</dt>
+<dd><p>the offset of the label from the plotted point.</p></dd>
+
+<dt>connected</dt>
+<dd><p>a logical value indicating whether new samples are connected.</p></dd>
+
+<dt>connect.col</dt>
+<dd><p>the colour of the connecting line.</p></dd>
+
+<dt>connect.lty</dt>
+<dd><p>the line type of the connecting line.</p></dd>
+
+<dt>connect.lwd</dt>
+<dd><p>the line width of the connecting line.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
+    <div class="dont-index"><p><a href="biplot.html">biplot</a>, <a href="samples.html">samples</a></p></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span>data <span class="op">=</span> <span class="va">iris</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">145</span>,<span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="samples.html">samples</a></span><span class="op">(</span>col <span class="op">=</span> <span class="st">"grey"</span><span class="op">)</span> <span class="op">|&gt;</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="interpolate.html">interpolate</a></span><span class="op">(</span>newdata <span class="op">=</span> <span class="va">iris</span><span class="op">[</span><span class="fl">146</span><span class="op">:</span><span class="fl">150</span>,<span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">newsamples</span><span class="op">(</span>col <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/grDevices/palettes.html" class="external-link">rainbow</a></span><span class="op">(</span><span class="fl">6</span><span class="op">)</span>, pch<span class="op">=</span><span class="fl">15</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="newsamples-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span></span></span>
+</code></pre></div>
+    </div>
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diff --git a/docs/reference/plot.biplot.html b/docs/reference/plot.biplot.html
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-    <h1>Generic Plotting function of objects of class biplot</h1>
-    
-    <div class="hidden name"><code>plot.biplot.Rd</code></div>
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+      <img src="../logo.png" class="logo" alt=""><h1>Generic Plotting function of objects of class biplot</h1>
+
+      <div class="d-none name"><code>plot.biplot.Rd</code></div>
     </div>
 
-    <div class="ref-description">
+    <div class="ref-description section level2">
     <p>Generic Plotting function of objects of class biplot</p>
     </div>
 
-    <div id="ref-usage">
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for biplot</span></span>
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'biplot'</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span></span>
 <span>  <span class="va">x</span>,</span>
 <span>  exp.factor <span class="op">=</span> <span class="fl">1.2</span>,</span>
 <span>  axis.predictivity <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>  sample.predictivity <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>  zoom <span class="op">=</span> <span class="cn">FALSE</span>,</span>
+<span>  add <span class="op">=</span> <span class="cn">FALSE</span>,</span>
 <span>  xlim <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>  ylim <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>  <span class="va">...</span></span>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>x</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>An object of class <code>biplot</code>.</p></dd>
 
 
-<dt>exp.factor</dt>
-<dd><p>numeric value with default axes of the biplot. Larger values for zooming out and
-smaller values for zooming in with respect to sample points
-in the biplot display.</p></dd>
+<dt id="arg-exp-factor">exp.factor<a class="anchor" aria-label="anchor" href="#arg-exp-factor"></a></dt>
+<dd><p>a numeric value with default axes of the biplot. Larger values are specified for zooming out with respect to sample points in the biplot display and smaller values are specified for zooming in with respect to sample points in the biplot display.</p></dd>
+
+
+<dt id="arg-axis-predictivity">axis.predictivity<a class="anchor" aria-label="anchor" href="#arg-axis-predictivity"></a></dt>
+<dd><p>either a logical or a numeric value between <code>0</code> and <code>1</code>. If it is a numeric value, this value is used as threshold so that only axes with axis predictivity larger than the threshold is displayed. If <code>axis.predictivity = TRUE</code>, the axis colour is 'diluted' in proportion with the axis predictivity.</p></dd>
 
 
-<dt>axis.predictivity</dt>
-<dd><p>either logical or a numeric value between 0 and 1.
-If it is a numeric value, this value is used as threshold so that
-only axes with axis predictivity larger than the threshold is displayed.
-If <code>axis.predictivity = TRUE</code>, the axis color is 'diluted' in
-proportion with the axis predictivity.</p></dd>
+<dt id="arg-sample-predictivity">sample.predictivity<a class="anchor" aria-label="anchor" href="#arg-sample-predictivity"></a></dt>
+<dd><p>either a logical or a numeric value between 0 and 1. If it is a numeric value, this value is used as threshold so that only samples with sample predictivity larger than the threshold is displayed. If <code>sample.predictivity = TRUE</code>, the sample size is shrinked in proportion with the sample predictivity.</p></dd>
 
 
-<dt>sample.predictivity</dt>
-<dd><p>either a logical or a numeric value between 0 and 1.
-If it is a numeric value, this value is used as threshold so that
-only samples with sample predictivity larger than the threshold is displayed.
-if <code>sample.predictivity = TRUE</code>, the sample size is shrinked in
-proportion with the sample predictivity.</p></dd>
+<dt id="arg-zoom">zoom<a class="anchor" aria-label="anchor" href="#arg-zoom"></a></dt>
+<dd><p>a logical value allowing the user to select an area to zoom into.</p></dd>
 
 
-<dt>zoom</dt>
-<dd><p>logical, allowing the user to select an area to zoom into</p></dd>
+<dt id="arg-add">add<a class="anchor" aria-label="anchor" href="#arg-add"></a></dt>
+<dd><p>a logical value allowing the user to add the biplot to a current plot. If <code>add = TRUE</code> the argument <code>zoom</code> is inactive.</p></dd>
 
 
-<dt>xlim</dt>
-<dd><p>horisontal limits of the plot</p></dd>
+<dt id="arg-xlim">xlim<a class="anchor" aria-label="anchor" href="#arg-xlim"></a></dt>
+<dd><p>the horizontal limits of the plot.</p></dd>
 
 
-<dt>ylim</dt>
-<dd><p>vertical limits of the plot</p></dd>
+<dt id="arg-ylim">ylim<a class="anchor" aria-label="anchor" href="#arg-ylim"></a></dt>
+<dd><p>the vertical limits of the plot.</p></dd>
 
 
-<dt>...</dt>
+<dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
 <dd><p>additional arguments.</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>An object of class <code>biplot</code>.</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>An object of class <code>biplot</code>.</p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span> <span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="plot.biplot-1.png" alt="" width="700" height="433"></span>
 </code></pre></div>
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-      <footer><div class="copyright">
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+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
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+<div class="pkgdown-footer-right">
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diff --git a/docs/reference/prediction-1.png b/docs/reference/prediction-1.png
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diff --git a/docs/reference/prediction.html b/docs/reference/prediction.html
index 54082bc..588d02a 100644
--- a/docs/reference/prediction.html
+++ b/docs/reference/prediction.html
@@ -1,146 +1,120 @@
 <!DOCTYPE html>
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-  <div class="col-md-9 contents">
-    <div class="page-header">
-    <h1>Prediction of samples</h1>
-    
-    <div class="hidden name"><code>prediction.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Predict samples to display on the biplot</h1>
+
+      <div class="d-none name"><code>prediction.Rd</code></div>
     </div>
 
-    <div class="ref-description">
-    <p>Prediction of samples</p>
+    <div class="ref-description section level2">
+    <p>This function makes predictions of sample points, variables and means and displays them on the biplot.</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">prediction</span><span class="op">(</span><span class="va">bp</span>, predict.samples <span class="op">=</span> <span class="cn">NULL</span>, predict.means <span class="op">=</span> <span class="cn">NULL</span>, which <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="va">bp</span><span class="op">$</span><span class="va">p</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
 
 
-<dt>predict.samples</dt>
+<dt id="arg-predict-samples">predict.samples<a class="anchor" aria-label="anchor" href="#arg-predict-samples"></a></dt>
 <dd><p>a vector specifying which samples to predict.</p></dd>
 
 
-<dt>predict.means</dt>
+<dt id="arg-predict-means">predict.means<a class="anchor" aria-label="anchor" href="#arg-predict-means"></a></dt>
 <dd><p>a vector specifying which group means to predict.</p></dd>
 
 
-<dt>which</dt>
+<dt id="arg-which">which<a class="anchor" aria-label="anchor" href="#arg-which"></a></dt>
 <dd><p>a vector specifying which variable to do the prediction.</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>A list object called <code>predict</code> appended to the object of class <code>biplot</code> with the following elements:</p>
+<dl><dt>samples</dt>
+<dd><p>a vector of indices of samples which are being predicted.</p></dd>
 
-<p>Object of class PCA with the following elements:</p>
-<dl><dt>predict.samples</dt>
-<dd><p>which samples are predicted.</p></dd>
+<dt>predict.means</dt>
+<dd><p>a vector of group names of groups for which the means are being predicted.</p></dd>
 
-<dt>predict.mat</dt>
-<dd><p>matrix of predicted samples.</p></dd>
+<dt>which</dt>
+<dd><p>the vector of indices variables which are being predicted.</p></dd>
 
-<dt>predict.means</dt>
-<dd><p>which group means are predicted.</p></dd>
+<dt>predict.mat</dt>
+<dd><p>the matrix of predicted samples.</p></dd>
 
 <dt>predict.means.mat</dt>
-<dd><p>matrix of predicted group means.</p></dd>
+<dd><p>the matrix of predicted group means.</p></dd>
 
 </dl></div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span>data <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span>group.aes<span class="op">=</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span>, show.class.means <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
 <span class="r-in"><span><span class="fu">prediction</span><span class="op">(</span><span class="fl">141</span><span class="op">:</span><span class="fl">145</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">3</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="prediction-1.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span></span></span>
 </code></pre></div>
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-</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
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+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
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diff --git a/docs/reference/print.biplot.html b/docs/reference/print.biplot.html
index a421862..1ce7b8e 100644
--- a/docs/reference/print.biplot.html
+++ b/docs/reference/print.biplot.html
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-    <h1>Generic print function of objects of class biplot</h1>
-    
-    <div class="hidden name"><code>print.biplot.Rd</code></div>
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+      <img src="../logo.png" class="logo" alt=""><h1>Generic print function for objects of class biplot</h1>
+
+      <div class="d-none name"><code>print.biplot.Rd</code></div>
     </div>
 
-    <div class="ref-description">
-    <p>Generic print function of objects of class biplot</p>
+    <div class="ref-description section level2">
+    <p>This function is used to print output when the biplot object is created.</p>
     </div>
 
-    <div id="ref-usage">
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for biplot</span></span>
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'biplot'</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">x</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>x</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>an object of class <code>biplot</code>.</p></dd>
 
 
-<dt>...</dt>
+<dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
 <dd><p>additional arguments.</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>no return value, called for side effects.</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>This function will not produce a return value, it is called for side effects.</p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="va">out</span> <span class="op">&lt;-</span> <span class="fu"><a href="biplot.html">biplot</a></span> <span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="va">out</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Object of class biplot, based on 150 samples and 4 variables.</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 4 numeric variables.</span>
+<span class="r-in"><span></span></span>
 </code></pre></div>
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+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Reflect the biplot about a chosen axis — reflect • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Reflect the biplot about a chosen axis — reflect"><meta name="description" content="This function provides the user with an option to reflect the biplot horizontally, vertically or diagonally."><meta property="og:description" content="This function provides the user with an option to reflect the biplot horizontally, vertically or diagonally."><meta property="og:image" content="/logo.png"></head><body>
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-  <div class="col-md-9 contents">
-    <div class="page-header">
-    <h1>Reflect</h1>
-    
-    <div class="hidden name"><code>reflect.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+      </ul></div>
+
+
+  </div>
+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Reflect the biplot about a chosen axis</h1>
+
+      <div class="d-none name"><code>reflect.Rd</code></div>
     </div>
 
-    <div class="ref-description">
-    <p>Reflect</p>
+    <div class="ref-description section level2">
+    <p>This function provides the user with an option to reflect the biplot horizontally, vertically or diagonally.</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">reflect</span><span class="op">(</span><span class="va">bp</span>, reflect.axis <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"FALSE"</span>, <span class="st">"x"</span>, <span class="st">"y"</span>, <span class="st">"xy"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
-<dd><p>object of class <code>biplot</code></p></dd>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
 
 
-<dt>reflect.axis</dt>
-<dd><p>Defaults to FALSE. Possible values are "x" for reflection about x-axis or "y" for reflection about y-axis.</p></dd>
-
-</dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code></p></dd>
 
-<p>An object of class <code>biplot</code></p>
 
+<dt id="arg-reflect-axis">reflect.axis<a class="anchor" aria-label="anchor" href="#arg-reflect-axis"></a></dt>
+<dd><p>a character string indicating which axis about to reflect. One of <code>FALSE</code> (default), "<code>x</code>" for reflection about the x-axis, "<code>y</code>" for reflection about the y-axis and "<code>xy</code>" for reflection about both axes.</p></dd>
 
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>An object of class <code>biplot</code></p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span>,group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">reflect</span><span class="op">(</span><span class="st">"x"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="reflect-1.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span>,group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">reflect</span><span class="op">(</span><span class="st">"y"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="reflect-2.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span>,group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">reflect</span><span class="op">(</span><span class="st">"xy"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="reflect-3.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span></span></span>
 </code></pre></div>
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diff --git a/docs/reference/regress-1.png b/docs/reference/regress-1.png
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diff --git a/docs/reference/regress.biplot.html b/docs/reference/regress.biplot.html
index 10648f0..ad9adb6 100644
--- a/docs/reference/regress.biplot.html
+++ b/docs/reference/regress.biplot.html
@@ -1,78 +1,53 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Regression biplot — regress.biplot • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.1/jquery.min.js" integrity="sha512-v2CJ7UaYy4JwqLDIrZUI/4hqeoQieOmAZNXBeQyjo21dadnwR+8ZaIJVT8EE2iyI61OV8e6M8PP2/4hpQINQ/g==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Regression biplot — regress.biplot"><meta property="og:description" content="Computes regression biplot axes"><meta property="og:image" content="/logo.png"><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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-    <div class="page-header">
-    <h1>Regression biplot</h1>
-    
-    <div class="hidden name"><code>regress.biplot.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+      </ul></div>
+
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+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Regression biplot</h1>
+
+      <div class="d-none name"><code>regress.biplot.Rd</code></div>
     </div>
 
-    <div class="ref-description">
+    <div class="ref-description section level2">
     <p>Computes regression biplot axes</p>
     </div>
 
-    <div id="ref-usage">
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for biplot</span></span>
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'biplot'</span></span>
 <span><span class="fu"><a href="regress.html">regress</a></span><span class="op">(</span></span>
 <span>  <span class="va">bp</span>,</span>
 <span>  <span class="va">Z</span>,</span>
@@ -82,65 +57,61 @@ <h1>Regression biplot</h1>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
 
 
-<dt>Z</dt>
+<dt id="arg-z">Z<a class="anchor" aria-label="anchor" href="#arg-z"></a></dt>
 <dd><p>the matrix of coordinates of the samples</p></dd>
 
 
-<dt>group.aes</dt>
+<dt id="arg-group-aes">group.aes<a class="anchor" aria-label="anchor" href="#arg-group-aes"></a></dt>
 <dd><p>vector of the same length as the number of rows in the data matrix
 for differentiated aesthetics for samples.</p></dd>
 
 
-<dt>show.group.means</dt>
+<dt id="arg-show-group-means">show.group.means<a class="anchor" aria-label="anchor" href="#arg-show-group-means"></a></dt>
 <dd><p>logical, indicating whether group means should be plotted in the biplot.</p></dd>
 
 
-<dt>axes</dt>
+<dt id="arg-axes">axes<a class="anchor" aria-label="anchor" href="#arg-axes"></a></dt>
 <dd><p>the type of axes to be fitted to the biplot. Options are 'regression' for linear
 regression axes (default) and 'splines' for B-spline axes.</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>an object of class biplot.</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>an object of class biplot.</p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="regress.html">regress</a></span><span class="op">(</span>Z <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/stats/cmdscale.html" class="external-link">cmdscale</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/dist.html" class="external-link">dist</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="regress.biplot-1.png" alt="" width="700" height="433"></span>
 <span class="r-in"><span></span></span>
 </code></pre></div>
     </div>
-  </div>
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
-    </nav></div>
-</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
 
 
-      <footer><div class="copyright">
-  <p></p><p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
-<div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.9.</p>
+<div class="pkgdown-footer-right">
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diff --git a/docs/reference/regress.html b/docs/reference/regress.html
new file mode 100644
index 0000000..d63271d
--- /dev/null
+++ b/docs/reference/regress.html
@@ -0,0 +1,110 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Regression biplot method — regress • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Regression biplot method — regress"><meta name="description" content="Regression biplot method"><meta property="og:description" content="Regression biplot method"><meta property="og:image" content="/logo.png"></head><body>
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+    <li><a class="dropdown-item" href="../articles/Biplots_in_3D.html">Three dimensional biplots</a></li>
+  </ul></li>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
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+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Regression biplot method</h1>
+
+      <div class="d-none name"><code>regress.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>Regression biplot method</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">regress</span><span class="op">(</span><span class="va">bp</span>, <span class="va">Z</span>, group.aes<span class="op">=</span><span class="cn">NULL</span>, show.group.means <span class="op">=</span> <span class="cn">TRUE</span>, </span>
+<span>               axes <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"regression"</span>, <span class="st">"splines"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code> obtained from preceding function <code><a href="biplot.html">biplot()</a></code>.</p></dd>
+
+
+<dt id="arg-z">Z<a class="anchor" aria-label="anchor" href="#arg-z"></a></dt>
+<dd><p>the matrix of coordinates of the samples</p></dd>
+
+
+<dt id="arg-group-aes">group.aes<a class="anchor" aria-label="anchor" href="#arg-group-aes"></a></dt>
+<dd><p>vector of the same length as the number of rows in the data matrix
+for differentiated aesthetics for samples.</p></dd>
+
+
+<dt id="arg-show-group-means">show.group.means<a class="anchor" aria-label="anchor" href="#arg-show-group-means"></a></dt>
+<dd><p>logical, indicating whether group means should be plotted in the biplot.</p></dd>
+
+
+<dt id="arg-axes">axes<a class="anchor" aria-label="anchor" href="#arg-axes"></a></dt>
+<dd><p>the type of axes to be fitted to the biplot. Options are 'regression' for linear
+regression axes (default) and 'splines' for B-spline axes.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>Object of class biplot</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">regress</span><span class="op">(</span>Z<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/stats/cmdscale.html" class="external-link">cmdscale</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/dist.html" class="external-link">dist</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="regress-1.png" alt="" width="700" height="433"></span>
+</code></pre></div>
+    </div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
+
+
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+</div>
+
+<div class="pkgdown-footer-right">
+  <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.2.</p>
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+
diff --git a/docs/reference/rotate-1.png b/docs/reference/rotate-1.png
index 42d0a04..ede40d6 100644
Binary files a/docs/reference/rotate-1.png and b/docs/reference/rotate-1.png differ
diff --git a/docs/reference/rotate.html b/docs/reference/rotate.html
index 44a4ac5..6eb5d88 100644
--- a/docs/reference/rotate.html
+++ b/docs/reference/rotate.html
@@ -1,124 +1,96 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Rotate — rotate • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.1/jquery.min.js" integrity="sha512-v2CJ7UaYy4JwqLDIrZUI/4hqeoQieOmAZNXBeQyjo21dadnwR+8ZaIJVT8EE2iyI61OV8e6M8PP2/4hpQINQ/g==" crossorigin="anonymous" referrerpolicy="no-referrer"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Rotate — rotate"><meta property="og:description" content="Rotate"><meta property="og:image" content="/logo.png"><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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+    <li><a class="dropdown-item" href="../articles/Biplots_in_1D.html">One dimensional biplots</a></li>
+    <li><a class="dropdown-item" href="../articles/Biplots_in_3D.html">Three dimensional biplots</a></li>
   </ul></li>
-      </ul><ul class="nav navbar-nav navbar-right"></ul></div><!--/.nav-collapse -->
-  </div><!--/.container -->
-</div><!--/.navbar -->
-
-      
-
-      </header><div class="row">
-  <div class="col-md-9 contents">
-    <div class="page-header">
-    <h1>Rotate</h1>
-    
-    <div class="hidden name"><code>rotate.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+      </ul></div>
+
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+  </div>
+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Rotate the biplot a chosen amount of degrees</h1>
+
+      <div class="d-none name"><code>rotate.Rd</code></div>
     </div>
 
-    <div class="ref-description">
-    <p>Rotate</p>
+    <div class="ref-description section level2">
+    <p>This function provides the user with an option to rotate the biplot anti-clockwise or clockwise.</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">rotate</span><span class="op">(</span><span class="va">bp</span>, rotate.degrees <span class="op">=</span> <span class="fl">0</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
-<dd><p>object of class <code>biplot</code></p></dd>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
 
 
-<dt>rotate.degrees</dt>
-<dd><p>Default is 0. Positive value results in anti-clockwise rotation and negative value in clockwise rotation.</p></dd>
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code></p></dd>
 
-</dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
 
-<p>An object of class <code>biplot</code>.</p>
+<dt id="arg-rotate-degrees">rotate.degrees<a class="anchor" aria-label="anchor" href="#arg-rotate-degrees"></a></dt>
+<dd><p>a value specifying the degrees the biplot should be rotated, with default <code>0</code>. A positive value results in anti-clockwise rotation and a negative value in clockwise rotation.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>An object of class <code>biplot</code>.</p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span>,group.aes <span class="op">=</span> <span class="va">iris</span><span class="op">[</span>,<span class="fl">5</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">rotate</span><span class="op">(</span><span class="fl">200</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-plt img"><img src="rotate-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span></span></span>
 </code></pre></div>
     </div>
-  </div>
-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
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+    </nav></aside></div>
 
 
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-  <p></p><p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
 </div>
 
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+++ b/docs/reference/samples.html
@@ -0,0 +1,261 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><title>Format aesthetics for the biplot samples — samples • biplotEZ</title><!-- favicons --><link rel="icon" type="image/png" sizes="96x96" href="../favicon-96x96.png"><link rel="icon" type="”image/svg+xml”" href="../favicon.svg"><link rel="apple-touch-icon" sizes="180x180" href="../apple-touch-icon.png"><link rel="icon" sizes="any" href="../favicon.ico"><link rel="manifest" href="../site.webmanifest"><script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"><link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"><script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"><link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Format aesthetics for the biplot samples — samples"><meta name="description" content="This function allows the user to format the aesthetics for the samples."><meta property="og:description" content="This function allows the user to format the aesthetics for the samples."><meta property="og:image" content="/logo.png"></head><body>
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+    <li><a class="dropdown-item" href="../articles/Biplots_in_3D.html">Three dimensional biplots</a></li>
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+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
+ <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"></form></li>
+      </ul></div>
+
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+  </div>
+</nav><div class="container template-reference-topic">
+<div class="row">
+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Format aesthetics for the biplot samples</h1>
+
+      <div class="d-none name"><code>samples.Rd</code></div>
+    </div>
+
+    <div class="ref-description section level2">
+    <p>This function allows the user to format the aesthetics for the samples.</p>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">samples</span> <span class="op">(</span><span class="va">bp</span>,  which <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="va">bp</span><span class="op">$</span><span class="va">g</span>, col <span class="op">=</span> <span class="va">ez.col</span>, pch <span class="op">=</span> <span class="fl">16</span>, cex <span class="op">=</span> <span class="fl">1</span>,</span>
+<span>label <span class="op">=</span> <span class="cn">FALSE</span>, label.name <span class="op">=</span> <span class="cn">NULL</span>, label.col<span class="op">=</span><span class="cn">NULL</span>, label.cex <span class="op">=</span> <span class="fl">0.75</span>, </span>
+<span>label.side <span class="op">=</span> <span class="st">"bottom"</span>, label.offset <span class="op">=</span> <span class="fl">0.5</span>,</span>
+<span>connected<span class="op">=</span><span class="cn">FALSE</span>, connect.col <span class="op">=</span> <span class="st">"black"</span>, connect.lty <span class="op">=</span> <span class="fl">1</span>, </span>
+<span>connect.lwd <span class="op">=</span> <span class="fl">1</span>, opacity <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
+<dd><p>an object of class <code>biplot</code>.</p></dd>
+
+
+<dt id="arg-which">which<a class="anchor" aria-label="anchor" href="#arg-which"></a></dt>
+<dd><p>a vector containing the groups or classes for which the samples should be displayed, with default <code>bp$g</code>.</p></dd>
+
+
+<dt id="arg-col">col<a class="anchor" aria-label="anchor" href="#arg-col"></a></dt>
+<dd><p>the colour(s) for the samples, with default <code>blue</code>.</p></dd>
+
+
+<dt id="arg-pch">pch<a class="anchor" aria-label="anchor" href="#arg-pch"></a></dt>
+<dd><p>the plotting character(s) for the samples, with default <code>16</code>.</p></dd>
+
+
+<dt id="arg-cex">cex<a class="anchor" aria-label="anchor" href="#arg-cex"></a></dt>
+<dd><p>the character expansion(s) for the samples, with default <code>1</code>.</p></dd>
+
+
+<dt id="arg-label">label<a class="anchor" aria-label="anchor" href="#arg-label"></a></dt>
+<dd><p>a logical value indicating whether the samples should be labelled, with default <code>FALSE</code>. Alternatively, specify <code>"ggrepel"</code> for non-overlapping placement of labels.</p></dd>
+
+
+<dt id="arg-label-name">label.name<a class="anchor" aria-label="anchor" href="#arg-label-name"></a></dt>
+<dd><p>a vector of the same length as <code>which</code> with label names for the samples, with default <code>NULL</code>. If <code>NULL</code>, the <code>rownames(bp)</code> are used. Alternatively, a custom vector of length <code>n</code> should be used.</p></dd>
+
+
+<dt id="arg-label-col">label.col<a class="anchor" aria-label="anchor" href="#arg-label-col"></a></dt>
+<dd><p>a vector of the same length as <code>which</code> with label colours for the samples, with default as the same colour of the sample points.</p></dd>
+
+
+<dt id="arg-label-cex">label.cex<a class="anchor" aria-label="anchor" href="#arg-label-cex"></a></dt>
+<dd><p>a vector of the same length as <code>which</code> with label text expansions for the samples, with default <code>0.75</code>.</p></dd>
+
+
+<dt id="arg-label-side">label.side<a class="anchor" aria-label="anchor" href="#arg-label-side"></a></dt>
+<dd><p>the side at which the label of the plotted point appears, with default <code>bottom</code>. Note that unlike the argument <code>pos</code> in <code><a href="https://rdrr.io/r/graphics/text.html" class="external-link">text()</a></code>, options are "<code>bottom</code>", "<code>left</code>", "<code>top</code>", "<code>right</code>" and not <code>1</code>, <code>2</code>, <code>3</code>, <code>4</code>.</p></dd>
+
+
+<dt id="arg-label-offset">label.offset<a class="anchor" aria-label="anchor" href="#arg-label-offset"></a></dt>
+<dd><p>the offset of the label from the plotted point. See <code><a href="https://rdrr.io/r/graphics/text.html" class="external-link">?text</a></code> for a detailed explanation of the argument <code>offset</code>.</p></dd>
+
+
+<dt id="arg-connected">connected<a class="anchor" aria-label="anchor" href="#arg-connected"></a></dt>
+<dd><p>a logical value indicating whether samples are connected in order of rows of the data matrix, with default <code>FALSE</code>.</p></dd>
+
+
+<dt id="arg-connect-col">connect.col<a class="anchor" aria-label="anchor" href="#arg-connect-col"></a></dt>
+<dd><p>the colour of the connecting line, with default <code>black</code>.</p></dd>
+
+
+<dt id="arg-connect-lty">connect.lty<a class="anchor" aria-label="anchor" href="#arg-connect-lty"></a></dt>
+<dd><p>the line type of the connecting line, with default <code>1</code>.</p></dd>
+
+
+<dt id="arg-connect-lwd">connect.lwd<a class="anchor" aria-label="anchor" href="#arg-connect-lwd"></a></dt>
+<dd><p>the line width of the connecting line, with default <code>1</code>.</p></dd>
+
+
+<dt id="arg-opacity">opacity<a class="anchor" aria-label="anchor" href="#arg-opacity"></a></dt>
+<dd><p>the opacity level of the plotted points, with default <code>1</code> for an opaque point.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>The object of class <code>biplot</code> will be appended with a list called <code>samples</code> containing the following elements:</p>
+<dl><dt>which</dt>
+<dd><p>a vector containing the groups or classes for which the samples (and means) are displayed.</p></dd>
+
+<dt>col</dt>
+<dd><p>the colour(s) of the samples.</p></dd>
+
+<dt>pch</dt>
+<dd><p>the plotting character(s) of the samples.</p></dd>
+
+<dt>cex</dt>
+<dd><p>the character expansion(s) of the plotting character(s) of the samples.</p></dd>
+
+<dt>label</dt>
+<dd><p>a logical value indicating whether samples are labelled.</p></dd>
+
+<dt>label.name</dt>
+<dd><p>the label names of the samples.</p></dd>
+
+<dt>label.col</dt>
+<dd><p>the label colours of the samples.</p></dd>
+
+<dt>label.cex</dt>
+<dd><p>the label text expansions of the samples.</p></dd>
+
+<dt>label.side</dt>
+<dd><p>the side at which the label of the plotted point appears..</p></dd>
+
+<dt>label.offset</dt>
+<dd><p>the offset of the label from the plotted point.</p></dd>
+
+<dt>connected</dt>
+<dd><p>a logical value indicating whether samples are connected in order of the rows of the data matrix.</p></dd>
+
+<dt>connect.col</dt>
+<dd><p>the colour of the connecting line.</p></dd>
+
+<dt>connect.lty</dt>
+<dd><p>the line type of the connecting line.</p></dd>
+
+<dt>connect.lwd</dt>
+<dd><p>the line width of the connecting line.</p></dd>
+
+<dt>opacity</dt>
+<dd><p>the opacity level of the plotted points.</p></dd>
+
+</dl></div>
+    <div class="section level2">
+    <h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></a></h2>
+    <p>The arguments <code>which</code>, <code>col</code>, <code>pch</code> and <code>cex</code> are based on the specification of <code>group.aes</code> or <code>classes</code>. If no groups are specified, a single colour, plotting character and / or character expansion is expected. If \(g\) groups are
+specified, vectors of length \(g\) is expected, or values are recycled to length \(g\).</p>
+<p>The arguments <code>label</code>, <code>label.cex</code>, <code>label.side</code> and <code>label.offset</code> are based on the sample size \(n\). A single value
+will be recycled \(n\) times or a vector of length \(n\) is expected.</p>
+    </div>
+    <div class="section level2">
+    <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
+    <div class="dont-index"><p><code><a href="biplot.html">biplot()</a></code></p></div>
+    </div>
+
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu">samples</span><span class="op">(</span>col<span class="op">=</span><span class="st">"purple"</span>,pch<span class="op">=</span><span class="fl">15</span>, opacity<span class="op">=</span><span class="fl">0.5</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="samples-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
+<span class="r-in"><span>  <span class="fu">samples</span><span class="op">(</span>col<span class="op">=</span><span class="st">"purple"</span>,pch<span class="op">=</span><span class="cn">NA</span>, opacity<span class="op">=</span><span class="fl">0.5</span>, label <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="samples-2.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
+<span class="r-in"><span>  <span class="fu">samples</span><span class="op">(</span>col<span class="op">=</span><span class="st">"purple"</span>,pch<span class="op">=</span><span class="cn">NA</span>, opacity<span class="op">=</span><span class="fl">0.5</span>, label <span class="op">=</span> <span class="cn">TRUE</span>, </span></span>
+<span class="r-in"><span>          label.name <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"s:"</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">150</span>, sep<span class="op">=</span><span class="st">""</span><span class="op">)</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
+<span class="r-in"><span>  <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="samples-3.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span><span class="fu"><a href="biplot.html">biplot</a></span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> </span></span>
+<span class="r-in"><span>  <span class="fu">samples</span><span class="op">(</span>col<span class="op">=</span><span class="st">"purple"</span>,pch<span class="op">=</span><span class="cn">NA</span>, opacity<span class="op">=</span><span class="fl">0.5</span>, label <span class="op">=</span> <span class="st">"ggrepel"</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="op">)</span></span></span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$x` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `x` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$y` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `y` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$z` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `z` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$x` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `x` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$y` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `y` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$z` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `z` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$x` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `x` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$y` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `y` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$z` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `z` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$x` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `x` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$y` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `y` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$z` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `z` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$x` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `x` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$y` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `y` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$z` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `z` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$x` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `x` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$y` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `y` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>Use of `df$z` is discouraged.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span style="color: #00BBBB;">ℹ</span> Use `z` instead.</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>ggrepel: 14 unlabeled data points (too many overlaps). Consider increasing max.overlaps</span>
+<span class="r-wrn co"><span class="r-pr">#&gt;</span> <span class="warning">Warning: </span>ggrepel: 14 unlabeled data points (too many overlaps). Consider increasing max.overlaps</span>
+<span class="r-plt img"><img src="samples-4.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span></span></span>
+</code></pre></div>
+    </div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
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index e262f99..3acd8b9 100644
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@@ -1,97 +1,73 @@
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+      <img src="../logo.png" class="logo" alt=""><h1>Computes the square root of the Manhattan distance An example of a Euclidean embeddable distance metric</h1>
 
-      </header><div class="row">
-  <div class="col-md-9 contents">
-    <div class="page-header">
-    <h1>Computes the square root of the Manhattan distance An example of a Euclidean embeddable distance metric</h1>
-    
-    <div class="hidden name"><code>sqrtManhattan.Rd</code></div>
+      <div class="d-none name"><code>sqrtManhattan.Rd</code></div>
     </div>
 
-    <div class="ref-description">
+    <div class="ref-description section level2">
     <p>Computes the square root of the Manhattan distance
 An example of a Euclidean embeddable distance metric</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">sqrtManhattan</span><span class="op">(</span><span class="va">X</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>X</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-x">X<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
 <dd><p>matrix of samples x variables for computation of samples x samples distance matrix</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>a dist object</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>a dist object</p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="fu">sqrtManhattan</span><span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>             1         2         3         4         5         6         7</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 2   0.8366600                                                            </span>
@@ -3395,27 +3371,23 @@ <h2>Examples</h2>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 150 0.9486833 1.2247449</span>
 </code></pre></div>
     </div>
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@@ -1,78 +1,53 @@
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-    <h1>Generic summary function of objects of class biplot</h1>
-    
-    <div class="hidden name"><code>summary.biplot.Rd</code></div>
+      </ul><ul class="navbar-nav"><li class="nav-item"><form class="form-inline" role="search">
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+  <main id="main" class="col-md-9"><div class="page-header">
+      <img src="../logo.png" class="logo" alt=""><h1>Generic summary function for objects of class biplot</h1>
+
+      <div class="d-none name"><code>summary.biplot.Rd</code></div>
     </div>
 
-    <div class="ref-description">
-    <p>Generic summary function of objects of class biplot</p>
+    <div class="ref-description section level2">
+    <p>This function is used to print summary output of the biplot. These summary outputs are related to measures of fit.</p>
     </div>
 
-    <div id="ref-usage">
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for biplot</span></span>
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="co"># S3 method for class 'biplot'</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span></span>
 <span>  <span class="va">object</span>,</span>
 <span>  adequacy <span class="op">=</span> <span class="cn">TRUE</span>,</span>
@@ -85,67 +60,67 @@ <h1>Generic summary function of objects of class biplot</h1>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>object</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-object">object<a class="anchor" aria-label="anchor" href="#arg-object"></a></dt>
 <dd><p>an object of class <code>biplot</code>.</p></dd>
 
 
-<dt>adequacy</dt>
-<dd><p>logical, whether variable adequacies should be reported.</p></dd>
+<dt id="arg-adequacy">adequacy<a class="anchor" aria-label="anchor" href="#arg-adequacy"></a></dt>
+<dd><p>a logical value indicating whether variable adequacies should be reported, with default <code>TRUE</code>.</p></dd>
 
 
-<dt>axis.predictivity</dt>
-<dd><p>logical, whether axis predictivities should be reported.</p></dd>
+<dt id="arg-axis-predictivity">axis.predictivity<a class="anchor" aria-label="anchor" href="#arg-axis-predictivity"></a></dt>
+<dd><p>a logical value indicating whether axis predictivities should be reported, with default <code>TRUE</code>.</p></dd>
 
 
-<dt>sample.predictivity</dt>
-<dd><p>logical, whether sample predictivities should be reported.</p></dd>
+<dt id="arg-sample-predictivity">sample.predictivity<a class="anchor" aria-label="anchor" href="#arg-sample-predictivity"></a></dt>
+<dd><p>a logical value indicating whether sample predictivities should be reported, with default <code>TRUE</code>.</p></dd>
 
 
-<dt>class.predictivity</dt>
-<dd><p>logical, whether class predictivities should be reported
+<dt id="arg-class-predictivity">class.predictivity<a class="anchor" aria-label="anchor" href="#arg-class-predictivity"></a></dt>
+<dd><p>a logical value indicating whether class predictivities should be reported, with default <code>TRUE</code>
 (only applicable to objects of class <code>CVA</code>).</p></dd>
 
 
-<dt>within.class.axis.predictivity</dt>
-<dd><p>logical, whether within class axis predictivity
-should be reported(only applicable to objects
+<dt id="arg-within-class-axis-predictivity">within.class.axis.predictivity<a class="anchor" aria-label="anchor" href="#arg-within-class-axis-predictivity"></a></dt>
+<dd><p>a logical value indicating whether within class axis predictivity
+should be reported, with default <code>TRUE</code> (only applicable to objects
 of class <code>CVA</code>).</p></dd>
 
 
-<dt>within.class.sample.predictivity</dt>
-<dd><p>logical, whether within class sample predictivity
-should be reported(only applicable to objects
+<dt id="arg-within-class-sample-predictivity">within.class.sample.predictivity<a class="anchor" aria-label="anchor" href="#arg-within-class-sample-predictivity"></a></dt>
+<dd><p>a logical value indicating whether within class sample predictivity
+should be reported, with default <code>TRUE</code> (only applicable to objects
 of class <code>CVA</code>).</p></dd>
 
 
-<dt>...</dt>
+<dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
 <dd><p>additional arguments.</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>no return value, called for side effects.</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>This function will not produce a return value, it is called for side effects.</p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="va">out</span> <span class="op">&lt;-</span> <span class="fu"><a href="biplot.html">biplot</a></span> <span class="op">(</span><span class="va">iris</span><span class="op">[</span>,<span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">]</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="PCA.html">PCA</a></span><span class="op">(</span><span class="op">)</span> <span class="op">|&gt;</span> <span class="fu"><a href="fit.measures.html">fit.measures</a></span><span class="op">(</span><span class="op">)</span></span></span>
 <span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">out</span><span class="op">)</span></span></span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Object of class biplot, based on 150 samples and 4 variables.</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 4 numeric variables.</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Quality of fit = 97.8% </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Adequacy of variables:</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Quality of fit in 2 dimension(s) = 97.8% </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Adequacy of variables in 2 dimension(s):</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Sepal.Length  Sepal.Width Petal.Length  Petal.Width </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    0.5617091    0.5402798    0.7639426    0.1340685 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Axis predictivity:</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Axis predictivity in 2 dimension(s):</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> Sepal.Length  Sepal.Width Petal.Length  Petal.Width </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>    0.9579017    0.8400028    0.9980931    0.9365937 </span>
-<span class="r-out co"><span class="r-pr">#&gt;</span> Sample predictivity:</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Sample predictivity in 2 dimension(s):</span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>         1         2         3         4         5         6         7         8 </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 0.9998927 0.9927400 0.9999141 0.9991226 0.9984312 0.9949770 0.9914313 0.9996346 </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>         9        10        11        12        13        14        15        16 </span>
@@ -184,29 +159,26 @@ <h2>Examples</h2>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 0.8947527 0.9797055 0.9458421 0.9902488 0.9674660 0.9350646 0.9636413 0.9867931 </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span>       145       146       147       148       149       150 </span>
 <span class="r-out co"><span class="r-pr">#&gt;</span> 0.9500265 0.9470544 0.9688318 0.9886543 0.8735433 0.9281727 </span>
+<span class="r-in"><span></span></span>
 </code></pre></div>
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+    <footer><div class="pkgdown-footer-left">
+  <p>Developed by Sugnet Lubbe, Niël le Roux, Johané Nienkemper-Swanepoel, Raeesa Ganey, Ruan Buys, Zoë-Mae Adams, Peter Manefeldt.</p>
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+++ b/docs/reference/translate_axes.html
@@ -1,114 +1,89 @@
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-    <h1>Translate biplot axes</h1>
-    
-    <div class="hidden name"><code>translate_axes.Rd</code></div>
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+      <img src="../logo.png" class="logo" alt=""><h1>Translate biplot axes</h1>
+
+      <div class="d-none name"><code>translate_axes.Rd</code></div>
     </div>
 
-    <div class="ref-description">
+    <div class="ref-description section level2">
     <p>Automatically or manually translate the axes away from the center of the plot</p>
     </div>
 
-    <div id="ref-usage">
+    <div class="section level2">
+    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">translate_axes</span><span class="op">(</span><span class="va">bp</span>, delta <span class="op">=</span> <span class="fl">0</span>, swop <span class="op">=</span> <span class="cn">FALSE</span>, distances <span class="op">=</span> <span class="cn">NULL</span><span class="op">)</span></span></code></pre></div>
     </div>
 
-    <div id="arguments">
-    <h2>Arguments</h2>
-    <dl><dt>bp</dt>
+    <div class="section level2">
+    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
+
+
+<dl><dt id="arg-bp">bp<a class="anchor" aria-label="anchor" href="#arg-bp"></a></dt>
 <dd><p>An object of class <code>biplot</code></p></dd>
 
 
-<dt>delta</dt>
+<dt id="arg-delta">delta<a class="anchor" aria-label="anchor" href="#arg-delta"></a></dt>
 <dd><p>numeric value indicating distance between axes</p></dd>
 
 
-<dt>swop</dt>
+<dt id="arg-swop">swop<a class="anchor" aria-label="anchor" href="#arg-swop"></a></dt>
 <dd><p>logical. Change the direction in which axes are translated</p></dd>
 
 
-<dt>distances</dt>
+<dt id="arg-distances">distances<a class="anchor" aria-label="anchor" href="#arg-distances"></a></dt>
 <dd><p>numeric vector of distances. Used to manually parallel translate the axes.</p></dd>
 
 </dl></div>
-    <div id="value">
-    <h2>Value</h2>
-    
-
-<p>An object of class <code>biplot</code> with the translated distances appended under bp$axes</p>
+    <div class="section level2">
+    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+    <p>An object of class <code>biplot</code> with the translated distances appended under bp$axes</p>
     </div>
-    <div id="details">
-    <h2>Details</h2>
+    <div class="section level2">
+    <h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></a></h2>
     <p>This function uses the same algorithm implemented in <code><a href="https://rdrr.io/pkg/bipl5/man/TDAbiplot.html" class="external-link">TDAbiplot</a></code>
 in the <code>bipl5</code> package. It translates the axes out of the center of the plot.
 Correlated axes generally gets translated in the same direction.</p>
 <p>This function calculates the <code>orthogx</code> and <code>orthogy</code> paramaters in <code><a href="axes.html">axes()</a></code></p>
     </div>
 
-    <div id="ref-examples">
-    <h2>Examples</h2>
+    <div class="section level2">
+    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
     <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span></span></span>
 <span class="r-in"><span><span class="co">#Translate the axes out of the plot center</span></span></span>
 <span class="r-in"><span></span></span>
@@ -126,27 +101,23 @@ <h2>Examples</h2>
 <span class="r-plt img"><img src="translate_axes-2.png" alt="" width="700" height="433"></span>
 </code></pre></div>
     </div>
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-  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
-    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
-    </nav></div>
-</div>
+  </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2>
+    </nav></aside></div>
 
 
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diff --git a/docs/search.json b/docs/search.json
new file mode 100644
index 0000000..61fe735
--- /dev/null
+++ b/docs/search.json
@@ -0,0 +1 @@
+[{"path":"/articles/biplotEZ.html","id":"what-is-a-pca-biplot","dir":"Articles","previous_headings":"","what":"What is a PCA biplot","title":"biplotEZ","text":"Consider data matrix 𝐗*:n×p\\mathbf{X}^{*}:n \\times p containing data nn objects pp variables. produce 2D biplot, need optimally approximate 𝐗=(𝐈n−1n𝟏𝟏′)𝐗*\\mathbf{X} = (\\mathbf{}_n-\\frac{1}{n}\\mathbf{11}')\\mathbf{X}^{*} (typically rank pp p<np<n) rank 22 matrix. terms least squares error, want min∥𝐗̂−𝐗∥2 min \\| \\hat{\\mathbf{X}}-\\mathbf{X} \\|^2  rank(𝐗̂)=2rank(\\hat{\\mathbf{X}})=2. shown Eckart Young (1936) singular value decomposition 𝐗=𝐔𝐃𝐕′\\mathbf{X} = \\mathbf{UDV'} 𝐗̂=𝐔𝐉𝐃𝐉𝐕′ \\hat{\\mathbf{X}} = \\mathbf{UJDJV'}  𝐉=[𝐈2𝟎𝟎𝟎] \\mathbf{J} = \\begin{bmatrix}               \\mathbf{}_2 & \\mathbf{0}\\\\               \\mathbf{0} & \\mathbf{0}              \\end{bmatrix}  essentially selecting first two columns 𝐔\\mathbf{U}, diagonal matrix first (largest) two singular values first two rows 𝐕′\\mathbf{V}'. Define 𝐉2=[𝐈2𝟎] \\mathbf{J}_2 = \\begin{bmatrix}                 \\mathbf{}_2\\\\                 \\mathbf{0}                \\end{bmatrix}  𝐉2𝐉2′=𝐉\\mathbf{J}_2\\mathbf{J}_2' = \\mathbf{J} can write 𝐗̂=(𝐔𝐃𝐉2)(𝐕𝐉2)′\\hat{\\mathbf{X}} = (\\mathbf{UDJ}_2)(\\mathbf{VJ}_2)'. Gabriel (1971) shows rank 22 matrix can written 𝐗̂=𝐆𝐇′\\begin{equation}   \\hat{\\mathbf{X}} = \\mathbf{G} \\mathbf{H}' \\tag{1} \\end{equation} 𝐆:n×2\\mathbf{G}:n \\times 2 𝐇:p×2\\mathbf{H}:p \\times 2.nn rows 𝐆\\mathbf{G} provide nn pairs 2D coordinates representing rows 𝐗̂\\hat{\\mathbf{X}} pp rows 𝐇\\mathbf{H} provide pp pairs 2D coordinates representing columns 𝐗̂\\hat{\\mathbf{X}}. Since 𝐗̂=(𝐔𝐃𝐉2)(𝐕𝐉2)′\\hat{\\mathbf{X}} = (\\mathbf{UDJ}_2)(\\mathbf{VJ}_2)', setting 𝐆=𝐔𝐃𝐉2\\mathbf{G}=\\mathbf{UDJ}_2 𝐇=𝐕𝐉2\\mathbf{H}=\\mathbf{VJ}_2 obtains best least squares approximation 𝐗\\mathbf{X}. Gabriel (1971) shows approximation distances rows optimal, approximation correlations cosines angles rows 𝐇\\mathbf{H} sub-optimal. rows 𝐆\\mathbf{G} plotted points, representing samples. rows 𝐇\\mathbf{H} provide directions axes variables. Since xij*−x‾j=xij≈x̂ij=𝐠()′𝐡(j) x^{*}_{ij}-\\bar{x}_j = x_{ij} \\approx \\hat{x}_{ij} = \\mathbf{g}_{()}'\\mathbf{h}_{(j)}  values predict μ\\mu variable jj form μ=𝐠′μ𝐡(j) \\mu = \\mathbf{g}'_{\\mu}\\mathbf{h}_{(j)}  defines straight line orthogonal 𝐡(j)\\mathbf{h}_{(j)} biplot space (see dotted red line Figure 1()). find intersection prediction line 𝐡(j)\\mathbf{h}_{(j)} note 𝐠′()𝐡(j)=∥𝐠()∥∥𝐡(j)∥cos(𝐠(),𝐡(j))=∥𝐩∥∥𝐡(j)∥ \\mathbf{g}'_{()}\\mathbf{h}_{(j)} = \\| \\mathbf{g}_{()} \\| \\| \\mathbf{h}_{(j)} \\| cos(\\mathbf{g}_{()},\\mathbf{h}_{(j)}) =  \\| \\mathbf{p} \\| \\| \\mathbf{h}_{(j)} \\|   𝐩\\mathbf{p} length orthogonal projection 𝐠()\\mathbf{g}_{()} 𝐡(j)\\mathbf{h}_{(j)}. illustrated Figure 1(b) triangle ABC: cos(θ)=ACABcos(\\theta) = \\frac{AC}{AB} AC=ABcos(θ)AC = AB cos(\\theta) length ACAC, written ∥𝐩∥\\| \\mathbf{p} \\| equal cosine times length ABAB, .e. cos(𝐠(),𝐡(j))∥𝐠()∥cos(\\mathbf{g}_{()},\\mathbf{h}_{(j)}) \\| \\mathbf{g}_{()} \\|. Figure 1: Calibration biplot axes. Since 𝐩\\mathbf{p} along 𝐡(j)\\mathbf{h}_{(j)} can write 𝐩=c𝐡(j)\\mathbf{p} = c\\mathbf{h}_{(j)} points prediction line μ=𝐠′μ𝐡(j)\\mu = \\mathbf{g}'_{\\mu}\\mathbf{h}_{(j)} project point cμ𝐡(j)c_{\\mu}\\mathbf{h}_{(j)}. solve cμc_{\\mu} μ=𝐠′μ𝐡(j)=∥𝐩∥∥𝐡(j)∥=∥cμ𝐡(j)∥∥𝐡(j)∥ \\mu = \\mathbf{g}'_{\\mu}\\mathbf{h}_{(j)}=\\| \\mathbf{p} \\| \\| \\mathbf{h}_{(j)} \\| =  \\| c_{\\mu}\\mathbf{h}_{(j)} \\| \\| \\mathbf{h}_{(j)} \\| cμ=μ𝐡(j)′𝐡(j). c_{\\mu} = \\frac{\\mu}{\\mathbf{h}_{(j)}'\\mathbf{h}_{(j)}}.  select ‘nice’ scale markers τ1,τ2,⋯τk\\tau_{1}, \\tau_{2}, \\cdots \\tau_{k} variable jj, τh−x‾j=μh\\tau_{h}-\\bar{x}_j = \\mu_{h} positions scale markers 𝐡(j)\\mathbf{h}_{(j)} given pμ1,pμ2,⋯pμkp_{\\mu_{1}}, p_{\\mu_{2}}, \\cdots p_{\\mu_{k}} pμh=cμh𝐡(j)=μh𝐡(j)′𝐡(j)𝐡(j) p_{\\mu_h} = c_{\\mu_h}\\mathbf{h}_{(j)} =  \\frac{\\mu_h}{\\mathbf{h}_{(j)}'\\mathbf{h}_{(j)}}\\mathbf{h}_{(j)} \\tag{2}  obtain PCA biplot 48×448\\times 4 rock data R call","code":"biplot(rock, scale = TRUE) |> PCA() |> plot()"},{"path":"/articles/biplotEZ.html","id":"the-function-biplot","dir":"Articles","previous_headings":"","what":"The function biplot()","title":"biplotEZ","text":"function biplot() takes data set (usually) outputs object class biplot. Apart specifying data set, can specify single variable classification purposes. want use variable state.region formatting, say colour coding samples according region, instead specify grouping.aes indicate pertains aesthetics, rather data structure. can include exclude aestethics variable data set. Next, look centring scaling numeric data matrix. saw section 1 , PCA computed centred data matrix. methods, centring either required effect methodology, therefore default center = TRUE. Since centring usually assumed, get warning message, explicitly choose set center = FALSE. default scaled FALSE, often variables different units measurement, advisable divide variable standard deviation accomplished setting `scale = TRUE’. final optional argument function specifying title plot. notice output , centring / scaling effect print method. however effect components object class biplot output. Note components means sd contain sample means sample sds either/center scaled TRUE. values FALSE, components contain zeros means /ones sd ensure back transformation affect.","code":"state.data <- data.frame (state.region, state.x77) biplot(state.data) #> Object of class biplot, based on 50 samples and 9 variables. #> 8 numeric variables. #> 1 categorical variable. biplot(state.x77, classes=state.region) #> Object of class biplot, based on 50 samples and 8 variables. #> 8 numeric variables. #> 4 classes: Northeast South North Central West biplot(state.x77, group.aes=state.region) #> Object of class biplot, based on 50 samples and 8 variables. #> 8 numeric variables. biplot(state.data)                 # centred, but no scaling #> Object of class biplot, based on 50 samples and 9 variables. #> 8 numeric variables. #> 1 categorical variable. biplot(state.data, scale = TRUE)   # centered and scaled #> Object of class biplot, based on 50 samples and 9 variables. #> 8 numeric variables. #> 1 categorical variable. biplot(state.data, center = FALSE) # no centring (usually not recommended) or scaling #> Object of class biplot, based on 50 samples and 9 variables. #> 8 numeric variables. #> 1 categorical variable. out <- biplot(state.data)                 # centred, but no scaling out$center #> [1] TRUE out$scaled #> [1] FALSE out$means #> Population     Income Illiteracy   Life.Exp     Murder    HS.Grad      Frost  #>  4246.4200  4435.8000     1.1700    70.8786     7.3780    53.1080   104.4600  #>       Area  #> 70735.8800 out$sd #> [1] 1 1 1 1 1 1 1 1 out <- biplot(state.data, scale = TRUE)   # centered and scaled out$center #> [1] TRUE out$scaled #> [1] TRUE out$means #> Population     Income Illiteracy   Life.Exp     Murder    HS.Grad      Frost  #>  4246.4200  4435.8000     1.1700    70.8786     7.3780    53.1080   104.4600  #>       Area  #> 70735.8800 out$sd #>   Population       Income   Illiteracy     Life.Exp       Murder      HS.Grad  #> 4.464491e+03 6.144699e+02 6.095331e-01 1.342394e+00 3.691540e+00 8.076998e+00  #>        Frost         Area  #> 5.198085e+01 8.532730e+04 out <- biplot(state.data, center = FALSE) # no centring (usually not recommended) or scaling out$center #> [1] FALSE out$scaled #> [1] FALSE out$means #> [1] 0 0 0 0 0 0 0 0 out$sd #> [1] 1 1 1 1 1 1 1 1"},{"path":"/articles/biplotEZ.html","id":"using-biplot-with-princomp-or-prcomp","dir":"Articles","previous_headings":"The function biplot()","what":"Using biplot() with princomp() or prcomp()","title":"biplotEZ","text":"user wish construct PCA biplot performing principal component analysis via built functions stats package, output either functions can piped biplot function, piping implies argument data now takes value object class prcomp princomp.","code":"princomp(state.x77) |> biplot() #> Object of class biplot, based on 50 samples and 8 variables. #> 8 numeric variables. out <- prcomp(state.x77, scale.=TRUE) |> biplot() rbind (head(out$raw.X,3),tail(out$raw.X,3)) #>               Population Income Illiteracy Life Exp Murder HS Grad Frost   Area #> Alabama             3615   3624        2.1    69.05   15.1    41.3    20  50708 #> Alaska               365   6315        1.5    69.31   11.3    66.7   152 566432 #> Arizona             2212   4530        1.8    70.55    7.8    58.1    15 113417 #> West Virginia       1799   3617        1.4    69.48    6.7    41.6   100  24070 #> Wisconsin           4589   4468        0.7    72.48    3.0    54.5   149  54464 #> Wyoming              376   4566        0.6    70.29    6.9    62.9   173  97203 rbind (head(out$X,3),tail(out$X,3)) #>                Population      Income Illiteracy   Life Exp     Murder #> Alabama       -0.14143156 -1.32113867   1.525758 -1.3621937  2.0918101 #> Alaska        -0.86939802  3.05824562   0.541398 -1.1685098  1.0624293 #> Arizona       -0.45568908  0.15330286   1.033578 -0.2447866  0.1143154 #> West Virginia -0.54819682 -1.33253061   0.377338 -1.0418703 -0.1836632 #> Wisconsin      0.07673438  0.05240289  -0.771082  1.1929438 -1.1859550 #> Wyoming       -0.86693413  0.21188994  -0.935142 -0.4384705 -0.1294853 #>                  HS Grad       Frost       Area #> Alabama       -1.4619293 -1.62482920 -0.2347183 #> Alaska         1.6828035  0.91456761  5.8093497 #> Arizona        0.6180514 -1.72101848  0.5002047 #> West Virginia -1.4247868 -0.08580083 -0.5469045 #> Wisconsin      0.1723413  0.85685405 -0.1906996 #> Wyoming        1.2123316  1.31856256  0.3101835 out$center #> [1] TRUE out$scaled #> [1] TRUE out$means #> Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost  #>  4246.4200  4435.8000     1.1700    70.8786     7.3780    53.1080   104.4600  #>       Area  #> 70735.8800 out$sd #>   Population       Income   Illiteracy     Life Exp       Murder      HS Grad  #> 4.464491e+03 6.144699e+02 6.095331e-01 1.342394e+00 3.691540e+00 8.076998e+00  #>        Frost         Area  #> 5.198085e+01 8.532730e+04"},{"path":"/articles/biplotEZ.html","id":"the-functions-pca-plot-and-legend-type","dir":"Articles","previous_headings":"","what":"The functions PCA(), plot() and legend.type()","title":"biplotEZ","text":"first argument function PCA() object class biplot, .e. output biplot() function. default construct 2D biplot (argument dim.biplot = 2) first two principal components (argument e.vects = 1:2). group.aes argument, specified function biplot(), allows grouping argument sample aesthetics. PCA biplot state.x77 data colouring according state.region obtained follows:  output PCA() object class PCA inherits class biplot. Four additional components present PCA object. matrix Z contains coordinates sample points, matrix Vr contains “coordinates” variables. notation equation (1), Z=𝐆:n×2\\mathbf{G}:n \\times 2 Vr=𝐇:p×2\\mathbf{H}:p \\times 2. component Xhat matrix 𝐗̂\\hat{\\mathbf{X}} left hand side equation (1). final component ax.one.unit contains rows expression equation (2) μh=1\\mu_h=1, words, one unit positive direction biplot axis. piping PCA class object (inheriting class biplot) generic plot() function, plot.biplot() function constructs biplot graphical device. add legend biplot, call  mentioned section 1 default choice 𝐆=𝐔𝐃𝐉2\\mathbf{G}=\\mathbf{UDJ}_2 𝐇=𝐕𝐉2\\mathbf{H}=\\mathbf{VJ}_2 provides exact representation distances rows 𝐗̂\\mathbf{\\hat{X}} optimal approximation least squares sense distances rows 𝐗\\mathbf{X} (samples). Alternatively, correlations variables (columns 𝐗\\mathbf{X}) can optimally approximated cosines angles axes, leaving approximation distances samples suboptimal. case 𝐆=𝐔𝐉2\\mathbf{G}=\\mathbf{UJ}_2 𝐇=𝐕𝐃𝐉2\\mathbf{H}=\\mathbf{VDJ}_2 biplot obtained setting argument correlation.biplot = TRUE.","code":"biplot(state.x77, scaled = TRUE) |>    PCA(group.aes = state.region) |> plot() biplot(state.x77, scaled = TRUE) |>    PCA(group.aes = state.region) |>    legend.type(samples = TRUE) |> plot() biplot(state.x77, scaled = TRUE) |>    PCA(group.aes = state.region, correlation.biplot = TRUE) |>    legend.type(samples = TRUE) |> plot()"},{"path":"/articles/biplotEZ.html","id":"the-function-samples","dir":"Articles","previous_headings":"","what":"The function samples()","title":"biplotEZ","text":"function controls aesthetics sample points biplot. function accepts first argument object class biplot aesthetics applied. Let us first construct PCA biplot state.x77 data samples coloured according state.division.  Since legend interferes sample points, choose place legend new page, setting new = TRUE legend.type function. Furthermore, wish select colours, defaults, divisions. can also change opacity sample colours argument opacity default 1.  Furthermore want use different plotting character central regions. want use pch = 15 first three final two divisions pch = 1 remaining four divisions.  increase size plotting characters eastern states, add following:  choose show samples central states, argument used either indicating number(s) sequence levels (= 4:7), shown , levels :  Note since four regions selected, colour (aesthetics) applied regions order specified . add sample names, label argument set TRUE. large sample sizes, recommended, overplotting render plot unusable. size labels controlled label.cex can specified either single value (samples) vector indicating size values individual sample. colour labels defaults colour(s) samples. However, individual label colours can spesified label.col, similar label.cex either single value vector length equal number samples.  can use arguments label.cex, label.side label.offset make plot legible little effort.  can also make use functionality ggrepel package place labels.  Additionally, user can add customised label names samples biplot. , label must set TRUE (\"ggrepel\") label.name set vector size n specifying label names samples. case, label name set first three characters state name (row names data).  data plotted biplot multivariate time series, can make sense connect data points order. Let us consider four quarters UKgas data set four variables represent years sample points PCA biplot.","code":"biplot(state.x77, scaled = TRUE) |>    PCA(group.aes = state.division) |>    legend.type(samples = TRUE) |> plot() biplot(state.x77, scaled = TRUE) |>    PCA(group.aes = state.division) |>    samples (col = c(\"red\", \"darkorange\", \"gold\", \"chartreuse4\",                     \"green\", \"salmon\", \"magenta\", \"#000000\", \"blue\"),opacity = 0.65,pch=19) |>   legend.type(samples = TRUE, new = TRUE) |> plot() levels (state.division) #> [1] \"New England\"        \"Middle Atlantic\"    \"South Atlantic\"     #> [4] \"East South Central\" \"West South Central\" \"East North Central\" #> [7] \"West North Central\" \"Mountain\"           \"Pacific\" biplot(state.x77, scaled = TRUE) |>    PCA(group.aes = state.division) |>    samples (col = c(\"red\", \"darkorange\", \"gold\", \"chartreuse4\",                     \"green\", \"salmon\", \"magenta\", \"black\", \"blue\"),            pch = c(15, 15, 15, 1, 1, 1, 1, 15, 15)) |>   legend.type(samples = TRUE, new = TRUE) |> plot() biplot(state.x77, scaled = TRUE) |>    PCA(group.aes = state.division) |>    samples (col = c(\"red\", \"darkorange\", \"gold\", \"chartreuse4\",                     \"green\", \"salmon\", \"magenta\", \"black\", \"blue\"),            pch = c(15, 15, 15, 1, 1, 1, 1, 15, 15),            cex = c(rep(1.5,4), c(1,1.5,1,1.5))) |>   legend.type(samples = TRUE, new = TRUE)  |> plot() biplot(state.x77, scaled = TRUE) |>    PCA(group.aes = state.division) |>    samples (col = c(\"red\", \"darkorange\", \"gold\", \"chartreuse4\",                     \"green\", \"salmon\", \"magenta\", \"black\", \"blue\"),            which = c(\"West North Central\", \"West South Central\", \"East South Central\",                       \"East North Central\")) |>   legend.type(samples = TRUE, new = TRUE)  |> plot() biplot(state.x77, scaled = TRUE) |> PCA() |>    samples (label = TRUE) |> plot() rownames(state.x77)[match(c(\"Pennsylvania\", \"New Jersey\", \"Massachusetts\",                             \"Minnesota\"), rownames(state.x77))] <- c(\"PA\", \"NJ\", \"MA\", \"MN\") above <- match(c(\"Alaska\", \"California\", \"Texas\", \"New York\", \"Nevada\", \"Georgia\", \"Alabama\",                  \"North Carolina\", \"Colorado\", \"Washington\", \"Illinois\", \"Michigan\", \"Arizon\",                  \"Florida\", \"Ohio\", \"NJ\", \"Kansas\"), rownames(state.x77)) right.side <- match(c(\"South Carolina\", \"Kentucky\", \"Rhode Island\", \"New Hampshire\", \"Virginia\",                       \"Missouri\", \"Delaware\", \"Hawaii\", \"Oregon\", \"PA\", \"Nebraska\", \"Montana\",                       \"Maryland\", \"Indiana\", \"Idaho\"), rownames(state.x77)) left.side <- match(c(\"Wyoming\", \"Iowa\", \"MN\", \"Connecticut\"), rownames(state.x77)) label.offset <- rep(0.3, nrow(state.x77)) label.offset[match(c(\"Colorado\", \"Kansas\", \"Idaho\"), rownames(state.x77))] <- c(0.8, 0.5, 0.8) label.side <- rep(\"bottom\", nrow(state.x77)) label.side[above] <- \"top\" label.side[right.side] <- \"right\" label.side[left.side] <- \"left\" biplot (state.x77, scaled=TRUE) |> PCA() |>   samples (label=TRUE, label.cex=0.6, label.side=label.side, label.offset=label.offset) |>   plot() biplot(state.x77, scaled = TRUE) |> PCA() |>    samples (label = \"ggrepel\") |> plot() #> Warning: Use of `df$x` is discouraged. #> ℹ Use `x` instead. #> Warning: Use of `df$y` is discouraged. #> ℹ Use `y` instead. #> Warning: Use of `df$z` is discouraged. #> ℹ Use `z` instead. #> Warning: Use of `df$x` is discouraged. #> ℹ Use `x` instead. #> Warning: Use of `df$y` is discouraged. #> ℹ Use `y` instead. #> Warning: Use of `df$z` is discouraged. #> ℹ Use `z` instead. #> Warning: Use of `df$x` is discouraged. #> ℹ Use `x` instead. #> Warning: Use of `df$y` is discouraged. #> ℹ Use `y` instead. #> Warning: Use of `df$z` is discouraged. #> ℹ Use `z` instead. #> Warning: Use of `df$x` is discouraged. #> ℹ Use `x` instead. #> Warning: Use of `df$y` is discouraged. #> ℹ Use `y` instead. #> Warning: Use of `df$z` is discouraged. #> ℹ Use `z` instead. #> Warning: Use of `df$x` is discouraged. #> ℹ Use `x` instead. #> Warning: Use of `df$y` is discouraged. #> ℹ Use `y` instead. #> Warning: Use of `df$z` is discouraged. #> ℹ Use `z` instead. #> Warning: Use of `df$x` is discouraged. #> ℹ Use `x` instead. #> Warning: Use of `df$y` is discouraged. #> ℹ Use `y` instead. #> Warning: Use of `df$z` is discouraged. #> ℹ Use `z` instead. biplot(state.x77, scaled = TRUE) |> PCA() |>    samples (label = \"TRUE\",label.name=strtrim(row.names(state.x77),3)) |> plot() gas.data <- matrix (UKgas, ncol=4, byrow=T) colnames(gas.data) <- paste(\"Q\", 1:4, sep=\"\") rownames(gas.data) <- 60:86 even.labels <- rep(c(TRUE, FALSE), 14) biplot(gas.data, scaled = TRUE) |> PCA() |>    samples (connected = TRUE, connect.col=\"red\", label = even.labels, label.cex=0.6) |>    plot()"},{"path":"/articles/biplotEZ.html","id":"the-function-means","dir":"Articles","previous_headings":"","what":"The function means()","title":"biplotEZ","text":"function means() allow changing aesthetics group means specified group.aes, argument show.class.means = TRUE call function PCA(). functionality means() mirrors samples() discussed detail vignette Class separation class means prominent PCA biplots.","code":""},{"path":"/articles/biplotEZ.html","id":"the-function-axes","dir":"Articles","previous_headings":"","what":"The function axes()","title":"biplotEZ","text":"Similar samples() function, function allows changing aestethics biplot axes. first argument axes() object class biplot. X.names argument typically specified user, required function allow specifying axes display argument, either speficying column numbers column names. arguments col, lwd lty pertains axes can specified either scaler value (recycled) vector length equal . construct PCA biplot rock data, displaying axes peri shape different colours two axes, different line widths line type 2, need following code:  following four arguments deal axis labels. argument label.dir based graphics parameter las allows labels either orthogonal axis direction (Orthog), horisontal (Hor) parallel plot Paral. argument label.line fulfills role line argument mtext() determine margin line (far plot) label placed label.col label.cex self-explanatory defaults axis colour size 0.75. Note illustration code colour vector three components, recycling applied.  function pretty() finds ‘nice’ tick marks value specified argument ticks determine desired number tick marks, although observed number different. tick.* arguments similar naming counterparts par() text(). Since tick labels important follow direction increasing values axes, setting tick.label = FALSE remove tick marks completely, limits labels smallest largest value visible plot. user like specify alternative names axes, can done argument ax.names.","code":"biplot(rock, scaled = TRUE) |> PCA() |>                                 axes(which = c(\"shape\",\"peri\"),                                      col=c(\"lightskyblue\",\"slategrey\"),                                     lwd = c(1,2), lty=2) |>                                plot() biplot(rock, scaled = TRUE) |> PCA() |>                                 axes(col=c(\"lightskyblue\",\"slategrey\",\"blue\"),                                     label.dir=\"Hor\", label.line=c(0,0.5,1,1.5)) |>                                plot() biplot(rock, scaled = TRUE) |> PCA() |>                                 axes(label.dir=\"Paral\",                                     ticks = c(3, 5, 5, 10), tick.label=c(F, F, T, T),                                     ax.names = c(\"area\", \"perimeter\", \"shape\",                                                   \"permeability in milli-Darcies\")) |>                                plot()"},{"path":"/articles/biplotEZ.html","id":"the-functions-fit-measures-and-summary","dir":"Articles","previous_headings":"","what":"The functions fit.measures() and summary()","title":"biplotEZ","text":"print method provides short summary biplot object. output summary() similar. Additional information biplot object added fit.measures() function.","code":"obj <- biplot(airquality) #> Warning in biplot(airquality): 42 rows deleted due to missing values   obj #> Object of class biplot, based on 111 samples and 6 variables. #> 6 numeric variables. #>  #> The following 42 sample-rows where removed due to missing values #>  5 6 10 11 25 26 27 32 33 34 35 36 37 39 42 43 45 46 52 53 54 55 56 57 58 59 60 61 65 72 75 83 84 96 97 98 102 103 107 115 119 150 summary(obj) #> Object of class biplot, based on 111 samples and 6 variables. #> 6 numeric variables. #>  #> The following 42 sample-rows were removed due to missing values #>  5 6 10 11 25 26 27 32 33 34 35 36 37 39 42 43 45 46 52 53 54 55 56 57 58 59 60 61 65 72 75 83 84 96 97 98 102 103 107 115 119 150"},{"path":"/articles/biplotEZ.html","id":"quality-of-approximation","dir":"Articles","previous_headings":"The functions fit.measures() and summary()","what":"Quality of approximation","title":"biplotEZ","text":"start identity 𝐗=𝐗̂+𝐗−𝐗̂ \\mathbf{X} = \\mathbf{\\hat{X}} + \\mathbf{X-\\hat{X}}  decomposes 𝐗\\mathbf{X} fitted part 𝐗̂=𝐔𝐉𝐃𝐉𝐕′=𝐔𝐃𝐉2(𝐕𝐉2)′=𝐔𝐃𝐕′𝐕𝐉2(𝐕𝐉2)′=𝐗𝐕𝐉𝐕′ \\mathbf{\\hat{X}} = \\mathbf{UJDJV'} = \\mathbf{UDJ}_2(\\mathbf{VJ}_2)' = \\mathbf{UDV'VJ}_2(\\mathbf{VJ}_2)' = \\mathbf{XVJV'} residual part 𝐗−𝐗̂\\mathbf{X-\\hat{X}}. lack fit quantified quantity minimising ∥𝐗̂−𝐗∥2 \\| \\hat{\\mathbf{X}}-\\mathbf{X} \\|^2  orthogonal decomposition ∥𝐗∥2=∥𝐗̂∥2+∥𝐗̂−𝐗∥2. \\|\\mathbf{X}\\|^2 = \\|\\hat{\\mathbf{X}}\\|^2 + \\|\\hat{\\mathbf{X}}-\\mathbf{X} \\|^2.  overall quality fit therefore defined quality=∥𝐗̂∥2∥𝐗∥2=tr(𝐗𝐗′)tr(𝐗̂𝐗̂′)=tr(𝐗′𝐗)tr(𝐗̂′𝐗̂)=tr(𝐕𝐃2𝐕′)tr(𝐕𝐃2𝐉𝐕′). quality = \\frac{\\|\\hat{\\mathbf{X}}\\|^2}{\\|\\mathbf{X}\\|^2} = \\frac{tr(\\mathbf{XX}')}{tr(\\mathbf{\\hat{X}\\hat{X}'})} = \\frac{tr(\\mathbf{X'X})}{tr(\\mathbf{\\hat{X}'\\hat{X}})} = \\frac{tr(\\mathbf{VD}^2\\mathbf{V'})}{tr(\\mathbf{VD}^2\\mathbf{JV'})}.  biplotEZ overall quality displayed percentage: quality=d12+d22d12+…+dp2100%. quality =\\frac{d_1^2+d_2^2}{d_1^2+\\dots+d_p^2}100\\%.","code":""},{"path":"/articles/biplotEZ.html","id":"adequacy-of-representation-of-the-variables","dir":"Articles","previous_headings":"The functions fit.measures() and summary()","what":"Adequacy of representation of the variables","title":"biplotEZ","text":"Researchers construct PCA biplot representing columns arrows (vectors) often fit biplot unit circle. rationale perfect representation variable unit length length arrow vs distance unit circle represent adequacy variable represented. fitting biplot calibrated axes, much easier read values variables, adequacy values can still computed diag(𝐕r𝐕r′)diag(𝐕𝐕′)=diag(𝐕r𝐕r′) \\frac{diag(\\mathbf{V}_r\\mathbf{V}_r')}{diag(\\mathbf{VV}')}= diag(\\mathbf{V}_r\\mathbf{V}_r') due orthogonality matrix 𝐕:p×p\\mathbf{V}:p \\times p.","code":""},{"path":"/articles/biplotEZ.html","id":"predictivities","dir":"Articles","previous_headings":"The functions fit.measures() and summary()","what":"Predictivities","title":"biplotEZ","text":"predictivity provides measure well original values recovered biplot. element well represented predictivity close one, indicating sample variable values prediction close observed values. element poorly represented, predicted values different original values predictivity value close zero.","code":""},{"path":"/articles/biplotEZ.html","id":"axis-predictivity","dir":"Articles","previous_headings":"The functions fit.measures() and summary() > Predictivities","what":"Axis predictivity","title":"biplotEZ","text":"predictivity pp variables computed elementwise ratios axispredictivity=diag(𝐗̂′𝐗̂)diag(𝐗′𝐗) axis \\: predictivity = \\frac{diag(\\mathbf{\\hat{X}'\\hat{X}})}{diag(\\mathbf{X'X})}","code":""},{"path":"/articles/biplotEZ.html","id":"sample-predictivity","dir":"Articles","previous_headings":"The functions fit.measures() and summary() > Predictivities","what":"Sample predictivity","title":"biplotEZ","text":"predictivity nn samples computed elementwise ratios samplepredictivity=diag(𝐗̂𝐗̂′)diag(𝐗𝐗′) sample \\: predictivity = \\frac{diag(\\mathbf{\\hat{X}\\hat{X}'})}{diag(\\mathbf{XX'})}  calling function fit.measures() quantities computed specific biplot object. values displayed summary() function.  necessary call plot() function obtain fit measures, one biplot methods, PCA() required, since measures differ depending type biplot constructed. suppress output fit measures, instance interest axis predictivity many samples result long output, can set call summary(). default measures set TRUE. axis predictivities sample predictivities can represented biplot two ways: setting either axis.predictivity / sample.predictivity TRUE, applies shading axes shrinking samples according predictivity values.  Comparing plot summary output clear variables Population Frost well represented can expected predictions variables less accurate. Furthermore, samples located close origin well represented located towards bottom right. typically case samples nearly orthogonal PCA plane projected close origin due orthogonality, poorly represented.","code":"obj <- biplot(state.x77, scale = TRUE) |> PCA() |>    fit.measures() |> plot() summary (obj) #> Object of class biplot, based on 50 samples and 8 variables. #> 8 numeric variables. #>  #> Quality of fit in 2 dimension(s) = 65.4%  #> Adequacy of variables in 2 dimension(s): #> Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost  #>  0.1848016  0.3586383  0.2215201  0.1760908  0.2915819  0.2696184  0.1513317  #>       Area  #>  0.3464170  #> Axis predictivity in 2 dimension(s): #> Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost  #>  0.3330216  0.7609185  0.7917091  0.6206172  0.8640485  0.7947530  0.4982299  #>       Area  #>  0.5675169  #> Sample predictivity in 2 dimension(s): #>        Alabama         Alaska        Arizona       Arkansas     California  #>     0.95126856     0.61373919     0.26327256     0.86308539     0.57062754  #>       Colorado    Connecticut       Delaware        Florida        Georgia  #>     0.83358779     0.59003002     0.18284712     0.49725356     0.94461052  #>         Hawaii          Idaho       Illinois        Indiana           Iowa  #>     0.01984127     0.70337480     0.33405270     0.30082350     0.96367113  #>         Kansas       Kentucky      Louisiana          Maine       Maryland  #>     0.86554676     0.87758262     0.93717163     0.66553856     0.06362508  #>             MA       Michigan             MN    Mississippi       Missouri  #>     0.47386267     0.26050188     0.89207404     0.93073099     0.11321791  #>        Montana       Nebraska         Nevada  New Hampshire             NJ  #>     0.44603781     0.93570441     0.22393876     0.87499561     0.15979033  #>     New Mexico       New York North Carolina   North Dakota           Ohio  #>     0.29304145     0.40609063     0.93004841     0.69011551     0.08810179  #>       Oklahoma         Oregon             PA   Rhode Island South Carolina  #>     0.37520943     0.36273523     0.02176080     0.58625617     0.93187284  #>   South Dakota      Tennessee          Texas           Utah        Vermont  #>     0.83804787     0.96006357     0.73748654     0.66209083     0.80365601  #>       Virginia     Washington  West Virginia      Wisconsin        Wyoming  #>     0.58564755     0.33877314     0.85231725     0.82519206     0.42499724 obj <- biplot(state.x77, scale = TRUE) |> PCA() |>    fit.measures()  summary (obj, adequacy = FALSE, sample.predictivity = FALSE) #> Object of class biplot, based on 50 samples and 8 variables. #> 8 numeric variables. #>  #> Quality of fit in 2 dimension(s) = 65.4%  #> Axis predictivity in 2 dimension(s): #> Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost  #>  0.3330216  0.7609185  0.7917091  0.6206172  0.8640485  0.7947530  0.4982299  #>       Area  #>  0.5675169 biplot(state.x77, scale = TRUE) |> PCA(group.aes = state.region) |>   samples (which = \"South\", pch = 15, label = T, label.cex=0.5) |>    axes (col = \"black\") |>   fit.measures() |> plot (sample.predictivity = TRUE,                           axis.predictivity = TRUE)"},{"path":"/articles/biplotEZ.html","id":"axes-represented-as-vectors","dir":"Articles","previous_headings":"The functions fit.measures() and summary() > Predictivities","what":"Axes represented as vectors","title":"biplotEZ","text":"user wishes view variables arrows biplot give information adequacy variables, can done axes() function, setting vectors = TRUE unit.circle = TRUE. adequacy value given squared length arrow.","code":"biplot(state.x77, scale = TRUE) |> PCA(group.aes = state.region) |>   axes (vectors = TRUE,unit.circle = TRUE) |>   fit.measures() |> plot ()"},{"path":[]},{"path":"/articles/biplotEZ_enhancements.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"biplotEZ enhancements","text":"enhancing biplot, various additional features can significantly improve interpretability utility. Introducing alpha bags helps visualize central region variability within group, providing robust measure data concentration. Adding confidence ellipses can illustrate spread correlation data points, making underlying structure evident. Including capability add new samples axes facilitates dynamic exploration comparison data sets. option predict samples means allows projection data points onto biplot display, aiding predictive analysis. Moreover, tools reflecting rotating biplot display can enhance visual representation aligning plot user’s analytical needs, offering clearer perspective relationships dimensions within data.","code":""},{"path":"/articles/biplotEZ_enhancements.html","id":"the-function-alpha-bags","dir":"Articles","previous_headings":"","what":"The function alpha.bags()","title":"biplotEZ enhancements","text":"α\\alpha-bag encloses α100%\\alpha100\\% inner data points cloud points. based concept halfspace location depth defined Tukey (1975). Rousseeuw, Ruts, Tukey (1999) generalised boxplot two-dimensional bagplot box replaced bag containing inner 50%50\\% observations. Gower, Lubbe, Roux (2011) replaces 50%50\\%-bag contour general α100%\\alpha100\\% contour referred α\\alpha-bag. number samples biplot larger, becomes difficult isolate individual observations. Often, grouping variable present, interest much individual samples, rather location spread groups. plot , enclose century’s number sunspots 95%95\\%-bag months used 12 different variables year (sample point). Note legend displays α\\alpha-bags samples = FALSE left default. can displayed, since α\\alpha-bags’ colour defaults colour sample points, necessary .  default one 95%95\\%-bag constructed group. general, alpha.bags() function accepts object class biplot first argument. next argument alpha can specified single value, construct series α\\alpha-bags group, alpha can vector argument. argument specifies groups fitted α\\alpha-bags. default opacity argument set 0.250.25, setting opacity = 0 removes fill α\\alpha-bags.  biplot , colours recycled alpha value. specify differential colours, can use col argument similarly lty lwd arguments. Since mostly interested location overlap clouds points can remove indivdiual samples setting samples (= NULL). default colours still used α\\alpha-bags chose specify different line types different α\\alpha values. opacity set 0.050.05 plots lighter shade inside α\\alpha-bags.  completely custom combination α\\alpha-bags, rely recycling specify arguments alpha, , col, lty, lwd vector. Since calculation halfspace location depth computationally intensive, random sample size 2500 chosen group construct α\\alpha-bag. sample size can changed argument max. Setting trace = FALSE suppress message “Computing α\\alpha” -bag groupX.”  function alpha.bags provides option plot samples sit outside α\\alpha-bags. done setting argument outlying=TRUE. Note argument may overwritten outlying set TRUE. happens particular samples() function differs alpha_bags() function.","code":"sunspots <- matrix (sunspot.month[1:(264*12)], ncol = 12, byrow = TRUE) years <- 1749:2012 rownames(sunspots) <- years colnames(sunspots) <- c(\"Jan\", \"Feb\", \"Mar\", \"Apr\", \"May\", \"Jun\",                         \"Jul\", \"Aug\", \"Sep\", \"Oct\", \"Nov\", \"Dec\") century <-paste(floor((years-1)/100)+1, ifelse (floor((years-1)/100)+1<21, \"th\",\"st\"), sep = \"-\") biplot(sunspots, group.aes=century) |> PCA() |>         axes (label.dir = \"Hor\", label.line = c(0.8, rep(0,10), 0.8)) |>         alpha.bags () |>          legend.type(bags = TRUE)  |> plot() #> Computing 0.95 -bag for 18-th  #> Computing 0.95 -bag for 19-th  #> Computing 0.95 -bag for 20-th  #> Computing 0.95 -bag for 21-st biplot(sunspots, group.aes=century) |> PCA() |>         axes (label.dir = \"Hor\", label.line = c(0.8, rep(0,10), 0.8)) |>         alpha.bags (alpha = c(0.9, 0.95, 0.99), which = c(1,4), opacity = 0) |>          legend.type(bags = TRUE)  |> plot() #> Computing 0.9 -bag for 18-th  #> Computing 0.9 -bag for 21-st  #> Computing 0.95 -bag for 18-th  #> Computing 0.95 -bag for 21-st  #> Computing 0.99 -bag for 18-th  #> Computing 0.99 -bag for 21-st biplot(sunspots, group.aes=century) |> PCA() |>         axes (label.dir = \"Hor\", label.line = c(0.8, rep(0,10), 0.8)) |>         samples (which = NULL) |>         alpha.bags (alpha = c(0.9, 0.95, 0.99), lty = c(1,3,5), opacity=0.05) |>          legend.type(bags = TRUE, new = TRUE)  |> plot() #> Computing 0.9 -bag for 18-th  #> Computing 0.9 -bag for 19-th  #> Computing 0.9 -bag for 20-th  #> Computing 0.9 -bag for 21-st  #> Computing 0.95 -bag for 18-th  #> Computing 0.95 -bag for 19-th  #> Computing 0.95 -bag for 20-th  #> Computing 0.95 -bag for 21-st  #> Computing 0.99 -bag for 18-th  #> Computing 0.99 -bag for 19-th  #> Computing 0.99 -bag for 20-th  #> Computing 0.99 -bag for 21-st biplot(sunspots, group.aes=century) |> PCA() |>         axes (label.dir = \"Hor\", label.line = c(0.8, rep(0,10), 0.8)) |>         samples (which = NULL) |>         alpha.bags (alpha = c(   0.9,   0.95,   0.99,             0.5,         0.6,     0.7),                      which = c(     1,      1,      2,               3,           3,      3),                     col   = c(\"brown\", \"red\", \"gold\",  \"deepskyblue2\", \"steelblue3\",\"blue\"),                     lty   = c(     1,      2,     10,               2,           2,      0),                     lwd   = c(     1,      1,      3,               1,           2,      1),                     opacity = 0.1) |> plot() #> Computing 0.9 -bag for 18-th  #> Computing 0.95 -bag for 18-th  #> Computing 0.99 -bag for 19-th  #> Computing 0.5 -bag for 20-th  #> Computing 0.6 -bag for 20-th  #> Computing 0.7 -bag for 20-th biplot(sunspots, group.aes=century) |> PCA() |>         alpha.bags (col   = c(\"brown\", \"red\", \"gold\",\"deepskyblue2\"),                     opacity = 0.1,outlying = TRUE) |> plot() #> Computing 0.95 -bag for 18-th  #> Computing 0.95 -bag for 19-th  #> Computing 0.95 -bag for 20-th  #> Computing 0.95 -bag for 21-st"},{"path":"/articles/biplotEZ_enhancements.html","id":"the-function-ellipses","dir":"Articles","previous_headings":"","what":"The function ellipses()","title":"biplotEZ enhancements","text":"observe random sample pp-variate normal distribution 𝐱‾\\bar{\\mathbf{x}} 𝐒\\mathbf{S} usual unbaised estimates mean vector covariance matrix, (𝐱−𝐱‾)′𝐒−1(𝐱−𝐱‾)=κ2 (\\mathbf{x} - \\bar{\\mathbf{x}})' \\mathbf{S}^{-1} (\\mathbf{x} - \\bar{\\mathbf{x}}) = \\kappa^2 traces ellipsoid pp dimensions. p=2p=2, choosing κ=(χ2,1−α2)12\\kappa = {(\\chi^{2}_{2,1-\\alpha})}^{\\frac{1}{2}} χ2,1−α2\\chi^{2}_{2,1-\\alpha} denotes (1−α)100(1-\\alpha)100-th percentage point χ22\\chi^2_2 distribution results ellipse covering approximately 100α%100\\alpha\\% configuration two-dimensional points. default arguments df = 2 alpha = 0.95, value κ\\kappa 2.4477472.447747 ellipse function constructs ellipse enclose approximately 95%95\\% observations bivariate normal distribution. argument kappa can specified directly, take precedence specification alpha. arguments ellipses() function operates identically corresponding arguments function alpha.bags(). Using α\\alpha-bags, rather ellipses recommended general, since construction ellipses based underlying assumption random sample observed normal distribution.","code":"biplot(sunspots, group.aes=century) |> PCA() |>         axes (label.dir = \"Hor\", label.line = c(0.8, rep(0,10), 0.8)) |>         samples (which = NULL) |>         ellipses (alpha = c(0.9, 0.95), lty = c(1,3,5), opacity = 0.1) |>          legend.type(ellipses = TRUE)  |> plot() #> Computing 2.15 -ellipse for 18-th  #> Computing 2.15 -ellipse for 19-th  #> Computing 2.15 -ellipse for 20-th  #> Computing 2.15 -ellipse for 21-st  #> Computing 2.45 -ellipse for 18-th  #> Computing 2.45 -ellipse for 19-th  #> Computing 2.45 -ellipse for 20-th  #> Computing 2.45 -ellipse for 21-st biplot(sunspots, group.aes=century) |> PCA() |>         axes (label.dir = \"Hor\", label.line = c(0.8, rep(0,10), 0.8)) |>         samples (which = NULL) |>         ellipses (kappa = 1:2, lty = c(1,3,5), opacity = 0.1) |>          legend.type(ellipses = TRUE) |> plot() #> Computing 1 -ellipse for 18-th  #> Computing 1 -ellipse for 19-th  #> Computing 1 -ellipse for 20-th  #> Computing 1 -ellipse for 21-st  #> Computing 2 -ellipse for 18-th  #> Computing 2 -ellipse for 19-th  #> Computing 2 -ellipse for 20-th  #> Computing 2 -ellipse for 21-st"},{"path":"/articles/biplotEZ_enhancements.html","id":"the-function-density2d","dir":"Articles","previous_headings":"","what":"The function density2D()","title":"biplotEZ enhancements","text":"function constructing two-dimensional PCA biplots top density plot two-dimensional PCA approximation input matrix. R function kde2d described Venables Ripley (2002) available package MASS used perform two-dimensional kernel density estimation axis-aligned bivariate normal kernel, evaluated square grid. function plots density group (specified argument ) data. following case, second group’s density plotted contours=TRUE. vector least two components specified col argument display colours density response surface. cuts-1 colours interpolated components col. default c(\"green\", \"yellow\", \"red\").  case, vector group.aes specified, samples form one group.","code":"biplot(state.x77,group.aes = state.region,scaled = TRUE) |> PCA() |>   density2D(which=2,col=c(\"white\",\"purple\",\"blue\",\"cyan\"),contours=TRUE) |> plot() biplot(state.x77,scaled = TRUE) |> PCA() |> samples(which=NULL) |>   density2D(which=1,col=c(\"white\",\"purple\",\"blue\",\"cyan\"),contours = TRUE,cuts = 20) |> plot()"},{"path":"/articles/biplotEZ_enhancements.html","id":"the-functions-interpolate-with-newsamples-and-newaxes","dir":"Articles","previous_headings":"","what":"The functions interpolate() with newsamples() and newaxes()","title":"biplotEZ enhancements","text":"process interpolation described Gower Hand (1996) process finding coordinates pp-dimensional sample lower dimensional biplot space. PCA showed section 1 biplotEZ vignette sample points represented 𝐆=𝐔𝐃𝐉2\\mathbf{G}=\\mathbf{UDJ}_2 can written 𝐆=𝐔𝐃𝐕′𝐕𝐉2=𝐗𝐕𝐉2\\mathbf{G}=\\mathbf{UDV'VJ}_2=\\mathbf{XVJ}_2. Finding position new sample 𝐱*:p×1\\mathbf{x}^*:p \\times 1 make use transformation 2D coordinates given 𝐳*′:2×1=𝐱*′𝐕𝐉2{\\mathbf{z}^*}':2 \\times 1 ={\\mathbf{x}^*}' \\mathbf{VJ}_2. Similarly, position new variable 𝐱*:n×1\\mathbf{x}^*:n \\times 1 added using regression method assumes 𝐱*\\mathbf{x}^* approximately linear function 𝐱*=𝐗𝐕r𝐛r\\mathbf{x}^* = \\mathbf{XV}_r\\mathbf{b}_r solution 𝐛̂r:r×1=(𝐕′r𝐗′𝐗𝐕r)−1𝐕r𝐗′𝐱*\\hat{\\mathbf{b}}_r :r \\times 1 = (\\mathbf{V}'_r\\mathbf{X}'\\mathbf{XV}_r)^{-1}\\mathbf{V}_r\\mathbf{X}'\\mathbf{x}^*. Adding samples variables plot facilitated function interpolate(). Note samples variables interpolated contribute construction biplot. reason Greenacre (2017) term supplementary points axes. function interpolate() accepts matrix data frame containing samples variables interpolated. argument newdata containing samples interpolated needs similar structure data set sent biplot(). biplot() received data frame, newdata can either another data frame matrix containing subset numerical variables. Similarly, argument newvariable containing new variables interpolated needs number samples data sent biplot(). Suppose construct PCA biplot first 4040 samples data set rock 88 new samples interpolated call :  function newsamples() operates similar samples, allowing changes aesthetics interpolated new samples. argument newsamples() since assumed samples interpolated represented biplot. arguments vectors length similar number samples newdata. change colour interpolated samples add labels, following call used:  Suppose constructing PCA biplot using three variables rock data, interpolating variable.  can change aesthetics new variables newaxes() function operates similarly axes() function.  function interpolate() also work new samples new variables need interpolated time. example:  Notice newdata number variables data sent biplot() newvariable number samples data sent biplot().","code":"biplot(rock[1:40,], scale = TRUE) |> PCA() |>    interpolate (newdata=rock[41:48,]) |> plot() biplot(rock[1:40,], scale = TRUE) |> PCA() |>    interpolate (rock[41:48,]) |>   newsamples (label = TRUE, label.side = \"top\", col = rainbow(10)) |> plot() biplot(rock[,c(1,2,4)], scale = TRUE) |> PCA() |>    interpolate (newvariable =rock[,3]) |> plot() biplot(rock[,c(1,2,4)], scale = TRUE) |> PCA() |>    interpolate (newvariable =rock[,3]) |>    newaxes(col=\"red\",ticks = 50,X.new.names = \"shape\") |> plot() biplot(rock[1:40,c(1,2,4)], scale = TRUE) |> PCA() |>    interpolate (newdata=rock[41:48,c(1,2,4)],newvariable =rock[1:40,3]) |>    newaxes(col=\"red\",ticks = 100,X.new.names = \"shape\") |> plot()"},{"path":"/articles/biplotEZ_enhancements.html","id":"the-function-prediction","dir":"Articles","previous_headings":"","what":"The function prediction()","title":"biplotEZ enhancements","text":"add prediction sample points biplot, function prediction() used.  addition predictions computed can accessed summary.method. arguments prediction() predict.means also () predict group means indicate axes’ predictions shown biplot. specifying predict.samples = TRUE /predict.means = TRUE samples /means predicted. Alternatively either arguments accepts vector indicating samples /means predict. example , mean values Central West regions predicted.","code":"out <- biplot(rock, scale = TRUE) |> PCA() |>           prediction (predict.samples = TRUE) |> plot() summary(out) #> Object of class biplot, based on 48 samples and 4 variables. #> 4 numeric variables. #>  #> Sample predictions #>         area      peri      shape        perm #> 1   5182.518 2694.6678 0.08624348   17.426253 #> 2   7691.949 3526.4942 0.13514234   35.517473 #> 3   8318.033 3628.6997 0.16177613   99.694598 #> 4   7636.831 3630.8908 0.11725845  -34.364599 #> 5   8084.856 3781.5005 0.12570117  -32.323140 #> 6   8499.105 3765.0371 0.15484655   57.771249 #> 7   9738.891 4180.1532 0.17843607   64.357324 #> 8   8877.364 3954.7565 0.15340118   24.056153 #> 9   8718.501 3605.5323 0.19094566  190.899483 #> 10  6776.004 2972.9886 0.15153800  170.463202 #> 11  9517.287 4203.7977 0.16081144    7.756551 #> 12  8667.626 3841.4265 0.15531722   47.357938 #> 13 10542.328 4258.1501 0.21989947  176.826997 #> 14  9102.060 3644.4083 0.21051537  243.662966 #> 15  9351.922 4027.1591 0.17428339   75.571235 #> 16  8590.817 3776.8963 0.15917449   68.935190 #> 17 11002.857 4604.0870 0.20238688   70.663421 #> 18 11465.727 4562.1556 0.23817832  184.664030 #> 19 11713.492 4918.0115 0.20549573   31.397809 #> 20  9794.836 4371.1960 0.15588772  -32.950729 #> 21  7486.756 3459.7842 0.13096481   33.297702 #> 22 11970.162 4545.5777 0.27319335  292.407085 #> 23 12048.397 4816.3066 0.24117196  154.306887 #> 24  8161.391 3531.7628 0.16489230  124.063184 #> 25  6473.046 1887.1108 0.28067750  726.488443 #> 26  3937.319 1270.4047 0.20059243  581.415341 #> 27  6361.245 2198.9634 0.23068527  528.041307 #> 28  4364.754 1641.8821 0.17743170  454.331807 #> 29  5961.529 1813.4043 0.25757496  668.505918 #> 30  5419.192 1075.2405 0.32352672  980.895692 #> 31  6687.830 1728.1793 0.31639877  858.392956 #> 32  6862.484 1912.2039 0.30251759  788.205529 #> 33  5072.364 1506.6448 0.24189571  668.903853 #> 34  5330.680 1039.1725 0.32272399  984.068789 #> 35  5510.961 1842.2520 0.22437503  564.315264 #> 36  6834.394 1864.9721 0.30716675  809.483177 #> 37  3788.048 1612.7808 0.14398515  358.372419 #> 38  3912.089  510.0085 0.30315670 1007.222092 #> 39  3569.066 1564.6150 0.13637128  342.959576 #> 40  5655.233 2040.8001 0.20653151  479.977300 #> 41  4984.153  680.9452 0.34932075 1119.421832 #> 42  1341.442 -373.1439 0.25731781 1006.268880 #> 43  6519.731  738.7171 0.44107961 1386.097805 #> 44  8964.500 1961.9907 0.43213873 1169.846628 #> 45  3589.848 1128.4355 0.19749274  594.085244 #> 46  2533.721  417.0546 0.22642373  791.127217 #> 47  4876.168 1721.4564 0.19972344  508.970410 #> 48  7521.495 2660.6426 0.24273124  492.744256 out <- biplot(state.x77, scale = TRUE) |> PCA(group.aes = state.region, show.class.means = TRUE) |>           prediction (predict.means = 3:4, which = c(\"Income\",\"Murder\",\"Population\")) |> plot() summary(out) #> Object of class biplot, based on 50 samples and 8 variables. #> 8 numeric variables. #>  #> Class mean predictions #>                 Income   Murder Population #> North Central 4611.672 5.108174   3211.604 #> West          4862.927 6.865661   5268.183"},{"path":"/articles/biplotEZ_enhancements.html","id":"the-functions-reflect-and-rotate","dir":"Articles","previous_headings":"","what":"The functions reflect() and rotate()","title":"biplotEZ enhancements","text":"function reflect() allows user reflect biplot display x-axis y-axis . argument reflect.axis offers options \"FALSE\",\"x\",\"y\",\"xy\". biplot reflected x-axis.  biplot reflected y-axis.  function rotate() allows user rotate biplot display certain value degrees. default 0 positive value results anti-clockwise rotation negative value clockwise rotation. example rotate.degrees set 100 degrees, biplot rotated 100 degrees anticlockwise direction.","code":"biplot(state.x77, scale = TRUE) |> PCA(group.aes = state.division) |> reflect(\"x\") |> plot() biplot(state.x77, scale = TRUE) |> PCA(group.aes = state.division) |> reflect(\"y\") |> plot() biplot(state.x77, scale = TRUE) |> PCA(group.aes = state.division) |> rotate(100) |> plot()"},{"path":"/articles/biplotEZ_enhancements.html","id":"zooming-in-on-the-biplot-with-zoom-true-in-plot","dir":"Articles","previous_headings":"","what":"Zooming in on the biplot with zoom = TRUE in plot()","title":"biplotEZ enhancements","text":"plot() function built-functionality zoom plot. done locator() function alters xlim ylim paramaters plot. implementation opens new graphics window promting locator function. illustrated : final plot rendered :","code":"biplot(state.x77,scaled = TRUE) |>    PCA() |>    samples(which=NULL) |>   density2D(which=1,col=c(\"white\",\"purple\",\"blue\",\"cyan\"),contours = TRUE,cuts = 20) |>    plot(zoom=TRUE)"},{"path":"/articles/biplotEZ_enhancements.html","id":"the-function-translate_axes","dir":"Articles","previous_headings":"","what":"The function translate_axes()","title":"biplotEZ enhancements","text":"function implements algorithm TDAbiplot() bipl5 package. allows translate axes plot center boundary using orthogonal parallel translation. axes can translated manually setting distance distance argument.","code":"biplot(state.x77,scaled=TRUE) |>    PCA() |>   translate_axes(delta = 0.02) |>   plot(exp.factor=3)"},{"path":"/articles/Biplots_in_1D.html","id":"one-dimensional-pca-biplot","dir":"Articles","previous_headings":"","what":"One-dimensional PCA biplot","title":"Biplots in 1D","text":"One-dimensional PCA biplots obtained specifying dim.biplot = 1 call PCA(). one-dimensional representation data displayed colour points top horizontal line. accompanying calibrated variable axes displayed horizontal lines . variable name displayed side variable increases.","code":"biplot(iris) |> PCA(group.aes = iris$Species,dim.biplot = 1)  |> plot()"},{"path":"/articles/Biplots_in_1D.html","id":"one-dimensional-cva-biplot","dir":"Articles","previous_headings":"","what":"One-dimensional CVA biplot","title":"Biplots in 1D","text":"Similarly CVA 1d biplot, dim.biplot = 1 specified call CVA(). one-dimensioal CVA biplot displays one-dimensional linear combination maximises class variance, relative within class variance.","code":"biplot(iris) |> CVA(classes = iris$Species,dim.biplot = 1) |>   axes(col=\"black\") |> plot()"},{"path":"/articles/Biplots_in_1D.html","id":"classification-using-classify","dir":"Articles","previous_headings":"One-dimensional CVA biplot","what":"Classification using classify()","title":"Biplots in 1D","text":"CVA models can employed classifier. New observations classified nearest class mean, means indicated shaded squares scatter line. classification regions displayed scatter line using classify().  print() function provides misclassification rate, well confusion matrix, CVA classifier applied training data.","code":"bp <- biplot(iris) |> CVA(classes = iris[,5],dim.biplot = 1)|>   axes(col=\"black\") |>    classify(borders = TRUE,opacity = 1)|>plot() print(bp) #> Object of class biplot, based on 150 samples and 5 variables. #> 4 numeric variables. #> 1 categorical variable. #> 3 classes: setosa versicolor virginica  #>  #> Misclassification rate is  0.02  #>  #> Confusion matrix  #>             Reference #> Prediction   setosa versicolor virginica #>   setosa         50          0         0 #>   versicolor      0         48         2 #>   virginica       0          1        49"},{"path":"/articles/Biplots_in_1D.html","id":"one-dimensional-ca-biplot","dir":"Articles","previous_headings":"","what":"One-dimensional CA biplot","title":"Biplots in 1D","text":"Similarly CA 1d biplot, dim.biplot = 1 specified call CA(). one-dimensional biplot constructed first columns 𝐔𝚲𝛄\\mathbf{U\\Lambda^\\gamma} $&\\mathbf{V\\Lambda^{1-\\gamma}}$. Consider HairEyeColor example discussed CA biplotEZ:","code":"biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = \"Princ\",    dim.biplot=1, lambda.scal = T) |> plot()"},{"path":"/articles/Biplots_in_1D.html","id":"the-function-interpolate","dir":"Articles","previous_headings":"","what":"The function interpolate()","title":"Biplots in 1D","text":"interpolate() allows new observations axes added biplot.","code":""},{"path":"/articles/Biplots_in_1D.html","id":"the-function-newsamples","dir":"Articles","previous_headings":"The function interpolate()","what":"The function newsamples()","title":"Biplots in 1D","text":"process adding new samples biplot, called interpolation utilises functions interpolate() newsamples(). functions work way call two-dimensional biplot. function interpolate() accepts argument newdata specify matrix data frame containing new samples interpolated. function newsamples() operates way samples() user can specify aesthetics interpolated samples.","code":"biplot(iris[c(1:50,101:150),1:4])|> PCA(dim.biplot = 1) |> axes(col=\"black\") |>    interpolate(newdata = iris[51:100,1:4]) |> newsamples(col=\"purple\") |> plot()"},{"path":"/articles/Biplots_in_1D.html","id":"the-function-newaxes","dir":"Articles","previous_headings":"The function interpolate()","what":"The function newaxes()","title":"Biplots in 1D","text":"interpolate new variables biplot, function interpolate() newaxes() called. function interpolate() accepts argument newvariable specify matrix data frame number rows data specified biplot() containing new variables interpolated. function newaxes() allows user specify aesthetics interpolated variables.","code":"biplot(iris[,1:3])|> PCA(dim.biplot = 1) |> axes(col=\"black\") |>    interpolate(newvariable = iris[,4]) |>    newaxes(col=\"darkred\",X.new.names = \"Petal.Width\") |> plot()"},{"path":[]},{"path":"/articles/Biplots_in_1D.html","id":"predicting-samples","dir":"Articles","previous_headings":"The function prediction()","what":"Predicting Samples","title":"Biplots in 1D","text":"add prediction samples biplot, prediction() function used. predict.samples argument takes vector indicating either row numbers samples predict set TRUE indicating predict samples. example , predictions samples 100 150 shown. aesthetics display predictions arguments axes() function: predict.col predict.lwd.","code":"biplot(iris) |>    PCA(group.aes = iris$Species,dim.biplot = 1,show.class.means = TRUE) |>    axes(col=\"black\",predict.col = \"darkred\") |>    prediction(predict.samples=100:150) |> plot()"},{"path":"/articles/Biplots_in_1D.html","id":"predicting-group-means","dir":"Articles","previous_headings":"The function prediction()","what":"Predicting Group Means","title":"Biplots in 1D","text":"Similarly, add prediction group means, function prediction() used. argument predict.means takes vector specifying group means predict. example , first group means predicted. Important note argument show.class.means must set TRUE PCA() function.","code":"biplot(iris) |>    PCA(group.aes = iris$Species,dim.biplot = 1,show.class.means = TRUE) |>    axes(col=\"black\",predict.col = \"darkred\") |> means(label=TRUE,which=1:3)|>   prediction(predict.means = 1) |> plot()"},{"path":"/articles/Biplots_in_1D.html","id":"ellipses-and-alpha-bags","dir":"Articles","previous_headings":"","what":"Ellipses and Alpha bags","title":"Biplots in 1D","text":"Ellipses added 1d biplot using ellipses() function works way 2d biplot. one dimension concentration ellipses simply confidence interval. concentration interval indicated using rectangles spanning range interval.  one-dimensional representation Alpha bag simply empirical interval. empirical interval indicated using rectangles spanning range interval.","code":"biplot(iris) |> PCA(group.aes = iris[,5],dim.biplot = 1) |>    axes(col=\"black\") |>    ellipses() |> plot() #> Computing 1.96 -ellipse for setosa  #> Computing 1.96 -ellipse for versicolor  #> Computing 1.96 -ellipse for virginica biplot(iris) |> PCA(group.aes = iris[,5],dim.biplot = 1) |>    axes(col=\"black\") |>    alpha.bags(alpha = 0.7) |> plot() #> Computing 0.7 -bag for setosa  #> Computing 0.7 -bag for versicolor  #> Computing 0.7 -bag for virginica"},{"path":"/articles/Biplots_in_1D.html","id":"the-function-density1d","dir":"Articles","previous_headings":"","what":"The function density1D()","title":"Biplots in 1D","text":"Overlapping points make distribution points scatter line difficult identify. density1D() uses kernel density estimation (KDE), adds density plot one-dimensional biplot.  KDE may smooth display distribution data. changing parameters KDE, able address issue. bandwidth kernel used density1D() controlled arguments h= kernel=, respectively. bandwidth h can take positive value, see ?stats::density detail. kernel can take kernel supported stats::density().  high concentration observations right plot now becomes evident. explore distributions observations, may want explore density groupings data. , simply specify group.aes= argument PCA(). density three species iris displayed.  display density certain groups, use = argument density1D().","code":"biplot(iris) |> PCA(dim.biplot = 1) |>    axes(col=\"black\") |>   density1D() |> plot() biplot(iris) |> PCA(dim.biplot = 1) |> axes(col='black') |>   density1D(h = 0.5 ,kernel = \"triangular\") |> plot() biplot(iris) |> PCA(group.aes = iris[,5],dim.biplot = 1) |>    axes(col=\"black\") |>   density1D() |> plot() biplot(iris) |> PCA(group.aes = iris[,5],dim.biplot = 1) |>    axes(col=\"black\") |>   density1D(which = c(2,3)) |> plot()"},{"path":"/articles/Biplots_in_1D.html","id":"the-function-legend-type","dir":"Articles","previous_headings":"","what":"The function legend.type()","title":"Biplots in 1D","text":"legend.type adds legend plot. separate legend created elements setting samples, means, bags ellipses equal TRUE. , add legend samples.  legends added, overlap elements plot displayed .  specifying new=TRUE, legends displayed new plot.  CVA biplot legend.type also displays legend classification regions `","code":"biplot(iris) |> PCA(group.aes  = iris[,5],dim.biplot = 1, show.class.means = TRUE) |>   axes(col=\"black\") |> density1D() |> samples(opacity=0.5)|> alpha.bags()|>   legend.type(samples = TRUE) |> plot() #> Computing 0.95 -bag for setosa  #> Computing 0.95 -bag for versicolor  #> Computing 0.95 -bag for virginica biplot(iris) |> PCA(group.aes  = iris[,5],dim.biplot = 1, show.class.means = TRUE) |>   axes(col=\"black\") |> density1D() |> samples(opacity=0.5)|> alpha.bags()|>   legend.type(samples = TRUE,means = TRUE, bags = TRUE) |> plot() #> Computing 0.95 -bag for setosa  #> Computing 0.95 -bag for versicolor  #> Computing 0.95 -bag for virginica biplot(iris) |> PCA(group.aes  = iris[,5],dim.biplot = 1, show.class.means = TRUE) |>   axes(col=\"black\") |> density1D() |> samples(opacity=0.5)|> alpha.bags()|>   legend.type(samples = TRUE,means = TRUE, bags = TRUE, new=TRUE) |> plot() #> Computing 0.95 -bag for setosa  #> Computing 0.95 -bag for versicolor  #> Computing 0.95 -bag for virginica bp <- biplot(iris) |> CVA(classes  = iris[,5],dim.biplot = 1, show.class.means = TRUE) |>   axes(col=\"black\") |> classify() |> density1D() |> samples(opacity=0.5)|> alpha.bags()|>   legend.type(samples = TRUE,means = TRUE, bags = TRUE, regions = TRUE, new=TRUE) |> plot() # #> Computing 0.95 -bag for setosa  #> Computing 0.95 -bag for versicolor  #> Computing 0.95 -bag for virginica"},{"path":"/articles/Biplots_in_1D.html","id":"the-function-fit-measures","dir":"Articles","previous_headings":"","what":"The function fit.measures()","title":"Biplots in 1D","text":"fit.measures() calculates measures fit biplot. Passing biplot object piped fit.measures() summary() output: plot: Quality fit. variable: Adequacy measure measure Axis Predictivity. sample: Sample Predictivity","code":"a <- biplot(iris) |> PCA(group.aes = iris[,5],dim.biplot = 1) |> fit.measures() summary(a) #> Object of class biplot, based on 150 samples and 5 variables. #> 4 numeric variables. #> 1 categorical variable. #>  #> Quality of fit in 1 dimension(s) = 92.5%  #> Adequacy of variables in 1 dimension(s): #> Sepal.Length  Sepal.Width Petal.Length  Petal.Width  #>  0.130600269  0.007144055  0.733884527  0.128371149  #> Axis predictivity in 1 dimension(s): #> Sepal.Length  Sepal.Width Petal.Length  Petal.Width  #>    0.8053299    0.1590003    0.9957524    0.9342141  #> Sample predictivity in 1 dimension(s): #>            1            2            3            4            5            6  #> 0.9859320755 0.9885358364 0.9974032622 0.9858701194 0.9843168833 0.8999107868  #>            7            8            9           10           11           12  #> 0.9904348916 0.9957802734 0.9612785710 0.9923358788 0.9370769165 0.9948836825  #>           13           14           15           16           17           18  #> 0.9875168089 0.9750670327 0.8294906959 0.7529871550 0.9071569468 0.9853898465  #>           19           20           21           22           23           24  #> 0.8616422955 0.9552462766 0.9620201204 0.9652955093 0.9901078239 0.9937624785  #>           25           26           27           28           29           30  #> 0.9810460091 0.9863832711 0.9951903602 0.9788910031 0.9826539385 0.9920053991  #>           31           32           33           34           35           36  #> 0.9923858356 0.9597307230 0.8986110971 0.8460407992 0.9949139602 0.9929589514  #>           37           38           39           40           41           42  #> 0.9371265524 0.9862655235 0.9733166664 0.9912721172 0.9891383317 0.8797484869  #>           43           44           45           46           47           48  #> 0.9825513928 0.9769811411 0.9396840258 0.9875952309 0.9530258191 0.9923056267  #>           49           50           51           52           53           54  #> 0.9503079288 0.9971653130 0.7221680790 0.8953237687 0.8532596845 0.0442100903  #>           55           56           57           58           59           60  #> 0.9129953358 0.6359273436 0.9116787898 0.3571098355 0.8281788080 0.0001270475  #>           61           62           63           64           65           66  #> 0.1332510142 0.8958907297 0.0818459091 0.9526971985 0.2540681791 0.7246059875  #>           67           68           69           70           71           72  #> 0.6197552004 0.1947357248 0.5937494624 0.0051154548 0.8476044276 0.6378818290  #>           73           74           75           76           77           78  #> 0.8806268185 0.8333647070 0.8003003948 0.7880417411 0.8419077254 0.9590386463  #>           79           80           81           82           83           84  #> 0.9582463503 0.2779242770 0.0082643376 0.0606288071 0.1243095987 0.9010013410  #>           85           86           87           88           89           90  #> 0.4112193414 0.7631565205 0.8696344890 0.5516294004 0.3190741381 0.0556990781  #>           91           92           93           94           95           96  #> 0.2922625503 0.9696427131 0.1971557114 0.3235202228 0.3247632177 0.5026574343  #>           97           98           99          100          101          102  #> 0.5643559551 0.9057638532 0.5676221930 0.4180323047 0.9171464166 0.8271416340  #>          103          104          105          106          107          108  #> 0.9806829065 0.9748867821 0.9851812054 0.9634762352 0.1357241699 0.9588447969  #>          109          110          111          112          113          114  #> 0.9664650500 0.9136258044 0.9543465424 0.9836661306 0.9843680241 0.7205977672  #>          115          116          117          118          119          120  #> 0.7597174900 0.9253702336 0.9925388347 0.8904535431 0.9774035332 0.7072260541  #>          121          122          123          124          125          126  #> 0.9631634829 0.6942722608 0.9562507107 0.9637593562 0.9632124205 0.9427733678  #>          127          128          129          130          131          132  #> 0.9657601543 0.9613019987 0.9845972460 0.9236214690 0.9539031336 0.8415331923  #>          133          134          135          136          137          138  #> 0.9775228161 0.9628241776 0.8556597753 0.9327799099 0.8909511203 0.9790497984  #>          139          140          141          142          143          144  #> 0.9273791355 0.9602863486 0.9614110358 0.8945281971 0.8271416340 0.9753298287  #>          145          146          147          148          149          150  #> 0.9351760753 0.9383233979 0.9136490692 0.9866832123 0.8702674447 0.8913242393"},{"path":[]},{"path":"/articles/Biplots_in_3D.html","id":"pca-3d-biplot","dir":"Articles","previous_headings":"","what":"PCA 3D biplot","title":"Biplots in 3D","text":"Three-dimensional PCA biplots obtained specifying dim.biplot = 3 call PCA(). package rgl required calling plot() biplot drawn rgl window. plot can interactively rotated zoomed using mouse buttons.","code":"biplot(iris) |> PCA(group.aes = iris$Species,dim.biplot = 3) |>   axes(col=\"black\") |> plot()"},{"path":"/articles/Biplots_in_3D.html","id":"adding-new-samples","dir":"Articles","previous_headings":"PCA 3D biplot","what":"Adding new samples","title":"Biplots in 3D","text":"process adding new samples biplot, called interpolation utilises functions interpolate() newsamples(). functions work way call two-dimensional biplot. function interpolate() accepts argument newdata specify matrix data frame containing new samples interpolated. function newsamples() operates way samples() user can specify aesthetics interpolated samples.","code":"biplot(iris[1:100,1:4])|> PCA(dim.biplot = 3) |> axes(col=\"black\") |>    interpolate(newdata = iris[101:150,1:4]) |> newsamples(col=\"purple\") |> plot()"},{"path":"/articles/Biplots_in_3D.html","id":"adding-new-variables","dir":"Articles","previous_headings":"PCA 3D biplot","what":"Adding new variables","title":"Biplots in 3D","text":"interpolate new variables biplot, function interpolate() newaxes() called. function interpolate() accepts argument newvariable specify matrix data frame number rows data specified biplot() containing new variables interpolated. function newaxes() allows user specify aesthetics interpolated variables.","code":"biplot(iris[,1:3])|> PCA(dim.biplot = 3) |> axes(col=\"black\") |>    interpolate(newvariable = iris[,4]) |>    newaxes(col=\"darkred\",X.new.names = \"Petal.Width\") |> plot()"},{"path":"/articles/Biplots_in_3D.html","id":"predicting-samples","dir":"Articles","previous_headings":"PCA 3D biplot","what":"Predicting samples","title":"Biplots in 3D","text":"add prediction samples biplot, prediction() function used. predict.samples argument takes vector indicating either row numbers samples predict set TRUE indicating predict samples. argument allows user select variable predict sample . example , samples 100 150 predictions shown variables 1 4. aesthetics display predictions arguments axes() function: predict.col predict.lwd.","code":"biplot(iris) |> PCA(group.aes = iris$Species,dim.biplot = 3,show.class.means = TRUE) |>    axes(col=\"black\",predict.col = \"orange\") |>     prediction(predict.samples=100:150,which = c(1,4))  |> plot()"},{"path":"/articles/Biplots_in_3D.html","id":"predicting-group-means","dir":"Articles","previous_headings":"PCA 3D biplot","what":"Predicting group means","title":"Biplots in 3D","text":"Similarly, add prediction group means, function prediction() used. argument predict.means takes vector specifying group means predict. example , first group means predicted. Important note argument show.class.means must set TRUE PCA() function.","code":"biplot(iris) |>    PCA(group.aes = iris$Species,dim.biplot = 3,show.class.means = TRUE) |>    axes(col=\"black\",predict.col = \"darkred\") |>    prediction(predict.means = 1) |> plot()"},{"path":"/articles/Biplots_in_3D.html","id":"ellipses","dir":"Articles","previous_headings":"PCA 3D biplot","what":"Ellipses","title":"Biplots in 3D","text":"Ellipses added 3D biplot using ellipses() function works way 2D biplot.","code":"biplot(iris) |> PCA(group.aes = iris[,5],dim.biplot = 3) |>    axes(col=\"black\") |>    ellipses(kappa = 3,opacity = 0.5) |> plot() #> Computing 3 -ellipse for setosa  #> Computing 3 -ellipse for versicolor  #> Computing 3 -ellipse for virginica"},{"path":"/articles/Biplots_in_3D.html","id":"cva-3d-biplot","dir":"Articles","previous_headings":"","what":"CVA 3d biplot","title":"Biplots in 3D","text":"Similarly CVA 3D biplot, dim.biplot = 3 specified call CVA().","code":"biplot(iris) |> CVA(classes = iris$Species,dim.biplot = 3) |>   axes(col=\"black\") |> plot() #> Warning in CVA.biplot(biplot(iris), classes = iris$Species, dim.biplot = 3): #> The dimension of the canonical space < dim.biplot sample.opt method used for #> additional dimension(s)."},{"path":"/articles/Biplots_in_3D.html","id":"ca-3d-biplot","dir":"Articles","previous_headings":"","what":"CA 3D biplot","title":"Biplots in 3D","text":"PCA(), three-dimensional CA biplots obtained specifying dim.biplot = 3 call CA(). , interactive biplot drawn separate rgl window. Consider HairEyeColor example discussed CA biplotEZ:  also illustrate three dimensional CA biplot SA Crime example:","code":"biplot(HairEyeColor[,,2], center = FALSE) |>    CA(variant = \"Symmetric\", dim.biplot = 3) |>   samples(col=c(\"darkred\",\"forestgreen\"), pch=c(15,17), label.col=\"black\") |>   plot() SACrime <- matrix(c(1235,432,1824,1322,573,588,624,169,629,34479,16833,46993,30606,13670,               16849,15861,9898,24915,2160,939,5257,4946,722,1271,881,775,1844,5946,               4418,15117,10258,5401,4273,4987,1956,10639,29508,15705,62703,37203,               11857,18855,14722,4924,42376,604,156,7466,3889,203,664,291,5,923,19875,               19885,57153,29410,11024,12202,10406,5431,32663,7086,4193,22152,9264,3760,               4752,3863,1337,8578,7929,4525,12348,24174,3198,1770,7004,2201,45985,764,               427,1501,1197,215,251,345,213,1850,3515,879,3674,4713,696,835,917,422,2836,               88,59,174,76,31,61,117,32,257,5499,2628,8073,6502,2816,2635,3017,1020,4000,               8939,4501,50970,24290,2447,5907,5528,1175,14555),nrow=9, ncol=14) dimnames(SACrime) <- list(paste(c(\"ECpe\", \"FrSt\", \"Gaut\", \"KZN\",  \"Limp\", \"Mpml\", \"NWst\", \"NCpe\",                             \"WCpe\")), paste(c(\"Arsn\", \"AGBH\", \"AtMr\", \"BNRs\", \"BRs\",  \"CrJk\",                                               \"CmAs\", \"CmRb\", \"DrgR\", \"InAs\", \"Mrd\", \"PubV\",                                                \"Rape\", \"RAC\" ))) names(dimnames(SACrime))[[1]] <- \"Provinces\" names(dimnames(SACrime))[[2]] <- \"Crimes\" biplot(SACrime, center = FALSE) |> CA(variant = \"Symmetric\", dim.biplot = 3) |>  samples(col=c(\"royalblue\",\"darkred\"), pch=c(15,17), label.col=\"black\") |> plot()"},{"path":"/articles/CA_in_biplotEZ.html","id":"what-is-a-correspondence-analysis","dir":"Articles","previous_headings":"","what":"What is a Correspondence Analysis?","title":"CA in biplotEZ","text":"simplest form Correspondence Analysis (CA) aims expose association two categorical variables utilising two-way frequency table. Numerous variants CA available application diverse problems, interested reader referred : Gower, Lubbe, Roux (2011), Beh Lombardo (2014). vignette, focus placed three EZ--use versions based Pearson residuals (Gower, Lubbe, Roux (2011) :300). Now, two-way frequency table also referred data matrix: 𝐗:r×c\\mathbf{X}:r\\times c. data matrix different continuous case used PCA() CVA() examples, represents cross-tabulations two categorical variables (.e. factors), finite number levels (.e response values). elements data matrix represent frequency co-occurrence two particular levels two variables. Consider HairEyeColor data set R, summarises hair eye color male female statistics students. purpose example male students considered: grand total table NN obtained total frequencies: ∑r=1R∑c=1Cxrc=N \\sum_{r=1}^{R}\\sum_{c=1}^{C}x_{rc}=N common work proportions rather frequencies terms correspondence matrix, 𝐏\\mathbf{P}: 𝐏=𝐗N \\mathbf{P}=\\frac{\\mathbf{X}}{N} useful summaries 𝐏\\mathbf{P} include row column masses (arbitrary row column rr cc, respectively), also expressed diagonal matrices: $$ \\mathbf{r}_r = \\sum_{c=1}^{C}p_{rc}; \\hspace{0.5 cm} \\mathbf{c}_c = \\sum_{r=1}^{R}p_{rc}\\\\ \\mathbf{r}=\\mathbf{P1}; \\hspace{0.5 cm} \\mathbf{c}=\\mathbf{P}^\\prime\\mathbf{1} $$ Diagonal matrices: $$ \\mathbf{D_r}=\\text{diag}(\\mathbf{r}); \\hspace{0.5 cm} \\mathbf{D_c}=\\text{diag}(\\mathbf{c}) $$ order obtain first form row column coordinates, singular value decomposition (SVD) matrix standardised Pearson residuals (𝐒\\mathbf{S}) computed: SVD(𝐒)=SVD(𝐃𝐫−𝟏𝟐(𝐏−𝐫𝐜′)𝐃𝐜−𝟏𝟐)=𝐔𝚲𝐕′ \\begin{aligned} \\text{SVD}(\\mathbf{S}) &= \\text{SVD}\\left(\\mathbf{D_r^{-\\frac{1}{2}}}(\\mathbf{P}-\\mathbf{rc^\\prime})\\mathbf{D_c^{-\\frac{1}{2}}}\\right)\\\\&= \\mathbf{U\\Lambda V^\\prime} \\end{aligned}  return value Standardised pearson residuals Smat singular value decomposition, SVD. linked χ2\\chi^2-statistic determine whether two categorical variables (.e. rows columns contingency table) independent. expected frequencies represented product row column masses (𝐫𝐜′\\mathbf{rc^\\prime}). Furthermore, since weights certain objects might substantially different others result distorted approximation lower dimension, χ2\\chi^2-distance, also referred weighted Euclidean distance, rather used measure distances CA. intuitive decision follows χ2\\chi^2-statistic test independence two categorical variables, case independence rows columns contingency table. (Beh Lombardo (2014), Greenacre (2017)).","code":"X <- HairEyeColor[,,2] X #>        Eye #> Hair    Brown Blue Hazel Green #>   Black    36    9     5     2 #>   Brown    66   34    29    14 #>   Red      16    7     7     7 #>   Blond     4   64     5     8 N <- sum(X) N #> [1] 313 P <- X/N P #>        Eye #> Hair          Brown        Blue       Hazel       Green #>   Black 0.115015974 0.028753994 0.015974441 0.006389776 #>   Brown 0.210862620 0.108626198 0.092651757 0.044728435 #>   Red   0.051118211 0.022364217 0.022364217 0.022364217 #>   Blond 0.012779553 0.204472843 0.015974441 0.025559105 rMass <- rowSums(P) rMass #>     Black     Brown       Red     Blond  #> 0.1661342 0.4568690 0.1182109 0.2587859 cMass <- colSums(P) cMass #>      Brown       Blue      Hazel      Green  #> 0.38977636 0.36421725 0.14696486 0.09904153 Dr <- diag(apply(P, 1, sum)) Dr #>           [,1]     [,2]      [,3]      [,4] #> [1,] 0.1661342 0.000000 0.0000000 0.0000000 #> [2,] 0.0000000 0.456869 0.0000000 0.0000000 #> [3,] 0.0000000 0.000000 0.1182109 0.0000000 #> [4,] 0.0000000 0.000000 0.0000000 0.2587859 Dc <- diag(apply(P, 2, sum)) Dc #>           [,1]      [,2]      [,3]       [,4] #> [1,] 0.3897764 0.0000000 0.0000000 0.00000000 #> [2,] 0.0000000 0.3642173 0.0000000 0.00000000 #> [3,] 0.0000000 0.0000000 0.1469649 0.00000000 #> [4,] 0.0000000 0.0000000 0.0000000 0.09904153 Smat <- sqrt(solve(Dr))%*%(P-(Dr %*%matrix(1, nrow = nrow(X),      ncol = ncol(X)) %*%  Dc))%*%sqrt(solve(Dc)) svd.out <- svd(Smat) svd.out #> $d #> [1] 5.499629e-01 1.806424e-01 7.541748e-02 8.574459e-17 #>  #> $u #>            [,1]       [,2]        [,3]      [,4] #> [1,] -0.3832205  0.7807477 -0.27828196 0.4075956 #> [2,] -0.3195599 -0.2982325  0.59335474 0.6759209 #> [3,] -0.1736837 -0.5332073 -0.75320188 0.3438181 #> [4,]  0.8490333  0.1310737 -0.05635808 0.5087101 #>  #> $v #>             [,1]       [,2]        [,3]      [,4] #> [1,] -0.61837991  0.4547976 -0.14487614 0.6243207 #> [2,]  0.75797511  0.2307003  0.08963172 0.6035041 #> [3,] -0.20612962 -0.5898626  0.68015284 0.3833600 #> [4,]  0.02430218 -0.6260980 -0.71300012 0.3147086"},{"path":[]},{"path":"/articles/CA_in_biplotEZ.html","id":"coordinates","dir":"Articles","previous_headings":"CA biplot","what":"Coordinates","title":"CA in biplotEZ","text":"order construct biplot distances row column coordinates meaningful asymmetric display constructed. means contribution singular values different row column coordinates. (Gabriel (1971)) standard coordinates expressed : $$ \\begin{aligned} \\text{Row standard coordinates:} \\hspace{0.5 cm}&\\mathbf{U}\\\\ \\text{Column standard coordinates:} \\hspace{0.5 cm}&\\mathbf{V} \\end{aligned} $$ principal coordinates expressed : $$ \\begin{aligned} \\text{Row principal coordinates:} \\hspace{0.5 cm}&\\mathbf{U\\Lambda}\\\\ \\text{Column principal coordinates:} \\hspace{0.5 cm}&\\mathbf{V\\Lambda} \\end{aligned} $$ including singular values magnitude association variables incorporated scaling coordinates. ca() function argument variant allows user choose three types CA biplots: Princ, Stand Symmetric. $$ \\begin{aligned} \\text{Row coordinates:} \\hspace{0.5 cm}&\\mathbf{U\\Lambda^\\gamma}\\\\ \\text{Column coordinates:} \\hspace{0.5 cm}&\\mathbf{V\\Lambda^{1-\\gamma}} \\end{aligned} $$ row standard (.e. column principal) coordinate biplot: Stand, results γ=0\\gamma=0. row principal (.e. column standard) coordinate biplot: Princ, results γ=1\\gamma=1. symmetric plot row column coordinates scaled equally: Symmetric, results γ=0.5\\gamma=0.5. return value rowcoor colcoor, respectively.","code":"gamma <- 0 rowcoor <- svd.out[[2]]%*%(diag(svd.out[[1]])^gamma) colcoor <- svd.out[[3]]%*%(diag(svd.out[[1]])^(1-gamma))"},{"path":"/articles/CA_in_biplotEZ.html","id":"lambda-scaling","dir":"Articles","previous_headings":"CA biplot","what":"Lambda scaling","title":"CA in biplotEZ","text":"presented Gower, Lubbe, Roux (2011) :24, constructing biplot representing rows coordinate matrix 𝐀\\mathbf{} 𝐁′\\mathbf{B}^\\prime. Take note inner product invariant 𝐀\\mathbf{} 𝐁\\mathbf{B} scaled inversely λ\\lambda. 𝐀𝐁=(λ𝐀)(𝐁/λ) \\mathbf{AB} = (\\lambda\\mathbf{})(\\mathbf{B}/\\lambda)  arbitrary value λ\\lambda can selected optimal value ensure average squared distance points λ𝐀\\lambda\\mathbf{} 𝐁/λ\\mathbf{B}/\\lambda equal. λ4=rc||𝐁||2||𝐀||2 \\lambda^4 =\\frac{r}{c}\\frac{||\\mathbf{B}||^2}{||\\mathbf{}||^2} default setting apply lambda-scaling (.e. λ=1\\lambda=1). return value lambda.val.","code":""},{"path":"/articles/CA_in_biplotEZ.html","id":"measures-of-fit","dir":"Articles","previous_headings":"CA biplot","what":"Measures of fit","title":"CA in biplotEZ","text":"quality, adequacy, row.predictivities column.predictivities available CA biplots. explained biplotEZ vignette, quality biplot measured ratio variance explained (sum squared singular values utilised (MM) components) total variance (sum squared singular values (pp)). ∑m=1Mλm2∑m=1pλm2 \\frac{\\sum_{m=1}^{M}\\lambda_m^2}{\\sum_{m=1}^{p}\\lambda_m^2}  adequacy refers representation variables. CA() factor variable represented columns treated variables calculated explained biplotEZ vignette: diag(𝐕r𝐕r′)diag(𝐕𝐕′)=diag(𝐕r𝐕r′)  \\frac{diag(\\mathbf{V}_r\\mathbf{V}_r')}{diag(\\mathbf{VV}')}= diag(\\mathbf{V}_r\\mathbf{V}_r') predictivities provide measure well original values recovered biplot. element well represented predictivity close one, indicating row column variable values prediction close observed values. element poorly represented, predicted values different original values predictivity value close zero. row.predictivities calculated follows (Gower, Lubbe, Roux (2011) :299): $$ diag(\\mathbf{U}\\mathbf{\\Sigma}\\mathbf{J}\\mathbf{\\Sigma}\\mathbf{U}')[diag(\\mathbf{U}\\mathbf{\\Sigma}\\mathbf{\\Sigma}\\mathbf{U}')]^{-1}\\\\ =diag(\\mathbf{U}\\mathbf{\\Sigma}^2\\mathbf{J}\\mathbf{U}')[diag(\\mathbf{U}\\mathbf{\\Sigma^2}\\mathbf{U}')]^{-1} $$ col.predictivities calculated follows (Gower, Lubbe, Roux (2011) :299): diag(𝐕𝚺2𝐉𝐕′)[diag(𝐕𝚺𝟐𝐕′)]−1 diag(\\mathbf{V}\\mathbf{\\Sigma}^2\\mathbf{J}\\mathbf{V}')[diag(\\mathbf{V}\\mathbf{\\Sigma^2}\\mathbf{V}')]^{-1}","code":""},{"path":"/articles/CA_in_biplotEZ.html","id":"the-function-ca","dir":"Articles","previous_headings":"","what":"The function CA()","title":"CA in biplotEZ","text":"function CA() requires two-way contingency table input return object class CA biplot. standard data matrix PCA CVA, scaling centering allowed two-way contingency table warning given either scale center specified TRUE biplot()`.","code":""},{"path":"/articles/CA_in_biplotEZ.html","id":"variantprinc","dir":"Articles","previous_headings":"The function CA()","what":"Variant=\"Princ\"","title":"CA in biplotEZ","text":"default CA biplot row principal coordinate biplot:","code":"biplot(HairEyeColor[,,2], center = FALSE) |> CA() |> plot()"},{"path":"/articles/CA_in_biplotEZ.html","id":"variantstand","dir":"Articles","previous_headings":"The function CA()","what":"Variant=\"Stand\"","title":"CA in biplotEZ","text":"construct CA biplot row standard coordinates:","code":"ca.out <- biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = \"Stand\") |>    plot()"},{"path":"/articles/CA_in_biplotEZ.html","id":"variantsymmetric","dir":"Articles","previous_headings":"The function CA()","what":"Variant=\"Symmetric\"","title":"CA in biplotEZ","text":"construct symmetric CA map:","code":"ca.out <- biplot(HairEyeColor[,,2], center = FALSE) |>    CA(variant = \"Symmetric\") |> plot() ca.out$lambda.val #> [1] 1"},{"path":"/articles/CA_in_biplotEZ.html","id":"measures-of-fit-1","dir":"Articles","previous_headings":"The function CA()","what":"Measures of fit","title":"CA in biplotEZ","text":"fit.mesaures() function utilised obtain specific fit measures explained .","code":"ca.out <- biplot(HairEyeColor[,,2], center = FALSE) |>    CA(variant = \"Symmetric\") |> fit.measures() print(\"Quality\") #> [1] \"Quality\" ca.out$quality #> [1] 0.9833094 print(\"Adequacy\") #> [1] \"Adequacy\" ca.out$adequacy #>        Brown   Blue  Hazel  Green #> Dim 1 0.3824 0.5745 0.0425 0.0006 #> Dim 2 0.5892 0.6277 0.3904 0.3926 #> Dim 3 0.6102 0.6358 0.8530 0.9010 #> Dim 4 1.0000 1.0000 1.0000 1.0000 print(\"Row predictivities\") #> [1] \"Row predictivities\" ca.out$row.predictivities #>        Black  Brown    Red  Blond #> Dim 1 0.6860 0.8630 0.4219 0.9974 #> Dim 2 0.9932 0.9441 0.8508 0.9999 #> Dim 3 1.0000 1.0000 1.0000 1.0000 #> Dim 4 1.0000 1.0000 1.0000 1.0000 print(\"Column predictivities\") #> [1] \"Column predictivities\" ca.out$col.predictivities #>        Brown   Blue  Hazel  Green #> Dim 1 0.9439 0.9898 0.4789 0.0113 #> Dim 2 0.9990 0.9997 0.9020 0.8177 #> Dim 3 1.0000 1.0000 1.0000 1.0000 #> Dim 4 1.0000 1.0000 1.0000 1.0000"},{"path":"/articles/CA_in_biplotEZ.html","id":"interpolating-new-samples","dir":"Articles","previous_headings":"The function CA()","what":"Interpolating new samples","title":"CA in biplotEZ","text":"Adding cross-tabulations two categorical variables plot facilitated function interpolate(). Note additional variables interpolated contribute construction biplot. reason Greenacre (2017) term supplementary points. function interpolate() accepts matrix data frame containing samples variables interpolated. argument newdata containing samples interpolated needs similar structure data set sent biplot(). biplot() received data frame, newdata can either another data frame matrix containing subset numerical variables. function newsamples() operates similar samples() enables aesthetic changes new samples.","code":"biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = \"Symmetric\") |>    samples(pch = c(0,2)) |> interpolate(newdata = HairEyeColor[,,1]) |>    newsamples(col = c(\"orange\",\"purple\"), pch = c(15,17)) |> plot()"},{"path":"/articles/CA_in_biplotEZ.html","id":"aesthetics-and-legend","dir":"Articles","previous_headings":"The function CA()","what":"Aesthetics and legend","title":"CA in biplotEZ","text":"sample() function utilised specify colours, plotting characters expansion samples.","code":"biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = \"Princ\") |>    samples(col = c(\"cyan\",\"purple\"), pch = c(15,17), label.side = c(\"bottom\",\"top\"),            label.cex = 1) |> legend.type(samples = TRUE, new = TRUE) |> plot() biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = \"Symmetric\") |>    samples(col = c(\"forestgreen\",\"magenta\"), pch = c(12,17),            label.side = c(\"top\",\"bottom\")) |>    legend.type(samples = TRUE) |> plot()"},{"path":"/articles/CA_in_biplotEZ.html","id":"additional-example","dir":"Articles","previous_headings":"The function CA()","what":"Additional example","title":"CA in biplotEZ","text":"Consider South African Crime data set 2008, extracted South African police website (http://www.saps.gov.za/). Gower, Lubbe, Roux (2011) :312.","code":"SACrime <- matrix(c(1235,432,1824,1322,573,588,624,169,629,34479,16833,46993,30606,13670,               16849,15861,9898,24915,2160,939,5257,4946,722,1271,881,775,1844,5946,               4418,15117,10258,5401,4273,4987,1956,10639,29508,15705,62703,37203,               11857,18855,14722,4924,42376,604,156,7466,3889,203,664,291,5,923,19875,               19885,57153,29410,11024,12202,10406,5431,32663,7086,4193,22152,9264,3760,               4752,3863,1337,8578,7929,4525,12348,24174,3198,1770,7004,2201,45985,764,               427,1501,1197,215,251,345,213,1850,3515,879,3674,4713,696,835,917,422,2836,               88,59,174,76,31,61,117,32,257,5499,2628,8073,6502,2816,2635,3017,1020,4000,               8939,4501,50970,24290,2447,5907,5528,1175,14555),nrow=9, ncol=14) dimnames(SACrime) <- list(paste(c(\"ECpe\", \"FrSt\", \"Gaut\", \"KZN\",  \"Limp\", \"Mpml\", \"NWst\", \"NCpe\",                             \"WCpe\")), paste(c(\"Arsn\", \"AGBH\", \"AtMr\", \"BNRs\", \"BRs\",  \"CrJk\",                                               \"CmAs\", \"CmRb\", \"DrgR\", \"InAs\", \"Mrd\", \"PubV\",                                                \"Rape\", \"RAC\" ))) names(dimnames(SACrime))[[1]] <- \"Provinces\" names(dimnames(SACrime))[[2]] <- \"Crimes\" SACrime #>          Crimes #> Provinces Arsn  AGBH AtMr  BNRs   BRs CrJk  CmAs  CmRb  DrgR InAs  Mrd PubV #>      ECpe 1235 34479 2160  5946 29508  604 19875  7086  7929  764 3515   88 #>      FrSt  432 16833  939  4418 15705  156 19885  4193  4525  427  879   59 #>      Gaut 1824 46993 5257 15117 62703 7466 57153 22152 12348 1501 3674  174 #>      KZN  1322 30606 4946 10258 37203 3889 29410  9264 24174 1197 4713   76 #>      Limp  573 13670  722  5401 11857  203 11024  3760  3198  215  696   31 #>      Mpml  588 16849 1271  4273 18855  664 12202  4752  1770  251  835   61 #>      NWst  624 15861  881  4987 14722  291 10406  3863  7004  345  917  117 #>      NCpe  169  9898  775  1956  4924    5  5431  1337  2201  213  422   32 #>      WCpe  629 24915 1844 10639 42376  923 32663  8578 45985 1850 2836  257 #>          Crimes #> Provinces Rape   RAC #>      ECpe 5499  8939 #>      FrSt 2628  4501 #>      Gaut 8073 50970 #>      KZN  6502 24290 #>      Limp 2816  2447 #>      Mpml 2635  5907 #>      NWst 3017  5528 #>      NCpe 1020  1175 #>      WCpe 4000 14555 biplot(SACrime, center = FALSE) |>    CA(variant = \"Symmetric\", lambda.scal = TRUE) |>    samples(col = c(\"cyan\",\"purple\"), pch = c(15,17), label.side = c(\"bottom\",\"top\")) |>   legend.type(samples = TRUE, new = TRUE) |> plot()"},{"path":[]},{"path":"/articles/Class_separation.html","id":"what-is-a-cva-biplot","dir":"Articles","previous_headings":"","what":"What is a CVA biplot","title":"Class separation","text":"Consider data matrix 𝐗:n×p\\mathbf{X}:n \\times p containing data nn objects pp variables. addition, vector 𝐠:n×1\\mathbf{g}:n \\times 1 contains information class membership observation. Let GG indicate total number classes. CVA closely related linear discriminant anlaysis, pp variables transformed pp new variables, called canonical variates, classes optimally separated canonical space. optimally separated, mean maximising class variance, relative within class variance. can formulated follows: Let 𝐆:n×G\\mathbf{G}:n \\times G indicator matrix gij=0g_{ij} = 0 unless observation ii belongs class jj gij=1g_{ij} = 1. matrix 𝐆′𝐆\\mathbf{G'G} diagonal matrix containing number observations per class diagonal. can form matrix class means 𝐗‾:G×p=(𝐆′𝐆)−1𝐆′𝐗\\bar{\\mathbf{X}}:G \\times p = (\\mathbf{G'G})^{-1} \\mathbf{G'X}. usual analysis variance total variance can decomposed class variance within class variance: 𝐓=𝐁+𝐖 \\mathbf{T} = \\mathbf{B} + \\mathbf{W} 𝐗′𝐗=𝐗‾′𝐂𝐗‾+𝐗′[𝐈−𝐆(𝐆′𝐆)−𝟏𝐂(𝐆′𝐆)−𝟏𝐆′]𝐗 \\mathbf{X'X} = \\mathbf{\\bar{\\mathbf{X}}'C \\bar{\\mathbf{X}}} + \\mathbf{X' [- G(G'G)^{-1}C(G'G)^{-1}G'] X} default choice centring matrix 𝐂=𝐆′𝐆\\mathbf{C = G'G} leads simplification 𝐗′𝐗=𝐗‾′𝐆′𝐆𝐗‾+𝐗′[𝐈−𝐆(𝐆′𝐆)−𝟏𝐆′]𝐗. \\mathbf{X'X} = \\mathbf{\\bar{\\mathbf{X}}'G'G \\bar{\\mathbf{X}}} + \\mathbf{X' [- G(G'G)^{-1}G'] X}. options 𝐂=𝐈\\mathbf{C = } 𝐂=(𝐈G−1G𝟏𝟏′)\\mathbf{C} = (\\mathbf{}_G - \\frac{1}{G}\\mathbf{11'}). find canonical variates want maximise ratio 𝐦′𝐁𝐦𝐦′𝐖𝐦 \\frac{\\mathbf{m'Bm}}{\\mathbf{m'Wm}} subject 𝐦′𝐖𝐦=1\\mathbf{m'Wm} = 1. can shown leads following equivalent eigen equations: 𝐖−1𝐁𝐌=𝐌𝚲 \\mathbf{W}^{-1}\\mathbf{BM} = \\mathbf{M \\Lambda} \\tag{1} 𝐁𝐌=𝐖𝐌𝚲 \\mathbf{BM} = \\mathbf{WM \\Lambda} (𝐖−12𝐁𝐖−12)𝐌=(𝐖−12𝐌)𝚲 (\\mathbf{W}^{-\\frac{1}{2}} \\mathbf{B} \\mathbf{W}^{-\\frac{1}{2}}) \\mathbf{M} = (\\mathbf{W}^{-\\frac{1}{2}} \\mathbf{M}) \\mathbf{\\Lambda} 𝐌′𝐁𝐌=𝚲\\mathbf{M'BM}= \\mathbf{\\Lambda} 𝐌′𝐖𝐌=𝐈\\mathbf{M'WM}= \\mathbf{}. Since matrix 𝐖−12𝐁𝐖−12\\mathbf{W}^{-\\frac{1}{2}} \\mathbf{B} \\mathbf{W}^{-\\frac{1}{2}} symmetric positive semi-definite eigenvalues matrix 𝚲\\mathbf{\\Lambda} positive ordered. rank 𝐁=min(p,G−1)\\mathbf{B} = min(p, G-1) first rank(𝐁)rank(\\mathbf{B}) eigenvalues non-zero. form canonical variates transformation 𝐘‾=𝐗‾𝐌. \\bar{\\mathbf{Y}} = \\bar{\\mathbf{X}}\\mathbf{M}. construct 2D biplot, plot first two canonical variates 𝐙‾=𝐗‾𝐌𝐉2\\bar{\\mathbf{Z}} = \\bar{\\mathbf{X}}\\mathbf{MJ}_2 𝐉2′=[𝐈2𝟎]\\mathbf{J}_2' = \\begin{bmatrix} \\mathbf{}_2 & \\mathbf{0} \\end{bmatrix}. add individual sample points transformation 𝐙=𝐗𝐌𝐉2 \\mathbf{Z} = \\mathbf{X}\\mathbf{MJ}_2  𝐉2=[𝐈2𝟎]. \\mathbf{J}_2 = \\begin{bmatrix}                 \\mathbf{}_2\\\\                 \\mathbf{0}                \\end{bmatrix}.  Interpolation new sample 𝐱*:p×1\\mathbf{x}^*:p \\times 1 follows 𝐳*′:2×1=𝐱*′𝐌𝐉2{\\mathbf{z}^*}':2 \\times 1 ={\\mathbf{x}^*}' \\mathbf{MJ}_2. Using inverse transformation 𝐱′=𝐲′𝐌−1\\mathbf{x}' = \\mathbf{y}'\\mathbf{M}^{-1}, points predict μ\\mu variable jj form μ=𝐲′𝐌−1𝐞j \\mu = \\mathbf{y}'\\mathbf{M}^{-1} \\mathbf{e}_j 𝐞j\\mathbf{e}_j vector zeros one position jj. points 2D biplot predict value μ\\mu μ=[z1z20…0]𝐌−1𝐞j \\mu = \\begin{bmatrix} z_1 & z_2 & 0 & \\dots & 0\\end{bmatrix}\\mathbf{M}^{-1} \\mathbf{e}_j defining prediction line μ=𝐳μ′𝐉2𝐌−1𝐞j. \\mu = \\mathbf{z}_{\\mu}' \\mathbf{J}_2 \\mathbf{M}^{-1} \\mathbf{e}_j. Writing 𝐡(j)=𝐉2𝐌−1𝐞j\\mathbf{h}_{(j)} = \\mathbf{J}_2 \\mathbf{M}^{-1} \\mathbf{e}_j construction biplot axes similar discussion biplotEZ vignette PCA biplots. direction axis given 𝐡(j)\\mathbf{h}_{(j)}. find intersection prediction line 𝐡(j)\\mathbf{h}_{(j)} note 𝐳′(μ)𝐡(j)=∥𝐳(μ)∥2∥𝐡(j)∥2cos(𝐳(μ),𝐡(j))=∥𝐩∥2∥𝐡(j)∥2 \\mathbf{z}'_{(\\mu)}\\mathbf{h}_{(j)} = \\| \\mathbf{z}_{(\\mu)} \\|^2 \\| \\mathbf{h}_{(j)} \\|^2 cos(\\mathbf{z}_{(\\mu)},\\mathbf{h}_{(j)}) =  \\| \\mathbf{p} \\|^2 \\| \\mathbf{h}_{(j)} \\|^2   𝐩\\mathbf{p} length orthogonal projection 𝐳(μ)\\mathbf{z}_{(\\mu)} 𝐡(j)\\mathbf{h}_{(j)}. Since 𝐩\\mathbf{p} along 𝐡(j)\\mathbf{h}_{(j)} can write 𝐩=c𝐡(j)\\mathbf{p} = c\\mathbf{h}_{(j)} points prediction line μ=𝐳′μ𝐡(j)\\mu = \\mathbf{z}'_{\\mu}\\mathbf{h}_{(j)} project point cμ𝐡(j)c_{\\mu}\\mathbf{h}_{(j)}. solve cμc_{\\mu} μ=𝐳′μ𝐡(j)=∥𝐩∥2∥𝐡(j)∥2=∥cμ𝐡(j)∥2∥𝐡(j)∥2 \\mu = \\mathbf{z}'_{\\mu}\\mathbf{h}_{(j)}=\\| \\mathbf{p} \\|^2 \\| \\mathbf{h}_{(j)} \\|^2 =  \\| c_{\\mu}\\mathbf{h}_{(j)} \\|^2 \\| \\mathbf{h}_{(j)} \\|^2 cμ=μ𝐡(j)′𝐡(j). c_{\\mu} = \\frac{\\mu}{\\mathbf{h}_{(j)}'\\mathbf{h}_{(j)}}.  select ‘nice’ scale markers τ1,τ2,⋯τk\\tau_{1}, \\tau_{2}, \\cdots \\tau_{k} variable jj, τh−x‾j=μh\\tau_{h}-\\bar{x}_j = \\mu_{h} positions scale markers 𝐡(j)\\mathbf{h}_{(j)} given pμ1,pμ2,⋯pμkp_{\\mu_{1}}, p_{\\mu_{2}}, \\cdots p_{\\mu_{k}} pμh=cμh𝐡(j)=μh𝐡(j)′𝐡(j)𝐡(j) p_{\\mu_h} = c_{\\mu_h}\\mathbf{h}_{(j)} =  \\frac{\\mu_h}{\\mathbf{h}_{(j)}'\\mathbf{h}_{(j)}}\\mathbf{h}_{(j)} =μh𝐞(j)′𝐌′−1𝐉𝐌−1𝐞(j)𝐉2𝐌−1𝐞(j) = \\frac{\\mu_h}{\\mathbf{e}_{(j)}' \\mathbf{M'}^{-1} \\mathbf{J} \\mathbf{M}^{-1} \\mathbf{e}_{(j)}}\\ \\mathbf{J}_2 \\mathbf{M}^{-1} \\mathbf{e}_{(j)} 𝐉=[𝐈2𝟎𝟎𝟎]. \\mathbf{J} = \\begin{bmatrix}               \\mathbf{}_2 & \\mathbf{0}\\\\               \\mathbf{0} & \\mathbf{0}              \\end{bmatrix}.","code":""},{"path":"/articles/Class_separation.html","id":"the-function-cva","dir":"Articles","previous_headings":"","what":"The function CVA()","title":"Class separation","text":"obtain CVA biplot state.x77 data set, optimally separating classes according state.region call  Fitting α\\alpha-bags classes makes easier compare class overlap separation. detailed discussion α\\alpha-bags, see biplotEZ vignette.","code":"biplot(state.x77) |>    CVA(classes = state.region) |>    plot() biplot(state.x77) |> CVA(classes = state.region) |> alpha.bags() |>    legend.type (bags = TRUE) |>    plot() #> Computing 0.95 -bag for Northeast  #> Computing 0.95 -bag for South  #> Computing 0.95 -bag for North Central  #> Computing 0.95 -bag for West"},{"path":"/articles/Class_separation.html","id":"the-function-means","dir":"Articles","previous_headings":"","what":"The function means()","title":"Class separation","text":"function controls aesthetics class means biplot. function accepts first argument object class biplot aesthetics applied. Let us first construct CVA biplot state.x77 data samples optimally separated according state.division.  Instead adding legend, can choose label class means. Furthermore, colour class mean defaults colour samples. wish select different colour plotting character class means.  choose show class means central states, argument used either indicating number(s) sequence levels (= 4:7), shown , levels :  size labels controlled label.cex can specified either single value (class means) vector indicating size values individual sample. colour labels defaults colour(s) class means. However, individual label colours can spesified label.col, similar label.cex either single value vector length equal number classes.  can also make use functionality ggrepel package place labels.","code":"biplot(state.x77, scaled = TRUE) |>    CVA(classes = state.division) |>    legend.type(means = TRUE) |>    plot() biplot(state.x77, scaled = TRUE) |>    CVA(classes = state.division) |>    means(label = TRUE, col = \"olivedrab\", pch = 15) |>    plot() biplot(state.x77, scaled = TRUE) |>    CVA(classes = state.division) |>    means (which = c(\"West North Central\", \"West South Central\", \"East South Central\",                       \"East North Central\"), label = TRUE) |>   plot() biplot(state.x77, scaled = TRUE) |>    CVA(classes = state.division) |>    means (col = \"olivedrab\", pch = 15, cex = 1.5,          label = TRUE, label.col = c(\"blue\",\"green\",\"gold\",\"cyan\",\"magenta\",                                      \"black\",\"red\",\"grey\",\"purple\")) |>   plot() biplot(state.x77, scaled = TRUE) |>    CVA(classes = state.division) |>    samples (label = \"ggrepel\", label.cex=0.65) |>    means (label = \"ggrepel\", label.cex=0.8) |> plot()"},{"path":"/articles/Class_separation.html","id":"the-function-classify","dir":"Articles","previous_headings":"","what":"The function classify()","title":"Class separation","text":"Classification regions can added CVA biplot function classify(). argument classify.regions must set equal TRUE render regions plot. arguments col, opacity borders allows change aesthetics regions.","code":"biplot(state.x77, scaled = TRUE) |>    CVA(classes = state.division) |>   classify(classify.regions = TRUE,opacity = 0.2) |>    plot()"},{"path":"/articles/Class_separation.html","id":"the-functions-fit-measures-and-summary","dir":"Articles","previous_headings":"","what":"The functions fit.measures() and summary()","title":"Class separation","text":"number fit measures specific CVA biplots. measures computed function fit.measures() results displayed function summary(). Canonical variate analysis can considered transformation original variables canonical space followed constructing PCA biplot canonical variables. matrix class means 𝐗‾=(𝐆′𝐆)−1𝐆′𝐗\\bar{\\mathbf{X}} = (\\mathbf{G'G})^{-1} \\mathbf{G'X} transformed 𝐗‾𝐋\\mathbf{\\bar{X}L} 𝐋\\mathbf{L} non-singular matrix 𝐋𝐋′=𝐖−1\\mathbf{LL'=W}^{-1}. Pricipal component analysis finds orthogonal matrix 𝐕\\mathbf{V} (𝐋′𝐗‾′𝐂𝐗‾𝐋)𝐕=𝐕𝚲 \\mathbf{(L'\\bar{X}'C\\bar{X}L)V=V \\Lambda} 𝐌=𝐋𝐕\\mathbf{M = LV} defined section 1. predicted values class means given 𝐗‾̂=𝐗‾𝐌𝐉𝐌−1. \\mathbf{\\hat{\\bar{X}}} = \\mathbf{\\bar{X}MJ}\\mathbf{M}^{-1}.","code":""},{"path":"/articles/Class_separation.html","id":"overall-quality-of-fit","dir":"Articles","previous_headings":"The functions fit.measures() and summary()","what":"Overall quality of fit","title":"Class separation","text":"Based two-step process described , two measures quality fit. quality approximation canonical variables 𝐗‾𝐋\\mathbf{\\bar{X}L} 22-dimensional display given Quality(canonicalvariables)=tr(𝚲𝐉)tr(𝚲) Quality (canonical \\: variables) = \\frac{tr(\\mathbf{\\Lambda J})}{tr(\\mathbf{\\Lambda)}}  quality approximation original variables 𝐗‾\\mathbf{\\bar{X}} 2D CVA biplot given Quality(originalvariables)=tr(𝚲𝐉)tr(𝚲) Quality (original \\: variables) = \\frac{tr(\\mathbf{\\Lambda J})}{tr(\\mathbf{\\Lambda)}}","code":""},{"path":"/articles/Class_separation.html","id":"adequacy-of-representation-of-variables","dir":"Articles","previous_headings":"The functions fit.measures() and summary()","what":"Adequacy of representation of variables","title":"Class separation","text":"adequacy variables represented biplot given elementwise ratios Adequacy=diag(𝐌𝐉𝐌′)diag(𝐌𝐌′). Adequacy = \\frac{diag(\\mathbf{MJM'})}{diag(\\mathbf{MM'})}.","code":""},{"path":[]},{"path":"/articles/Class_separation.html","id":"between-class-predictivity","dir":"Articles","previous_headings":"The functions fit.measures() and summary() > Predictivity","what":"Between class predictivity","title":"Class separation","text":"axis class mean predictivities defined terms weighted class means.","code":""},{"path":"/articles/Class_separation.html","id":"axis-predictivity","dir":"Articles","previous_headings":"The functions fit.measures() and summary() > Predictivity > Between class predictivity","what":"Axis predictivity","title":"Class separation","text":"elementwise ratios predictivity axes given axispredictivity=diag(𝐗‾̂′𝐂𝐗‾̂)diag(𝐗‾′𝐂𝐗‾). axis \\: predictivity = \\frac{diag(\\mathbf{\\hat{\\bar{X}}}'\\mathbf{C\\hat{\\bar{X}}})}{diag(\\mathbf{\\bar{X}}'\\mathbf{C\\bar{X}})}.","code":""},{"path":"/articles/Class_separation.html","id":"class-predictivity","dir":"Articles","previous_headings":"The functions fit.measures() and summary() > Predictivity > Between class predictivity","what":"Class predictivity","title":"Class separation","text":"Similarly class means elementwise ratio computed classpredictivity=diag(𝐂12𝐗‾̂′𝐖−𝟏𝐗‾̂𝐂12)diag(𝐂12𝐗‾′𝐖−𝟏𝐗‾𝐂12). class \\: predictivity = \\frac{diag(\\mathbf{C}^{\\frac{1}{2}}\\mathbf{\\hat{\\bar{X}}}'\\mathbf{W^{-1}}\\mathbf{\\hat{\\bar{X}}}\\mathbf{C}^{\\frac{1}{2}})}{diag(\\mathbf{C}^{\\frac{1}{2}}\\mathbf{\\bar{X}}'\\mathbf{W^{-1}}\\mathbf{\\bar{X}}\\mathbf{C}^{\\frac{1}{2}})}.","code":""},{"path":"/articles/Class_separation.html","id":"within-class-predictivity","dir":"Articles","previous_headings":"The functions fit.measures() and summary() > Predictivity","what":"Within class predictivity","title":"Class separation","text":"define matrix samples deviations class means (𝐈−𝐇)𝐗=(𝐈n−𝐆(𝐆′𝐆)−1𝐆′)𝐗 (\\mathbf{-H})\\mathbf{X}=(\\mathbf{}_n-\\mathbf{G}(\\mathbf{G'G})^{-1}\\mathbf{G}')\\mathbf{X} 𝐇=𝐆(𝐆′𝐆)−1𝐆′\\mathbf{H} = \\mathbf{G}(\\mathbf{G'G})^{-1}\\mathbf{G}'.","code":""},{"path":"/articles/Class_separation.html","id":"within-class-axis-predictivity","dir":"Articles","previous_headings":"The functions fit.measures() and summary() > Predictivity > Within class predictivity","what":"Within class axis predictivity","title":"Class separation","text":"within class axis predictivity computed elementwise ratios withinclassaxispredictivity=diag(𝐗̂′(𝐈−𝐇)𝐗̂)diag(𝐗′(𝐈−𝐇)𝐗). within \\: class \\: axis \\: predictivity = \\frac{diag(\\mathbf{\\hat{X}}'(\\mathbf{-H)\\hat{X}})}{diag(\\mathbf{X}'(\\mathbf{-H)X})}.","code":""},{"path":"/articles/Class_separation.html","id":"within-class-sample-predictivity","dir":"Articles","previous_headings":"The functions fit.measures() and summary() > Predictivity > Within class predictivity","what":"Within class sample predictivity","title":"Class separation","text":"Unlike PCA biplots, sample predictivity CVA biplots computed observations expressed deviations class means. elementwise ratios obtained withinclassaxispredictivity=diag((𝐈−𝐇)𝐗̂𝐖−1𝐗̂′(𝐈−𝐇))diag((𝐈−𝐇)𝐗𝐖−1𝐗′(𝐈−𝐇)). within \\: class \\: axis \\: predictivity = \\frac{diag(\\mathbf{(-H)\\hat{X}}\\mathbf{W}^{-1}\\mathbf{\\hat{X}'(-H)})}{diag(\\mathbf{(-H)X}\\mathbf{W}^{-1}\\mathbf{X'(-H)})}.  display fit measures, create biplot object measures added function fit.measures() call summary().  call biplot(), CVA() fit.measures() required () create object class biplot, (b) extend object class CVA (c) compute fit measures. call function plot() optional. possible select fit measures display summary() function measures default TRUE.","code":"obj <- biplot(state.x77, scaled = TRUE) |>         CVA(classes = state.division) |>         fit.measures() |>        plot() summary (obj) #> Object of class biplot, based on 50 samples and 8 variables. #> 8 numeric variables. #> 9 classes: New England Middle Atlantic South Atlantic East South Central West South Central East North Central West North Central Mountain Pacific  #>  #> Quality of fit of canonical variables in 2 dimension(s) = 70.7%  #> Quality of fit of original variables in 2 dimension(s) = 70.5%  #> Adequacy of variables in 2 dimension(s): #> Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost  #> 0.41716176 0.15621549 0.16136381 0.09759664 0.19426796 0.55332679 0.50497634  #>       Area  #> 0.40661470  #> Axis predictivity in 2 dimension(s): #> Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost  #>  0.1859124  0.4019427  0.8195756  0.6925389  0.7685373  0.9506355  0.7819324  #>       Area  #>  0.8458143  #> Class predictivity in 2 dimension(s): #>        New England    Middle Atlantic     South Atlantic East South Central  #>          0.7922047          0.6570417          0.8191791          0.8777759  #> West South Central East North Central West North Central           Mountain  #>          0.7416085          0.6370315          0.3265978          0.6825966  #>            Pacific  #>          0.6700194  #> Within class axis predictivity in 2 dimension(s): #> Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost  #> 0.04212318 0.09357501 0.25675620 0.19900223 0.29474972 0.75215233 0.31027358  #>       Area  #> 0.12741853  #> Within class sample predictivity in 2 dimension(s): #>        Alabama         Alaska        Arizona       Arkansas     California  #>    0.722548912    0.163442379    0.333341120    0.268976273    0.229139828  #>       Colorado    Connecticut       Delaware        Florida        Georgia  #>    0.264963758    0.082284385    0.593415987    0.461070888    0.636531435  #>         Hawaii          Idaho       Illinois        Indiana           Iowa  #>    0.015640188    0.113711473    0.338612599    0.389208196    0.507060148  #>         Kansas       Kentucky      Louisiana          Maine       Maryland  #>    0.784831952    0.314119027    0.078465054    0.008388471    0.306141816  #>  Massachusetts       Michigan      Minnesota    Mississippi       Missouri  #>    0.076563044    0.218470793    0.645446212    0.046129058    0.710971640  #>        Montana       Nebraska         Nevada  New Hampshire     New Jersey  #>    0.086279776    0.810374638    0.090490164    0.298187909    0.003496353  #>     New Mexico       New York North Carolina   North Dakota           Ohio  #>    0.007134343    0.024268121    0.422776032    0.446240464    0.277262145  #>       Oklahoma         Oregon   Pennsylvania   Rhode Island South Carolina  #>    0.450104680    0.108636860    0.033945796    0.415029328    0.261568299  #>   South Dakota      Tennessee          Texas           Utah        Vermont  #>    0.134881180    0.247921823    0.110537439    0.500454605    0.159941068  #>       Virginia     Washington  West Virginia      Wisconsin        Wyoming  #>    0.310439564    0.030877305    0.066303623    0.295499472    0.474458397 obj <- biplot(state.x77, scaled = TRUE) |>         CVA(classes = state.region) |>         fit.measures() summary (obj, adequacy = FALSE, within.class.axis.predictivity = FALSE,          within.class.sample.predictivity = FALSE) #> Object of class biplot, based on 50 samples and 8 variables. #> 8 numeric variables. #> 4 classes: Northeast South North Central West  #>  #> Quality of fit of canonical variables in 2 dimension(s) = 91.9%  #> Quality of fit of original variables in 2 dimension(s) = 95.3%  #> Axis predictivity in 2 dimension(s): #> Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost  #>  0.9873763  0.9848608  0.8757913  0.9050208  0.9955088  0.9970346  0.9558192  #>       Area  #>  0.9344651  #> Class predictivity in 2 dimension(s): #>     Northeast         South North Central          West  #>     0.8031465     0.9985089     0.6449906     0.9988469"},{"path":"/articles/Class_separation.html","id":"additional-cva-dimensions","dir":"Articles","previous_headings":"","what":"Additional CVA dimensions","title":"Class separation","text":"mentioned eigen equation (1) min(p,G−1)min(p, G-1) non-zero eigenvalues. implies CVA biplot G=2G=2 groups, reduces single dimension. write 𝐌=[𝐦1𝐌*] \\mathbf{M} = \\begin{bmatrix}              \\mathbf{m}_1 & \\mathbf{M}^*              \\end{bmatrix}  columns 𝐌*\\mathbf{M}^* forms basis orthogonal complement canonical space defined 𝐦\\mathbf{m}_1. argument low.dim determines uniquely define second third dimensions. default low.dim = \"sample.opt\" selects dimensions minimising total squared reconstruction error samples. representation canonical variates 𝐙‾=𝐗‾𝐦1\\bar{\\mathbf{Z}} = \\bar{\\mathbf{X}}\\mathbf{m}_1 exact first dimension, representation individual samples 𝐙=𝐗𝐦1{\\mathbf{Z}} = {\\mathbf{X}}\\mathbf{m}_1. define 𝐗̂=𝐗𝐌𝐉𝐌−1\\mathbf{\\hat{X}} = \\mathbf{XMJ}\\mathbf{M}^{-1} 𝐉\\mathbf{J} square matrix zeros except 11 first diagonal position, total square reconstruction error samples given TSRES=tr(𝐗−𝐗̂)′(𝐗−𝐗̂). TSRES = tr{(\\mathbf{X}-\\mathbf{\\hat{X}})'(\\mathbf{X}-\\mathbf{\\hat{X}})}.  Define 𝐌−1=[𝐌(1):(G−1)×p𝐌(2):(p−G+1)×p] \\mathbf{M}^{-1} = \\begin{bmatrix} \\mathbf{M}^{(1)}:(G-1) \\times p \\\\ \\mathbf{M}^{(2)}: (p-G+1) \\times p \\end{bmatrix} TSRESTSRES minimised 𝐌opt=[𝐌1𝐌*𝐕]   \\mathbf{M}^{opt} = \\begin{bmatrix}   \\mathbf{M}_1 & \\mathbf{M}^*\\mathbf{V}   \\end{bmatrix} 𝐕\\mathbf{V} matrix right singular vectors 𝐌(2)𝐌(2)′\\mathbf{M}^{(2)}\\mathbf{M}^{(2)'}.  le Roux Gardner-Lubbe (2024) discuss alternative method obtaining additional dimensions. assuming underlying normal distributions, Bhattacharyya distance can optimised. method specific two class case utilised find third dimension 3D CVA biplot three classes.","code":"state.2group <- ifelse(state.division == \"New England\" |                         state.division == \"Middle Atlantic\"  |                        state.division == \"South Atlantic\" |                        state.division == \"Pacific\",                        \"Coastal\", \"Central\") biplot (state.x77) |> CVA (state.2group) |> legend.type(means=TRUE) |> plot() #> Warning in CVA.biplot(biplot(state.x77), state.2group): The dimension of the #> canonical space < dim.biplot sample.opt method used for additional #> dimension(s). biplot (state.x77) |> CVA (state.2group, low.dim=\"Bha\") |> legend.type(means=TRUE) |> plot() #> Warning in CVA.biplot(biplot(state.x77), state.2group, low.dim = \"Bha\"): The #> dimension of the canonical space < dim.biplot Bhattacharyya.dist method used #> for additional dimension(s)."},{"path":"/articles/Class_separation.html","id":"analysis-of-distance-aod","dir":"Articles","previous_headings":"","what":"Analysis of Distance (AoD)","title":"Class separation","text":"Similar variance decomposition CVA, analysis distance decomposes total sum squared distances sum squared distances class means component sum squared distances within classes component. Consider Euclidean embeddable distance metric ψij=ψ(𝐱,𝐱j)\\psi_{ij}=\\psi(\\mathbf{x}_i,\\mathbf{x}_j). Euclidean embeddable metric possible find high dimensional coordinates 𝐲\\mathbf{y}_i 𝐲j\\mathbf{y}_j Euclidean distance 𝐲\\mathbf{y}_i 𝐲j\\mathbf{y}_j equal ψij\\psi_{ij}. Let matrix 𝚿̃\\mathbf{\\tilde\\Psi} contain values −12ψij2-\\frac{1}2{}\\psi_{ij}^2 similarly 𝚫̃\\mathbf{\\tilde\\Delta} values −12δhk2-\\frac{1}2{}\\delta_{hk}^2 δhk\\delta_{hk} represent distance class means hh kk. 𝐓=𝐁+𝐖 \\mathbf{T} = \\mathbf{B} + \\mathbf{W} 𝟏′𝚿̃𝟏=𝐧′𝚫̃𝐧+∑k=1Gnnk𝐠k′𝚿̃𝐠k \\mathbf{1'\\tilde\\Psi1} = \\mathbf{n'\\tilde\\Delta n} + \\sum_{k=1}^{G} \\frac{n}{n_k} \\mathbf{g}_k'\\mathbf{\\tilde\\Psi}\\mathbf{g}_k  𝐧=(𝐆′𝐆)𝟏\\mathbf{n}=\\mathbf{(G'G)1}. Thus, AoD differs CVA allowing Euclidean embeddable measure inter-class distance. CVA, distances may represented maps point representing class means, supplemented additional points representing within-group variation. Principal coordinate analysis performed, G×GG \\times G matrix 𝚫̃\\mathbf{\\tilde\\Delta}.  default linear regression biplot axes fitted plot. Alternatively, spline axes can constructed.  illustration Euclidean embeddable distance metric, Euclidean distance , can construct AoD biplot square root Manhattan distance.","code":"biplot(state.x77, scaled = TRUE) |> AoD(classes = state.region) |> plot() biplot(state.x77, scaled = TRUE) |> AoD(classes = state.region, axes = \"splines\") |> plot() #> Calculating spline axis for variable 1  #> Calculating spline axis for variable 2  #> Calculating spline axis for variable 3  #> Calculating spline axis for variable 4  #> Calculating spline axis for variable 5  #> Calculating spline axis for variable 6  #> Calculating spline axis for variable 7  #> Calculating spline axis for variable 8 biplot(state.x77, scaled = TRUE) |>    AoD(classes = state.region, axes = \"splines\", dist.func=sqrtManhattan) |> plot() #> Calculating spline axis for variable 1  #> Calculating spline axis for variable 2  #> Calculating spline axis for variable 3  #> Calculating spline axis for variable 4  #> Calculating spline axis for variable 5  #> Calculating spline axis for variable 6  #> Calculating spline axis for variable 7  #> Calculating spline axis for variable 8"},{"path":[]},{"path":"/articles/MDS.html","id":"what-is-mds","dir":"Articles","previous_headings":"","what":"What is MDS","title":"MDS","text":"general, multidimensional scaling deals constructing low dimensional map nn samples Euclidean distances samples match given set dissimilarities 𝚫:n×n\\mathbf{\\Delta}:n \\times n closely possible. focus Principal Coordinate Analysis (PCO), approach based singular value decomposition matrix. However, regression biplot provides general structure fitting 2D map samples biplot axes.","code":""},{"path":"/articles/MDS.html","id":"regression-biplot","dir":"Articles","previous_headings":"","what":"Regression biplot","title":"MDS","text":"function regress accepts arguments object class biplot. call function biplot contain data set used construct biplot axes. second argument Z contains coordinates samples MDS map. default linear regression axes fitted plot. 𝐗\\mathbf{X} denote data matrix, directions biplot axes found solving regression equation 𝐗=𝐙𝐇′+𝐄. \\mathbf{X} = \\mathbf{ZH}' + \\mathbf{E}.  matrix 𝐇′=(𝐙′𝐙)−1𝐙′𝐗\\mathbf{H}'=(\\mathbf{Z'Z})^{-1}\\mathbf{Z'X} calibration axes proceed analogous equation (2) biplotEZ vignette. coordinates marker /mu/mu biplot axis jj given follows pμ=μ𝐡(j)′𝐡(j)𝐡(j). p_{\\mu} =  \\frac{\\mu}{\\mathbf{h}_{(j)}'\\mathbf{h}_{(j)}}\\mathbf{h}_{(j)}.  flexibility provided approximating biplot axes using B-splines. calibrated trajectory represented matrix 𝐇:m×2\\mathbf{H}:m \\times 2 snakes samples points 𝐙\\mathbf{Z} marker trajectory closest particular sample gives predicted value sample particular variable. retain smoothness trajectory 𝐇\\mathbf{H}, B-splines used.","code":"biplot(rock) |>    regress(Z = MASS::sammon(dist(scale(rock), method=\"manhattan\"))$points) |>    plot() #> Initial stress        : 0.02554 #> stress after  10 iters: 0.01094, magic = 0.500 #> stress after  20 iters: 0.01080, magic = 0.500 #> stress after  30 iters: 0.01078, magic = 0.500 biplot(rock) |>    regress(Z = MASS::sammon(dist(scale(rock), method=\"manhattan\"))$points,           axes = \"splines\") |>    plot() #> Initial stress        : 0.02554 #> stress after  10 iters: 0.01094, magic = 0.500 #> stress after  20 iters: 0.01080, magic = 0.500 #> stress after  30 iters: 0.01078, magic = 0.500 #> Calculating spline axis for variable 1  #> Calculating spline axis for variable 2  #> Calculating spline axis for variable 3  #> Calculating spline axis for variable 4"},{"path":"/articles/MDS.html","id":"principal-coordinate-analysis-pco-biplots","dir":"Articles","previous_headings":"","what":"Principal Coordinate Analysis (PCO) biplots","title":"MDS","text":"Let 𝚫̃\\mathbf{\\tilde\\Delta} n×nn \\times n matrix containing values −12δij2-\\frac{1}{2}\\delta_{ij}^2 δij\\delta_{ij} represent dissimilarity objects ii jj. possible find set coordinates 𝐘:n×m\\mathbf{Y}:n\\times m typically m=n−1m = n-1 Euclidean distances rows 𝐘\\mathbf{Y} exactly match dissimilarities δij\\delta_{ij}, dissimilarity known Euclidean embeddable distance metric. J. C. Gower (1982) shows distances δij\\delta_{ij} Euclidean embeddable, (𝐈−𝟏𝐬′)𝚫̃(𝐈−𝐬𝟏′) (\\mathbf{}-\\mathbf{1s}')\\mathbf{\\tilde\\Delta} (\\mathbf{}-\\mathbf{s1}') positive semi-definite. Euclidean representation samples obtained 𝐘=𝐕𝚲12\\mathbf{Y=V\\Lambda}^{\\frac{1}{2}} (𝐈−𝟏𝐬′)𝚫̃(𝐈−𝐬𝟏′)=𝐕𝚲𝐕′(\\mathbf{}-\\mathbf{1s}')\\mathbf{\\tilde\\Delta} (\\mathbf{}-\\mathbf{s1}') = \\mathbf{V \\Lambda V'}. Since coordinates 𝐘\\mathbf{Y} already referred principal axes 𝐘′𝐘=𝚲\\mathbf{Y'Y=\\Lambda}, representation samples 2D biplot obtained first two columns 𝐘\\mathbf{Y}. addition exact biplot axis representations discussed J. C. Gower, Lubbe, Roux (2011) approximate axes can obtained. Linear axes fitted regression method. variables data matrix 𝐗:n×p\\mathbf{X}:n \\times p can represented biplot axes PCO biplot sample points 𝐙=𝐕𝚲12𝐉2\\mathbf{Z=V\\Lambda}^{\\frac{1}{2}}\\mathbf{J}_2 according regression method discussed section 2 .  Using B-splines instead linear regression provides user flexibility. achieved setting argument axes = \"splines\".  default distance metric used analysis Euclidean distance. user can also specify distance matrix Dmat n×nn \\times n matrix dist object. illustration metric Euclidean embeddable, Clark’s distance δij2=∑k=1p(xik−xjkxik+xjk)2 \\delta_{ij}^2 = \\sum_{k=1}^{p}\\left(\\frac{x_{ik}-x_{jk}}{x_{ik}+x_{jk}}\\right)^2 defined John C. Gower Ngouenet (2005) calculated used constructing PCO biplot. Note metric defined strictly positive values, data scaled values 11 22.  Alternatively, user can specify function computes distance matrix dist object. Manhattan distance Euclidean embeddable, square root distance . function sqrtManhattan included example function computing Euclidean embeddable dist object.","code":"biplot(rock, scale = TRUE) |> PCO() |> plot() biplot(rock, scale = TRUE) |> PCO(axes = \"splines\") |> plot() #> Calculating spline axis for variable 1  #> Calculating spline axis for variable 2  #> Calculating spline axis for variable 3  #> Calculating spline axis for variable 4 Clark.dist <- function(X) {   n <- nrow(X)   p <- ncol(X)   Dmat <- matrix (0, nrow=n, ncol=n)   for (i in 1:(n-1))     for (j in (i+1):n)       Dmat[i,j] <- sum(((X[i,] - X[j,])/(X[i,] + X[j,]))^2)   sqrt(Dmat + t(Dmat)) } my.data <- scale(rock, center=apply(rock,2,min), scale=diff(apply(rock,2,range)))+1 biplot(rock) |> PCO(Dmat = Clark.dist (rock), axes = \"splines\") |> plot() #> Calculating spline axis for variable 1  #> Calculating spline axis for variable 2  #> Calculating spline axis for variable 3  #> Calculating spline axis for variable 4 sqrtManhattan #> function (X)  #> { #>     sqrt(stats::dist(X, method = \"manhattan\")) #> } #> <bytecode: 0x000001fc00ec0e68> #> <environment: namespace:biplotEZ> biplot(rock, scaled = TRUE) |> PCO(dist.func = sqrtManhattan) |> plot()"},{"path":[]},{"path":"/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Sugnet Lubbe. Author, maintainer, copyright holder. Niël le Roux. Author. Johané Nienkemper-Swanepoel. Author. Raeesa Ganey. Author. Ruan Buys. Author. Zoë-Mae Adams. Author. Peter Manefeldt. Author.","code":""},{"path":"/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Lubbe S, le Roux N, Nienkemper-Swanepoel J, Ganey R, Buys R, Adams Z, Manefeldt P (2025). biplotEZ: EZ--Use Biplots. R package version 2.3.","code":"@Manual{,   title = {biplotEZ: EZ-to-Use Biplots},   author = {Sugnet Lubbe and Niël {le Roux} and Johané Nienkemper-Swanepoel and Raeesa Ganey and Ruan Buys and Zoë-Mae Adams and Peter Manefeldt},   year = {2025},   note = {R package version 2.3}, }"},{"path":"/index.html","id":"biplotez","dir":"","previous_headings":"","what":"EZ-to-Use Biplots","title":"EZ-to-Use Biplots","text":"goal biplotEZ provide users EZ--use platform visually representing data biplots. Currently, package includes principal component analysis (PCA) canonical variate analysis (CVA) biplots. accompanied various formatting options samples axes. Alpha-bags concentration ellipses included visual enhancements interpretation.","code":""},{"path":"/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"EZ-to-Use Biplots","text":"can install development version biplotEZ like :","code":"library(devtools) devtools::install_github(\"MuViSU/biplotEZ\")"},{"path":"/index.html","id":"example","dir":"","previous_headings":"","what":"Example","title":"EZ-to-Use Biplots","text":"basic example shows construct PCA biplot:  PCA biplot provides visual representation overall data set, optimally representing variance 1, 2 3 dimensions, CVA biplot aims optimally separate specified groups data. basic example shows construct CVA biplot:  --top example changing formatting adding bells whistles:","code":"library(biplotEZ) #>  #> Attaching package: 'biplotEZ' #> The following object is masked from 'package:stats': #>  #>     biplot biplot (iris[,1:4], Title=\"Test PCA biplot\") |> PCA() |> plot() biplot (iris[,1:4], Title=\"Test CVA biplot\") |> CVA(classes=iris[,5]) |> plot() biplot (iris[,1:4], group.aes=iris[,5]) |> PCA() |>    samples(col=\"gold\", pch=15) |>   axes(which=2:3, col=\"cyan\", label.cex=1.2, tick.col=\"blue\",                                               tick.label.col=\"purple\") |>   alpha.bags (alpha=c(0.5,0.75,0.95), which=3, col=\"red\", lty=1:3, lwd=3) |>   ellipses(alpha=0.9, which=1:2, col=c(\"green\",\"olivedrab\")) |>   legend.type(bags = TRUE, ellipses=TRUE) |>   plot() #> Computing 0.5 -bag for virginica  #> Computing 0.75 -bag for virginica  #> Computing 0.95 -bag for virginica  #> Computing 2.15 -ellipse for setosa  #> Computing 2.15 -ellipse for versicolor"},{"path":"/index.html","id":"ca-biplot","dir":"","previous_headings":"","what":"CA biplot","title":"EZ-to-Use Biplots","text":"default CA biplots represents row principal coordinates call :  change row standard coordinates use call :","code":"biplot(HairEyeColor[,,2], center = FALSE) |> CA() |> plot() biplot(HairEyeColor[,,2], center = FALSE) |>    CA(variant = \"Stand\") |> samples(col=c(\"magenta\",\"purple\"), pch=c(15,18)) |> plot()"},{"path":"/index.html","id":"regression-biplot","dir":"","previous_headings":"","what":"Regression biplot","title":"EZ-to-Use Biplots","text":"function regress linear regression biplot axes can fitted biplot","code":"out <- biplot(iris) |> PCO(dist.func = sqrtManhattan)  biplot(iris) |> regress(out$Z) |> plot()"},{"path":"/index.html","id":"report-bugs-and-support","dir":"","previous_headings":"","what":"Report Bugs and Support","title":"EZ-to-Use Biplots","text":"encounter issues questions, please open issue GitHub repository.","code":""},{"path":"/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"MIT License","title":"MIT License","text":"Copyright (c) 2024 biplotEZ authors Permission hereby granted, free charge, person obtaining copy software associated documentation files (“Software”), deal Software without restriction, including without limitation rights use, copy, modify, merge, publish, distribute, sublicense, /sell copies Software, permit persons Software furnished , subject following conditions: copyright notice permission notice shall included copies substantial portions Software. SOFTWARE PROVIDED “”, WITHOUT WARRANTY KIND, EXPRESS IMPLIED, INCLUDING LIMITED WARRANTIES MERCHANTABILITY, FITNESS PARTICULAR PURPOSE NONINFRINGEMENT. EVENT SHALL AUTHORS COPYRIGHT HOLDERS LIABLE CLAIM, DAMAGES LIABILITY, WHETHER ACTION CONTRACT, TORT OTHERWISE, ARISING , CONNECTION SOFTWARE USE DEALINGS SOFTWARE.","code":""},{"path":"/reference/alpha.bags.html","id":null,"dir":"Reference","previous_headings":"","what":"Create alpha bags — alpha.bags","title":"Create alpha bags — alpha.bags","text":"function produces \\(\\alpha\\)-bags, useful graphical summary scatter plot. alpha-bag refers contour contains \\(\\alpha\\)% observations.","code":""},{"path":"/reference/alpha.bags.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create alpha bags — alpha.bags","text":"","code":"alpha.bags(bp, alpha = 0.95, which = NULL, col = ez.col[which], lty = 1, lwd = 1, max = 2500, trace = TRUE, opacity = 0.25, outlying=FALSE)"},{"path":"/reference/alpha.bags.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create alpha bags — alpha.bags","text":"bp object class biplot. alpha numeric vector 0 1 determine coverage bag (\\(\\alpha\\)), default 0.95. numeric vector indicating selection groups classes fitted \\(\\alpha\\)-bags. col vector colours \\(\\alpha\\)-bags. Multiple \\(\\alpha\\) bags one group displayed colour. lty vector line types \\(\\alpha\\)-bags. line type used per value \\(\\alpha\\). lwd vector line widths \\(\\alpha\\)-bags. line width used per value \\(\\alpha\\). max maximum number samples include \\(\\alpha\\)-bag calculations, default 2500. samples group, random sample size max taken computations. trace logical, indicating progress computation. opacity level opacity, default 0.5. outlying logical indicating whether outlying points plotted. Note argument may overwritten TRUE","code":""},{"path":"/reference/alpha.bags.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create alpha bags — alpha.bags","text":"list following components available: alpha.bags list coordinates \\(\\alpha\\)-bags group. col vector colours \\(\\alpha\\)-bags. lty vector line types \\(\\alpha\\)-bags. lwd vector line widths \\(\\alpha\\)-bags.","code":""},{"path":"/reference/alpha.bags.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Create alpha bags — alpha.bags","text":"Gower, J., Gardner-Lubbe, S. & Le Roux, N. (2011, ISBN: 978-0-470-01255-0) Understanding Biplots. Chichester, England: John Wiley & Sons Ltd.","code":""},{"path":"/reference/alpha.bags.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create alpha bags — alpha.bags","text":"","code":"biplot (iris[,1:4]) |> PCA(group.aes=iris[,5]) |> alpha.bags(alpha=0.95) |> plot() #> Computing 0.95 -bag for setosa  #> Computing 0.95 -bag for versicolor  #> Computing 0.95 -bag for virginica   biplot (iris[,1:4],group.aes=iris[,5]) |> PCA() |> alpha.bags(alpha=0.95) |> plot() #> Computing 0.95 -bag for setosa  #> Computing 0.95 -bag for versicolor  #> Computing 0.95 -bag for virginica"},{"path":"/reference/AoD.biplot.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate elements for the Analysis of Distance (AoD) biplot — AoD.biplot","title":"Calculate elements for the Analysis of Distance (AoD) biplot — AoD.biplot","text":"function used construct AoD biplot","code":""},{"path":"/reference/AoD.biplot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate elements for the Analysis of Distance (AoD) biplot — AoD.biplot","text":"","code":"# S3 method for class 'biplot' AoD(   bp,   classes = bp$classes,   dist.func = NULL,   dist.func.cat = NULL,   dim.biplot = c(2, 1, 3),   e.vects = 1:ncol(bp$X),   weighted = c(\"unweighted\", \"weighted\"),   show.class.means = TRUE,   axes = c(\"regression\", \"splines\"),   ... )"},{"path":"/reference/AoD.biplot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate elements for the Analysis of Distance (AoD) biplot — AoD.biplot","text":"bp object class biplot obtained preceding function biplot(). classes vector length number rows data matrix class indicator samples. dist.func character string indicating distance function used compute Euclidean embeddable distances samples. One NULL (default) computes Euclidean distance functions can used dist() function. dist.func.cat character string indicating distance function used compute Euclidean embeddable distances samples. One NULL (default) computes extended matching coefficient functions. dim.biplot dimension biplot. values 1, 2 3 accepted, default 2. e.vects vector indicating eigenvectors (canonical variates) plotted biplot, default 1:dim.biplot. weighted character string indicating weighting classes. One \"unweighted\" class receive equal weighting \"weighted\" class receive class sizes weights. show.class.means logical value indicating whether plot class means biplot. axes character string indicating type biplot axes used biplot. One \"regression\" \"splines\". ... arguments dist.func.","code":""},{"path":"/reference/AoD.biplot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate elements for the Analysis of Distance (AoD) biplot — AoD.biplot","text":"object class biplot.","code":""},{"path":"/reference/AoD.biplot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate elements for the Analysis of Distance (AoD) biplot — AoD.biplot","text":"","code":"biplot(iris) |> AoD(classes = iris[,5]) |> plot()"},{"path":"/reference/AoD.html","id":null,"dir":"Reference","previous_headings":"","what":"Use the Analysis of Distance (AoD) method to construct the biplot — AoD","title":"Use the Analysis of Distance (AoD) method to construct the biplot — AoD","text":"function appends biplot object elements resulting using AoD method.","code":""},{"path":"/reference/AoD.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Use the Analysis of Distance (AoD) method to construct the biplot — AoD","text":"","code":"AoD(bp, classes=bp$classes, dist.func=NULL, dist.func.cat=NULL, dim.biplot = c(2,1,3), e.vects = 1:ncol(bp$X),  weighted = c(\"unweighted\",\"weighted\"), show.class.means = TRUE,  axes = c(\"regression\",\"splines\"), ...)"},{"path":"/reference/AoD.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Use the Analysis of Distance (AoD) method to construct the biplot — AoD","text":"bp object class biplot obtained preceding function biplot(). classes vector length number rows data matrix class indicator samples. dist.func character string indicating distance function used compute Euclidean embeddable distances samples. One NULL (default) computes Euclidean distance functions can used dist() function. dist.func.cat character string indicating distance function used compute Euclidean embeddable distances samples. One NULL (default) computes extended matching coefficient functions. dim.biplot dimension biplot. values 1, 2 3 accepted, default 2. e.vects vector indicating eigenvectors (canonical variates) plotted biplot, default 1:dim.biplot. weighted character string indicating weighting classes. One \"unweighted\" class receive equal weighting \"weighted\" class receive class sizes weights. show.class.means logical value indicating whether plot class means biplot. axes character string indicating type biplot axes used biplot. One \"regression\" \"splines\". ... arguments dist.func.","code":""},{"path":"/reference/AoD.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Use the Analysis of Distance (AoD) method to construct the biplot — AoD","text":"Object class biplot","code":""},{"path":"/reference/AoD.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Use the Analysis of Distance (AoD) method to construct the biplot — AoD","text":"","code":"biplot(iris[,1:4]) |> AoD(classes=iris[,5]) #> Object of class biplot, based on 150 samples and 4 variables. #> 4 numeric variables. #> 3 classes: setosa versicolor virginica  # create a CVA biplot biplot(iris[,1:4]) |> AoD(classes=iris[,5]) |> plot()"},{"path":"/reference/axes.html","id":null,"dir":"Reference","previous_headings":"","what":"Format aesthetics for the biplot axes — axes","title":"Format aesthetics for the biplot axes — axes","text":"function allows user format aesthetics biplot axes.","code":""},{"path":"/reference/axes.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Format aesthetics for the biplot axes — axes","text":"","code":"axes(bp, X.names=colnames(bp$X), which = 1:bp$p, col = grey(0.7), lwd = 1, lty = 1, label.dir = \"Orthog\", label.col = col, label.cex = 0.75, label.line = 0.1,  label.offset=rep(0,4), ticks = 5, tick.col = col, tick.size = 1, tick.label = TRUE,  tick.label.side = \"below\", tick.label.col = tick.col, tick.label.cex = 0.6, predict.col = col, predict.lwd = lwd, predict.lty = lty, ax.names = X.names, orthogx = 0, orthogy = 0, vectors = FALSE, unit.circle=FALSE)"},{"path":"/reference/axes.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Format aesthetics for the biplot axes — axes","text":"bp object class biplot. X.names vector column names bp specify axes labelled. vector containing columns variables axes displayed, default 1:p. col colour(s) axes, default grey(0.7). Alternatively, provide vector colours corresponding X.names. lwd line width(s) axes, default 1. lty line type(s) axes, default 1. label.dir character string indicating placement axis titles side figure. One \"Orthog\" axis titles appear orthogonal side figure (default) , \"Hor\" axis titles appear horizontally \"Paral\" axis titles appear parallel side figure. label.col colour(s) axis labels, default, col. label.cex label expansion axis labels, default 0.75. label.line distance axis title side figure, default 0.1. label.offset four-component numeric vector controlling distances axis titles displayed side figure, default rep(0,4). Sides numbered 1 4 according R conventions. ticks integer-valued vector indicating number tickmarks axis, default 5 axis. tick.col colour(s) tick marks, default col. tick.size vector specifying sizes tick marks axis, default 1 . tick.label logical value indicating whether axes labelled, default TRUE. tick.label.side character string indicating position tick label. One \"\" label appear tick mark (default) \"\" label appear tick mark. tick.label.col colour(s) tick mark labels, default tick.col. tick.label.cex label expansion tick mark labels, default 0.6. predict.col colour(s) predicted samples, default col. predict.lwd line width(s) predicted samples, default lwd. predict.lty line type(s) predicted samples, default lty. ax.names vector size p containing user defined titles axes. orthogx numeric vector size p specifying x-coordinate parallel transformation axis, default 0 axis. used dim.biplot = 2. orthogy numeric vector size p specifying y-coordinate parallel transformation axis, default 0 axis. used dim.biplot = 2. vectors logical value indicating whether vector representation (calibrated axes) displayed biplot. used PCA biplot produced. unit.circle logical value indicating whether unit circle displayed biplot.","code":""},{"path":"/reference/axes.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Format aesthetics for the biplot axes — axes","text":"object class biplot appended list called axes containing following elements: vector containing columns axes displayed. col colour(s) axes. lwd line width(s) axes. lty line type(s) axes. label.dir placement axis titles side figure. label.col colour(s) axis titles. label.cex label expansion(s) axis titles. label.line distance(s) axis titles side figure. ticks number tick marks per axis. tick.col colour(s) tick marks. tick.size size(s) tick marks. tick.label logical value(s) indicating whether axes labelled. tick.label.side position tick mark labels. tick.label.col colour(s) tick mark labels. tick.label.cex expansion(s) tick mark labels. predict.col colour(s) predicted samples. predict.lty line type(s) predicted samples. predict.lwd line width(s) predicted samples. names user defined axis titles. orthogx horizontal translations axis. orthogy vertical translations axis. vectors logical value indicating whether calibrated axes plotted.","code":""},{"path":[]},{"path":"/reference/axes.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Format aesthetics for the biplot axes — axes","text":"","code":"biplot(iris[,1:4]) |> PCA() |> axes(col=\"purple\") |> plot()  biplot(iris[,1:4]) |> PCA() |> samples(col=\"purple\",pch=15) |> axes() |> plot()"},{"path":"/reference/axes_coordinates.html","id":null,"dir":"Reference","previous_headings":"","what":"Calibrate Biplot Axes — axes_coordinates","title":"Calibrate Biplot Axes — axes_coordinates","text":"Convenience function obtain coordinates calibrated ticks marks biplot","code":""},{"path":"/reference/axes_coordinates.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calibrate Biplot Axes — axes_coordinates","text":"","code":"axes_coordinates(x)"},{"path":"/reference/axes_coordinates.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calibrate Biplot Axes — axes_coordinates","text":"x object class biplot","code":""},{"path":"/reference/axes_coordinates.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calibrate Biplot Axes — axes_coordinates","text":"ordered list containing coordinates tick marks plotted biplot","code":""},{"path":"/reference/axes_coordinates.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calibrate Biplot Axes — axes_coordinates","text":"","code":"x<-biplot(iris) |> PCA() coordinates<-axes_coordinates(x)"},{"path":"/reference/biplot.html","id":null,"dir":"Reference","previous_headings":"","what":"First step to create a new biplot with biplotEZ — biplot","title":"First step to create a new biplot with biplotEZ — biplot","text":"function produces list elements used producing biplot, provides useful data analysis tool allows visual appraisal structure large data matrices. Biplots multivariate analogue scatter plots. approximate multivariate distribution sample dimensions superimpose display representations variables samples measured.","code":""},{"path":"/reference/biplot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"First step to create a new biplot with biplotEZ — biplot","text":"","code":"biplot(data, classes = NULL, group.aes = NULL, center = TRUE, scaled = FALSE, Title = NULL)"},{"path":"/reference/biplot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"First step to create a new biplot with biplotEZ — biplot","text":"data data frame numeric matrix containing variables user wants analyse. classes vector identifying class membership. group.aes vector identifying groups aesthetic formatting. center logical value indicating whether data column centered, default TRUE. scaled logical value indicating whether data standardised unit column variances, default FALSE. Title title biplot rendered, enter text \"  \".","code":""},{"path":"/reference/biplot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"First step to create a new biplot with biplotEZ — biplot","text":"list following components available: X matrix centered scaled numeric variables. Xcat data frame categorical variables. raw.X original data. classes vector category levels class variable. used colour, pch cex specifications. na.action vector observations removed. center logical value indicating whether \\(\\mathbf{X}\\) centered. scaled logical value indicating whether \\(\\mathbf{X}\\) scaled. means vector means numeric variable. sd vector standard deviations numeric variable. n number observations. p number variables. group.aes vector category levels grouping variable. used colour, pch cex specifications. g.names descriptive names used group labels. g number groups. Title title biplot rendered","code":""},{"path":"/reference/biplot.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"First step to create a new biplot with biplotEZ — biplot","text":"function entry-level function biplotEZ construct biplot display. initialises object class biplot can piped various functions build biplot display.","code":""},{"path":"/reference/biplot.html","id":"useful-links","dir":"Reference","previous_headings":"","what":"Useful links","title":"First step to create a new biplot with biplotEZ — biplot","text":"biplot display can built four broad steps depending needs display. Firstly, choose appropriate method construct display; Secondly, change aesthetics display; Thirdly, append display supplementary features axes, samples means; Finally, superimpose shapes, characters elements onto display. 1. Different types biplots: PCA(): Principal Component Analysis biplot various dimensions CVA(): Canonical Variate Analysis biplot PCO(): Principal Coordinate Analysis biplot CA(): Correspondence Analysis biplot regress(): Regression biplot method 2. Customise biplot display aesthetic functions: samples(): Change formatting sample points biplot display axes(): Change formatting biplot axes 3. Supplement existing biplot additional axes, samples group means: newsamples(): Add change formatting additional samples newaxes(): Add change formatting additional axes means(): Insert class means display, format appropriately 4. Append biplot display: alpha.bags(): Add \\(\\alpha\\)-bags ellipses(): Add ellipses density2D(): Add 2D density regions useful links: plot() fit.measures() legend.type() interpolate() prediction() classify() reflect() rotate()","code":""},{"path":"/reference/biplot.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"First step to create a new biplot with biplotEZ — biplot","text":"Gabriel, K.R. (1971) biplot graphic display matrices application principal component analysis. Biometrika. 58(3):453–467. Gower, J., Gardner-Lubbe, S. & Le Roux, N. (2011, ISBN: 978-0-470-01255-0) Understanding Biplots. Chichester, England: John Wiley & Sons Ltd. Gower, J.C. & Hand, D.J.(1996, ISBN: 0-412-71630-5) Biplots. London: Chapman & Hall.","code":""},{"path":"/reference/biplot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"First step to create a new biplot with biplotEZ — biplot","text":"","code":"biplot(data = iris) #> Object of class biplot, based on 150 samples and 5 variables. #> 4 numeric variables. #> 1 categorical variable. # create a PCA biplot biplot(data = iris) |> PCA() |> plot()"},{"path":[]},{"path":"/reference/biplotEZ.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"biplotEZ: EZ-to-Use Biplots — biplotEZ","text":"goal biplotEZ provide users EZ--use platform visually representing data biplots. Currently, package includes principal component analysis (PCA) canonical variate analysis (CVA) biplots. accompanied various formatting options samples axes. Alpha-bags concentration ellipses included visual enhancements interpretation.","code":""},{"path":[]},{"path":"/reference/biplotEZ.html","id":"author-s-","dir":"Reference","previous_headings":"","what":"Author(s)","title":"biplotEZ: EZ-to-Use Biplots — biplotEZ","text":"Sugnet Lubbe (Maintainer, muvisu@sun.ac.za) Niël le Roux Johané Nienkemper-Swanepoel Raeesa Ganey Ruan Buys Zoë-Mae Adams Peter Manefeldt","code":""},{"path":"/reference/biplotEZ.html","id":"core-functions","dir":"Reference","previous_headings":"","what":"Core Functions","title":"biplotEZ: EZ-to-Use Biplots — biplotEZ","text":"biplot PCA CVA CA","code":""},{"path":"/reference/biplotEZ.html","id":"code-availability","dir":"Reference","previous_headings":"","what":"Code Availability","title":"biplotEZ: EZ-to-Use Biplots — biplotEZ","text":"newest version package can obtained GitHub: https://github.com/MuViSU/biplotEZ","code":""},{"path":"/reference/CA.biplot.html","id":null,"dir":"Reference","previous_headings":"","what":"CA biplot — CA.biplot","title":"CA biplot — CA.biplot","text":"Performs calculations CA biplot.","code":""},{"path":"/reference/CA.biplot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"CA biplot — CA.biplot","text":"","code":"# S3 method for class 'biplot' CA(   bp,   dim.biplot = c(2, 1, 3),   e.vects = 1:ncol(bp$X),   variant = \"Princ\",   lambda.scal = FALSE )"},{"path":"/reference/CA.biplot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"CA biplot — CA.biplot","text":"bp object class biplot obtained preceding function biplot(center = FALSE). order maintain frequency table, input centered scaled. CA, bp contingency table. dim.biplot dimension biplot. values 1, 2 3 accepted, default 2. e.vects eigenvectors (canonical variates) extract, default 1:dim.biplot. variant correspondence analysis variant, default \"Princ\", presents biplot rows principal coordinates columns standard coordinates. variant = \"Stand\", presents biplot rows standard coordinates columns principal coordinates. variant = \"symmetric\", presents symmetric biplot row column standard coordinates scaled equally singular values. lambda.scal logical value request lambda-scaling, default FALSE. Controls stretching shrinking column row distances.","code":""},{"path":"/reference/CA.biplot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"CA biplot — CA.biplot","text":"object class CA, inherits class biplot.","code":""},{"path":"/reference/CA.biplot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"CA biplot — CA.biplot","text":"","code":"biplot(HairEyeColor[,,2], center = FALSE) |> CA() |> plot()"},{"path":"/reference/CA.html","id":null,"dir":"Reference","previous_headings":"","what":"Correspondence Analysis (CA) method — CA","title":"Correspondence Analysis (CA) method — CA","text":"function produces list elements used CA biplot construction approximation Pearson residuals.","code":""},{"path":"/reference/CA.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Correspondence Analysis (CA) method — CA","text":"","code":"CA(bp, dim.biplot = c(2,1,3), e.vects = 1:ncol(bp$X), variant = \"Princ\",  lambda.scal = FALSE)"},{"path":"/reference/CA.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Correspondence Analysis (CA) method — CA","text":"bp object class biplot obtained preceding function biplot(center = FALSE). order maintain frequency table, input centered scaled. CA, bp contingency table. dim.biplot dimension biplot. values 1, 2 3 accepted, default 2. e.vects eigenvectors (canonical variates) extract, default 1:dim.biplot. variant correspondence analysis variant, default \"Princ\", presents biplot rows principal coordinates columns standard coordinates. variant = \"Stand\", presents biplot rows standard coordinates columns principal coordinates. variant = \"symmetric\", presents symmetric biplot row column standard coordinates scaled equally singular values. lambda.scal logical value request lambda-scaling, default FALSE. Controls stretching shrinking column row distances.","code":""},{"path":"/reference/CA.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Correspondence Analysis (CA) method — CA","text":"list following components available: Z Combined data frame row column coordinates. r Numer levels row factor. c Numer levels column factor. Dr Diagonal matrix row profiles. Dc Diagonal matrix column profiles. Drh Weighted row profiles. Dch Weighted column profiles. rowcoor Row coordinates based selected variant. colcoor Column coordinates based selected variant. P Correspondence Matrix. Smat Standardised Pearson residuals. SVD Singular value decomposition solution: d, u, v. e.vects Depending specified CA argument. dim.biplot dimension biplot. lambda.val computed lambda value lambda-scaling requested. gamma Contribution singular values, based CA variant.","code":""},{"path":[]},{"path":"/reference/CA.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Correspondence Analysis (CA) method — CA","text":"","code":"# Creating a CA biplot with rows in principal coordinates: biplot(HairEyeColor[,,2], center = FALSE) |> CA() |> plot()  # Creating a CA biplot with rows in standard coordinates: biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = \"Stand\") |>  samples(col=c(\"magenta\",\"purple\"), pch = c(15,17), label.col = \"black\") |> plot()  # Creating a CA biplot with rows and columns scaled equally: biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = \"Symmetric\") |>  samples(col = c(\"magenta\",\"purple\"), pch = c(15,17), label.col = \"black\") |> plot()"},{"path":"/reference/CATPCA.html","id":null,"dir":"Reference","previous_headings":"","what":"Categorical Principal Component Analysis — CATPCA","title":"Categorical Principal Component Analysis — CATPCA","text":"Categorical Principal Component Analysis","code":""},{"path":"/reference/CATPCA.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Categorical Principal Component Analysis — CATPCA","text":"","code":"CATPCA(bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X), group.aes = NULL, show.class.means = FALSE)"},{"path":"/reference/CATPCA.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Categorical Principal Component Analysis — CATPCA","text":"bp object class biplot obtained preceding function biplot(). dim.biplot dimension biplot. values 1, 2 3 accepted, default 2. e.vects eigenvectors (principal components) extract, default 1:dim.biplot. group.aes vector length number rows data matrix differentiated aesthetics samples. show.class.means logical, indicating whether group means plotted biplot.","code":""},{"path":"/reference/CATPCA.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Categorical Principal Component Analysis — CATPCA","text":"object class biplot","code":""},{"path":"/reference/CATPCA.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Categorical Principal Component Analysis — CATPCA","text":"","code":"CATPCA (iris)"},{"path":"/reference/classification.biplot.html","id":null,"dir":"Reference","previous_headings":"","what":"classification biplot — classification.biplot","title":"classification biplot — classification.biplot","text":"Performs calculations classification biplot.","code":""},{"path":"/reference/classification.biplot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"classification biplot — classification.biplot","text":"","code":"# S3 method for class 'biplot' classification(   bp,   Pmat,   dim.biplot = c(2, 1, 3),   e.vects = 1:ncol(bp$X),   group.aes = NULL,   axes = \"regression\",   col = ez.col,   opacity = 0.4,   borders = FALSE )"},{"path":"/reference/classification.biplot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"classification biplot — classification.biplot","text":"bp object class biplot obtained preceding function biplot(). Pmat matrix containing posterior probability classes dim.biplot dimension biplot. values 1, 2 3 accepted, default 2. e.vects eigenvectors (principal components) extract, default 1:dim.biplot. group.aes vector length number rows data matrix differentiated aesthetics samples. axes type axes, defaults \"regression\" col colour classification regions opacity opacity classification regions borders logical, indicating whether borders added classification regions","code":""},{"path":"/reference/classification.biplot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"classification biplot — classification.biplot","text":"object class biplot.","code":""},{"path":"/reference/classification.html","id":null,"dir":"Reference","previous_headings":"","what":"Classification biplot method — classification","title":"Classification biplot method — classification","text":"function produces list elements used constructing classification biplot.","code":""},{"path":"/reference/classification.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Classification biplot method — classification","text":"","code":"classification(bp, Pmat, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X), group.aes=NULL, axes = \"regression\", col=ez.col, opacity=0.4, borders = FALSE)"},{"path":"/reference/classification.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Classification biplot method — classification","text":"bp object class biplot obtained preceding function biplot(). Pmat matrix containing posterior probability classes dim.biplot dimension biplot. values 1, 2 3 accepted, default 2. e.vects eigenvectors (principal components) extract, default 1:dim.biplot. group.aes vector length number rows data matrix differentiated aesthetics samples. axes type axes, defaults \"regression\" col colour classification regions opacity opacity classification regions borders logical, indicating whether borders added classification regions","code":""},{"path":"/reference/classification.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Classification biplot method — classification","text":"Object class biplot following elements:","code":""},{"path":"/reference/classification.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Classification biplot method — classification","text":"Gardner-Lubbe, S., 2016. triplot multiclass classification visualisation. Computational Statistics & Data Analysis, 94, pp.20-32.","code":""},{"path":"/reference/classification.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Classification biplot method — classification","text":"","code":"biplot(iris[,1:4]) |>  classification(predict(MASS::lda(Species ~ ., data = iris))$posterior) #> Object of class biplot, based on 150 samples and 4 variables. #> 4 numeric variables. # create a classification biplot biplot(iris[,1:4]) |>  classification(predict(MASS::lda(Species ~ ., data = iris))$posterior) |>  plot()"},{"path":"/reference/classify.html","id":null,"dir":"Reference","previous_headings":"","what":"Classify samples into classes — classify","title":"Classify samples into classes — classify","text":"Classify samples classes","code":""},{"path":"/reference/classify.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Classify samples into classes — classify","text":"","code":"classify(   bp,   classify.regions = TRUE,   col = ez.col,   opacity = 0.4,   borders = FALSE )"},{"path":"/reference/classify.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Classify samples into classes — classify","text":"bp object class biplot classify.regions logical value indicating whether classifications regions shown biplot, default TRUE. col colours classification regions opacity opacity levels classification regions borders border colours classification regions","code":""},{"path":"/reference/classify.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Classify samples into classes — classify","text":"list object called classify appended object class biplot following elements: table confusion matrix resulting classification classes. rate classification accuracy rate. classify.regions logical value indicating whether classification regions shown biplot. aes list chosen aesthetics colours, opacity levels border colours classification regions.","code":""},{"path":"/reference/classify.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Classify samples into classes — classify","text":"","code":"biplot(iris[,1:4],classes = iris[,5]) |> CVA() |> axes(col=\"black\") |>    classify(col=c(\"red\",\"blue\",\"orange\"),opacity=0.1) |> plot()"},{"path":"/reference/CLPs.html","id":null,"dir":"Reference","previous_headings":"","what":"Format aesthetics for the category level points — CLPs","title":"Format aesthetics for the category level points — CLPs","text":"function allows user format aesthetics category level points (CLPs).","code":""},{"path":"/reference/CLPs.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Format aesthetics for the category level points — CLPs","text":"","code":"CLPs (bp,  which = 1:ncol(bp$Xcat), col = \"black\", cex = 0.6)"},{"path":"/reference/CLPs.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Format aesthetics for the category level points — CLPs","text":"bp object class biplot. vector containing columns variables CLPs displayed, default 1:ncol(Xcat). col colour(s) CLPs, default black. cex character expansion(s) CLPs, default 0.6.","code":""},{"path":"/reference/CLPs.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Format aesthetics for the category level points — CLPs","text":"object class biplot appended list called CLP.aes containing following elements  list following components available: vector containing columns variables CLPs displayed. col colour(s) CLPs. cex character expansion(s) plotting characters CLPs.","code":""},{"path":[]},{"path":"/reference/CLPs.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Format aesthetics for the category level points — CLPs","text":"","code":"mtdf <- as.data.frame(mtcars) mtdf$cyl <- factor(mtdf$cyl) mtdf$vs <- factor(mtdf$vs) mtdf$am <- factor(mtdf$am) mtdf$gear <- factor(mtdf$gear) mtdf$carb <- factor(mtdf$carb) biplot(mtdf[,-11], scaled = TRUE) |> AoD(classes = mtdf[,11]) |>  CLPs(col = list(rep(\"olivedrab\",3), rep(\"orange\",2),                 rep(\"coral\",2), rep(\"brown\",3))) |>  plot()"},{"path":"/reference/CLRs.html","id":null,"dir":"Reference","previous_headings":"","what":"Format aesthetics for the category level regions — CLRs","title":"Format aesthetics for the category level regions — CLRs","text":"function allows user format aesthetics category level points (CLRs).","code":""},{"path":"/reference/CLRs.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Format aesthetics for the category level regions — CLRs","text":"","code":"CLRs (bp,  which = 1, col = \"black\")"},{"path":"/reference/CLRs.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Format aesthetics for the category level regions — CLRs","text":"bp object class biplot. column name number CLRs displayed, default 1. one variable can selected time. col colours CLRs, default colorRampPalette(c(\"black\",\"white\")).","code":""},{"path":"/reference/CLRs.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Format aesthetics for the category level regions — CLRs","text":"object class biplot appended list called CLP.aes containing following elements  list following components available: variable number CLRs displayed. col colours CLRs.","code":""},{"path":[]},{"path":"/reference/CLRs.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Format aesthetics for the category level regions — CLRs","text":"","code":"mtdf <- as.data.frame(mtcars) mtdf$cyl <- factor(mtdf$cyl) mtdf$vs <- factor(mtdf$vs) mtdf$am <- factor(mtdf$am) mtdf$gear <- factor(mtdf$gear) mtdf$carb <- factor(mtdf$carb) #biplot(mtdf[,-11], scaled = TRUE) |> PCO(group.aes = mtdf[,11]) |>  #CLRs(which = 10, col = \"coral\") |> plot()"},{"path":"/reference/CVA.biplot.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate elements for the CVA biplot — CVA.biplot","title":"Calculate elements for the CVA biplot — CVA.biplot","text":"function performs calculations construction CVA biplot.","code":""},{"path":"/reference/CVA.biplot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate elements for the CVA biplot — CVA.biplot","text":"","code":"# S3 method for class 'biplot' CVA(   bp,   classes = bp$classes,   dim.biplot = c(2, 1, 3),   e.vects = 1:ncol(bp$X),   weightedCVA = \"weighted\",   show.class.means = TRUE,   low.dim = \"sample.opt\" )"},{"path":"/reference/CVA.biplot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate elements for the CVA biplot — CVA.biplot","text":"bp object class biplot obtained preceding function biplot(). classes vector length number rows data matrix class indicator samples. dim.biplot dimension biplot. values 1, 2 3 accepted, default 2. e.vects vector indicating eigenvectors (canonical variates) plotted biplot, default 1:dim.biplot. weightedCVA character string indicating type CVA perform. One \"weighted\" (default) weighted CVA performed (centring matrix diagonal matrix class sizes (\\(\\mathbf{C} = \\mathbf{N}\\)), \"unweightedCent\" unweighted CVA performed (centring matrix usual centring matrix (\\(\\mathbf{C} = \\mathbf{}_{G} - G^{-1}\\mathbf{1}_{G}\\mathbf{1}_{G}'\\))) \"unweightedI\" unweighted CVA performed retaining weighted centroid (centring matrix indicator matrix (\\(\\mathbf{C} = \\mathbf{}_{G}\\))). show.class.means logical value indicating whether plot class means biplot. low.dim character string indicating method use construct additional dimension(s) dimension canonical space smaller dim.biplot. One \"sample.opt\" (default) maximising sample predictivity individual samples biplot \"Bhattacharyya.dist\" based decomposition Bhattacharyya distance component sample means component dissimilarity sample covariance matrices.","code":""},{"path":"/reference/CVA.biplot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate elements for the CVA biplot — CVA.biplot","text":"object class CVA, inherits class biplot.","code":""},{"path":"/reference/CVA.biplot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate elements for the CVA biplot — CVA.biplot","text":"","code":"biplot(iris[,1:4]) |> CVA(classes=iris[,5]) #> Object of class biplot, based on 150 samples and 4 variables. #> 4 numeric variables. #> 3 classes: setosa versicolor virginica"},{"path":"/reference/CVA.html","id":null,"dir":"Reference","previous_headings":"","what":"Perform Canonical Variate Analysis (CVA) — CVA","title":"Perform Canonical Variate Analysis (CVA) — CVA","text":"function appends biplot object elements resulting performing CVA.","code":""},{"path":"/reference/CVA.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Perform Canonical Variate Analysis (CVA) — CVA","text":"","code":"CVA(bp, classes=bp$classes, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X),            weightedCVA = \"weighted\", show.class.means = TRUE,            low.dim = \"sample.opt\")"},{"path":"/reference/CVA.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Perform Canonical Variate Analysis (CVA) — CVA","text":"bp object class biplot obtained preceding function biplot(). classes vector length number rows data matrix class indicator samples. dim.biplot dimension biplot. values 1, 2 3 accepted, default 2. e.vects vector indicating eigenvectors (canonical variates) plotted biplot, default 1:dim.biplot. weightedCVA character string indicating type CVA perform. One \"weighted\" (default) weighted CVA performed (centring matrix diagonal matrix class sizes (\\(\\mathbf{C} = \\mathbf{N}\\)), \"unweightedCent\" unweighted CVA performed (centring matrix usual centring matrix (\\(\\mathbf{C} = \\mathbf{}_{G} - G^{-1}\\mathbf{1}_{G}\\mathbf{1}_{G}'\\))) \"unweightedI\" unweighted CVA performed retaining weighted centroid (centring matrix indicator matrix (\\(\\mathbf{C} = \\mathbf{}_{G}\\))). show.class.means logical value indicating whether plot class means biplot. low.dim character string indicating method use construct additional dimension(s) dimension canonical space smaller dim.biplot. One \"sample.opt\" (default) maximising sample predictivity individual samples biplot \"Bhattacharyya.dist\" based decomposition Bhattacharyya distance component sample means component dissimilarity sample covariance matrices.","code":""},{"path":"/reference/CVA.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Perform Canonical Variate Analysis (CVA) — CVA","text":"Object class CVA following elements: X matrix centered scaled numeric variables. Xcat data frame categorical variables. raw.X original data. classes vector category levels class variable. used colour, pch cex specifications. na.action vector observations removed. center logical value indicating whether \\(\\mathbf{X}\\) centered. scaled logical value indicating whether \\(\\mathbf{X}\\) scaled. means vector means numerical variable. sd vector standard deviations numerical variable. n number observations. p number variables. group.aes vector category levels grouping variable. used colour, pch cex specifications. g.names descriptive names used group labels. g number groups. Title title biplot rendered. Lmat matrix transformation canonical space. Linv inverse \\(\\mathbf{L}\\). eigenvalues vector eigenvalues two-sided eigenvalue problem. Z matrix row containing details points plotted (.e. coordinates). ax.one.unit one unit positive direction biplot axis. Gmat indicator matrix defining membership classes. Xmeans matrix class means. Zmeans matrix class mean coordinates plotted biplot. e.vects vector indicating canonical variates plotted biplot. Cmat centring matrix based different choices weighting described arguments. Bmat class sums squares cross products matrix. Wmat within class sums squares cross products matrix. Mrr matrix used prediction canonical space (inverse \\(\\mathbf{M}=\\mathbf{LV})\\). Mr first r dimensions solution plotted. Nmat matrix class sizes diagonal. lambda.mat matrix eigenvalues \\(\\mathbf{W}^{-1/2}\\mathbf{BW}^{-1/2}\\) diagonal. class.means logical value indicating whether class means plotted biplot. dim.biplot dimension biplot. low.dim method used construct additional dimension(s).","code":""},{"path":[]},{"path":"/reference/CVA.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Perform Canonical Variate Analysis (CVA) — CVA","text":"","code":"biplot(iris[,1:4]) |> CVA(classes=iris[,5]) #> Object of class biplot, based on 150 samples and 4 variables. #> 4 numeric variables. #> 3 classes: setosa versicolor virginica  # create a CVA biplot biplot(iris[,1:4]) |> CVA(classes=iris[,5]) |> plot()"},{"path":"/reference/CVAlowdim.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct additional dimensions when the dimension of the canonical space is smaller than the dimension of the biplot — CVAlowdim","title":"Construct additional dimensions when the dimension of the canonical space is smaller than the dimension of the biplot — CVAlowdim","text":"function used add dimensions CVA biplot dimension canonical space \\(K\\) smaller dimension biplot (dim.biplot). function already used CVA calculations, therefore used isolation.","code":""},{"path":"/reference/CVAlowdim.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct additional dimensions when the dimension of the canonical space is smaller than the dimension of the biplot — CVAlowdim","text":"","code":"CVAlowdim(bp, G, W, Mmat, low.dim, K, e.vects)"},{"path":"/reference/CVAlowdim.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct additional dimensions when the dimension of the canonical space is smaller than the dimension of the biplot — CVAlowdim","text":"bp object class biplot. G indicator matrix defining membership classes. W within class sums squares cross products matrix. Mmat eigenvector matrix CVA. low.dim character string indicating method use construct additional dimension(s) dimension canonical space smaller dim.biplot. One \"sample.opt\" (default) maximising sample predictivity individual samples biplot Bhattacharyya.dist based decomposition Bhattacharyya distance component sample means component dissimilarity sample covariance matrices. K dimension canonical space. e.vects vector indicating canonical variates plotted biplot, default 1:dim.biplot","code":""},{"path":"/reference/CVAlowdim.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Construct additional dimensions when the dimension of the canonical space is smaller than the dimension of the biplot — CVAlowdim","text":"list three components: Mr first r dimensions solution plotted. Mrr matrix used prediction canonical space. Lmat matrix transformation canonical space.","code":""},{"path":"/reference/density1D.html","id":null,"dir":"Reference","previous_headings":"","what":"Creates a kernel density in 1-dimension — density1D","title":"Creates a kernel density in 1-dimension — density1D","text":"Creates kernel density 1-dimension","code":""},{"path":"/reference/density1D.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Creates a kernel density in 1-dimension — density1D","text":"","code":"density1D(   bp,   which = NULL,   h = \"nrd0\",   kernel = \"gaussian\",   col = ez.col,   lwd = 1.5,   legend.mar = c(2, 5, 0, 5) )"},{"path":"/reference/density1D.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Creates a kernel density in 1-dimension — density1D","text":"bp object class biplot group. h bandwidth. kernel character string giving smoothing kernel used. col colours used density curves. lwd linewidth density curve. legend.mar margin line legend.","code":""},{"path":"/reference/density1D.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Creates a kernel density in 1-dimension — density1D","text":"object class biplot.","code":""},{"path":"/reference/density1D.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Creates a kernel density in 1-dimension — density1D","text":"","code":"biplot (iris,classes=iris[,5]) |> CVA(dim=1) |> density1D() |> plot()"},{"path":"/reference/density2D.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a density in 2-dimensions — density2D","title":"Create a density in 2-dimensions — density2D","text":"Create density 2-dimensions","code":""},{"path":"/reference/density2D.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a density in 2-dimensions — density2D","text":"","code":"density2D(   bp,   which = NULL,   contours = F,   h = NULL,   n = 100,   col = c(\"green\", \"yellow\", \"red\"),   contour.col = \"black\",   cuts = 50,   cex = 0.6,   tcl = -0.2,   mgp = c(0, -0.25, 0),   layout.heights = c(100, 10),   legend.mar = c(2, 5, 0, 5) )"},{"path":"/reference/density2D.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a density in 2-dimensions — density2D","text":"bp object class biplot group create density; limited single group time. NULL, density drawn data points. contours logical indicating whether contours added density plot h vector bandwidths x y directions, see kde2d. n number grid points direction. Can scalar length-2 integer vector. col vector colours use form 'continuous' sequence colours. contour.col colour contours. cuts number colours col. cex character expansion. tcl length tick marks fraction height line text. mgp margin line. layout.heights vector values heights rows. legend.mar margin line legend.","code":""},{"path":"/reference/density2D.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create a density in 2-dimensions — density2D","text":"object class biplot.","code":""},{"path":"/reference/density2D.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a density in 2-dimensions — density2D","text":"","code":"biplot(iris[,1:4],group.aes = iris[,5]) |> PCA() |>    density2D(which=3,col=c(\"white\",\"purple\",\"cyan\",\"blue\")) |> plot()  biplot(iris[,1:4],group.aes = iris[,5]) |> PCA() |>    density2D(which=3,col=c(\"white\",\"purple\",\"cyan\",\"blue\"),contours = TRUE,   contour.col = \"grey\") |> plot()"},{"path":"/reference/ellipses.html","id":null,"dir":"Reference","previous_headings":"","what":"Concentration ellipses (\\(\\kappa\\)-ellipses) — ellipses","title":"Concentration ellipses (\\(\\kappa\\)-ellipses) — ellipses","text":"function produces \\(\\kappa\\)-ellipses, useful geometrical description data points sample mean.","code":""},{"path":"/reference/ellipses.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Concentration ellipses (\\(\\kappa\\)-ellipses) — ellipses","text":"","code":"ellipses(bp, df=2, kappa = NULL, which = NULL, alpha = 0.95, col = bp$sample$col[which], lty = 1, lwd = 1, opacity = 0.25, trace = TRUE)"},{"path":"/reference/ellipses.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Concentration ellipses (\\(\\kappa\\)-ellipses) — ellipses","text":"bp object class biplot. df degrees freedom, default 2. kappa value construct \\(\\kappa\\)-ellipse (value \\(\\kappa\\)). selection group ellipse construction. alpha size \\(\\alpha\\)-bag, default 0.95. col colour ellipse. Multiple \\(\\kappa\\)-ellipse one group displayed colour. lty line type ellipse. line type used per value \\(\\kappa\\). lwd line width ellipse. line width used per value \\(\\kappa\\). opacity level opacity, default 0.25. trace logical, indicating progress computation.","code":""},{"path":"/reference/ellipses.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Concentration ellipses (\\(\\kappa\\)-ellipses) — ellipses","text":"list following components available: conc.ellipses list coordinates \\(\\kappa\\)-ellipses group. col vector colours \\(\\kappa\\)-ellipses. lty vector line types \\(\\kappa\\)-ellipses. lwd vector line widths \\(\\kappa\\)-ellipses. alpha vector \\(\\alpha\\) values.","code":""},{"path":"/reference/ellipses.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Concentration ellipses (\\(\\kappa\\)-ellipses) — ellipses","text":"Gower, J., Gardner-Lubbe, S. & Le Roux, N. (2011, ISBN: 978-0-470-01255-0) Understanding Biplots. Chichester, England: John Wiley & Sons Ltd.","code":""},{"path":"/reference/ellipses.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Concentration ellipses (\\(\\kappa\\)-ellipses) — ellipses","text":"","code":"biplot (iris[,1:4]) |> PCA(group.aes=iris[,5]) |> ellipses(kappa=2) |> plot() #> Computing 2 -ellipse for setosa  #> Computing 2 -ellipse for versicolor  #> Computing 2 -ellipse for virginica"},{"path":"/reference/extended.matching.coefficient.html","id":null,"dir":"Reference","previous_headings":"","what":"Extended matching coefficient — extended.matching.coefficient","title":"Extended matching coefficient — extended.matching.coefficient","text":"Extended matching coefficient","code":""},{"path":"/reference/extended.matching.coefficient.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extended matching coefficient — extended.matching.coefficient","text":"","code":"extended.matching.coefficient(X)"},{"path":"/reference/extended.matching.coefficient.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extended matching coefficient — extended.matching.coefficient","text":"X data frame containing categorical variables used computing EMC distance","code":""},{"path":"/reference/extended.matching.coefficient.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Extended matching coefficient — extended.matching.coefficient","text":"dist object","code":""},{"path":"/reference/extended.matching.coefficient.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Extended matching coefficient — extended.matching.coefficient","text":"","code":"mtdf <- as.data.frame(mtcars) mtdf$cyl <- factor(mtdf$cyl) mtdf$vs <- factor(mtdf$vs) mtdf$am <- factor(mtdf$am) mtdf$gear <- factor(mtdf$gear) mtdf$carb <- factor(mtdf$carb) extended.matching.coefficient(mtdf[,8:11]) #>           1        2        3        4        5        6        7        8 #> 2  0.000000                                                                #> 3  1.414214 1.414214                                                       #> 4  2.000000 2.000000 1.414214                                              #> 5  1.732051 1.732051 2.000000 1.414214                                     #> 6  2.000000 2.000000 1.414214 0.000000 1.414214                            #> 7  1.414214 1.414214 2.000000 1.414214 1.000000 1.414214                   #> 8  1.732051 1.732051 1.414214 1.414214 1.414214 1.414214 1.732051          #> 9  1.732051 1.732051 1.414214 1.414214 1.414214 1.414214 1.732051 0.000000 #> 10 1.414214 1.414214 1.414214 1.414214 1.732051 1.414214 1.414214 1.000000 #> 11 1.414214 1.414214 1.414214 1.414214 1.732051 1.414214 1.414214 1.000000 #> 12 1.732051 1.732051 2.000000 1.414214 1.000000 1.414214 1.000000 1.732051 #> 13 1.732051 1.732051 2.000000 1.414214 1.000000 1.414214 1.000000 1.732051 #> 14 1.732051 1.732051 2.000000 1.414214 1.000000 1.414214 1.000000 1.732051 #> 15 1.414214 1.414214 2.000000 1.414214 1.000000 1.414214 0.000000 1.732051 #> 16 1.414214 1.414214 2.000000 1.414214 1.000000 1.414214 0.000000 1.732051 #> 17 1.414214 1.414214 2.000000 1.414214 1.000000 1.414214 0.000000 1.732051 #> 18 1.414214 1.414214 0.000000 1.414214 2.000000 1.414214 2.000000 1.414214 #> 19 1.414214 1.414214 1.000000 1.732051 1.732051 1.732051 2.000000 1.000000 #> 20 1.414214 1.414214 0.000000 1.414214 2.000000 1.414214 2.000000 1.414214 #> 21 2.000000 2.000000 1.414214 0.000000 1.414214 0.000000 1.414214 1.414214 #> 22 1.732051 1.732051 2.000000 1.414214 0.000000 1.414214 1.000000 1.414214 #> 23 1.732051 1.732051 2.000000 1.414214 0.000000 1.414214 1.000000 1.414214 #> 24 1.414214 1.414214 2.000000 1.414214 1.000000 1.414214 0.000000 1.732051 #> 25 1.732051 1.732051 2.000000 1.414214 0.000000 1.414214 1.000000 1.414214 #> 26 1.414214 1.414214 0.000000 1.414214 2.000000 1.414214 2.000000 1.414214 #> 27 1.414214 1.414214 1.732051 2.000000 1.414214 2.000000 1.732051 1.732051 #> 28 1.732051 1.732051 1.414214 1.732051 1.732051 1.732051 2.000000 1.414214 #> 29 1.000000 1.000000 1.732051 2.000000 1.732051 2.000000 1.414214 2.000000 #> 30 1.414214 1.414214 1.732051 2.000000 1.732051 2.000000 1.732051 2.000000 #> 31 1.414214 1.414214 1.732051 2.000000 1.732051 2.000000 1.732051 2.000000 #> 32 1.414214 1.414214 1.000000 1.732051 1.732051 1.732051 2.000000 1.000000 #>           9       10       11       12       13       14       15       16 #> 2                                                                          #> 3                                                                          #> 4                                                                          #> 5                                                                          #> 6                                                                          #> 7                                                                          #> 8                                                                          #> 9                                                                          #> 10 1.000000                                                                #> 11 1.000000 0.000000                                                       #> 12 1.732051 1.732051 1.732051                                              #> 13 1.732051 1.732051 1.732051 0.000000                                     #> 14 1.732051 1.732051 1.732051 0.000000 0.000000                            #> 15 1.732051 1.414214 1.414214 1.000000 1.000000 1.000000                   #> 16 1.732051 1.414214 1.414214 1.000000 1.000000 1.000000 0.000000          #> 17 1.732051 1.414214 1.414214 1.000000 1.000000 1.000000 0.000000 0.000000 #> 18 1.414214 1.414214 1.414214 2.000000 2.000000 2.000000 2.000000 2.000000 #> 19 1.000000 1.414214 1.414214 2.000000 2.000000 2.000000 2.000000 2.000000 #> 20 1.414214 1.414214 1.414214 2.000000 2.000000 2.000000 2.000000 2.000000 #> 21 1.414214 1.414214 1.414214 1.414214 1.414214 1.414214 1.414214 1.414214 #> 22 1.414214 1.732051 1.732051 1.000000 1.000000 1.000000 1.000000 1.000000 #> 23 1.414214 1.732051 1.732051 1.000000 1.000000 1.000000 1.000000 1.000000 #> 24 1.732051 1.414214 1.414214 1.000000 1.000000 1.000000 0.000000 0.000000 #> 25 1.414214 1.732051 1.732051 1.000000 1.000000 1.000000 1.000000 1.000000 #> 26 1.414214 1.414214 1.414214 2.000000 2.000000 2.000000 2.000000 2.000000 #> 27 1.732051 2.000000 2.000000 1.732051 1.732051 1.732051 1.732051 1.732051 #> 28 1.414214 1.732051 1.732051 2.000000 2.000000 2.000000 2.000000 2.000000 #> 29 2.000000 1.732051 1.732051 1.732051 1.732051 1.732051 1.414214 1.414214 #> 30 2.000000 2.000000 2.000000 1.732051 1.732051 1.732051 1.732051 1.732051 #> 31 2.000000 2.000000 2.000000 1.732051 1.732051 1.732051 1.732051 1.732051 #> 32 1.000000 1.414214 1.414214 2.000000 2.000000 2.000000 2.000000 2.000000 #>          17       18       19       20       21       22       23       24 #> 2                                                                          #> 3                                                                          #> 4                                                                          #> 5                                                                          #> 6                                                                          #> 7                                                                          #> 8                                                                          #> 9                                                                          #> 10                                                                         #> 11                                                                         #> 12                                                                         #> 13                                                                         #> 14                                                                         #> 15                                                                         #> 16                                                                         #> 17                                                                         #> 18 2.000000                                                                #> 19 2.000000 1.000000                                                       #> 20 2.000000 0.000000 1.000000                                              #> 21 1.414214 1.414214 1.732051 1.414214                                     #> 22 1.000000 2.000000 1.732051 2.000000 1.414214                            #> 23 1.000000 2.000000 1.732051 2.000000 1.414214 0.000000                   #> 24 0.000000 2.000000 2.000000 2.000000 1.414214 1.000000 1.000000          #> 25 1.000000 2.000000 1.732051 2.000000 1.414214 0.000000 0.000000 1.000000 #> 26 2.000000 0.000000 1.000000 0.000000 1.414214 2.000000 2.000000 2.000000 #> 27 1.732051 1.732051 1.414214 1.732051 2.000000 1.414214 1.414214 1.732051 #> 28 2.000000 1.414214 1.000000 1.414214 1.732051 1.732051 1.732051 2.000000 #> 29 1.414214 1.732051 1.732051 1.732051 2.000000 1.732051 1.732051 1.414214 #> 30 1.732051 1.732051 1.732051 1.732051 2.000000 1.732051 1.732051 1.732051 #> 31 1.732051 1.732051 1.732051 1.732051 2.000000 1.732051 1.732051 1.732051 #> 32 2.000000 1.000000 0.000000 1.000000 1.732051 1.732051 1.732051 2.000000 #>          25       26       27       28       29       30       31 #> 2                                                                 #> 3                                                                 #> 4                                                                 #> 5                                                                 #> 6                                                                 #> 7                                                                 #> 8                                                                 #> 9                                                                 #> 10                                                                #> 11                                                                #> 12                                                                #> 13                                                                #> 14                                                                #> 15                                                                #> 16                                                                #> 17                                                                #> 18                                                                #> 19                                                                #> 20                                                                #> 21                                                                #> 22                                                                #> 23                                                                #> 24                                                                #> 25                                                                #> 26 2.000000                                                       #> 27 1.414214 1.732051                                              #> 28 1.732051 1.414214 1.000000                                     #> 29 1.732051 1.732051 1.000000 1.414214                            #> 30 1.732051 1.732051 1.000000 1.414214 1.000000                   #> 31 1.732051 1.732051 1.000000 1.414214 1.000000 1.000000          #> 32 1.732051 1.000000 1.414214 1.000000 1.732051 1.732051 1.732051"},{"path":"/reference/fit.measures.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute measures of fit for the biplot. — fit.measures","title":"Compute measures of fit for the biplot. — fit.measures","text":"function computes measures fit biplot. biplot object augmented additional items, can differ depending type biplot. measures provide information overall quality fit adequacy representation variables.","code":""},{"path":"/reference/fit.measures.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute measures of fit for the biplot. — fit.measures","text":"","code":"fit.measures(bp)"},{"path":"/reference/fit.measures.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute measures of fit for the biplot. — fit.measures","text":"bp object class biplot.","code":""},{"path":"/reference/fit.measures.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute measures of fit for the biplot. — fit.measures","text":"object class biplot. object augmented additional items, depending type biplot object. quality overall quality fit. adequacy adequacy representation variables. object class PCA: axis.predictivity fit measure individual axis. sample.predictivity fit measure individual sample. object class CVA: axis.predictivity fit measure individual axis. class.predictivity fit measure class mean. within.class.axis.predictivity fit measure axis based values expressed deviations class means. within.class.sample.predictivity fit measure sample expressed deviation class mean. object class CA: row.predictivity fit measure row input matrix individual sample. col.predictivity fit measure column input matrix individual sample. Xhat predicted matrix per row profile","code":""},{"path":"/reference/fit.measures.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute measures of fit for the biplot. — fit.measures","text":"","code":"out <- biplot (iris[,1:4]) |> PCA() |> fit.measures() summary(out) #> Object of class biplot, based on 150 samples and 4 variables. #> 4 numeric variables. #>  #> Quality of fit in 2 dimension(s) = 97.8%  #> Adequacy of variables in 2 dimension(s): #> Sepal.Length  Sepal.Width Petal.Length  Petal.Width  #>    0.5617091    0.5402798    0.7639426    0.1340685  #> Axis predictivity in 2 dimension(s): #> Sepal.Length  Sepal.Width Petal.Length  Petal.Width  #>    0.9579017    0.8400028    0.9980931    0.9365937  #> Sample predictivity in 2 dimension(s): #>         1         2         3         4         5         6         7         8  #> 0.9998927 0.9927400 0.9999141 0.9991226 0.9984312 0.9949770 0.9914313 0.9996346  #>         9        10        11        12        13        14        15        16  #> 0.9998677 0.9941340 0.9991205 0.9949153 0.9945491 0.9996034 0.9942676 0.9897890  #>        17        18        19        20        21        22        23        24  #> 0.9937752 0.9990534 0.9972926 0.9928624 0.9896250 0.9932656 0.9918132 0.9955885  #>        25        26        27        28        29        30        31        32  #> 0.9812917 0.9897303 0.9979903 0.9990514 0.9963870 0.9975607 0.9985741 0.9876345  #>        33        34        35        36        37        38        39        40  #> 0.9833383 0.9957412 0.9970200 0.9935405 0.9859750 0.9953399 0.9994047 0.9990244  #>        41        42        43        44        45        46        47        48  #> 0.9980903 0.9756895 0.9953372 0.9830035 0.9763861 0.9959863 0.9905695 0.9987006  #>        49        50        51        52        53        54        55        56  #> 0.9996383 0.9987482 0.9275369 0.9996655 0.9544488 0.9460515 0.9172857 0.9061058  #>        57        58        59        60        61        62        63        64  #> 0.9727694 0.9996996 0.8677939 0.8686502 0.9613130 0.9328852 0.4345132 0.9679973  #>        65        66        67        68        69        70        71        72  #> 0.7995848 0.9083037 0.7968614 0.5835260 0.7900027 0.8575646 0.8524748 0.6615410  #>        73        74        75        76        77        78        79        80  #> 0.9367709 0.8661203 0.8350955 0.8929908 0.8702600 0.9873164 0.9969031 0.6815512  #>        81        82        83        84        85        86        87        88  #> 0.8937189 0.8409681 0.7829405 0.9848354 0.6901625 0.8073582 0.9666041 0.6665514  #>        89        90        91        92        93        94        95        96  #> 0.6993846 0.9909923 0.9008345 0.9710941 0.8037223 0.9913632 0.9744493 0.7089660  #>        97        98        99       100       101       102       103       104  #> 0.9071738 0.9064541 0.9625371 0.9872279 0.9171603 0.9636413 0.9976224 0.9829885  #>       105       106       107       108       109       110       111       112  #> 0.9854704 0.9888092 0.8464463 0.9729353 0.9771293 0.9794313 0.9746239 0.9977302  #>       113       114       115       116       117       118       119       120  #> 0.9941859 0.9605563 0.8476794 0.9289985 0.9929982 0.9916850 0.9818957 0.9493751  #>       121       122       123       124       125       126       127       128  #> 0.9865358 0.8716778 0.9728177 0.9846364 0.9840890 0.9861783 0.9854516 0.9691512  #>       129       130       131       132       133       134       135       136  #> 0.9942007 0.9585884 0.9705389 0.9937852 0.9874192 0.9723192 0.9230503 0.9794405  #>       137       138       139       140       141       142       143       144  #> 0.8947527 0.9797055 0.9458421 0.9902488 0.9674660 0.9350646 0.9636413 0.9867931  #>       145       146       147       148       149       150  #> 0.9500265 0.9470544 0.9688318 0.9886543 0.8735433 0.9281727"},{"path":"/reference/interpolate.html","id":null,"dir":"Reference","previous_headings":"","what":"Interpolate supplementary points and variables to add to the biplot — interpolate","title":"Interpolate supplementary points and variables to add to the biplot — interpolate","text":"function adds supplementary points variables plot new data set.","code":""},{"path":"/reference/interpolate.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Interpolate supplementary points and variables to add to the biplot — interpolate","text":"","code":"interpolate(bp, newdata = NULL, newvariable = NULL)"},{"path":"/reference/interpolate.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Interpolate supplementary points and variables to add to the biplot — interpolate","text":"bp object class biplot obtained preceding function biplot(). newdata new data set, similar structure data set supplied biplot() containing supplementary data points added onto biplot. newvariable new data set, similar structure data set supplied biplot() containing supplementary variables added onto biplot.","code":""},{"path":"/reference/interpolate.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Interpolate supplementary points and variables to add to the biplot — interpolate","text":"object class biplot appended following elements: Xnew.raw new data. Xnew matrix centered scaled new numeric variables new data. Xnew.cat matrix categorical variables new data. Znew matrix coordinates new data biplot. object class CA following additional elements appended: newrowcoor matrix row coordinates new data biplot. newcolcoor matrix column coordinates new data biplot.","code":""},{"path":"/reference/interpolate.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Interpolate supplementary points and variables to add to the biplot — interpolate","text":"","code":"biplot(data = iris[1:145,]) |> PCA() |> interpolate(newdata = iris[146:150,]) |> plot()  biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = \"Symmetric\") |>       interpolate(newdata = HairEyeColor[,,1]) |> plot()"},{"path":"/reference/legend.type.html","id":null,"dir":"Reference","previous_headings":"","what":"Format the legend for the biplot — legend.type","title":"Format the legend for the biplot — legend.type","text":"function enables user format legend make required selection display.","code":""},{"path":"/reference/legend.type.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Format the legend for the biplot — legend.type","text":"","code":"legend.type(bp, samples = FALSE, means = FALSE, bags = FALSE,                    ellipses=FALSE,regions=FALSE, new=FALSE, ...)"},{"path":"/reference/legend.type.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Format the legend for the biplot — legend.type","text":"bp object class biplot. samples logical value indicating whether legend printed samples, default FALSE. means logical value indicating whether legend printed means, default FALSE. bags logical value indicating whether legend printed bags, default FALSE. ellipses logical value indicating whether legend printed concentration ellipses, default FALSE. regions logical value indicating whether legend printed classification regions, default FALSE. new logical value indicating whether legend appear new window, default FALSE. ... additional arguments sent legend().","code":""},{"path":"/reference/legend.type.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Format the legend for the biplot — legend.type","text":"list following components available: samples logical value indicating whether legend samples provided. means logical value indicating whether legend class means provided. bags logical value indicating whether legend \\(\\alpha\\)-bags provided. ellipses logical value indicating whether legend \\(\\kappa\\)-ellipses provided. regions logical value indicating whether legend classification regions provided. new logical value indicating whether legend appears new plot.","code":""},{"path":"/reference/legend.type.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Format the legend for the biplot — legend.type","text":"","code":"biplot (iris[,1:4], Title=\"Test biplot\") |> PCA(group.aes = iris[,5]) |>     legend.type(samples=TRUE) |> plot()"},{"path":"/reference/means.html","id":null,"dir":"Reference","previous_headings":"","what":"Format aesthetics for the class or group means — means","title":"Format aesthetics for the class or group means — means","text":"function allows user format aesthetics class means group means.","code":""},{"path":"/reference/means.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Format aesthetics for the class or group means — means","text":"","code":"means (bp,  which = NULL, col = NULL, pch = 15, cex = 1, label = FALSE, label.col = NULL,label.cex = 0.75, label.side = \"bottom\", label.offset = 0.5, opacity = 1, shade.darker = TRUE)"},{"path":"/reference/means.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Format aesthetics for the class or group means — means","text":"bp object class biplot. vector containing groups classes means displayed, default bp$g. col colour(s) means, default colour samples. pch plotting character(s) means, default 15. cex character expansion(s) means, default 1. label logical value indicating whether means labelled, default TRUE. label.col vector length label colours means, default colour means. label.cex vector length label text expansions means, default 0.75. label.side side label plotted mean point appears, default bottom. Note unlike argument pos text(), options \"bottom\", \"left\", \"top\", \"right\" 1, 2, 3, 4. label.offset offset label plotted mean point. See ?text detailed explanation argument offset. opacity transparency means. shade.darker logical value indicating whether colour mean points made shade darker default specified colour, default TRUE.","code":""},{"path":"/reference/means.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Format aesthetics for the class or group means — means","text":"object class biplot appended list called means containing following elements: vector containing groups classes means displayed. col colour(s) means. pch plotting character(s) means. cex character expansion(s) plotting character(s) means. label logical value indicating whether means labelled. label.col label colours means. label.cex label text expansions samples. label.side side label plotted mean point appears. label.offset offset label plotted mean point. opacity opacity level plotted points.","code":""},{"path":"/reference/means.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Format aesthetics for the class or group means — means","text":"number classes groups (defined group.aes) indicated g. argument length g, recycling used.","code":""},{"path":[]},{"path":"/reference/means.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Format aesthetics for the class or group means — means","text":"","code":"biplot(iris[,1:4]) |> PCA() |>           means(col = \"purple\", pch = 15, cex = 2) |> plot()"},{"path":"/reference/newaxes.html","id":null,"dir":"Reference","previous_headings":"","what":"Format aesthetics for the supplementary (new) biplot axes — newaxes","title":"Format aesthetics for the supplementary (new) biplot axes — newaxes","text":"function allows user format aesthetics supplementary (new) biplot axes.","code":""},{"path":"/reference/newaxes.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Format aesthetics for the supplementary (new) biplot axes — newaxes","text":"","code":"newaxes(bp, X.new.names=bp$var.names, which = 1:bp$num.vars, col = \"orange\", lwd = 1,  lty = 1, label.dir = \"Orthog\", label.col = col, label.cex = 0.75, label.line = 0.1,  ticks = 5, tick.col = col, tick.size = 1, tick.label = TRUE, tick.label.col = tick.col,  tick.label.cex = 0.6, tick.label.side = \"below\", predict.col = col, predict.lwd = lwd,  predict.lty = lty, ax.names = X.new.names, orthogx = 0, orthogy = 0)"},{"path":"/reference/newaxes.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Format aesthetics for the supplementary (new) biplot axes — newaxes","text":"bp object class biplot. X.new.names vector new column names bp specify axes labelled. vector containing new columns variables axes displayed, default 1:num.vars. col colour(s) axes, default grey(0.7). Alternatively, provide vector colours corresponding X.names. lwd line width(s) axes, default 1. lty line type(s) axes, default 1. label.dir character string indicating placement axis titles side figure. One \"Orthog\" axis titles appear orthogonal side figure (default) , \"Hor\" axis titles appear horizontally \"Paral\" axis titles appear parallel side figure. label.col colour(s) axis labels, default, col. label.cex label expansion axis labels, default 0.75. label.line distance axis title side figure, default 0.1. ticks integer-valued vector indicating number tickmarks axis, default 5 axis. tick.col colour(s) tick marks, default col. tick.size vector specifying sizes tick marks axis, default 1 . tick.label logical value indicating whether axes labelled, default TRUE. tick.label.col colour(s) tick mark labels, default tick.col. tick.label.cex label expansion tick mark labels, default 0.6. tick.label.side character string indicating position tick label. One \"\" label appear tick mark (default) \"\" label appear tick mark. predict.col colour(s) predicted samples, default col. predict.lwd line width(s) predicted samples, default lwd. predict.lty line type(s) predicted samples, default lty. ax.names vector size p containing user defined titles axes. orthogx numeric vector size p specifying x-coordinate parallel transformation axis, default 0 axis. used dim.biplot = 2. orthogy numeric vector size p specifying y-coordinate parallel transformation axis, default 0 axis. used dim.biplot = 2.","code":""},{"path":"/reference/newaxes.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Format aesthetics for the supplementary (new) biplot axes — newaxes","text":"object class biplot appended list called newaxes containing elements similar axes.","code":""},{"path":[]},{"path":"/reference/newaxes.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Format aesthetics for the supplementary (new) biplot axes — newaxes","text":"","code":"biplot(data = iris[,1:2]) |> PCA() |> interpolate(newvariable = iris[3:4]) |>    newaxes(col=\"gold\") |> plot()"},{"path":"/reference/newsamples.html","id":null,"dir":"Reference","previous_headings":"","what":"Format aesthetics for the supplementary (new) biplot samples — newsamples","title":"Format aesthetics for the supplementary (new) biplot samples — newsamples","text":"function allows formatting changes new samples.","code":""},{"path":"/reference/newsamples.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Format aesthetics for the supplementary (new) biplot samples — newsamples","text":"","code":"newsamples (bp,  col = \"darkorange1\", pch = 1, cex = 1, label = FALSE, label.name = NULL, label.col = NULL,label.cex = 0.75, label.side = \"bottom\",  label.offset = 0.5, connected = FALSE, connect.col = \"black\", connect.lty=1,  connect.lwd=1)"},{"path":"/reference/newsamples.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Format aesthetics for the supplementary (new) biplot samples — newsamples","text":"bp object class biplot. col colour(s) new samples, default darkorange1. pch plotting character(s) new samples, default 1. cex character expansion(s) new samples, default 1. label logical value indicating whether new samples labelled , default FALSE. label.name label names new samples. label.col vector length number new samples containing colour(s) labels new samples, default colour sample points. label.cex label text expansion(s) new samples, default 0.75. label.side side label plotted point appears, default bottom. Note unlike argument pos text(), options \"bottom\", \"left\", \"top\",\"right\" 1, 2, 3, 4. label.offset offset label plotted point. See ?text detailed explanation argument offset. connected logical value indicating whether samples connected order rows data matrix, default FALSE. connect.col colour connecting line, default black. connect.lty line type connecting line, default 1. connect.lwd line width connecting line, default 1.","code":""},{"path":"/reference/newsamples.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Format aesthetics for the supplementary (new) biplot samples — newsamples","text":"object class biplot appended list called newsamples containing following elements: col colour(s) new samples. pch plotting character(s) new samples. cex character expansion(s) plotting character(s) new samples. label logical value indicating whether new samples labelled. label.col label colours new samples. label.cex label text expansions new samples. label.side side label plotted point appears. label.offset offset label plotted point. connected logical value indicating whether new samples connected. connect.col colour connecting line. connect.lty line type connecting line. connect.lwd line width connecting line.","code":""},{"path":[]},{"path":"/reference/newsamples.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Format aesthetics for the supplementary (new) biplot samples — newsamples","text":"","code":"biplot(data = iris[1:145,]) |> PCA() |> samples(col = \"grey\") |> interpolate(newdata = iris[146:150,]) |> newsamples(col = rainbow(6), pch=15) |> plot()"},{"path":"/reference/PCA.biplot.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate elements for the PCA biplot — PCA.biplot","title":"Calculate elements for the PCA biplot — PCA.biplot","text":"function performs calculations construction PCA biplot.","code":""},{"path":"/reference/PCA.biplot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate elements for the PCA biplot — PCA.biplot","text":"","code":"# S3 method for class 'biplot' PCA(   bp,   dim.biplot = c(2, 1, 3),   e.vects = 1:ncol(bp$X),   group.aes = NULL,   show.class.means = FALSE,   correlation.biplot = FALSE )"},{"path":"/reference/PCA.biplot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate elements for the PCA biplot — PCA.biplot","text":"bp object class biplot obtained preceding function biplot(). dim.biplot dimension biplot. values 1, 2 3 accepted, default 2. e.vects vector indicating eigenvectors (principal components) plotted biplot, default 1:dim.biplot. group.aes vector length number rows data matrix differentiated aesthetics samples. show.class.means logical value indicating whether group means plotted biplot. correlation.biplot logical value. FALSE, distances sample points optimally approximated biplot. TRUE, correlations variables optimally approximated cosine angles axes. Default FALSE.","code":""},{"path":"/reference/PCA.biplot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate elements for the PCA biplot — PCA.biplot","text":"object class PCA, inherits class biplot.","code":""},{"path":"/reference/PCA.biplot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate elements for the PCA biplot — PCA.biplot","text":"","code":"biplot(iris[,1:4]) |> PCA() #> Object of class biplot, based on 150 samples and 4 variables. #> 4 numeric variables. # create a PCA biplot biplot(data = iris) |> PCA() |> plot()"},{"path":"/reference/PCA.html","id":null,"dir":"Reference","previous_headings":"","what":"Perform Principal Components Analysis (PCA) — PCA","title":"Perform Principal Components Analysis (PCA) — PCA","text":"function appends biplot object elements resulting performing PCA.","code":""},{"path":"/reference/PCA.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Perform Principal Components Analysis (PCA) — PCA","text":"","code":"PCA(bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X), group.aes = NULL, show.class.means = FALSE, correlation.biplot = FALSE)"},{"path":"/reference/PCA.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Perform Principal Components Analysis (PCA) — PCA","text":"bp object class biplot obtained preceding function biplot(). dim.biplot dimension biplot. values 1, 2 3 accepted, default 2. e.vects vector indicating eigenvectors (principal components) plotted biplot, default 1:dim.biplot. group.aes vector length number rows data matrix differentiated aesthetics samples. show.class.means logical value indicating whether group means plotted biplot. correlation.biplot logical value. FALSE, distances sample points optimally approximated biplot. TRUE, correlations variables optimally approximated cosine angles axes. Default FALSE.","code":""},{"path":"/reference/PCA.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Perform Principal Components Analysis (PCA) — PCA","text":"object class PCA following elements: X matrix centered scaled numeric variables. Xcat data frame categorical variables. raw.X original data. classes vector category levels class variable. used colour, pch cex specifications. na.action vector observations removed. center logical value indicating whether \\(\\mathbf{X}\\) centered. scaled logical value indicating whether \\(\\mathbf{X}\\) scaled. means vector means numerical variable. sd vector standard deviations numerical variable. n number observations. p number variables. group.aes vector category levels grouping variable. used colour, pch cex specification. g.names descriptive names used group labels. g number groups. Title title biplot rendered. Z matrix row containing details points plotted (.e. coordinates). Lmat matrix transformation principal components. Linv inverse \\(\\mathbf{L}\\). eigenvalues vector eigenvalues covariance matrix \\(\\mathbf{X}\\). ax.one.unit one unit positive direction biplot axis. e.vects vector indicating principal components plotted biplot. Vr 1:dim.biplot columns \\(\\mathbf{V}\\). dim.biplot dimension biplot. class.means logical value indicating whether group means plotted biplot. Zmeans matrix class mean coordinates plotted biplot.","code":""},{"path":"/reference/PCA.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Perform Principal Components Analysis (PCA) — PCA","text":"Gabriel, K.R. (1971) biplot graphic display matrices application principal component analysis. Biometrika. 58(3):453–467.","code":""},{"path":[]},{"path":"/reference/PCA.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Perform Principal Components Analysis (PCA) — PCA","text":"","code":"biplot(iris[,1:4]) |> PCA() #> Object of class biplot, based on 150 samples and 4 variables. #> 4 numeric variables. # create a PCA biplot biplot(data = iris) |> PCA() |> plot()"},{"path":"/reference/PCO.biplot.html","id":null,"dir":"Reference","previous_headings":"","what":"PCO biplot — PCO.biplot","title":"PCO biplot — PCO.biplot","text":"Computes Principal Coordinate Analysis biplot","code":""},{"path":"/reference/PCO.biplot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"PCO biplot — PCO.biplot","text":"","code":"# S3 method for class 'biplot' PCO(   bp,   Dmat = NULL,   dist.func = NULL,   dist.func.cat = NULL,   dim.biplot = c(2, 1, 3),   e.vects = NULL,   group.aes = NULL,   show.class.means = FALSE,   axes = c(\"regression\", \"splines\"),   ... )"},{"path":"/reference/PCO.biplot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"PCO biplot — PCO.biplot","text":"bp object class biplot obtained preceding function biplot(). Dmat nxn matrix Euclidean embeddable distances samples dist.func function compute Euclidean embeddable distances samples. default NULL computes Euclidean distance. dist.func.cat function compute Euclidean embeddable distance categorical variables samples. default NULL computes extended matching coefficient. dim.biplot dimension biplot. values 1, 2 3 accepted, default 2. e.vects e.vects eigenvectors (canonical variates) extract, default 1:dim.biplot. group.aes vector length number rows data matrix differentiated aesthetics samples. show.class.means logical, indicating whether plot class means biplot. axes type biplot axes, currently regression axes implemented ... arguments dist.func","code":""},{"path":"/reference/PCO.biplot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"PCO biplot — PCO.biplot","text":"object class biplot.","code":""},{"path":"/reference/PCO.biplot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"PCO biplot — PCO.biplot","text":"","code":"biplot(iris) |> PCO(dist.func=sqrtManhattan) |> plot()"},{"path":"/reference/PCO.html","id":null,"dir":"Reference","previous_headings":"","what":"Principal Coordinate Analysis (PCO) biplot method — PCO","title":"Principal Coordinate Analysis (PCO) biplot method — PCO","text":"Principal Coordinate Analysis (PCO) biplot method","code":""},{"path":"/reference/PCO.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Principal Coordinate Analysis (PCO) biplot method — PCO","text":"","code":"PCO(bp, Dmat=NULL, dist.func=NULL, dist.func.cat=NULL,            dim.biplot = c(2,1,3), e.vects = NULL, group.aes=NULL,            show.class.means = FALSE, axes = c(\"regression\",\"splines\"), ...)"},{"path":"/reference/PCO.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Principal Coordinate Analysis (PCO) biplot method — PCO","text":"bp object class biplot obtained preceding function biplot(). Dmat nxn matrix Euclidean embeddable distances samples dist.func function compute Euclidean embeddable distances samples. default NULL computes Euclidean distance. dist.func.cat function compute Euclidean embeddable distance categorical variables samples. default NULL computes extended matching coefficient. dim.biplot dimension biplot. values 1, 2 3 accepted, default 2. e.vects e.vects eigenvectors (canonical variates) extract, default 1:dim.biplot. group.aes vector length number rows data matrix differentiated aesthetics samples. show.class.means logical, indicating whether plot class means biplot. axes type biplot axes, currently regression axes implemented ... arguments dist.func","code":""},{"path":"/reference/PCO.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Principal Coordinate Analysis (PCO) biplot method — PCO","text":"Object class biplot","code":""},{"path":"/reference/PCO.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Principal Coordinate Analysis (PCO) biplot method — PCO","text":"","code":"biplot(iris[,1:4]) |> PCO(dist.func = sqrtManhattan) #> Object of class biplot, based on 150 samples and 4 variables. #> 4 numeric variables. # create a CVA biplot biplot(iris[,1:4]) |> PCO(dist.func = sqrtManhattan) |> plot()"},{"path":"/reference/plot.biplot.html","id":null,"dir":"Reference","previous_headings":"","what":"Generic Plotting function of objects of class biplot — plot.biplot","title":"Generic Plotting function of objects of class biplot — plot.biplot","text":"Generic Plotting function objects class biplot","code":""},{"path":"/reference/plot.biplot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generic Plotting function of objects of class biplot — plot.biplot","text":"","code":"# S3 method for class 'biplot' plot(   x,   exp.factor = 1.2,   axis.predictivity = NULL,   sample.predictivity = NULL,   zoom = FALSE,   add = FALSE,   xlim = NULL,   ylim = NULL,   ... )"},{"path":"/reference/plot.biplot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generic Plotting function of objects of class biplot — plot.biplot","text":"x object class biplot. exp.factor numeric value default axes biplot. Larger values specified zooming respect sample points biplot display smaller values specified zooming respect sample points biplot display. axis.predictivity either logical numeric value 0 1. numeric value, value used threshold axes axis predictivity larger threshold displayed. axis.predictivity = TRUE, axis colour 'diluted' proportion axis predictivity. sample.predictivity either logical numeric value 0 1. numeric value, value used threshold samples sample predictivity larger threshold displayed. sample.predictivity = TRUE, sample size shrinked proportion sample predictivity. zoom logical value allowing user select area zoom . add logical value allowing user add biplot current plot. add = TRUE argument zoom inactive. xlim horizontal limits plot. ylim vertical limits plot. ... additional arguments.","code":""},{"path":"/reference/plot.biplot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generic Plotting function of objects of class biplot — plot.biplot","text":"object class biplot.","code":""},{"path":"/reference/plot.biplot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generic Plotting function of objects of class biplot — plot.biplot","text":"","code":"biplot (iris[,1:4]) |> PCA() |> plot()"},{"path":"/reference/prediction.html","id":null,"dir":"Reference","previous_headings":"","what":"Predict samples to display on the biplot — prediction","title":"Predict samples to display on the biplot — prediction","text":"function makes predictions sample points, variables means displays biplot.","code":""},{"path":"/reference/prediction.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Predict samples to display on the biplot — prediction","text":"","code":"prediction(bp, predict.samples = NULL, predict.means = NULL, which = 1:bp$p)"},{"path":"/reference/prediction.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Predict samples to display on the biplot — prediction","text":"bp object class biplot obtained preceding function biplot(). predict.samples vector specifying samples predict. predict.means vector specifying group means predict. vector specifying variable prediction.","code":""},{"path":"/reference/prediction.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Predict samples to display on the biplot — prediction","text":"list object called predict appended object class biplot following elements: samples vector indices samples predicted. predict.means vector group names groups means predicted. vector indices variables predicted. predict.mat matrix predicted samples. predict.means.mat matrix predicted group means.","code":""},{"path":"/reference/prediction.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Predict samples to display on the biplot — prediction","text":"","code":"biplot(data = iris[,1:4]) |> PCA(group.aes=iris[,5], show.class.means = TRUE) |>  prediction(141:145,1:3) |> plot()"},{"path":"/reference/print.biplot.html","id":null,"dir":"Reference","previous_headings":"","what":"Generic print function for objects of class biplot — print.biplot","title":"Generic print function for objects of class biplot — print.biplot","text":"function used print output biplot object created.","code":""},{"path":"/reference/print.biplot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generic print function for objects of class biplot — print.biplot","text":"","code":"# S3 method for class 'biplot' print(x, ...)"},{"path":"/reference/print.biplot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generic print function for objects of class biplot — print.biplot","text":"x object class biplot. ... additional arguments.","code":""},{"path":"/reference/print.biplot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generic print function for objects of class biplot — print.biplot","text":"function produce return value, called side effects.","code":""},{"path":"/reference/print.biplot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generic print function for objects of class biplot — print.biplot","text":"","code":"out <- biplot (iris[,1:4]) |> PCA() out #> Object of class biplot, based on 150 samples and 4 variables. #> 4 numeric variables."},{"path":"/reference/reflect.html","id":null,"dir":"Reference","previous_headings":"","what":"Reflect the biplot about a chosen axis — reflect","title":"Reflect the biplot about a chosen axis — reflect","text":"function provides user option reflect biplot horizontally, vertically diagonally.","code":""},{"path":"/reference/reflect.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Reflect the biplot about a chosen axis — reflect","text":"","code":"reflect(bp, reflect.axis = c(\"FALSE\", \"x\", \"y\", \"xy\"))"},{"path":"/reference/reflect.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Reflect the biplot about a chosen axis — reflect","text":"bp object class biplot reflect.axis character string indicating axis reflect. One FALSE (default), \"x\" reflection x-axis, \"y\" reflection y-axis \"xy\" reflection axes.","code":""},{"path":"/reference/reflect.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Reflect the biplot about a chosen axis — reflect","text":"object class biplot","code":""},{"path":"/reference/reflect.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Reflect the biplot about a chosen axis — reflect","text":"","code":"biplot(iris[,1:4],group.aes = iris[,5]) |> PCA() |> reflect(\"x\") |> plot()  biplot(iris[,1:4],group.aes = iris[,5]) |> PCA() |> reflect(\"y\") |> plot()  biplot(iris[,1:4],group.aes = iris[,5]) |> PCA() |> reflect(\"xy\") |> plot()"},{"path":"/reference/regress.biplot.html","id":null,"dir":"Reference","previous_headings":"","what":"Regression biplot — regress.biplot","title":"Regression biplot — regress.biplot","text":"Computes regression biplot axes","code":""},{"path":"/reference/regress.biplot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Regression biplot — regress.biplot","text":"","code":"# S3 method for class 'biplot' regress(   bp,   Z,   group.aes = NULL,   show.group.means = TRUE,   axes = c(\"regression\", \"splines\") )"},{"path":"/reference/regress.biplot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Regression biplot — regress.biplot","text":"bp object class biplot obtained preceding function biplot(). Z matrix coordinates samples group.aes vector length number rows data matrix differentiated aesthetics samples. show.group.means logical, indicating whether group means plotted biplot. axes type axes fitted biplot. Options 'regression' linear regression axes (default) 'splines' B-spline axes.","code":""},{"path":"/reference/regress.biplot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Regression biplot — regress.biplot","text":"object class biplot.","code":""},{"path":"/reference/regress.biplot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Regression biplot — regress.biplot","text":"","code":"biplot(iris) |> regress(Z = cmdscale(dist(iris[,1:4]))) |> plot()"},{"path":"/reference/regress.html","id":null,"dir":"Reference","previous_headings":"","what":"Regression biplot method — regress","title":"Regression biplot method — regress","text":"Regression biplot method","code":""},{"path":"/reference/regress.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Regression biplot method — regress","text":"","code":"regress(bp, Z, group.aes=NULL, show.group.means = TRUE,                 axes = c(\"regression\", \"splines\"))"},{"path":"/reference/regress.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Regression biplot method — regress","text":"bp object class biplot obtained preceding function biplot(). Z matrix coordinates samples group.aes vector length number rows data matrix differentiated aesthetics samples. show.group.means logical, indicating whether group means plotted biplot. axes type axes fitted biplot. Options 'regression' linear regression axes (default) 'splines' B-spline axes.","code":""},{"path":"/reference/regress.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Regression biplot method — regress","text":"Object class biplot","code":""},{"path":"/reference/regress.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Regression biplot method — regress","text":"","code":"biplot(iris[,1:4]) |> regress(Z=cmdscale(dist(iris[,1:4]))) |> plot()"},{"path":"/reference/rotate.html","id":null,"dir":"Reference","previous_headings":"","what":"Rotate the biplot a chosen amount of degrees — rotate","title":"Rotate the biplot a chosen amount of degrees — rotate","text":"function provides user option rotate biplot anti-clockwise clockwise.","code":""},{"path":"/reference/rotate.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Rotate the biplot a chosen amount of degrees — rotate","text":"","code":"rotate(bp, rotate.degrees = 0)"},{"path":"/reference/rotate.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Rotate the biplot a chosen amount of degrees — rotate","text":"bp object class biplot rotate.degrees value specifying degrees biplot rotated, default 0. positive value results anti-clockwise rotation negative value clockwise rotation.","code":""},{"path":"/reference/rotate.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Rotate the biplot a chosen amount of degrees — rotate","text":"object class biplot.","code":""},{"path":"/reference/rotate.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Rotate the biplot a chosen amount of degrees — rotate","text":"","code":"biplot(iris[,1:4],group.aes = iris[,5]) |> PCA() |> rotate(200) |> plot()"},{"path":"/reference/samples.html","id":null,"dir":"Reference","previous_headings":"","what":"Format aesthetics for the biplot samples — samples","title":"Format aesthetics for the biplot samples — samples","text":"function allows user format aesthetics samples.","code":""},{"path":"/reference/samples.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Format aesthetics for the biplot samples — samples","text":"","code":"samples (bp,  which = 1:bp$g, col = ez.col, pch = 16, cex = 1, label = FALSE, label.name = NULL, label.col=NULL, label.cex = 0.75,  label.side = \"bottom\", label.offset = 0.5, connected=FALSE, connect.col = \"black\", connect.lty = 1,  connect.lwd = 1, opacity = 1)"},{"path":"/reference/samples.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Format aesthetics for the biplot samples — samples","text":"bp object class biplot. vector containing groups classes samples displayed, default bp$g. col colour(s) samples, default blue. pch plotting character(s) samples, default 16. cex character expansion(s) samples, default 1. label logical value indicating whether samples labelled, default FALSE. Alternatively, specify \"ggrepel\" non-overlapping placement labels. label.name vector length label names samples, default NULL. NULL, rownames(bp) used. Alternatively, custom vector length n used. label.col vector length label colours samples, default colour sample points. label.cex vector length label text expansions samples, default 0.75. label.side side label plotted point appears, default bottom. Note unlike argument pos text(), options \"bottom\", \"left\", \"top\", \"right\" 1, 2, 3, 4. label.offset offset label plotted point. See ?text detailed explanation argument offset. connected logical value indicating whether samples connected order rows data matrix, default FALSE. connect.col colour connecting line, default black. connect.lty line type connecting line, default 1. connect.lwd line width connecting line, default 1. opacity opacity level plotted points, default 1 opaque point.","code":""},{"path":"/reference/samples.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Format aesthetics for the biplot samples — samples","text":"object class biplot appended list called samples containing following elements: vector containing groups classes samples (means) displayed. col colour(s) samples. pch plotting character(s) samples. cex character expansion(s) plotting character(s) samples. label logical value indicating whether samples labelled. label.name label names samples. label.col label colours samples. label.cex label text expansions samples. label.side side label plotted point appears.. label.offset offset label plotted point. connected logical value indicating whether samples connected order rows data matrix. connect.col colour connecting line. connect.lty line type connecting line. connect.lwd line width connecting line. opacity opacity level plotted points.","code":""},{"path":"/reference/samples.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Format aesthetics for the biplot samples — samples","text":"arguments , col, pch cex based specification group.aes classes. groups specified, single colour, plotting character / character expansion expected. \\(g\\) groups specified, vectors length \\(g\\) expected, values recycled length \\(g\\). arguments label, label.cex, label.side label.offset based sample size \\(n\\). single value recycled \\(n\\) times vector length \\(n\\) expected.","code":""},{"path":[]},{"path":"/reference/samples.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Format aesthetics for the biplot samples — samples","text":"","code":"biplot(iris[,1:4]) |> PCA() |> samples(col=\"purple\",pch=15, opacity=0.5) |> plot()  biplot(iris[,1:4]) |> PCA() |>    samples(col=\"purple\",pch=NA, opacity=0.5, label = TRUE) |> plot()  biplot(iris[,1:4]) |> PCA() |>    samples(col=\"purple\",pch=NA, opacity=0.5, label = TRUE,            label.name = paste(\"s:\",1:150, sep=\"\")) |>    plot()  biplot(iris[,1:4]) |> PCA() |>    samples(col=\"purple\",pch=NA, opacity=0.5, label = \"ggrepel\") |> plot() #> Warning: Use of `df$x` is discouraged. #> ℹ Use `x` instead. #> Warning: Use of `df$y` is discouraged. #> ℹ Use `y` instead. #> Warning: Use of `df$z` is discouraged. #> ℹ Use `z` instead. #> Warning: Use of `df$x` is discouraged. #> ℹ Use `x` instead. #> Warning: Use of `df$y` is discouraged. #> ℹ Use `y` instead. #> Warning: Use of `df$z` is discouraged. #> ℹ Use `z` instead. #> Warning: Use of `df$x` is discouraged. #> ℹ Use `x` instead. #> Warning: Use of `df$y` is discouraged. #> ℹ Use `y` instead. #> Warning: Use of `df$z` is discouraged. #> ℹ Use `z` instead. #> Warning: Use of `df$x` is discouraged. #> ℹ Use `x` instead. #> Warning: Use of `df$y` is discouraged. #> ℹ Use `y` instead. #> Warning: Use of `df$z` is discouraged. #> ℹ Use `z` instead. #> Warning: Use of `df$x` is discouraged. #> ℹ Use `x` instead. #> Warning: Use of `df$y` is discouraged. #> ℹ Use `y` instead. #> Warning: Use of `df$z` is discouraged. #> ℹ Use `z` instead. #> Warning: Use of `df$x` is discouraged. #> ℹ Use `x` instead. #> Warning: Use of `df$y` is discouraged. #> ℹ Use `y` instead. #> Warning: Use of `df$z` is discouraged. #> ℹ Use `z` instead. #> Warning: ggrepel: 14 unlabeled data points (too many overlaps). Consider increasing max.overlaps #> Warning: ggrepel: 14 unlabeled data points (too many overlaps). Consider increasing max.overlaps"},{"path":"/reference/sqrtManhattan.html","id":null,"dir":"Reference","previous_headings":"","what":"Computes the square root of the Manhattan distance An example of a Euclidean embeddable distance metric — sqrtManhattan","title":"Computes the square root of the Manhattan distance An example of a Euclidean embeddable distance metric — sqrtManhattan","text":"Computes square root Manhattan distance example Euclidean embeddable distance metric","code":""},{"path":"/reference/sqrtManhattan.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Computes the square root of the Manhattan distance An example of a Euclidean embeddable distance metric — sqrtManhattan","text":"","code":"sqrtManhattan(X)"},{"path":"/reference/sqrtManhattan.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Computes the square root of the Manhattan distance An example of a Euclidean embeddable distance metric — sqrtManhattan","text":"X matrix samples x variables computation samples x samples distance matrix","code":""},{"path":"/reference/sqrtManhattan.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Computes the square root of the Manhattan distance An example of a Euclidean embeddable distance metric — sqrtManhattan","text":"dist object","code":""},{"path":"/reference/sqrtManhattan.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Computes the square root of the Manhattan distance An example of a Euclidean embeddable distance metric — sqrtManhattan","text":"","code":"sqrtManhattan(iris[,1:4]) #>             1         2         3         4         5         6         7 #> 2   0.8366600                                                             #> 3   0.8944272 0.7071068                                                   #> 4   1.0000000 0.7071068 0.6324555                                         #> 5   0.4472136 0.8366600 0.8944272 1.0000000                               #> 6   1.0954451 1.3784049 1.4142136 1.4142136 1.0954451                     #> 7   0.8366600 0.8944272 0.7071068 0.7071068 0.8366600 1.3038405           #> 8   0.5477226 0.7745967 0.8366600 0.8366600 0.5477226 1.1401754 0.7745967 #> 9   1.1401754 0.7745967 0.8366600 0.7071068 1.1401754 1.5811388 0.8944272 #> 10  0.8944272 0.5477226 0.7745967 0.6324555 0.8944272 1.3416408 0.9486833 #> 11  0.7745967 1.1401754 1.1832160 1.1832160 0.7745967 0.7745967 1.1401754 #> 12  0.7745967 0.8366600 0.7745967 0.7745967 0.7745967 1.1832160 0.7071068 #> 13  0.9486833 0.4472136 0.7071068 0.7071068 0.9486833 1.4491377 0.8944272 #> 14  1.3038405 1.0000000 0.9486833 0.9486833 1.3038405 1.7029386 1.0954451 #> 15  1.1832160 1.4491377 1.4142136 1.5491933 1.1832160 1.0954451 1.4491377 #> 16  1.3416408 1.5811388 1.6124515 1.6124515 1.3416408 1.0000000 1.5165751 #> 17  1.0000000 1.3038405 1.2649111 1.4142136 1.0000000 0.6324555 1.2247449 #> 18  0.3162278 0.8944272 0.9486833 1.0488088 0.5477226 1.0488088 0.7745967 #> 19  1.1401754 1.4142136 1.4491377 1.4491377 1.1401754 0.7071068 1.3416408 #> 20  0.7071068 1.0954451 1.1401754 1.1401754 0.7071068 0.8366600 1.0000000 #> 21  0.8366600 1.0954451 1.1401754 1.1401754 0.9486833 0.8366600 1.0954451 #> 22  0.7071068 1.0954451 1.1401754 1.1401754 0.7071068 0.8366600 1.0000000 #> 23  1.0000000 1.1401754 0.8944272 1.0000000 0.8944272 1.4142136 0.8366600 #> 24  0.8944272 1.0488088 1.0954451 1.0954451 1.0000000 1.0000000 1.0488088 #> 25  0.9486833 1.0000000 0.9486833 0.9486833 0.9486833 1.2247449 0.8944272 #> 26  0.8944272 0.5477226 0.8944272 0.7745967 0.8944272 1.2649111 1.0488088 #> 27  0.7745967 0.9486833 1.0000000 1.0000000 0.7745967 1.0000000 0.8366600 #> 28  0.4472136 0.9486833 1.0000000 1.0000000 0.6324555 1.0000000 0.9486833 #> 29  0.4472136 0.8366600 0.8944272 1.0000000 0.6324555 1.0954451 0.8366600 #> 30  0.9486833 0.7745967 0.5477226 0.5477226 0.9486833 1.3038405 0.7745967 #> 31  0.9486833 0.6324555 0.7071068 0.5477226 0.9486833 1.3038405 0.8944272 #> 32  0.8366600 1.0954451 1.1401754 1.1401754 0.9486833 0.8366600 1.0000000 #> 33  0.9486833 1.2649111 1.3038405 1.3038405 0.9486833 0.9486833 1.2649111 #> 34  1.0488088 1.3416408 1.3784049 1.4491377 1.0488088 0.9486833 1.3416408 #> 35  0.8366600 0.4472136 0.7071068 0.5477226 0.8366600 1.3038405 0.8944272 #> 36  0.7745967 0.7071068 0.6324555 0.8944272 0.7745967 1.3416408 0.9486833 #> 37  0.7071068 1.0954451 1.0488088 1.2247449 0.8366600 1.0488088 1.0954451 #> 38  0.6324555 0.8366600 0.8944272 1.0000000 0.4472136 1.1832160 0.8366600 #> 39  1.1401754 0.7745967 0.7071068 0.7071068 1.1401754 1.5811388 0.8944272 #> 40  0.4472136 0.8366600 0.8944272 0.8944272 0.6324555 1.0954451 0.8366600 #> 41  0.5477226 0.8944272 0.8366600 1.0488088 0.5477226 1.1401754 0.7745967 #> 42  1.4142136 1.1401754 1.0954451 1.0954451 1.4142136 1.7320508 1.1401754 #> 43  1.0488088 0.8944272 0.5477226 0.7071068 1.0488088 1.5165751 0.7745967 #> 44  0.8366600 1.0954451 1.1401754 1.1401754 0.8366600 1.0488088 1.0000000 #> 45  1.0000000 1.3038405 1.3416408 1.3416408 1.0000000 0.7745967 1.2247449 #> 46  0.9486833 0.4472136 0.7071068 0.7071068 0.9486833 1.3784049 0.7745967 #> 47  0.7071068 1.0954451 1.1401754 1.1401754 0.7071068 0.8366600 1.0954451 #> 48  0.8944272 0.7071068 0.4472136 0.4472136 0.8944272 1.4142136 0.5477226 #> 49  0.7071068 1.0954451 1.1401754 1.1401754 0.7071068 0.8366600 1.0954451 #> 50  0.5477226 0.6324555 0.7071068 0.8366600 0.5477226 1.2247449 0.7745967 #> 51  2.5884358 2.6076810 2.6267851 2.6267851 2.6267851 2.5099801 2.6457513 #> 52  2.4494897 2.4698178 2.4899799 2.4899799 2.4899799 2.3664319 2.5099801 #> 53  2.6457513 2.6267851 2.6832816 2.6457513 2.6832816 2.5690465 2.7018512 #> 54  2.3021729 2.2360680 2.3452079 2.3021729 2.3452079 2.2135944 2.3664319 #> 55  2.5690465 2.5099801 2.6076810 2.5690465 2.6076810 2.4899799 2.6267851 #> 56  2.3452079 2.2803509 2.3874673 2.3452079 2.3874673 2.2583180 2.4083189 #> 57  2.4698178 2.5298221 2.5495098 2.5495098 2.5099801 2.3874673 2.5298221 #> 58  2.0000000 1.8165902 1.9493589 1.8973666 2.0000000 2.0493902 1.9748418 #> 59  2.5298221 2.4698178 2.5690465 2.5298221 2.5690465 2.4494897 2.5884358 #> 60  2.1447611 2.0736441 2.1908902 2.1447611 2.1908902 2.1447611 2.2135944 #> 61  2.1213203 2.0000000 2.1213203 2.0736441 2.1213203 2.1679483 2.1447611 #> 62  2.3237900 2.2583180 2.3664319 2.3237900 2.3664319 2.2360680 2.3874673 #> 63  2.3664319 2.3021729 2.4083189 2.3664319 2.4083189 2.2803509 2.4289916 #> 64  2.4698178 2.4083189 2.5099801 2.4698178 2.5099801 2.3874673 2.5298221 #> 65  2.0976177 2.0248457 2.1447611 2.0976177 2.1447611 2.0000000 2.1679483 #> 66  2.4899799 2.4698178 2.5298221 2.4899799 2.5298221 2.4083189 2.5495098 #> 67  2.3237900 2.2583180 2.3664319 2.3237900 2.3664319 2.2360680 2.3874673 #> 68  2.2360680 2.1679483 2.2803509 2.2360680 2.2803509 2.1447611 2.3021729 #> 69  2.6076810 2.5495098 2.6457513 2.6076810 2.6457513 2.5298221 2.6645825 #> 70  2.2135944 2.1447611 2.2583180 2.2135944 2.2583180 2.1213203 2.2803509 #> 71  2.4698178 2.4899799 2.5099801 2.5099801 2.5099801 2.3874673 2.5298221 #> 72  2.3237900 2.2583180 2.3664319 2.3237900 2.3664319 2.2360680 2.3874673 #> 73  2.6457513 2.5884358 2.6832816 2.6457513 2.6832816 2.5690465 2.7018512 #> 74  2.4494897 2.3874673 2.4899799 2.4494897 2.4899799 2.3664319 2.5099801 #> 75  2.4289916 2.3664319 2.4698178 2.4289916 2.4698178 2.3452079 2.4899799 #> 76  2.4899799 2.4289916 2.5298221 2.4899799 2.5298221 2.4083189 2.5495098 #> 77  2.6457513 2.5884358 2.6832816 2.6457513 2.6832816 2.5690465 2.7018512 #> 78  2.6832816 2.6267851 2.7202941 2.6832816 2.7202941 2.6076810 2.7386128 #> 79  2.4289916 2.3664319 2.4698178 2.4289916 2.4698178 2.3452079 2.4899799 #> 80  2.0976177 2.0248457 2.1447611 2.0976177 2.1447611 2.0000000 2.1679483 #> 81  2.1908902 2.1213203 2.2360680 2.1908902 2.2360680 2.0976177 2.2583180 #> 82  2.1447611 2.0736441 2.1908902 2.1447611 2.1908902 2.0493902 2.2135944 #> 83  2.2360680 2.1679483 2.2803509 2.2360680 2.2803509 2.1447611 2.3021729 #> 84  2.6076810 2.5495098 2.6457513 2.6076810 2.6457513 2.5298221 2.6645825 #> 85  2.2803509 2.2135944 2.3237900 2.2803509 2.3237900 2.1908902 2.3452079 #> 86  2.3452079 2.4494897 2.4698178 2.4698178 2.3874673 2.2583180 2.4083189 #> 87  2.5690465 2.5495098 2.6076810 2.5690465 2.6076810 2.4899799 2.6267851 #> 88  2.5495098 2.4899799 2.5884358 2.5495098 2.5884358 2.4698178 2.6076810 #> 89  2.1908902 2.1213203 2.2360680 2.1908902 2.2360680 2.0976177 2.2583180 #> 90  2.2583180 2.1908902 2.3021729 2.2583180 2.3021729 2.1679483 2.3237900 #> 91  2.3021729 2.2360680 2.3452079 2.3021729 2.3452079 2.2135944 2.3664319 #> 92  2.4289916 2.3664319 2.4698178 2.4289916 2.4698178 2.3452079 2.4899799 #> 93  2.2803509 2.2135944 2.3237900 2.2803509 2.3237900 2.1908902 2.3452079 #> 94  2.0000000 1.8708287 2.0000000 1.9493589 2.0000000 2.0493902 2.0248457 #> 95  2.2803509 2.2135944 2.3237900 2.2803509 2.3237900 2.1908902 2.3452079 #> 96  2.2135944 2.1447611 2.2583180 2.2135944 2.2583180 2.1213203 2.2803509 #> 97  2.2583180 2.1908902 2.3021729 2.2583180 2.3021729 2.1679483 2.3237900 #> 98  2.3874673 2.3237900 2.4289916 2.3874673 2.4289916 2.3021729 2.4494897 #> 99  1.8708287 1.7888544 1.9235384 1.8708287 1.9235384 1.9235384 1.9493589 #> 100 2.2583180 2.1908902 2.3021729 2.2583180 2.3021729 2.1679483 2.3237900 #> 101 2.8809721 2.9325757 2.9495762 2.9495762 2.9154759 2.8106939 2.9325757 #> 102 2.6267851 2.5690465 2.6645825 2.6267851 2.6645825 2.5495098 2.6832816 #> 103 2.9832868 2.9325757 3.0166206 2.9832868 3.0166206 2.9154759 3.0331502 #> 104 2.7568098 2.7018512 2.7928480 2.7568098 2.7928480 2.6832816 2.8106939 #> 105 2.8809721 2.8284271 2.9154759 2.8809721 2.9154759 2.8106939 2.9325757 #> 106 3.1780497 3.1304952 3.2093613 3.1780497 3.2093613 3.1144823 3.2249031 #> 107 2.4083189 2.2583180 2.3664319 2.3237900 2.4083189 2.4494897 2.3874673 #> 108 3.0495901 3.0000000 3.0822070 3.0495901 3.0822070 2.9832868 3.0983867 #> 109 2.9325757 2.8809721 2.9664794 2.9325757 2.9664794 2.8635642 2.9832868 #> 110 3.0331502 3.1464265 3.1622777 3.1622777 3.0331502 2.9325757 3.1144823 #> 111 2.6832816 2.7018512 2.7202941 2.7202941 2.7202941 2.6076810 2.7386128 #> 112 2.7748874 2.7202941 2.8106939 2.7748874 2.8106939 2.7018512 2.8284271 #> 113 2.8635642 2.8106939 2.8982753 2.8635642 2.8982753 2.7928480 2.9154759 #> 114 2.6457513 2.5884358 2.6832816 2.6457513 2.6832816 2.5690465 2.7018512 #> 115 2.7018512 2.6457513 2.7386128 2.7018512 2.7386128 2.6267851 2.7568098 #> 116 2.7568098 2.7748874 2.7928480 2.7928480 2.7928480 2.6832816 2.8106939 #> 117 2.7568098 2.7018512 2.7928480 2.7568098 2.7928480 2.6832816 2.8106939 #> 118 3.1937439 3.3015148 3.3166248 3.3166248 3.1937439 3.0331502 3.2710854 #> 119 3.3316662 3.2863353 3.3615473 3.3316662 3.3615473 3.2710854 3.3763886 #> 120 2.6645825 2.6076810 2.7018512 2.6645825 2.7018512 2.5884358 2.7202941 #> 121 2.9154759 2.9325757 2.9495762 2.9495762 2.9495762 2.8460499 2.9664794 #> 122 2.5495098 2.4899799 2.5884358 2.5495098 2.5884358 2.4698178 2.6076810 #> 123 3.2249031 3.1780497 3.2557641 3.2249031 3.2557641 3.1622777 3.2710854 #> 124 2.6645825 2.6076810 2.7018512 2.6645825 2.7018512 2.5884358 2.7202941 #> 125 2.8284271 2.8809721 2.8982753 2.8982753 2.8635642 2.7568098 2.8809721 #> 126 2.9325757 2.9495762 2.9664794 2.9664794 2.9664794 2.8635642 2.9832868 #> 127 2.6076810 2.5495098 2.6457513 2.6076810 2.6457513 2.5298221 2.6645825 #> 128 2.5690465 2.5099801 2.6076810 2.5690465 2.6076810 2.4899799 2.6267851 #> 129 2.8460499 2.7928480 2.8809721 2.8460499 2.8809721 2.7748874 2.8982753 #> 130 2.8982753 2.8460499 2.9325757 2.8982753 2.9325757 2.8284271 2.9495762 #> 131 3.0659419 3.0166206 3.0983867 3.0659419 3.0983867 3.0000000 3.1144823 #> 132 3.1464265 3.2557641 3.2710854 3.2710854 3.1464265 2.9832868 3.2249031 #> 133 2.8635642 2.8106939 2.8982753 2.8635642 2.8982753 2.7928480 2.9154759 #> 134 2.6267851 2.5690465 2.6645825 2.6267851 2.6645825 2.5495098 2.6832816 #> 135 2.7018512 2.6457513 2.7386128 2.7018512 2.7386128 2.6267851 2.7568098 #> 136 3.1464265 3.0983867 3.1780497 3.1464265 3.1780497 3.0822070 3.1937439 #> 137 2.7748874 2.8635642 2.8809721 2.8809721 2.8106939 2.7018512 2.8284271 #> 138 2.7202941 2.7018512 2.7568098 2.7202941 2.7568098 2.6457513 2.7748874 #> 139 2.5298221 2.4698178 2.5690465 2.5298221 2.5690465 2.4494897 2.5884358 #> 140 2.8460499 2.8284271 2.8809721 2.8460499 2.8809721 2.7748874 2.8982753 #> 141 2.8982753 2.8809721 2.9325757 2.8982753 2.9325757 2.8284271 2.9495762 #> 142 2.8284271 2.8106939 2.8635642 2.8284271 2.8635642 2.7568098 2.8809721 #> 143 2.6267851 2.5690465 2.6645825 2.6267851 2.6645825 2.5495098 2.6832816 #> 144 2.9325757 2.9495762 2.9664794 2.9664794 2.9664794 2.8635642 2.9832868 #> 145 2.8982753 2.9495762 2.9664794 2.9664794 2.9325757 2.8284271 2.9495762 #> 146 2.8284271 2.7748874 2.8635642 2.8284271 2.8635642 2.7568098 2.8809721 #> 147 2.7386128 2.6832816 2.7748874 2.7386128 2.7748874 2.6645825 2.7928480 #> 148 2.7386128 2.6832816 2.7748874 2.7386128 2.7748874 2.6645825 2.7928480 #> 149 2.7018512 2.7928480 2.8106939 2.8106939 2.7386128 2.6267851 2.7568098 #> 150 2.5690465 2.5099801 2.6076810 2.5690465 2.6076810 2.4899799 2.6267851 #>             8         9        10        11        12        13        14 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9   1.0954451                                                             #> 10  0.7071068 0.9486833                                                   #> 11  0.8366600 1.3784049 1.0954451                                         #> 12  0.5477226 1.0488088 0.7745967 1.0000000                               #> 13  0.8944272 0.7745967 0.5477226 1.2247449 0.8366600                     #> 14  1.2649111 0.7745967 1.0488088 1.5165751 1.2247449 0.8944272           #> 15  1.3038405 1.6431677 1.4832397 1.0000000 1.4142136 1.5165751 1.6431677 #> 16  1.3784049 1.7606817 1.5491933 1.0954451 1.4832397 1.6431677 1.8708287 #> 17  1.1401754 1.5165751 1.3416408 0.7745967 1.2649111 1.3784049 1.5811388 #> 18  0.6324555 1.1832160 0.9486833 0.8366600 0.8366600 1.0000000 1.3416408 #> 19  1.1832160 1.6124515 1.3784049 0.8366600 1.2247449 1.4832397 1.7320508 #> 20  0.7745967 1.3416408 1.0488088 0.7071068 0.9486833 1.1832160 1.4832397 #> 21  0.7745967 1.3416408 1.0488088 0.7071068 0.8366600 1.1832160 1.4832397 #> 22  0.7745967 1.3416408 1.0488088 0.7071068 0.9486833 1.1832160 1.4832397 #> 23  1.0488088 1.1401754 1.1832160 1.1832160 1.0000000 1.1401754 1.0488088 #> 24  0.8366600 1.3038405 1.0000000 1.0954451 0.8944272 1.1401754 1.4491377 #> 25  0.7745967 1.1832160 0.9486833 1.1401754 0.5477226 1.0000000 1.3416408 #> 26  0.7071068 0.9486833 0.6324555 1.0954451 0.7745967 0.7071068 1.1401754 #> 27  0.5477226 1.2247449 0.8944272 1.0000000 0.6324555 1.0488088 1.3784049 #> 28  0.5477226 1.2247449 0.8944272 0.6324555 0.7745967 1.0488088 1.3784049 #> 29  0.5477226 1.1401754 0.8944272 0.7745967 0.7745967 0.9486833 1.3038405 #> 30  0.7745967 0.8944272 0.7071068 1.1401754 0.5477226 0.7745967 1.0954451 #> 31  0.7745967 0.8944272 0.5477226 1.1401754 0.5477226 0.6324555 1.0954451 #> 32  0.7745967 1.3416408 1.0488088 0.7071068 0.9486833 1.1832160 1.4832397 #> 33  1.0000000 1.4832397 1.1401754 0.8366600 1.1401754 1.2649111 1.5491933 #> 34  1.1832160 1.5491933 1.3784049 0.8366600 1.3038405 1.4142136 1.6733201 #> 35  0.6324555 0.8944272 0.3162278 1.0488088 0.7071068 0.6324555 1.0954451 #> 36  0.7071068 1.0488088 0.7745967 1.0954451 0.8944272 0.8366600 1.0488088 #> 37  0.8944272 1.3416408 1.1401754 0.7071068 1.0488088 1.1832160 1.4142136 #> 38  0.7071068 1.1401754 0.7745967 0.8944272 0.7745967 0.8366600 1.2247449 #> 39  1.0954451 0.4472136 0.9486833 1.3784049 1.0488088 0.7745967 0.6324555 #> 40  0.3162278 1.1401754 0.7745967 0.7745967 0.6324555 0.9486833 1.3038405 #> 41  0.6324555 1.1832160 0.9486833 0.9486833 0.8366600 1.0000000 1.2649111 #> 42  1.3784049 0.9486833 1.2649111 1.6124515 1.3416408 1.1401754 1.1401754 #> 43  1.0000000 0.6324555 0.9486833 1.3038405 0.9486833 0.8944272 0.7745967 #> 44  0.7745967 1.3416408 1.0488088 1.0488088 0.8366600 1.1832160 1.4832397 #> 45  1.0488088 1.5165751 1.2649111 1.0000000 1.0954451 1.3784049 1.6431677 #> 46  0.8944272 0.7745967 0.7071068 1.2247449 0.8366600 0.4472136 1.0000000 #> 47  0.7745967 1.3416408 1.0488088 0.7071068 0.8366600 1.1832160 1.4832397 #> 48  0.8366600 0.7071068 0.7745967 1.1832160 0.7745967 0.7071068 0.9486833 #> 49  0.7745967 1.3416408 1.0488088 0.3162278 0.9486833 1.1832160 1.4832397 #> 50  0.4472136 1.0000000 0.7071068 0.9486833 0.7071068 0.7745967 1.1832160 #> 51  2.5690465 2.7202941 2.5884358 2.5495098 2.5884358 2.6457513 2.7928480 #> 52  2.4289916 2.5884358 2.4494897 2.4083189 2.4494897 2.5099801 2.6645825 #> 53  2.6267851 2.7386128 2.6076810 2.6076810 2.6457513 2.6645825 2.8106939 #> 54  2.2803509 2.3237900 2.2583180 2.2583180 2.3021729 2.2803509 2.4494897 #> 55  2.5495098 2.5884358 2.5298221 2.5298221 2.5690465 2.5495098 2.7018512 #> 56  2.3237900 2.3664319 2.3021729 2.3021729 2.3452079 2.3237900 2.4899799 #> 57  2.4494897 2.6457513 2.5099801 2.4289916 2.4698178 2.5690465 2.7202941 #> 58  1.9235384 1.9235384 1.8439089 2.0976177 1.8973666 1.8708287 2.0736441 #> 59  2.5099801 2.5495098 2.4899799 2.4899799 2.5298221 2.5099801 2.6645825 #> 60  2.1213203 2.1679483 2.0976177 2.1908902 2.1447611 2.1213203 2.3021729 #> 61  2.0493902 2.0976177 2.0248457 2.2135944 2.0736441 2.0493902 2.2360680 #> 62  2.3021729 2.3874673 2.2803509 2.2803509 2.3237900 2.3021729 2.4698178 #> 63  2.3452079 2.3874673 2.3237900 2.3237900 2.3664319 2.3452079 2.5099801 #> 64  2.4494897 2.4899799 2.4289916 2.4289916 2.4698178 2.4494897 2.6076810 #> 65  2.0736441 2.1213203 2.0493902 2.0493902 2.0976177 2.0736441 2.2583180 #> 66  2.4698178 2.5884358 2.4494897 2.4494897 2.4899799 2.5099801 2.6645825 #> 67  2.3021729 2.3874673 2.2803509 2.2803509 2.3237900 2.3021729 2.4698178 #> 68  2.2135944 2.2583180 2.1908902 2.1908902 2.2360680 2.2135944 2.3874673 #> 69  2.5884358 2.6267851 2.5690465 2.5690465 2.6076810 2.5884358 2.7386128 #> 70  2.1908902 2.2360680 2.1679483 2.1679483 2.2135944 2.1908902 2.3664319 #> 71  2.4494897 2.6076810 2.4698178 2.4289916 2.4698178 2.5298221 2.6832816 #> 72  2.3021729 2.3452079 2.2803509 2.2803509 2.3237900 2.3021729 2.4698178 #> 73  2.6267851 2.6645825 2.6076810 2.6076810 2.6457513 2.6267851 2.7748874 #> 74  2.4289916 2.4698178 2.4083189 2.4083189 2.4494897 2.4289916 2.5884358 #> 75  2.4083189 2.4494897 2.3874673 2.3874673 2.4289916 2.4083189 2.5690465 #> 76  2.4698178 2.5495098 2.4494897 2.4494897 2.4899799 2.4698178 2.6267851 #> 77  2.6267851 2.6645825 2.6076810 2.6076810 2.6457513 2.6267851 2.7748874 #> 78  2.6645825 2.7386128 2.6457513 2.6457513 2.6832816 2.6645825 2.8106939 #> 79  2.4083189 2.4494897 2.3874673 2.3874673 2.4289916 2.4083189 2.5690465 #> 80  2.0736441 2.1213203 2.0493902 2.0493902 2.0976177 2.0736441 2.2583180 #> 81  2.1679483 2.2135944 2.1447611 2.1447611 2.1908902 2.1679483 2.3452079 #> 82  2.1213203 2.1679483 2.0976177 2.0976177 2.1447611 2.1213203 2.3021729 #> 83  2.2135944 2.2583180 2.1908902 2.1908902 2.2360680 2.2135944 2.3874673 #> 84  2.5884358 2.6267851 2.5690465 2.5690465 2.6076810 2.5884358 2.7386128 #> 85  2.2583180 2.3452079 2.2360680 2.2360680 2.2803509 2.2583180 2.4289916 #> 86  2.3237900 2.5690465 2.4289916 2.3021729 2.3452079 2.4899799 2.6457513 #> 87  2.5495098 2.6645825 2.5298221 2.5298221 2.5690465 2.5884358 2.7386128 #> 88  2.5298221 2.5690465 2.5099801 2.5099801 2.5495098 2.5298221 2.6832816 #> 89  2.1679483 2.2583180 2.1447611 2.1447611 2.1908902 2.1679483 2.3452079 #> 90  2.2360680 2.2803509 2.2135944 2.2135944 2.2583180 2.2360680 2.4083189 #> 91  2.2803509 2.3237900 2.2583180 2.2583180 2.3021729 2.2803509 2.4494897 #> 92  2.4083189 2.4899799 2.3874673 2.3874673 2.4289916 2.4083189 2.5690465 #> 93  2.2583180 2.3021729 2.2360680 2.2360680 2.2803509 2.2583180 2.4289916 #> 94  1.9235384 1.9748418 1.8973666 2.0976177 1.9493589 1.9235384 2.1213203 #> 95  2.2583180 2.3021729 2.2360680 2.2360680 2.2803509 2.2583180 2.4289916 #> 96  2.1908902 2.2803509 2.1679483 2.1679483 2.2135944 2.1908902 2.3664319 #> 97  2.2360680 2.2803509 2.2135944 2.2135944 2.2583180 2.2360680 2.4083189 #> 98  2.3664319 2.4083189 2.3452079 2.3452079 2.3874673 2.3664319 2.5298221 #> 99  1.8439089 1.8973666 1.8165902 1.9748418 1.8708287 1.8439089 2.0493902 #> 100 2.2360680 2.2803509 2.2135944 2.2135944 2.2583180 2.2360680 2.4083189 #> 101 2.8635642 3.0331502 2.9154759 2.8460499 2.8809721 2.9664794 3.0983867 #> 102 2.6076810 2.6457513 2.5884358 2.5884358 2.6267851 2.6076810 2.7568098 #> 103 2.9664794 3.0331502 2.9495762 2.9495762 2.9832868 2.9664794 3.0983867 #> 104 2.7386128 2.7748874 2.7202941 2.7202941 2.7568098 2.7386128 2.8809721 #> 105 2.8635642 2.9325757 2.8460499 2.8460499 2.8809721 2.8635642 3.0000000 #> 106 3.1622777 3.2249031 3.1464265 3.1464265 3.1780497 3.1622777 3.2863353 #> 107 2.3452079 2.3452079 2.2803509 2.4899799 2.3237900 2.3021729 2.4698178 #> 108 3.0331502 3.0659419 3.0166206 3.0166206 3.0495901 3.0331502 3.1622777 #> 109 2.9154759 2.9495762 2.8982753 2.8982753 2.9325757 2.9154759 3.0495901 #> 110 3.0495901 3.2403703 3.1304952 2.9664794 3.0659419 3.1780497 3.3015148 #> 111 2.6645825 2.8106939 2.6832816 2.6457513 2.6832816 2.7386128 2.8809721 #> 112 2.7568098 2.7928480 2.7386128 2.7386128 2.7748874 2.7568098 2.8982753 #> 113 2.8460499 2.9154759 2.8284271 2.8284271 2.8635642 2.8460499 2.9832868 #> 114 2.6267851 2.6645825 2.6076810 2.6076810 2.6457513 2.6267851 2.7748874 #> 115 2.6832816 2.7202941 2.6645825 2.6645825 2.7018512 2.6832816 2.8284271 #> 116 2.7386128 2.8809721 2.7568098 2.7202941 2.7568098 2.8106939 2.9495762 #> 117 2.7386128 2.8106939 2.7202941 2.7202941 2.7568098 2.7386128 2.8809721 #> 118 3.2093613 3.3911650 3.2863353 3.0983867 3.2249031 3.3316662 3.4496377 #> 119 3.3166248 3.3466401 3.3015148 3.3015148 3.3316662 3.3166248 3.4351128 #> 120 2.6457513 2.6832816 2.6267851 2.6267851 2.6645825 2.6457513 2.7928480 #> 121 2.8982753 3.0331502 2.9154759 2.8809721 2.9154759 2.9664794 3.0983867 #> 122 2.5298221 2.5690465 2.5099801 2.5099801 2.5495098 2.5298221 2.6832816 #> 123 3.2093613 3.2403703 3.1937439 3.1937439 3.2249031 3.2093613 3.3316662 #> 124 2.6457513 2.6832816 2.6267851 2.6267851 2.6645825 2.6457513 2.7928480 #> 125 2.8106939 2.9832868 2.8635642 2.7928480 2.8284271 2.9154759 3.0495901 #> 126 2.9154759 3.0495901 2.9325757 2.8982753 2.9325757 2.9832868 3.1144823 #> 127 2.5884358 2.6267851 2.5690465 2.5690465 2.6076810 2.5884358 2.7386128 #> 128 2.5495098 2.6267851 2.5298221 2.5298221 2.5690465 2.5495098 2.7018512 #> 129 2.8284271 2.8635642 2.8106939 2.8106939 2.8460499 2.8284271 2.9664794 #> 130 2.8809721 2.9495762 2.8635642 2.8635642 2.8982753 2.8809721 3.0166206 #> 131 3.0495901 3.0822070 3.0331502 3.0331502 3.0659419 3.0495901 3.1780497 #> 132 3.1622777 3.3466401 3.2403703 3.0495901 3.1780497 3.2863353 3.4058773 #> 133 2.8460499 2.8809721 2.8284271 2.8284271 2.8635642 2.8460499 2.9832868 #> 134 2.6076810 2.6457513 2.5884358 2.5884358 2.6267851 2.6076810 2.7568098 #> 135 2.6832816 2.7202941 2.6645825 2.6645825 2.7018512 2.6832816 2.8284271 #> 136 3.1304952 3.1937439 3.1144823 3.1144823 3.1464265 3.1304952 3.2557641 #> 137 2.7568098 2.9664794 2.8460499 2.7386128 2.7748874 2.8982753 3.0331502 #> 138 2.7018512 2.8106939 2.6832816 2.6832816 2.7202941 2.7386128 2.8809721 #> 139 2.5099801 2.5884358 2.4899799 2.4899799 2.5298221 2.5099801 2.6645825 #> 140 2.8284271 2.9325757 2.8106939 2.8106939 2.8460499 2.8635642 3.0000000 #> 141 2.8809721 2.9832868 2.8635642 2.8635642 2.8982753 2.9154759 3.0495901 #> 142 2.8106939 2.9154759 2.7928480 2.7928480 2.8284271 2.8460499 2.9832868 #> 143 2.6076810 2.6457513 2.5884358 2.5884358 2.6267851 2.6076810 2.7568098 #> 144 2.9154759 3.0495901 2.9325757 2.8982753 2.9325757 2.9832868 3.1144823 #> 145 2.8809721 3.0495901 2.9325757 2.8635642 2.8982753 2.9832868 3.1144823 #> 146 2.8106939 2.8809721 2.7928480 2.7928480 2.8284271 2.8106939 2.9495762 #> 147 2.7202941 2.7568098 2.7018512 2.7018512 2.7386128 2.7202941 2.8635642 #> 148 2.7202941 2.7928480 2.7018512 2.7018512 2.7386128 2.7202941 2.8635642 #> 149 2.6832816 2.8982753 2.7748874 2.6645825 2.7018512 2.8284271 2.9664794 #> 150 2.5495098 2.6267851 2.5298221 2.5298221 2.5690465 2.5495098 2.7018512 #>            15        16        17        18        19        20        21 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16  1.0000000                                                             #> 17  0.8944272 1.0000000                                                   #> 18  1.2247449 1.3038405 0.9486833                                         #> 19  0.9486833 0.9486833 0.9486833 1.0954451                               #> 20  1.1401754 1.1401754 0.8366600 0.6324555 0.8944272                     #> 21  1.2247449 1.3038405 1.0488088 0.8944272 0.8944272 1.0000000           #> 22  1.2247449 1.1401754 0.8366600 0.6324555 1.0000000 0.4472136 1.0000000 #> 23  1.3416408 1.6124515 1.2649111 1.0488088 1.4491377 1.1401754 1.3038405 #> 24  1.4832397 1.4142136 1.1832160 0.8366600 1.1401754 0.9486833 0.8366600 #> 25  1.5165751 1.5811388 1.3784049 1.0000000 1.2649111 1.0954451 0.8944272 #> 26  1.4832397 1.5491933 1.3416408 0.9486833 1.3038405 1.0488088 0.9486833 #> 27  1.4142136 1.3416408 1.0954451 0.7071068 1.1401754 0.8366600 0.8366600 #> 28  1.1832160 1.2649111 1.0000000 0.5477226 1.0488088 0.7071068 0.7071068 #> 29  1.1832160 1.3416408 1.0000000 0.5477226 1.1401754 0.8366600 0.7071068 #> 30  1.5165751 1.5811388 1.3784049 1.0000000 1.3416408 1.0954451 1.0000000 #> 31  1.5165751 1.5811388 1.3784049 1.0000000 1.3416408 1.0954451 1.0000000 #> 32  1.2247449 1.1401754 0.8366600 0.7745967 1.0000000 0.8944272 0.6324555 #> 33  1.0488088 1.0488088 0.9486833 1.0000000 1.0954451 0.7745967 1.0954451 #> 34  0.8366600 0.8366600 0.8366600 1.0954451 1.0000000 1.0000000 1.0954451 #> 35  1.4491377 1.5165751 1.3038405 0.8944272 1.3416408 1.0000000 1.0000000 #> 36  1.2649111 1.5491933 1.1832160 0.8366600 1.3784049 1.0488088 1.0488088 #> 37  0.9486833 1.2247449 0.8366600 0.7745967 1.0000000 1.0000000 0.7745967 #> 38  1.2649111 1.4142136 1.0954451 0.7071068 1.2247449 0.8366600 1.0488088 #> 39  1.5811388 1.7606817 1.4491377 1.1832160 1.6124515 1.3416408 1.3416408 #> 40  1.2649111 1.3416408 1.0954451 0.5477226 1.1401754 0.7071068 0.7071068 #> 41  1.2247449 1.3784049 0.9486833 0.4472136 1.1832160 0.7745967 1.0000000 #> 42  1.7888544 1.8973666 1.6124515 1.3784049 1.7606817 1.5165751 1.5811388 #> 43  1.5165751 1.7029386 1.3784049 1.0954451 1.5491933 1.2649111 1.2649111 #> 44  1.4491377 1.3784049 1.1401754 0.7745967 1.1832160 0.8944272 1.0000000 #> 45  1.3416408 1.2649111 1.0000000 0.9486833 0.9486833 0.7071068 1.0488088 #> 46  1.5165751 1.5811388 1.3038405 0.8944272 1.4142136 1.0954451 1.1832160 #> 47  1.1401754 1.2247449 0.9486833 0.7745967 0.8944272 0.4472136 0.8944272 #> 48  1.4832397 1.6124515 1.3416408 0.9486833 1.4491377 1.1401754 1.1401754 #> 49  1.0488088 1.1401754 0.8366600 0.7745967 0.8944272 0.6324555 0.7745967 #> 50  1.3038405 1.4491377 1.1401754 0.6324555 1.2649111 0.8944272 0.8944272 #> 51  2.5884358 2.5884358 2.5884358 2.5690465 2.4494897 2.6076810 2.4494897 #> 52  2.4494897 2.4494897 2.4494897 2.4289916 2.3021729 2.4698178 2.3021729 #> 53  2.6457513 2.6457513 2.6457513 2.6267851 2.5099801 2.6645825 2.5099801 #> 54  2.4289916 2.3874673 2.3021729 2.2803509 2.2360680 2.3237900 2.1447611 #> 55  2.5690465 2.5690465 2.5690465 2.5495098 2.4289916 2.5884358 2.4289916 #> 56  2.3874673 2.3452079 2.3452079 2.3237900 2.1908902 2.3664319 2.1908902 #> 57  2.4698178 2.4698178 2.4698178 2.4494897 2.3237900 2.4899799 2.3237900 #> 58  2.3237900 2.2803509 2.1447611 1.9748418 2.1213203 2.0248457 1.9748418 #> 59  2.5298221 2.5298221 2.5298221 2.5099801 2.3874673 2.5495098 2.3874673 #> 60  2.4083189 2.3664319 2.2360680 2.1213203 2.2135944 2.1679483 2.0736441 #> 61  2.4289916 2.3874673 2.2583180 2.0976177 2.2360680 2.1447611 2.0976177 #> 62  2.3237900 2.3237900 2.3237900 2.3021729 2.1679483 2.3452079 2.1679483 #> 63  2.3664319 2.3664319 2.3664319 2.3452079 2.2135944 2.3874673 2.2135944 #> 64  2.4698178 2.4698178 2.4698178 2.4494897 2.3237900 2.4899799 2.3237900 #> 65  2.1908902 2.1447611 2.0976177 2.0736441 1.9748418 2.1213203 1.9235384 #> 66  2.4899799 2.4899799 2.4899799 2.4698178 2.3452079 2.5099801 2.3452079 #> 67  2.4083189 2.3664319 2.3237900 2.3021729 2.2135944 2.3452079 2.1679483 #> 68  2.2360680 2.2360680 2.2360680 2.2135944 2.0736441 2.2583180 2.0736441 #> 69  2.6076810 2.6076810 2.6076810 2.5884358 2.4698178 2.6267851 2.4698178 #> 70  2.3021729 2.2583180 2.2135944 2.1908902 2.0976177 2.2360680 2.0493902 #> 71  2.4698178 2.4698178 2.4698178 2.4494897 2.3237900 2.4899799 2.3237900 #> 72  2.3237900 2.3237900 2.3237900 2.3021729 2.1679483 2.3452079 2.1679483 #> 73  2.6457513 2.6457513 2.6457513 2.6267851 2.5099801 2.6645825 2.5099801 #> 74  2.4494897 2.4494897 2.4494897 2.4289916 2.3021729 2.4698178 2.3021729 #> 75  2.4289916 2.4289916 2.4289916 2.4083189 2.2803509 2.4494897 2.2803509 #> 76  2.4899799 2.4899799 2.4899799 2.4698178 2.3452079 2.5099801 2.3452079 #> 77  2.6457513 2.6457513 2.6457513 2.6267851 2.5099801 2.6645825 2.5099801 #> 78  2.6832816 2.6832816 2.6832816 2.6645825 2.5495098 2.7018512 2.5495098 #> 79  2.4289916 2.4289916 2.4289916 2.4083189 2.2803509 2.4494897 2.2803509 #> 80  2.1447611 2.0976177 2.0976177 2.0736441 1.9235384 2.1213203 1.9235384 #> 81  2.3237900 2.2803509 2.1908902 2.1679483 2.1213203 2.2135944 2.0248457 #> 82  2.2803509 2.2360680 2.1447611 2.1213203 2.0736441 2.1679483 1.9748418 #> 83  2.2360680 2.2360680 2.2360680 2.2135944 2.0736441 2.2583180 2.0736441 #> 84  2.6076810 2.6076810 2.6076810 2.5884358 2.4698178 2.6267851 2.4698178 #> 85  2.4494897 2.4083189 2.2803509 2.2583180 2.2583180 2.3021729 2.1213203 #> 86  2.3452079 2.3452079 2.3452079 2.3237900 2.1908902 2.3664319 2.1908902 #> 87  2.5690465 2.5690465 2.5690465 2.5495098 2.4289916 2.5884358 2.4289916 #> 88  2.5495098 2.5495098 2.5495098 2.5298221 2.4083189 2.5690465 2.4083189 #> 89  2.2803509 2.2360680 2.1908902 2.1679483 2.0736441 2.2135944 2.0248457 #> 90  2.3874673 2.3452079 2.2583180 2.2360680 2.1908902 2.2803509 2.0976177 #> 91  2.4289916 2.3874673 2.3021729 2.2803509 2.2360680 2.3237900 2.1447611 #> 92  2.4289916 2.4289916 2.4289916 2.4083189 2.2803509 2.4494897 2.2803509 #> 93  2.2803509 2.2803509 2.2803509 2.2583180 2.1213203 2.3021729 2.1213203 #> 94  2.3237900 2.2803509 2.1447611 1.9748418 2.1213203 2.0248457 1.9748418 #> 95  2.3664319 2.3237900 2.2803509 2.2583180 2.1679483 2.3021729 2.1213203 #> 96  2.2583180 2.2135944 2.2135944 2.1908902 2.0493902 2.2360680 2.0493902 #> 97  2.3021729 2.2583180 2.2583180 2.2360680 2.0976177 2.2803509 2.0976177 #> 98  2.3874673 2.3874673 2.3874673 2.3664319 2.2360680 2.4083189 2.2360680 #> 99  2.2135944 2.1679483 2.0248457 1.8439089 2.0000000 1.8973666 1.8439089 #> 100 2.3021729 2.2583180 2.2583180 2.2360680 2.0976177 2.2803509 2.0976177 #> 101 2.8809721 2.8809721 2.8809721 2.8635642 2.7568098 2.8982753 2.7568098 #> 102 2.6267851 2.6267851 2.6267851 2.6076810 2.4899799 2.6457513 2.4899799 #> 103 2.9832868 2.9832868 2.9832868 2.9664794 2.8635642 3.0000000 2.8635642 #> 104 2.7568098 2.7568098 2.7568098 2.7386128 2.6267851 2.7748874 2.6267851 #> 105 2.8809721 2.8809721 2.8809721 2.8635642 2.7568098 2.8982753 2.7568098 #> 106 3.1780497 3.1780497 3.1780497 3.1622777 3.0659419 3.1937439 3.0659419 #> 107 2.6832816 2.6457513 2.5298221 2.3874673 2.5099801 2.4289916 2.3874673 #> 108 3.0495901 3.0495901 3.0495901 3.0331502 2.9325757 3.0659419 2.9325757 #> 109 2.9325757 2.9325757 2.9325757 2.9154759 2.8106939 2.9495762 2.8106939 #> 110 3.0000000 3.0000000 3.0000000 3.0166206 2.8809721 3.0166206 2.9495762 #> 111 2.6832816 2.6832816 2.6832816 2.6645825 2.5495098 2.7018512 2.5495098 #> 112 2.7748874 2.7748874 2.7748874 2.7568098 2.6457513 2.7928480 2.6457513 #> 113 2.8635642 2.8635642 2.8635642 2.8460499 2.7386128 2.8809721 2.7386128 #> 114 2.6832816 2.6457513 2.6457513 2.6267851 2.5099801 2.6645825 2.5099801 #> 115 2.7018512 2.7018512 2.7018512 2.6832816 2.5690465 2.7202941 2.5690465 #> 116 2.7568098 2.7568098 2.7568098 2.7386128 2.6267851 2.7748874 2.6267851 #> 117 2.7568098 2.7568098 2.7568098 2.7386128 2.6267851 2.7748874 2.6267851 #> 118 3.0983867 3.0983867 3.0983867 3.1780497 2.9832868 3.1144823 3.1144823 #> 119 3.3316662 3.3316662 3.3316662 3.3166248 3.2249031 3.3466401 3.2249031 #> 120 2.6645825 2.6645825 2.6645825 2.6457513 2.5298221 2.6832816 2.5298221 #> 121 2.9154759 2.9154759 2.9154759 2.8982753 2.7928480 2.9325757 2.7928480 #> 122 2.6267851 2.5884358 2.5495098 2.5298221 2.4494897 2.5690465 2.4083189 #> 123 3.2249031 3.2249031 3.2249031 3.2093613 3.1144823 3.2403703 3.1144823 #> 124 2.6645825 2.6645825 2.6645825 2.6457513 2.5298221 2.6832816 2.5298221 #> 125 2.8284271 2.8284271 2.8284271 2.8106939 2.7018512 2.8460499 2.7018512 #> 126 2.9325757 2.9325757 2.9325757 2.9154759 2.8106939 2.9495762 2.8106939 #> 127 2.6076810 2.6076810 2.6076810 2.5884358 2.4698178 2.6267851 2.4698178 #> 128 2.5690465 2.5690465 2.5690465 2.5495098 2.4289916 2.5884358 2.4289916 #> 129 2.8460499 2.8460499 2.8460499 2.8284271 2.7202941 2.8635642 2.7202941 #> 130 2.8982753 2.8982753 2.8982753 2.8809721 2.7748874 2.9154759 2.7748874 #> 131 3.0659419 3.0659419 3.0659419 3.0495901 2.9495762 3.0822070 2.9495762 #> 132 3.0495901 3.0495901 3.0495901 3.1304952 2.9325757 3.0659419 3.0659419 #> 133 2.8635642 2.8635642 2.8635642 2.8460499 2.7386128 2.8809721 2.7386128 #> 134 2.6267851 2.6267851 2.6267851 2.6076810 2.4899799 2.6457513 2.4899799 #> 135 2.7018512 2.7018512 2.7018512 2.6832816 2.5690465 2.7202941 2.5690465 #> 136 3.1464265 3.1464265 3.1464265 3.1304952 3.0331502 3.1622777 3.0331502 #> 137 2.7748874 2.7748874 2.7748874 2.7568098 2.6457513 2.7928480 2.6457513 #> 138 2.7202941 2.7202941 2.7202941 2.7018512 2.5884358 2.7386128 2.5884358 #> 139 2.5298221 2.5298221 2.5298221 2.5099801 2.3874673 2.5495098 2.3874673 #> 140 2.8460499 2.8460499 2.8460499 2.8284271 2.7202941 2.8635642 2.7202941 #> 141 2.8982753 2.8982753 2.8982753 2.8809721 2.7748874 2.9154759 2.7748874 #> 142 2.8284271 2.8284271 2.8284271 2.8106939 2.7018512 2.8460499 2.7018512 #> 143 2.6267851 2.6267851 2.6267851 2.6076810 2.4899799 2.6457513 2.4899799 #> 144 2.9325757 2.9325757 2.9325757 2.9154759 2.8106939 2.9495762 2.8106939 #> 145 2.8982753 2.8982753 2.8982753 2.8809721 2.7748874 2.9154759 2.7748874 #> 146 2.8284271 2.8284271 2.8284271 2.8106939 2.7018512 2.8460499 2.7018512 #> 147 2.7386128 2.7386128 2.7386128 2.7202941 2.6076810 2.7568098 2.6076810 #> 148 2.7386128 2.7386128 2.7386128 2.7202941 2.6076810 2.7568098 2.6076810 #> 149 2.7018512 2.7018512 2.7018512 2.6832816 2.5690465 2.7202941 2.5690465 #> 150 2.5690465 2.5690465 2.5690465 2.5495098 2.4289916 2.5884358 2.4289916 #>            22        23        24        25        26        27        28 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23  1.1401754                                                             #> 24  0.8366600 1.3416408                                                   #> 25  1.0954451 1.1401754 0.9486833                                         #> 26  1.0488088 1.2649111 0.8944272 0.9486833                               #> 27  0.7071068 1.1832160 0.6324555 0.8366600 0.7745967                     #> 28  0.7071068 1.0954451 0.8944272 0.9486833 0.8944272 0.7745967           #> 29  0.8366600 1.0954451 0.8944272 0.9486833 0.8944272 0.7745967 0.4472136 #> 30  1.0954451 1.0488088 0.9486833 0.7745967 0.7071068 0.8366600 0.9486833 #> 31  1.0954451 1.1401754 0.9486833 0.7745967 0.5477226 0.8366600 0.9486833 #> 32  0.7745967 1.3038405 0.8366600 1.0954451 1.0488088 0.7071068 0.7071068 #> 33  0.8944272 1.3038405 1.2247449 1.2649111 1.2247449 1.1401754 0.8366600 #> 34  1.0954451 1.3784049 1.3784049 1.4142136 1.3784049 1.3038405 1.0488088 #> 35  1.0000000 1.1401754 0.9486833 0.8944272 0.5477226 0.8366600 0.8366600 #> 36  1.0488088 1.0000000 1.0000000 1.0488088 0.7745967 0.8944272 0.8944272 #> 37  1.0000000 1.1401754 1.1401754 1.1832160 1.1401754 1.0488088 0.7071068 #> 38  0.8366600 0.8944272 1.0954451 0.9486833 1.0000000 0.8944272 0.7745967 #> 39  1.3416408 1.0488088 1.3038405 1.1832160 0.9486833 1.2247449 1.2247449 #> 40  0.7071068 1.0954451 0.7745967 0.8366600 0.7745967 0.6324555 0.4472136 #> 41  0.7745967 0.9486833 0.9486833 1.0000000 0.9486833 0.7071068 0.7071068 #> 42  1.5165751 1.3416408 1.4832397 1.4491377 1.2649111 1.4142136 1.4832397 #> 43  1.2649111 0.9486833 1.2247449 1.0954451 1.0488088 1.1401754 1.1401754 #> 44  0.7745967 1.2247449 0.7071068 1.0000000 0.9486833 0.5477226 0.8366600 #> 45  0.7071068 1.3416408 0.8944272 0.9486833 1.1832160 0.8944272 1.0000000 #> 46  1.0954451 1.1401754 1.0488088 1.0000000 0.7071068 0.9486833 1.0488088 #> 47  0.6324555 1.1401754 0.9486833 1.0000000 0.9486833 0.8366600 0.7071068 #> 48  1.1401754 0.8944272 1.0954451 0.9486833 0.8944272 1.0000000 1.0000000 #> 49  0.6324555 1.1401754 1.0488088 1.0954451 1.0488088 0.9486833 0.5477226 #> 50  0.8944272 1.0488088 0.8366600 0.8944272 0.7071068 0.7071068 0.7071068 #> 51  2.5690465 2.7748874 2.4289916 2.5298221 2.5495098 2.5099801 2.5495098 #> 52  2.4289916 2.6457513 2.2803509 2.3874673 2.4083189 2.3664319 2.4083189 #> 53  2.6267851 2.8284271 2.4899799 2.5884358 2.5690465 2.5690465 2.6076810 #> 54  2.2803509 2.5099801 2.1213203 2.2360680 2.1679483 2.2135944 2.2583180 #> 55  2.5495098 2.7568098 2.4083189 2.5099801 2.4494897 2.4899799 2.5298221 #> 56  2.3237900 2.5495098 2.1679483 2.2803509 2.2135944 2.2583180 2.3021729 #> 57  2.4494897 2.6645825 2.3021729 2.4083189 2.4698178 2.3874673 2.4289916 #> 58  1.9748418 2.1447611 1.7888544 1.8165902 1.7888544 1.8439089 2.0000000 #> 59  2.5099801 2.7202941 2.3664319 2.4698178 2.4083189 2.4494897 2.4899799 #> 60  2.1213203 2.3664319 1.9493589 2.0736441 2.0000000 2.0493902 2.0976177 #> 61  2.0976177 2.3021729 1.9235384 2.0000000 1.9235384 1.9748418 2.1213203 #> 62  2.3021729 2.5298221 2.1447611 2.2583180 2.1908902 2.2360680 2.2803509 #> 63  2.3452079 2.5690465 2.1908902 2.3021729 2.2360680 2.2803509 2.3237900 #> 64  2.4494897 2.6645825 2.3021729 2.4083189 2.3452079 2.3874673 2.4289916 #> 65  2.0736441 2.3237900 1.8973666 2.0248457 1.9493589 2.0000000 2.0493902 #> 66  2.4698178 2.6832816 2.3237900 2.4289916 2.4083189 2.4083189 2.4494897 #> 67  2.3021729 2.5298221 2.1447611 2.2583180 2.1908902 2.2360680 2.2803509 #> 68  2.2135944 2.4494897 2.0493902 2.1679483 2.0976177 2.1447611 2.1908902 #> 69  2.5884358 2.7928480 2.4494897 2.5495098 2.4899799 2.5298221 2.5690465 #> 70  2.1908902 2.4289916 2.0248457 2.1447611 2.0736441 2.1213203 2.1679483 #> 71  2.4494897 2.6645825 2.3021729 2.4083189 2.4289916 2.3874673 2.4289916 #> 72  2.3021729 2.5298221 2.1447611 2.2583180 2.1908902 2.2360680 2.2803509 #> 73  2.6267851 2.8284271 2.4899799 2.5884358 2.5298221 2.5690465 2.6076810 #> 74  2.4289916 2.6457513 2.2803509 2.3874673 2.3237900 2.3664319 2.4083189 #> 75  2.4083189 2.6267851 2.2583180 2.3664319 2.3021729 2.3452079 2.3874673 #> 76  2.4698178 2.6832816 2.3237900 2.4289916 2.3664319 2.4083189 2.4494897 #> 77  2.6267851 2.8284271 2.4899799 2.5884358 2.5298221 2.5690465 2.6076810 #> 78  2.6645825 2.8635642 2.5298221 2.6267851 2.5690465 2.6076810 2.6457513 #> 79  2.4083189 2.6267851 2.2583180 2.3664319 2.3021729 2.3452079 2.3874673 #> 80  2.0736441 2.3237900 1.8973666 2.0248457 1.9493589 2.0000000 2.0493902 #> 81  2.1679483 2.4083189 2.0000000 2.1213203 2.0493902 2.0976177 2.1447611 #> 82  2.1213203 2.3664319 1.9493589 2.0736441 2.0000000 2.0493902 2.0976177 #> 83  2.2135944 2.4494897 2.0493902 2.1679483 2.0976177 2.1447611 2.1908902 #> 84  2.5884358 2.7928480 2.4494897 2.5495098 2.4899799 2.5298221 2.5690465 #> 85  2.2583180 2.4899799 2.0976177 2.2135944 2.1447611 2.1908902 2.2360680 #> 86  2.3237900 2.5495098 2.2135944 2.2803509 2.3874673 2.2583180 2.3021729 #> 87  2.5495098 2.7568098 2.4083189 2.5099801 2.4899799 2.4899799 2.5298221 #> 88  2.5298221 2.7386128 2.3874673 2.4899799 2.4289916 2.4698178 2.5099801 #> 89  2.1679483 2.4083189 2.0000000 2.1213203 2.0493902 2.0976177 2.1447611 #> 90  2.2360680 2.4698178 2.0736441 2.1908902 2.1213203 2.1679483 2.2135944 #> 91  2.2803509 2.5099801 2.1213203 2.2360680 2.1679483 2.2135944 2.2583180 #> 92  2.4083189 2.6267851 2.2583180 2.3664319 2.3021729 2.3452079 2.3874673 #> 93  2.2583180 2.4899799 2.0976177 2.2135944 2.1447611 2.1908902 2.2360680 #> 94  1.9748418 2.1908902 1.7888544 1.8708287 1.7888544 1.8439089 2.0000000 #> 95  2.2583180 2.4899799 2.0976177 2.2135944 2.1447611 2.1908902 2.2360680 #> 96  2.1908902 2.4289916 2.0248457 2.1447611 2.0736441 2.1213203 2.1679483 #> 97  2.2360680 2.4698178 2.0736441 2.1908902 2.1213203 2.1679483 2.2135944 #> 98  2.3664319 2.5884358 2.2135944 2.3237900 2.2583180 2.3021729 2.3452079 #> 99  1.8439089 2.1213203 1.6431677 1.7888544 1.7029386 1.7606817 1.8708287 #> 100 2.2360680 2.4698178 2.0736441 2.1908902 2.1213203 2.1679483 2.2135944 #> 101 2.8635642 3.0495901 2.7386128 2.8284271 2.8809721 2.8106939 2.8460499 #> 102 2.6076810 2.8106939 2.4698178 2.5690465 2.5099801 2.5495098 2.5884358 #> 103 2.9664794 3.1464265 2.8460499 2.9325757 2.8809721 2.9154759 2.9495762 #> 104 2.7386128 2.9325757 2.6076810 2.7018512 2.6457513 2.6832816 2.7202941 #> 105 2.8635642 3.0495901 2.7386128 2.8284271 2.7748874 2.8106939 2.8460499 #> 106 3.1622777 3.3316662 3.0495901 3.1304952 3.0822070 3.1144823 3.1464265 #> 107 2.3874673 2.5298221 2.2360680 2.2583180 2.2360680 2.2803509 2.4083189 #> 108 3.0331502 3.2093613 2.9154759 3.0000000 2.9495762 2.9832868 3.0166206 #> 109 2.9154759 3.0983867 2.7928480 2.8809721 2.8284271 2.8635642 2.8982753 #> 110 2.9832868 3.1622777 2.9664794 3.0166206 3.0983867 3.0000000 3.0000000 #> 111 2.6645825 2.8635642 2.5298221 2.6267851 2.6457513 2.6076810 2.6457513 #> 112 2.7568098 2.9495762 2.6267851 2.7202941 2.6645825 2.7018512 2.7386128 #> 113 2.8460499 3.0331502 2.7202941 2.8106939 2.7568098 2.7928480 2.8284271 #> 114 2.6267851 2.8284271 2.4899799 2.5884358 2.5298221 2.5690465 2.6076810 #> 115 2.6832816 2.8809721 2.5495098 2.6457513 2.5884358 2.6267851 2.6645825 #> 116 2.7386128 2.9325757 2.6076810 2.7018512 2.7202941 2.6832816 2.7202941 #> 117 2.7386128 2.9325757 2.6076810 2.7018512 2.6457513 2.6832816 2.7202941 #> 118 3.1144823 3.3166248 3.1304952 3.1780497 3.2557641 3.1622777 3.1622777 #> 119 3.3166248 3.4785054 3.2093613 3.2863353 3.2403703 3.2710854 3.3015148 #> 120 2.6457513 2.8460499 2.5099801 2.6076810 2.5495098 2.5884358 2.6267851 #> 121 2.8982753 3.0822070 2.7748874 2.8635642 2.8809721 2.8460499 2.8809721 #> 122 2.5298221 2.7386128 2.3874673 2.4899799 2.4289916 2.4698178 2.5099801 #> 123 3.2093613 3.3763886 3.0983867 3.1780497 3.1304952 3.1622777 3.1937439 #> 124 2.6457513 2.8460499 2.5099801 2.6076810 2.5495098 2.5884358 2.6267851 #> 125 2.8106939 3.0000000 2.6832816 2.7748874 2.8284271 2.7568098 2.7928480 #> 126 2.9154759 3.0983867 2.7928480 2.8809721 2.8982753 2.8635642 2.8982753 #> 127 2.5884358 2.7928480 2.4494897 2.5495098 2.4899799 2.5298221 2.5690465 #> 128 2.5495098 2.7568098 2.4083189 2.5099801 2.4494897 2.4899799 2.5298221 #> 129 2.8284271 3.0166206 2.7018512 2.7928480 2.7386128 2.7748874 2.8106939 #> 130 2.8809721 3.0659419 2.7568098 2.8460499 2.7928480 2.8284271 2.8635642 #> 131 3.0495901 3.2249031 2.9325757 3.0166206 2.9664794 3.0000000 3.0331502 #> 132 3.0659419 3.2710854 3.0822070 3.1304952 3.2093613 3.1144823 3.1144823 #> 133 2.8460499 3.0331502 2.7202941 2.8106939 2.7568098 2.7928480 2.8284271 #> 134 2.6076810 2.8106939 2.4698178 2.5690465 2.5099801 2.5495098 2.5884358 #> 135 2.6832816 2.8809721 2.5495098 2.6457513 2.5884358 2.6267851 2.6645825 #> 136 3.1304952 3.3015148 3.0166206 3.0983867 3.0495901 3.0822070 3.1144823 #> 137 2.7568098 2.9495762 2.6645825 2.7202941 2.8106939 2.7018512 2.7386128 #> 138 2.7018512 2.8982753 2.5690465 2.6645825 2.6457513 2.6457513 2.6832816 #> 139 2.5099801 2.7202941 2.3664319 2.4698178 2.4083189 2.4494897 2.4899799 #> 140 2.8284271 3.0166206 2.7018512 2.7928480 2.7748874 2.7748874 2.8106939 #> 141 2.8809721 3.0659419 2.7568098 2.8460499 2.8284271 2.8284271 2.8635642 #> 142 2.8106939 3.0000000 2.6832816 2.7748874 2.7568098 2.7568098 2.7928480 #> 143 2.6076810 2.8106939 2.4698178 2.5690465 2.5099801 2.5495098 2.5884358 #> 144 2.9154759 3.0983867 2.7928480 2.8809721 2.8982753 2.8635642 2.8982753 #> 145 2.8809721 3.0659419 2.7568098 2.8460499 2.8982753 2.8284271 2.8635642 #> 146 2.8106939 3.0000000 2.6832816 2.7748874 2.7202941 2.7568098 2.7928480 #> 147 2.7202941 2.9154759 2.5884358 2.6832816 2.6267851 2.6645825 2.7018512 #> 148 2.7202941 2.9154759 2.5884358 2.6832816 2.6267851 2.6645825 2.7018512 #> 149 2.6832816 2.8809721 2.5884358 2.6457513 2.7386128 2.6267851 2.6645825 #> 150 2.5495098 2.7568098 2.4083189 2.5099801 2.4494897 2.4899799 2.5298221 #>            29        30        31        32        33        34        35 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30  0.9486833                                                             #> 31  0.9486833 0.4472136                                                   #> 32  0.7071068 1.0954451 1.0954451                                         #> 33  0.9486833 1.2649111 1.2649111 1.0954451                               #> 34  1.0488088 1.4142136 1.4142136 1.0954451 0.7745967                     #> 35  0.8366600 0.6324555 0.4472136 1.0000000 1.1832160 1.3416408           #> 36  0.7745967 0.8366600 0.8366600 1.0488088 1.2247449 1.3038405 0.7071068 #> 37  0.7071068 1.1832160 1.1832160 0.7745967 1.0954451 0.8944272 1.0954451 #> 38  0.7745967 0.9486833 0.9486833 1.0488088 0.9486833 1.1401754 0.8366600 #> 39  1.1401754 0.8944272 0.8944272 1.3416408 1.4832397 1.5491933 0.8944272 #> 40  0.4472136 0.8366600 0.8366600 0.7071068 0.9486833 1.1401754 0.7071068 #> 41  0.7071068 1.0000000 1.0000000 0.8944272 1.0954451 1.1832160 0.8944272 #> 42  1.4142136 1.2247449 1.2247449 1.5165751 1.7029386 1.7606817 1.2247449 #> 43  1.0488088 0.7745967 0.8944272 1.2649111 1.4142136 1.4832397 0.8944272 #> 44  0.9486833 1.0000000 1.0000000 0.8944272 1.1832160 1.3416408 1.0000000 #> 45  1.0954451 1.2247449 1.2247449 1.0488088 1.0488088 1.2247449 1.2247449 #> 46  0.9486833 0.7745967 0.6324555 1.0954451 1.3416408 1.4142136 0.6324555 #> 47  0.8366600 1.0000000 1.0000000 1.0000000 0.7745967 1.0000000 1.0000000 #> 48  0.8944272 0.5477226 0.7071068 1.1401754 1.3038405 1.3784049 0.7071068 #> 49  0.7071068 1.0954451 1.0954451 0.7745967 0.7745967 0.8944272 1.0000000 #> 50  0.5477226 0.7745967 0.7745967 0.8944272 1.0954451 1.1832160 0.6324555 #> 51  2.5495098 2.5690465 2.5690465 2.4494897 2.6832816 2.6457513 2.5690465 #> 52  2.4083189 2.4289916 2.4289916 2.3021729 2.5495098 2.5099801 2.4289916 #> 53  2.6076810 2.6267851 2.5884358 2.5099801 2.7386128 2.7018512 2.5884358 #> 54  2.2583180 2.2803509 2.2360680 2.1447611 2.4083189 2.3664319 2.2360680 #> 55  2.5298221 2.5495098 2.5099801 2.4289916 2.6645825 2.6267851 2.5099801 #> 56  2.3021729 2.3237900 2.2803509 2.1908902 2.4494897 2.4083189 2.2803509 #> 57  2.4289916 2.4899799 2.4899799 2.3237900 2.5690465 2.5298221 2.4899799 #> 58  2.0000000 1.8708287 1.8165902 1.9748418 2.1679483 2.2583180 1.8165902 #> 59  2.4899799 2.5099801 2.4698178 2.3874673 2.6267851 2.5884358 2.4698178 #> 60  2.0976177 2.1213203 2.0736441 2.0736441 2.2583180 2.3452079 2.0736441 #> 61  2.1213203 2.0493902 2.0000000 2.0976177 2.2803509 2.3664319 2.0000000 #> 62  2.2803509 2.3021729 2.2583180 2.1679483 2.4289916 2.3874673 2.2583180 #> 63  2.3237900 2.3452079 2.3021729 2.2135944 2.4698178 2.4289916 2.3021729 #> 64  2.4289916 2.4494897 2.4083189 2.3237900 2.5690465 2.5298221 2.4083189 #> 65  2.0493902 2.0736441 2.0248457 1.9235384 2.2135944 2.1679483 2.0248457 #> 66  2.4494897 2.4698178 2.4289916 2.3452079 2.5884358 2.5495098 2.4289916 #> 67  2.2803509 2.3021729 2.2583180 2.1679483 2.4289916 2.3874673 2.2583180 #> 68  2.1908902 2.2135944 2.1679483 2.0736441 2.3452079 2.3021729 2.1679483 #> 69  2.5690465 2.5884358 2.5495098 2.4698178 2.7018512 2.6645825 2.5495098 #> 70  2.1679483 2.1908902 2.1447611 2.0493902 2.3237900 2.2803509 2.1447611 #> 71  2.4289916 2.4494897 2.4494897 2.3237900 2.5690465 2.5298221 2.4494897 #> 72  2.2803509 2.3021729 2.2583180 2.1679483 2.4289916 2.3874673 2.2583180 #> 73  2.6076810 2.6267851 2.5884358 2.5099801 2.7386128 2.7018512 2.5884358 #> 74  2.4083189 2.4289916 2.3874673 2.3021729 2.5495098 2.5099801 2.3874673 #> 75  2.3874673 2.4083189 2.3664319 2.2803509 2.5298221 2.4899799 2.3664319 #> 76  2.4494897 2.4698178 2.4289916 2.3452079 2.5884358 2.5495098 2.4289916 #> 77  2.6076810 2.6267851 2.5884358 2.5099801 2.7386128 2.7018512 2.5884358 #> 78  2.6457513 2.6645825 2.6267851 2.5495098 2.7748874 2.7386128 2.6267851 #> 79  2.3874673 2.4083189 2.3664319 2.2803509 2.5298221 2.4899799 2.3664319 #> 80  2.0493902 2.0736441 2.0248457 1.9235384 2.2135944 2.1679483 2.0248457 #> 81  2.1447611 2.1679483 2.1213203 2.0248457 2.3021729 2.2583180 2.1213203 #> 82  2.0976177 2.1213203 2.0736441 1.9748418 2.2583180 2.2135944 2.0736441 #> 83  2.1908902 2.2135944 2.1679483 2.0736441 2.3452079 2.3021729 2.1679483 #> 84  2.5690465 2.5884358 2.5495098 2.4698178 2.7018512 2.6645825 2.5495098 #> 85  2.2360680 2.2583180 2.2135944 2.1213203 2.3874673 2.3874673 2.2135944 #> 86  2.3021729 2.4083189 2.4083189 2.1908902 2.4494897 2.4083189 2.4083189 #> 87  2.5298221 2.5495098 2.5099801 2.4289916 2.6645825 2.6267851 2.5099801 #> 88  2.5099801 2.5298221 2.4899799 2.4083189 2.6457513 2.6076810 2.4899799 #> 89  2.1447611 2.1679483 2.1213203 2.0248457 2.3021729 2.2583180 2.1213203 #> 90  2.2135944 2.2360680 2.1908902 2.0976177 2.3664319 2.3237900 2.1908902 #> 91  2.2583180 2.2803509 2.2360680 2.1447611 2.4083189 2.3664319 2.2360680 #> 92  2.3874673 2.4083189 2.3664319 2.2803509 2.5298221 2.4899799 2.3664319 #> 93  2.2360680 2.2583180 2.2135944 2.1213203 2.3874673 2.3452079 2.2135944 #> 94  2.0000000 1.9235384 1.8708287 1.9748418 2.1679483 2.2583180 1.8708287 #> 95  2.2360680 2.2583180 2.2135944 2.1213203 2.3874673 2.3452079 2.2135944 #> 96  2.1679483 2.1908902 2.1447611 2.0493902 2.3237900 2.2803509 2.1447611 #> 97  2.2135944 2.2360680 2.1908902 2.0976177 2.3664319 2.3237900 2.1908902 #> 98  2.3452079 2.3664319 2.3237900 2.2360680 2.4899799 2.4494897 2.3237900 #> 99  1.8708287 1.8439089 1.7888544 1.8439089 2.0493902 2.1447611 1.7888544 #> 100 2.2135944 2.2360680 2.1908902 2.0976177 2.3664319 2.3237900 2.1908902 #> 101 2.8460499 2.8982753 2.8982753 2.7568098 2.9664794 2.9325757 2.8982753 #> 102 2.5884358 2.6076810 2.5690465 2.4899799 2.7202941 2.6832816 2.5690465 #> 103 2.9495762 2.9664794 2.9325757 2.8635642 3.0659419 3.0331502 2.9325757 #> 104 2.7202941 2.7386128 2.7018512 2.6267851 2.8460499 2.8106939 2.7018512 #> 105 2.8460499 2.8635642 2.8284271 2.7568098 2.9664794 2.9325757 2.8284271 #> 106 3.1464265 3.1622777 3.1304952 3.0659419 3.2557641 3.2249031 3.1304952 #> 107 2.4083189 2.3021729 2.2583180 2.3874673 2.5495098 2.6267851 2.2583180 #> 108 3.0166206 3.0331502 3.0000000 2.9325757 3.1304952 3.0983867 3.0000000 #> 109 2.8982753 2.9154759 2.8809721 2.8106939 3.0166206 2.9832868 2.8809721 #> 110 3.0331502 3.1144823 3.1144823 2.9495762 3.0822070 3.0495901 3.1144823 #> 111 2.6457513 2.6645825 2.6645825 2.5495098 2.7748874 2.7386128 2.6645825 #> 112 2.7386128 2.7568098 2.7202941 2.6457513 2.8635642 2.8284271 2.7202941 #> 113 2.8284271 2.8460499 2.8106939 2.7386128 2.9495762 2.9154759 2.8106939 #> 114 2.6076810 2.6267851 2.5884358 2.5099801 2.7386128 2.7018512 2.5884358 #> 115 2.6645825 2.6832816 2.6457513 2.5690465 2.7928480 2.7568098 2.6457513 #> 116 2.7202941 2.7386128 2.7386128 2.6267851 2.8460499 2.8106939 2.7386128 #> 117 2.7202941 2.7386128 2.7018512 2.6267851 2.8460499 2.8106939 2.7018512 #> 118 3.1937439 3.2710854 3.2710854 3.1144823 3.1780497 3.1464265 3.2710854 #> 119 3.3015148 3.3166248 3.2863353 3.2249031 3.4058773 3.3763886 3.2863353 #> 120 2.6267851 2.6457513 2.6076810 2.5298221 2.7568098 2.7202941 2.6076810 #> 121 2.8809721 2.8982753 2.8982753 2.7928480 3.0000000 2.9664794 2.8982753 #> 122 2.5099801 2.5298221 2.4899799 2.4083189 2.6457513 2.6076810 2.4899799 #> 123 3.1937439 3.2093613 3.1780497 3.1144823 3.3015148 3.2710854 3.1780497 #> 124 2.6267851 2.6457513 2.6076810 2.5298221 2.7568098 2.7202941 2.6076810 #> 125 2.7928480 2.8460499 2.8460499 2.7018512 2.9154759 2.8809721 2.8460499 #> 126 2.8982753 2.9154759 2.9154759 2.8106939 3.0166206 2.9832868 2.9154759 #> 127 2.5690465 2.5884358 2.5495098 2.4698178 2.7018512 2.6645825 2.5495098 #> 128 2.5298221 2.5495098 2.5099801 2.4289916 2.6645825 2.6267851 2.5099801 #> 129 2.8106939 2.8284271 2.7928480 2.7202941 2.9325757 2.8982753 2.7928480 #> 130 2.8635642 2.8809721 2.8460499 2.7748874 2.9832868 2.9495762 2.8460499 #> 131 3.0331502 3.0495901 3.0166206 2.9495762 3.1464265 3.1144823 3.0166206 #> 132 3.1464265 3.2249031 3.2249031 3.0659419 3.1304952 3.0983867 3.2249031 #> 133 2.8284271 2.8460499 2.8106939 2.7386128 2.9495762 2.9154759 2.8106939 #> 134 2.5884358 2.6076810 2.5690465 2.4899799 2.7202941 2.6832816 2.5690465 #> 135 2.6645825 2.6832816 2.6457513 2.5690465 2.7928480 2.7568098 2.6457513 #> 136 3.1144823 3.1304952 3.0983867 3.0331502 3.2249031 3.1937439 3.0983867 #> 137 2.7386128 2.8284271 2.8284271 2.6457513 2.8635642 2.8284271 2.8284271 #> 138 2.6832816 2.7018512 2.6645825 2.5884358 2.8106939 2.7748874 2.6645825 #> 139 2.4899799 2.5099801 2.4698178 2.3874673 2.6267851 2.5884358 2.4698178 #> 140 2.8106939 2.8284271 2.7928480 2.7202941 2.9325757 2.8982753 2.7928480 #> 141 2.8635642 2.8809721 2.8460499 2.7748874 2.9832868 2.9495762 2.8460499 #> 142 2.7928480 2.8106939 2.7748874 2.7018512 2.9154759 2.8809721 2.7748874 #> 143 2.5884358 2.6076810 2.5690465 2.4899799 2.7202941 2.6832816 2.5690465 #> 144 2.8982753 2.9154759 2.9154759 2.8106939 3.0166206 2.9832868 2.9154759 #> 145 2.8635642 2.9154759 2.9154759 2.7748874 2.9832868 2.9495762 2.9154759 #> 146 2.7928480 2.8106939 2.7748874 2.7018512 2.9154759 2.8809721 2.7748874 #> 147 2.7018512 2.7202941 2.6832816 2.6076810 2.8284271 2.7928480 2.6832816 #> 148 2.7018512 2.7202941 2.6832816 2.6076810 2.8284271 2.7928480 2.6832816 #> 149 2.6645825 2.7568098 2.7568098 2.5690465 2.7928480 2.7568098 2.7568098 #> 150 2.5298221 2.5495098 2.5099801 2.4289916 2.6645825 2.6267851 2.5099801 #>            36        37        38        39        40        41        42 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37  0.9486833                                                             #> 38  0.8944272 0.9486833                                                   #> 39  0.9486833 1.2649111 1.1401754                                         #> 40  0.7745967 0.8366600 0.7745967 1.1401754                               #> 41  0.7071068 0.7745967 0.7071068 1.0954451 0.7071068                     #> 42  1.2649111 1.5165751 1.4142136 0.9486833 1.4142136 1.3038405           #> 43  0.8366600 1.1832160 1.0488088 0.4472136 1.0488088 1.0000000 1.0488088 #> 44  1.0488088 1.0954451 0.9486833 1.3416408 0.8366600 0.7745967 1.5165751 #> 45  1.2649111 1.2247449 1.0954451 1.5165751 1.0000000 1.0488088 1.6733201 #> 46  0.8366600 1.1832160 0.9486833 0.7745967 0.9486833 0.8944272 1.0488088 #> 47  1.0488088 1.0000000 0.8366600 1.3416408 0.7071068 0.8944272 1.5811388 #> 48  0.7745967 1.1401754 0.8944272 0.7071068 0.8944272 0.9486833 1.0954451 #> 49  1.0488088 0.7745967 0.8366600 1.3416408 0.7071068 0.8944272 1.5811388 #> 50  0.5477226 0.8944272 0.7071068 1.0000000 0.5477226 0.6324555 1.3038405 #> 51  2.5884358 2.5298221 2.6645825 2.7202941 2.5495098 2.6076810 2.8106939 #> 52  2.4494897 2.3874673 2.5298221 2.5884358 2.4083189 2.4698178 2.6832816 #> 53  2.6457513 2.5884358 2.7202941 2.7386128 2.6076810 2.6645825 2.8284271 #> 54  2.3021729 2.2360680 2.3874673 2.3664319 2.2583180 2.3237900 2.1679483 #> 55  2.5690465 2.5099801 2.6457513 2.6267851 2.5298221 2.5884358 2.6457513 #> 56  2.3452079 2.2803509 2.4289916 2.4083189 2.3021729 2.3664319 2.4289916 #> 57  2.5099801 2.4083189 2.5495098 2.6457513 2.4289916 2.4899799 2.7386128 #> 58  1.9493589 2.1213203 2.0000000 1.9748418 1.9493589 1.9748418 1.7888544 #> 59  2.5298221 2.4698178 2.6076810 2.5884358 2.4899799 2.5495098 2.6457513 #> 60  2.1447611 2.2135944 2.2360680 2.2135944 2.0976177 2.1679483 2.1908902 #> 61  2.0736441 2.2360680 2.1679483 2.1447611 2.0736441 2.0976177 1.9235384 #> 62  2.3237900 2.2583180 2.4083189 2.3874673 2.2803509 2.3452079 2.4899799 #> 63  2.3664319 2.3021729 2.4494897 2.4289916 2.3237900 2.3874673 2.2360680 #> 64  2.4698178 2.4083189 2.5495098 2.5298221 2.4289916 2.4899799 2.5884358 #> 65  2.0976177 2.0248457 2.1908902 2.1679483 2.0493902 2.1213203 2.2360680 #> 66  2.4899799 2.4289916 2.5690465 2.5884358 2.4494897 2.5099801 2.6832816 #> 67  2.3237900 2.2583180 2.4083189 2.3874673 2.2803509 2.3452079 2.4899799 #> 68  2.2360680 2.1679483 2.3237900 2.3021729 2.1908902 2.2583180 2.2803509 #> 69  2.6076810 2.5495098 2.6832816 2.6645825 2.5690465 2.6267851 2.4899799 #> 70  2.2135944 2.1447611 2.3021729 2.2803509 2.1679483 2.2360680 2.1679483 #> 71  2.4698178 2.4083189 2.5495098 2.6076810 2.4289916 2.4899799 2.7018512 #> 72  2.3237900 2.2583180 2.4083189 2.3874673 2.2803509 2.3452079 2.4083189 #> 73  2.6457513 2.5884358 2.7202941 2.7018512 2.6076810 2.6645825 2.6076810 #> 74  2.4494897 2.3874673 2.5298221 2.5099801 2.4083189 2.4698178 2.5298221 #> 75  2.4289916 2.3664319 2.5099801 2.4899799 2.3874673 2.4494897 2.5495098 #> 76  2.4899799 2.4289916 2.5690465 2.5495098 2.4494897 2.5099801 2.6457513 #> 77  2.6457513 2.5884358 2.7202941 2.7018512 2.6076810 2.6645825 2.7202941 #> 78  2.6832816 2.6267851 2.7568098 2.7386128 2.6457513 2.7018512 2.8284271 #> 79  2.4289916 2.3664319 2.5099801 2.4899799 2.3874673 2.4494897 2.5495098 #> 80  2.0976177 2.0248457 2.1908902 2.1679483 2.0493902 2.1213203 2.0976177 #> 81  2.1908902 2.1213203 2.2803509 2.2583180 2.1447611 2.2135944 2.0976177 #> 82  2.1447611 2.0736441 2.2360680 2.2135944 2.0976177 2.1679483 2.0493902 #> 83  2.2360680 2.1679483 2.3237900 2.3021729 2.1908902 2.2583180 2.2803509 #> 84  2.6076810 2.5495098 2.6832816 2.6645825 2.5690465 2.6267851 2.6457513 #> 85  2.2803509 2.2583180 2.3664319 2.3452079 2.2360680 2.3021729 2.4494897 #> 86  2.4289916 2.2803509 2.4289916 2.5690465 2.3021729 2.3664319 2.6645825 #> 87  2.5690465 2.5099801 2.6457513 2.6645825 2.5298221 2.5884358 2.7568098 #> 88  2.5495098 2.4899799 2.6267851 2.6076810 2.5099801 2.5690465 2.4289916 #> 89  2.1908902 2.1213203 2.2803509 2.2583180 2.1447611 2.2135944 2.3664319 #> 90  2.2583180 2.1908902 2.3452079 2.3237900 2.2135944 2.2803509 2.2135944 #> 91  2.3021729 2.2360680 2.3874673 2.3664319 2.2583180 2.3237900 2.3021729 #> 92  2.4289916 2.3664319 2.5099801 2.4899799 2.3874673 2.4494897 2.5884358 #> 93  2.2803509 2.2135944 2.3664319 2.3452079 2.2360680 2.3021729 2.2803509 #> 94  1.9493589 2.1213203 2.0493902 2.0248457 1.9493589 1.9748418 1.7888544 #> 95  2.2803509 2.2135944 2.3664319 2.3452079 2.2360680 2.3021729 2.3237900 #> 96  2.2135944 2.1447611 2.3021729 2.2803509 2.1679483 2.2360680 2.3874673 #> 97  2.2583180 2.1908902 2.3452079 2.3237900 2.2135944 2.2803509 2.3874673 #> 98  2.3874673 2.3237900 2.4698178 2.4494897 2.3452079 2.4083189 2.5099801 #> 99  1.8708287 2.0000000 1.9748418 1.9493589 1.8165902 1.8973666 1.8165902 #> 100 2.2583180 2.1908902 2.3452079 2.3237900 2.2135944 2.2803509 2.3452079 #> 101 2.9154759 2.8284271 2.9495762 3.0331502 2.8460499 2.8982753 3.1144823 #> 102 2.6267851 2.5690465 2.7018512 2.6832816 2.5884358 2.6457513 2.6645825 #> 103 2.9832868 2.9325757 3.0495901 3.0331502 2.9495762 3.0000000 3.1144823 #> 104 2.7568098 2.7018512 2.8284271 2.8106939 2.7202941 2.7748874 2.8635642 #> 105 2.8809721 2.8284271 2.9495762 2.9325757 2.8460499 2.8982753 3.0166206 #> 106 3.1780497 3.1304952 3.2403703 3.2249031 3.1464265 3.1937439 3.3015148 #> 107 2.3664319 2.5099801 2.4083189 2.3874673 2.3664319 2.3874673 2.2803509 #> 108 3.0495901 3.0000000 3.1144823 3.0983867 3.0166206 3.0659419 3.1464265 #> 109 2.9325757 2.8809721 3.0000000 2.9832868 2.8982753 2.9495762 2.8982753 #> 110 3.1304952 2.9832868 3.0659419 3.2403703 3.0331502 3.0495901 3.3166248 #> 111 2.6832816 2.6267851 2.7568098 2.8106939 2.6457513 2.7018512 2.8982753 #> 112 2.7748874 2.7202941 2.8460499 2.8284271 2.7386128 2.7928480 2.8106939 #> 113 2.8635642 2.8106939 2.9325757 2.9154759 2.8284271 2.8809721 3.0000000 #> 114 2.6457513 2.5884358 2.7202941 2.7018512 2.6076810 2.6645825 2.6076810 #> 115 2.7018512 2.6457513 2.7748874 2.7568098 2.6645825 2.7202941 2.7748874 #> 116 2.7568098 2.7018512 2.8284271 2.8809721 2.7202941 2.7748874 2.9664794 #> 117 2.7568098 2.7018512 2.8284271 2.8106939 2.7202941 2.7748874 2.8982753 #> 118 3.2863353 3.1464265 3.2249031 3.3911650 3.1937439 3.2093613 3.4641016 #> 119 3.3316662 3.2863353 3.3911650 3.3763886 3.3015148 3.3466401 3.3316662 #> 120 2.6645825 2.6076810 2.7386128 2.7202941 2.6267851 2.6832816 2.5495098 #> 121 2.9154759 2.8635642 2.9832868 3.0331502 2.8809721 2.9325757 3.1144823 #> 122 2.5495098 2.4899799 2.6267851 2.6076810 2.5099801 2.5690465 2.6267851 #> 123 3.2249031 3.1780497 3.2863353 3.2710854 3.1937439 3.2403703 3.2863353 #> 124 2.6645825 2.6076810 2.7386128 2.7202941 2.6267851 2.6832816 2.7018512 #> 125 2.8635642 2.7748874 2.8982753 2.9832868 2.7928480 2.8460499 3.0659419 #> 126 2.9325757 2.8809721 3.0000000 3.0495901 2.8982753 2.9495762 3.1304952 #> 127 2.6076810 2.5495098 2.6832816 2.6645825 2.5690465 2.6267851 2.6832816 #> 128 2.5690465 2.5099801 2.6457513 2.6267851 2.5298221 2.5884358 2.7202941 #> 129 2.8460499 2.7928480 2.9154759 2.8982753 2.8106939 2.8635642 2.9154759 #> 130 2.8982753 2.8460499 2.9664794 2.9495762 2.8635642 2.9154759 3.0331502 #> 131 3.0659419 3.0166206 3.1304952 3.1144823 3.0331502 3.0822070 3.1304952 #> 132 3.2403703 3.0983867 3.1780497 3.3466401 3.1464265 3.1622777 3.4205263 #> 133 2.8635642 2.8106939 2.9325757 2.9154759 2.8284271 2.8809721 2.9325757 #> 134 2.6267851 2.5690465 2.7018512 2.6832816 2.5884358 2.6457513 2.7018512 #> 135 2.7018512 2.6457513 2.7748874 2.7568098 2.6645825 2.7202941 2.7018512 #> 136 3.1464265 3.0983867 3.2093613 3.1937439 3.1144823 3.1622777 3.2710854 #> 137 2.8460499 2.7202941 2.8460499 2.9664794 2.7386128 2.7928480 3.0495901 #> 138 2.7202941 2.6645825 2.7928480 2.8106939 2.6832816 2.7386128 2.8982753 #> 139 2.5298221 2.4698178 2.6076810 2.5884358 2.4899799 2.5495098 2.6832816 #> 140 2.8460499 2.7928480 2.9154759 2.9325757 2.8106939 2.8635642 3.0166206 #> 141 2.8982753 2.8460499 2.9664794 2.9832868 2.8635642 2.9154759 3.0659419 #> 142 2.8284271 2.7748874 2.8982753 2.9154759 2.7928480 2.8460499 3.0000000 #> 143 2.6267851 2.5690465 2.7018512 2.6832816 2.5884358 2.6457513 2.6645825 #> 144 2.9325757 2.8809721 3.0000000 3.0495901 2.8982753 2.9495762 3.1304952 #> 145 2.9325757 2.8460499 2.9664794 3.0495901 2.8635642 2.9154759 3.1304952 #> 146 2.8284271 2.7748874 2.8982753 2.8809721 2.7928480 2.8460499 2.9664794 #> 147 2.7386128 2.6832816 2.8106939 2.7928480 2.7018512 2.7568098 2.7018512 #> 148 2.7386128 2.6832816 2.8106939 2.7928480 2.7018512 2.7568098 2.8809721 #> 149 2.7748874 2.6457513 2.7748874 2.8982753 2.6645825 2.7202941 2.9832868 #> 150 2.5690465 2.5099801 2.6457513 2.6267851 2.5298221 2.5884358 2.7202941 #>            43        44        45        46        47        48        49 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44  1.2649111                                                             #> 45  1.4491377 0.9486833                                                   #> 46  0.8944272 1.0954451 1.3038405                                         #> 47  1.2649111 0.8944272 0.7071068 1.1832160                               #> 48  0.5477226 1.1401754 1.3416408 0.7071068 1.1401754                     #> 49  1.2649111 1.0000000 0.9486833 1.1832160 0.6324555 1.1401754           #> 50  0.8944272 0.8944272 1.1401754 0.7745967 0.8944272 0.7071068 0.8944272 #> 51  2.6832816 2.4899799 2.5099801 2.6076810 2.6076810 2.6267851 2.5690465 #> 52  2.5495098 2.3452079 2.3664319 2.4698178 2.4698178 2.4899799 2.4289916 #> 53  2.7386128 2.5495098 2.5690465 2.6267851 2.6645825 2.6832816 2.6267851 #> 54  2.4083189 2.1908902 2.2135944 2.2360680 2.3237900 2.3452079 2.2803509 #> 55  2.6645825 2.4698178 2.4899799 2.5099801 2.5884358 2.6076810 2.5495098 #> 56  2.4494897 2.2360680 2.2583180 2.2803509 2.3664319 2.3874673 2.3237900 #> 57  2.6076810 2.3664319 2.3874673 2.5298221 2.4899799 2.5495098 2.4494897 #> 58  2.0248457 1.8165902 1.8973666 1.8165902 2.0248457 1.9493589 2.0736441 #> 59  2.6267851 2.4289916 2.4494897 2.4698178 2.5495098 2.5690465 2.5099801 #> 60  2.2583180 2.0248457 2.0493902 2.0736441 2.1679483 2.1908902 2.1679483 #> 61  2.1908902 1.9493589 2.0248457 2.0000000 2.1447611 2.1213203 2.1908902 #> 62  2.4289916 2.2135944 2.2360680 2.2583180 2.3452079 2.3664319 2.3021729 #> 63  2.4698178 2.2583180 2.2803509 2.3021729 2.3874673 2.4083189 2.3452079 #> 64  2.5690465 2.3664319 2.3874673 2.4083189 2.4899799 2.5099801 2.4494897 #> 65  2.2135944 1.9748418 2.0000000 2.0248457 2.1213203 2.1447611 2.0736441 #> 66  2.5884358 2.3874673 2.4083189 2.4698178 2.5099801 2.5298221 2.4698178 #> 67  2.4289916 2.2135944 2.2360680 2.2583180 2.3452079 2.3664319 2.3021729 #> 68  2.3452079 2.1213203 2.1447611 2.1679483 2.2583180 2.2803509 2.2135944 #> 69  2.7018512 2.5099801 2.5298221 2.5495098 2.6267851 2.6457513 2.5884358 #> 70  2.3237900 2.0976177 2.1213203 2.1447611 2.2360680 2.2583180 2.1908902 #> 71  2.5690465 2.3664319 2.3874673 2.4899799 2.4899799 2.5099801 2.4494897 #> 72  2.4289916 2.2135944 2.2360680 2.2583180 2.3452079 2.3664319 2.3021729 #> 73  2.7386128 2.5495098 2.5690465 2.5884358 2.6645825 2.6832816 2.6267851 #> 74  2.5495098 2.3452079 2.3664319 2.3874673 2.4698178 2.4899799 2.4289916 #> 75  2.5298221 2.3237900 2.3452079 2.3664319 2.4494897 2.4698178 2.4083189 #> 76  2.5884358 2.3874673 2.4083189 2.4289916 2.5099801 2.5298221 2.4698178 #> 77  2.7386128 2.5495098 2.5690465 2.5884358 2.6645825 2.6832816 2.6267851 #> 78  2.7748874 2.5884358 2.6076810 2.6267851 2.7018512 2.7202941 2.6645825 #> 79  2.5298221 2.3237900 2.3452079 2.3664319 2.4494897 2.4698178 2.4083189 #> 80  2.2135944 1.9748418 2.0000000 2.0248457 2.1213203 2.1447611 2.0736441 #> 81  2.3021729 2.0736441 2.0976177 2.1213203 2.2135944 2.2360680 2.1679483 #> 82  2.2583180 2.0248457 2.0493902 2.0736441 2.1679483 2.1908902 2.1213203 #> 83  2.3452079 2.1213203 2.1447611 2.1679483 2.2583180 2.2803509 2.2135944 #> 84  2.7018512 2.5099801 2.5298221 2.5495098 2.6267851 2.6457513 2.5884358 #> 85  2.3874673 2.1679483 2.1908902 2.2135944 2.3021729 2.3237900 2.2583180 #> 86  2.5298221 2.2360680 2.2583180 2.4494897 2.3664319 2.4698178 2.3237900 #> 87  2.6645825 2.4698178 2.4899799 2.5495098 2.5884358 2.6076810 2.5495098 #> 88  2.6457513 2.4494897 2.4698178 2.4899799 2.5690465 2.5884358 2.5298221 #> 89  2.3021729 2.0736441 2.0976177 2.1213203 2.2135944 2.2360680 2.1679483 #> 90  2.3664319 2.1447611 2.1679483 2.1908902 2.2803509 2.3021729 2.2360680 #> 91  2.4083189 2.1908902 2.2135944 2.2360680 2.3237900 2.3452079 2.2803509 #> 92  2.5298221 2.3237900 2.3452079 2.3664319 2.4494897 2.4698178 2.4083189 #> 93  2.3874673 2.1679483 2.1908902 2.2135944 2.3021729 2.3237900 2.2583180 #> 94  2.0736441 1.8165902 1.8973666 1.8708287 2.0248457 2.0000000 2.0736441 #> 95  2.3874673 2.1679483 2.1908902 2.2135944 2.3021729 2.3237900 2.2583180 #> 96  2.3237900 2.0976177 2.1213203 2.1447611 2.2360680 2.2583180 2.1908902 #> 97  2.3664319 2.1447611 2.1679483 2.1908902 2.2803509 2.3021729 2.2360680 #> 98  2.4899799 2.2803509 2.3021729 2.3237900 2.4083189 2.4289916 2.3664319 #> 99  2.0000000 1.7320508 1.7606817 1.7888544 1.8973666 1.9235384 1.9493589 #> 100 2.3664319 2.1447611 2.1679483 2.1908902 2.2803509 2.3021729 2.2360680 #> 101 3.0000000 2.7928480 2.8106939 2.9325757 2.8982753 2.9495762 2.8635642 #> 102 2.7202941 2.5298221 2.5495098 2.5690465 2.6457513 2.6645825 2.6076810 #> 103 3.0659419 2.8982753 2.9154759 2.9325757 3.0000000 3.0166206 2.9664794 #> 104 2.8460499 2.6645825 2.6832816 2.7018512 2.7748874 2.7928480 2.7386128 #> 105 2.9664794 2.7928480 2.8106939 2.8284271 2.8982753 2.9154759 2.8635642 #> 106 3.2557641 3.0983867 3.1144823 3.1304952 3.1937439 3.2093613 3.1622777 #> 107 2.4289916 2.2583180 2.3237900 2.2583180 2.4289916 2.3664319 2.4698178 #> 108 3.1304952 2.9664794 2.9832868 3.0000000 3.0659419 3.0822070 3.0331502 #> 109 3.0166206 2.8460499 2.8635642 2.8809721 2.9495762 2.9664794 2.9154759 #> 110 3.2093613 2.9495762 2.9325757 3.1464265 3.0166206 3.1622777 2.9832868 #> 111 2.7748874 2.5884358 2.6076810 2.7018512 2.7018512 2.7202941 2.6645825 #> 112 2.8635642 2.6832816 2.7018512 2.7202941 2.7928480 2.8106939 2.7568098 #> 113 2.9495762 2.7748874 2.7928480 2.8106939 2.8809721 2.8982753 2.8460499 #> 114 2.7386128 2.5495098 2.5690465 2.5884358 2.6645825 2.6832816 2.6267851 #> 115 2.7928480 2.6076810 2.6267851 2.6457513 2.7202941 2.7386128 2.6832816 #> 116 2.8460499 2.6645825 2.6832816 2.7748874 2.7748874 2.7928480 2.7386128 #> 117 2.8460499 2.6645825 2.6832816 2.7018512 2.7748874 2.7928480 2.7386128 #> 118 3.3615473 3.1144823 3.0331502 3.3015148 3.1144823 3.3166248 3.1144823 #> 119 3.4058773 3.2557641 3.2710854 3.2863353 3.3466401 3.3615473 3.3166248 #> 120 2.7568098 2.5690465 2.5884358 2.6076810 2.6832816 2.7018512 2.6457513 #> 121 3.0000000 2.8284271 2.8460499 2.9325757 2.9325757 2.9495762 2.8982753 #> 122 2.6457513 2.4494897 2.4698178 2.4899799 2.5690465 2.5884358 2.5298221 #> 123 3.3015148 3.1464265 3.1622777 3.1780497 3.2403703 3.2557641 3.2093613 #> 124 2.7568098 2.5690465 2.5884358 2.6076810 2.6832816 2.7018512 2.6457513 #> 125 2.9495762 2.7386128 2.7568098 2.8809721 2.8460499 2.8982753 2.8106939 #> 126 3.0166206 2.8460499 2.8635642 2.9495762 2.9495762 2.9664794 2.9154759 #> 127 2.7018512 2.5099801 2.5298221 2.5495098 2.6267851 2.6457513 2.5884358 #> 128 2.6645825 2.4698178 2.4899799 2.5099801 2.5884358 2.6076810 2.5495098 #> 129 2.9325757 2.7568098 2.7748874 2.7928480 2.8635642 2.8809721 2.8284271 #> 130 2.9832868 2.8106939 2.8284271 2.8460499 2.9154759 2.9325757 2.8809721 #> 131 3.1464265 2.9832868 3.0000000 3.0166206 3.0822070 3.0983867 3.0495901 #> 132 3.3166248 3.0659419 2.9832868 3.2557641 3.0659419 3.2710854 3.0659419 #> 133 2.9495762 2.7748874 2.7928480 2.8106939 2.8809721 2.8982753 2.8460499 #> 134 2.7202941 2.5298221 2.5495098 2.5690465 2.6457513 2.6645825 2.6076810 #> 135 2.7928480 2.6076810 2.6267851 2.6457513 2.7202941 2.7386128 2.6832816 #> 136 3.2249031 3.0659419 3.0822070 3.0983867 3.1622777 3.1780497 3.1304952 #> 137 2.9325757 2.6832816 2.7018512 2.8635642 2.7928480 2.8809721 2.7568098 #> 138 2.8106939 2.6267851 2.6457513 2.7018512 2.7386128 2.7568098 2.7018512 #> 139 2.6267851 2.4289916 2.4494897 2.4698178 2.5495098 2.5690465 2.5099801 #> 140 2.9325757 2.7568098 2.7748874 2.8284271 2.8635642 2.8809721 2.8284271 #> 141 2.9832868 2.8106939 2.8284271 2.8809721 2.9154759 2.9325757 2.8809721 #> 142 2.9154759 2.7386128 2.7568098 2.8106939 2.8460499 2.8635642 2.8106939 #> 143 2.7202941 2.5298221 2.5495098 2.5690465 2.6457513 2.6645825 2.6076810 #> 144 3.0166206 2.8460499 2.8635642 2.9495762 2.9495762 2.9664794 2.9154759 #> 145 3.0166206 2.8106939 2.8284271 2.9495762 2.9154759 2.9664794 2.8809721 #> 146 2.9154759 2.7386128 2.7568098 2.7748874 2.8460499 2.8635642 2.8106939 #> 147 2.8284271 2.6457513 2.6645825 2.6832816 2.7568098 2.7748874 2.7202941 #> 148 2.8284271 2.6457513 2.6645825 2.6832816 2.7568098 2.7748874 2.7202941 #> 149 2.8635642 2.6076810 2.6267851 2.7928480 2.7202941 2.8106939 2.6832816 #> 150 2.6645825 2.4698178 2.4899799 2.5099801 2.5884358 2.6076810 2.5495098 #>            50        51        52        53        54        55        56 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44                                                                        #> 45                                                                        #> 46                                                                        #> 47                                                                        #> 48                                                                        #> 49                                                                        #> 50                                                                        #> 51  2.5690465                                                             #> 52  2.4289916 0.9486833                                                   #> 53  2.6267851 0.7071068 1.0000000                                         #> 54  2.2803509 1.7888544 1.5811388 1.8165902                               #> 55  2.5495098 1.0488088 0.7745967 1.0000000 1.5165751                     #> 56  2.3237900 1.4142136 1.1401754 1.4491377 1.0954451 1.0488088           #> 57  2.4494897 1.0000000 0.7071068 1.0488088 1.6733201 0.9486833 1.2649111 #> 58  1.9235384 2.1679483 2.0000000 2.1908902 1.3038405 1.9493589 1.6431677 #> 59  2.5099801 0.9486833 0.8944272 1.0000000 1.5165751 0.6324555 1.0488088 #> 60  2.1213203 1.7606817 1.5491933 1.7888544 0.9486833 1.4832397 1.1401754 #> 61  2.0493902 2.1908902 2.0248457 2.2135944 1.2649111 1.9748418 1.6733201 #> 62  2.3021729 1.3784049 1.0000000 1.3416408 1.2247449 1.0954451 0.9486833 #> 63  2.3452079 1.7606817 1.5491933 1.7888544 0.9486833 1.4832397 1.3038405 #> 64  2.4494897 1.0954451 0.9486833 1.1401754 1.4142136 0.8366600 0.8944272 #> 65  2.0736441 1.7029386 1.4832397 1.7320508 1.0488088 1.4832397 1.0488088 #> 66  2.4698178 0.8366600 0.7745967 0.8944272 1.5811388 0.8944272 1.2247449 #> 67  2.3021729 1.3784049 1.0000000 1.3416408 1.2247449 1.0954451 0.7071068 #> 68  2.2135944 1.6431677 1.4142136 1.6733201 1.0488088 1.3416408 0.9486833 #> 69  2.5884358 1.4491377 1.0954451 1.4142136 1.2247449 1.0000000 1.1401754 #> 70  2.1908902 1.7888544 1.5811388 1.8165902 0.7745967 1.5165751 1.0954451 #> 71  2.4494897 1.2649111 1.0488088 1.2247449 1.6124515 1.2247449 1.1832160 #> 72  2.3021729 1.4491377 1.1832160 1.4832397 1.0488088 1.0954451 0.9486833 #> 73  2.6267851 1.3038405 1.0954451 1.0954451 1.4491377 0.8944272 1.2247449 #> 74  2.4289916 1.2247449 1.0954451 1.2649111 1.3784049 0.8944272 0.8366600 #> 75  2.4083189 1.1832160 0.8366600 1.2247449 1.3416408 0.8366600 1.0000000 #> 76  2.4698178 0.9486833 0.7745967 1.0000000 1.5165751 0.7745967 1.1401754 #> 77  2.6267851 0.8366600 1.0954451 0.7745967 1.6431677 0.7745967 1.2247449 #> 78  2.6645825 1.0488088 1.0954451 0.7745967 1.8165902 1.0000000 1.4491377 #> 79  2.4083189 1.2649111 0.8366600 1.2247449 1.3416408 0.8366600 0.7745967 #> 80  2.0736441 1.8708287 1.6733201 1.8973666 1.1401754 1.6124515 1.2247449 #> 81  2.1679483 1.8708287 1.6733201 1.8973666 0.7071068 1.6124515 1.2247449 #> 82  2.1213203 1.9235384 1.7320508 1.9493589 0.8366600 1.6733201 1.3038405 #> 83  2.2135944 1.6431677 1.4142136 1.6733201 0.9486833 1.3416408 0.9486833 #> 84  2.5884358 1.4491377 1.2649111 1.2649111 1.5165751 1.0954451 1.1401754 #> 85  2.2583180 1.4491377 1.0954451 1.4142136 1.2247449 1.1832160 0.8366600 #> 86  2.3664319 1.2649111 0.8366600 1.3038405 1.5491933 1.1401754 1.0954451 #> 87  2.5495098 0.7071068 0.7745967 0.6324555 1.7029386 0.7745967 1.3038405 #> 88  2.5298221 1.4142136 1.1401754 1.4491377 1.0954451 1.0488088 1.0954451 #> 89  2.1679483 1.5165751 1.2649111 1.5491933 0.9486833 1.3416408 0.8366600 #> 90  2.2360680 1.7320508 1.5165751 1.7606817 0.4472136 1.4491377 1.0000000 #> 91  2.2803509 1.6124515 1.3784049 1.6431677 0.8944272 1.3038405 0.7745967 #> 92  2.4083189 1.0954451 0.8366600 1.1401754 1.4142136 0.8366600 0.8944272 #> 93  2.2583180 1.6431677 1.4142136 1.6733201 0.8366600 1.3416408 0.9486833 #> 94  1.9235384 2.1679483 2.0000000 2.1908902 1.2247449 1.9493589 1.6431677 #> 95  2.2583180 1.5811388 1.3416408 1.6124515 0.8366600 1.2649111 0.7071068 #> 96  2.1908902 1.4832397 1.2247449 1.5165751 1.0954451 1.3038405 0.7745967 #> 97  2.2360680 1.4832397 1.2247449 1.5165751 1.0000000 1.2247449 0.6324555 #> 98  2.3664319 1.2649111 0.9486833 1.3038405 1.2649111 0.9486833 0.8944272 #> 99  1.8439089 2.1447611 1.9748418 2.1679483 1.3416408 1.9235384 1.6124515 #> 100 2.2360680 1.5491933 1.3038405 1.5811388 0.8944272 1.2247449 0.6324555 #> 101 2.8635642 1.7888544 1.6431677 1.7029386 2.2360680 1.7606817 1.9493589 #> 102 2.6076810 1.6124515 1.4491377 1.4491377 1.5491933 1.3038405 1.1832160 #> 103 2.9664794 1.4832397 1.7029386 1.3784049 2.2360680 1.6431677 1.9493589 #> 104 2.7386128 1.5165751 1.3416408 1.3416408 1.8708287 1.2649111 1.5165751 #> 105 2.8635642 1.6124515 1.5165751 1.4491377 2.0976177 1.4491377 1.7888544 #> 106 3.1622777 1.8439089 2.0248457 1.7606817 2.4899799 1.9748418 2.2360680 #> 107 2.3452079 1.8165902 1.5491933 1.7888544 1.3038405 1.4832397 1.2247449 #> 108 3.0331502 1.6124515 1.8165902 1.5165751 2.2803509 1.7029386 2.0000000 #> 109 2.9154759 1.5811388 1.6124515 1.4142136 1.9235384 1.4142136 1.7606817 #> 110 3.0822070 1.7606817 1.9493589 1.7320508 2.5099801 2.0000000 2.2583180 #> 111 2.6645825 1.2247449 1.0954451 1.0954451 1.9235384 1.1832160 1.5811388 #> 112 2.7568098 1.4832397 1.3038405 1.3038405 1.7888544 1.1401754 1.4832397 #> 113 2.8460499 1.3784049 1.4832397 1.1832160 2.0736441 1.4142136 1.7606817 #> 114 2.6267851 1.7029386 1.5491933 1.5491933 1.4491377 1.4142136 1.2247449 #> 115 2.6832816 1.7320508 1.5811388 1.5811388 1.7320508 1.4491377 1.3416408 #> 116 2.7386128 1.4491377 1.2649111 1.3416408 2.0248457 1.4142136 1.7029386 #> 117 2.7386128 1.3784049 1.2649111 1.1832160 1.9235384 1.1832160 1.5811388 #> 118 3.2403703 2.0248457 2.1908902 2.0000000 2.7018512 2.2360680 2.4698178 #> 119 3.3166248 2.0976177 2.2583180 2.0248457 2.5298221 2.1213203 2.3664319 #> 120 2.6457513 1.5491933 1.3784049 1.3784049 1.3416408 1.2247449 1.2649111 #> 121 2.8982753 1.4142136 1.5811388 1.3038405 2.2360680 1.6431677 1.9493589 #> 122 2.5298221 1.6124515 1.4491377 1.4491377 1.4832397 1.3038405 1.0954451 #> 123 3.2093613 1.9235384 2.0976177 1.8439089 2.4698178 1.9493589 2.2135944 #> 124 2.6457513 1.3416408 1.1401754 1.1401754 1.6124515 0.9486833 1.2649111 #> 125 2.8106939 1.4491377 1.4832397 1.3416408 2.1679483 1.5491933 1.8708287 #> 126 2.9154759 1.3784049 1.6124515 1.3416408 2.2583180 1.6733201 1.9748418 #> 127 2.5884358 1.3038405 1.0954451 1.1832160 1.5811388 0.8944272 1.1401754 #> 128 2.5495098 1.3038405 1.0954451 1.0954451 1.6431677 1.0954451 1.2247449 #> 129 2.8284271 1.6124515 1.4491377 1.4491377 1.9493589 1.3038405 1.6124515 #> 130 2.8809721 1.3038405 1.5491933 1.1832160 2.1213203 1.4832397 1.8165902 #> 131 3.0495901 1.6431677 1.8439089 1.5491933 2.2583180 1.6733201 1.9748418 #> 132 3.1937439 1.9493589 2.1213203 1.9235384 2.6457513 2.1679483 2.4083189 #> 133 2.8460499 1.6431677 1.4832397 1.4832397 1.9748418 1.3416408 1.6431677 #> 134 2.6076810 1.2649111 1.0488088 1.0488088 1.6124515 0.8366600 1.1832160 #> 135 2.6832816 1.5491933 1.4491377 1.4491377 1.6124515 1.3038405 1.3416408 #> 136 3.1304952 1.7888544 1.9748418 1.7029386 2.4494897 1.9235384 2.1908902 #> 137 2.7928480 1.6733201 1.5165751 1.5811388 2.1447611 1.6431677 1.8439089 #> 138 2.7018512 1.3784049 1.1832160 1.1832160 1.9235384 1.2649111 1.5811388 #> 139 2.5099801 1.3038405 1.0954451 1.1832160 1.5811388 1.0954451 1.1401754 #> 140 2.8284271 1.2649111 1.4491377 1.0488088 2.0976177 1.4491377 1.7888544 #> 141 2.8809721 1.5165751 1.5491933 1.3416408 2.1679483 1.5491933 1.8708287 #> 142 2.8106939 1.2247449 1.4142136 1.0000000 2.0736441 1.4142136 1.7606817 #> 143 2.6076810 1.6124515 1.4491377 1.4491377 1.5491933 1.3038405 1.1832160 #> 144 2.9154759 1.5165751 1.6124515 1.4142136 2.2583180 1.6733201 1.9748418 #> 145 2.8809721 1.5811388 1.6124515 1.4832397 2.2583180 1.6733201 1.9748418 #> 146 2.8106939 1.3784049 1.4142136 1.1832160 2.0248457 1.3416408 1.7029386 #> 147 2.7202941 1.4832397 1.3038405 1.3038405 1.6124515 1.1401754 1.4142136 #> 148 2.7202941 1.3416408 1.2247449 1.1401754 1.8973666 1.1401754 1.5491933 #> 149 2.7202941 1.6124515 1.4491377 1.5165751 2.0493902 1.5811388 1.7320508 #> 150 2.5495098 1.4491377 1.2649111 1.2649111 1.6431677 1.2649111 1.2247449 #>            57        58        59        60        61        62        63 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44                                                                        #> 45                                                                        #> 46                                                                        #> 47                                                                        #> 48                                                                        #> 49                                                                        #> 50                                                                        #> 51                                                                        #> 52                                                                        #> 53                                                                        #> 54                                                                        #> 55                                                                        #> 56                                                                        #> 57                                                                        #> 58  2.0736441                                                             #> 59  1.0488088 1.9493589                                                   #> 60  1.6431677 1.2649111 1.5491933                                         #> 61  2.0976177 0.8366600 1.9748418 1.3038405                               #> 62  1.1401754 1.7320508 1.1832160 1.1832160 1.7606817                     #> 63  1.6431677 1.4142136 1.4832397 1.3416408 1.3038405 1.2649111           #> 64  0.8944272 1.8708287 0.8366600 1.3784049 1.8973666 0.9486833 1.3784049 #> 65  1.5811388 1.3416408 1.4142136 1.0000000 1.3784049 1.0954451 1.3416408 #> 66  1.0488088 2.0000000 0.7745967 1.5491933 2.0248457 1.0954451 1.5491933 #> 67  1.1401754 1.7320508 1.1832160 1.1832160 1.7606817 0.7745967 1.4832397 #> 68  1.5165751 1.4142136 1.3416408 1.0954451 1.4491377 1.0000000 0.8944272 #> 69  1.2247449 1.7888544 1.1832160 1.4832397 1.7029386 1.1832160 1.0954451 #> 70  1.6733201 1.2247449 1.5165751 0.9486833 1.2649111 1.2247449 0.9486833 #> 71  0.8944272 2.0248457 1.3038405 1.5811388 2.0493902 1.0488088 1.6431677 #> 72  1.3038405 1.6124515 1.0954451 1.0954451 1.6431677 0.8944272 1.0000000 #> 73  1.0488088 1.8973666 1.0954451 1.5491933 1.9235384 1.2649111 1.4142136 #> 74  1.0488088 1.7888544 0.8944272 1.4142136 1.8165902 1.0954451 1.2649111 #> 75  1.0954451 1.8165902 0.7071068 1.3784049 1.8439089 0.9486833 1.3038405 #> 76  1.0488088 1.9493589 0.6324555 1.4832397 1.9748418 1.0000000 1.4832397 #> 77  1.1401754 2.0493902 0.7745967 1.6124515 2.0736441 1.3416408 1.6124515 #> 78  1.0488088 2.1908902 1.0000000 1.7888544 2.2135944 1.3416408 1.7888544 #> 79  1.0000000 1.8165902 0.9486833 1.3038405 1.8439089 0.7071068 1.3038405 #> 80  1.7606817 1.0954451 1.6124515 1.1832160 1.1401754 1.3416408 1.0954451 #> 81  1.7606817 1.0954451 1.6124515 1.0000000 1.1401754 1.3416408 1.0000000 #> 82  1.8165902 1.0000000 1.6733201 1.0954451 1.0488088 1.4142136 1.0000000 #> 83  1.5165751 1.4142136 1.3416408 0.8944272 1.4491377 1.0000000 1.0000000 #> 84  1.1401754 1.9493589 1.2649111 1.4832397 1.9748418 1.1832160 1.4832397 #> 85  1.2247449 1.6733201 1.2649111 1.0954451 1.7029386 0.8944272 1.5491933 #> 86  0.7745967 1.9748418 1.2247449 1.5165751 2.0000000 0.9486833 1.5165751 #> 87  0.8366600 2.0976177 0.7745967 1.6733201 2.1213203 1.1832160 1.6733201 #> 88  1.2649111 1.7029386 1.0488088 1.4491377 1.6733201 1.2247449 1.0488088 #> 89  1.3784049 1.5491933 1.2649111 1.0000000 1.5811388 0.7745967 1.2649111 #> 90  1.6124515 1.3038405 1.4491377 0.8366600 1.3416408 1.1401754 1.0488088 #> 91  1.4832397 1.4491377 1.3038405 1.0488088 1.4832397 1.1401754 1.2247449 #> 92  0.8944272 1.8708287 0.8366600 1.3784049 1.8973666 0.8366600 1.3784049 #> 93  1.5165751 1.4142136 1.3416408 1.0000000 1.4491377 1.0000000 0.8944272 #> 94  2.0736441 0.4472136 1.9493589 1.2649111 0.7071068 1.7320508 1.3416408 #> 95  1.4491377 1.4832397 1.2649111 0.8944272 1.5165751 0.8944272 1.1832160 #> 96  1.3416408 1.5811388 1.2247449 1.1401754 1.6124515 0.7071068 1.2247449 #> 97  1.3416408 1.5811388 1.1401754 1.0488088 1.6124515 0.7071068 1.2247449 #> 98  1.0954451 1.7606817 0.8366600 1.3038405 1.7888544 0.8366600 1.2247449 #> 99  2.0493902 0.8366600 1.9235384 1.2247449 1.0954451 1.7029386 1.5165751 #> 100 1.4142136 1.5165751 1.2247449 0.9486833 1.5491933 0.8366600 1.1401754 #> 101 1.4832397 2.5495098 1.8165902 2.2135944 2.5690465 1.8708287 2.2135944 #> 102 1.3416408 1.9748418 1.4491377 1.5165751 2.0000000 1.3038405 1.6431677 #> 103 1.6733201 2.5495098 1.6431677 2.2135944 2.5690465 1.8708287 2.2135944 #> 104 1.2247449 2.2360680 1.3416408 1.8439089 2.2583180 1.4832397 1.8439089 #> 105 1.4832397 2.4289916 1.5165751 2.0736441 2.4494897 1.7029386 2.0736441 #> 106 2.0000000 2.7748874 1.9748418 2.4698178 2.7928480 2.1679483 2.4698178 #> 107 1.5811388 1.4142136 1.6124515 1.1832160 1.5165751 1.4142136 1.6124515 #> 108 1.7888544 2.5884358 1.7029386 2.2583180 2.6076810 1.9748418 2.2583180 #> 109 1.5811388 2.2803509 1.4832397 2.0000000 2.3021729 1.7888544 1.8973666 #> 110 1.8708287 2.7928480 2.0000000 2.4899799 2.8106939 2.1908902 2.4899799 #> 111 1.0488088 2.2803509 1.2649111 1.8973666 2.3021729 1.4832397 1.8973666 #> 112 1.2649111 2.1679483 1.3038405 1.7606817 2.1908902 1.5165751 1.7606817 #> 113 1.4491377 2.4083189 1.4142136 2.0493902 2.4289916 1.6733201 2.0493902 #> 114 1.4491377 1.8973666 1.5491933 1.5491933 1.9235384 1.4142136 1.6124515 #> 115 1.4832397 2.1213203 1.5811388 1.7029386 2.1447611 1.4491377 1.8165902 #> 116 1.2247449 2.3664319 1.4832397 2.0000000 2.3874673 1.6124515 2.0000000 #> 117 1.2247449 2.2803509 1.2649111 1.8973666 2.3021729 1.4832397 1.8973666 #> 118 2.1213203 2.9664794 2.2360680 2.6832816 2.9832868 2.4083189 2.6832816 #> 119 2.2360680 2.8106939 2.1679483 2.5495098 2.8284271 2.3874673 2.5099801 #> 120 1.3416408 1.8708287 1.3784049 1.5811388 1.7888544 1.3038405 1.2247449 #> 121 1.5491933 2.5495098 1.6431677 2.2135944 2.5690465 1.8708287 2.2135944 #> 122 1.3416408 1.9235384 1.4491377 1.4491377 1.9493589 1.3038405 1.7029386 #> 123 2.0736441 2.7568098 2.0000000 2.4494897 2.7748874 2.2360680 2.4494897 #> 124 1.0000000 2.0248457 1.1401754 1.5811388 2.0493902 1.3038405 1.5811388 #> 125 1.3784049 2.4899799 1.5491933 2.1447611 2.5099801 1.7888544 2.1447611 #> 126 1.5811388 2.5690465 1.6733201 2.2360680 2.5884358 1.8973666 2.2360680 #> 127 0.9486833 2.0000000 1.0954451 1.5491933 2.0248457 1.1832160 1.5491933 #> 128 0.9486833 2.0493902 1.1832160 1.6124515 2.0736441 1.0954451 1.6124515 #> 129 1.4142136 2.3021729 1.4491377 1.9235384 2.3237900 1.6431677 1.9235384 #> 130 1.5165751 2.4494897 1.4832397 2.0976177 2.4698178 1.7320508 2.0976177 #> 131 1.8165902 2.5690465 1.7320508 2.2360680 2.5884358 2.0000000 2.2360680 #> 132 2.0493902 2.9154759 2.1679483 2.6267851 2.9325757 2.3452079 2.6267851 #> 133 1.4491377 2.3237900 1.4832397 1.9493589 2.3452079 1.6733201 1.9493589 #> 134 1.0000000 2.0248457 1.0488088 1.5811388 2.0493902 1.2247449 1.5811388 #> 135 1.4142136 2.0248457 1.3784049 1.6431677 2.0493902 1.4491377 1.5811388 #> 136 1.9493589 2.7386128 1.9235384 2.4289916 2.7568098 2.1213203 2.4289916 #> 137 1.3416408 2.4698178 1.7029386 2.1213203 2.4899799 1.7606817 2.1213203 #> 138 1.1401754 2.2803509 1.3416408 1.8973666 2.3021729 1.4832397 1.8973666 #> 139 0.9486833 2.0000000 1.1832160 1.5491933 2.0248457 1.0000000 1.5491933 #> 140 1.4142136 2.4289916 1.4491377 2.0736441 2.4494897 1.7029386 2.0736441 #> 141 1.5165751 2.4899799 1.5491933 2.1447611 2.5099801 1.7888544 2.1447611 #> 142 1.3784049 2.4083189 1.4142136 2.0493902 2.4289916 1.6733201 2.0493902 #> 143 1.3416408 1.9748418 1.4491377 1.5165751 2.0000000 1.3038405 1.6431677 #> 144 1.5811388 2.5690465 1.6733201 2.2360680 2.5884358 1.8973666 2.2360680 #> 145 1.5165751 2.5690465 1.6733201 2.2360680 2.5884358 1.8973666 2.2360680 #> 146 1.3784049 2.3664319 1.3416408 2.0000000 2.3874673 1.6124515 2.0000000 #> 147 1.1832160 2.0248457 1.3038405 1.7029386 2.0493902 1.4491377 1.5811388 #> 148 1.1832160 2.2583180 1.2247449 1.8708287 2.2803509 1.4491377 1.8708287 #> 149 1.2649111 2.3874673 1.6431677 2.0248457 2.4083189 1.6431677 2.0248457 #> 150 1.1401754 2.0493902 1.3416408 1.6124515 2.0736441 1.0954451 1.6733201 #>            64        65        66        67        68        69        70 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44                                                                        #> 45                                                                        #> 46                                                                        #> 47                                                                        #> 48                                                                        #> 49                                                                        #> 50                                                                        #> 51                                                                        #> 52                                                                        #> 53                                                                        #> 54                                                                        #> 55                                                                        #> 56                                                                        #> 57                                                                        #> 58                                                                        #> 59                                                                        #> 60                                                                        #> 61                                                                        #> 62                                                                        #> 63                                                                        #> 64                                                                        #> 65  1.3038405                                                             #> 66  1.0488088 1.4832397                                                   #> 67  0.9486833 1.0954451 1.1832160                                         #> 68  1.2247449 1.0954451 1.4142136 1.1832160                               #> 69  1.0488088 1.5491933 1.2649111 1.1832160 1.3416408                     #> 70  1.4142136 0.9486833 1.5811388 1.2247449 0.8366600 1.3784049           #> 71  1.0000000 1.5165751 1.3038405 1.0488088 1.4491377 1.3784049 1.6124515 #> 72  0.9486833 1.0000000 1.1832160 1.1832160 0.8944272 1.1832160 1.0488088 #> 73  0.9486833 1.6124515 1.2649111 1.2649111 1.4142136 0.8944272 1.4491377 #> 74  0.5477226 1.3416408 1.1832160 1.0954451 1.0954451 1.0954451 1.3038405 #> 75  0.8944272 1.2247449 0.8366600 1.1401754 1.1401754 1.1401754 1.3416408 #> 76  0.9486833 1.4142136 0.4472136 1.0954451 1.3416408 1.1832160 1.5165751 #> 77  0.9486833 1.6124515 0.8944272 1.3416408 1.4832397 1.2649111 1.6431677 #> 78  1.1401754 1.7320508 1.0000000 1.3416408 1.6733201 1.4142136 1.8165902 #> 79  0.6324555 1.2247449 1.0488088 0.7071068 1.1401754 0.9486833 1.3416408 #> 80  1.5165751 0.8944272 1.6733201 1.4142136 0.8944272 1.5491933 0.8366600 #> 81  1.5165751 1.0000000 1.6733201 1.3416408 1.0000000 1.4142136 0.5477226 #> 82  1.5811388 1.0000000 1.7320508 1.4142136 1.0000000 1.4832397 0.7071068 #> 83  1.2247449 0.8944272 1.4142136 1.1832160 0.6324555 1.3416408 0.7071068 #> 84  0.9486833 1.5491933 1.4142136 1.1832160 1.3416408 1.1832160 1.5165751 #> 85  1.0488088 1.1832160 1.2649111 0.4472136 1.2649111 1.2649111 1.3038405 #> 86  1.0000000 1.4491377 1.1401754 0.9486833 1.3784049 1.2247449 1.5491933 #> 87  0.9486833 1.6124515 0.6324555 1.1832160 1.5491933 1.2649111 1.7029386 #> 88  1.0954451 1.4491377 1.1401754 1.3038405 1.2247449 0.7071068 1.2649111 #> 89  1.1401754 0.7745967 1.2649111 0.7745967 0.8944272 1.4142136 0.9486833 #> 90  1.3416408 0.9486833 1.5165751 1.1401754 0.9486833 1.3038405 0.6324555 #> 91  1.1832160 1.1401754 1.3784049 0.9486833 0.9486833 1.2247449 0.8944272 #> 92  0.4472136 1.3038405 0.9486833 0.8366600 1.2247449 1.0488088 1.4142136 #> 93  1.2247449 1.0000000 1.4142136 1.1832160 0.6324555 1.2649111 0.7071068 #> 94  1.8708287 1.3416408 2.0000000 1.7320508 1.4142136 1.7320508 1.2247449 #> 95  1.1401754 0.8944272 1.3416408 0.8944272 0.7745967 1.2649111 0.8366600 #> 96  1.0954451 0.9486833 1.2247449 0.8366600 0.8366600 1.3784049 1.0000000 #> 97  1.0000000 0.8366600 1.2247449 0.8366600 0.8366600 1.3038405 1.0000000 #> 98  0.7745967 1.1401754 0.9486833 1.0488088 1.0488088 1.0488088 1.2649111 #> 99  1.8439089 1.3038405 1.9748418 1.7029386 1.4491377 1.8165902 1.1832160 #> 100 1.0954451 0.8366600 1.3038405 0.9486833 0.7071068 1.3038405 0.8944272 #> 101 1.7320508 2.1679483 1.8165902 1.8708287 2.1213203 1.9235384 2.2360680 #> 102 1.1832160 1.5811388 1.5811388 1.2247449 1.3784049 1.3784049 1.5491933 #> 103 1.7320508 2.1679483 1.6431677 1.8708287 2.1213203 1.9235384 2.2360680 #> 104 1.2247449 1.7888544 1.4832397 1.4832397 1.7320508 1.4832397 1.8708287 #> 105 1.5491933 2.0248457 1.5811388 1.7029386 1.9748418 1.7606817 2.0976177 #> 106 2.0493902 2.4289916 1.9748418 2.1679483 2.3874673 2.2135944 2.4899799 #> 107 1.4491377 1.5491933 1.6733201 1.1832160 1.4832397 1.3416408 1.3784049 #> 108 1.7888544 2.2135944 1.7606817 1.9748418 2.1679483 1.9748418 2.2803509 #> 109 1.5811388 2.0493902 1.5491933 1.7888544 1.8973666 1.5491933 1.9235384 #> 110 2.0736441 2.4494897 1.9493589 2.1908902 2.4083189 2.2360680 2.5099801 #> 111 1.3038405 1.8439089 1.2649111 1.4832397 1.7888544 1.5491933 1.9235384 #> 112 1.2649111 1.8165902 1.4491377 1.5165751 1.6431677 1.3784049 1.7888544 #> 113 1.5165751 2.0000000 1.4142136 1.6733201 1.9493589 1.7320508 2.0736441 #> 114 1.3038405 1.6124515 1.6733201 1.2649111 1.4832397 1.3416408 1.4491377 #> 115 1.3416408 1.7029386 1.7029386 1.3784049 1.5811388 1.5811388 1.7320508 #> 116 1.4491377 1.9493589 1.4832397 1.6124515 1.8973666 1.6733201 2.0248457 #> 117 1.3038405 1.8439089 1.3416408 1.4832397 1.7888544 1.5491933 1.9235384 #> 118 2.3021729 2.6457513 2.1908902 2.4083189 2.6076810 2.4494897 2.7018512 #> 119 2.2360680 2.5884358 2.2135944 2.3874673 2.4698178 2.2583180 2.5298221 #> 120 1.0954451 1.6431677 1.5165751 1.3038405 1.4491377 0.8366600 1.4832397 #> 121 1.7320508 2.1679483 1.5811388 1.8708287 2.1213203 1.9235384 2.2360680 #> 122 1.1832160 1.4491377 1.5811388 1.0488088 1.4491377 1.4491377 1.4832397 #> 123 2.0736441 2.4494897 2.0493902 2.2360680 2.3664319 2.1908902 2.4698178 #> 124 1.0000000 1.6431677 1.3038405 1.3038405 1.4491377 1.1401754 1.6124515 #> 125 1.6431677 2.0976177 1.4832397 1.7888544 2.0493902 1.8439089 2.1679483 #> 126 1.7606817 2.1908902 1.6124515 1.8973666 2.1447611 1.9493589 2.2583180 #> 127 0.8366600 1.5491933 1.2649111 1.1832160 1.4142136 1.0954451 1.5811388 #> 128 0.8366600 1.5491933 1.2649111 1.0954451 1.4832397 1.2649111 1.6431677 #> 129 1.4142136 1.9235384 1.5811388 1.6431677 1.8165902 1.5811388 1.9493589 #> 130 1.5811388 2.0493902 1.4832397 1.7320508 2.0000000 1.7888544 2.1213203 #> 131 1.8165902 2.2360680 1.7888544 2.0000000 2.1447611 1.9493589 2.2583180 #> 132 2.2360680 2.5884358 2.1213203 2.3452079 2.5495098 2.3874673 2.6457513 #> 133 1.4491377 1.9493589 1.6124515 1.6733201 1.8439089 1.6124515 1.9748418 #> 134 0.8944272 1.5811388 1.2247449 1.2247449 1.4491377 1.1401754 1.6124515 #> 135 1.0954451 1.7029386 1.5165751 1.4491377 1.5165751 1.3038405 1.6124515 #> 136 2.0000000 2.3874673 1.9235384 2.1213203 2.3452079 2.1679483 2.4494897 #> 137 1.6124515 2.0736441 1.7029386 1.7606817 2.0248457 1.8165902 2.1447611 #> 138 1.3038405 1.8439089 1.3416408 1.4832397 1.7888544 1.5491933 1.9235384 #> 139 0.8366600 1.4832397 1.2649111 1.0000000 1.4142136 1.2649111 1.5811388 #> 140 1.5491933 2.0248457 1.3784049 1.7029386 1.9748418 1.7606817 2.0976177 #> 141 1.6431677 2.0976177 1.4832397 1.7888544 2.0493902 1.8439089 2.1679483 #> 142 1.5165751 2.0000000 1.3416408 1.6733201 1.9493589 1.7320508 2.0736441 #> 143 1.1832160 1.5811388 1.5811388 1.2247449 1.3784049 1.3784049 1.5491933 #> 144 1.7606817 2.1908902 1.6124515 1.8973666 2.1447611 1.9493589 2.2583180 #> 145 1.7606817 2.1908902 1.6124515 1.8973666 2.1447611 1.9493589 2.2583180 #> 146 1.4491377 1.9493589 1.3416408 1.6124515 1.8973666 1.6733201 2.0248457 #> 147 1.1832160 1.7606817 1.4491377 1.4491377 1.5811388 1.1401754 1.6124515 #> 148 1.2649111 1.8165902 1.3038405 1.4491377 1.7606817 1.5165751 1.8973666 #> 149 1.4832397 1.9748418 1.6431677 1.6431677 1.9235384 1.7029386 2.0493902 #> 150 1.0488088 1.5491933 1.4142136 1.0954451 1.4832397 1.4142136 1.6431677 #>            71        72        73        74        75        76        77 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44                                                                        #> 45                                                                        #> 46                                                                        #> 47                                                                        #> 48                                                                        #> 49                                                                        #> 50                                                                        #> 51                                                                        #> 52                                                                        #> 53                                                                        #> 54                                                                        #> 55                                                                        #> 56                                                                        #> 57                                                                        #> 58                                                                        #> 59                                                                        #> 60                                                                        #> 61                                                                        #> 62                                                                        #> 63                                                                        #> 64                                                                        #> 65                                                                        #> 66                                                                        #> 67                                                                        #> 68                                                                        #> 69                                                                        #> 70                                                                        #> 71                                                                        #> 72  1.3784049                                                             #> 73  1.2247449 1.2649111                                                   #> 74  1.1401754 0.8944272 1.0000000                                         #> 75  1.3416408 0.8366600 1.1401754 0.9486833                               #> 76  1.3038405 1.0954451 1.1832160 1.0954451 0.7071068                     #> 77  1.3038405 1.2649111 1.0000000 1.0000000 1.0488088 0.8944272           #> 78  1.1401754 1.4832397 1.0954451 1.2649111 1.2247449 1.0000000 0.8944272 #> 79  1.0000000 0.9486833 1.0488088 0.8366600 0.8944272 0.9486833 1.1401754 #> 80  1.7029386 1.1832160 1.6124515 1.4142136 1.4491377 1.6124515 1.7320508 #> 81  1.7029386 1.1832160 1.5491933 1.4142136 1.4491377 1.6124515 1.7320508 #> 82  1.7606817 1.2649111 1.6124515 1.4832397 1.5165751 1.6733201 1.7888544 #> 83  1.4491377 0.7745967 1.4142136 1.0954451 1.1401754 1.3416408 1.4832397 #> 84  1.0488088 1.2649111 0.8944272 1.0000000 1.3038405 1.3416408 1.1832160 #> 85  1.1401754 1.2649111 1.3416408 1.1832160 1.2247449 1.1832160 1.4142136 #> 86  0.8944272 1.2247449 1.3038405 1.1401754 1.1832160 1.1401754 1.3784049 #> 87  1.1401754 1.3416408 1.0954451 1.0954451 1.0488088 0.7745967 0.7745967 #> 88  1.4832397 1.0488088 0.9486833 1.0488088 0.8944272 1.0488088 1.2247449 #> 89  1.3038405 0.8944272 1.4832397 1.1832160 1.0488088 1.1832160 1.4832397 #> 90  1.5491933 0.9486833 1.3784049 1.3038405 1.2649111 1.4491377 1.5811388 #> 91  1.4142136 1.1401754 1.3038405 1.0488088 1.1832160 1.3038405 1.4491377 #> 92  1.0000000 0.9486833 1.0488088 0.7071068 0.8944272 0.8366600 1.0488088 #> 93  1.4491377 0.7745967 1.3416408 1.0954451 1.1401754 1.3416408 1.4832397 #> 94  2.0248457 1.6124515 1.8973666 1.7888544 1.8165902 1.9493589 2.0493902 #> 95  1.3784049 0.8944272 1.3416408 1.0954451 1.0488088 1.2649111 1.4142136 #> 96  1.2649111 0.9486833 1.4491377 1.0488088 1.0000000 1.1401754 1.4491377 #> 97  1.2649111 0.8366600 1.3784049 1.0488088 0.8944272 1.1401754 1.3784049 #> 98  1.2649111 0.7071068 1.1401754 0.8366600 0.4472136 0.8366600 1.1401754 #> 99  2.0000000 1.5811388 1.8708287 1.7606817 1.7888544 1.9235384 2.0248457 #> 100 1.3416408 0.7071068 1.3784049 1.0488088 1.0000000 1.2247449 1.3784049 #> 101 1.5491933 1.9748418 1.7029386 1.8165902 1.8439089 1.8165902 1.8165902 #> 102 1.0000000 1.4491377 1.1401754 1.2247449 1.4832397 1.5165751 1.3784049 #> 103 1.6733201 1.9748418 1.7029386 1.8165902 1.7888544 1.6431677 1.5165751 #> 104 1.2247449 1.5491933 1.1832160 1.3416408 1.3784049 1.4142136 1.3416408 #> 105 1.4832397 1.8165902 1.5165751 1.6431677 1.6124515 1.5165751 1.5165751 #> 106 2.0000000 2.2583180 2.0248457 2.1213203 2.0976177 1.9748418 1.8708287 #> 107 1.4491377 1.5491933 1.4142136 1.4832397 1.5811388 1.6124515 1.6733201 #> 108 1.7888544 2.0248457 1.7606817 1.8708287 1.8439089 1.7606817 1.5811388 #> 109 1.5811388 1.7888544 1.2649111 1.6124515 1.6431677 1.5491933 1.3416408 #> 110 1.9235384 2.2803509 2.0493902 2.1447611 2.1213203 2.0000000 1.8973666 #> 111 1.0488088 1.6124515 1.2649111 1.4142136 1.3784049 1.2649111 1.2649111 #> 112 1.2649111 1.5165751 1.0488088 1.3038405 1.3416408 1.3784049 1.2247449 #> 113 1.4491377 1.7888544 1.4832397 1.6124515 1.5811388 1.4142136 1.2649111 #> 114 1.1401754 1.5491933 1.0954451 1.3416408 1.5811388 1.6124515 1.4832397 #> 115 1.1832160 1.5811388 1.3784049 1.3784049 1.6124515 1.6431677 1.5165751 #> 116 1.2247449 1.7320508 1.4142136 1.5491933 1.5165751 1.4832397 1.4832397 #> 117 1.2247449 1.6124515 1.2649111 1.4142136 1.3784049 1.2649111 1.2649111 #> 118 2.1679483 2.4899799 2.2803509 2.3664319 2.3452079 2.2360680 2.1447611 #> 119 2.2360680 2.3874673 2.0736441 2.2583180 2.2803509 2.2135944 2.0248457 #> 120 1.2649111 1.3784049 0.8366600 1.1401754 1.4142136 1.4491377 1.3038405 #> 121 1.5491933 1.9748418 1.7029386 1.8165902 1.7888544 1.6431677 1.5165751 #> 122 1.0000000 1.4491377 1.2247449 1.2247449 1.4832397 1.5165751 1.3784049 #> 123 2.0736441 2.2360680 2.0000000 2.0976177 2.1213203 2.0493902 1.8439089 #> 124 1.0000000 1.3038405 0.7071068 1.0488088 1.1832160 1.2247449 1.0488088 #> 125 1.4491377 1.8973666 1.6124515 1.7320508 1.7029386 1.5491933 1.4832397 #> 126 1.5811388 2.0000000 1.7320508 1.8439089 1.8165902 1.6733201 1.5491933 #> 127 0.8366600 1.1832160 0.8944272 0.8944272 1.1401754 1.1832160 1.0000000 #> 128 0.7071068 1.2649111 1.0000000 1.0000000 1.2247449 1.1832160 1.1832160 #> 129 1.4142136 1.6431677 1.3038405 1.4491377 1.4832397 1.5165751 1.3784049 #> 130 1.6431677 1.8439089 1.5491933 1.6733201 1.6431677 1.4832397 1.3416408 #> 131 1.8165902 2.0000000 1.7320508 1.8439089 1.8708287 1.7888544 1.5491933 #> 132 2.0976177 2.4289916 2.2135944 2.3021729 2.2803509 2.1679483 2.0736441 #> 133 1.4491377 1.6733201 1.3416408 1.4832397 1.5165751 1.5491933 1.4142136 #> 134 1.1832160 1.2247449 0.7071068 0.9486833 1.0954451 1.1401754 0.9486833 #> 135 1.4142136 1.3784049 1.0488088 1.1401754 1.4142136 1.4491377 1.3038405 #> 136 1.9493589 2.2135944 1.9748418 2.0736441 2.0493902 1.9235384 1.8165902 #> 137 1.4142136 1.8708287 1.5811388 1.7029386 1.7320508 1.7029386 1.7029386 #> 138 1.1401754 1.6124515 1.2649111 1.4142136 1.3784049 1.3416408 1.3416408 #> 139 0.5477226 1.2649111 1.0954451 1.0000000 1.2247449 1.1832160 1.1832160 #> 140 1.4142136 1.8165902 1.5165751 1.6431677 1.6124515 1.4491377 1.3038405 #> 141 1.5165751 1.8973666 1.6124515 1.7320508 1.7029386 1.5491933 1.4832397 #> 142 1.3784049 1.7888544 1.4832397 1.6124515 1.5811388 1.4142136 1.2649111 #> 143 1.0000000 1.4491377 1.1401754 1.2247449 1.4832397 1.5165751 1.3784049 #> 144 1.5811388 2.0000000 1.7320508 1.8439089 1.8165902 1.6733201 1.5491933 #> 145 1.5811388 2.0000000 1.7320508 1.8439089 1.8165902 1.6733201 1.6124515 #> 146 1.3784049 1.7320508 1.4142136 1.5491933 1.5165751 1.3416408 1.2649111 #> 147 1.1832160 1.4491377 0.7071068 1.2247449 1.3416408 1.3784049 1.2247449 #> 148 1.1832160 1.5811388 1.2247449 1.3784049 1.3416408 1.2247449 1.2247449 #> 149 1.2649111 1.7606817 1.5165751 1.5811388 1.6733201 1.6431677 1.6431677 #> 150 0.7071068 1.4142136 1.1832160 1.1832160 1.3784049 1.3416408 1.3416408 #>            78        79        80        81        82        83        84 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44                                                                        #> 45                                                                        #> 46                                                                        #> 47                                                                        #> 48                                                                        #> 49                                                                        #> 50                                                                        #> 51                                                                        #> 52                                                                        #> 53                                                                        #> 54                                                                        #> 55                                                                        #> 56                                                                        #> 57                                                                        #> 58                                                                        #> 59                                                                        #> 60                                                                        #> 61                                                                        #> 62                                                                        #> 63                                                                        #> 64                                                                        #> 65                                                                        #> 66                                                                        #> 67                                                                        #> 68                                                                        #> 69                                                                        #> 70                                                                        #> 71                                                                        #> 72                                                                        #> 73                                                                        #> 74                                                                        #> 75                                                                        #> 76                                                                        #> 77                                                                        #> 78                                                                        #> 79  1.2247449                                                             #> 80  1.8973666 1.4491377                                                   #> 81  1.8973666 1.4491377 0.8944272                                         #> 82  1.9493589 1.5165751 0.7745967 0.4472136                               #> 83  1.6733201 1.1401754 0.8944272 0.8944272 1.0000000                     #> 84  1.0954451 0.9486833 1.6124515 1.6124515 1.6733201 1.3416408           #> 85  1.4142136 0.8366600 1.4832397 1.3416408 1.4142136 1.2649111 1.2649111 #> 86  1.3038405 0.7745967 1.6431677 1.6431677 1.7029386 1.3784049 1.1401754 #> 87  0.7745967 1.0488088 1.7888544 1.7888544 1.8439089 1.5491933 1.2649111 #> 88  1.4491377 1.0954451 1.4491377 1.3038405 1.3784049 1.2247449 1.3038405 #> 89  1.5491933 1.0488088 1.1832160 1.0954451 1.1832160 0.8944272 1.4142136 #> 90  1.7606817 1.2649111 1.0488088 0.7071068 0.8366600 0.8366600 1.4491377 #> 91  1.6431677 1.0954451 1.1401754 0.9486833 1.0488088 0.9486833 1.3038405 #> 92  1.1401754 0.6324555 1.5165751 1.5165751 1.5811388 1.2247449 1.0488088 #> 93  1.6733201 1.1401754 0.8944272 0.8944272 1.0000000 0.4472136 1.3416408 #> 94  2.1908902 1.8165902 1.0954451 1.0954451 1.0000000 1.4142136 1.9493589 #> 95  1.6124515 1.0488088 1.0954451 1.0000000 1.0954451 0.7745967 1.2649111 #> 96  1.5165751 1.0000000 1.1401754 1.1401754 1.2247449 0.8366600 1.3784049 #> 97  1.5165751 0.8944272 1.1401754 1.1401754 1.2247449 0.8366600 1.3038405 #> 98  1.3038405 0.7745967 1.3784049 1.3784049 1.4491377 1.0488088 1.2247449 #> 99  2.1679483 1.7888544 1.1401754 1.1401754 1.1401754 1.3784049 1.9235384 #> 100 1.5811388 1.0000000 1.0488088 1.0488088 1.1401754 0.7071068 1.3038405 #> 101 1.5811388 1.7888544 2.3021729 2.3021729 2.3452079 2.1213203 1.6431677 #> 102 1.2247449 1.1832160 1.6431677 1.6431677 1.7029386 1.3784049 0.7071068 #> 103 1.3038405 1.7888544 2.3021729 2.3021729 2.3452079 2.1213203 1.6431677 #> 104 1.0954451 1.3038405 1.9493589 1.9493589 2.0000000 1.7320508 1.0954451 #> 105 1.2247449 1.6124515 2.1679483 2.1679483 2.2135944 1.9748418 1.4491377 #> 106 1.7029386 2.0976177 2.5495098 2.5495098 2.5884358 2.3874673 1.9748418 #> 107 1.6733201 1.3038405 1.6124515 1.4142136 1.4832397 1.4832397 1.4142136 #> 108 1.4491377 1.8439089 2.3452079 2.3452079 2.3874673 2.1679483 1.7029386 #> 109 1.1832160 1.6431677 2.0493902 2.0000000 2.0493902 1.8973666 1.3416408 #> 110 1.7320508 2.1213203 2.5690465 2.5690465 2.6076810 2.4083189 2.0000000 #> 111 0.8944272 1.3784049 2.0000000 2.0000000 2.0493902 1.7888544 1.1832160 #> 112 1.0488088 1.3416408 1.8708287 1.8708287 1.9235384 1.6431677 0.9486833 #> 113 1.0000000 1.5811388 2.1447611 2.1447611 2.1908902 1.9493589 1.4142136 #> 114 1.3416408 1.3038405 1.6124515 1.5491933 1.6124515 1.4832397 1.0000000 #> 115 1.3784049 1.3416408 1.8165902 1.8165902 1.8708287 1.5811388 1.0488088 #> 116 1.1832160 1.5165751 2.0976177 2.0976177 2.1447611 1.8973666 1.3416408 #> 117 0.8944272 1.3784049 2.0000000 2.0000000 2.0493902 1.7888544 1.1832160 #> 118 2.0000000 2.3452079 2.7568098 2.7568098 2.7928480 2.6076810 2.2360680 #> 119 1.9748418 2.2803509 2.5884358 2.5884358 2.6267851 2.4698178 2.0736441 #> 120 1.3038405 1.0954451 1.6431677 1.5165751 1.5811388 1.4491377 0.8366600 #> 121 1.3038405 1.7888544 2.3021729 2.3021729 2.3452079 2.1213203 1.6431677 #> 122 1.3038405 1.1832160 1.6431677 1.5811388 1.6431677 1.4491377 1.0488088 #> 123 1.7888544 2.1213203 2.5298221 2.5298221 2.5690465 2.3664319 1.9493589 #> 124 0.9486833 1.0954451 1.7029386 1.7029386 1.7606817 1.4491377 0.8366600 #> 125 1.1832160 1.7029386 2.2360680 2.2360680 2.2803509 2.0493902 1.5491933 #> 126 1.3416408 1.8165902 2.3237900 2.3237900 2.3664319 2.1447611 1.6733201 #> 127 1.0000000 0.9486833 1.6733201 1.6733201 1.7320508 1.4142136 0.8944272 #> 128 0.8944272 0.9486833 1.7320508 1.7320508 1.7888544 1.4832397 0.8944272 #> 129 1.2247449 1.4832397 2.0248457 2.0248457 2.0736441 1.8165902 1.2247449 #> 130 1.1832160 1.6431677 2.1908902 2.1908902 2.2360680 2.0000000 1.4832397 #> 131 1.4832397 1.8708287 2.3237900 2.3237900 2.3664319 2.1447611 1.6733201 #> 132 1.9235384 2.2803509 2.7018512 2.7018512 2.7386128 2.5495098 2.1679483 #> 133 1.2649111 1.5165751 2.0493902 2.0493902 2.0976177 1.8439089 1.2649111 #> 134 0.9486833 1.0000000 1.7029386 1.7029386 1.7606817 1.4491377 0.7071068 #> 135 1.3784049 1.2649111 1.7029386 1.7029386 1.7606817 1.5165751 0.9486833 #> 136 1.6431677 2.0493902 2.5099801 2.5099801 2.5495098 2.3452079 1.9235384 #> 137 1.4491377 1.6733201 2.2135944 2.2135944 2.2583180 2.0248457 1.5165751 #> 138 1.0000000 1.3784049 2.0000000 2.0000000 2.0493902 1.7888544 1.1832160 #> 139 1.0000000 0.8366600 1.6733201 1.6733201 1.7320508 1.4142136 0.8944272 #> 140 1.0488088 1.6124515 2.1679483 2.1679483 2.2135944 1.9748418 1.4491377 #> 141 1.1832160 1.7029386 2.2360680 2.2360680 2.2803509 2.0493902 1.5491933 #> 142 1.0000000 1.5811388 2.1447611 2.1447611 2.1908902 1.9493589 1.4142136 #> 143 1.2247449 1.1832160 1.6431677 1.6431677 1.7029386 1.3784049 0.7071068 #> 144 1.3416408 1.8165902 2.3237900 2.3237900 2.3664319 2.1447611 1.6733201 #> 145 1.3416408 1.8165902 2.3237900 2.3237900 2.3664319 2.1447611 1.6733201 #> 146 0.8944272 1.5165751 2.0976177 2.0976177 2.1447611 1.8973666 1.3416408 #> 147 1.0488088 1.2649111 1.7606817 1.7029386 1.7606817 1.5811388 0.9486833 #> 148 0.8366600 1.3416408 1.9748418 1.9748418 2.0248457 1.7606817 1.1401754 #> 149 1.3784049 1.5491933 2.1213203 2.1213203 2.1679483 1.9235384 1.3784049 #> 150 1.0000000 1.0488088 1.7320508 1.7320508 1.7888544 1.4832397 0.7745967 #>            85        86        87        88        89        90        91 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44                                                                        #> 45                                                                        #> 46                                                                        #> 47                                                                        #> 48                                                                        #> 49                                                                        #> 50                                                                        #> 51                                                                        #> 52                                                                        #> 53                                                                        #> 54                                                                        #> 55                                                                        #> 56                                                                        #> 57                                                                        #> 58                                                                        #> 59                                                                        #> 60                                                                        #> 61                                                                        #> 62                                                                        #> 63                                                                        #> 64                                                                        #> 65                                                                        #> 66                                                                        #> 67                                                                        #> 68                                                                        #> 69                                                                        #> 70                                                                        #> 71                                                                        #> 72                                                                        #> 73                                                                        #> 74                                                                        #> 75                                                                        #> 76                                                                        #> 77                                                                        #> 78                                                                        #> 79                                                                        #> 80                                                                        #> 81                                                                        #> 82                                                                        #> 83                                                                        #> 84                                                                        #> 85                                                                        #> 86  1.0488088                                                             #> 87  1.2649111 1.1401754                                                   #> 88  1.3784049 1.3416408 1.3038405                                         #> 89  0.8944272 1.2247449 1.4142136 1.3038405                               #> 90  1.1401754 1.4832397 1.6431677 1.1832160 0.8366600                     #> 91  0.9486833 1.3416408 1.5165751 1.0954451 0.9486833 0.7745967           #> 92  0.9486833 0.8944272 0.9486833 1.0954451 1.0488088 1.3416408 1.1832160 #> 93  1.2649111 1.3784049 1.5491933 1.1401754 0.8944272 0.7071068 0.8366600 #> 94  1.6733201 1.9748418 2.0976177 1.6431677 1.5491933 1.3038405 1.4491377 #> 95  1.0000000 1.3038405 1.4832397 1.1401754 0.6324555 0.7071068 0.7071068 #> 96  0.9486833 1.1832160 1.3784049 1.2649111 0.5477226 1.0000000 0.8944272 #> 97  0.9486833 1.1832160 1.3784049 1.1832160 0.5477226 0.8944272 0.8944272 #> 98  1.1401754 1.0954451 1.1401754 0.8944272 0.9486833 1.1832160 1.0954451 #> 99  1.6431677 1.9493589 2.0736441 1.7320508 1.5165751 1.2649111 1.4142136 #> 100 1.0488088 1.2649111 1.4491377 1.1832160 0.5477226 0.7745967 0.8944272 #> 101 1.9235384 1.6733201 1.7029386 1.9493589 2.0248457 2.1908902 2.0976177 #> 102 1.3038405 1.3416408 1.4491377 1.4832397 1.4491377 1.4832397 1.3416408 #> 103 1.9235384 1.8439089 1.5165751 1.9493589 2.0248457 2.1908902 2.0976177 #> 104 1.5491933 1.4491377 1.3416408 1.5165751 1.6733201 1.8165902 1.7029386 #> 105 1.7606817 1.6733201 1.4491377 1.7888544 1.8708287 2.0493902 1.9493589 #> 106 2.2135944 2.1447611 1.8708287 2.2360680 2.3021729 2.4494897 2.3664319 #> 107 1.0954451 1.4491377 1.6733201 1.4491377 1.4142136 1.2247449 1.1401754 #> 108 2.0248457 1.9493589 1.6431677 2.0000000 2.1213203 2.2360680 2.1447611 #> 109 1.8439089 1.7606817 1.4142136 1.5811388 1.9493589 1.8708287 1.8165902 #> 110 2.2360680 1.9748418 1.8439089 2.2583180 2.3237900 2.4698178 2.3874673 #> 111 1.5491933 1.3038405 1.0954451 1.5811388 1.6733201 1.8708287 1.7606817 #> 112 1.5811388 1.4832397 1.3038405 1.4142136 1.7029386 1.7320508 1.6124515 #> 113 1.7320508 1.6431677 1.2649111 1.7606817 1.8439089 2.0248457 1.9235384 #> 114 1.3416408 1.4491377 1.5491933 1.4491377 1.4832397 1.3784049 1.3038405 #> 115 1.4491377 1.4832397 1.5811388 1.6733201 1.5811388 1.6733201 1.5491933 #> 116 1.6733201 1.4491377 1.3416408 1.7029386 1.7888544 1.9748418 1.8708287 #> 117 1.5491933 1.4491377 1.1832160 1.5811388 1.6733201 1.8708287 1.7606817 #> 118 2.4494897 2.2135944 2.0976177 2.4698178 2.5298221 2.6645825 2.5884358 #> 119 2.4289916 2.3664319 2.1213203 2.2803509 2.5099801 2.4899799 2.4083189 #> 120 1.3784049 1.3416408 1.3784049 1.0954451 1.5165751 1.4142136 1.3416408 #> 121 1.9235384 1.7320508 1.4491377 1.9493589 2.0248457 2.1908902 2.0976177 #> 122 1.1401754 1.3416408 1.4491377 1.5491933 1.3038405 1.4142136 1.2649111 #> 123 2.2803509 2.2135944 1.9493589 2.2135944 2.3664319 2.4289916 2.3452079 #> 124 1.3784049 1.2649111 1.1401754 1.1832160 1.5165751 1.5491933 1.4142136 #> 125 1.8439089 1.5811388 1.3416408 1.8708287 1.9493589 2.1213203 2.0248457 #> 126 1.9493589 1.7606817 1.4832397 1.9748418 2.0493902 2.2135944 2.1213203 #> 127 1.2649111 1.1401754 1.0954451 1.2247449 1.4142136 1.5165751 1.3784049 #> 128 1.1832160 1.0488088 1.0954451 1.3784049 1.3416408 1.5811388 1.4491377 #> 129 1.7029386 1.6124515 1.4491377 1.6124515 1.8165902 1.8973666 1.7888544 #> 130 1.7888544 1.7029386 1.3416408 1.8165902 1.8973666 2.0736441 1.9748418 #> 131 2.0493902 1.9748418 1.6733201 1.9748418 2.1447611 2.2135944 2.1213203 #> 132 2.3874673 2.1447611 2.0248457 2.4083189 2.4698178 2.6076810 2.5298221 #> 133 1.7320508 1.6431677 1.4832397 1.6431677 1.8439089 1.9235384 1.8165902 #> 134 1.3038405 1.2649111 1.0488088 1.1832160 1.4491377 1.5491933 1.4142136 #> 135 1.5165751 1.4832397 1.4491377 1.3416408 1.5811388 1.5491933 1.4142136 #> 136 2.1679483 2.0976177 1.8165902 2.1908902 2.2583180 2.4083189 2.3237900 #> 137 1.8165902 1.4832397 1.5811388 1.8439089 1.9235384 2.0976177 2.0000000 #> 138 1.5491933 1.3784049 1.1832160 1.5811388 1.6733201 1.8708287 1.7606817 #> 139 1.0954451 0.9486833 1.0954451 1.3784049 1.2649111 1.5165751 1.3784049 #> 140 1.7606817 1.6124515 1.2247449 1.7888544 1.8708287 2.0493902 1.9493589 #> 141 1.8439089 1.7029386 1.3416408 1.8708287 1.9493589 2.1213203 2.0248457 #> 142 1.7320508 1.5811388 1.1832160 1.7606817 1.8439089 2.0248457 1.9235384 #> 143 1.3038405 1.3416408 1.4491377 1.4832397 1.4491377 1.4832397 1.3416408 #> 144 1.9493589 1.7606817 1.4832397 1.9748418 2.0493902 2.2135944 2.1213203 #> 145 1.9493589 1.7029386 1.4832397 1.9748418 2.0493902 2.2135944 2.1213203 #> 146 1.6733201 1.5811388 1.1832160 1.7029386 1.7888544 1.9748418 1.8708287 #> 147 1.5165751 1.4142136 1.3038405 1.1832160 1.6431677 1.5491933 1.4832397 #> 148 1.5165751 1.4142136 1.1401754 1.5491933 1.6431677 1.8439089 1.7320508 #> 149 1.7029386 1.3416408 1.5165751 1.7888544 1.8165902 2.0000000 1.8973666 #> 150 1.1832160 1.1401754 1.2649111 1.5165751 1.3416408 1.5811388 1.4491377 #>            92        93        94        95        96        97        98 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44                                                                        #> 45                                                                        #> 46                                                                        #> 47                                                                        #> 48                                                                        #> 49                                                                        #> 50                                                                        #> 51                                                                        #> 52                                                                        #> 53                                                                        #> 54                                                                        #> 55                                                                        #> 56                                                                        #> 57                                                                        #> 58                                                                        #> 59                                                                        #> 60                                                                        #> 61                                                                        #> 62                                                                        #> 63                                                                        #> 64                                                                        #> 65                                                                        #> 66                                                                        #> 67                                                                        #> 68                                                                        #> 69                                                                        #> 70                                                                        #> 71                                                                        #> 72                                                                        #> 73                                                                        #> 74                                                                        #> 75                                                                        #> 76                                                                        #> 77                                                                        #> 78                                                                        #> 79                                                                        #> 80                                                                        #> 81                                                                        #> 82                                                                        #> 83                                                                        #> 84                                                                        #> 85                                                                        #> 86                                                                        #> 87                                                                        #> 88                                                                        #> 89                                                                        #> 90                                                                        #> 91                                                                        #> 92                                                                        #> 93  1.2247449                                                             #> 94  1.8708287 1.4142136                                                   #> 95  1.1401754 0.7745967 1.4832397                                         #> 96  1.0000000 0.8366600 1.5811388 0.7071068                               #> 97  1.0000000 0.8366600 1.5811388 0.5477226 0.4472136                     #> 98  0.7745967 1.0488088 1.7606817 0.9486833 0.8944272 0.7745967           #> 99  1.8439089 1.3784049 0.8366600 1.4491377 1.5491933 1.5491933 1.7320508 #> 100 1.0954451 0.7071068 1.5165751 0.5477226 0.6324555 0.4472136 0.8944272 #> 101 1.7320508 2.1213203 2.5495098 2.0736441 2.0000000 2.0000000 1.8439089 #> 102 1.2649111 1.3784049 1.9748418 1.3038405 1.4142136 1.3416408 1.4142136 #> 103 1.7320508 2.1213203 2.5495098 2.0736441 2.0000000 2.0000000 1.8439089 #> 104 1.3038405 1.7320508 2.2360680 1.6733201 1.6431677 1.5811388 1.3784049 #> 105 1.5491933 1.9748418 2.4289916 1.9235384 1.8439089 1.8439089 1.6733201 #> 106 2.0493902 2.3874673 2.7748874 2.3452079 2.2803509 2.2803509 2.1447611 #> 107 1.4491377 1.4142136 1.4832397 1.2649111 1.4491377 1.3784049 1.5165751 #> 108 1.8439089 2.1679483 2.5884358 2.1213203 2.0976177 2.0493902 1.8973666 #> 109 1.6431677 1.8439089 2.2803509 1.8439089 1.9235384 1.8708287 1.7029386 #> 110 2.0736441 2.4083189 2.7928480 2.3664319 2.3021729 2.3021729 2.1679483 #> 111 1.3038405 1.7888544 2.2803509 1.7320508 1.6431677 1.6431677 1.4491377 #> 112 1.3416408 1.6431677 2.1679483 1.5811388 1.6733201 1.6124515 1.4142136 #> 113 1.5165751 1.9493589 2.4083189 1.8973666 1.8165902 1.8165902 1.6431677 #> 114 1.3784049 1.4142136 1.8973666 1.3416408 1.4491377 1.3784049 1.5165751 #> 115 1.4142136 1.5811388 2.1213203 1.5165751 1.5491933 1.4832397 1.5491933 #> 116 1.4491377 1.8973666 2.3664319 1.8439089 1.7606817 1.7606817 1.5811388 #> 117 1.3038405 1.7888544 2.2803509 1.7320508 1.6431677 1.6431677 1.4491377 #> 118 2.3021729 2.6076810 2.9664794 2.5690465 2.5099801 2.5099801 2.3874673 #> 119 2.2803509 2.4289916 2.8106939 2.4289916 2.4899799 2.4494897 2.3237900 #> 120 1.1832160 1.3784049 1.8165902 1.3784049 1.4832397 1.4142136 1.3416408 #> 121 1.7320508 2.1213203 2.5495098 2.0736441 2.0000000 2.0000000 1.8439089 #> 122 1.2649111 1.4491377 1.9235384 1.2247449 1.3416408 1.2649111 1.4142136 #> 123 2.1213203 2.3664319 2.7568098 2.3237900 2.3452079 2.3021729 2.1679483 #> 124 1.0954451 1.4491377 2.0248457 1.3784049 1.4832397 1.4142136 1.1832160 #> 125 1.6431677 2.0493902 2.4899799 2.0000000 1.9235384 1.9235384 1.7606817 #> 126 1.7606817 2.1447611 2.5690465 2.0976177 2.0248457 2.0248457 1.8708287 #> 127 0.9486833 1.4142136 2.0000000 1.3416408 1.3784049 1.3038405 1.0488088 #> 128 0.8366600 1.4832397 2.0493902 1.4142136 1.3038405 1.3038405 1.1401754 #> 129 1.4832397 1.8165902 2.3021729 1.7606817 1.7888544 1.7320508 1.5491933 #> 130 1.5811388 2.0000000 2.4494897 1.9493589 1.8708287 1.8708287 1.7029386 #> 131 1.8708287 2.1447611 2.5690465 2.0976177 2.1213203 2.0736441 1.9235384 #> 132 2.2360680 2.5495098 2.9154759 2.5099801 2.4494897 2.4494897 2.3237900 #> 133 1.5165751 1.8439089 2.3237900 1.7888544 1.8165902 1.7606817 1.5811388 #> 134 1.0000000 1.4491377 2.0248457 1.3784049 1.4142136 1.3416408 1.0954451 #> 135 1.1832160 1.4491377 2.0248457 1.4491377 1.5491933 1.4832397 1.3416408 #> 136 2.0000000 2.3452079 2.7386128 2.3021729 2.2360680 2.2360680 2.0976177 #> 137 1.6124515 2.0248457 2.4698178 1.9748418 1.8973666 1.8973666 1.7320508 #> 138 1.3038405 1.7888544 2.2803509 1.7320508 1.6431677 1.6431677 1.4491377 #> 139 0.8366600 1.4142136 2.0000000 1.3416408 1.2247449 1.2247449 1.1401754 #> 140 1.5491933 1.9748418 2.4289916 1.9235384 1.8439089 1.8439089 1.6733201 #> 141 1.6431677 2.0493902 2.4899799 2.0000000 1.9235384 1.9235384 1.7606817 #> 142 1.5165751 1.9493589 2.4083189 1.8973666 1.8165902 1.8165902 1.6431677 #> 143 1.2649111 1.3784049 1.9748418 1.3038405 1.4142136 1.3416408 1.4142136 #> 144 1.7606817 2.1447611 2.5690465 2.0976177 2.0248457 2.0248457 1.8708287 #> 145 1.7606817 2.1447611 2.5690465 2.0976177 2.0248457 2.0248457 1.8708287 #> 146 1.4491377 1.8973666 2.3664319 1.8439089 1.7606817 1.7606817 1.5811388 #> 147 1.2649111 1.5165751 2.0248457 1.5165751 1.6124515 1.5491933 1.3416408 #> 148 1.2649111 1.7606817 2.2583180 1.7029386 1.6124515 1.6124515 1.4142136 #> 149 1.4832397 1.9235384 2.3874673 1.8708287 1.7888544 1.7888544 1.6124515 #> 150 1.0488088 1.4832397 2.0493902 1.4142136 1.3038405 1.3038405 1.3038405 #>            99       100       101       102       103       104       105 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44                                                                        #> 45                                                                        #> 46                                                                        #> 47                                                                        #> 48                                                                        #> 49                                                                        #> 50                                                                        #> 51                                                                        #> 52                                                                        #> 53                                                                        #> 54                                                                        #> 55                                                                        #> 56                                                                        #> 57                                                                        #> 58                                                                        #> 59                                                                        #> 60                                                                        #> 61                                                                        #> 62                                                                        #> 63                                                                        #> 64                                                                        #> 65                                                                        #> 66                                                                        #> 67                                                                        #> 68                                                                        #> 69                                                                        #> 70                                                                        #> 71                                                                        #> 72                                                                        #> 73                                                                        #> 74                                                                        #> 75                                                                        #> 76                                                                        #> 77                                                                        #> 78                                                                        #> 79                                                                        #> 80                                                                        #> 81                                                                        #> 82                                                                        #> 83                                                                        #> 84                                                                        #> 85                                                                        #> 86                                                                        #> 87                                                                        #> 88                                                                        #> 89                                                                        #> 90                                                                        #> 91                                                                        #> 92                                                                        #> 93                                                                        #> 94                                                                        #> 95                                                                        #> 96                                                                        #> 97                                                                        #> 98                                                                        #> 99                                                                        #> 100 1.4832397                                                             #> 101 2.5298221 2.0493902                                                   #> 102 1.9493589 1.3416408 1.6124515                                         #> 103 2.5298221 2.0493902 1.2649111 1.6124515                               #> 104 2.2135944 1.6431677 1.2247449 1.1401754 1.2247449                     #> 105 2.4083189 1.8973666 1.0000000 1.4142136 0.8944272 0.9486833           #> 106 2.7568098 2.3237900 1.6124515 1.9493589 1.0954451 1.6431677 1.4142136 #> 107 1.5165751 1.3784049 2.1213203 1.3784049 2.1213203 1.7320508 1.9748418 #> 108 2.5690465 2.0976177 1.5491933 1.7320508 1.0000000 1.3038405 1.3416408 #> 109 2.2583180 1.8708287 1.4491377 1.3784049 1.1401754 1.0000000 1.0488088 #> 110 2.7748874 2.3452079 1.1401754 1.9748418 1.1401754 1.6733201 1.3784049 #> 111 2.2583180 1.7029386 1.3038405 1.1401754 1.3038405 1.0954451 1.0488088 #> 112 2.1447611 1.6124515 1.4142136 0.8944272 1.3416408 0.8366600 1.0954451 #> 113 2.3874673 1.8708287 1.3038405 1.3784049 0.8366600 1.0000000 0.8366600 #> 114 1.8708287 1.3784049 1.7029386 0.7071068 1.7029386 1.3416408 1.5165751 #> 115 2.0976177 1.4832397 1.4142136 0.7745967 1.6124515 1.3038405 1.3416408 #> 116 2.3452079 1.8165902 1.0488088 1.3038405 1.3038405 1.0954451 0.9486833 #> 117 2.2583180 1.7029386 1.3038405 1.2247449 1.1401754 0.6324555 0.8366600 #> 118 2.9495762 2.5495098 1.7029386 2.2135944 1.5165751 1.9493589 1.7029386 #> 119 2.7928480 2.4494897 1.7888544 2.0493902 1.4832397 1.8708287 1.6733201 #> 120 1.8973666 1.4142136 1.8439089 1.0954451 1.8439089 1.3784049 1.6733201 #> 121 2.5298221 2.0493902 1.0954451 1.6124515 0.8944272 1.2247449 0.8944272 #> 122 1.8973666 1.2649111 1.6733201 0.7745967 1.6733201 1.3038405 1.4832397 #> 123 2.7386128 2.3021729 1.7606817 1.9235384 1.3038405 1.6733201 1.5811388 #> 124 2.0000000 1.4142136 1.5491933 0.8944272 1.5491933 0.9486833 1.3416408 #> 125 2.4698178 1.9748418 1.0488088 1.5165751 0.9486833 1.0954451 0.8366600 #> 126 2.5495098 2.0736441 1.3038405 1.7029386 0.8366600 1.2649111 1.2247449 #> 127 1.9748418 1.3038405 1.5811388 0.9486833 1.5811388 1.0000000 1.3784049 #> 128 2.0248457 1.3784049 1.5165751 0.9486833 1.5165751 1.0000000 1.3038405 #> 129 2.2803509 1.7320508 1.1832160 1.1832160 1.0954451 0.7071068 0.7745967 #> 130 2.4289916 1.9235384 1.5165751 1.6431677 0.8366600 1.1832160 1.1401754 #> 131 2.5495098 2.0736441 1.5165751 1.6431677 0.9486833 1.3416408 1.3038405 #> 132 2.8982753 2.4899799 1.7320508 2.1447611 1.4832397 1.8708287 1.7320508 #> 133 2.3021729 1.7606817 1.1401754 1.2247449 1.1401754 0.7745967 0.7071068 #> 134 2.0000000 1.3416408 1.5491933 1.0000000 1.5491933 0.9486833 1.3416408 #> 135 2.0000000 1.4832397 1.5491933 1.1832160 1.5491933 0.9486833 1.3416408 #> 136 2.7202941 2.2803509 1.4142136 1.8973666 1.0000000 1.5811388 1.2649111 #> 137 2.4494897 1.9493589 0.7745967 1.4832397 1.3416408 1.0488088 1.0000000 #> 138 2.2583180 1.7029386 1.2247449 1.2247449 1.2247449 0.6324555 0.9486833 #> 139 1.9748418 1.3038405 1.5811388 0.9486833 1.5811388 1.0954451 1.3784049 #> 140 2.4083189 1.8973666 1.3416408 1.4142136 0.8944272 1.1401754 1.0000000 #> 141 2.4698178 1.9748418 1.0488088 1.5165751 1.0488088 1.0954451 0.8366600 #> 142 2.3874673 1.8708287 1.3784049 1.3784049 1.1401754 1.3416408 1.1401754 #> 143 1.9493589 1.3416408 1.6124515 0.0000000 1.6124515 1.1401754 1.4142136 #> 144 2.5495098 2.0736441 0.9486833 1.6431677 0.8366600 1.2649111 0.8366600 #> 145 2.5495098 2.0736441 0.8366600 1.6431677 1.1401754 1.2649111 0.9486833 #> 146 2.3452079 1.8165902 1.3038405 1.3038405 1.1401754 1.1832160 0.9486833 #> 147 2.0000000 1.5491933 1.5491933 0.8944272 1.5491933 1.0488088 1.3416408 #> 148 2.2360680 1.6733201 1.3416408 1.0954451 1.1832160 0.9486833 0.8944272 #> 149 2.3664319 1.8439089 1.0000000 1.3416408 1.4142136 1.1401754 1.0954451 #> 150 2.0248457 1.3784049 1.5165751 0.7071068 1.5165751 1.0000000 1.3038405 #>           106       107       108       109       110       111       112 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44                                                                        #> 45                                                                        #> 46                                                                        #> 47                                                                        #> 48                                                                        #> 49                                                                        #> 50                                                                        #> 51                                                                        #> 52                                                                        #> 53                                                                        #> 54                                                                        #> 55                                                                        #> 56                                                                        #> 57                                                                        #> 58                                                                        #> 59                                                                        #> 60                                                                        #> 61                                                                        #> 62                                                                        #> 63                                                                        #> 64                                                                        #> 65                                                                        #> 66                                                                        #> 67                                                                        #> 68                                                                        #> 69                                                                        #> 70                                                                        #> 71                                                                        #> 72                                                                        #> 73                                                                        #> 74                                                                        #> 75                                                                        #> 76                                                                        #> 77                                                                        #> 78                                                                        #> 79                                                                        #> 80                                                                        #> 81                                                                        #> 82                                                                        #> 83                                                                        #> 84                                                                        #> 85                                                                        #> 86                                                                        #> 87                                                                        #> 88                                                                        #> 89                                                                        #> 90                                                                        #> 91                                                                        #> 92                                                                        #> 93                                                                        #> 94                                                                        #> 95                                                                        #> 96                                                                        #> 97                                                                        #> 98                                                                        #> 99                                                                        #> 100                                                                       #> 101                                                                       #> 102                                                                       #> 103                                                                       #> 104                                                                       #> 105                                                                       #> 106                                                                       #> 107 2.3874673                                                             #> 108 1.0000000 2.1679483                                                   #> 109 1.5811388 1.7888544 1.2247449                                         #> 110 1.3784049 2.4083189 1.3038405 1.6124515                               #> 111 1.7029386 1.7888544 1.5811388 1.3416408 1.6124515                     #> 112 1.7320508 1.6431677 1.4832397 1.0488088 1.7606817 0.9486833           #> 113 1.3784049 1.9493589 1.3038405 1.0954451 1.4142136 1.0000000 1.0488088 #> 114 2.0248457 1.2649111 1.8708287 1.4142136 2.0493902 1.2649111 1.1401754 #> 115 1.9493589 1.5811388 1.8439089 1.5811388 1.8165902 1.2247449 1.1832160 #> 116 1.7029386 1.8973666 1.6431677 1.4142136 1.4832397 0.7745967 0.9486833 #> 117 1.5811388 1.7888544 1.3038405 1.0000000 1.6124515 0.8944272 0.8366600 #> 118 1.0488088 2.6076810 1.4491377 1.8973666 1.2649111 1.8973666 2.0248457 #> 119 1.0000000 2.4289916 1.3416408 1.6431677 1.5811388 1.9748418 1.8439089 #> 120 2.1447611 1.4491377 1.8973666 1.4491377 2.1679483 1.4491377 1.2649111 #> 121 1.4142136 2.1213203 1.3416408 1.2247449 1.1401754 1.1401754 1.3416408 #> 122 2.0000000 1.3038405 1.8439089 1.5811388 2.0248457 1.2247449 1.1832160 #> 123 0.7071068 2.3664319 1.0488088 1.5491933 1.5491933 1.7888544 1.7029386 #> 124 1.8973666 1.4491377 1.6124515 1.2247449 1.9235384 1.0488088 0.7745967 #> 125 1.4491377 2.0493902 1.3784049 1.0954451 1.2649111 1.0000000 1.2247449 #> 126 1.2247449 2.1447611 0.8366600 1.1832160 1.0954451 1.3416408 1.4491377 #> 127 1.9235384 1.4142136 1.6431677 1.3416408 1.9493589 1.0954451 0.9486833 #> 128 1.8708287 1.4832397 1.6431677 1.4142136 1.8973666 1.0000000 1.0488088 #> 129 1.5491933 1.8165902 1.4142136 1.0488088 1.5811388 1.0488088 0.7745967 #> 130 1.3038405 2.0493902 0.9486833 1.0954451 1.3416408 1.4142136 1.3784049 #> 131 1.0488088 2.1447611 0.7071068 1.1832160 1.2649111 1.5491933 1.3784049 #> 132 1.1832160 2.5495098 1.3416408 1.8165902 1.3038405 1.8165902 1.9493589 #> 133 1.5811388 1.8439089 1.4491377 1.0954451 1.5491933 1.0954451 0.8366600 #> 134 1.8973666 1.5811388 1.6124515 1.3038405 1.9235384 1.0488088 0.8944272 #> 135 1.8973666 1.6431677 1.6124515 1.1401754 1.9235384 1.4491377 1.0954451 #> 136 0.8944272 2.3452079 1.0954451 1.5165751 1.1401754 1.6431677 1.6733201 #> 137 1.7320508 2.0248457 1.6733201 1.4491377 1.3038405 1.1401754 1.2649111 #> 138 1.6431677 1.7888544 1.3784049 1.0954451 1.6124515 0.8944272 0.8366600 #> 139 1.9235384 1.4142136 1.7029386 1.4832397 1.9493589 1.0954451 1.1401754 #> 140 1.4142136 1.9748418 1.3416408 1.2247449 1.3784049 0.9486833 1.0954451 #> 141 1.5165751 2.0493902 1.4491377 1.1832160 1.2649111 1.0954451 1.2247449 #> 142 1.5811388 1.9493589 1.5165751 1.4142136 1.4142136 0.8944272 1.2247449 #> 143 1.9493589 1.3784049 1.7320508 1.3784049 1.9748418 1.1401754 0.8944272 #> 144 1.3784049 2.1447611 1.3038405 1.1832160 1.0954451 1.1832160 1.3784049 #> 145 1.5811388 2.1447611 1.5165751 1.2649111 1.0954451 1.1832160 1.3784049 #> 146 1.5811388 1.8973666 1.5165751 1.2649111 1.4832397 0.8944272 1.0488088 #> 147 1.8973666 1.4491377 1.6733201 1.1401754 1.9235384 1.0488088 0.7745967 #> 148 1.6124515 1.7606817 1.4832397 1.2247449 1.6431677 0.5477226 0.7745967 #> 149 1.7888544 1.9235384 1.7320508 1.5165751 1.4491377 1.0488088 1.1832160 #> 150 1.8708287 1.4832397 1.6431677 1.4142136 1.8973666 1.0000000 1.0488088 #>           113       114       115       116       117       118       119 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44                                                                        #> 45                                                                        #> 46                                                                        #> 47                                                                        #> 48                                                                        #> 49                                                                        #> 50                                                                        #> 51                                                                        #> 52                                                                        #> 53                                                                        #> 54                                                                        #> 55                                                                        #> 56                                                                        #> 57                                                                        #> 58                                                                        #> 59                                                                        #> 60                                                                        #> 61                                                                        #> 62                                                                        #> 63                                                                        #> 64                                                                        #> 65                                                                        #> 66                                                                        #> 67                                                                        #> 68                                                                        #> 69                                                                        #> 70                                                                        #> 71                                                                        #> 72                                                                        #> 73                                                                        #> 74                                                                        #> 75                                                                        #> 76                                                                        #> 77                                                                        #> 78                                                                        #> 79                                                                        #> 80                                                                        #> 81                                                                        #> 82                                                                        #> 83                                                                        #> 84                                                                        #> 85                                                                        #> 86                                                                        #> 87                                                                        #> 88                                                                        #> 89                                                                        #> 90                                                                        #> 91                                                                        #> 92                                                                        #> 93                                                                        #> 94                                                                        #> 95                                                                        #> 96                                                                        #> 97                                                                        #> 98                                                                        #> 99                                                                        #> 100                                                                       #> 101                                                                       #> 102                                                                       #> 103                                                                       #> 104                                                                       #> 105                                                                       #> 106                                                                       #> 107                                                                       #> 108                                                                       #> 109                                                                       #> 110                                                                       #> 111                                                                       #> 112                                                                       #> 113                                                                       #> 114 1.4832397                                                             #> 115 1.3784049 0.9486833                                                   #> 116 1.0000000 1.4142136 1.1401754                                         #> 117 0.7745967 1.4142136 1.3784049 1.0000000                               #> 118 1.7320508 2.2803509 2.1679483 1.8439089 1.8973666                     #> 119 1.7029386 2.0736441 2.0000000 1.8708287 1.8708287 1.2247449           #> 120 1.6431677 1.0488088 1.3416408 1.5811388 1.4491377 2.3874673 2.1908902 #> 121 0.8366600 1.7029386 1.4832397 0.9486833 1.1401754 1.5811388 1.6124515 #> 122 1.4491377 0.7071068 0.8944272 1.3784049 1.3784049 2.2583180 2.1447611 #> 123 1.5491933 2.0000000 1.9748418 1.8439089 1.6733201 1.0954451 0.8366600 #> 124 1.3038405 1.0488088 1.1832160 1.2247449 1.0488088 2.1679483 2.0000000 #> 125 0.7745967 1.6124515 1.5165751 1.0000000 1.0000000 1.6124515 1.7606817 #> 126 1.1832160 1.8439089 1.8165902 1.4142136 1.1832160 1.4832397 1.5811388 #> 127 1.3416408 1.0954451 1.1401754 1.2649111 1.0954451 2.1908902 2.0736441 #> 128 1.2649111 1.0954451 1.1401754 1.1832160 1.0000000 2.1447611 2.1213203 #> 129 0.8366600 1.3038405 1.1832160 0.9486833 0.8366600 1.8708287 1.7320508 #> 130 1.0954451 1.7888544 1.7606817 1.4832397 1.0954451 1.6733201 1.6431677 #> 131 1.2649111 1.7888544 1.7606817 1.6124515 1.3416408 1.4832397 1.3038405 #> 132 1.7029386 2.2135944 2.1908902 1.8708287 1.8165902 0.8366600 1.4832397 #> 133 0.8944272 1.3416408 1.1401754 0.8944272 0.8944272 1.8439089 1.7029386 #> 134 1.3038405 1.2247449 1.1832160 1.2247449 1.0488088 2.1679483 2.0493902 #> 135 1.3784049 1.3038405 1.4142136 1.4491377 1.1401754 2.1679483 1.9493589 #> 136 1.3038405 1.9748418 1.7888544 1.5165751 1.5165751 1.2247449 1.0954451 #> 137 1.1401754 1.5811388 1.2649111 0.8366600 1.1401754 1.7606817 1.8973666 #> 138 0.8944272 1.4142136 1.3784049 0.8944272 0.4472136 1.8973666 1.9235384 #> 139 1.3416408 1.0954451 1.1401754 1.2649111 1.0954451 2.1908902 2.1679483 #> 140 0.5477226 1.5165751 1.4142136 0.9486833 0.9486833 1.7029386 1.7320508 #> 141 0.7745967 1.6124515 1.3038405 0.8944272 1.0000000 1.7320508 1.7029386 #> 142 0.8944272 1.4832397 1.2247449 0.8944272 1.1832160 1.7888544 1.7606817 #> 143 1.3784049 0.7071068 0.7745967 1.3038405 1.2247449 2.2135944 2.0493902 #> 144 0.8944272 1.7320508 1.5165751 1.0000000 1.1832160 1.5491933 1.5811388 #> 145 1.0000000 1.7320508 1.4491377 1.0000000 1.1832160 1.6733201 1.7606817 #> 146 0.7745967 1.4142136 1.1401754 0.7745967 1.0000000 1.8439089 1.7606817 #> 147 1.3038405 0.8366600 1.1832160 1.2247449 1.1401754 2.1679483 1.9493589 #> 148 0.8366600 1.2247449 1.1832160 0.8366600 0.7071068 1.9235384 1.8973666 #> 149 1.1401754 1.4491377 1.1832160 0.7071068 1.1401754 1.8165902 1.9493589 #> 150 1.2649111 1.0000000 0.9486833 1.1832160 1.0000000 2.1447611 2.1213203 #>           120       121       122       123       124       125       126 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44                                                                        #> 45                                                                        #> 46                                                                        #> 47                                                                        #> 48                                                                        #> 49                                                                        #> 50                                                                        #> 51                                                                        #> 52                                                                        #> 53                                                                        #> 54                                                                        #> 55                                                                        #> 56                                                                        #> 57                                                                        #> 58                                                                        #> 59                                                                        #> 60                                                                        #> 61                                                                        #> 62                                                                        #> 63                                                                        #> 64                                                                        #> 65                                                                        #> 66                                                                        #> 67                                                                        #> 68                                                                        #> 69                                                                        #> 70                                                                        #> 71                                                                        #> 72                                                                        #> 73                                                                        #> 74                                                                        #> 75                                                                        #> 76                                                                        #> 77                                                                        #> 78                                                                        #> 79                                                                        #> 80                                                                        #> 81                                                                        #> 82                                                                        #> 83                                                                        #> 84                                                                        #> 85                                                                        #> 86                                                                        #> 87                                                                        #> 88                                                                        #> 89                                                                        #> 90                                                                        #> 91                                                                        #> 92                                                                        #> 93                                                                        #> 94                                                                        #> 95                                                                        #> 96                                                                        #> 97                                                                        #> 98                                                                        #> 99                                                                        #> 100                                                                       #> 101                                                                       #> 102                                                                       #> 103                                                                       #> 104                                                                       #> 105                                                                       #> 106                                                                       #> 107                                                                       #> 108                                                                       #> 109                                                                       #> 110                                                                       #> 111                                                                       #> 112                                                                       #> 113                                                                       #> 114                                                                       #> 115                                                                       #> 116                                                                       #> 117                                                                       #> 118                                                                       #> 119                                                                       #> 120                                                                       #> 121 1.8439089                                                             #> 122 1.2649111 1.6733201                                                   #> 123 2.1213203 1.5811388 1.9748418                                         #> 124 1.0954451 1.5491933 1.0000000 1.8708287                               #> 125 1.7606817 0.7071068 1.5811388 1.6124515 1.4491377                     #> 126 1.8708287 1.0488088 1.8165902 1.3416408 1.5811388 1.0954451           #> 127 1.1401754 1.5811388 0.9486833 1.8973666 0.5477226 1.4832397 1.6124515 #> 128 1.1401754 1.5165751 0.9486833 1.9493589 0.7071068 1.4142136 1.5491933 #> 129 1.4832397 1.0954451 1.2649111 1.5811388 1.0954451 0.9486833 1.3784049 #> 130 1.7029386 1.1401754 1.7606817 1.4142136 1.5165751 1.1832160 0.7745967 #> 131 1.8708287 1.3038405 1.7606817 1.0000000 1.5811388 1.3416408 0.8944272 #> 132 2.3237900 1.6124515 2.1908902 1.2247449 2.0976177 1.5811388 1.3784049 #> 133 1.5165751 1.0488088 1.3038405 1.6124515 1.1401754 1.0000000 1.4142136 #> 134 1.0000000 1.5491933 1.1832160 1.8708287 0.7745967 1.4491377 1.5811388 #> 135 1.0954451 1.5491933 1.4142136 1.8708287 1.1832160 1.4491377 1.5811388 #> 136 2.0976177 1.1832160 1.9493589 1.0488088 1.8439089 1.3784049 1.1401754 #> 137 1.7320508 1.0000000 1.5491933 1.8708287 1.4142136 0.9486833 1.4491377 #> 138 1.4491377 1.1401754 1.3784049 1.7320508 1.0488088 1.0000000 1.1832160 #> 139 1.1401754 1.5811388 0.9486833 2.0000000 0.8366600 1.4832397 1.6124515 #> 140 1.6733201 0.7745967 1.4832397 1.5811388 1.3416408 0.8366600 1.1401754 #> 141 1.7606817 0.7071068 1.5811388 1.6733201 1.4491377 0.7745967 1.2649111 #> 142 1.6431677 0.8366600 1.4491377 1.7320508 1.3038405 1.0954451 1.3416408 #> 143 1.0954451 1.6124515 0.7745967 1.9235384 0.8944272 1.5165751 1.7029386 #> 144 1.8708287 0.5477226 1.7029386 1.5491933 1.5811388 0.7745967 1.0000000 #> 145 1.8708287 0.7071068 1.7029386 1.7320508 1.5811388 0.6324555 1.2649111 #> 146 1.5811388 0.9486833 1.3784049 1.7320508 1.2247449 1.0000000 1.4142136 #> 147 1.0000000 1.5491933 1.0954451 1.8708287 0.6324555 1.4491377 1.6431677 #> 148 1.4142136 1.1832160 1.1832160 1.7029386 1.0000000 1.0488088 1.3784049 #> 149 1.6124515 1.0954451 1.4142136 1.9235384 1.3416408 1.0488088 1.5165751 #> 150 1.1401754 1.5165751 0.9486833 1.9493589 0.9486833 1.4142136 1.5491933 #>           127       128       129       130       131       132       133 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44                                                                        #> 45                                                                        #> 46                                                                        #> 47                                                                        #> 48                                                                        #> 49                                                                        #> 50                                                                        #> 51                                                                        #> 52                                                                        #> 53                                                                        #> 54                                                                        #> 55                                                                        #> 56                                                                        #> 57                                                                        #> 58                                                                        #> 59                                                                        #> 60                                                                        #> 61                                                                        #> 62                                                                        #> 63                                                                        #> 64                                                                        #> 65                                                                        #> 66                                                                        #> 67                                                                        #> 68                                                                        #> 69                                                                        #> 70                                                                        #> 71                                                                        #> 72                                                                        #> 73                                                                        #> 74                                                                        #> 75                                                                        #> 76                                                                        #> 77                                                                        #> 78                                                                        #> 79                                                                        #> 80                                                                        #> 81                                                                        #> 82                                                                        #> 83                                                                        #> 84                                                                        #> 85                                                                        #> 86                                                                        #> 87                                                                        #> 88                                                                        #> 89                                                                        #> 90                                                                        #> 91                                                                        #> 92                                                                        #> 93                                                                        #> 94                                                                        #> 95                                                                        #> 96                                                                        #> 97                                                                        #> 98                                                                        #> 99                                                                        #> 100                                                                       #> 101                                                                       #> 102                                                                       #> 103                                                                       #> 104                                                                       #> 105                                                                       #> 106                                                                       #> 107                                                                       #> 108                                                                       #> 109                                                                       #> 110                                                                       #> 111                                                                       #> 112                                                                       #> 113                                                                       #> 114                                                                       #> 115                                                                       #> 116                                                                       #> 117                                                                       #> 118                                                                       #> 119                                                                       #> 120                                                                       #> 121                                                                       #> 122                                                                       #> 123                                                                       #> 124                                                                       #> 125                                                                       #> 126                                                                       #> 127                                                                       #> 128 0.6324555                                                             #> 129 1.1401754 1.2247449                                                   #> 130 1.5491933 1.4832397 1.3038405                                         #> 131 1.6124515 1.6733201 1.3038405 1.0000000                               #> 132 2.1213203 2.0736441 1.8439089 1.5811388 1.3784049                     #> 133 1.1832160 1.2649111 0.3162278 1.3416408 1.3416408 1.8708287           #> 134 0.8366600 0.9486833 1.0954451 1.3784049 1.5811388 2.0976177 1.1401754 #> 135 1.2247449 1.2247449 1.0954451 1.3784049 1.5811388 2.0976177 1.1401754 #> 136 1.8708287 1.8165902 1.4832397 1.2247449 0.9486833 1.2649111 1.4491377 #> 137 1.4491377 1.3784049 1.0000000 1.5165751 1.6431677 1.7888544 0.9486833 #> 138 1.0954451 1.0000000 0.8366600 1.1832160 1.4142136 1.8165902 0.8944272 #> 139 0.6324555 0.4472136 1.3038405 1.5491933 1.7320508 2.1213203 1.3416408 #> 140 1.3784049 1.3038405 1.0000000 1.1401754 1.3038405 1.6733201 1.0488088 #> 141 1.4832397 1.4142136 0.9486833 1.2649111 1.4142136 1.7606817 0.8944272 #> 142 1.3416408 1.2649111 1.2247449 1.3416408 1.4832397 1.8165902 1.1832160 #> 143 0.9486833 0.9486833 1.1832160 1.6431677 1.6431677 2.1447611 1.2247449 #> 144 1.6124515 1.5491933 1.1401754 1.1832160 1.2649111 1.5811388 1.0954451 #> 145 1.6124515 1.5491933 1.1401754 1.3416408 1.4832397 1.7029386 1.0954451 #> 146 1.2649111 1.1832160 1.0488088 1.3416408 1.4832397 1.8708287 1.0000000 #> 147 0.8366600 0.9486833 1.0954451 1.5811388 1.5811388 2.0976177 1.1401754 #> 148 1.0488088 0.9486833 0.8944272 1.3038405 1.4491377 1.8439089 0.9486833 #> 149 1.3038405 1.2247449 1.0954451 1.5811388 1.7029386 1.8439089 1.0488088 #> 150 0.8944272 0.6324555 1.2247449 1.4832397 1.6733201 2.0736441 1.2649111 #>           134       135       136       137       138       139       140 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44                                                                        #> 45                                                                        #> 46                                                                        #> 47                                                                        #> 48                                                                        #> 49                                                                        #> 50                                                                        #> 51                                                                        #> 52                                                                        #> 53                                                                        #> 54                                                                        #> 55                                                                        #> 56                                                                        #> 57                                                                        #> 58                                                                        #> 59                                                                        #> 60                                                                        #> 61                                                                        #> 62                                                                        #> 63                                                                        #> 64                                                                        #> 65                                                                        #> 66                                                                        #> 67                                                                        #> 68                                                                        #> 69                                                                        #> 70                                                                        #> 71                                                                        #> 72                                                                        #> 73                                                                        #> 74                                                                        #> 75                                                                        #> 76                                                                        #> 77                                                                        #> 78                                                                        #> 79                                                                        #> 80                                                                        #> 81                                                                        #> 82                                                                        #> 83                                                                        #> 84                                                                        #> 85                                                                        #> 86                                                                        #> 87                                                                        #> 88                                                                        #> 89                                                                        #> 90                                                                        #> 91                                                                        #> 92                                                                        #> 93                                                                        #> 94                                                                        #> 95                                                                        #> 96                                                                        #> 97                                                                        #> 98                                                                        #> 99                                                                        #> 100                                                                       #> 101                                                                       #> 102                                                                       #> 103                                                                       #> 104                                                                       #> 105                                                                       #> 106                                                                       #> 107                                                                       #> 108                                                                       #> 109                                                                       #> 110                                                                       #> 111                                                                       #> 112                                                                       #> 113                                                                       #> 114                                                                       #> 115                                                                       #> 116                                                                       #> 117                                                                       #> 118                                                                       #> 119                                                                       #> 120                                                                       #> 121                                                                       #> 122                                                                       #> 123                                                                       #> 124                                                                       #> 125                                                                       #> 126                                                                       #> 127                                                                       #> 128                                                                       #> 129                                                                       #> 130                                                                       #> 131                                                                       #> 132                                                                       #> 133                                                                       #> 134                                                                       #> 135 1.0000000                                                             #> 136 1.8439089 1.8439089                                                   #> 137 1.4142136 1.4142136 1.5491933                                         #> 138 1.0488088 1.1401754 1.5811388 1.0488088                               #> 139 1.0488088 1.3038405 1.8708287 1.4491377 1.0954451                     #> 140 1.3416408 1.4832397 1.3416408 1.1832160 0.9486833 1.3784049           #> 141 1.4491377 1.4491377 1.3038405 0.8366600 1.0000000 1.4832397 0.8366600 #> 142 1.3038405 1.6431677 1.3784049 1.2247449 1.1832160 1.3416408 0.7071068 #> 143 1.0000000 1.1832160 1.8973666 1.4832397 1.2247449 0.9486833 1.4142136 #> 144 1.5811388 1.5811388 1.1401754 1.0488088 1.1832160 1.6124515 0.9486833 #> 145 1.5811388 1.5811388 1.3784049 0.8366600 1.1832160 1.6124515 1.0488088 #> 146 1.2247449 1.5165751 1.3784049 1.1401754 1.0954451 1.2649111 0.8366600 #> 147 0.8944272 1.1832160 1.8439089 1.4142136 1.1401754 1.0488088 1.3416408 #> 148 1.0000000 1.3416408 1.5491933 1.1832160 0.8366600 1.0488088 0.8944272 #> 149 1.3416408 1.4142136 1.6124515 0.6324555 1.0488088 1.3038405 1.0954451 #> 150 0.9486833 1.2247449 1.8165902 1.3784049 1.0000000 0.6324555 1.3038405 #>           141       142       143       144       145       146       147 #> 2                                                                         #> 3                                                                         #> 4                                                                         #> 5                                                                         #> 6                                                                         #> 7                                                                         #> 8                                                                         #> 9                                                                         #> 10                                                                        #> 11                                                                        #> 12                                                                        #> 13                                                                        #> 14                                                                        #> 15                                                                        #> 16                                                                        #> 17                                                                        #> 18                                                                        #> 19                                                                        #> 20                                                                        #> 21                                                                        #> 22                                                                        #> 23                                                                        #> 24                                                                        #> 25                                                                        #> 26                                                                        #> 27                                                                        #> 28                                                                        #> 29                                                                        #> 30                                                                        #> 31                                                                        #> 32                                                                        #> 33                                                                        #> 34                                                                        #> 35                                                                        #> 36                                                                        #> 37                                                                        #> 38                                                                        #> 39                                                                        #> 40                                                                        #> 41                                                                        #> 42                                                                        #> 43                                                                        #> 44                                                                        #> 45                                                                        #> 46                                                                        #> 47                                                                        #> 48                                                                        #> 49                                                                        #> 50                                                                        #> 51                                                                        #> 52                                                                        #> 53                                                                        #> 54                                                                        #> 55                                                                        #> 56                                                                        #> 57                                                                        #> 58                                                                        #> 59                                                                        #> 60                                                                        #> 61                                                                        #> 62                                                                        #> 63                                                                        #> 64                                                                        #> 65                                                                        #> 66                                                                        #> 67                                                                        #> 68                                                                        #> 69                                                                        #> 70                                                                        #> 71                                                                        #> 72                                                                        #> 73                                                                        #> 74                                                                        #> 75                                                                        #> 76                                                                        #> 77                                                                        #> 78                                                                        #> 79                                                                        #> 80                                                                        #> 81                                                                        #> 82                                                                        #> 83                                                                        #> 84                                                                        #> 85                                                                        #> 86                                                                        #> 87                                                                        #> 88                                                                        #> 89                                                                        #> 90                                                                        #> 91                                                                        #> 92                                                                        #> 93                                                                        #> 94                                                                        #> 95                                                                        #> 96                                                                        #> 97                                                                        #> 98                                                                        #> 99                                                                        #> 100                                                                       #> 101                                                                       #> 102                                                                       #> 103                                                                       #> 104                                                                       #> 105                                                                       #> 106                                                                       #> 107                                                                       #> 108                                                                       #> 109                                                                       #> 110                                                                       #> 111                                                                       #> 112                                                                       #> 113                                                                       #> 114                                                                       #> 115                                                                       #> 116                                                                       #> 117                                                                       #> 118                                                                       #> 119                                                                       #> 120                                                                       #> 121                                                                       #> 122                                                                       #> 123                                                                       #> 124                                                                       #> 125                                                                       #> 126                                                                       #> 127                                                                       #> 128                                                                       #> 129                                                                       #> 130                                                                       #> 131                                                                       #> 132                                                                       #> 133                                                                       #> 134                                                                       #> 135                                                                       #> 136                                                                       #> 137                                                                       #> 138                                                                       #> 139                                                                       #> 140                                                                       #> 141                                                                       #> 142 0.8944272                                                             #> 143 1.5165751 1.3784049                                                   #> 144 0.7745967 1.0000000 1.6431677                                         #> 145 0.6324555 1.0954451 1.6431677 0.7745967                               #> 146 0.7745967 0.6324555 1.3038405 1.0000000 1.0000000                     #> 147 1.4491377 1.3038405 0.8944272 1.5811388 1.5811388 1.2247449           #> 148 1.0488088 0.9486833 1.0954451 1.2247449 1.2247449 0.7071068 1.0000000 #> 149 1.0488088 1.1401754 1.3416408 1.1401754 1.0488088 1.0488088 1.3416408 #> 150 1.4142136 1.2649111 0.7071068 1.5491933 1.5491933 1.1832160 1.0488088 #>           148       149 #> 2                       #> 3                       #> 4                       #> 5                       #> 6                       #> 7                       #> 8                       #> 9                       #> 10                      #> 11                      #> 12                      #> 13                      #> 14                      #> 15                      #> 16                      #> 17                      #> 18                      #> 19                      #> 20                      #> 21                      #> 22                      #> 23                      #> 24                      #> 25                      #> 26                      #> 27                      #> 28                      #> 29                      #> 30                      #> 31                      #> 32                      #> 33                      #> 34                      #> 35                      #> 36                      #> 37                      #> 38                      #> 39                      #> 40                      #> 41                      #> 42                      #> 43                      #> 44                      #> 45                      #> 46                      #> 47                      #> 48                      #> 49                      #> 50                      #> 51                      #> 52                      #> 53                      #> 54                      #> 55                      #> 56                      #> 57                      #> 58                      #> 59                      #> 60                      #> 61                      #> 62                      #> 63                      #> 64                      #> 65                      #> 66                      #> 67                      #> 68                      #> 69                      #> 70                      #> 71                      #> 72                      #> 73                      #> 74                      #> 75                      #> 76                      #> 77                      #> 78                      #> 79                      #> 80                      #> 81                      #> 82                      #> 83                      #> 84                      #> 85                      #> 86                      #> 87                      #> 88                      #> 89                      #> 90                      #> 91                      #> 92                      #> 93                      #> 94                      #> 95                      #> 96                      #> 97                      #> 98                      #> 99                      #> 100                     #> 101                     #> 102                     #> 103                     #> 104                     #> 105                     #> 106                     #> 107                     #> 108                     #> 109                     #> 110                     #> 111                     #> 112                     #> 113                     #> 114                     #> 115                     #> 116                     #> 117                     #> 118                     #> 119                     #> 120                     #> 121                     #> 122                     #> 123                     #> 124                     #> 125                     #> 126                     #> 127                     #> 128                     #> 129                     #> 130                     #> 131                     #> 132                     #> 133                     #> 134                     #> 135                     #> 136                     #> 137                     #> 138                     #> 139                     #> 140                     #> 141                     #> 142                     #> 143                     #> 144                     #> 145                     #> 146                     #> 147                     #> 148                     #> 149 1.0954451           #> 150 0.9486833 1.2247449"},{"path":"/reference/summary.biplot.html","id":null,"dir":"Reference","previous_headings":"","what":"Generic summary function for objects of class biplot — summary.biplot","title":"Generic summary function for objects of class biplot — summary.biplot","text":"function used print summary output biplot. summary outputs related measures fit.","code":""},{"path":"/reference/summary.biplot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generic summary function for objects of class biplot — summary.biplot","text":"","code":"# S3 method for class 'biplot' summary(   object,   adequacy = TRUE,   axis.predictivity = TRUE,   sample.predictivity = TRUE,   class.predictivity = TRUE,   within.class.axis.predictivity = TRUE,   within.class.sample.predictivity = TRUE,   ... )"},{"path":"/reference/summary.biplot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generic summary function for objects of class biplot — summary.biplot","text":"object object class biplot. adequacy logical value indicating whether variable adequacies reported, default TRUE. axis.predictivity logical value indicating whether axis predictivities reported, default TRUE. sample.predictivity logical value indicating whether sample predictivities reported, default TRUE. class.predictivity logical value indicating whether class predictivities reported, default TRUE (applicable objects class CVA). within.class.axis.predictivity logical value indicating whether within class axis predictivity reported, default TRUE (applicable objects class CVA). within.class.sample.predictivity logical value indicating whether within class sample predictivity reported, default TRUE (applicable objects class CVA). ... additional arguments.","code":""},{"path":"/reference/summary.biplot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generic summary function for objects of class biplot — summary.biplot","text":"function produce return value, called side effects.","code":""},{"path":"/reference/summary.biplot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generic summary function for objects of class biplot — summary.biplot","text":"","code":"out <- biplot (iris[,1:4]) |> PCA() |> fit.measures() summary(out) #> Object of class biplot, based on 150 samples and 4 variables. #> 4 numeric variables. #>  #> Quality of fit in 2 dimension(s) = 97.8%  #> Adequacy of variables in 2 dimension(s): #> Sepal.Length  Sepal.Width Petal.Length  Petal.Width  #>    0.5617091    0.5402798    0.7639426    0.1340685  #> Axis predictivity in 2 dimension(s): #> Sepal.Length  Sepal.Width Petal.Length  Petal.Width  #>    0.9579017    0.8400028    0.9980931    0.9365937  #> Sample predictivity in 2 dimension(s): #>         1         2         3         4         5         6         7         8  #> 0.9998927 0.9927400 0.9999141 0.9991226 0.9984312 0.9949770 0.9914313 0.9996346  #>         9        10        11        12        13        14        15        16  #> 0.9998677 0.9941340 0.9991205 0.9949153 0.9945491 0.9996034 0.9942676 0.9897890  #>        17        18        19        20        21        22        23        24  #> 0.9937752 0.9990534 0.9972926 0.9928624 0.9896250 0.9932656 0.9918132 0.9955885  #>        25        26        27        28        29        30        31        32  #> 0.9812917 0.9897303 0.9979903 0.9990514 0.9963870 0.9975607 0.9985741 0.9876345  #>        33        34        35        36        37        38        39        40  #> 0.9833383 0.9957412 0.9970200 0.9935405 0.9859750 0.9953399 0.9994047 0.9990244  #>        41        42        43        44        45        46        47        48  #> 0.9980903 0.9756895 0.9953372 0.9830035 0.9763861 0.9959863 0.9905695 0.9987006  #>        49        50        51        52        53        54        55        56  #> 0.9996383 0.9987482 0.9275369 0.9996655 0.9544488 0.9460515 0.9172857 0.9061058  #>        57        58        59        60        61        62        63        64  #> 0.9727694 0.9996996 0.8677939 0.8686502 0.9613130 0.9328852 0.4345132 0.9679973  #>        65        66        67        68        69        70        71        72  #> 0.7995848 0.9083037 0.7968614 0.5835260 0.7900027 0.8575646 0.8524748 0.6615410  #>        73        74        75        76        77        78        79        80  #> 0.9367709 0.8661203 0.8350955 0.8929908 0.8702600 0.9873164 0.9969031 0.6815512  #>        81        82        83        84        85        86        87        88  #> 0.8937189 0.8409681 0.7829405 0.9848354 0.6901625 0.8073582 0.9666041 0.6665514  #>        89        90        91        92        93        94        95        96  #> 0.6993846 0.9909923 0.9008345 0.9710941 0.8037223 0.9913632 0.9744493 0.7089660  #>        97        98        99       100       101       102       103       104  #> 0.9071738 0.9064541 0.9625371 0.9872279 0.9171603 0.9636413 0.9976224 0.9829885  #>       105       106       107       108       109       110       111       112  #> 0.9854704 0.9888092 0.8464463 0.9729353 0.9771293 0.9794313 0.9746239 0.9977302  #>       113       114       115       116       117       118       119       120  #> 0.9941859 0.9605563 0.8476794 0.9289985 0.9929982 0.9916850 0.9818957 0.9493751  #>       121       122       123       124       125       126       127       128  #> 0.9865358 0.8716778 0.9728177 0.9846364 0.9840890 0.9861783 0.9854516 0.9691512  #>       129       130       131       132       133       134       135       136  #> 0.9942007 0.9585884 0.9705389 0.9937852 0.9874192 0.9723192 0.9230503 0.9794405  #>       137       138       139       140       141       142       143       144  #> 0.8947527 0.9797055 0.9458421 0.9902488 0.9674660 0.9350646 0.9636413 0.9867931  #>       145       146       147       148       149       150  #> 0.9500265 0.9470544 0.9688318 0.9886543 0.8735433 0.9281727"},{"path":"/reference/translate_axes.html","id":null,"dir":"Reference","previous_headings":"","what":"Translate biplot axes — translate_axes","title":"Translate biplot axes — translate_axes","text":"Automatically manually translate axes away center plot","code":""},{"path":"/reference/translate_axes.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Translate biplot axes — translate_axes","text":"","code":"translate_axes(bp, delta = 0, swop = FALSE, distances = NULL)"},{"path":"/reference/translate_axes.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Translate biplot axes — translate_axes","text":"bp object class biplot delta numeric value indicating distance axes swop logical. Change direction axes translated distances numeric vector distances. Used manually parallel translate axes.","code":""},{"path":"/reference/translate_axes.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Translate biplot axes — translate_axes","text":"object class biplot translated distances appended bp$axes","code":""},{"path":"/reference/translate_axes.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Translate biplot axes — translate_axes","text":"function uses algorithm implemented TDAbiplot bipl5 package. translates axes center plot. Correlated axes generally gets translated direction. function calculates orthogx orthogy paramaters axes()","code":""},{"path":"/reference/translate_axes.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Translate biplot axes — translate_axes","text":"","code":"#Translate the axes out of the plot center  bp <- biplot(state.x77,scaled = TRUE)|>        CVA(state.region) |>        translate_axes(swop=TRUE,delta =0.2)|>       plot(exp.factor=3)   #adjust the distance of an axis  dist <- bp$axes$translate_distance dist[7] <- 0.4 bp |> translate_axes(delta = 0.2, distances=dist) |> plot()"}]
diff --git a/docs/sitemap.xml b/docs/sitemap.xml
index 578e488..73bae06 100644
--- a/docs/sitemap.xml
+++ b/docs/sitemap.xml
@@ -1,168 +1,63 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
-  <url>
-    <loc>/404.html</loc>
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-  </url>
-  <url>
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-    <loc>/reference/CVA.html</loc>
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-    <loc>/reference/density2D.html</loc>
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-  </url>
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-  <url>
-    <loc>/reference/newsamples.html</loc>
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-    <loc>/reference/PCA.biplot.html</loc>
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-    <loc>/reference/PCA.html</loc>
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-    <loc>/reference/PCO.biplot.html</loc>
-  </url>
-  <url>
-    <loc>/reference/PCO.html</loc>
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-    <loc>/reference/plot.biplot.html</loc>
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-  </url>
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-    <loc>/reference/print.biplot.html</loc>
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-    <loc>/reference/regress.biplot.html</loc>
-  </url>
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-    <loc>/reference/regress.html</loc>
-  </url>
-  <url>
-    <loc>/reference/rotate.html</loc>
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-    <loc>/reference/samples.html</loc>
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-    <loc>/reference/sqrtManhattan.html</loc>
-  </url>
-  <url>
-    <loc>/reference/summary.biplot.html</loc>
-  </url>
-  <url>
-    <loc>/reference/translate_axes.html</loc>
-  </url>
+<urlset xmlns = 'http://www.sitemaps.org/schemas/sitemap/0.9'>
+<url><loc>/404.html</loc></url>
+<url><loc>/articles/biplotEZ.html</loc></url>
+<url><loc>/articles/biplotEZ_enhancements.html</loc></url>
+<url><loc>/articles/Biplots_in_1D.html</loc></url>
+<url><loc>/articles/Biplots_in_3D.html</loc></url>
+<url><loc>/articles/CA_in_biplotEZ.html</loc></url>
+<url><loc>/articles/Class_separation.html</loc></url>
+<url><loc>/articles/index.html</loc></url>
+<url><loc>/articles/MDS.html</loc></url>
+<url><loc>/authors 2.html</loc></url>
+<url><loc>/authors.html</loc></url>
+<url><loc>/index.html</loc></url>
+<url><loc>/LICENSE-text.html</loc></url>
+<url><loc>/LICENSE.html</loc></url>
+<url><loc>/reference/alpha.bags.html</loc></url>
+<url><loc>/reference/AoD.biplot.html</loc></url>
+<url><loc>/reference/AoD.html</loc></url>
+<url><loc>/reference/axes.html</loc></url>
+<url><loc>/reference/axes_coordinates.html</loc></url>
+<url><loc>/reference/biplot.html</loc></url>
+<url><loc>/reference/biplotEZ.html</loc></url>
+<url><loc>/reference/CA.biplot.html</loc></url>
+<url><loc>/reference/CA.html</loc></url>
+<url><loc>/reference/CATPCA.html</loc></url>
+<url><loc>/reference/classification.biplot.html</loc></url>
+<url><loc>/reference/classification.html</loc></url>
+<url><loc>/reference/classify.html</loc></url>
+<url><loc>/reference/CLPs.html</loc></url>
+<url><loc>/reference/CLRs.html</loc></url>
+<url><loc>/reference/CVA.biplot.html</loc></url>
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+<url><loc>/reference/CVAlowdim.html</loc></url>
+<url><loc>/reference/density1D.html</loc></url>
+<url><loc>/reference/density2D.html</loc></url>
+<url><loc>/reference/ellipses.html</loc></url>
+<url><loc>/reference/extended.matching.coefficient.html</loc></url>
+<url><loc>/reference/fit.measures.html</loc></url>
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+<url><loc>/reference/summary.biplot.html</loc></url>
+<url><loc>/reference/translate_axes.html</loc></url>
 </urlset>
+
diff --git a/man/CA.Rd b/man/CA.Rd
index c1fe9ce..56db4c8 100644
--- a/man/CA.Rd
+++ b/man/CA.Rd
@@ -27,13 +27,19 @@ A list with the following components is available:
 \item{Z}{Combined data frame of the row and column coordinates.}
 \item{r}{Numer of levels in the row factor.}
 \item{c}{Numer of levels in the column factor.}
+\item{Dr}{Diagonal matrix of row profiles.}
+\item{Dc}{Diagonal matrix of column profiles.}
+\item{Drh}{Weighted row profiles.}
+\item{Dch}{Weighted column profiles.}
 \item{rowcoor}{Row coordinates based on the selected \code{variant}.}
 \item{colcoor}{Column coordinates based on the selected \code{variant}.}
-\item{P}{Correspondence Matrix}
+\item{P}{Correspondence Matrix.}
 \item{Smat}{Standardised Pearson residuals.}
 \item{SVD}{Singular value decomposition solution: \code{d, u, v}.}
-\item{qual}{Quality of the approximation.}
+\item{e.vects}{Depending on what was specified in \code{CA} argument.}
+\item{dim.biplot}{The dimension of the biplot.}
 \item{lambda.val}{The computed lambda value if lambda-scaling is requested.}
+\item{gamma}{Contribution of the singular values, based on the CA variant.}
 }
 \description{
 This function produces a list of elements to be used for CA biplot construction by approximation of the Pearson residuals.
diff --git a/man/CATPCA.Rd b/man/CATPCA.Rd
deleted file mode 100644
index 3ef0405..0000000
--- a/man/CATPCA.Rd
+++ /dev/null
@@ -1,30 +0,0 @@
-% Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/CATPCA.R
-\name{CATPCA}
-\alias{CATPCA}
-\title{Categorical Principal Component Analysis}
-\usage{
-CATPCA(bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X),
-group.aes = NULL, show.class.means = FALSE)
-}
-\arguments{
-\item{bp}{an object of class \code{biplot} obtained from preceding function \code{biplot()}.}
-
-\item{dim.biplot}{dimension of the biplot. Only values 1, 2 and 3 are accepted, with default \code{2}.}
-
-\item{e.vects}{which eigenvectors (principal components) to extract, with default \code{1:dim.biplot}.}
-
-\item{group.aes}{vector of the same length as the number of rows in the data matrix
-for differentiated aesthetics for samples.}
-
-\item{show.class.means}{logical, indicating whether group means should be plotted in the biplot.}
-}
-\value{
-an object of class \code{biplot}
-}
-\description{
-Categorical Principal Component Analysis
-}
-\examples{
-CATPCA (iris)
-}
diff --git a/man/CatPCA.Rd b/man/CatPCA.Rd
new file mode 100644
index 0000000..210d477
--- /dev/null
+++ b/man/CatPCA.Rd
@@ -0,0 +1,65 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/CATPCA.R
+\name{CatPCA}
+\alias{CatPCA}
+\title{Perform Categorical Principal Components Analysis (CatPCA)}
+\usage{
+CatPCA(bp, cat.type = NULL, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X),
+group.aes = NULL, show.class.means = FALSE, epsilon = 1e-6)
+}
+\arguments{
+\item{bp}{an object of class \code{biplot} obtained from preceding function \code{biplot()}.}
+
+\item{cat.type}{a vector indicating whether each categorical variables is \code{nominal} or \code{ordinal}.}
+
+\item{dim.biplot}{the dimension of the biplot. Only values \code{1}, \code{2} and \code{3} are accepted, with default \code{2}.}
+
+\item{e.vects}{the vector indicating which eigenvectors (principal components) should be plotted in the biplot, with default \code{1:dim.biplot}.}
+
+\item{group.aes}{a vector of the same length as the number of rows in the data matrix
+for differentiated aesthetics for samples.}
+
+\item{show.class.means}{a logical value indicating whether group means should be plotted in the biplot.}
+
+\item{epsilon}{convergence criteria for iterative algorithm with defaults 1e-6.}
+}
+\value{
+An object of class CatPCA with the following elements:
+\item{X}{the matrix of the centered and scaled numeric variables.}
+\item{Xcat}{the data frame of the categorical variables.}
+\item{raw.X}{the original data.}
+\item{classes}{the vector of category levels for the class variable. This is to be used for \code{colour}, \code{pch} and \code{cex} specifications.}
+\item{na.action}{the vector of observations that have been removed.}
+\item{center}{a logical value indicating whether \eqn{\mathbf{X}} is centered.}
+\item{scaled}{a logical value indicating whether \eqn{\mathbf{X}} is scaled.}
+\item{means}{the vector of means for each numerical variable.}
+\item{sd}{the vector of standard deviations for each numerical variable.}
+\item{n}{the number of observations.}
+\item{p}{the number of variables.}
+\item{group.aes}{the vector of category levels for the grouping variable. This is to be used for \code{colour}, \code{pch} and \code{cex} specification.}
+\item{g.names}{the descriptive names to be used for group labels.}
+\item{g}{the number of groups.}
+\item{Title}{the title of the biplot rendered.}
+\item{Z}{the matrix with each row containing the details of the points that are plotted (i.e. coordinates).}
+\item{Lmat}{the matrix for transformation to the principal components.}
+\item{Linv}{the inverse of \eqn{\mathbf{L}}.}
+\item{eigenvalues}{the vector of eigenvalues of the covariance matrix of \eqn{\mathbf{X}}.}
+\item{all.ax.one.unit}{one unit in the positive direction of each biplot axis.}
+\item{ax.type}{one of numeric, ordinal or nominal.}
+\item{ax.one.unit}{one unit in the positive direction of each numeric biplot axis.}
+\item{nom.levels}{a list with the levels of each nominal variable}
+\item{ord.levels}{a list with the levels of each ordinal variable}
+\item{e.vects}{the vector indicating which principal components are plotted in the biplot.}
+\item{dim.biplot}{the dimension of the biplot.}
+\item{class.means}{a logical value indicating whether group means are plotted in the biplot.}
+\item{Zmeans}{the matrix of class mean coordinates that are plotted in the biplot.}
+}
+\description{
+This function appends the \code{biplot} object with elements resulting from performing CatPCA.
+}
+\examples{
+biplot(iris) |> CatPCA()
+# create a CatPCA biplot
+biplot(data = iris) |> CatPCA() |> plot()
+
+}
diff --git a/man/CatPCA.biplot.Rd b/man/CatPCA.biplot.Rd
new file mode 100644
index 0000000..904cad7
--- /dev/null
+++ b/man/CatPCA.biplot.Rd
@@ -0,0 +1,44 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/CATPCA.R
+\name{CatPCA.biplot}
+\alias{CatPCA.biplot}
+\title{Calculate elements for the CatPCA biplot}
+\usage{
+\method{CatPCA}{biplot}(
+  bp,
+  cat.type = NULL,
+  dim.biplot = c(2, 1, 3),
+  e.vects = 1:ncol(bp$X),
+  group.aes = NULL,
+  show.class.means = FALSE,
+  epsilon = 1e-06
+)
+}
+\arguments{
+\item{bp}{an object of class \code{biplot} obtained from preceding function \code{biplot()}.}
+
+\item{cat.type}{a vector indicating whether each categorical variables is \code{nominal} or \code{ordinal}.}
+
+\item{dim.biplot}{the dimension of the biplot. Only values \code{1}, \code{2} and \code{3} are accepted, with default \code{2}.}
+
+\item{e.vects}{the vector indicating which eigenvectors (principal components) should be plotted in the biplot, with default \code{1:dim.biplot}.}
+
+\item{group.aes}{a vector of the same length as the number of rows in the data matrix
+for differentiated aesthetics for samples.}
+
+\item{show.class.means}{a logical value indicating whether group means should be plotted in the biplot.}
+
+\item{epsilon}{convergence criteria for iterative algorithm with defaults 1e-6.}
+}
+\value{
+an object of class \code{CatPCA}, inherits from classes \code{PCA} and \code{biplot}.
+}
+\description{
+This function performs calculations for the construction of a CatPCA biplot.
+}
+\examples{
+biplot(iris) |> CatPCA()
+# create a CatPCA biplot
+biplot(data = iris) |> CatPCA() |> plot()
+
+}
diff --git a/man/PCA.Rd b/man/PCA.Rd
index fd92002..3e6b480 100644
--- a/man/PCA.Rd
+++ b/man/PCA.Rd
@@ -4,8 +4,9 @@
 \alias{PCA}
 \title{Perform Principal Components Analysis (PCA)}
 \usage{
-PCA(bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X),
-group.aes = NULL, show.class.means = FALSE, correlation.biplot = FALSE)
+PCA(bp, dim.biplot = c(2, 1, 3), e.vects = 1:ncol(bp$X), 
+           group.aes=NULL, show.class.means = FALSE,
+           correlation.biplot=FALSE, ...)
 }
 \arguments{
 \item{bp}{an object of class \code{biplot} obtained from preceding function \code{biplot()}.}
@@ -23,6 +24,8 @@ for differentiated aesthetics for samples.}
 optimally approximated in the biplot. If \code{TRUE}, the correlations between
 variables are optimally approximated by the cosine of the angles between
 axes. Default is \code{FALSE}.}
+
+\item{...}{additional arguments.}
 }
 \value{
 An object of class PCA with the following elements:
diff --git a/man/PCA.biplot.Rd b/man/PCA.biplot.Rd
index 3325156..bfe5f63 100644
--- a/man/PCA.biplot.Rd
+++ b/man/PCA.biplot.Rd
@@ -10,7 +10,8 @@
   e.vects = 1:ncol(bp$X),
   group.aes = NULL,
   show.class.means = FALSE,
-  correlation.biplot = FALSE
+  correlation.biplot = FALSE,
+  ...
 )
 }
 \arguments{
@@ -29,6 +30,8 @@ for differentiated aesthetics for samples.}
 optimally approximated in the biplot. If \code{TRUE}, the correlations between
 variables are optimally approximated by the cosine of the angles between
 axes. Default is \code{FALSE}.}
+
+\item{...}{additional arguments.}
 }
 \value{
 an object of class \code{PCA}, inherits from class \code{biplot}.
diff --git a/man/alpha.bags.Rd b/man/alpha.bags.Rd
index b3b1cb6..11f9dfd 100644
--- a/man/alpha.bags.Rd
+++ b/man/alpha.bags.Rd
@@ -46,5 +46,5 @@ biplot (iris[,1:4],group.aes=iris[,5]) |> PCA() |> alpha.bags(alpha=0.95) |> plo
 
 }
 \references{
-Gower, J., Gardner-Lubbe, S. & Le Roux, N. (2011, ISBN: 978-0-470-01255-0) \emph{Understanding Biplots.} Chichester, England: John Wiley & Sons Ltd.\if{html}{\out{<br>}}\if{html}{\out{<br>}}
+Gower, J., Gardner-Lubbe, S. & Le Roux, N. (2011, ISBN: 978-0-470-01255-0) \emph{Understanding Biplots.} Chichester, England: John Wiley & Sons Ltd.
 }
diff --git a/man/axes_coordinates.Rd b/man/axes_coordinates.Rd
deleted file mode 100644
index 1456bbf..0000000
--- a/man/axes_coordinates.Rd
+++ /dev/null
@@ -1,21 +0,0 @@
-% Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/calibrate_axes.R
-\name{axes_coordinates}
-\alias{axes_coordinates}
-\title{Calibrate Biplot Axes}
-\usage{
-axes_coordinates(x)
-}
-\arguments{
-\item{x}{an object of class \code{biplot}}
-}
-\value{
-An ordered list containing the coordinates the of tick marks to plotted on the biplot
-}
-\description{
-Convenience function to obtain the coordinates of the calibrated ticks marks on the biplot
-}
-\examples{
-x<-biplot(iris) |> PCA()
-coordinates<-axes_coordinates(x)
-}
diff --git a/man/biplot.Rd b/man/biplot.Rd
index 55e9b5b..17bebb3 100644
--- a/man/biplot.Rd
+++ b/man/biplot.Rd
@@ -109,7 +109,9 @@ biplot(data = iris) |> PCA() |> plot()
 
 }
 \references{
-Gabriel, K.R. (1971) The biplot graphic display of matrices with application to principal component analysis. \emph{Biometrika.} 58(3):453–467.\if{html}{\out{<br>}}\if{html}{\out{<br>}}
-Gower, J., Gardner-Lubbe, S. & Le Roux, N. (2011, ISBN: 978-0-470-01255-0) \emph{Understanding Biplots.} Chichester, England: John Wiley & Sons Ltd.\if{html}{\out{<br>}}\if{html}{\out{<br>}}
+Gabriel, K.R. (1971) The biplot graphic display of matrices with application to principal component analysis. \emph{Biometrika.} 58(3):453–467.
+
+Gower, J., Gardner-Lubbe, S. & Le Roux, N. (2011, ISBN: 978-0-470-01255-0) \emph{Understanding Biplots.} Chichester, England: John Wiley & Sons Ltd.
+
 Gower, J.C. & Hand, D.J.(1996, ISBN: 0-412-71630-5) \emph{Biplots.} London: Chapman & Hall.
 }
diff --git a/man/density2D.Rd b/man/density2D.Rd
index 1d6b628..812e4e0 100644
--- a/man/density2D.Rd
+++ b/man/density2D.Rd
@@ -23,7 +23,8 @@ density2D(
 \arguments{
 \item{bp}{object of class \code{biplot}}
 
-\item{which}{which group.}
+\item{which}{which group to create a density; limited to only a single group at a time.
+If NULL, density drawn over all data points.}
 
 \item{contours}{logical indicating whether contours are added to the density plot}
 
diff --git a/man/interpolate.Rd b/man/interpolate.Rd
index be428d9..25c316c 100644
--- a/man/interpolate.Rd
+++ b/man/interpolate.Rd
@@ -4,7 +4,7 @@
 \alias{interpolate}
 \title{Interpolate supplementary points and variables to add to the biplot}
 \usage{
-interpolate(bp, newdata = NULL, newvariable = NULL)
+interpolate(bp, newdata = NULL, newvariable = NULL, new.group.aes = NULL)
 }
 \arguments{
 \item{bp}{an object of class \code{biplot} obtained from preceding function \code{biplot()}.}
@@ -14,6 +14,8 @@ containing supplementary data points to be added onto the biplot.}
 
 \item{newvariable}{a new data set, similar in structure to the data set supplied to \code{biplot()}
 containing supplementary variables to be added onto the biplot.}
+
+\item{new.group.aes}{aesthetics for the new samples}
 }
 \value{
 The object of class \code{biplot} will be appended with the following elements:
@@ -21,6 +23,7 @@ The object of class \code{biplot} will be appended with the following elements:
 \item{Xnew}{the matrix of the centered and scaled new numeric variables of new data.}
 \item{Xnew.cat}{the matrix of the categorical variables of new data.}
 \item{Znew}{the matrix of the coordinates of the new data in the biplot.}
+\item{new.group.aes}{aeshetics for the new samples}
 
 For an object of class \code{CA} the following additional elements will be appended:
 \item{newrowcoor}{the matrix of row coordinates of the new data in the biplot.}
@@ -31,6 +34,7 @@ This function adds supplementary points and variables to the plot from a new dat
 }
 \examples{
 biplot(data = iris[1:145,]) |> PCA() |> interpolate(newdata = iris[146:150,]) |> plot()
-biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = "Symmetric") |> interpolate(newdata = HairEyeColor[,,1]) |> plot()
+biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = "Symmetric") |> 
+     interpolate(newdata = HairEyeColor[,,1]) |> plot()
 
 }
diff --git a/man/means.Rd b/man/means.Rd
index 3d728e4..51a57da 100644
--- a/man/means.Rd
+++ b/man/means.Rd
@@ -4,14 +4,15 @@
 \alias{means}
 \title{Format aesthetics for the class or group means}
 \usage{
-means (bp,  which = NULL, col = NULL, pch = 15, cex = 1, label = FALSE,
+means (bp,  which =  bp$samples$which, col = NULL, pch = 15, cex = 1, label = FALSE,
 label.col = NULL,label.cex = 0.75, label.side = "bottom", label.offset = 0.5,
 opacity = 1, shade.darker = TRUE)
 }
 \arguments{
 \item{bp}{an object of class \code{biplot}.}
 
-\item{which}{a vector containing the groups or classes for which the means should be displayed, with default \code{bp$g}.}
+\item{which}{a vector containing the groups or classes for which the means should be displayed, with default
+the \code{which} argument of samples.}
 
 \item{col}{the colour(s) for the means, with default as the colour of the samples.}
 
diff --git a/man/nom.axes.Rd b/man/nom.axes.Rd
new file mode 100644
index 0000000..d481753
--- /dev/null
+++ b/man/nom.axes.Rd
@@ -0,0 +1,99 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/aesthetics.R
+\name{nom.axes}
+\alias{nom.axes}
+\title{Format aesthetics for the nominal biplot axes}
+\usage{
+nom.axes(bp, X.names=colnames(bp$Xcat)[bp$ax.type$ax.type=="nominal"], 
+         which =1:sum(bp$ax.type$ax.type=="nominal"), col = NULL, lwd = 1, 
+         lty = 1, label.dir = "Orthog", label.col = "black", label.cex = 0.75, 
+         label.line = 0.1, label.offset=rep(0,4), ticks = 5, tick.col = "black", 
+         tick.size = 1, tick.label = TRUE, tick.label.side = "below", 
+         tick.label.col = tick.col, tick.label.cex = 0.6, predict.col = col, 
+         predict.lwd = lwd, predict.lty = lty, ax.names = X.names, 
+         orthogx = 0, orthogy = 0)
+}
+\arguments{
+\item{bp}{an object of class \code{biplot}.}
+
+\item{X.names}{a vector of column names of \code{bp} to specify which axes should be labelled.}
+
+\item{which}{a vector containing the columns or variables for which the axes should be displayed, with default \code{1:p}.}
+
+\item{col}{a list with each component the colour(s) for the levels of that axis.}
+
+\item{lwd}{the line width(s) for the axes, with default \code{1}.}
+
+\item{lty}{the line type(s) for the axes, with default \code{1}.}
+
+\item{label.dir}{a character string indicating the placement of the axis titles to the side of the figure. One of "\code{Orthog}" for axis titles to appear orthogonal to the side of the figure (default) , "\code{Hor}" for axis titles to appear horizontally or "\code{Paral}" for axis titles to appear parallel to the side of the figure.}
+
+\item{label.col}{the colour(s) for the axis labels, with default, \code{col}.}
+
+\item{label.cex}{the label expansion for the axis labels, with default \code{0.75}.}
+
+\item{label.line}{the distance of the axis title from the side of the figure, with default \code{0.1}.}
+
+\item{label.offset}{a four-component numeric vector controlling the distances axis titles are displayed from the side of the figure, with default \code{rep(0,4)}. Sides are numbered \code{1} to \code{4} according to \code{R} conventions.}
+
+\item{ticks}{an integer-valued vector indicating the number of tickmarks for each axis, with default \code{5} for each axis.}
+
+\item{tick.col}{the colour(s) for the tick marks, with default \code{col}.}
+
+\item{tick.size}{a vector specifying the sizes of tick marks for each axis, with default \code{1} for each .}
+
+\item{tick.label}{a logical value indicating whether the axes should be labelled, with default \code{TRUE}.}
+
+\item{tick.label.side}{a character string indicating the position of the tick label. One of "\code{below}" for the label to appear below the tick mark (default) or "\code{above}" for the label to appear above the tick mark.}
+
+\item{tick.label.col}{the colour(s) for the tick mark labels, with default \code{tick.col}.}
+
+\item{tick.label.cex}{the label expansion for the tick mark labels, with default \code{0.6}.}
+
+\item{predict.col}{the colour(s) for the predicted samples, with default \code{col}.}
+
+\item{predict.lwd}{the line width(s) for the predicted samples, with default \code{lwd}.}
+
+\item{predict.lty}{the line type(s) for the predicted samples, with default \code{lty}.}
+
+\item{ax.names}{a vector of size \code{p} containing user defined titles for the axes.}
+
+\item{orthogx}{a numeric vector of size \code{p} specifying the x-coordinate of the parallel transformation of each axis, with default \code{0} for each axis. This is only used when \code{dim.biplot = 2}.}
+
+\item{orthogy}{a numeric vector of size \code{p} specifying the y-coordinate of the parallel transformation of each axis, with default \code{0} for each axis. This is only used when \code{dim.biplot = 2}.}
+}
+\value{
+The object of class \code{biplot} will be appended with a list called \code{axes} containing the following elements:
+\item{which}{a vector containing the columns for which the axes are displayed.}
+\item{col}{the colour(s) of the axes.}
+\item{lwd}{the line width(s) of the axes.}
+\item{lty}{the line type(s) of the axes.}
+\item{label.dir}{the placement of the axis titles to the side of the figure.}
+\item{label.col}{the colour(s) of the axis titles.}
+\item{label.cex}{the label expansion(s) of the axis titles.}
+\item{label.line}{the distance(s) of the axis titles from the side of the figure.}
+\item{ticks}{the number of tick marks per axis.}
+\item{tick.col}{the colour(s) of the tick marks.}
+\item{tick.size}{the size(s) of the tick marks.}
+\item{tick.label}{logical value(s) indicating whether axes are labelled.}
+\item{tick.label.side}{the position of the tick mark labels.}
+\item{tick.label.col}{the colour(s) of the tick mark labels.}
+\item{tick.label.cex}{the expansion(s) of the tick mark labels.}
+\item{predict.col}{the colour(s) of the predicted samples.}
+\item{predict.lty}{the line type(s) of the predicted samples.}
+\item{predict.lwd}{the line width(s) of the predicted samples.}
+\item{names}{the user defined axis titles.}
+\item{orthogx}{the horizontal translations for each axis.}
+\item{orthogy}{the vertical translations for each axis.}
+\item{vectors}{a logical value indicating whether calibrated axes are plotted.}
+}
+\description{
+This function allows the user to format the aesthetics for the nominal biplot axes.
+}
+\examples{
+biplot(iris) |> CatPCA() |> nom.axes(col=c("blue","magenta","gold")) |> plot()
+
+}
+\seealso{
+\code{\link[=biplot]{biplot()}}
+}
diff --git a/man/ord.axes.Rd b/man/ord.axes.Rd
new file mode 100644
index 0000000..ab20667
--- /dev/null
+++ b/man/ord.axes.Rd
@@ -0,0 +1,103 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/aesthetics.R
+\name{ord.axes}
+\alias{ord.axes}
+\title{Format aesthetics for the ordinal biplot axes}
+\usage{
+ord.axes(bp, X.names=colnames(bp$Xcat)[bp$ax.type$ax.type=="ordinal"], 
+         which =1:sum(bp$ax.type$ax.type=="ordinal"), col = grey(0.7), 
+         reverse = rep(FALSE, sum(bp$ax.type$ax.type=="ordinal")), lwd.factor = 1.5, 
+         lwd = 1, lty = 1, label.dir = "Orthog", label.col = col, label.cex = 0.75, 
+         label.line = 0.1, label.offset=rep(0,4), ticks = 5, tick.col = col, 
+         tick.size = 1, tick.label = TRUE, tick.label.side = "below", 
+         tick.label.col = tick.col, tick.label.cex = 0.6, 
+         predict.col = col, predict.lwd = lwd, predict.lty = lty, ax.names = X.names, 
+         orthogx = 0, orthogy = 0)
+}
+\arguments{
+\item{bp}{an object of class \code{biplot}.}
+
+\item{X.names}{a vector of column names of \code{bp} to specify which axes should be labelled.}
+
+\item{which}{a vector containing the columns or variables for which the axes should be displayed, with default \code{1:p}.}
+
+\item{col}{the colour(s) for the axes, with default \code{grey(0.7)}. Alternatively, provide a vector of colours corresponding to \code{X.names}.}
+
+\item{reverse}{logical indicator to switch the narrow to wide calibration on the axis}
+
+\item{lwd.factor}{a numeric value for increasing line width for each consecutive level}
+
+\item{lwd}{the line width(s) for the axes, with default \code{1}.}
+
+\item{lty}{the line type(s) for the axes, with default \code{1}.}
+
+\item{label.dir}{a character string indicating the placement of the axis titles to the side of the figure. One of "\code{Orthog}" for axis titles to appear orthogonal to the side of the figure (default) , "\code{Hor}" for axis titles to appear horizontally or "\code{Paral}" for axis titles to appear parallel to the side of the figure.}
+
+\item{label.col}{the colour(s) for the axis labels, with default, \code{col}.}
+
+\item{label.cex}{the label expansion for the axis labels, with default \code{0.75}.}
+
+\item{label.line}{the distance of the axis title from the side of the figure, with default \code{0.1}.}
+
+\item{label.offset}{a four-component numeric vector controlling the distances axis titles are displayed from the side of the figure, with default \code{rep(0,4)}. Sides are numbered \code{1} to \code{4} according to \code{R} conventions.}
+
+\item{ticks}{an integer-valued vector indicating the number of tickmarks for each axis, with default \code{5} for each axis.}
+
+\item{tick.col}{the colour(s) for the tick marks, with default \code{col}.}
+
+\item{tick.size}{a vector specifying the sizes of tick marks for each axis, with default \code{1} for each .}
+
+\item{tick.label}{a logical value indicating whether the axes should be labelled, with default \code{TRUE}.}
+
+\item{tick.label.side}{a character string indicating the position of the tick label. One of "\code{below}" for the label to appear below the tick mark (default) or "\code{above}" for the label to appear above the tick mark.}
+
+\item{tick.label.col}{the colour(s) for the tick mark labels, with default \code{tick.col}.}
+
+\item{tick.label.cex}{the label expansion for the tick mark labels, with default \code{0.6}.}
+
+\item{predict.col}{the colour(s) for the predicted samples, with default \code{col}.}
+
+\item{predict.lwd}{the line width(s) for the predicted samples, with default \code{lwd}.}
+
+\item{predict.lty}{the line type(s) for the predicted samples, with default \code{lty}.}
+
+\item{ax.names}{a vector of size \code{p} containing user defined titles for the axes.}
+
+\item{orthogx}{a numeric vector of size \code{p} specifying the x-coordinate of the parallel transformation of each axis, with default \code{0} for each axis. This is only used when \code{dim.biplot = 2}.}
+
+\item{orthogy}{a numeric vector of size \code{p} specifying the y-coordinate of the parallel transformation of each axis, with default \code{0} for each axis. This is only used when \code{dim.biplot = 2}.}
+}
+\value{
+The object of class \code{biplot} will be appended with a list called \code{axes} containing the following elements:
+\item{which}{a vector containing the columns for which the axes are displayed.}
+\item{col}{the colour(s) of the axes.}
+\item{lwd.factor}{the factor with which to increase the line width for each level.}
+\item{reverse}{whether the axis goes narrow to wide or vice versa.}
+\item{lwd}{the line width(s) of the axes.}
+\item{lty}{the line type(s) of the axes.}
+\item{label.dir}{the placement of the axis titles to the side of the figure.}
+\item{label.col}{the colour(s) of the axis titles.}
+\item{label.cex}{the label expansion(s) of the axis titles.}
+\item{label.line}{the distance(s) of the axis titles from the side of the figure.}
+\item{ticks}{the number of tick marks per axis.}
+\item{tick.col}{the colour(s) of the tick marks.}
+\item{tick.size}{the size(s) of the tick marks.}
+\item{tick.label}{logical value(s) indicating whether axes are labelled.}
+\item{tick.label.side}{the position of the tick mark labels.}
+\item{tick.label.col}{the colour(s) of the tick mark labels.}
+\item{tick.label.cex}{the expansion(s) of the tick mark labels.}
+\item{predict.col}{the colour(s) of the predicted samples.}
+\item{predict.lty}{the line type(s) of the predicted samples.}
+\item{predict.lwd}{the line width(s) of the predicted samples.}
+\item{names}{the user defined axis titles.}
+\item{orthogx}{the horizontal translations for each axis.}
+\item{orthogy}{the vertical translations for each axis.}
+\item{vectors}{a logical value indicating whether calibrated axes are plotted.}
+}
+\description{
+This function allows the user to format the aesthetics for the ordinal biplot axes.
+}
+\examples{
+biplot(iris) |> CatPCA(cat.type = "ord") |> ord.axes(col="purple") |> plot()
+
+}
diff --git a/man/plot.biplot.Rd b/man/plot.biplot.Rd
index acfd611..86f51b4 100644
--- a/man/plot.biplot.Rd
+++ b/man/plot.biplot.Rd
@@ -10,6 +10,7 @@
   axis.predictivity = NULL,
   sample.predictivity = NULL,
   zoom = FALSE,
+  add = FALSE,
   xlim = NULL,
   ylim = NULL,
   ...
@@ -26,6 +27,8 @@
 
 \item{zoom}{a logical value allowing the user to select an area to zoom into.}
 
+\item{add}{a logical value allowing the user to add the biplot to a current plot. If \code{add = TRUE} the argument \code{zoom} is inactive.}
+
 \item{xlim}{the horizontal limits of the plot.}
 
 \item{ylim}{the vertical limits of the plot.}
diff --git a/man/ties.Rd b/man/ties.Rd
new file mode 100644
index 0000000..7fe9785
--- /dev/null
+++ b/man/ties.Rd
@@ -0,0 +1,21 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/utility.R
+\name{ties}
+\alias{ties}
+\title{Applies primary or secondary approach to ties}
+\usage{
+ties(d, delta, method = c("primary", "secondary"))
+}
+\arguments{
+\item{d}{observed dissimilarities}
+
+\item{delta}{given dissimilarities to match (order)}
+
+\item{method}{either \code{primary} or \code{secondary} approach to ties}
+}
+\value{
+a vector of ordered values
+}
+\description{
+Applies primary or secondary approach to ties
+}
diff --git a/src/.gitignore b/src/.gitignore
new file mode 100644
index 0000000..22034c4
--- /dev/null
+++ b/src/.gitignore
@@ -0,0 +1,3 @@
+*.o
+*.so
+*.dll
diff --git a/src/LnjTinyNew.cpp b/src/LnjTinyNew.cpp
new file mode 100644
index 0000000..dbeb1a2
--- /dev/null
+++ b/src/LnjTinyNew.cpp
@@ -0,0 +1,445 @@
+#include <Rcpp.h>
+#include <cmath>
+using namespace Rcpp;
+
+// Khaled: differences with fortran:
+//Optimize alfunc by computing Z directly from BVEC and combining loops
+
+//- Eliminated intermediate B matrix creation by computing Z = M %*% B directly from BVEC vector
+//- Combined three separate loops (exind, prediction, loss calculation) into single pass
+
+
+// [[Rcpp::export]]
+double alfunc(NumericVector BVEC,
+              NumericMatrix X,
+              NumericVector Y,
+              NumericMatrix M,
+              NumericVector MU,
+              double LAMBDA,
+              double CONST1,
+              double CONST2,
+              int U, int V) {
+  // to remain consistent with the paper, we should set const1 = 1 and lambda = 0.
+  int n = X.nrow();
+  int p = X.ncol();
+  int nmu = MU.length();
+  int uv = U + V;
+  
+  // Compute Z = M %*% B directly from BVEC without creating B
+  NumericMatrix Z(nmu, p);
+  
+  for(int j = 0; j < p; j++) {
+    int bvec_offset = j * uv;  // Starting index in BVEC for column j
+    for(int i = 0; i < nmu; i++) {
+      Z(i, j) = 0.0;
+      for(int k = 0; k < uv; k++) {
+        Z(i, j) += M(i, k) * BVEC[bvec_offset + k];
+      }
+    }
+  }
+  
+  // Combined loop: find nearest index, get prediction, and calculate loss
+  double temp1 = 0.0;
+  
+  for(int i = 0; i < n; i++) {
+    int closest_idx = 0;
+    double rmin = 1.0e9;
+    
+    // Find closest Z row to X row i
+    for(int j = 0; j < nmu; j++) {
+      double temp_dist = 0.0;
+      for(int k = 0; k < p; k++) {
+        double diff = X(i, k) - Z(j, k);
+        temp_dist += diff * diff;
+      }
+      
+      if(temp_dist < rmin) {
+        rmin = temp_dist;
+        closest_idx = j;
+      }
+    }
+    
+    // Calculate loss immediately using the closest index
+    double diff = Y[i] - MU[closest_idx];
+    temp1 += diff * diff;
+  }
+  
+  double loss = temp1 / CONST1;
+  
+  // Add penalty term if lambda > 0
+  if(LAMBDA > 0.0 && nmu > 2) {
+    double temp2 = 0.0;
+    for(int j = 0; j < p; j++) {
+      for(int i = 1; i < (nmu - 1); i++) {
+        double diff = Z(i - 1, j) - 2.0 * Z(i, j) + Z(i + 1, j);
+        temp2 += diff * diff;
+      }
+    }
+    loss += LAMBDA * temp2 / CONST2;
+  }
+  
+  return loss;
+}
+
+//Khaled:
+// ========== SIMPLEX SETUP ==========
+NumericMatrix varset(NumericVector BVEC, int U, int V, int P, double TAU) {
+  int andim = (U + V) * P;
+  NumericMatrix AP(andim + 1, andim);
+  
+  // First row: BVEC unchanged
+  for(int j = 0; j < andim; j++) {
+    AP(0, j) = BVEC[j];
+  }
+  
+  // Remaining rows: BVEC with TAU added to successive elements
+  for(int i = 1; i <= andim; i++) {
+    for(int j = 0; j < andim; j++) {
+      AP(i, j) = BVEC[j];
+    }
+    AP(i, i - 1) += TAU;
+    //Khaled:
+    //Alternative way for AP(i, i - 1).
+    //Adding a fixed TAU, regardless of the scale of the BVEC components, is problematic. 
+    //It may be better to scale TAU relative to each component to achieve global optimization. 
+    //If you want to use the following approach, please uncomment these lines and comment out AP above.
+    //If you activate the following code, be careful that TAU cannot be a fixed constant. 
+    //In this case, interpret TAU as a relative step size (e.g., TAU = 0.05 means a 5% perturbation), not an absolute one.
+
+    // // Relative perturbation: TAU * |BVEC[i-1]| or TAU if near zero
+    // double delta = fabs(BVEC[i - 1]) > 1e-8 ? 
+    //                TAU * fabs(BVEC[i - 1]) : TAU;
+    // AP(i, i - 1) += delta;
+  }
+  
+  return AP;
+}
+
+// ========== SIMPLEX OPERATIONS ==========
+double amotry(NumericMatrix& PMAT,       
+              NumericVector& YVEK,       
+              NumericVector& PSUM,       
+              int IHI, 
+              double FAC,
+              const NumericMatrix& X,     
+              const NumericVector& Y,     
+              const NumericMatrix& M,     
+              const NumericVector& MU,     
+              double LAMBDA,             
+              double CONST1,              
+              double CONST2,              
+              int U,                      
+              int V){
+  //PMAT: The simplex matrix - each row is a vertex (parameter vector)
+  //YVEK: Function values at each vertex (loss at each simplex point)
+  //PSUM: Sum of all vertices (used to compute centroid efficiently)
+  //IHI: Index of the highest (worst) point in the simplex (0-indexed in C++)
+  //FAC: Extrapolation factor.
+  //All other inputs are for loss function evaluation (passed by value)
+  //What thi function do:
+  //Extrapolates by a factor FAC through the face of the simplex across 
+  //from the highest point, tries it, and replaces the high point if 
+  //the new point is better
+  int ndim = PMAT.ncol();
+  NumericVector PTRY(ndim);
+  
+  double fac1 = (1.0 - FAC) / ndim;
+  double fac2 = fac1 - FAC;
+  
+  for(int j = 0; j < ndim; j++) {
+    PTRY[j] = PSUM[j] * fac1 - PMAT(IHI, j) * fac2;
+  }
+  
+  double ytry = alfunc(PTRY, X, Y, M, MU, LAMBDA, CONST1, CONST2, U, V);
+  
+  if(ytry < YVEK[IHI]) {
+    YVEK[IHI] = ytry;
+    for(int j = 0; j < ndim; j++) {
+      PSUM[j] = PSUM[j] - PMAT(IHI, j) + PTRY[j];
+      PMAT(IHI, j) = PTRY[j];
+    }
+  }
+  
+  return ytry;
+// Khaled:  pass-by-reference eliminates the need to return PMAT, YVEK, and PSUM,
+// since they are modified in place; the calling function only requires ytry for its control-flow logic.
+}
+
+// ========== OPTIMIZER ==========
+
+List amoeba(NumericMatrix PMAT, NumericVector YVEK,
+                 double FTOL, int ITMAX,
+                 NumericMatrix X, NumericVector Y, NumericMatrix M,
+                 NumericVector MU, double LAMBDA,
+                 double CONST1, double CONST2, int U, int V, double TINY) {
+  
+  int ndim = PMAT.ncol();
+  int mp = PMAT.nrow();
+  int iter = 0;
+  int erro = 0;
+  
+  if(ndim > 20) {
+    erro = 5;
+    return List::create(Named("PMAT") = PMAT,
+                       Named("YVEK") = YVEK,
+                       Named("ITER") = iter,
+                       Named("ERRO") = erro);
+  }
+  
+  NumericVector PSUM(ndim);
+  
+  while(true) {
+    // Compute PSUM
+    for(int j = 0; j < ndim; j++) {
+      double sum1 = 0.0;
+      for(int i = 0; i < mp; i++) {
+        sum1 += PMAT(i, j);
+      }
+      PSUM[j] = sum1;
+    }
+    
+    // Find ILO, IHI, INHI
+    int ilo = 0;
+    int ihi, inhi;
+    
+    if(YVEK[0] > YVEK[1]) {
+      ihi = 0;
+      inhi = 1;
+    } else {
+      ihi = 1;
+      inhi = 0;
+    }
+    
+    for(int i = 0; i < mp; i++) {
+      if(YVEK[i] <= YVEK[ilo]) ilo = i;
+      if(YVEK[i] > YVEK[ihi]) {
+        inhi = ihi;
+        ihi = i;
+      } else if(YVEK[i] > YVEK[inhi]) {
+        if(i != ihi) inhi = i;
+      }
+    }
+    
+    // Check convergence
+    double rtol = 2.0 * fabs(YVEK[ihi] - YVEK[ilo]) / 
+                  (fabs(YVEK[ihi]) + fabs(YVEK[ilo]) + TINY);
+    
+    if(rtol < FTOL) {
+      // Put best point in slot 0
+      double swap = YVEK[0];
+      YVEK[0] = YVEK[ilo];
+      YVEK[ilo] = swap;
+      
+      for(int j = 0; j < ndim; j++) {
+        swap = PMAT(0, j);
+        PMAT(0, j) = PMAT(ilo, j);
+        PMAT(ilo, j) = swap;
+      }
+      
+      break;
+    }
+    
+    // Check iteration limit
+    if(iter >= ITMAX) {
+      erro = 1;
+      break;
+    }
+    
+    iter += 2;
+    
+    // Try reflection
+    double ytry = amotry(PMAT, YVEK, PSUM, ihi, -1.0,
+                              X, Y, M, MU, LAMBDA, CONST1, CONST2, U, V);
+    
+    if(ytry <= YVEK[ilo]) {
+      // Try expansion
+      ytry = amotry(PMAT, YVEK, PSUM, ihi, 2.0,
+                        X, Y, M, MU, LAMBDA, CONST1, CONST2, U, V);
+    } else if(ytry >= YVEK[inhi]) {
+      // Try contraction
+      double ysave = YVEK[ihi];
+      ytry = amotry(PMAT, YVEK, PSUM, ihi, 0.5,
+                        X, Y, M, MU, LAMBDA, CONST1, CONST2, U, V);
+      
+      if(ytry >= ysave) {
+        // Shrink simplex
+        for(int i = 0; i < mp; i++) {
+          if(i != ilo) {
+            for(int j = 0; j < ndim; j++) {
+              PSUM[j] = 0.5 * (PMAT(i, j) + PMAT(ilo, j));
+              PMAT(i, j) = PSUM[j];
+            }
+            YVEK[i] = alfunc(PSUM, X, Y, M, MU, LAMBDA, 
+                                 CONST1, CONST2, U, V);
+          }
+        }
+        iter += ndim;
+      }
+    } else {
+      iter -= 1;
+    }
+  }
+  
+  return List::create(Named("PMAT") = PMAT,
+                     Named("YVEK") = YVEK,
+                     Named("ITER") = iter,
+                     Named("ERRO") = erro);
+}
+
+// ========== MAIN WRAPPER ==========
+
+// [[Rcpp::export]]
+List optimize_spline(NumericVector BVEC,
+                          NumericMatrix X,
+                          NumericVector Y,
+                          NumericMatrix M,
+                          NumericVector MU,
+                          double LAMBDA,
+                          double CONST1,
+                          double CONST2,
+                          int U, int V,
+                          double TAU,
+                          double FTOL,
+                          double TINY,
+                          int ITMAX) {
+  
+  int p = X.ncol();
+  int andim = (U + V) * p;
+  int erro = 0;
+  
+  // ========== STAGE 1 ==========
+  
+  // Create simplex
+  NumericMatrix AP1 = varset(BVEC, U, V, p, TAU);
+  
+  // Evaluate at each vertex
+  NumericVector AY1(andim + 1);
+  for(int i = 0; i <= andim; i++) {
+    NumericVector tempvk(andim);
+    for(int j = 0; j < andim; j++) {
+      tempvk[j] = AP1(i, j);
+    }
+    AY1[i] = alfunc(tempvk, X, Y, M, MU, LAMBDA, CONST1, CONST2, U, V);
+  }
+  
+  // Run amoeba
+  List result1 = amoeba(AP1, AY1, FTOL, ITMAX, 
+                            X, Y, M, MU, LAMBDA, CONST1, CONST2, U, V, TINY);
+  
+  NumericMatrix PMAT1 = result1["PMAT"];
+  NumericVector YVEK1 = result1["YVEK"];
+  int iter1 = result1["ITER"];
+  erro = result1["ERRO"];
+  
+  if(erro != 0) {
+    NumericVector bvec_out(andim);
+    for(int j = 0; j < andim; j++) {
+      bvec_out[j] = PMAT1(0, j);
+    }
+    
+    return List::create(Named("LOSS") = YVEK1[0],
+                       Named("BVEC") = bvec_out,
+                       Named("LOSS1") = YVEK1[0],
+                       Named("ITER1") = iter1,
+                       Named("ITER") = 0,
+                       Named("ERRO") = erro);
+  }
+  
+  double loss1 = YVEK1[0];
+  
+  // ========== STAGE 2 ==========
+  
+  // Extract best from stage 1
+  NumericVector BVEC2(andim);
+  for(int j = 0; j < andim; j++) {
+    BVEC2[j] = PMAT1(0, j);
+  }
+  
+  // Create new simplex
+  NumericMatrix AP2 = varset(BVEC2, U, V, p, TAU);
+  
+  // Evaluate at each vertex
+  NumericVector AY2(andim + 1);
+  for(int i = 0; i <= andim; i++) {
+    NumericVector tempvk(andim);
+    for(int j = 0; j < andim; j++) {
+      tempvk[j] = AP2(i, j);
+    }
+    AY2[i] = alfunc(tempvk, X, Y, M, MU, LAMBDA, CONST1, CONST2, U, V);
+  }
+  
+  // Run amoeba again
+  List result2 = amoeba(AP2, AY2, FTOL, ITMAX,
+                            X, Y, M, MU, LAMBDA, CONST1, CONST2, U, V, TINY);
+  
+  NumericMatrix PMAT2 = result2["PMAT"];
+  NumericVector YVEK2 = result2["YVEK"];
+  int iter2 = result2["ITER"];
+  erro = result2["ERRO"];
+  
+  double loss = YVEK2[0];
+  
+  // Extract final BVEC
+  NumericVector bvec_out(andim);
+  for(int j = 0; j < andim; j++) {
+    bvec_out[j] = PMAT2(0, j);
+  }
+  
+  return List::create(Named("LOSS") = loss,
+                     Named("BVEC") = bvec_out,
+                     Named("LOSS1") = loss1,
+                     Named("ITER1") = iter1,
+                     Named("ITER") = iter2,
+                     Named("ERRO") = erro);
+}
+
+
+
+
+
+// ========== ADDITIONAL FUNCTIONS (NOT USED IN OPTIMIZER) ==========
+
+//These two functions (mipd and inddup) are not used in the Nelder–Mead algorithm or in biplot.spline.axis. They are rewritten to align with the original Fortran code (although they may be used elsewhere in the library).
+
+double mipd(NumericVector X, NumericVector Y) {
+  int n = X.length();
+  double d = 0.0;
+  int count = 0;
+  
+  for(int i = 1; i < n; i++) {
+    for(int j = 0; j < i; j++) {
+      double dx = X[i] - X[j];
+      double dy = Y[i] - Y[j];
+      d += sqrt(dx * dx + dy * dy);
+      count++;
+    }
+  }
+  
+  return d / count;
+}
+
+
+LogicalVector inddup(NumericVector X, NumericVector Y, 
+                          NumericVector RW, double FRAC) {
+  int n = X.length();
+  double xtol = FRAC * (RW[1] - RW[0]);
+  double ytol = FRAC * (RW[3] - RW[2]);
+  
+  LogicalVector DUP(n);
+  DUP[0] = false;
+  
+  for(int i = 1; i < n; i++) {
+    DUP[i] = false;
+    for(int j = 0; j < i; j++) {
+      double dx = fabs(X[i] - X[j]);
+      double dy = fabs(Y[i] - Y[j]);
+      
+      if(dx < xtol && dy < ytol) {
+        DUP[i] = true;
+        break;
+      }
+    }
+  }
+  
+  return DUP;
+}
\ No newline at end of file
diff --git a/src/LnjTinyNew.f b/src/LnjTinyNew.f
deleted file mode 100644
index 8e021d0..0000000
--- a/src/LnjTinyNew.f
+++ /dev/null
@@ -1,512 +0,0 @@
-      SUBROUTINE MIPD(X,Y,N,D)
-      IMPLICIT DOUBLE PRECISION(A-H,O-Z)
-      DIMENSION X(N), Y(N)
-      D = 0.D0
-      DIV = DBLE(N*(N-1)/2)
-      DO 23284 I = 2,N 
-      DO 23286 J = 1,I-1 
-      D = D + SQRT((X(I)-X(J))**2 + (Y(I)-Y(J))**2)
-23286 CONTINUE
-23284 CONTINUE
-      D = D/DIV
-      RETURN
-      END
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-
-
-      SUBROUTINE INDDUP(X,Y,N,RW,FRAC,DUP)
-      IMPLICIT DOUBLE PRECISION(A-H,O-Z)
-      LOGICAL DUP(N)
-      DIMENSION X(N), Y(N), RW(4)
-      XTOL = FRAC*(RW(2)-RW(1))
-      YTOL = FRAC*(RW(4)-RW(3))
-      DUP(1) = .FALSE.
-      DO 23182 I = 2,N 
-      DUP(I) = .FALSE.
-      DO 23184 J = 1,I-1 
-      DX = ABS(X(I)-X(J))
-      DY = ABS(Y(I)-Y(J))
-      IF(.NOT.(DX .LT. XTOL .AND. DY .LT. YTOL))GOTO 23186
-      DUP(I) = .TRUE.
-      GOTO 23185
-23186 CONTINUE
-23184 CONTINUE
-23185 CONTINUE
-23182 CONTINUE
-      RETURN
-      END
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC      
-      
-      SUBROUTINE MATM ( A1, A2B1, B2, A, B, OUT)
-
-C     This subroutine performs matrix multiplication.
-C     This should be improved with optimised code (such as from 
-C          Linpack, etc.)
-      IMPLICIT NONE
-      INTEGER A1, A2B1, B2
-      DOUBLE PRECISION A(A1,A2B1), B(A2B1,B2), OUT(A1,B2)
-
-C     DUMMIES
-
-      INTEGER I, J, K
-
-      DO 300,J=1,B2
-        DO 200,I=1,A1
-          OUT(I,J)=0
-          DO 100,K=1,A2B1
-            OUT(I,J)=OUT(I,J)+A(I,K)*B(K,J)
-100       CONTINUE
-
-200     CONTINUE
-
-300   CONTINUE
-
-      END 
-
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-
-      SUBROUTINE EXIND (Z, X, N, P, NMU, IND)
-
-C     This subroutine returns the indices of EXact shortest distances.
-C     Tested against R output -- works
-      IMPLICIT NONE
-      INTEGER  N, P, NMU, IND(N)
-      DOUBLE PRECISION Z(NMU,P), X(N,P)
-
-C     DATA Ind/n*0.0/
-
-C     DUMMIES
-
-      INTEGER I, J, K
-      DOUBLE PRECISION TEMP1, RMIN
-
-      DO 300, I=1,N
-        Ind(I)=0
-        RMIN = 1.0D+09
-        DO 200, J=1,NMU
-          TEMP1=0.0
-          DO 100, K=1,P
-            TEMP1=TEMP1+( X(I,K)-Z(J,K) )**2
-100       CONTINUE
-          IF (TEMP1 .LT. RMIN) THEN
-            RMIN=TEMP1
-            IND(I)=J
-          END IF         
-200     CONTINUE
-300   CONTINUE
-
-      END
-
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-
-      DOUBLE PRECISION FUNCTION ALFUNC (BVEC, X, N, P, NMU, IND, MU, 
-     + PRED, LAMBDA, Y, CONST1, CONST2, U, V, M)
-
-C     This subroutine calculates the loss function.
-C     const1 and const2 are the two scaling constants used in the 
-C               loss function...
-C     ... they are calculated once in R itself.
-      IMPLICIT NONE
-      INTEGER N, P, NMU, IND(N), U, V
-      DOUBLE PRECISION LAMBDA
-      DOUBLE PRECISION  X(N,P), MU(NMU), PRED(NMU), 
-     + Y(N), CONST1, CONST2, M(NMU,U+V), BVEC((U+V)*P)
-C     NOTE Bvec is a vector here
-
-C     common block
-
-C      COMMON /CSHARE/X, N, P, NMU, IND, MU, PRED, LAMBDA, Y
-C    +   CONST1, CONST2, U, V, M, BVEC
-C     DUMMIES
-
-      INTEGER I, J
-      DOUBLE PRECISION   Z(NMU, P), TEMP1, TEMP2
-
-CCCCCCCCCCCC
-
-      ALFUNC=0.0
-
-      CALL MATM( NMU, U+V, P, M, BVEC, Z)
-
-      CALL EXIND(Z,X,N,P,NMU,IND)
-      
-        DO 100, I=1,N
-        PRED(I)=MU(IND(I))
-100   CONTINUE
-
-CCCCCCCCCCCC
-
-      TEMP1=0.0      
-      DO 500, I=1,N
-        TEMP1=TEMP1+ ( Y(I)-PRED(I) )**2
-500   CONTINUE
-
-      ALFUNC= TEMP1/CONST1
-
-
-      IF (LAMBDA .GT. 0.0) THEN
-        TEMP2=0.0
-        DO 700, J=1,P
-          DO 600, I=2,(NMU-1)
-            TEMP2=TEMP2+( Z(I-1,J)-2*Z(I,J)+Z(I+1,J) )**2
-600       CONTINUE
-700     CONTINUE
-        ALFUNC=ALFUNC+LAMBDA*TEMP2/CONST2
-      END IF       
-
-C     Checked Fortran Loss against R. Matches.
-
-      END
-
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC 
-
-      SUBROUTINE VARSET (BVEC, AP, U, V, P, TAU)
-
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-CC     This subtroutine sets Ap and Ay for subroutine L. Dirty work.
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC   
-      IMPLICIT NONE
-      INTEGER U, V, P
-
-      DOUBLE PRECISION AP((U+V)*P+1,(U+V)*P), BVEC((U+V)*P), TAU
-
-      INTEGER I,J, ANDIM
-        
-      ANDIM=(U+V)*P
-
-C     The first Ap is Bvec:
-      DO 100, J=1,ANDIM
-        AP(1,J)=BVEC(J)
-100   CONTINUE
-  
-C     Adding a number tau to a successive element in each successive
-C     row of Ap:
-      DO 300, I=2,(ANDIM+1)
-        DO 200, J=1,ANDIM
-          AP(I,J)=BVEC(J)
-200     CONTINUE
-      AP(I,I-1)=AP(I,I-1)+TAU
-300   CONTINUE
-
-      END
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-
-
-      SUBROUTINE L (LOSS, X, N, P, NMU, IND, MU, PRED, LAMBDA, Y, 
-     +CONST1, CONST2, U, V, M, BVEC, TAU, AY, TEMPVK, ITER, FTOL, 
-     +LOSS1, ITER1, ERRO, CONST3, ITMAX)
-
-      IMPLICIT NONE
-
-C     iter1 sends back the total number of iterations in the first call 
-C      to amoeba; iter sends back the total number of iterations in the
-C           second call to amoeba.
-
-      EXTERNAL ALFUNC
-
-      DOUBLE PRECISION ALFUNC
-
-!CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-!C     This is the subroutine actually called from within R.
-!CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-
-      INTEGER N, P, NMU, IND(N), U, V, ITER, ITER1, ERRO, ITMAX
-      DOUBLE PRECISION TAU, LAMBDA, CONST3
-      DOUBLE PRECISION LOSS, LOSS1, X(N,P), MU(NMU), PRED(NMU), FTOL
-      DOUBLE PRECISION Y(N), CONST1, CONST2, M(NMU,U+V), BVEC((U+V)*P)
-      
-C     NOTE Bvec is a vector here.
-
-C     ALFUNC IS THE NAME OF THE FUNCTION THAT CALCULATES THE LOSS.
-
-      INTEGER ANDIM
-      DOUBLE PRECISION AP((U+V)*P+1,(U+V)*P), AY((U+V)*P+1)
-     
-C     The Ap's are the N+1=(u+v)*p+1 points defining the simplex; 
-C         it's used in amoeba.
-C     The Ay's are the N+1=(u+v)*p+1 loss function evaluations for each
-C        of the Ap rows; it's used in amoeba.
-C     Ap1st stores the first set of Aps. Except for the first row,
-C        they are reused for the second call to amoeba.
-C     LOSS1 indicates the loss after the first call of amoeba.
-
-
-      INTEGER I, J
-      DOUBLE PRECISION TEMPVK((U+V)*P)
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-      ERRO=0
-      ANDIM=(U+V)*P
-
-C     Setting Ap before the first call to amoeba:
-
-      CALL VARSET (BVEC, AP, U, V, P, TAU)
- 
-C     Evaluating Ap to get Ay:
-
-      DO 200, I=1,(ANDIM+1)
-        DO 100, J=1,ANDIM
-          TEMPVK(J)=AP(I,J)
-100     CONTINUE
-C     Evaluating the successive Ay's:
-      AY(I)=ALFUNC(TEMPVK, X, N, P, NMU, IND, MU, PRED, LAMBDA, Y,
-     +CONST1, CONST2, U, V, M)
-200   CONTINUE
-C   Checked the AY(I) values against those from R (before creating 
-C   the VARSET function).
-
-C     Calling amoeba for the FIRST TIME:
-
-      CALL AMOEBA(AP, AY, ANDIM+1, ANDIM, ANDIM, FTOL, ALFUNC, ITER,
-     +X, N, P, NMU, IND, MU, PRED, LAMBDA, Y, CONST1, CONST2, U, V, 
-     +M, ERRO, CONST3,ITMAX) 
-C     Error check
-      IF (ERRO .NE. 0) GO TO 9999
-C     Saving the number of iterations in the first call to amoeba:      
-      ITER1=ITER
-
-C     Saving the loss from the first call to amoeba:
-      LOSS1=AY(1)
-
-C     Setting Ap before the second call to amoeba: 
-    
-      DO 300, J=1,ANDIM
-        BVEC(J)=AP(1,J)
-300   CONTINUE
-
-      CALL VARSET (BVEC, AP, U, V, P, TAU)
-
-C  Evaluating Ap to get Ay:
-
-      DO 500, I=1,(ANDIM+1)
-        DO 400, J=1,ANDIM
-          TEMPVK(J)=AP(I,J)
-400     CONTINUE
-
-C Evaluating the successive Ay's:
-      AY(I)=ALFUNC(TEMPVK, X, N, P, NMU, IND, MU, PRED,
-     +LAMBDA, Y, CONST1, CONST2, U, V, M)
-500   CONTINUE
-
-C Checked the AY(I) values against those from R 
-C (before creating the VARSET function).
-
-C Calling amoeba for the SECOND time:
-
-      CALL AMOEBA(AP, AY, ANDIM+1, ANDIM, ANDIM, FTOL, ALFUNC, ITER,
-     +X, N, P, NMU, IND, MU, PRED, LAMBDA, Y, CONST1, CONST2, U, 
-     +V, M, ERRO, CONST3,ITMAX) 
-
-C     Error check
-      IF (ERRO .NE. 0) GO TO 9999
-
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-
-C   RETURN VALUES:    (carefully check)
-
-      LOSS=AY(1)
-      DO 600, J=1, ANDIM
-        BVEC(J)=AP(1,J)
-600   CONTINUE
-
-9999  END
-
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-      SUBROUTINE AMOEBA (PMAT, YVEK, MP, NP, NDIM, FTOL, FUNK, ITER,
-     +QX, QN, QP, QNMU, QIND, QMU, QPRED, QLAMBD, QY, QCONS1, QCONS2,
-     +QU, QV, QM, ERRO, TINY, ITMAX)
-C second and third lines of arguments added myself.
-
-C MP is the number of rows of PMAT.
-C NP is the number of columns of PMAT.
-    
-      IMPLICIT NONE
-      INTEGER NMAX, ITMAX, MP, NP, NDIM, ITER, ERRO
-      DOUBLE PRECISION TINY, CONST3
-      PARAMETER (NMAX=20)
-      
-      DOUBLE PRECISION PMAT(MP, NP), YVEK(MP), FTOL, FUNK
-
-      EXTERNAL FUNK
-
-      INTEGER QN, QP, QNMU, QIND(QN), QU, QV
-      DOUBLE PRECISION QX(QN, QP), QMU(QNMU), QPRED(QNMU), QLAMBD, 
-     +  QY(QN), QCONS1, QCONS2, QM(QNMU,QU+QV)
-
-      INTEGER I, IHI, ILO, INHI, J
-      DOUBLE PRECISION RTOL, SUM1, SWAP, YSAVE, YTRY, PSUM(NMAX)
-      DOUBLE PRECISION AMOTRY
-
-CCCCCCCCCCCCCCCCCCCCCCCCCCC
-                                                             
-C      USES AMOTRY, FUNK,
-C      Multidimensional minimization of the function funk(x) 
-C      where x(1:ndim) is a vector
-C      in ndim dimensions, by the downhill simplex method of Nelder 
-C      and Mead. The matrix
-C      pmat(1:ndim+1,1:ndim) is input. Its ndim+1 rows are 
-C      ndim-dimensional vectors which are
-C      the vertices of the starting simplex. Also input is the vector 
-C      yvek(1:ndim+1), whose compo-
-C      nents must be pre-initialized to the values of funk evaluated
-C      at the ndim+1 vertices (rows)
-C      of p; and ftol the fractional convergence tolerance to be 
-C      achieved in the function value
-C      (n.b.!). On output, p and y will have been reset to ndim+1 new 
-C      points all within ftol of
-C      a minimum function value, and iter gives the number of 
-C      function evaluations taken.
-
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-      CONST3 = 0.0001
-      TINY=CONST3
-      ITER=0
-      ERRO=0
-      IF (NDIM .GT. NMAX) THEN
-      ERRO=5
-      GO TO 999
-      END IF
-                                       
-10    DO 40, J=1,NDIM
-        SUM1=0.0
-        DO 30, I=1,NDIM+1
-          SUM1=SUM1+PMAT(I,J)
-30      CONTINUE 
-        PSUM(J)=SUM1
-40    CONTINUE 
-                                      
-50    ILO=1
-                                      
-      IF (YVEK(1) .GT. YVEK(2)) THEN                                   
-        IHI=1
-        INHI=2
-      ELSE
-        IHI=2
-        INHI=1
-      END IF
-                                      
-      DO 60, I=1,NDIM+1 
-        IF(YVEK(I) .LE. YVEK(ILO)) ILO=I
-        IF(YVEK(I) .GT. YVEK(IHI)) THEN
-          INHI=IHI
-          IHI=I
-        ELSE IF(YVEK(I) .GT. YVEK(INHI)) THEN
-          IF(I .NE. IHI) INHI=I
-        END IF
-60    CONTINUE   
-
-      RTOL=2.0*DABS(YVEK(IHI)-YVEK(ILO))/(DABS(YVEK(IHI))
-     + +DABS(YVEK(ILO))+TINY)
-     
-C Compute the fractional range from highest to lowest and return if 
-C satisfactory.
-C If returning, put best point and value in slot 1.
-                     
-      IF (RTOL .LT. FTOL) THEN
-        SWAP=YVEK(1)
-        YVEK(1)=YVEK(ILO)
-        YVEK(ILO)=SWAP
-        DO 70, J=1,NDIM
-          SWAP=PMAT(1,J)
-          PMAT(1,J)=PMAT(ILO,J)
-          PMAT(ILO,J)=SWAP
-70    CONTINUE
-        RETURN
-      END IF
-      IF (ITER .GE. ITMAX) THEN 
-      ERRO=1
-      GO TO 999
-      END IF      
-C      'ITMAX exceeded in AMOEBA'
-      ITER=ITER+2
-C Begin a new iteration. First extrapolate by a factor -1 through the
-C face of the simplex across from the highest point i.e. reflect simplex
-C from highest point
-    
-      YTRY=AMOTRY(PMAT, YVEK, PSUM, MP, NP, NDIM, FUNK, IHI, -1.0D+00,
-     + QX, QN, QP,QNMU, QIND, QMU, QPRED, QLAMBD, QY, QCONS1, QCONS2, 
-     + QU, QV, QM)
-
-      IF (YTRY .LE. YVEK(ILO)) THEN
-      YTRY=AMOTRY(PMAT, YVEK, PSUM, MP, NP, NDIM, FUNK, IHI, 2.0D+00, 
-     + QX, QN, QP,QNMU, QIND, QMU, QPRED, QLAMBD, QY, QCONS1, QCONS2, 
-     + QU, QV, QM)
-      ELSE IF (YTRY .GE. YVEK(INHI)) THEN
-        YSAVE=YVEK(IHI)
-        YTRY=AMOTRY(PMAT, YVEK, PSUM, MP, NP, NDIM,FUNK, IHI, 0.5D+00, 
-     + QX, QN, QP, QNMU, QIND, QMU, QPRED, QLAMBD, QY, QCONS1, 
-     + QCONS2, +  QU, QV, QM)
-                                          
-        IF (YTRY .GE. YSAVE) THEN                                   
-          DO 90, I=1,NDIM+1
-            IF(I .NE. ILO) THEN
-              DO 80, J=1,NDIM
-                PSUM(J)=0.5*(PMAT(I,J)+PMAT(ILO,J))
-                PMAT(I,J)=PSUM(J)
-80            CONTINUE 
-              YVEK(I)=FUNK(PSUM, QX, QN, QP, QNMU, QIND, QMU, QPRED, 
-     +                QLAMBD, QY, QCONS1, QCONS2, QU, QV, QM)
-            END IF
-90        CONTINUE
-       
-         ITER=ITER+NDIM
-
-         GOTO 10
-
-        END IF
-      ELSE
-        ITER=ITER-1
-      END IF
-      GOTO 50
-999   END 
-
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-
-      DOUBLE PRECISION FUNCTION AMOTRY(PMAT, YVEK, PSUM, MP, NP, NDIM,
-     + FUNK,IHI, FAC,
-     + QX, QN, QP, QNMU, QIND, QMU, QPRED, QLAMBD, 
-     + QY, QCONS1, QCONS2, QU, QV, QM)
-     
-      IMPLICIT NONE
-      INTEGER IHI, MP, NDIM, NP, NMAX
-      DOUBLE PRECISION FAC, PMAT(MP,NP), PSUM(NP), YVEK(MP), FUNK
- 
-      PARAMETER (NMAX=20)
-      EXTERNAL FUNK
-C Extrapolates by a factor FAC through the face of the simplex across 
-C from the highest point, tries it, and replaces the high point if 
-C the new point is better
-      INTEGER J, QN, QP, QNMU, QIND(QN), QU, QV
-      DOUBLE PRECISION FAC1, FAC2, YTRY, PTRY(NMAX)
-      DOUBLE PRECISION QLAMBD, QX(QN,QP), QMU(QNMU)
-      DOUBLE PRECISION QPRED(QNMU), QY(QN), QCONS1, QCONS2  
-      DOUBLE PRECISION QM(QNMU,QU+QV) 
-
-CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
-
-      FAC1=(1.0-FAC)/NDIM
-      FAC2=FAC1-FAC
-      DO 10, J=1,NDIM
-        PTRY(J)=PSUM(J)*FAC1-PMAT(IHI,J)*FAC2
-10    CONTINUE 
-
-      YTRY=FUNK(PTRY, QX, QN, QP, QNMU, QIND, QMU, QPRED, QLAMBD, QY, 
-     +          QCONS1, QCONS2, QU, QV, QM)
-                             
-      IF (YTRY .LT. YVEK(IHI)) THEN
-        YVEK(IHI)=YTRY
-        DO 20, J=1,NDIM
-          PSUM(J)=PSUM(J)-PMAT(IHI,J)+PTRY(J)
-          PMAT(IHI,J)=PTRY(J)
-20        CONTINUE
-      END IF
-      AMOTRY=YTRY
-      
-      END
-      
-
diff --git a/src/LnjTinyNew.o b/src/LnjTinyNew.o
index ba8eb59..cf64b5e 100644
Binary files a/src/LnjTinyNew.o and b/src/LnjTinyNew.o differ
diff --git a/src/RcppExports.cpp b/src/RcppExports.cpp
new file mode 100644
index 0000000..3d9eb9e
--- /dev/null
+++ b/src/RcppExports.cpp
@@ -0,0 +1,67 @@
+// Generated by using Rcpp::compileAttributes() -> do not edit by hand
+// Generator token: 10BE3573-1514-4C36-9D1C-5A225CD40393
+
+#include <Rcpp.h>
+
+using namespace Rcpp;
+
+#ifdef RCPP_USE_GLOBAL_ROSTREAM
+Rcpp::Rostream<true>&  Rcpp::Rcout = Rcpp::Rcpp_cout_get();
+Rcpp::Rostream<false>& Rcpp::Rcerr = Rcpp::Rcpp_cerr_get();
+#endif
+
+// alfunc
+double alfunc(NumericVector BVEC, NumericMatrix X, NumericVector Y, NumericMatrix M, NumericVector MU, double LAMBDA, double CONST1, double CONST2, int U, int V);
+RcppExport SEXP _biplotEZ_alfunc(SEXP BVECSEXP, SEXP XSEXP, SEXP YSEXP, SEXP MSEXP, SEXP MUSEXP, SEXP LAMBDASEXP, SEXP CONST1SEXP, SEXP CONST2SEXP, SEXP USEXP, SEXP VSEXP) {
+BEGIN_RCPP
+    Rcpp::RObject rcpp_result_gen;
+    Rcpp::RNGScope rcpp_rngScope_gen;
+    Rcpp::traits::input_parameter< NumericVector >::type BVEC(BVECSEXP);
+    Rcpp::traits::input_parameter< NumericMatrix >::type X(XSEXP);
+    Rcpp::traits::input_parameter< NumericVector >::type Y(YSEXP);
+    Rcpp::traits::input_parameter< NumericMatrix >::type M(MSEXP);
+    Rcpp::traits::input_parameter< NumericVector >::type MU(MUSEXP);
+    Rcpp::traits::input_parameter< double >::type LAMBDA(LAMBDASEXP);
+    Rcpp::traits::input_parameter< double >::type CONST1(CONST1SEXP);
+    Rcpp::traits::input_parameter< double >::type CONST2(CONST2SEXP);
+    Rcpp::traits::input_parameter< int >::type U(USEXP);
+    Rcpp::traits::input_parameter< int >::type V(VSEXP);
+    rcpp_result_gen = Rcpp::wrap(alfunc(BVEC, X, Y, M, MU, LAMBDA, CONST1, CONST2, U, V));
+    return rcpp_result_gen;
+END_RCPP
+}
+// optimize_spline
+List optimize_spline(NumericVector BVEC, NumericMatrix X, NumericVector Y, NumericMatrix M, NumericVector MU, double LAMBDA, double CONST1, double CONST2, int U, int V, double TAU, double FTOL, double TINY, int ITMAX);
+RcppExport SEXP _biplotEZ_optimize_spline(SEXP BVECSEXP, SEXP XSEXP, SEXP YSEXP, SEXP MSEXP, SEXP MUSEXP, SEXP LAMBDASEXP, SEXP CONST1SEXP, SEXP CONST2SEXP, SEXP USEXP, SEXP VSEXP, SEXP TAUSEXP, SEXP FTOLSEXP, SEXP TINYSEXP, SEXP ITMAXSEXP) {
+BEGIN_RCPP
+    Rcpp::RObject rcpp_result_gen;
+    Rcpp::RNGScope rcpp_rngScope_gen;
+    Rcpp::traits::input_parameter< NumericVector >::type BVEC(BVECSEXP);
+    Rcpp::traits::input_parameter< NumericMatrix >::type X(XSEXP);
+    Rcpp::traits::input_parameter< NumericVector >::type Y(YSEXP);
+    Rcpp::traits::input_parameter< NumericMatrix >::type M(MSEXP);
+    Rcpp::traits::input_parameter< NumericVector >::type MU(MUSEXP);
+    Rcpp::traits::input_parameter< double >::type LAMBDA(LAMBDASEXP);
+    Rcpp::traits::input_parameter< double >::type CONST1(CONST1SEXP);
+    Rcpp::traits::input_parameter< double >::type CONST2(CONST2SEXP);
+    Rcpp::traits::input_parameter< int >::type U(USEXP);
+    Rcpp::traits::input_parameter< int >::type V(VSEXP);
+    Rcpp::traits::input_parameter< double >::type TAU(TAUSEXP);
+    Rcpp::traits::input_parameter< double >::type FTOL(FTOLSEXP);
+    Rcpp::traits::input_parameter< double >::type TINY(TINYSEXP);
+    Rcpp::traits::input_parameter< int >::type ITMAX(ITMAXSEXP);
+    rcpp_result_gen = Rcpp::wrap(optimize_spline(BVEC, X, Y, M, MU, LAMBDA, CONST1, CONST2, U, V, TAU, FTOL, TINY, ITMAX));
+    return rcpp_result_gen;
+END_RCPP
+}
+
+static const R_CallMethodDef CallEntries[] = {
+    {"_biplotEZ_alfunc", (DL_FUNC) &_biplotEZ_alfunc, 10},
+    {"_biplotEZ_optimize_spline", (DL_FUNC) &_biplotEZ_optimize_spline, 14},
+    {NULL, NULL, 0}
+};
+
+RcppExport void R_init_biplotEZ(DllInfo *dll) {
+    R_registerRoutines(dll, NULL, CallEntries, NULL, NULL);
+    R_useDynamicSymbols(dll, FALSE);
+}
diff --git a/src/biplotEZ.dll b/src/biplotEZ.dll
index 950f6ce..32b842e 100644
Binary files a/src/biplotEZ.dll and b/src/biplotEZ.dll differ
diff --git a/src/biplotEZ.so b/src/biplotEZ.so
deleted file mode 100755
index d5cd639..0000000
Binary files a/src/biplotEZ.so and /dev/null differ
diff --git a/src/registerDynamicSymbol.o b/src/registerDynamicSymbol.o
index f413dc8..020062c 100644
Binary files a/src/registerDynamicSymbol.o and b/src/registerDynamicSymbol.o differ
diff --git a/tests/temp/Check_CRAN.R b/tests/temp/Check_CRAN.R
new file mode 100644
index 0000000..7cee6a2
--- /dev/null
+++ b/tests/temp/Check_CRAN.R
@@ -0,0 +1,10 @@
+setwd("C:/Users/29827094/Documents/GitHub/biplotEZ")
+devtools::document()
+#?biplotEZ
+# 1. Recompile Rcpp bindings from src/
+Rcpp::compileAttributes()
+
+
+# 3. Check for any issues
+devtools::check()
+#install.packages(c("geometry", "rgl", "R.devices"))
diff --git a/tests/temp/compare_Rcpp_FORTRAN.R b/tests/temp/compare_Rcpp_FORTRAN.R
new file mode 100644
index 0000000..be3e597
--- /dev/null
+++ b/tests/temp/compare_Rcpp_FORTRAN.R
@@ -0,0 +1,367 @@
+library(Rcpp)
+library(splines)
+#chang this according to your path
+setwd("C:\\Users\\29827094\\Documents\\GitHub\\biplotEZ")
+# Compile Rcpp code (has alfunc_rcpp and optimize_spline_rcpp)
+sourceCpp("src\\LnjTinyNew.cpp")
+
+# Load FORTRAN code
+dyn.load("tests\\temp\\fortran.dll")
+
+# ========================================
+# I fixed all the randomness in this code (using seed), so you should see a similar result for Rcpp and Fortran.
+# ========================================
+
+biplot.spline.axis <- function(j, X, Y, means, sd, n.int, 
+                                spline.control, dmeth=0, 
+                                optim_method = "rcpp",
+                                fix_seed = TRUE,  # NEW PARAMETER
+                                base_seed = NULL, # NEW PARAMETER
+                                sampling_seed = NULL, # NEW: separate seed for sampling
+                                ...) {
+  n <- nrow(X)
+  p <- ncol(X)
+  
+  # Set seed BEFORE sampling if provided
+  #new
+  if (!is.null(sampling_seed)) {
+    set.seed(sampling_seed)
+  }
+  #I dont know why we have this:
+  if (n > 103) {  
+    my.sample <- sample(1:n, size=103, replace=F)
+    X <- X[my.sample,]
+    Y <- Y[my.sample,]
+    n <- nrow(X)
+  }
+  
+  # Extract control parameters
+  tau <- spline.control$tau
+  nmu <- spline.control$nmu
+  u <- spline.control$u
+  v <- spline.control$v
+  lambda <- spline.control$lambda
+  smallsigma <- spline.control$smallsigma
+  bigsigma <- spline.control$bigsigma
+  gamma <- spline.control$gamma
+  bigsigmaactivate <- spline.control$bigsigmaactivate
+  eps <- spline.control$eps
+  tiny <- spline.control$tiny
+  itmax <- spline.control$itmax
+  ftol <- spline.control$ftol
+  
+  cat("Calculating spline axis for variable", j, "using", optim_method, "\n")
+  
+  if(dmeth==1) stop("dmeth should be equal to zero or integer greater than 1 \n")  
+  
+  Ytilde <- scale(scale(Y, center=FALSE, scale=1/sd), 
+                  center=-1*means, scale=FALSE)
+  
+  ytilde <- Ytilde[,j]
+  mutilde <- seq(from=min(ytilde), to=max(ytilde), length.out=nmu)
+  y <- Y[,j]
+  rangey <- max(y) - min(y)
+  mu <- seq(from=min(y)-.3*rangey, to=max(y)+.3*rangey, length.out=nmu)
+  markers <- (pretty(ytilde) - means[j]) / sd[j]
+  mu <- sort(c(mu, markers))
+  mu <- unique(mu)
+  nmu <- length(mu)
+  
+  if (v > 0) {
+    knots <- seq.int(from=0, to=1, length.out=v+2)[-c(1, v+2)]
+    knots <- stats::quantile(y, knots)
+    M <- splines::bs(mu, knots=knots, degree=u, intercept=FALSE)
+  } else {
+    M <- splines::bs(mu, df=u+v, degree=u, intercept=FALSE)
+  }
+  
+  M <- scale(M, scale=FALSE, center=M[which.min(abs(mu)),])
+  Breg <- t(solve(t(X)%*%X)%*%t(X)%*%y)
+  Zreg <- mu%*%Breg / sum(Breg^2)
+  Bvec <- as.vector(solve(t(M)%*%M)%*%t(M)%*%Zreg)
+  
+  const1 <- sum(y^2)
+  const2 <- sum(X^2) / (n*p)
+  
+  # ========================================
+  # OPTIMIZATION WRAPPER
+  # ========================================
+  
+  optimtouse <- function(Bvec) {
+    timetemp <- proc.time()[3]
+    
+    if (optim_method == "rcpp") {
+      # Use Rcpp two-stage
+      returned_data <- optimize_spline(
+        BVEC = Bvec, X = X, Y = y, M = M, MU = mu,
+        LAMBDA = lambda, CONST1 = const1, CONST2 = const2,
+        U = u, V = v, TAU = tau, FTOL = ftol, TINY = tiny, ITMAX = itmax
+      )
+      
+      if(returned_data$ERRO > 0) {
+        cat("  Error code:", returned_data$ERRO, "\n")
+      }
+      
+      aa <- list(
+        BestValue = returned_data$LOSS,
+        BestSolution = returned_data$BVEC,
+        ConvergenceCode = returned_data$ERRO,
+        iter1 = returned_data$ITER1,
+        iter = returned_data$ITER,
+        TimeTaken = proc.time()[3] - timetemp
+      )
+      
+    } else if (optim_method == "fortran") {
+      # Use FORTRAN two-stage
+      returned_data <- .Fortran("l",
+        LOSS = as.double(0),
+        X = as.double(X),
+        N = as.integer(n),
+        P = as.integer(p),
+        NMU = as.integer(nmu),
+        IND = as.integer(rep(0, n)),
+        MU = as.double(mu),
+        PRED = as.double(rep(0, n)),
+        LAMBDA = as.double(lambda),
+        Y = as.double(y),
+        CONST1 = as.double(const1),
+        CONST2 = as.double(const2),
+        U = as.integer(u),
+        V = as.integer(v),
+        M = as.double(M),
+        BVEC = as.double(Bvec),
+        TAU = as.double(tau),
+        AY = as.double(rep(0, (u+v)*p+1)),
+        TEMPVK = as.double(rep(0, (u+v)*p)),
+        ITER = as.integer(0),
+        FTOL = as.double(ftol),
+        LOSS1 = as.double(0),
+        ITER1 = as.integer(0),
+        ERRO = as.integer(0),
+        CONST3 = as.double(tiny),
+        ITMAX = as.integer(itmax)
+      )
+      
+      if(returned_data$ERRO > 0) {
+        cat("  Error code:", returned_data$ERRO, "\n")
+      }
+      
+      aa <- list(
+        BestValue = returned_data$LOSS,
+        BestSolution = returned_data$BVEC,
+        ConvergenceCode = returned_data$ERRO,
+        iter1 = returned_data$ITER1,
+        iter = returned_data$ITER,
+        TimeTaken = proc.time()[3] - timetemp
+      )
+    }
+    
+    aa
+  }
+  
+  EuclidDist2 <- function(X, Y) {
+    n <- nrow(X)
+    m <- nrow(Y)
+    bx <- rowSums(X^2)
+    by <- rowSums(Y^2)
+    outer(bx, by, FUN = "+") - 2 * X %*% t(Y)
+  }
+  
+  # Variable initialization
+  outBestValues <- rep(NA, gamma+1)
+  outBestSolutions <- matrix(nrow=2*(u+v), ncol=gamma+1)
+  outTimeTaken <- rep(NA, gamma+1)
+  BestSolutionsFrequency <- rep(NA, gamma+1)
+  BestSolutionsIndices <- rep(NA, gamma+1)
+  
+  # ========================================
+  # PRE-GENERATE ALL RANDOM PERTURBATIONS
+  #new
+  # ========================================
+  if (fix_seed && !is.null(base_seed)) {
+    set.seed(base_seed)
+  }
+  
+  # Pre-generate random perturbations for all gamma iterations
+  random_perturbations <- list()
+  for (gammacounter in 2:(gamma+1)) {
+    # Generate perturbation for this iteration
+    # We don't know yet if it will use smallsigma or bigsigma,
+    # so we pre-generate both and decide later
+    random_perturbations[[gammacounter]] <- list(
+      small = stats::rnorm((u+v)*2, mean=0, sd=smallsigma),
+      big = stats::rnorm((u+v)*2, mean=0, sd=bigsigma)
+    )
+  }
+  
+  # Initial coefficients
+  temp <- optimtouse(Bvec)
+  outBestValues[1] <- temp$BestValue
+  outBestSolutions[,1] <- temp$BestSolution
+  outTimeTaken[1] <- temp$TimeTaken
+  BestSolutionsFrequency[1] <- 1
+  BestSolutionsIndices[1] <- 1
+  DistinctSolutions <- 1
+  PreviousBestSolution <- NA
+  nSameSolutionConsecutively <- 0
+  
+  # Multi-start optimization
+  for (gammacounter in 2:(gamma+1)) {
+    # Use pre-generated perturbations
+    if (nSameSolutionConsecutively >= bigsigmaactivate) {
+      perturbation <- random_perturbations[[gammacounter]]$big
+    } else {
+      perturbation <- random_perturbations[[gammacounter]]$small
+    }
+    
+    temp <- optimtouse(outBestSolutions[,which.min(outBestValues)] + perturbation)
+    
+    outTimeTaken[gammacounter] <- temp$TimeTaken
+    tempSquaredDistances <- EuclidDist2(matrix(temp$BestSolution, nrow=1),
+                                         t(outBestSolutions[,1:DistinctSolutions]))
+    
+    if (any(tempSquaredDistances < eps)) {
+      BestSolutionsIndices[gammacounter] <- tempAA <- which.min(tempSquaredDistances)
+      BestSolutionsFrequency[tempAA] <- BestSolutionsFrequency[tempAA] + 1
+      if (!is.na(PreviousBestSolution) && tempAA == PreviousBestSolution) {
+        nSameSolutionConsecutively <- nSameSolutionConsecutively + 1
+      } else {
+        PreviousBestSolution <- tempAA
+        nSameSolutionConsecutively <- 0
+      }
+    } else {
+      DistinctSolutions <- DistinctSolutions + 1
+      outBestValues[DistinctSolutions] <- temp$BestValue
+      outBestSolutions[,DistinctSolutions] <- temp$BestSolution
+      BestSolutionsFrequency[DistinctSolutions] <- 1
+      BestSolutionsIndices[gammacounter] <- DistinctSolutions
+      nSameSolutionConsecutively <- 0
+    }
+  }
+  
+  axis.points <- cbind(M %*% matrix(outBestSolutions[,which.min(outBestValues)], ncol=2), 
+                       mu, 0)
+  
+  for (i in 1:nrow(axis.points)) {
+    if (any(zapsmall(axis.points[i,3] - markers) == 0)) {
+      axis.points[i, 4] <- 1
+    }
+  }
+  
+  axis.points[,3] <- axis.points[,3] * sd[j] + means[j]
+  
+  # Return with attributes
+  attr(axis.points, "loss") <- min(outBestValues, na.rm=TRUE)
+  attr(axis.points, "bvec") <- outBestSolutions[,which.min(outBestValues)]
+  attr(axis.points, "total_time") <- sum(outTimeTaken, na.rm=TRUE)
+  attr(axis.points, "distinct_solutions") <- DistinctSolutions
+  
+  axis.points
+}
+
+# ========================================
+# EXAMPLE 1: CALCULATE LOSS FUNCTION
+# ========================================
+
+set.seed(123)
+
+n <- 150
+p <- 2
+Y <- matrix(rnorm(n * 2), ncol = 2)
+Y[, 2] <- Y[, 1] + rnorm(n, 0, 0.5)
+
+means <- colMeans(Y)
+sd <- apply(Y, 2, sd)
+X <- Y[, 1:2] + matrix(rnorm(n * p, 0, 0.3), ncol = p)
+
+spline.control <- list(
+  tau = 0.01, nmu = 10, u = 3, v = 0, lambda = 0.1,
+  smallsigma = 0.1, bigsigma = 1.0, gamma = 3, bigsigmaactivate = 2,
+  eps = 1e-6, tiny = 1e-4, itmax = 500, ftol = 1e-4
+)
+
+j <- 1
+y <- Y[, j]
+rangey <- max(y) - min(y)
+mu <- seq(from=min(y)-.3*rangey, to=max(y)+.3*rangey, length.out=10)
+M <- splines::bs(mu, df=3, degree=3, intercept=FALSE)
+M <- scale(M, scale=FALSE, center=M[which.min(abs(mu)),])
+
+const1 <- sum(y^2)
+const2 <- sum(X^2) / (n*p)
+lambda <- 0.1
+u <- 3
+v <- 1
+
+# Test Bvec
+Bvec_test <- rnorm((u+v)*p)
+
+
+loss_value <- alfunc(Bvec_test, X, y, M, mu, lambda, const1, const2, u, v)
+cat("Test Bvec:", round(Bvec_test, 4), "\n")
+cat("Loss value:", loss_value, "\n\n")
+
+# ========================================
+# EXAMPLE 2: COMPARE RCPP VS FORTRAN
+# ========================================
+
+
+# WITH FIXED SEED FOR REPRODUCIBILITY
+
+COMPARISON_SEED <- 999  # Use same seed for both methods
+SAMPLING_SEED <- 777    # NEW: Separate seed for data sampling
+
+# Method 1: Rcpp
+cat("1. Running Rcpp...\n")
+time_rcpp <- system.time({
+  result_rcpp <- biplot.spline.axis(
+    j = 1, X = X, Y = Y, means = means, sd = sd,
+    n.int = NULL, spline.control = spline.control,
+    dmeth = 0, optim_method = "rcpp",
+    fix_seed = TRUE, base_seed = COMPARISON_SEED,
+    sampling_seed = SAMPLING_SEED  # NEW: Control sampling
+  )
+})
+
+# Method 2: FORTRAN
+cat("\n2. Running FORTRAN...\n")
+time_fortran <- system.time({
+  result_fortran <- biplot.spline.axis(
+    j = 1, X = X, Y = Y, means = means, sd = sd,
+    n.int = NULL, spline.control = spline.control,
+    dmeth = 0, optim_method = "fortran",
+    fix_seed = TRUE, base_seed = COMPARISON_SEED,
+    sampling_seed = SAMPLING_SEED  # NEW: Control sampling
+  )
+})
+
+# ========================================
+# COMPARE RESULTS
+# ========================================
+
+cat("\n========================================\n")
+cat("COMPARISON RESULTS\n")
+cat("========================================\n\n")
+
+
+cat("LOSS VALUES:\n")
+loss_rcpp <- attr(result_rcpp, "loss")
+loss_fortran <- attr(result_fortran, "loss")
+
+cat(sprintf("  %-15s: %.12f\n", "Rcpp", loss_rcpp))
+cat(sprintf("  %-15s: %.12f\n", "FORTRAN", loss_fortran))
+cat("\n")
+
+cat("COEFFICIENT VECTORS (bvec):\n")
+bvec_rcpp <- attr(result_rcpp, "bvec")
+bvec_fortran <- attr(result_fortran, "bvec")
+
+cat("  Rcpp:    ", round(bvec_rcpp, 6), "\n")
+cat("  FORTRAN: ", round(bvec_fortran, 6), "\n")
+cat("\n")
+
+
+#cat("TIMING (seconds):\n")
+#cat(sprintf("  %-15s: %7.3f\n", "Rcpp", time_rcpp[3]))
+#cat(sprintf("  %-15s: %7.3f\n", "FORTRAN", time_fortran[3]))
+
diff --git a/tests/temp/fortran.R b/tests/temp/fortran.R
new file mode 100644
index 0000000..0f68db6
--- /dev/null
+++ b/tests/temp/fortran.R
@@ -0,0 +1,527 @@
+
+library(splines)
+
+# Load FORTRAN code
+dyn.load("C:\\Users\\29827094\\Documents\\GitHub\\biplotEZ\\src\\biplotEZ.dll")
+
+
+biplot.spline.axis <- function(j, X, Y, means, sd, n.int, 
+                                spline.control, dmeth=0, ...) {
+  
+  n <- nrow(X)
+  p <- ncol(X)
+  if (n > 103) {  
+    my.sample <- sample(1:n, size=103, replace=F)
+    X <- X[my.sample,]
+    Y <- Y[my.sample,]
+    n <- nrow(X)
+  }
+  
+  # Extract control parameters
+  tau <- spline.control$tau
+  nmu <- spline.control$nmu
+  u <- spline.control$u
+  v <- spline.control$v
+  lambda <- spline.control$lambda
+  smallsigma <- spline.control$smallsigma
+  bigsigma <- spline.control$bigsigma
+  gamma <- spline.control$gamma
+  bigsigmaactivate <- spline.control$bigsigmaactivate
+  eps <- spline.control$eps
+  tiny <- spline.control$tiny
+  itmax <- spline.control$itmax
+  ftol <- spline.control$ftol
+  
+#  
+#   if (v > 0) {
+#     itmax <- itmax * (1 + v)
+#     ftol <- ftol * 10
+#   }
+  
+  cat("Calculating spline axis for variable", j)
+  
+  if(dmeth==1) stop("dmeth should be equal to zero or integer greater than 1 \n")  
+  
+  Ytilde <- scale(scale(Y, center=FALSE, scale=1/sd), 
+                  center=-1*means, scale=FALSE)
+  
+  ytilde <- Ytilde[,j]
+  mutilde <- seq(from=min(ytilde), to=max(ytilde), length.out=nmu)
+  y <- Y[,j]
+  rangey <- max(y) - min(y)
+  mu <- seq(from=min(y)-.3*rangey, to=max(y)+.3*rangey, length.out=nmu)
+  markers <- (pretty(ytilde) - means[j]) / sd[j]
+  mu <- sort(c(mu, markers))
+  mu <- unique(mu)
+  nmu <- length(mu)
+  
+  if (v > 0) {
+    knots <- seq.int(from=0, to=1, length.out=v+2)[-c(1, v+2)]
+    knots <- stats::quantile(y, knots)
+    M <- splines::bs(mu, knots=knots, degree=u, intercept=FALSE)
+  } else {
+    M <- splines::bs(mu, df=u+v, degree=u, intercept=FALSE)
+  }
+  
+  M <- scale(M, scale=FALSE, center=M[which.min(abs(mu)),])
+  Breg <- t(solve(t(X)%*%X)%*%t(X)%*%y)
+  Zreg <- mu%*%Breg / sum(Breg^2)
+  Bvec <- as.vector(solve(t(M)%*%M)%*%t(M)%*%Zreg)
+  
+  const1 <- sum(y^2)
+  const2 <- sum(X^2) / (n*p)
+  
+  # ========================================
+  #OPTIMIZATION FUNCTION
+  # ========================================
+  
+  optimtouse <- function(Bvec) {
+    timetemp <- proc.time()[3]
+    
+    
+    if (length(Bvec) != 2*(u+v)) {
+      if (length(Bvec) < 2*(u+v)) {
+        Bvec <- c(Bvec, rep(0, 2*(u+v) - length(Bvec)))
+      } else {
+        Bvec <- Bvec[1:(2*(u+v))]
+      }
+    }
+    
+    # Check for NA/Inf
+    if (any(is.na(Bvec)) || any(is.infinite(Bvec))) {
+      Bvec[is.na(Bvec) | is.infinite(Bvec)] <- rnorm(sum(is.na(Bvec) | is.infinite(Bvec)), 0, 0.01)
+    }
+    
+    returned_data <- .Fortran("l",
+      LOSS = as.double(0),
+      X = as.double(X),
+      N = as.integer(n),
+      P = as.integer(p),
+      NMU = as.integer(nmu),
+      IND = as.integer(rep(0, n)),
+      MU = as.double(mu),
+      PRED = as.double(rep(0, n)),
+      LAMBDA = as.double(lambda),
+      Y = as.double(y),
+      CONST1 = as.double(const1),
+      CONST2 = as.double(const2),
+      U = as.integer(u),
+      V = as.integer(v),
+      M = as.double(M),
+      BVEC = as.double(Bvec),
+      TAU = as.double(tau),
+      AY = as.double(rep(0, (u+v)*p+1)),
+      TEMPVK = as.double(rep(0, (u+v)*p)),
+      ITER = as.integer(0),
+      FTOL = as.double(ftol),
+      LOSS1 = as.double(0),
+      ITER1 = as.integer(0),
+      ERRO = as.integer(0),
+      CONST3 = as.double(tiny),
+      ITMAX = as.integer(itmax)
+    )
+    
+    aa <- list(
+      BestValue = returned_data$LOSS,
+      BestSolution = returned_data$BVEC,
+      ConvergenceCode = returned_data$ERRO,
+      iter1 = returned_data$ITER1,
+      iter = returned_data$ITER,
+      TimeTaken = proc.time()[3] - timetemp
+    )
+    
+    aa
+  }
+  
+  EuclidDist2 <- function(X, Y) {
+    n <- nrow(X)
+    m <- nrow(Y)
+    bx <- rowSums(X^2)
+    by <- rowSums(Y^2)
+    outer(bx, by, FUN = "+") - 2 * X %*% t(Y)
+  }
+  
+  # Variable initialization
+  outBestValues <- rep(NA, gamma+1)
+  outBestSolutions <- matrix(nrow=2*(u+v), ncol=gamma+1)
+  outTimeTaken <- rep(NA, gamma+1)
+  BestSolutionsFrequency <- rep(NA, gamma+1)
+  BestSolutionsIndices <- rep(NA, gamma+1)
+  
+#   # Initial coefficients - ensure correct dimensions
+#   Bvec_initial <- rep(Bvec, length.out=2*(u+v))
+#   if (length(Bvec) < 2*(u+v)) {
+#     Bvec_initial[(length(Bvec)+1):(2*(u+v))] <- rnorm(2*(u+v) - length(Bvec), 0, 0.01)
+#   }
+  
+#   # Scale initial values to avoid numerical issues
+#   if (max(abs(Bvec_initial)) > 5) {
+#     Bvec_initial <- Bvec_initial / max(abs(Bvec_initial)) * 1
+#   }
+  
+#   # For v > 0, try starting from smaller values
+#   if (v > 0 && max(abs(Bvec_initial)) > 2) {
+#     Bvec_initial <- Bvec_initial * 0.5
+#   }
+  
+  temp <- optimtouse(Bvec)
+  outBestValues[1] <- temp$BestValue
+  outBestSolutions[,1] <- temp$BestSolution
+  outTimeTaken[1] <- temp$TimeTaken
+  BestSolutionsFrequency[1] <- 1
+  BestSolutionsIndices[1] <- 1
+  DistinctSolutions <- 1
+  PreviousBestSolution <- NA
+  nSameSolutionConsecutively <- 0
+  
+  # Multi-start optimization
+  for (gammacounter in 2:(gamma+1)) {
+    if (nSameSolutionConsecutively >= bigsigmaactivate) {
+      temp <- optimtouse(outBestSolutions[,which.min(outBestValues)] + 
+                         stats::rnorm((u+v)*2, mean=0, sd=bigsigma))
+    } else {
+      temp <- optimtouse(outBestSolutions[,which.min(outBestValues)] + 
+                         stats::rnorm((u+v)*2, mean=0, sd=smallsigma))
+    }
+    
+    outTimeTaken[gammacounter] <- temp$TimeTaken
+    tempSquaredDistances <- EuclidDist2(matrix(temp$BestSolution, nrow=1),
+                                         t(outBestSolutions[,1:DistinctSolutions]))
+    
+    if (any(tempSquaredDistances < eps)) {
+      BestSolutionsIndices[gammacounter] <- tempAA <- which.min(tempSquaredDistances)
+      BestSolutionsFrequency[tempAA] <- BestSolutionsFrequency[tempAA] + 1
+      if (!is.na(PreviousBestSolution) && tempAA == PreviousBestSolution) {
+        nSameSolutionConsecutively <- nSameSolutionConsecutively + 1
+      } else {
+        PreviousBestSolution <- tempAA
+        nSameSolutionConsecutively <- 0
+      }
+    } else {
+      DistinctSolutions <- DistinctSolutions + 1
+      outBestValues[DistinctSolutions] <- temp$BestValue
+      outBestSolutions[,DistinctSolutions] <- temp$BestSolution
+      BestSolutionsFrequency[DistinctSolutions] <- 1
+      BestSolutionsIndices[gammacounter] <- DistinctSolutions
+      nSameSolutionConsecutively <- 0
+    }
+  }
+  
+  axis.points <- cbind(M %*% matrix(outBestSolutions[,which.min(outBestValues)], ncol=2), 
+                       mu, 0)
+  
+  for (i in 1:nrow(axis.points)) {
+    if (any(zapsmall(axis.points[i,3] - markers) == 0)) {
+      axis.points[i, 4] <- 1
+    }
+  }
+  
+  axis.points[,3] <- axis.points[,3] * sd[j] + means[j]
+  
+  # Return with attributes
+  attr(axis.points, "loss") <- min(outBestValues, na.rm=TRUE)
+  attr(axis.points, "bvec") <- outBestSolutions[,which.min(outBestValues)]
+  attr(axis.points, "total_time") <- sum(outTimeTaken, na.rm=TRUE)
+  attr(axis.points, "distinct_solutions") <- DistinctSolutions
+  
+  axis.points
+}
+
+
+
+biplot.spline.axis <- function(j, X, Y, means, sd, 
+                               n.int, spline.control, dmeth=0, ... ){
+  n <- nrow(X)
+  p <- ncol(X)
+  if (n > 103){  
+      my.sample <- sample (1:n, size=103, replace=F)
+      X <- X[my.sample,]
+      Y <- Y[my.sample,]
+      n <- nrow(X)
+    }
+  
+  tau <- spline.control$tau
+  nmu <- spline.control$nmu
+  u <- spline.control$u
+  v <- spline.control$v
+  lambda <- spline.control$lambda
+  smallsigma <- spline.control$smallsigma
+  bigsigma <- spline.control$bigsigma
+  gamma <- spline.control$gamma
+  bigsigmaactivate <- spline.control$bigsigmaactivate
+  eps <- spline.control$eps
+  tiny <- spline.control$tiny
+  itmax <- spline.control$itmax
+  ftol <- spline.control$ftol
+  
+  cat ("Calculating spline axis for variable", j, "\n")
+  if(dmeth==1) stop("dmeth should be equal to zero or integer greater than 1 \n")  
+  Ytilde <- scale(scale(Y, center=FALSE, scale=1/sd), center=-1*means, scale=FALSE)
+  
+  ytilde <- Ytilde[,j]
+  mutilde <- seq(from=min(ytilde),to=max(ytilde),length.out=nmu)
+  y <- Y[,j]
+  rangey <- max(y)-min(y)
+  mu <- seq(from=min(y)-.3*rangey,to=max(y)+.3*rangey,length.out=nmu)
+  markers <- (pretty(ytilde)-means[j])/sd[j]
+  mu <- sort(c(mu,markers))
+  mu <- unique(mu)
+  nmu <- length(mu)
+  
+  if (v>0){
+    knots <- seq.int(from=0,to=1,length.out=v+2)[-c(1,v+2)]
+    knots <- stats::quantile(y,knots)
+    M <- splines::bs(mu,knots=knots,degree=u,intercept=FALSE)
+  } else M <- splines::bs(mu,df=u+v,degree=u,intercept=FALSE)
+  M <- scale(M,scale=FALSE,center=M[which.min(abs(mu)),]) # To ensure that the spline passes through the origin at the calibration which represents the mean of the variable
+  Breg <- t(solve(t(X)%*%X)%*%t(X)%*%y)
+  Zreg <- mu%*%Breg/sum(Breg^2)
+  Bvec <- as.vector(solve(t(M)%*%M)%*%t(M)%*%Zreg)  # Closest to regression biplot
+  
+  const1 <- sum(y^2)
+  const2 <- sum(X^2)/(n*p)
+  TotalNumberOfLossFunctionCalls <- 0
+  
+  optimtouse <- function(Bvec){
+    timetemp <- proc.time()[3]
+    LOSS <- 1.0
+    LOSS1 <- 1.0
+    Ind <- rep(1,n)
+    pred <- rep(0,nmu)
+    deltmp <- 0
+    tau <- tau
+    #.5 # the choice of tau seems to affect perfomance quite substantially.
+    # tau is used to specify the points on the inital simplex.
+    Ay <- rep(0,(u+v)*p+1)
+    TEMPVK <- rep(0,(u+v)*p)
+    iter1 <- 0
+    iter <- 0
+    ERRO <- 0
+    
+    # Prepare for Fortran subroutine
+    storage.mode(X) <- "double"
+    storage.mode(Ind) <- "integer"
+    storage.mode(mu) <- "double"
+    storage.mode(pred) <- "double"
+    storage.mode(y) <- "double"
+    storage.mode(M) <- "double"
+    storage.mode(Bvec) <- "double"
+    storage.mode(Ay) <- "double"
+    storage.mode(TEMPVK) <- "double"
+  
+    returned_data <- .Fortran("l",
+      LOSS = as.double(0),
+      X = as.double(X),
+      N = as.integer(n),
+      P = as.integer(p),
+      NMU = as.integer(nmu),
+      IND = as.integer(rep(0, n)),
+      MU = as.double(mu),
+      PRED = as.double(rep(0, n)),
+      LAMBDA = as.double(lambda),
+      Y = as.double(y),
+      CONST1 = as.double(const1),
+      CONST2 = as.double(const2),
+      U = as.integer(u),
+      V = as.integer(v),
+      M = as.double(M),
+      BVEC = as.double(Bvec),
+      TAU = as.double(tau),
+      AY = as.double(rep(0, (u+v)*p+1)),
+      TEMPVK = as.double(rep(0, (u+v)*p)),
+      ITER = as.integer(0),
+      FTOL = as.double(ftol),
+      LOSS1 = as.double(0),
+      ITER1 = as.integer(0),
+      ERRO = as.integer(0),
+      CONST3 = as.double(tiny),
+      ITMAX = as.integer(itmax)
+    )
+    
+    aa <- list(
+      BestValue = returned_data$LOSS,
+      BestSolution = returned_data$BVEC,
+      ConvergenceCode = returned_data$ERRO,
+      iter1 = returned_data$ITER1,
+      iter = returned_data$ITER,
+      TimeTaken = proc.time()[3] - timetemp
+    )
+    
+    aa
+  }
+  EuclidDist2 <- function (X, Y){
+    n <- nrow(X)
+    m <- nrow(Y)
+    bx <- rowSums(X^2)
+    by <- rowSums(Y^2)
+    outer(bx, by, FUN = "+") - 2 * X %*% t(Y)
+  }
+  
+  ### Variable initialisation
+  outBestValues <- rep(NA,gamma+1)
+  outBestSolutions <- matrix(nrow=2*(u+v),ncol=gamma+1)
+  outTimeTaken <- rep(NA,gamma+1) # Is made one element longer at each iteration.
+  BestSolutionsFrequency <- rep(NA,gamma+1)
+  BestSolutionsIndices <- rep(NA,gamma+1) # Is made one element longer at each iteration.
+  SquaredDistancesBetweenBestSolutions <- matrix(nrow=gamma+1,ncol=gamma+1)
+  
+  ### Initial coefficients closest to regression biplot
+  temp <- optimtouse(Bvec)
+  outBestValues[1] <- temp$BestValue
+  outBestSolutions[,1] <- temp$BestSolution
+  outTimeTaken[1] <- temp$TimeTaken
+  BestSolutionsFrequency[1] <- 1
+  BestSolutionsIndices[1] <- 1
+  DistinctSolutions <- 1
+  PreviousBestSolution <- NA
+  nSameSolutionConsecutively <- 0
+  BigSigmaActivations <- NULL
+  
+  test.iter <- temp$iter
+  test.iter1 <- temp$iter1
+  
+  ### Last best coefficients perturbed
+  for (gammacounter in 2:(gamma+1)){
+    if (nSameSolutionConsecutively>=bigsigmaactivate){
+      temp <- optimtouse(outBestSolutions[,which.min(outBestValues)]+stats::rnorm((u+v)*2,mean=0,sd=bigsigma))
+      BigSigmaActivations <- c(BigSigmaActivations,gammacounter)
+    }
+    else temp <- optimtouse(outBestSolutions[,which.min(outBestValues)]+stats::rnorm((u+v)*2,mean=0,sd=smallsigma))
+    outTimeTaken[gammacounter] <- temp$TimeTaken
+    tempSquaredDistances <- EuclidDist2(matrix(temp$BestSolution,nrow=1),t(outBestSolutions[,1:DistinctSolutions]))
+    if (any(tempSquaredDistances<eps)){
+      BestSolutionsIndices[gammacounter] <- tempAA<-which.min(tempSquaredDistances)
+      BestSolutionsFrequency[tempAA] <- BestSolutionsFrequency[tempAA]+1
+      if (!is.na(PreviousBestSolution) && tempAA==PreviousBestSolution) nSameSolutionConsecutively<-nSameSolutionConsecutively+1
+      else{
+        PreviousBestSolution <- tempAA
+        nSameSolutionConsecutively <- 0
+      }
+    }
+    else{
+      DistinctSolutions <- DistinctSolutions+1
+      outBestValues[DistinctSolutions] <- temp$BestValue
+      outBestSolutions[,DistinctSolutions] <- temp$BestSolution
+      BestSolutionsFrequency[DistinctSolutions] <- 1
+      BestSolutionsIndices[gammacounter] <- DistinctSolutions
+      SquaredDistancesBetweenBestSolutions[1:(DistinctSolutions-1),DistinctSolutions]<-tempSquaredDistances
+      nSameSolutionConsecutively <- 0
+    }
+  }
+  axis.points <- cbind(M%*%matrix(outBestSolutions[,which.min(outBestValues)],ncol=2), mu, 0)
+  
+  for (i in 1:nrow(axis.points)) if (any(zapsmall(axis.points[i,3] - markers) == 0)) axis.points[i, 4] <- 1
+  axis.points[,3] <- axis.points[,3]*sd[j] + means[j]
+  axis.points
+}
+
+
+
+
+set.seed(123)
+
+n <- 180
+p <- 2 
+
+
+n_vars <- 4
+Y <- matrix(rnorm(n * n_vars), ncol = n_vars)
+
+Y[, 2] <- Y[, 1] + rnorm(n, 0, 0.5)
+Y[, 3] <- -Y[, 1] + rnorm(n, 0, 0.5)
+Y[, 4] <- Y[, 2] + Y[, 3] + rnorm(n, 0, 0.5)
+
+means <- colMeans(Y)
+sd <- apply(Y, 2, sd)
+
+X <- Y[, 1:2] + matrix(rnorm(n * p, 0, 0.3), ncol = p)
+
+u <- 3
+v <- 2
+spline.control <- list(
+  tau = 0.01, nmu = 10, u = u, v =v, lambda = 0.1,
+  smallsigma = 0.1, bigsigma = 1.0, gamma = 3, bigsigmaactivate = 2,
+  eps = 1e-6, tiny = 1e-4, itmax = 1000, ftol = 1e-4
+)
+
+j <- 1
+y <- Y[, j]
+rangey <- max(y) - min(y)
+mu <- seq(from=min(y)-.3*rangey, to=max(y)+.3*rangey, length.out=50)
+M <- splines::bs(mu, df=3, degree=3, intercept=FALSE)
+M <- scale(M, scale=FALSE, center=M[which.min(abs(mu)),])
+
+const1 <- sum(y^2)
+const2 <- sum(X^2) / (n*p)
+lambda <- 0.1
+
+
+# Test Bvec
+Bvec_test <- rnorm((u+v)*p)
+
+result_optim <- biplot.spline.axis(
+  j = 1, X = X, Y = Y, means = means, sd = sd,
+  n.int = NULL, spline.control = spline.control,
+  dmeth = 0
+)
+
+loss <- attr(result_optim, "loss")
+
+
+par(mfrow = c(1, 1), mar = c(4, 4, 3, 1))
+
+plot(X[, 1], X[, 2], pch = 19, col = "gray70",
+     xlab = "Dim 1", ylab = "Dim 2",
+     main = sprintf("R optim (Loss=%.4f)", loss), asp = 1)
+grid()
+lines(result_optim[, 1], result_optim[, 2], col = "darkgreen", lwd = 2)
+
+
+#All variables
+
+all_results <- list()
+all_losses <- numeric(n_vars)
+
+for(j in 1:n_vars) {
+  cat("\nProcessing variable", j, "...\n")
+  all_results[[j]] <- biplot.spline.axis(
+    j = j, X = X, Y = Y, means = means, sd = sd,
+    n.int = NULL, spline.control = spline.control, dmeth = 0
+  )
+  all_losses[j] <- attr(all_results[[j]], "loss")
+  cat("  Loss:", all_losses[j], "\n")
+  cat("  Distinct solutions:", attr(all_results[[j]], "distinct_solutions"), "\n")
+}
+
+
+par(mfrow = c(1, 1), mar = c(4, 4, 3, 1))
+plot(X[, 1], X[, 2], 
+     pch = 19, col = "gray70",
+     xlab = "Dimension 1", ylab = "Dimension 2",
+     main = "All Spline Axes (optim method)",
+     asp = 1)
+grid()
+
+colors <- c("blue", "red", "green", "purple")
+for(j in 1:n_vars) {
+  lines(all_results[[j]][, 1], all_results[[j]][, 2], 
+        col = colors[j], lwd = 2)
+  # Label the axis
+  mid <- ceiling(nrow(all_results[[j]]) / 2)
+  text(all_results[[j]][mid, 1], all_results[[j]][mid, 2],
+       paste("Var", j), pos = 3, col = colors[j], font = 2)
+}
+
+legend("topright", legend = paste("Variable", 1:n_vars),
+       col = colors, lwd = 2, cex = 0.8)
+
+
+
+
+
+
+
+
+
+
+
diff --git a/tests/temp/fortran.dll b/tests/temp/fortran.dll
new file mode 100644
index 0000000..1db4f01
Binary files /dev/null and b/tests/temp/fortran.dll differ
diff --git a/tests/temp/replace_fortran_with_Rcpp.R b/tests/temp/replace_fortran_with_Rcpp.R
new file mode 100644
index 0000000..7f7d42c
--- /dev/null
+++ b/tests/temp/replace_fortran_with_Rcpp.R
@@ -0,0 +1,278 @@
+
+
+library(Rcpp)
+library(splines)
+#  chenge this path according to your system
+sourceCpp("C:\\Users\\29827094\\Documents\\GitHub\\biplotEZ\\src\\LnjTinyNew.cpp")
+
+
+
+
+biplot.spline.axis <- function(j, X, Y, means, sd, 
+                               n.int, spline.control, dmeth=0, ... ){
+  n <- nrow(X)
+  p <- ncol(X)
+  if (n > 103){  
+      my.sample <- sample (1:n, size=103, replace=F)
+      X <- X[my.sample,]
+      Y <- Y[my.sample,]
+      n <- nrow(X)
+    }
+  
+  tau <- spline.control$tau
+  nmu <- spline.control$nmu
+  u <- spline.control$u
+  v <- spline.control$v
+  lambda <- spline.control$lambda
+  smallsigma <- spline.control$smallsigma
+  bigsigma <- spline.control$bigsigma
+  gamma <- spline.control$gamma
+  bigsigmaactivate <- spline.control$bigsigmaactivate
+  eps <- spline.control$eps
+  tiny <- spline.control$tiny
+  itmax <- spline.control$itmax
+  ftol <- spline.control$ftol
+  
+  cat ("Calculating spline axis for variable", j, "\n")
+  if(dmeth==1) stop("dmeth should be equal to zero or integer greater than 1 \n")  
+  Ytilde <- scale(scale(Y, center=FALSE, scale=1/sd), center=-1*means, scale=FALSE)
+  
+  ytilde <- Ytilde[,j]
+  mutilde <- seq(from=min(ytilde),to=max(ytilde),length.out=nmu)
+  y <- Y[,j]
+  rangey <- max(y)-min(y)
+  mu <- seq(from=min(y)-.3*rangey,to=max(y)+.3*rangey,length.out=nmu)
+  markers <- (pretty(ytilde)-means[j])/sd[j]
+  mu <- sort(c(mu,markers))
+  mu <- unique(mu)
+  nmu <- length(mu)
+  
+  if (v>0){
+    knots <- seq.int(from=0,to=1,length.out=v+2)[-c(1,v+2)]
+    knots <- stats::quantile(y,knots)
+    M <- splines::bs(mu,knots=knots,degree=u,intercept=FALSE)
+  } else M <- splines::bs(mu,df=u+v,degree=u,intercept=FALSE)
+  M <- scale(M,scale=FALSE,center=M[which.min(abs(mu)),]) # To ensure that the spline passes through the origin at the calibration which represents the mean of the variable
+  Breg <- t(solve(t(X)%*%X)%*%t(X)%*%y)
+  Zreg <- mu%*%Breg/sum(Breg^2)
+  Bvec <- as.vector(solve(t(M)%*%M)%*%t(M)%*%Zreg)  # Closest to regression biplot
+  
+  const1 <- sum(y^2)
+  const2 <- sum(X^2)/(n*p)
+  TotalNumberOfLossFunctionCalls <- 0
+  optimtouse <- function(Bvec) {
+    timetemp <- proc.time()[3]
+  
+      # Use Rcpp optimize_spline function
+    returned_data <- optimize_spline(
+      BVEC = Bvec, 
+      X = X, 
+      Y = y, 
+      M = M, 
+      MU = mu,
+      LAMBDA = lambda, 
+      CONST1 = const1, 
+      CONST2 = const2,
+      U = u, 
+      V = v, 
+      TAU = tau, 
+      FTOL = ftol, 
+      TINY = tiny, 
+      ITMAX = itmax
+    )
+    
+    if(returned_data$ERRO > 0) {
+      cat("  Warning: Error code =", returned_data$ERRO, "\n")
+    }
+    
+    aa <- list(
+      BestValue = returned_data$LOSS,
+      BestSolution = returned_data$BVEC,
+      ConvergenceCode = returned_data$ERRO,
+      iter1 = returned_data$ITER1,
+      iter = returned_data$ITER,
+      TimeTaken = proc.time()[3] - timetemp
+    )
+    
+    aa
+  }
+
+  EuclidDist2 <- function (X, Y) {
+    n <- nrow(X)
+    m <- nrow(Y)
+    bx <- rowSums(X^2)
+    by <- rowSums(Y^2)
+    outer(bx, by, FUN = "+") - 2 * X %*% t(Y)
+  }
+  
+  ### Variable initialisation
+  outBestValues <- rep(NA,gamma+1)
+  outBestSolutions <- matrix(nrow=2*(u+v),ncol=gamma+1)
+  outTimeTaken <- rep(NA,gamma+1) # Is made one element longer at each iteration.
+  BestSolutionsFrequency <- rep(NA,gamma+1)
+  BestSolutionsIndices <- rep(NA,gamma+1) # Is made one element longer at each iteration.
+  SquaredDistancesBetweenBestSolutions <- matrix(nrow=gamma+1,ncol=gamma+1)
+  
+  ### Initial coefficients closest to regression biplot
+  temp <- optimtouse(Bvec)
+  outBestValues[1] <- temp$BestValue
+  outBestSolutions[,1] <- temp$BestSolution
+  outTimeTaken[1] <- temp$TimeTaken
+  BestSolutionsFrequency[1] <- 1
+  BestSolutionsIndices[1] <- 1
+  DistinctSolutions <- 1
+  PreviousBestSolution <- NA
+  nSameSolutionConsecutively <- 0
+  BigSigmaActivations <- NULL
+  
+  test.iter <- temp$iter
+  test.iter1 <- temp$iter1
+  
+  ### Last best coefficients perturbed
+  for (gammacounter in 2:(gamma+1)){
+    if (nSameSolutionConsecutively>=bigsigmaactivate){
+      temp <- optimtouse(outBestSolutions[,which.min(outBestValues)]+stats::rnorm((u+v)*2,mean=0,sd=bigsigma))
+      BigSigmaActivations <- c(BigSigmaActivations,gammacounter)
+    }
+    else temp <- optimtouse(outBestSolutions[,which.min(outBestValues)]+stats::rnorm((u+v)*2,mean=0,sd=smallsigma))
+    outTimeTaken[gammacounter] <- temp$TimeTaken
+    tempSquaredDistances <- EuclidDist2(matrix(temp$BestSolution,nrow=1),t(outBestSolutions[,1:DistinctSolutions]))
+    if (any(tempSquaredDistances<eps)){
+      BestSolutionsIndices[gammacounter] <- tempAA<-which.min(tempSquaredDistances)
+      BestSolutionsFrequency[tempAA] <- BestSolutionsFrequency[tempAA]+1
+      if (!is.na(PreviousBestSolution) && tempAA==PreviousBestSolution) nSameSolutionConsecutively<-nSameSolutionConsecutively+1
+      else{
+        PreviousBestSolution <- tempAA
+        nSameSolutionConsecutively <- 0
+      }
+    }
+    else{
+      DistinctSolutions <- DistinctSolutions+1
+      outBestValues[DistinctSolutions] <- temp$BestValue
+      outBestSolutions[,DistinctSolutions] <- temp$BestSolution
+      BestSolutionsFrequency[DistinctSolutions] <- 1
+      BestSolutionsIndices[gammacounter] <- DistinctSolutions
+      SquaredDistancesBetweenBestSolutions[1:(DistinctSolutions-1),DistinctSolutions]<-tempSquaredDistances
+      nSameSolutionConsecutively <- 0
+    }
+  }
+  axis.points <- cbind(M%*%matrix(outBestSolutions[,which.min(outBestValues)],ncol=2), mu, 0)
+  
+  for (i in 1:nrow(axis.points)) if (any(zapsmall(axis.points[i,3] - markers) == 0)) axis.points[i, 4] <- 1
+  axis.points[,3] <- axis.points[,3]*sd[j] + means[j]
+  axis.points
+}
+
+
+
+
+
+
+
+
+
+set.seed(123)
+
+n <- 180
+p <- 2 
+
+
+n_vars <- 4
+Y <- matrix(rnorm(n * n_vars), ncol = n_vars)
+
+Y[, 2] <- Y[, 1] + rnorm(n, 0, 0.5)
+Y[, 3] <- -Y[, 1] + rnorm(n, 0, 0.5)
+Y[, 4] <- Y[, 2] + Y[, 3] + rnorm(n, 0, 0.5)
+
+means <- colMeans(Y)
+sd <- apply(Y, 2, sd)
+
+X <- Y[, 1:2] + matrix(rnorm(n * p, 0, 0.3), ncol = p)
+
+u <- 3
+v <- 2
+spline.control <- list(
+  tau = 0.01, nmu = 10, u = u, v = v, lambda = 0.1,
+  smallsigma = 0.1, bigsigma = 1.0, gamma = 3, bigsigmaactivate = 2,
+  eps = 1e-6, tiny = 1e-4, itmax = 1000, ftol = 1e-4
+)
+
+j <- 1
+y <- Y[, j]
+rangey <- max(y) - min(y)
+mu <- seq(from=min(y)-.3*rangey, to=max(y)+.3*rangey, length.out=50)
+M <- splines::bs(mu, df=3, degree=3, intercept=FALSE)
+M <- scale(M, scale=FALSE, center=M[which.min(abs(mu)),])
+
+const1 <- sum(y^2)
+const2 <- sum(X^2) / (n*p)
+lambda <- 0.1
+
+
+# Test Bvec
+Bvec_test <- rnorm((u+v)*p)
+
+result_optim <- biplot.spline.axis(
+  j = 1, X = X, Y = Y, means = means, sd = sd,
+  n.int = NULL, spline.control = spline.control,
+  dmeth = 0
+)
+
+loss <- attr(result_optim, "loss")
+
+
+par(mfrow = c(1, 1), mar = c(4, 4, 3, 1))
+
+plot(X[, 1], X[, 2], pch = 19, col = "gray70",
+     xlab = "Dim 1", ylab = "Dim 2",
+     main = sprintf("R optim (Loss=%.4f)", loss), asp = 1)
+grid()
+lines(result_optim[, 1], result_optim[, 2], col = "darkgreen", lwd = 2)
+
+
+#All variables
+
+all_results <- list()
+all_losses <- numeric(n_vars)
+
+for(j in 1:n_vars) {
+  cat("\nProcessing variable", j, "...\n")
+  all_results[[j]] <- biplot.spline.axis(
+    j = j, X = X, Y = Y, means = means, sd = sd,
+    n.int = NULL, spline.control = spline.control, dmeth = 0
+  )
+  all_losses[j] <- attr(all_results[[j]], "loss")
+  cat("  Loss:", all_losses[j], "\n")
+  cat("  Distinct solutions:", attr(all_results[[j]], "distinct_solutions"), "\n")
+}
+
+
+par(mfrow = c(1, 1), mar = c(4, 4, 3, 1))
+plot(X[, 1], X[, 2], 
+     pch = 19, col = "gray70",
+     xlab = "Dimension 1", ylab = "Dimension 2",
+     main = "All Spline Axes (optim method)",
+     asp = 1)
+grid()
+
+colors <- c("blue", "red", "green", "purple")
+for(j in 1:n_vars) {
+  lines(all_results[[j]][, 1], all_results[[j]][, 2], 
+        col = colors[j], lwd = 2)
+  # Label the axis
+  mid <- ceiling(nrow(all_results[[j]]) / 2)
+  text(all_results[[j]][mid, 1], all_results[[j]][mid, 2],
+       paste("Var", j), pos = 3, col = colors[j], font = 2)
+}
+
+legend("topright", legend = paste("Variable", 1:n_vars),
+       col = colors, lwd = 2, cex = 0.8)
+
+
+
+
+
+
+
+
+
diff --git a/vignettes/Biplots_in_1D.Rmd b/vignettes/Biplots_in_1D.Rmd
index 285c0ce..7613492 100644
--- a/vignettes/Biplots_in_1D.Rmd
+++ b/vignettes/Biplots_in_1D.Rmd
@@ -26,8 +26,6 @@ library(biplotEZ)
 ```
 
 
-<img src='../man/figures/logo.png' alt='alt text' style='width:10%; height:auto;' class="center">
-
 This vignette illustrates how to create one-dimensional biplot. The biplotEZ vignette demonstrates many functions of the functions in the package. The vignette will serve as a supplement to the biplotEZ vignette.
 
 
diff --git a/vignettes/Biplots_in_1D.html b/vignettes/Biplots_in_1D.html
index b44f70c..2c5fe5c 100644
--- a/vignettes/Biplots_in_1D.html
+++ b/vignettes/Biplots_in_1D.html
@@ -60,7 +60,7 @@
 }
 @media print {
 pre > code.sourceCode { white-space: pre-wrap; }
-pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
+pre > code.sourceCode > span { display: inline-block; text-indent: -5em; padding-left: 5em; }
 }
 pre.numberSource code
 { counter-reset: source-line 0; }
@@ -347,31 +347,32 @@ <h1 class="title toc-ignore">Biplots in 1D</h1>
 <li><a href="#classification-using-classify" id="toc-classification-using-classify"><span class="toc-section-number">2.1</span> Classification using
 <code>classify()</code></a></li>
 </ul></li>
-<li><a href="#the-function-interpolate" id="toc-the-function-interpolate"><span class="toc-section-number">3</span> The function
+<li><a href="#one-dimensional-ca-biplot" id="toc-one-dimensional-ca-biplot"><span class="toc-section-number">3</span> One-dimensional CA biplot</a></li>
+<li><a href="#the-function-interpolate" id="toc-the-function-interpolate"><span class="toc-section-number">4</span> The function
 <code>interpolate()</code></a>
 <ul>
-<li><a href="#the-function-newsamples" id="toc-the-function-newsamples"><span class="toc-section-number">3.1</span> The function
+<li><a href="#the-function-newsamples" id="toc-the-function-newsamples"><span class="toc-section-number">4.1</span> The function
 <code>newsamples()</code></a></li>
-<li><a href="#the-function-newaxes" id="toc-the-function-newaxes"><span class="toc-section-number">3.2</span> The function
+<li><a href="#the-function-newaxes" id="toc-the-function-newaxes"><span class="toc-section-number">4.2</span> The function
 <code>newaxes()</code></a></li>
 </ul></li>
-<li><a href="#the-function-prediction" id="toc-the-function-prediction"><span class="toc-section-number">4</span> The function
+<li><a href="#the-function-prediction" id="toc-the-function-prediction"><span class="toc-section-number">5</span> The function
 <code>prediction()</code></a>
 <ul>
-<li><a href="#predicting-samples" id="toc-predicting-samples"><span class="toc-section-number">4.1</span> Predicting Samples</a></li>
-<li><a href="#predicting-group-means" id="toc-predicting-group-means"><span class="toc-section-number">4.2</span> Predicting Group Means</a></li>
+<li><a href="#predicting-samples" id="toc-predicting-samples"><span class="toc-section-number">5.1</span> Predicting Samples</a></li>
+<li><a href="#predicting-group-means" id="toc-predicting-group-means"><span class="toc-section-number">5.2</span> Predicting Group Means</a></li>
 </ul></li>
-<li><a href="#ellipses-and-alpha-bags" id="toc-ellipses-and-alpha-bags"><span class="toc-section-number">5</span> Ellipses and Alpha bags</a></li>
-<li><a href="#the-function-density1d" id="toc-the-function-density1d"><span class="toc-section-number">6</span> The function
+<li><a href="#ellipses-and-alpha-bags" id="toc-ellipses-and-alpha-bags"><span class="toc-section-number">6</span> Ellipses and Alpha bags</a></li>
+<li><a href="#the-function-density1d" id="toc-the-function-density1d"><span class="toc-section-number">7</span> The function
 <code>density1D()</code></a></li>
-<li><a href="#the-function-legend.type" id="toc-the-function-legend.type"><span class="toc-section-number">7</span> The function
+<li><a href="#the-function-legend.type" id="toc-the-function-legend.type"><span class="toc-section-number">8</span> The function
 <code>legend.type()</code></a></li>
-<li><a href="#fit-measures" id="toc-fit-measures"><span class="toc-section-number">8</span> Fit measures</a></li>
-<li><a href="#references" id="toc-references"><span class="toc-section-number">9</span> References</a></li>
+<li><a href="#the-function-fit.measures" id="toc-the-function-fit.measures"><span class="toc-section-number">9</span> The function
+<code>fit.measures()</code></a></li>
+<li><a href="#references" id="toc-references"><span class="toc-section-number">10</span> References</a></li>
 </ul>
 </div>
 
-<p><img 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" alt="alt text" style="width:10%; height:auto;" class="center"></p>
 <p>This vignette illustrates how to create one-dimensional biplot. The
 biplotEZ vignette demonstrates many functions of the functions in the
 package. The vignette will serve as a supplement to the biplotEZ
@@ -386,7 +387,7 @@ <h1><span class="header-section-number">1</span> One-dimensional PCA
 variable axes are displayed as horizontal lines below. The variable name
 is displayed on the side to which the variable increases.</p>
 <div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris<span class="sc">$</span>Species,<span class="at">dim.biplot =</span> <span class="dv">1</span>)  <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 </div>
 <div id="one-dimensional-cva-biplot" class="section level1" number="2">
 <h1><span class="header-section-number">2</span> One-dimensional CVA
@@ -397,7 +398,7 @@ <h1><span class="header-section-number">2</span> One-dimensional CVA
 the between class variance, relative to the within class variance.</p>
 <div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">CVA</span>(<span class="at">classes =</span> iris<span class="sc">$</span>Species,<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span></span>
 <span id="cb2-2"><a href="#cb2-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 <div id="classification-using-classify" class="section level2" number="2.1">
 <h2><span class="header-section-number">2.1</span> Classification using
 <code>classify()</code></h2>
@@ -408,7 +409,7 @@ <h2><span class="header-section-number">2.1</span> Classification using
 <div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" tabindex="-1"></a>bp <span class="ot">&lt;-</span> <span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">CVA</span>(<span class="at">classes =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">1</span>)<span class="sc">|&gt;</span></span>
 <span id="cb3-2"><a href="#cb3-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> </span>
 <span id="cb3-3"><a href="#cb3-3" tabindex="-1"></a>  <span class="fu">classify</span>(<span class="at">borders =</span> <span class="cn">TRUE</span>,<span class="at">opacity =</span> <span class="dv">1</span>)<span class="sc">|&gt;</span><span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 <p>The <code>print()</code> function provides the misclassification
 rate, as well as the confusion matrix, of the CVA classifier applied to
 the training data.</p>
@@ -428,13 +429,25 @@ <h2><span class="header-section-number">2.1</span> Classification using
 <span id="cb4-14"><a href="#cb4-14" tabindex="-1"></a><span class="co">#&gt;   virginica       0          1        49</span></span></code></pre></div>
 </div>
 </div>
-<div id="the-function-interpolate" class="section level1" number="3">
-<h1><span class="header-section-number">3</span> The function
+<div id="one-dimensional-ca-biplot" class="section level1" number="3">
+<h1><span class="header-section-number">3</span> One-dimensional CA
+biplot</h1>
+<p>Similarly for a CA 1d biplot, <code>dim.biplot = 1</code> is
+specified in the call to <code>CA()</code>. The one-dimensional biplot
+is constructed from the first columns of <span class="math inline">\(\mathbf{U\Lambda^\gamma}\)</span> and <span class="math inline">\(&amp;\mathbf{V\Lambda^{1-\gamma}}\)</span>.</p>
+<p>Consider the <code>HairEyeColor</code> example again as discussed in
+<code>CA in biplotEZ</code>:</p>
+<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" tabindex="-1"></a><span class="fu">biplot</span>(HairEyeColor[,,<span class="dv">2</span>], <span class="at">center =</span> <span class="cn">FALSE</span>) <span class="sc">|&gt;</span> <span class="fu">CA</span>(<span class="at">variant =</span> <span class="st">&quot;Princ&quot;</span>, </span>
+<span id="cb5-2"><a href="#cb5-2" tabindex="-1"></a>  <span class="at">dim.biplot=</span><span class="dv">1</span>, <span class="at">lambda.scal =</span> T) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+</div>
+<div id="the-function-interpolate" class="section level1" number="4">
+<h1><span class="header-section-number">4</span> The function
 <code>interpolate()</code></h1>
 <p><code>interpolate()</code> allows for new observations or axes to be
 added to the biplot.</p>
-<div id="the-function-newsamples" class="section level2" number="3.1">
-<h2><span class="header-section-number">3.1</span> The function
+<div id="the-function-newsamples" class="section level2" number="4.1">
+<h2><span class="header-section-number">4.1</span> The function
 <code>newsamples()</code></h2>
 <p>The process of adding new samples to the biplot, called interpolation
 utilises the functions <code>interpolate()</code> and
@@ -445,12 +458,12 @@ <h2><span class="header-section-number">3.1</span> The function
 interpolated. The function <code>newsamples()</code> operates the same
 way as <code>samples()</code> in that the user can specify the
 aesthetics of the interpolated samples.</p>
-<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" tabindex="-1"></a><span class="fu">biplot</span>(iris[<span class="fu">c</span>(<span class="dv">1</span><span class="sc">:</span><span class="dv">50</span>,<span class="dv">101</span><span class="sc">:</span><span class="dv">150</span>),<span class="dv">1</span><span class="sc">:</span><span class="dv">4</span>])<span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb5-2"><a href="#cb5-2" tabindex="-1"></a>  <span class="fu">interpolate</span>(<span class="at">newdata =</span> iris[<span class="dv">51</span><span class="sc">:</span><span class="dv">100</span>,<span class="dv">1</span><span class="sc">:</span><span class="dv">4</span>]) <span class="sc">|&gt;</span> <span class="fu">newsamples</span>(<span class="at">col=</span><span class="st">&quot;purple&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" tabindex="-1"></a><span class="fu">biplot</span>(iris[<span class="fu">c</span>(<span class="dv">1</span><span class="sc">:</span><span class="dv">50</span>,<span class="dv">101</span><span class="sc">:</span><span class="dv">150</span>),<span class="dv">1</span><span class="sc">:</span><span class="dv">4</span>])<span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb6-2"><a href="#cb6-2" tabindex="-1"></a>  <span class="fu">interpolate</span>(<span class="at">newdata =</span> iris[<span class="dv">51</span><span class="sc">:</span><span class="dv">100</span>,<span class="dv">1</span><span class="sc">:</span><span class="dv">4</span>]) <span class="sc">|&gt;</span> <span class="fu">newsamples</span>(<span class="at">col=</span><span class="st">&quot;purple&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" 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" /><!-- --></p>
 </div>
-<div id="the-function-newaxes" class="section level2" number="3.2">
-<h2><span class="header-section-number">3.2</span> The function
+<div id="the-function-newaxes" class="section level2" number="4.2">
+<h2><span class="header-section-number">4.2</span> The function
 <code>newaxes()</code></h2>
 <p>To interpolate new variables to the biplot, the function
 <code>interpolate()</code> and <code>newaxes()</code> are called. The
@@ -460,17 +473,17 @@ <h2><span class="header-section-number">3.2</span> The function
 the new variables to be interpolated. The function
 <code>newaxes()</code> allows the user to specify the aesthetics of the
 interpolated variables.</p>
-<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" tabindex="-1"></a><span class="fu">biplot</span>(iris[,<span class="dv">1</span><span class="sc">:</span><span class="dv">3</span>])<span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb6-2"><a href="#cb6-2" tabindex="-1"></a>  <span class="fu">interpolate</span>(<span class="at">newvariable =</span> iris[,<span class="dv">4</span>]) <span class="sc">|&gt;</span> </span>
-<span id="cb6-3"><a href="#cb6-3" tabindex="-1"></a>  <span class="fu">newaxes</span>(<span class="at">col=</span><span class="st">&quot;darkred&quot;</span>,<span class="at">X.new.names =</span> <span class="st">&quot;Petal.Width&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" tabindex="-1"></a><span class="fu">biplot</span>(iris[,<span class="dv">1</span><span class="sc">:</span><span class="dv">3</span>])<span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb7-2"><a href="#cb7-2" tabindex="-1"></a>  <span class="fu">interpolate</span>(<span class="at">newvariable =</span> iris[,<span class="dv">4</span>]) <span class="sc">|&gt;</span> </span>
+<span id="cb7-3"><a href="#cb7-3" tabindex="-1"></a>  <span class="fu">newaxes</span>(<span class="at">col=</span><span class="st">&quot;darkred&quot;</span>,<span class="at">X.new.names =</span> <span class="st">&quot;Petal.Width&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 </div>
 </div>
-<div id="the-function-prediction" class="section level1" number="4">
-<h1><span class="header-section-number">4</span> The function
+<div id="the-function-prediction" class="section level1" number="5">
+<h1><span class="header-section-number">5</span> The function
 <code>prediction()</code></h1>
-<div id="predicting-samples" class="section level2" number="4.1">
-<h2><span class="header-section-number">4.1</span> Predicting
+<div id="predicting-samples" class="section level2" number="5.1">
+<h2><span class="header-section-number">5.1</span> Predicting
 Samples</h2>
 <p>To add the prediction of samples on the biplot, the
 <code>prediction()</code> function is used. The
@@ -480,14 +493,14 @@ <h2><span class="header-section-number">4.1</span> Predicting
 for samples 100 to 150 are shown. The aesthetics for the display of the
 predictions are arguments in the <code>axes()</code> function:
 <code>predict.col</code> and <code>predict.lwd</code>.</p>
-<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> </span>
-<span id="cb7-2"><a href="#cb7-2" tabindex="-1"></a>  <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris<span class="sc">$</span>Species,<span class="at">dim.biplot =</span> <span class="dv">1</span>,<span class="at">show.class.means =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb7-3"><a href="#cb7-3" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>,<span class="at">predict.col =</span> <span class="st">&quot;darkred&quot;</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb7-4"><a href="#cb7-4" tabindex="-1"></a>  <span class="fu">prediction</span>(<span class="at">predict.samples=</span><span class="dv">100</span><span class="sc">:</span><span class="dv">150</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> </span>
+<span id="cb8-2"><a href="#cb8-2" tabindex="-1"></a>  <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris<span class="sc">$</span>Species,<span class="at">dim.biplot =</span> <span class="dv">1</span>,<span class="at">show.class.means =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb8-3"><a href="#cb8-3" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>,<span class="at">predict.col =</span> <span class="st">&quot;darkred&quot;</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb8-4"><a href="#cb8-4" tabindex="-1"></a>  <span class="fu">prediction</span>(<span class="at">predict.samples=</span><span class="dv">100</span><span class="sc">:</span><span class="dv">150</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 </div>
-<div id="predicting-group-means" class="section level2" number="4.2">
-<h2><span class="header-section-number">4.2</span> Predicting Group
+<div id="predicting-group-means" class="section level2" number="5.2">
+<h2><span class="header-section-number">5.2</span> Predicting Group
 Means</h2>
 <p>Similarly, to add the prediction of group means, the function
 <code>prediction()</code> is used. The argument
@@ -496,50 +509,50 @@ <h2><span class="header-section-number">4.2</span> Predicting Group
 predicted. Important to note that the argument
 <code>show.class.means</code> must be set to TRUE in the
 <code>PCA()</code> function.</p>
-<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> </span>
-<span id="cb8-2"><a href="#cb8-2" tabindex="-1"></a>  <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris<span class="sc">$</span>Species,<span class="at">dim.biplot =</span> <span class="dv">1</span>,<span class="at">show.class.means =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb8-3"><a href="#cb8-3" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>,<span class="at">predict.col =</span> <span class="st">&quot;darkred&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">means</span>(<span class="at">label=</span><span class="cn">TRUE</span>,<span class="at">which=</span><span class="dv">1</span><span class="sc">:</span><span class="dv">3</span>)<span class="sc">|&gt;</span></span>
-<span id="cb8-4"><a href="#cb8-4" tabindex="-1"></a>  <span class="fu">prediction</span>(<span class="at">predict.means =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> </span>
+<span id="cb9-2"><a href="#cb9-2" tabindex="-1"></a>  <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris<span class="sc">$</span>Species,<span class="at">dim.biplot =</span> <span class="dv">1</span>,<span class="at">show.class.means =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb9-3"><a href="#cb9-3" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>,<span class="at">predict.col =</span> <span class="st">&quot;darkred&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">means</span>(<span class="at">label=</span><span class="cn">TRUE</span>,<span class="at">which=</span><span class="dv">1</span><span class="sc">:</span><span class="dv">3</span>)<span class="sc">|&gt;</span></span>
+<span id="cb9-4"><a href="#cb9-4" tabindex="-1"></a>  <span class="fu">prediction</span>(<span class="at">predict.means =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 </div>
 </div>
-<div id="ellipses-and-alpha-bags" class="section level1" number="5">
-<h1><span class="header-section-number">5</span> Ellipses and Alpha
+<div id="ellipses-and-alpha-bags" class="section level1" number="6">
+<h1><span class="header-section-number">6</span> Ellipses and Alpha
 bags</h1>
 <p>Ellipses are added to a 1d biplot using the <code>ellipses()</code>
 function which works in the same way as a 2d biplot. In one dimension
 concentration ellipses are simply a confidence interval. The
 concentration interval is indicated using rectangles spanning the range
 of the interval.</p>
-<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb9-2"><a href="#cb9-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb9-3"><a href="#cb9-3" tabindex="-1"></a>  <span class="fu">ellipses</span>() <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span>
-<span id="cb9-4"><a href="#cb9-4" tabindex="-1"></a><span class="co">#&gt; Computing 1.96 -ellipse for setosa </span></span>
-<span id="cb9-5"><a href="#cb9-5" tabindex="-1"></a><span class="co">#&gt; Computing 1.96 -ellipse for versicolor </span></span>
-<span id="cb9-6"><a href="#cb9-6" tabindex="-1"></a><span class="co">#&gt; Computing 1.96 -ellipse for virginica</span></span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb10-2"><a href="#cb10-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb10-3"><a href="#cb10-3" tabindex="-1"></a>  <span class="fu">ellipses</span>() <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span>
+<span id="cb10-4"><a href="#cb10-4" tabindex="-1"></a><span class="co">#&gt; Computing 1.96 -ellipse for setosa </span></span>
+<span id="cb10-5"><a href="#cb10-5" tabindex="-1"></a><span class="co">#&gt; Computing 1.96 -ellipse for versicolor </span></span>
+<span id="cb10-6"><a href="#cb10-6" tabindex="-1"></a><span class="co">#&gt; Computing 1.96 -ellipse for virginica</span></span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 <p>The one-dimensional representation of an Alpha bag will simply be an
 empirical interval. The empirical interval is indicated using rectangles
 spanning the range of the interval.</p>
-<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb10-2"><a href="#cb10-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb10-3"><a href="#cb10-3" tabindex="-1"></a>  <span class="fu">alpha.bags</span>(<span class="at">alpha =</span> <span class="fl">0.7</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span>
-<span id="cb10-4"><a href="#cb10-4" tabindex="-1"></a><span class="co">#&gt; Computing 0.7 -bag for setosa </span></span>
-<span id="cb10-5"><a href="#cb10-5" tabindex="-1"></a><span class="co">#&gt; Computing 0.7 -bag for versicolor </span></span>
-<span id="cb10-6"><a href="#cb10-6" tabindex="-1"></a><span class="co">#&gt; Computing 0.7 -bag for virginica</span></span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb11-2"><a href="#cb11-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb11-3"><a href="#cb11-3" tabindex="-1"></a>  <span class="fu">alpha.bags</span>(<span class="at">alpha =</span> <span class="fl">0.7</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span>
+<span id="cb11-4"><a href="#cb11-4" tabindex="-1"></a><span class="co">#&gt; Computing 0.7 -bag for setosa </span></span>
+<span id="cb11-5"><a href="#cb11-5" tabindex="-1"></a><span class="co">#&gt; Computing 0.7 -bag for versicolor </span></span>
+<span id="cb11-6"><a href="#cb11-6" tabindex="-1"></a><span class="co">#&gt; Computing 0.7 -bag for virginica</span></span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 </div>
-<div id="the-function-density1d" class="section level1" number="6">
-<h1><span class="header-section-number">6</span> The function
+<div id="the-function-density1d" class="section level1" number="7">
+<h1><span class="header-section-number">7</span> The function
 <code>density1D()</code></h1>
 <p>Overlapping points make the distribution of points on the scatter
 line difficult to identify. <code>density1D()</code> uses kernel density
 estimation (KDE), which adds a density plot to the one-dimensional
 biplot.</p>
-<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb11-2"><a href="#cb11-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span></span>
-<span id="cb11-3"><a href="#cb11-3" tabindex="-1"></a>  <span class="fu">density1D</span>() <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb12-2"><a href="#cb12-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span></span>
+<span id="cb12-3"><a href="#cb12-3" tabindex="-1"></a>  <span class="fu">density1D</span>() <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 <p>This KDE may be too smooth to display the distribution of the data.
 By changing the parameters of the KDE, we are able to address this
 issue. The bandwidth and kernel used in <code>density1D()</code> are
@@ -547,72 +560,72 @@ <h1><span class="header-section-number">6</span> The function
 respectively. The bandwidth <code>h</code> can take any positive value,
 see <code>?stats::density</code> for more detail. <code>kernel</code>
 can take on any kernel supported by <code>stats::density()</code>.</p>
-<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&#39;black&#39;</span>) <span class="sc">|&gt;</span></span>
-<span id="cb12-2"><a href="#cb12-2" tabindex="-1"></a>  <span class="fu">density1D</span>(<span class="at">h =</span> <span class="fl">0.5</span> ,<span class="at">kernel =</span> <span class="st">&quot;triangular&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&#39;black&#39;</span>) <span class="sc">|&gt;</span></span>
+<span id="cb13-2"><a href="#cb13-2" tabindex="-1"></a>  <span class="fu">density1D</span>(<span class="at">h =</span> <span class="fl">0.5</span> ,<span class="at">kernel =</span> <span class="st">&quot;triangular&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 <p>The high concentration of observations in the right of the plot now
 becomes evident. To further explore the distributions of the
 observations, we may want to explore the density of groupings in the
 data. To do this, simply specify the <code>group.aes=</code> argument in
 <code>PCA()</code>. Here the density of the three species of iris is
 displayed.</p>
-<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb13-2"><a href="#cb13-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span></span>
-<span id="cb13-3"><a href="#cb13-3" tabindex="-1"></a>  <span class="fu">density1D</span>() <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
-<p>To only display the density of certain groups, use the
-<code>which=</code> argument in <code>density1D()</code>.</p>
 <div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> </span>
 <span id="cb14-2"><a href="#cb14-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span></span>
-<span id="cb14-3"><a href="#cb14-3" tabindex="-1"></a>  <span class="fu">density1D</span>(<span class="at">which =</span> <span class="fu">c</span>(<span class="dv">2</span>,<span class="dv">3</span>)) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<span id="cb14-3"><a href="#cb14-3" tabindex="-1"></a>  <span class="fu">density1D</span>() <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>To only display the density of certain groups, use the
+<code>which=</code> argument in <code>density1D()</code>.</p>
+<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb15-2"><a href="#cb15-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span></span>
+<span id="cb15-3"><a href="#cb15-3" tabindex="-1"></a>  <span class="fu">density1D</span>(<span class="at">which =</span> <span class="fu">c</span>(<span class="dv">2</span>,<span class="dv">3</span>)) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAqAAAAJACAMAAABlpiR1AAAAmVBMVEUAAAAAADoAAGYAAP8AOmYAOpAAZpAAZrYA/wA6AAA6ADo6AGY6OmY6OpA6ZrY6kNtmAABmADpmAGZmOgBmOjpmOpBmZgBmZjpmZmZmtrZmtv+QOgCQOjqQOmaQZgCQZpCQkDqQkLaQtpCQ27aQ2/+2ZgC2Zjq225C2///bkDrbtmbb/9vb////tmb/1wD/25D//7b//9v////DtlxNAAAACXBIWXMAAA7DAAAOwwHHb6hkAAAWvUlEQVR4nO2dDXvaSJZG6Y+ZuHsmSW93ejfjpGd2Z0w27AR/8P9/3EoghHgNoqokode+5zxPHGN0XS/2cakkEHexATBmMXcAgD4QFKxBULAGQcEaBAVrEBSsQVCwBkHBGgQFaxAUrEFQsAZBwRoEBWsQFKxBULAGQcEaBAVrEBSsQVCwBkHBGgQFaxAUrEFQsAZBwRoEBWsQFKxBULAGQcEaBAVrEBSsQVCwBkHBGgQFaxAUrEFQsAZBwRoEBWsQFKxBULAGQcEaBAVrEBSsQVCwBkHBGgQFaxAUrEFQsAZBwRoEBWsQFKxBULAGQcEaBAVrEBSsQVCwBkHBGgQFaxAUrEFQsAZBwRoEBWsQFKxBULAGQcEaBAVrEBSsQVCwBkHBGgQFaxAUrEFQsAZBwRoEBWsQFKxBULAGQcEaBAVrnAVdgBXzSDDLqGk4ZwsIgirO2QKCoIpztoAgqOKcLSAIqjhnCwiCKs7ZAoKginO2gCCo4pwtIAiqOGcLCIIqztkCgqCKc7aAIKjinC0gCKo4ZwsIgirO2QKCoIpztsHc1MwdIgsEVZyzDWUr58syFEEV52wDacx8UYYiqOKcbRAHL1+SoQiqOGcbQtdKBLUcNQ3nbAM4njVfjqEIqjhnK0f26i9nJ4+ginO2dG5ujs4oPRMSQQ1HTcM5WzLt8fq5E0sIajhqGs7ZUukeD505M/9SDEVQxTlbIinyIajfqGk4Z0sj7QjohRiKoIpztjTS1ENQu1HTcM6WRKp5advd7yiPMxAEVZyzJTGioK2a8ymKoIpztiTGE/TIypkMRVDFOVsK6WvLC1vqpDmPoQiqOGdLYSxBn+/UZ9nNI6jinC2BjIPzvk1PyoigDjhnSyDn7NH5bc9MljMYiqCKc7YERhH07M78+oYiqOKc7TJZp9/PbNyz1rz+MhRBFedsl8l7fujk1r0SXt1QBFWcs11msKCXDETQuXHOdpHMJ9ifb35xhrz2FIqginO2i+S+AkS3T9APQWfGOdtFBgqaND1e11AEVZyzXSL7JXTHBWm7bwSdF+dsl8h/jWe3InV5eVVDEVRxznaJQYImH/4g6Kw4Z7tAwYvku4ImF13TUARVnLNdoOQqjrYmwzoEnRPnbBcYImiWdFc0FEEV52z9FF0G1xRlnn+/nqEIqjhn62eQoHlVCDofztn6KbuQeFuV+wQmgs6Hc7Z+hgiaW3U1QxFUcc7WS+E7MdRl+boh6Gw4Z+ul9K1Cbop0u5ahCKo4Z+ulXNAS2RB0Lpyz9VH8Xktlgl7LUARVnLP1Uf5mYDcI6jFqGs7Z+igXtEw1BJ0J52w9DHg3xULVrmMogirO2XoYMIEWll7n6iQEVZyz9TBkD19qaPGQGSCo4pyth2JB78trr2EogirO2c4z6BAJQT1GTcM523mGHcMb7+MRVHHOdp4he3jrKRRBFedsZxl4EhRBLUZNwznbWYZNoEPLpwRBFedsZxlqmO8UiqCKc7ZzDH6a03cKRVDFOds5BvuFoA6jpuGc7RzD/Srex09tKIIqztnOMMILmWynUARVnLOdYU5BpzYUQRXnbGcYY/pznUIRVHHOdppRZj/XKRRBFedspxll8kPQ+UdNwznbaeYWdFJDEVRxznaSkeY+0ykUQRXnbCcZ6fDm+hc1JYGginO2kxgIOqGhCKo4ZzvFaLtmzykUQRXnbKcY7QSm5xSKoIpzthPcOAg64RSKoIpzthOMd/A9RNDpDEVQxTnbCUY8O2RpKIIqztmeM+bZy2GCTmQogirO2Z5jI+hUUyiCKs7ZnjHu0z+OhiKo4pztGU6CTmMogirO2ZTyc0xTCDqJoQiqOGdTxn6Bx9ApdAJDEVRxziaMPIGOMIWObyiCKs7ZhNGfPR8q6ASGIqjinO2YCZ6b9DMUQRXnbMdM8PKjwYKOriiCKs7ZjpjixR0jCDqyoQiqOGfrMuAI6fz5oDEErQwdUVEEVZyzdRjiZ88Jy1EMHXMSRVDFOVuHiV69OY6gIyqKoIpztgNTvTRuLEFHUxRBFedsLdO9rGM8Q8dRFEEV52wNg9afm6sJOoqiCKo4Z9tyM6Wf4wo6wgE9girO2TYj6HnpRUfjGjpYUQRVnLPdjKDnpRfFjSzo0P08giq+2cawc3P5VZsTGDpAUQRVXLONY2fCq4pHF3TQJIqgime2sfScR9ABhiKoYpltPD/nEbTcUARVHLNd008zQxFUMcx25Wd3JhG09JI6BFX8so0pTJIlToYiqGKX7ep+TiVokaEIqrhlG/fJ8bQhJzM0X1EEVcyyjSpLqh9TCVowhyKo4pVtXD9nFzR/DkVQxSrbPH46GYqgilO2cReDGWpMtgrNNhRBFadsc/k55RSaaSiCKkbZZtq/b4d2MRRBFZ9sM/o56RSaFQZBFZtsY05iBScgpzQ0Iw+CKi7ZxnyBSMlTOFPu5DMiIahikm00P4pfzz6poMmGIqjikW0kP++HXG4xraGJiiKoYpFtnHeZG3pF5eSGJsRDUMUg2xiXbo7yFnPTrkOTJlEEVWbPNvyNGcZ7/8OpDb08iyKoMne2YU4M368fM9Klzj1cCIygypzZBr0xw/3Ycu4Y5c0i+ukLjqDKDNluWrLK7o+ZKNymk2+6IfTRtF9GUGXxUri/nzvBhBwe2zwSzDJqGs7ZAoKginO2gCCo4pwtIAiqOGcLCIIqztkCgqCKc7aAIKjinC0gCKo4ZwsIgirO2QKCoIpztoAgqOKcLSAIqjhnCwiCKs7ZAoKginO2gCCo4pwtIAiqOGcLCIIqztkCgqCKc7aAIKjinC0gCKqkZ/vhhx8On/2w/dBLWZ7mWrXDRWvtxWvbT27aj9vPbrrUt+7v77s3jzaQq+52tzfNv/3H+vq1/Seda9qOLm7bl232F7rv7+nccdgyCwRVkrMdpLuo5gBDb44M3HRMvUlhZ17PfQno5aPPLr9Ub9vriI+2arfMevwIqqRmO0iX6meJoSrVwdR0P88YmurnJX3P+rs52qpGdE0BQZXUC2Mb5w6fJZB/+a1atf/C83vmErS+/vnMPUdbbS8m7t5IZB4JZhk1DWbQPJhBrwxr0D7RTvjJGvS6cBTPUfwrERSuAIIqztkCgqCKc7aAIKjinC0gCKo4ZwsIgirO2QKCoIpztoAgqOKcLSAIqjhnCwiCKs7ZAoKginO2gCCo4pwtIAiqOGcLCIIqztkCgqCKc7aAIKjinC0gCKo4ZwsIgirO2QKCoIpztoAgqOKcLSAIqjhnCwiCKs7ZAoKginO2gCCo4pwtIAiqOGcLCIIqztkCgqCKc7aAIKjinC0gCKo4ZwsIgirO2QKCoIpztoAgqOKcLSAIqjhnCwiCKs7ZAoKginO2gCCo4pwtIAiqOGcLCIIqztkCgqDKyWyDAr/MYpPUCKog6MwDPxP08ZfF4vuvp7d9+MvX9uPZLfruTohgBoLOPLAK+vjL7Waz+tO3k9siaM8XB31H+2KT1IudfY//cVfPpNVE+vjrfy++u6vE+2mxuBVBd1s8vP17fVd968cP/6q+9L9/+c/tF66Uf2LyOxLDlGyePjWz5/L9ZvWm0u5P39bff62NbSfHvaC7LR5+er9ZVzXVrfV3d/VGzRcyJBjfq9FgBp154OcHSetFPWduJ9Ffv9Z7/KfPd/V91a0jQZst6lvVv+qzesPG4rzdPIL6F5ukbm48/HxXHytVotYWbpbVDntZHzodC7rbovHx4e03BC3/jvbFJqkXm/Wb+v/lbT0jbnbTZOVdPZHqLr7Zghl0jO9oX2ySujmKr7VcbleSj7+8qf/bSvfz3bM16P6u6t9hDfqqBV293/633K6DCigtbOuKR14tFm+GlJUOvKqPbd4PqeuM3JwHrW9W/2+Xov+1vVVt/eNvtzv96iP6OvVui72P1a0/f757+lQdxb9iQde7H1mzLM+ntLCtKx653jUus06uHJcVD1zX/iPnmFnruiM/U2W7Bk0l/wzomVGNOM728Pb/toI+fvipaDoqLmzrikdefSyaQduy4oErvhS6vavrjlwu6NOn0l3PCxK0Wmivt4Kuv/+6WeVPR+WFbV3xyMvqd1xQ2JYVD7xpjmuK67oj81y8cpTtaDm1LlhXDSpcDxq5/hUXFB6VFSYfNoEejYygimZrZtD3RdNReWFbVz5y2QzalhUPvHn8vWwFuq/rjoygyglB6x/csujAdLMpLtzWDRp5VVa4Gjzww7uisl2djIyginO2gCCo4pwtIAiqOGcLCIIqztkCgqCKc7aAIKjinC0gCKo4ZwsIgirO2QKCoIpztoAgqOKcLSAIqjhnCwiCKs7ZAoKginO2gCCo4pwtIAiqOGcLCIIqztkCgqCKc7aAIKjinC0gCKo4ZwsIgirO2QKCoIpztoAgqOKcLSAIqjhnCwiCKs7ZAoKginO2gCCo4pwtIAiqOGcLCIIqztkCgqCKc7aAIKjinC0gCKosjv4rKZ26xjja+DWvTNDLjXHr/gDrunHj+k3zDvtPn267DUcR1KrmdQma0Bi37iqz+vi+bS+DoN41r0vQlMa4b789ff5n/eGu6aXz429/63bERVCrmtclaEJj3Lod6e///uNr03S07ka2uO12xJ2rqy+cZiJV+plu1IuNceuZ8121Eq0+7Ps5trv47RbMoFY1r03QzaXGuJvV7ep2s35fLUH3s+oSQX1rXpegCY1xq22+VHv8d1/umEFfQs3rEjShMe7m8cO2j/hfDx1xFwjqW/O6BE1ojFtNmPU0Wzf8292q7+p2xHV+EiEgr0zQY7Ia4+5Z7M421axS+1gt9zXLQ3FqTd3z9MyZ27PDbJo1TCoZsbqJ6k8SfwSHR7FM7uDa1vT170ZQZdH+9tepv51q6buraT/Jq0nsmn347uuzT5ddKEzdfJdold7Qu62pllTrxL+37iM/27/7VQtaRCvovhN3Eq0AGSYcNk1uibkrefqfpz8y+6BnTrm7RPUeZJn+M9jWPLz9ltPreP/Iz7afRVBlsdxNnG0n7hSW+8l2md7e8rBp8m+0LckVNCNWJ1G9D/6YXLjvpZ26YOnU9PwEEFRZNGvPvoXRCdr1avLCtd10mTPj7EqyZ9CcWEeJ0tfhu5pqWdC+rCF9nPP9uxFUWRx+Kakz6Hr/2pP1++TfaLvp06fU/Xvnu+cJmhFr001Ur10Tl/FtTTVO6nLi8Mh7+ncjqFLNm2+an1jyLn65r9l+klezTJ+p22FyZ9CMWLutq0TNw0n862lr6mVBbk1f/24EVZyzBQRBFedsAUFQxTlbQBBUcc4WEARVnLMFBEEV52wBQVDFOVtAEFRxzhYQBFWcswUEQRXnbAFBUMU5W0AQVHHOFhAEVZyzBQRBFedsAUFQxTlbQBBUcc4WEARVnLMFBEEV52wBQVDFOVtAEFRxzhYQBFWcswUEQRXnbAFBUMU5W0AQVHHOFhAEVZyzBQRBFedsAUFQxTlbQBBUcc4WEARVnLMFBEEV52wBQVAlI5tv2xnf5ja5JYttp9XOG1Qe3h63ab7a83a53SbBmaP6gqBWwywOHYJ3IOgkmw6psS25oqD1uzFvW1hvPxy1r24M3DW4fnj79+0b6NZdrD/8q9vFetKU1+Tq7Xyhl52BDz/fNS2s6waW3fbVe0Gbe5um1XUHwe/uul2s8yQYXavxYAa1Gma/Br3dt7Ded7T89VjQzr37Hqyf77otLidNeU0Q1GqYRXcfXve53DWoPrSv3gt6uLfWctuPFUGn/fb2JVcWtOmvVs2P3fbVhxm1uZcZtGTTITW2JdcVtGlhvZdu3766swbdd7Zuulh/F15QmJ6OoLsW1k+fvv/abV+9W6K+ae7d+1jd+vPnu24X68xRfUnPltv/MquzcUtep+KGrL5yzSipTYoPg2R1X2oqcrr31ZSrUnYGdOio05OcLbPl8LYkvX1wpyT/DyG5T/Oear2WOUTRg9n0tDU+Q5kq9UyQ/Qc3eNTrkJqtoOXwluTOxi3Zgmb1ad4N8eGn3Nlws/qYPYNu+rpynobn4pX0bEWC5vSq3pHbqTivT/OOdbUzyP3LqTvBZv+1ZT98BFWmFTSns3FL5oqyYKVXkyt1LWduTfYEiqDPmFLQ9M7GLZmdijtV2aNkZlsXzKA9bY3PgKDKlIJmdDbu1uTPutkz27Jgzl3l1/S0NT4DgirO2QKCoIpztoAgqOKcLSAIqjhnCwiCKs7ZAoKginO2gCCo4pwtIAiqOGcLCIIqztkCgqCKc7aAIKjinC0gCKo4ZwsIgirO2QKCoIpztoAgqOKcLSAIqjhnCwiCKs7ZAoKginO2gCCo4pwtIAiqOGcLCIIqztkCgqCKc7aAIKjinC0gCKo4ZwsIgirO2QKCoIpztoAgqOKcLSAIqjhnCwiCKs7ZAoKginO2gCCokpZt0CN4ocWzDI2gCoJaDX2xHXfdx2FdN0JZv2nuevp0W9zmeFjYq4CgVkNfbMddv/306mP3fagRNHmr11U8p6A97bjffnv6/M/6w13TwevH3/5W3Id7WNirMEfLaTjPpXbcj79+ffz93398bVod1z0QF7fFfbj3Eoyq1Lgwg1oNfbEddz1zvqtWotWHfRfZdhdfvJtH0JdYPOcufnO2Hfdmdbu63azfV0vQ/ay6RNCX6tiLFvR0O+7q6P1Ltcd/9+WOGRSuz8V23JvHD2+/VTv6vx76cC/CC7os7FTa1pU0F96R31n2uK545JJOzcd1RUNfbMddfaHuI1W38Nvdqu8q7sPdjupLQrbq77jo+LCtK2ku3HyL/BbLR3UDRi5qbtypKxuaZ5KUhGzVerxoImvrSpoLbyltsdzWFY+8Jb9Tc6eubGgEVVIEvS3rdNzWlTQXbigTtK0bMHJJp+ZuXdnQCKpcYwatyW6nuWOgoANGLuvUfFyXPzSCKtdYg5Y0F24YOoMWj1zQqfm4rmxoBFUmP4qvW1KXNBfeMUTQQSOXdGo+1BUPjaCKc7aAIKjinC0gCKo4ZwsIgirO2QKCoIpztoAgqOKcLSAIqjhnCwiCKs7ZAoKginO2gCCo4pwtIAiqOGcLCIIqztkCgqCKc7aAIKjinC0gCKo4ZwsIgirO2QKCoIpztoAgqOKcLSAIqjhnCwiCKs7ZAoKginO2gCCo4pwtIAiqOGcLCIIqztkCgqCKc7aAIKjinC0gCKo4ZwsIgirO2QKCoIpztoAgqOKcLSAIqjhnCwiCKs7ZAoKginO2gCCo4pwtIAiqOGcLCIIqztkCgqCKc7aAIKjinC0gCKo4ZwsIgirO2QKCoIpztoAgqOKcLSAIqjhnCwiCKs7ZAoKginO2gCCo4pwtIAiqOGcLCIIqztkCgqCKc7aAIKiyACvmkWCWUQESQVCwBkHBGgQFaxAUrEFQsAZBwRoEBWsQFKxBULAGQcEaBAVrEBSsQVCwBkHBGgQFaxAUrEFQsAZBwRoEBWsQFKxBULAGQcEaBAVrEBSsQVCwBkHBGgQFaxAUrEFQsAZBwRoEBWsQFKxBULAGQcEaBAVrEBSsQVCwBkHBGgQFaxAUrEFQsAZBwRoEBWsQFKxBULAGQcEaBAVrEBSsQVCwBkHBGgQFaxAUrEFQsAZBwRoEBWsQFKxBULAGQcEaBAVrEBSsQVCwBkHBGgQFaxAUrEFQsAZBwRoEBWsQFKxBULAGQcEaBAVrEBSsQVCwBkHBGgQFaxAUrEFQsAZBwRoEBWsQFKxBULAGQcEaBAVrEBSsQVCwBkHBGgQFaxAUrEFQsAZBwRoEBWsQFKxBULAGQcEaBAVrEBSs+X+p/5GSKZTg7QAAAABJRU5ErkJggg==" /><!-- --></p>
 </div>
-<div id="the-function-legend.type" class="section level1" number="7">
-<h1><span class="header-section-number">7</span> The function
+<div id="the-function-legend.type" class="section level1" number="8">
+<h1><span class="header-section-number">8</span> The function
 <code>legend.type()</code></h1>
 <p><code>legend.type</code> adds a legend to the plot. A separate legend
 is created for each of the elements by setting each of
 <code>samples</code>, <code>means</code>, <code>bags</code> and
 <code>ellipses</code> equal to <code>TRUE</code>. Here, we add a legend
 for the samples.</p>
-<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes  =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">1</span>, <span class="at">show.class.means =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span></span>
-<span id="cb15-2"><a href="#cb15-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">density1D</span>() <span class="sc">|&gt;</span> <span class="fu">samples</span>(<span class="at">opacity=</span><span class="fl">0.5</span>)<span class="sc">|&gt;</span> <span class="fu">alpha.bags</span>()<span class="sc">|&gt;</span></span>
-<span id="cb15-3"><a href="#cb15-3" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span>
-<span id="cb15-4"><a href="#cb15-4" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for setosa </span></span>
-<span id="cb15-5"><a href="#cb15-5" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for versicolor </span></span>
-<span id="cb15-6"><a href="#cb15-6" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for virginica</span></span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
-<p>If other legends are added, they will overlap with the elements of
-the plot as displayed below.</p>
 <div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes  =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">1</span>, <span class="at">show.class.means =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span></span>
 <span id="cb16-2"><a href="#cb16-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">density1D</span>() <span class="sc">|&gt;</span> <span class="fu">samples</span>(<span class="at">opacity=</span><span class="fl">0.5</span>)<span class="sc">|&gt;</span> <span class="fu">alpha.bags</span>()<span class="sc">|&gt;</span></span>
-<span id="cb16-3"><a href="#cb16-3" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>,<span class="at">means =</span> <span class="cn">TRUE</span>, <span class="at">bags =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span>
+<span id="cb16-3"><a href="#cb16-3" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span>
 <span id="cb16-4"><a href="#cb16-4" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for setosa </span></span>
 <span id="cb16-5"><a href="#cb16-5" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for versicolor </span></span>
 <span id="cb16-6"><a href="#cb16-6" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for virginica</span></span></code></pre></div>
-<p><img 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" /><!-- --></p>
-<p>By specifying <code>new=TRUE</code>, the legends will be displayed on
-a new plot.</p>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>If other legends are added, they will overlap with the elements of
+the plot as displayed below.</p>
 <div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes  =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">1</span>, <span class="at">show.class.means =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span></span>
 <span id="cb17-2"><a href="#cb17-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">density1D</span>() <span class="sc">|&gt;</span> <span class="fu">samples</span>(<span class="at">opacity=</span><span class="fl">0.5</span>)<span class="sc">|&gt;</span> <span class="fu">alpha.bags</span>()<span class="sc">|&gt;</span></span>
-<span id="cb17-3"><a href="#cb17-3" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>,<span class="at">means =</span> <span class="cn">TRUE</span>, <span class="at">bags =</span> <span class="cn">TRUE</span>, <span class="at">new=</span><span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span>
+<span id="cb17-3"><a href="#cb17-3" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>,<span class="at">means =</span> <span class="cn">TRUE</span>, <span class="at">bags =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span>
 <span id="cb17-4"><a href="#cb17-4" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for setosa </span></span>
 <span id="cb17-5"><a href="#cb17-5" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for versicolor </span></span>
 <span id="cb17-6"><a href="#cb17-6" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for virginica</span></span></code></pre></div>
-<p><img 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" /><!-- --><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAqAAAAJACAMAAABlpiR1AAAAe1BMVEUAAAAAADoAAGYAAL8AAP8AOpAAZrYAvwAA/wA6AAA6ADo6AGY6Ojo6kNtmAABmADpmZmZmtrZmtv9/f/9//3+QOgCQkGaQ27aQ2/+2ZgC2tma225C2/7a2//+/oQDbkDrb/7bb////tmb/1wD/25D/63///7b//9v///8mnv5mAAAACXBIWXMAAA7DAAAOwwHHb6hkAAAQAElEQVR4nO3dfVvb2IHGYQ/dpDvdhbQkmcbtzNJ4E8L3/4TVq30MQRaS8Xm4et9/JBhDdHL0u2TL6ODNAwTb1B4ATBEo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBESw5081b8h8xTnf9cla3Okzy2Uu1xXmj7An0seWyl2uMUaCXJYyvVHqdAK0keW6n2OAVaSfLYSrXHKdBKksdWqj1OgVaSPLZS7XEKtJLksZVqj1OglSSPrVR7nAKtJHlspdrjFGglyWMr1R6nQCtJHlup9jgFWkny2Eq1xynQSpLHVqo9ToFWcs6x7W5nfM1m88uX8cbdcOP+pr3S7P3U99Wewxduf85UnGEzZ1J7cqeccWz3N6f3yq4JcjcWum0++PZr803f/vJl+tvqz+Hx9j9+/Dj51XOmYsZmLqX25E65bKA/Pl83f27fD1/f3rh79/Vhd/XHqe+sPYdH2//48UShAj2bFWP79mvzuNzuiOaRenPd3Wxj624U926Hv/tv6b6+77E/krZ/3k0+uq8d51mU2//48XGhC6bi9GYup/bkTjke239NOv7OLrZdM+F33SP1dX/YaD9xf/P+cG97uLwbH9T7x/LdUaDt1/zvsCvnjvPyJgNdMhWnN3M5tSd3yvKxjY/L/SN1c6vdK/1jeJPe/t4PX8YD50N50HzYH043t/c3zeHmYTtZaO05nAx0yVSc3szl1J7cKcvHdn9THgibiW/3Sj//3Y3D88rd/oHtKNDhJGl/3+QT0dpzOPkcdMlUzNjMxdSe3Ckrxvbjc/eUajesRyz2Sn8A6Z9wNc/Krv45HjaOHuK752RXv38YH/4njy2153D6LH7BVMzZzKXUntwpK8fWHAT3rxodHTbGe/uXkZo/utOHo5Ok3rf/GW5Mv9ZUew5Pb3/+VKzazGuoPblTVo6t2RP7l1SOnniNn+mOlrvxce3oZabe3buv/U57Qw/xP/XCqVi6mddQe3KnrDhJaqe+e5Go/aA5QnSnCOOp63hvG9/9zf4UvXyhvv2y/kZX7Ns5SXpi0VS8fDOvpvbkTlkxtvYZV9da++jdHh225Yt/473djzO3+xdXhp9u/vj8vv8JZ39H6guEc7e/aCpevpnXUntypySPrVR7nC4WqSR5bKXa4xRoJcljK9Uep0ArSR5bqfY4BVpJ8thKtccp0EqSx1aqPU6BVpI8tlLtcQq0klca20+v2H3uMt45y0Bqz+Gai2peMBUCfeySY3tmr8xaBlJ7Ds+8fYHOVT/QectAas/h8fY/ffq07p8T6FyLxzZc4dH+ALr/id79h982V38Myxv6HXA3PEgPP/MbrjMvvvrwD51aBlJ7Do+2/+nTUaFnmwqBPrV4bN1P0x+2774eljk0x71xeUO3A9p72kPieNVE+8nDx+1V9K15y0Bqz2G5/U+fjgs921QI9Knjsf33pOPvbI95zZwXyxyuy8UPt8PD9cPhurPmk8XH5QVOp5eB1J7DqUDPNhUCfWrd2eluvEh3WOawX/xwuGL3oVz7cFt+PPw785aB1J7DyUDPNRUCfWrF2JrzmuZh7WiZw37xQ7dXhvPw/dqH/V4pr+2duQyk9hxOPQc921QI9Kk114Ne/d4fOfqbh3nurtidc9h4wTKQ2nM4fRa/fip+uplLqT25U1aM7f7mr91zr2KZw/6jGU+8xq+etwyk9hxOb/9MUyHQp9aMbdu9cHJY5nB7WPywP3Vtz3B/fuq63yuzloHUnsMT2z/TVAj0iTVjGxaADcsc+nkeljecfvGv2CtzloHUnsMT2z/XVAj0seSxlWqP08UilSSPrVR7nAKtJHlspdrjFGglyWMr1R6nQCtJHlup9jgFWkny2Eq1xynQSpLHVqo9ToFWsnpsTy+9LT8z9cvaX/SGH7XncM72l0/FizZzfrUnd0q9sb3sDT9qz6EjaCXVxvbCN/yoPYfH2//+/fslNnMptSd3yuolH39vr4XoFy1sm4fp3/ofPt/f/O3m6XqHFW/4UXsOj7b//ftRoWun4rnNXEztyZ2yesnHv7p90F3+3uyY3WbcK/1vyzxa77DmDT9qz2G5/e/fjwtdOxXPbOZyak/ulOOx/f+k4+/cr3MYribrjyPbca9c7691HK81W/WGH7XncCrQtVPxzGYup/bkTlm95KOf99vxYFh+ZrgYstwRi9/wo/YcTga6ciqe2czl1J7cKauXfOz3wd2ze2U8MV/zhh+153DqOejaqXhuMxdTe3KnrF7yMf+wseoNP2rP4fRZ/OKpmN7MpdSe3ClnWfLR7YOhuKd7ZXziteoNP2rP4dwlH0umYvZmXkvtyZ2yesnHfh88OnU97JVxvcOqN/yoPYdzlnwsnorZm3kltSd3yuolH4e90j2P/Ef/RpVHe2V88W/NG37UnsM5Sz6WT8XczbyS2pM75dxjm/HW74vUnsMF218yFQJ97Hxj6554lb/G5axqz+GLtr98KgT62BnH1v1ijRlX7CxSew5ftv3FUyHQx5LHVqo9TlczVZI8tlLtcQq0kuSxlWqPU6CVJI+tVHucAq0keWyl2uMUaCXJYyvVHqdAK0keW6n2OAVaSfLYSrXHKdBKksdWqj1OgVayeSv+Q+apzn+uylZhJoESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gRJNoEQTKNEESjSBEk2gRBMo0QRKNIESTaBEEyjRBEo0gb59mwup85+rslXO6UL7UKAsI1CiCZRoAiWaQIkmUKIJlGgCJZpAiSZQogmUaAIlmkCJ9sJ9uLu9yGbORKBvX7EP/9Sb+ur7G4FyUQIl2nSg337dbDZtk3fN39fdzXdfH3bdjeLe7fD3rM1ckEDfvslAv/3aZLdr2rv75Utz47o/grafuL95f7h3+/6h+4p5m7kggb59k4Hurv7o/r6/ue5vtYH++Nzd+OXL/t4PX4aWZ23mggT69k0Gen/TN7jrDo9Ng22gfYrdjaHQ9itOPMYLlGWmn4P++Nw9u9wNK9+KQPtjaf/cs3mCevVPR1Bew+mz+G3zYD4+wTw6go73dh96iOdVnN6HTZT7V5eOnoOOn+mei+48xPMaJvdhV2H7R3eO3hwsu7Ol8Sx+vLc9eN7fdC88LdvMqxHo2ze9D9snn92hsn0dtD1QbsvXQcd779q/tpOvMwmUZVwsQjSBEk2gRBMo0QRKNIESTaBEEyjRlu/Dn15d/9wl9wJlmWIf/rm36p8TKOclUKJNBdpfQtddLNL/9P3+w2+bqz+GpUh9i+097x8exp/PD2tCiq9+spkLEujbNxXoj89tett3Xw9Lkt593S9F6lps72kvcRqvcGo/efi4+eqnm7kggb59kw/xd80BsMmvWJJ0XS5Uuh0WKz0crhFtPll8fLgCT6AsMxlodzwcL6gfliTtFyodrq5/KNcp3ZYf/2wzFyTQt2/6JGn7vn2EP1qStF+o1AX6l/4i0P06pX2g5XX4DwJlqRMXLF/93h9E+5uH5Lqr6x1BeXXT+/D+5q/d09BiSdL+oxnPQQXKWif24bZ7DemwJOn2sFBpfxbfnuz//CxeoKx1Yh8OizWHJUl9csNSpNOvgwqU1VwsQjSBEk2gRBMo0QRKNIESTaBEm7MPn16FXH5m1hsrCJRlin34f73X3swFCfTtEyjRpgIdl3z8vb0spF+/sd1sfvmt/zn8/c3fbp4u/XjmHWkEyjJTgY5LPv7V5diu39g2je42Y6D9b7Y9Wvrx3DvSCJRlJh/i90s+hgvr+kPqdgz0en/Z53jZ3bPvSCNQlpkMdFjy0Sd4Oy5HKj8zXBdaNvnTd6QRKMtMnyT1Sz72Od49G+iw9OPZd6QRKMvMWfIx/wj67DvSCJRl5i756HLs07t7Guj4HPTZd6QRKMvMWfKxz/HRWfwh0HHpx7PvSCNQlpmz5OMQaPsy59U/+jeVPQp0fB30uXekESjLLNiHu8N7yL7mZs5AoG/fi/Zh9xy0/I02r7OZsxHo2/eyfdj9jpEZFy+t3My5CPTtcz0o0QRKNIESTaBEEyjRBEo0gRJNoEQTKNE2F1LnP1dlqzCTQIkmUKIJlGgCJZpAiSZQogmUaAIlmkCJJlCiCZRoAiWaQIkmUKIJlGgCJZpAiSZQogmUaAIlmkCJJlCiCZRoAiWaQIkmUKIJlGgCJZpAiSZQogmUaAIlmkCJJlCiCZRoAiWaQIkmUKIJlGgCJZpAiSZQogmUaAIlmkCJJlCiCZRoAiWaQIkmUKIJlGgCJZpAiSZQogmUaAIlmkCJJlCiCZRoAiWaQIkmUKIJlGgCJZpAiSZQogmUaAIlmkCJJlCiCZRoAiWaQIkmUKIJlGgCJZpAiSZQogmUaAIlmkCJJlCiCZRoAiWaQIkmUKIJlGgCJZpAiSZQogmUaAIlmkCJJlCiCZRoAiXavwGcNDUgHIQr0QAAAABJRU5ErkJggg==" /><!-- --></p>
-<p>For the CVA biplot <code>legend.type</code> also displays a legend
-for classification regions if `</p>
-<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" tabindex="-1"></a>bp <span class="ot">&lt;-</span> <span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">CVA</span>(<span class="at">classes  =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">1</span>, <span class="at">show.class.means =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span></span>
-<span id="cb18-2"><a href="#cb18-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">classify</span>() <span class="sc">|&gt;</span> <span class="fu">density1D</span>() <span class="sc">|&gt;</span> <span class="fu">samples</span>(<span class="at">opacity=</span><span class="fl">0.5</span>)<span class="sc">|&gt;</span> <span class="fu">alpha.bags</span>()<span class="sc">|&gt;</span></span>
-<span id="cb18-3"><a href="#cb18-3" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>,<span class="at">means =</span> <span class="cn">TRUE</span>, <span class="at">bags =</span> <span class="cn">TRUE</span>, <span class="at">regions =</span> <span class="cn">TRUE</span>, <span class="at">new=</span><span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>() <span class="co">#</span></span>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>By specifying <code>new=TRUE</code>, the legends will be displayed on
+a new plot.</p>
+<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes  =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">1</span>, <span class="at">show.class.means =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span></span>
+<span id="cb18-2"><a href="#cb18-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">density1D</span>() <span class="sc">|&gt;</span> <span class="fu">samples</span>(<span class="at">opacity=</span><span class="fl">0.5</span>)<span class="sc">|&gt;</span> <span class="fu">alpha.bags</span>()<span class="sc">|&gt;</span></span>
+<span id="cb18-3"><a href="#cb18-3" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>,<span class="at">means =</span> <span class="cn">TRUE</span>, <span class="at">bags =</span> <span class="cn">TRUE</span>, <span class="at">new=</span><span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span>
 <span id="cb18-4"><a href="#cb18-4" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for setosa </span></span>
 <span id="cb18-5"><a href="#cb18-5" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for versicolor </span></span>
 <span id="cb18-6"><a href="#cb18-6" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for virginica</span></span></code></pre></div>
-<p><img 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" /><!-- --><img src="data:image/png;base64,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" 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-<pre><code>#&gt; [1] &quot;#0000FF66&quot; &quot;#00FF0066&quot; &quot;#FFD70066&quot;</code></pre>
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" /><!-- --><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>For the CVA biplot <code>legend.type</code> also displays a legend
+for classification regions if `</p>
+<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" tabindex="-1"></a>bp <span class="ot">&lt;-</span> <span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">CVA</span>(<span class="at">classes  =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">1</span>, <span class="at">show.class.means =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span></span>
+<span id="cb19-2"><a href="#cb19-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">classify</span>() <span class="sc">|&gt;</span> <span class="fu">density1D</span>() <span class="sc">|&gt;</span> <span class="fu">samples</span>(<span class="at">opacity=</span><span class="fl">0.5</span>)<span class="sc">|&gt;</span> <span class="fu">alpha.bags</span>()<span class="sc">|&gt;</span></span>
+<span id="cb19-3"><a href="#cb19-3" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>,<span class="at">means =</span> <span class="cn">TRUE</span>, <span class="at">bags =</span> <span class="cn">TRUE</span>, <span class="at">regions =</span> <span class="cn">TRUE</span>, <span class="at">new=</span><span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>() <span class="co">#</span></span>
+<span id="cb19-4"><a href="#cb19-4" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for setosa </span></span>
+<span id="cb19-5"><a href="#cb19-5" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for versicolor </span></span>
+<span id="cb19-6"><a href="#cb19-6" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for virginica</span></span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --><img role="img" 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/><!-- --></p>
 </div>
-<div id="fit-measures" class="section level1" number="8">
-<h1><span class="header-section-number">8</span> Fit measures</h1>
+<div id="the-function-fit.measures" class="section level1" number="9">
+<h1><span class="header-section-number">9</span> The function
+<code>fit.measures()</code></h1>
 <p><code>fit.measures()</code> calculates measures of fit for the
 biplot. Passing a biplot object which has been piped to
 <code>fit.measures()</code> to <code>summary()</code> will output:</p>
@@ -628,14 +641,14 @@ <h1><span class="header-section-number">8</span> Fit measures</h1>
 <span id="cb20-4"><a href="#cb20-4" tabindex="-1"></a><span class="co">#&gt; 4 numeric variables.</span></span>
 <span id="cb20-5"><a href="#cb20-5" tabindex="-1"></a><span class="co">#&gt; 1 categorical variable.</span></span>
 <span id="cb20-6"><a href="#cb20-6" tabindex="-1"></a><span class="co">#&gt; </span></span>
-<span id="cb20-7"><a href="#cb20-7" tabindex="-1"></a><span class="co">#&gt; Quality of fit = 92.5% </span></span>
-<span id="cb20-8"><a href="#cb20-8" tabindex="-1"></a><span class="co">#&gt; Adequacy of variables:</span></span>
+<span id="cb20-7"><a href="#cb20-7" tabindex="-1"></a><span class="co">#&gt; Quality of fit in 1 dimension(s) = 92.5% </span></span>
+<span id="cb20-8"><a href="#cb20-8" tabindex="-1"></a><span class="co">#&gt; Adequacy of variables in 1 dimension(s):</span></span>
 <span id="cb20-9"><a href="#cb20-9" tabindex="-1"></a><span class="co">#&gt; Sepal.Length  Sepal.Width Petal.Length  Petal.Width </span></span>
 <span id="cb20-10"><a href="#cb20-10" tabindex="-1"></a><span class="co">#&gt;  0.130600269  0.007144055  0.733884527  0.128371149 </span></span>
-<span id="cb20-11"><a href="#cb20-11" tabindex="-1"></a><span class="co">#&gt; Axis predictivity:</span></span>
+<span id="cb20-11"><a href="#cb20-11" tabindex="-1"></a><span class="co">#&gt; Axis predictivity in 1 dimension(s):</span></span>
 <span id="cb20-12"><a href="#cb20-12" tabindex="-1"></a><span class="co">#&gt; Sepal.Length  Sepal.Width Petal.Length  Petal.Width </span></span>
 <span id="cb20-13"><a href="#cb20-13" tabindex="-1"></a><span class="co">#&gt;    0.8053299    0.1590003    0.9957524    0.9342141 </span></span>
-<span id="cb20-14"><a href="#cb20-14" tabindex="-1"></a><span class="co">#&gt; Sample predictivity:</span></span>
+<span id="cb20-14"><a href="#cb20-14" tabindex="-1"></a><span class="co">#&gt; Sample predictivity in 1 dimension(s):</span></span>
 <span id="cb20-15"><a href="#cb20-15" tabindex="-1"></a><span class="co">#&gt;            1            2            3            4            5            6 </span></span>
 <span id="cb20-16"><a href="#cb20-16" tabindex="-1"></a><span class="co">#&gt; 0.9859320755 0.9885358364 0.9974032622 0.9858701194 0.9843168833 0.8999107868 </span></span>
 <span id="cb20-17"><a href="#cb20-17" tabindex="-1"></a><span class="co">#&gt;            7            8            9           10           11           12 </span></span>
@@ -687,8 +700,8 @@ <h1><span class="header-section-number">8</span> Fit measures</h1>
 <span id="cb20-63"><a href="#cb20-63" tabindex="-1"></a><span class="co">#&gt;          145          146          147          148          149          150 </span></span>
 <span id="cb20-64"><a href="#cb20-64" tabindex="-1"></a><span class="co">#&gt; 0.9351760753 0.9383233979 0.9136490692 0.9866832123 0.8702674447 0.8913242393</span></span></code></pre></div>
 </div>
-<div id="references" class="section level1" number="9">
-<h1><span class="header-section-number">9</span> References</h1>
+<div id="references" class="section level1" number="10">
+<h1><span class="header-section-number">10</span> References</h1>
 </div>
 
 
diff --git a/vignettes/Biplots_in_3D.html b/vignettes/Biplots_in_3D.html
deleted file mode 100644
index 4b0f394..0000000
--- a/vignettes/Biplots_in_3D.html
+++ /dev/null
@@ -1,9393 +0,0 @@
-<!DOCTYPE html>
-
-<html>
-
-<head>
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-  // delegateMethod(a, b, "method2");
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-  // include - if true, only return elements with given className;
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-
-  // @param tasks Array of strings (or falsy value, in which case no-op).
-  //   Each element must be a valid JavaScript expression that yields a
-  //   function. Or, can be an array of objects with "code" and "data"
-  //   properties; in this case, the "code" property should be a string
-  //   of JS that's an expr that yields a function, and "data" should be
-  //   an object that will be added as an additional argument when that
-  //   function is called.
-  // @param target The object that will be "this" for each function
-  //   execution.
-  // @param args Array of arguments to be passed to the functions. (The
-  //   same arguments will be passed to all functions.)
-  function evalAndRun(tasks, target, args) {
-    if (tasks) {
-      forEach(tasks, function(task) {
-        var theseArgs = args;
-        if (typeof(task) === "object") {
-          theseArgs = theseArgs.concat([task.data]);
-          task = task.code;
-        }
-        var taskFunc = tryEval(task);
-        if (typeof(taskFunc) !== "function") {
-          throw new Error("Task must be a function! Source:\n" + task);
-        }
-        taskFunc.apply(target, theseArgs);
-      });
-    }
-  }
-
-  // Attempt eval() both with and without enclosing in parentheses.
-  // Note that enclosing coerces a function declaration into
-  // an expression that eval() can parse
-  // (otherwise, a SyntaxError is thrown)
-  function tryEval(code) {
-    var result = null;
-    try {
-      result = eval("(" + code + ")");
-    } catch(error) {
-      if (!(error instanceof SyntaxError)) {
-        throw error;
-      }
-      try {
-        result = eval(code);
-      } catch(e) {
-        if (e instanceof SyntaxError) {
-          throw error;
-        } else {
-          throw e;
-        }
-      }
-    }
-    return result;
-  }
-
-  function initSizing(el) {
-    var sizing = sizingPolicy(el);
-    if (!sizing)
-      return;
-
-    var cel = document.getElementById("htmlwidget_container");
-    if (!cel)
-      return;
-
-    if (typeof(sizing.padding) !== "undefined") {
-      document.body.style.margin = "0";
-      document.body.style.padding = paddingToCss(unpackPadding(sizing.padding));
-    }
-
-    if (sizing.fill) {
-      document.body.style.overflow = "hidden";
-      document.body.style.width = "100%";
-      document.body.style.height = "100%";
-      document.documentElement.style.width = "100%";
-      document.documentElement.style.height = "100%";
-      cel.style.position = "absolute";
-      var pad = unpackPadding(sizing.padding);
-      cel.style.top = pad.top + "px";
-      cel.style.right = pad.right + "px";
-      cel.style.bottom = pad.bottom + "px";
-      cel.style.left = pad.left + "px";
-      el.style.width = "100%";
-      el.style.height = "100%";
-
-      return {
-        getWidth: function() { return cel.getBoundingClientRect().width; },
-        getHeight: function() { return cel.getBoundingClientRect().height; }
-      };
-
-    } else {
-      el.style.width = px(sizing.width);
-      el.style.height = px(sizing.height);
-
-      return {
-        getWidth: function() { return cel.getBoundingClientRect().width; },
-        getHeight: function() { return cel.getBoundingClientRect().height; }
-      };
-    }
-  }
-
-  // Default implementations for methods
-  var defaults = {
-    find: function(scope) {
-      return querySelectorAll(scope, "." + this.name);
-    },
-    renderError: function(el, err) {
-      var $el = $(el);
-
-      this.clearError(el);
-
-      // Add all these error classes, as Shiny does
-      var errClass = "shiny-output-error";
-      if (err.type !== null) {
-        // use the classes of the error condition as CSS class names
-        errClass = errClass + " " + $.map(asArray(err.type), function(type) {
-          return errClass + "-" + type;
-        }).join(" ");
-      }
-      errClass = errClass + " htmlwidgets-error";
-
-      // Is el inline or block? If inline or inline-block, just display:none it
-      // and add an inline error.
-      var display = $el.css("display");
-      $el.data("restore-display-mode", display);
-
-      if (display === "inline" || display === "inline-block") {
-        $el.hide();
-        if (err.message !== "") {
-          var errorSpan = $("<span>").addClass(errClass);
-          errorSpan.text(err.message);
-          $el.after(errorSpan);
-        }
-      } else if (display === "block") {
-        // If block, add an error just after the el, set visibility:none on the
-        // el, and position the error to be on top of the el.
-        // Mark it with a unique ID and CSS class so we can remove it later.
-        $el.css("visibility", "hidden");
-        if (err.message !== "") {
-          var errorDiv = $("<div>").addClass(errClass).css("position", "absolute")
-            .css("top", el.offsetTop)
-            .css("left", el.offsetLeft)
-            // setting width can push out the page size, forcing otherwise
-            // unnecessary scrollbars to appear and making it impossible for
-            // the element to shrink; so use max-width instead
-            .css("maxWidth", el.offsetWidth)
-            .css("height", el.offsetHeight);
-          errorDiv.text(err.message);
-          $el.after(errorDiv);
-
-          // Really dumb way to keep the size/position of the error in sync with
-          // the parent element as the window is resized or whatever.
-          var intId = setInterval(function() {
-            if (!errorDiv[0].parentElement) {
-              clearInterval(intId);
-              return;
-            }
-            errorDiv
-              .css("top", el.offsetTop)
-              .css("left", el.offsetLeft)
-              .css("maxWidth", el.offsetWidth)
-              .css("height", el.offsetHeight);
-          }, 500);
-        }
-      }
-    },
-    clearError: function(el) {
-      var $el = $(el);
-      var display = $el.data("restore-display-mode");
-      $el.data("restore-display-mode", null);
-
-      if (display === "inline" || display === "inline-block") {
-        if (display)
-          $el.css("display", display);
-        $(el.nextSibling).filter(".htmlwidgets-error").remove();
-      } else if (display === "block"){
-        $el.css("visibility", "inherit");
-        $(el.nextSibling).filter(".htmlwidgets-error").remove();
-      }
-    },
-    sizing: {}
-  };
-
-  // Called by widget bindings to register a new type of widget. The definition
-  // object can contain the following properties:
-  // - name (required) - A string indicating the binding name, which will be
-  //   used by default as the CSS classname to look for.
-  // - initialize (optional) - A function(el) that will be called once per
-  //   widget element; if a value is returned, it will be passed as the third
-  //   value to renderValue.
-  // - renderValue (required) - A function(el, data, initValue) that will be
-  //   called with data. Static contexts will cause this to be called once per
-  //   element; Shiny apps will cause this to be called multiple times per
-  //   element, as the data changes.
-  window.HTMLWidgets.widget = function(definition) {
-    if (!definition.name) {
-      throw new Error("Widget must have a name");
-    }
-    if (!definition.type) {
-      throw new Error("Widget must have a type");
-    }
-    // Currently we only support output widgets
-    if (definition.type !== "output") {
-      throw new Error("Unrecognized widget type '" + definition.type + "'");
-    }
-    // TODO: Verify that .name is a valid CSS classname
-
-    // Support new-style instance-bound definitions. Old-style class-bound
-    // definitions have one widget "object" per widget per type/class of
-    // widget; the renderValue and resize methods on such widget objects
-    // take el and instance arguments, because the widget object can't
-    // store them. New-style instance-bound definitions have one widget
-    // object per widget instance; the definition that's passed in doesn't
-    // provide renderValue or resize methods at all, just the single method
-    //   factory(el, width, height)
-    // which returns an object that has renderValue(x) and resize(w, h).
-    // This enables a far more natural programming style for the widget
-    // author, who can store per-instance state using either OO-style
-    // instance fields or functional-style closure variables (I guess this
-    // is in contrast to what can only be called C-style pseudo-OO which is
-    // what we required before).
-    if (definition.factory) {
-      definition = createLegacyDefinitionAdapter(definition);
-    }
-
-    if (!definition.renderValue) {
-      throw new Error("Widget must have a renderValue function");
-    }
-
-    // For static rendering (non-Shiny), use a simple widget registration
-    // scheme. We also use this scheme for Shiny apps/documents that also
-    // contain static widgets.
-    window.HTMLWidgets.widgets = window.HTMLWidgets.widgets || [];
-    // Merge defaults into the definition; don't mutate the original definition.
-    var staticBinding = extend({}, defaults, definition);
-    overrideMethod(staticBinding, "find", function(superfunc) {
-      return function(scope) {
-        var results = superfunc(scope);
-        // Filter out Shiny outputs, we only want the static kind
-        return filterByClass(results, "html-widget-output", false);
-      };
-    });
-    window.HTMLWidgets.widgets.push(staticBinding);
-
-    if (shinyMode) {
-      // Shiny is running. Register the definition with an output binding.
-      // The definition itself will not be the output binding, instead
-      // we will make an output binding object that delegates to the
-      // definition. This is because we foolishly used the same method
-      // name (renderValue) for htmlwidgets definition and Shiny bindings
-      // but they actually have quite different semantics (the Shiny
-      // bindings receive data that includes lots of metadata that it
-      // strips off before calling htmlwidgets renderValue). We can't
-      // just ignore the difference because in some widgets it's helpful
-      // to call this.renderValue() from inside of resize(), and if
-      // we're not delegating, then that call will go to the Shiny
-      // version instead of the htmlwidgets version.
-
-      // Merge defaults with definition, without mutating either.
-      var bindingDef = extend({}, defaults, definition);
-
-      // This object will be our actual Shiny binding.
-      var shinyBinding = new Shiny.OutputBinding();
-
-      // With a few exceptions, we'll want to simply use the bindingDef's
-      // version of methods if they are available, otherwise fall back to
-      // Shiny's defaults. NOTE: If Shiny's output bindings gain additional
-      // methods in the future, and we want them to be overrideable by
-      // HTMLWidget binding definitions, then we'll need to add them to this
-      // list.
-      delegateMethod(shinyBinding, bindingDef, "getId");
-      delegateMethod(shinyBinding, bindingDef, "onValueChange");
-      delegateMethod(shinyBinding, bindingDef, "onValueError");
-      delegateMethod(shinyBinding, bindingDef, "renderError");
-      delegateMethod(shinyBinding, bindingDef, "clearError");
-      delegateMethod(shinyBinding, bindingDef, "showProgress");
-
-      // The find, renderValue, and resize are handled differently, because we
-      // want to actually decorate the behavior of the bindingDef methods.
-
-      shinyBinding.find = function(scope) {
-        var results = bindingDef.find(scope);
-
-        // Only return elements that are Shiny outputs, not static ones
-        var dynamicResults = results.filter(".html-widget-output");
-
-        // It's possible that whatever caused Shiny to think there might be
-        // new dynamic outputs, also caused there to be new static outputs.
-        // Since there might be lots of different htmlwidgets bindings, we
-        // schedule execution for later--no need to staticRender multiple
-        // times.
-        if (results.length !== dynamicResults.length)
-          scheduleStaticRender();
-
-        return dynamicResults;
-      };
-
-      // Wrap renderValue to handle initialization, which unfortunately isn't
-      // supported natively by Shiny at the time of this writing.
-
-      shinyBinding.renderValue = function(el, data) {
-        Shiny.renderDependencies(data.deps);
-        // Resolve strings marked as javascript literals to objects
-        if (!(data.evals instanceof Array)) data.evals = [data.evals];
-        for (var i = 0; data.evals && i < data.evals.length; i++) {
-          window.HTMLWidgets.evaluateStringMember(data.x, data.evals[i]);
-        }
-        if (!bindingDef.renderOnNullValue) {
-          if (data.x === null) {
-            el.style.visibility = "hidden";
-            return;
-          } else {
-            el.style.visibility = "inherit";
-          }
-        }
-        if (!elementData(el, "initialized")) {
-          initSizing(el);
-
-          elementData(el, "initialized", true);
-          if (bindingDef.initialize) {
-            var rect = el.getBoundingClientRect();
-            var result = bindingDef.initialize(el, rect.width, rect.height);
-            elementData(el, "init_result", result);
-          }
-        }
-        bindingDef.renderValue(el, data.x, elementData(el, "init_result"));
-        evalAndRun(data.jsHooks.render, elementData(el, "init_result"), [el, data.x]);
-      };
-
-      // Only override resize if bindingDef implements it
-      if (bindingDef.resize) {
-        shinyBinding.resize = function(el, width, height) {
-          // Shiny can call resize before initialize/renderValue have been
-          // called, which doesn't make sense for widgets.
-          if (elementData(el, "initialized")) {
-            bindingDef.resize(el, width, height, elementData(el, "init_result"));
-          }
-        };
-      }
-
-      Shiny.outputBindings.register(shinyBinding, bindingDef.name);
-    }
-  };
-
-  var scheduleStaticRenderTimerId = null;
-  function scheduleStaticRender() {
-    if (!scheduleStaticRenderTimerId) {
-      scheduleStaticRenderTimerId = setTimeout(function() {
-        scheduleStaticRenderTimerId = null;
-        window.HTMLWidgets.staticRender();
-      }, 1);
-    }
-  }
-
-  // Render static widgets after the document finishes loading
-  // Statically render all elements that are of this widget's class
-  window.HTMLWidgets.staticRender = function() {
-    var bindings = window.HTMLWidgets.widgets || [];
-    forEach(bindings, function(binding) {
-      var matches = binding.find(document.documentElement);
-      forEach(matches, function(el) {
-        var sizeObj = initSizing(el, binding);
-
-        var getSize = function(el) {
-          if (sizeObj) {
-            return {w: sizeObj.getWidth(), h: sizeObj.getHeight()}
-          } else {
-            var rect = el.getBoundingClientRect();
-            return {w: rect.width, h: rect.height}
-          }
-        };
-
-        if (hasClass(el, "html-widget-static-bound"))
-          return;
-        el.className = el.className + " html-widget-static-bound";
-
-        var initResult;
-        if (binding.initialize) {
-          var size = getSize(el);
-          initResult = binding.initialize(el, size.w, size.h);
-          elementData(el, "init_result", initResult);
-        }
-
-        if (binding.resize) {
-          var lastSize = getSize(el);
-          var resizeHandler = function(e) {
-            var size = getSize(el);
-            if (size.w === 0 && size.h === 0)
-              return;
-            if (size.w === lastSize.w && size.h === lastSize.h)
-              return;
-            lastSize = size;
-            binding.resize(el, size.w, size.h, initResult);
-          };
-
-          on(window, "resize", resizeHandler);
-
-          // This is needed for cases where we're running in a Shiny
-          // app, but the widget itself is not a Shiny output, but
-          // rather a simple static widget. One example of this is
-          // an rmarkdown document that has runtime:shiny and widget
-          // that isn't in a render function. Shiny only knows to
-          // call resize handlers for Shiny outputs, not for static
-          // widgets, so we do it ourselves.
-          if (window.jQuery) {
-            window.jQuery(document).on(
-              "shown.htmlwidgets shown.bs.tab.htmlwidgets shown.bs.collapse.htmlwidgets",
-              resizeHandler
-            );
-            window.jQuery(document).on(
-              "hidden.htmlwidgets hidden.bs.tab.htmlwidgets hidden.bs.collapse.htmlwidgets",
-              resizeHandler
-            );
-          }
-
-          // This is needed for the specific case of ioslides, which
-          // flips slides between display:none and display:block.
-          // Ideally we would not have to have ioslide-specific code
-          // here, but rather have ioslides raise a generic event,
-          // but the rmarkdown package just went to CRAN so the
-          // window to getting that fixed may be long.
-          if (window.addEventListener) {
-            // It's OK to limit this to window.addEventListener
-            // browsers because ioslides itself only supports
-            // such browsers.
-            on(document, "slideenter", resizeHandler);
-            on(document, "slideleave", resizeHandler);
-          }
-        }
-
-        var scriptData = document.querySelector("script[data-for='" + el.id + "'][type='application/json']");
-        if (scriptData) {
-          var data = JSON.parse(scriptData.textContent || scriptData.text);
-          // Resolve strings marked as javascript literals to objects
-          if (!(data.evals instanceof Array)) data.evals = [data.evals];
-          for (var k = 0; data.evals && k < data.evals.length; k++) {
-            window.HTMLWidgets.evaluateStringMember(data.x, data.evals[k]);
-          }
-          binding.renderValue(el, data.x, initResult);
-          evalAndRun(data.jsHooks.render, initResult, [el, data.x]);
-        }
-      });
-    });
-
-    invokePostRenderHandlers();
-  }
-
-
-  function has_jQuery3() {
-    if (!window.jQuery) {
-      return false;
-    }
-    var $version = window.jQuery.fn.jquery;
-    var $major_version = parseInt($version.split(".")[0]);
-    return $major_version >= 3;
-  }
-
-  /*
-  / Shiny 1.4 bumped jQuery from 1.x to 3.x which means jQuery's
-  / on-ready handler (i.e., $(fn)) is now asyncronous (i.e., it now
-  / really means $(setTimeout(fn)).
-  / https://jquery.com/upgrade-guide/3.0/#breaking-change-document-ready-handlers-are-now-asynchronous
-  /
-  / Since Shiny uses $() to schedule initShiny, shiny>=1.4 calls initShiny
-  / one tick later than it did before, which means staticRender() is
-  / called renderValue() earlier than (advanced) widget authors might be expecting.
-  / https://github.com/rstudio/shiny/issues/2630
-  /
-  / For a concrete example, leaflet has some methods (e.g., updateBounds)
-  / which reference Shiny methods registered in initShiny (e.g., setInputValue).
-  / Since leaflet is privy to this life-cycle, it knows to use setTimeout() to
-  / delay execution of those methods (until Shiny methods are ready)
-  / https://github.com/rstudio/leaflet/blob/18ec981/javascript/src/index.js#L266-L268
-  /
-  / Ideally widget authors wouldn't need to use this setTimeout() hack that
-  / leaflet uses to call Shiny methods on a staticRender(). In the long run,
-  / the logic initShiny should be broken up so that method registration happens
-  / right away, but binding happens later.
-  */
-  function maybeStaticRenderLater() {
-    if (shinyMode && has_jQuery3()) {
-      window.jQuery(window.HTMLWidgets.staticRender);
-    } else {
-      window.HTMLWidgets.staticRender();
-    }
-  }
-
-  if (document.addEventListener) {
-    document.addEventListener("DOMContentLoaded", function() {
-      document.removeEventListener("DOMContentLoaded", arguments.callee, false);
-      maybeStaticRenderLater();
-    }, false);
-  } else if (document.attachEvent) {
-    document.attachEvent("onreadystatechange", function() {
-      if (document.readyState === "complete") {
-        document.detachEvent("onreadystatechange", arguments.callee);
-        maybeStaticRenderLater();
-      }
-    });
-  }
-
-
-  window.HTMLWidgets.getAttachmentUrl = function(depname, key) {
-    // If no key, default to the first item
-    if (typeof(key) === "undefined")
-      key = 1;
-
-    var link = document.getElementById(depname + "-" + key + "-attachment");
-    if (!link) {
-      throw new Error("Attachment " + depname + "/" + key + " not found in document");
-    }
-    return link.getAttribute("href");
-  };
-
-  window.HTMLWidgets.dataframeToD3 = function(df) {
-    var names = [];
-    var length;
-    for (var name in df) {
-        if (df.hasOwnProperty(name))
-            names.push(name);
-        if (typeof(df[name]) !== "object" || typeof(df[name].length) === "undefined") {
-            throw new Error("All fields must be arrays");
-        } else if (typeof(length) !== "undefined" && length !== df[name].length) {
-            throw new Error("All fields must be arrays of the same length");
-        }
-        length = df[name].length;
-    }
-    var results = [];
-    var item;
-    for (var row = 0; row < length; row++) {
-        item = {};
-        for (var col = 0; col < names.length; col++) {
-            item[names[col]] = df[names[col]][row];
-        }
-        results.push(item);
-    }
-    return results;
-  };
-
-  window.HTMLWidgets.transposeArray2D = function(array) {
-      if (array.length === 0) return array;
-      var newArray = array[0].map(function(col, i) {
-          return array.map(function(row) {
-              return row[i]
-          })
-      });
-      return newArray;
-  };
-  // Split value at splitChar, but allow splitChar to be escaped
-  // using escapeChar. Any other characters escaped by escapeChar
-  // will be included as usual (including escapeChar itself).
-  function splitWithEscape(value, splitChar, escapeChar) {
-    var results = [];
-    var escapeMode = false;
-    var currentResult = "";
-    for (var pos = 0; pos < value.length; pos++) {
-      if (!escapeMode) {
-        if (value[pos] === splitChar) {
-          results.push(currentResult);
-          currentResult = "";
-        } else if (value[pos] === escapeChar) {
-          escapeMode = true;
-        } else {
-          currentResult += value[pos];
-        }
-      } else {
-        currentResult += value[pos];
-        escapeMode = false;
-      }
-    }
-    if (currentResult !== "") {
-      results.push(currentResult);
-    }
-    return results;
-  }
-  // Function authored by Yihui/JJ Allaire
-  window.HTMLWidgets.evaluateStringMember = function(o, member) {
-    var parts = splitWithEscape(member, '.', '\\');
-    for (var i = 0, l = parts.length; i < l; i++) {
-      var part = parts[i];
-      // part may be a character or 'numeric' member name
-      if (o !== null && typeof o === "object" && part in o) {
-        if (i == (l - 1)) { // if we are at the end of the line then evalulate
-          if (typeof o[part] === "string")
-            o[part] = tryEval(o[part]);
-        } else { // otherwise continue to next embedded object
-          o = o[part];
-        }
-      }
-    }
-  };
-
-  // Retrieve the HTMLWidget instance (i.e. the return value of an
-  // HTMLWidget binding's initialize() or factory() function)
-  // associated with an element, or null if none.
-  window.HTMLWidgets.getInstance = function(el) {
-    return elementData(el, "init_result");
-  };
-
-  // Finds the first element in the scope that matches the selector,
-  // and returns the HTMLWidget instance (i.e. the return value of
-  // an HTMLWidget binding's initialize() or factory() function)
-  // associated with that element, if any. If no element matches the
-  // selector, or the first matching element has no HTMLWidget
-  // instance associated with it, then null is returned.
-  //
-  // The scope argument is optional, and defaults to window.document.
-  window.HTMLWidgets.find = function(scope, selector) {
-    if (arguments.length == 1) {
-      selector = scope;
-      scope = document;
-    }
-
-    var el = scope.querySelector(selector);
-    if (el === null) {
-      return null;
-    } else {
-      return window.HTMLWidgets.getInstance(el);
-    }
-  };
-
-  // Finds all elements in the scope that match the selector, and
-  // returns the HTMLWidget instances (i.e. the return values of
-  // an HTMLWidget binding's initialize() or factory() function)
-  // associated with the elements, in an array. If elements that
-  // match the selector don't have an associated HTMLWidget
-  // instance, the returned array will contain nulls.
-  //
-  // The scope argument is optional, and defaults to window.document.
-  window.HTMLWidgets.findAll = function(scope, selector) {
-    if (arguments.length == 1) {
-      selector = scope;
-      scope = document;
-    }
-
-    var nodes = scope.querySelectorAll(selector);
-    var results = [];
-    for (var i = 0; i < nodes.length; i++) {
-      results.push(window.HTMLWidgets.getInstance(nodes[i]));
-    }
-    return results;
-  };
-
-  var postRenderHandlers = [];
-  function invokePostRenderHandlers() {
-    while (postRenderHandlers.length) {
-      var handler = postRenderHandlers.shift();
-      if (handler) {
-        handler();
-      }
-    }
-  }
-
-  // Register the given callback function to be invoked after the
-  // next time static widgets are rendered.
-  window.HTMLWidgets.addPostRenderHandler = function(callback) {
-    postRenderHandlers.push(callback);
-  };
-
-  // Takes a new-style instance-bound definition, and returns an
-  // old-style class-bound definition. This saves us from having
-  // to rewrite all the logic in this file to accomodate both
-  // types of definitions.
-  function createLegacyDefinitionAdapter(defn) {
-    var result = {
-      name: defn.name,
-      type: defn.type,
-      initialize: function(el, width, height) {
-        return defn.factory(el, width, height);
-      },
-      renderValue: function(el, x, instance) {
-        return instance.renderValue(x);
-      },
-      resize: function(el, width, height, instance) {
-        return instance.resize(width, height);
-      }
-    };
-
-    if (defn.find)
-      result.find = defn.find;
-    if (defn.renderError)
-      result.renderError = defn.renderError;
-    if (defn.clearError)
-      result.clearError = defn.clearError;
-
-    return result;
-  }
-})();
-</script>
-<script>/* el is the div, holding the rgl object as el.rglinstance,
-     which holds x as el.rglinstance.scene
-   x is the JSON encoded rglwidget.
-*/
-
-
-HTMLWidgets.widget({
-
-  name: 'rglWebGL',
-
-  type: 'output',
-
-  factory: function(el, width, height) {
-    el.width = width;
-    el.height = height;
-    var rgl = new rglwidgetClass(),
-        onchangeselection = function(e) {
-          for (var i = 0; i < rgl.scene.crosstalk.sel_handle.length; i++)
-            rgl.clearBrush(except = e.rglSubsceneId);
-          rgl.selection(e, false);
-        },
-        onchangefilter = function(e) {
-          rgl.selection(e, true);
-        };
-    
-    return { 
-      renderValue: function(x) {
-        var i, pel, player, groups,
-            inShiny = (typeof Shiny !== "undefined");
-      
-        x.crosstalk.group = groups = [].concat(x.crosstalk.group);
-        x.crosstalk.id = [].concat(x.crosstalk.id);
-        x.crosstalk.key = [].concat(x.crosstalk.key);
-        x.crosstalk.sel_handle = new Array(groups.length);
-        x.crosstalk.fil_handle = new Array(groups.length);
-        x.crosstalk.selection = [];
-        for (i = 0; i < groups.length; i++) {
-          x.crosstalk.sel_handle[i] = new crosstalk.SelectionHandle(groups[i], {sharedId: x.crosstalk.id[i]});
-          x.crosstalk.sel_handle[i].on("change", onchangeselection);
-          x.crosstalk.fil_handle[i] = new crosstalk.FilterHandle(groups[i], {sharedId: x.crosstalk.id[i]});
-          x.crosstalk.fil_handle[i].on("change", onchangefilter);
-        }
-        if (inShiny) {
-          // Shiny calls this multiple times, so we need extra cleanup
-          // between
-          rgl.sphere = undefined;
-        }
-        rgl.initialize(el, x);
-        rgl.initGL();
-  
-  /* We might have been called after (some of) the players were rendered.
-     We need to make sure we respond to their initial values. */
-
-        if (typeof x.players !== "undefined") {
-          var players = [].concat(x.players);
-          for (i = 0; i < players.length; i++) {
-            pel = document.getElementById(players[i]);
-            if (pel) {
-              player = pel.rglPlayer;
-              if (player && (!player.initialized || inShiny)) {
-                rgl.Player(pel, player);
-                player.initialized = true;
-              }
-            }
-          }
-        }
-        rgl.drag = 0;
-        rgl.drawScene();
-      },
-
-      resize: function(width, height) {
-        el.width = width;
-        el.height = height;
-        el.rglinstance.resize(el);
-        el.rglinstance.drawScene();
-      }
-    };
-  }
-});
-</script>
-<style type="text/css">.rglPlayer {
-width: auto;
-height: auto;
-}
-.rglPlayer .rgl-button {
-width: auto;
-display: inline-block;
-font-size: 75%;
-}
-.rglPlayer .rgl-slider {
-display: inline-block;
-width: 30%;
-}
-.rglPlayer .rgl-label {
-display: inline;
-padding-left: 6px;
-padding-right: 6px;
-}
-</style>
-<script>//// To generate the help pages for this library, use
-
-// jsdoc --template /usr/local/lib/node_modules/foodoc/template *.src.js -R README.md -c JSDoc.json
-
-// To test, set environment variable RGL_DEBUGGING=true
-// before building.
-
-/* globals rglwidgetClass: true */
-
-/**
- * The class of an rgl widget
- * @class
-*/
-rglwidgetClass = function() {
-    this.canvas = null;
-    this.userMatrix = new CanvasMatrix4();
-    this.types = [];
-    this.prMatrix = new CanvasMatrix4();
-    this.mvMatrix = new CanvasMatrix4();
-    this.vp = null;
-    this.prmvMatrix = null;
-    this.origs = null;
-    this.gl = null;
-    this.scene = null;
-    this.select = {state: "inactive", subscene: null, region: {p1: {x:0, y:0}, p2: {x:0, y:0}}};
-    this.drawing = false;
-};
-
-    rglwidgetClass.f_is_lit = 1;
-    rglwidgetClass.f_is_smooth = 2;
-    rglwidgetClass.f_has_texture = 4;
-    rglwidgetClass.f_depth_sort = 8;
-    rglwidgetClass.f_fixed_quads = 16;
-    rglwidgetClass.f_is_transparent = 32;
-    rglwidgetClass.f_is_lines = 64;
-    rglwidgetClass.f_sprites_3d = 128;
-    rglwidgetClass.f_is_subscene = 256;
-    rglwidgetClass.f_is_clipplanes = 512;
-    rglwidgetClass.f_fixed_size = 1024;
-    rglwidgetClass.f_is_points = 2048;
-    rglwidgetClass.f_is_twosided = 4096;
-    rglwidgetClass.f_fat_lines = 8192;
-    rglwidgetClass.f_is_brush = 16384;
-    rglwidgetClass.f_has_fog = 32768;
-    rglwidgetClass.f_rotating = 65536;
-    
-    rglwidgetClass.prototype.fogNone = 0;
-    rglwidgetClass.prototype.fogLinear = 1;
-    rglwidgetClass.prototype.fogExp = 2;
-    rglwidgetClass.prototype.fogExp2 = 3;
-
-    /**
-     * Methods related to obsolete approaches.
-     * @name ___OBSOLETE_METHODS___
-     * @memberof rglwidgetClass
-     * @kind function
-     * @instance
-     */
-     
-    /**
-     * Start the writeWebGL scene. This is only used by writeWebGL; rglwidget has
-       no debug element.
-     */
-    rglwidgetClass.prototype.start = function() {
-      if (typeof this.prefix !== "undefined") {
-        this.debugelement = document.getElementById(this.prefix + "debug");
-        this.debug("");
-      }
-      this.drag = 0;
-      this.drawScene();
-    };
-</script>
-<script>    /**
-     * Utility methods
-     * @name ___UTILITY_METHODS___
-     * @memberof rglwidgetClass
-     * @kind function
-     * @instance
-     */
-     
-    /**
-     * Multiply matrix by vector
-     * @returns {number[]}
-     * @param M {number[][]} Left operand
-     * @param v {number[]} Right operand
-     */
-    rglwidgetClass.multMV = function(M, v) {
-        return [ M.m11 * v[0] + M.m12 * v[1] + M.m13 * v[2] + M.m14 * v[3],
-                 M.m21 * v[0] + M.m22 * v[1] + M.m23 * v[2] + M.m24 * v[3],
-                 M.m31 * v[0] + M.m32 * v[1] + M.m33 * v[2] + M.m34 * v[3],
-                 M.m41 * v[0] + M.m42 * v[1] + M.m43 * v[2] + M.m44 * v[3]
-               ];
-    };
-    
-    /**
-     * Multiply row vector by Matrix
-     * @returns {number[]}
-     * @param v {number[]} left operand
-     * @param M {number[][]} right operand
-     */
-    rglwidgetClass.multVM = function(v, M) {
-        return [ M.m11 * v[0] + M.m21 * v[1] + M.m31 * v[2] + M.m41 * v[3],
-                 M.m12 * v[0] + M.m22 * v[1] + M.m32 * v[2] + M.m42 * v[3],
-                 M.m13 * v[0] + M.m23 * v[1] + M.m33 * v[2] + M.m43 * v[3],
-                 M.m14 * v[0] + M.m24 * v[1] + M.m34 * v[2] + M.m44 * v[3]
-               ];
-    };
-    
-    /**
-     * Euclidean length of a vector
-     * @returns {number}
-     * @param v {number[]}
-     */
-    rglwidgetClass.vlen = function(v) {
-      return Math.sqrt(rglwidgetClass.dotprod(v, v));
-    };
-
-    /**
-     * Dot product of two vectors
-     * @instance rglwidgetClass
-     * @returns {number}
-     * @param a {number[]}
-     * @param b {number[]}
-     */
-    rglwidgetClass.dotprod = function(a, b) {
-      return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
-    };
-
-    /**
-     * Cross product of two vectors
-     * @returns {number[]}
-     * @param a {number[]}
-     * @param b {number[]}
-     */
-    rglwidgetClass.xprod = function(a, b) {
-      return [a[1]*b[2] - a[2]*b[1],
-          a[2]*b[0] - a[0]*b[2],
-          a[0]*b[1] - a[1]*b[0]];
-    };
-
-    /**
-     * Bind vectors or matrices by columns
-     * @returns {number[][]}
-     * @param a {number[][]}
-     * @param b {number[]|number[][]}
-     */
-    rglwidgetClass.cbind = function(a, b) {
-      if (b.length < a.length)
-        b = rglwidgetClass.repeatToLen(b, a.length);
-      else if (a.length < b.length)
-        a = rglwidgetClass.repeatToLen(a, b.length);
-      return a.map(function(currentValue, index) {
-            return [].concat(currentValue).concat(b[index]);
-      });
-    };
-
-    /**
-     * Swap elements
-     * @returns {any[]}
-     * @param a {any[]}
-     * @param i {number} Element to swap
-     * @param j {number} Other element to swap
-     */
-    rglwidgetClass.swap = function(a, i, j) {
-      var temp = a[i];
-      a[i] = a[j];
-      a[j] = temp;
-    };
-
-    /**
-     * Flatten a matrix into a vector
-     * @returns {any[]}
-     * @param a {any[][]}
-     */
-    rglwidgetClass.flatten = function(arr, result) {
-      var value;
-      if (typeof result === "undefined") result = [];
-      for (var i = 0, length = arr.length; i < length; i++) {
-        value = arr[i];
-        if (Array.isArray(value)) {
-          rglwidgetClass.flatten(value, result);
-        } else {
-          result.push(value);
-        }
-      }
-      return result;
-    };
-
-    /**
-     * set element of 1d or 2d array as if it was flattened.
-     * Column major, zero based!
-     * @returns {any[]|any[][]}
-     * @param {any[]|any[][]} a - array
-     * @param {number} i - element
-     * @param {any} value
-     */
-    rglwidgetClass.prototype.setElement = function(a, i, value) {
-      if (Array.isArray(a[0])) {
-        var dim = a.length,
-            col = Math.floor(i/dim),
-            row = i % dim;
-        a[row][col] = value;
-      } else {
-        a[i] = value;
-      }
-    };
-
-    /**
-     * Transpose an array
-     * @returns {any[][]}
-     * @param {any[][]} a
-     */
-    rglwidgetClass.prototype.transpose = function(a) {
-      var newArray = [],
-          n = a.length,
-          m = a[0].length,
-          i;
-      for(i = 0; i < m; i++){
-        newArray.push([]);
-      }
-
-      for(i = 0; i < n; i++){
-        for(var j = 0; j < m; j++){
-          newArray[j].push(a[i][j]);
-        }
-      }
-      return newArray;
-    };
-
-    /**
-     * Calculate sum of squares of a numeric vector
-     * @returns {number}
-     * @param {number[]} x
-     */
-    rglwidgetClass.prototype.sumsq = function(x) {
-      var result = 0, i;
-      for (i=0; i < x.length; i++)
-        result += x[i]*x[i];
-      return result;
-    };
-
-    /**
-     * Convert a matrix to a CanvasMatrix4
-     * @returns {CanvasMatrix4}
-     * @param {number[][]|number[]} mat
-     */
-    rglwidgetClass.prototype.toCanvasMatrix4 = function(mat) {
-      if (mat instanceof CanvasMatrix4)
-        return mat;
-      var result = new CanvasMatrix4();
-      mat = rglwidgetClass.flatten(this.transpose(mat));
-      result.load(mat);
-      return result;
-    };
-
-    /**
-     * Convert an R-style numeric colour string to an rgb vector
-     * @returns {number[]}
-     * @param {string} s
-     */
-    /* jshint bitwise:false */ 
-    rglwidgetClass.prototype.stringToRgb = function(s) {
-      s = s.replace("#", "");
-      var bigint = parseInt(s, 16);
-      return [((bigint >> 16) & 255)/255,
-              ((bigint >> 8) & 255)/255,
-               (bigint & 255)/255];
-    };
-    /* jshint bitwise:true */
-    /**
-     * Which list does a particular id come from?
-     * @returns { string }
-     * @param {number} id The id to look up.
-     */
-    rglwidgetClass.prototype.whichList = function(id) {
-      var obj = this.getObj(id),
-          flags = obj.flags;
-        if (obj.type === "light")
-          return "lights";
-        if (rglwidgetClass.isSet(flags, rglwidgetClass.f_is_subscene))
-            return "subscenes";
-        if (rglwidgetClass.isSet(flags, rglwidgetClass.f_is_clipplanes))
-            return "clipplanes";
-        if (rglwidgetClass.isSet(flags, rglwidgetClass.f_is_transparent))
-            return "transparent";
-        return "opaque";
-    };
-    
-    /**
-     * Take a component-by-component product of two 3 vectors
-     * @returns {number[]}
-     * @param {number[]} x
-     * @param {number[]} y
-     */
-    rglwidgetClass.prototype.componentProduct = function(x, y) {
-      if (typeof y === "undefined") {
-        this.alertOnce("Bad arg to componentProduct");
-      }
-      var result = new Float32Array(3), i;
-      for (i = 0; i<3; i++)
-        result[i] = x[i]*y[i];
-      return result;
-    };
-
-    /**
-     * Get next higher power of two
-     * @returns { number }
-     * @param { number } value - input value
-     */
-    rglwidgetClass.prototype.getPowerOfTwo = function(value) {
-      var pow = 1;
-      while(pow<value) {
-        pow *= 2;
-      }
-      return pow;
-    };
-
-    /**
-     * Unique entries
-     * @returns { any[] }
-     * @param { any[] } arr - An array
-     */
-    rglwidgetClass.prototype.unique = function(arr) {
-      arr = [].concat(arr);
-      return arr.filter(function(value, index, self) {
-        return self.indexOf(value) === index;
-      });
-    };
-
-    /**
-     * Shallow compare of arrays
-     * @returns { boolean }
-     * @param { any[] } a - An array
-     * @param { any[] } b - Another array
-     */
-    rglwidgetClass.prototype.equalArrays = function(a, b) {
-      return a === b || (a && b &&
-                      a.length === b.length &&
-                      a.every(function(v, i) {return v === b[i];}));
-    };
-    
-    /**
-     * Repeat an array to a desired length
-     * @returns {any[]}
-     * @param {any | any[]} arr The input array
-     * @param {number} len The desired output length
-     */
-    rglwidgetClass.repeatToLen = function(arr, len) {
-      arr = [].concat(arr);
-      if (!arr.length) 
-        throw new RangeError("array is length 0");
-      while (arr.length < len/2)
-        arr = arr.concat(arr);
-      return arr.concat(arr.slice(0, len - arr.length));
-    };
-
-    /**
-     * Give a single alert message, not to be repeated.
-     * @param {string} msg  The message to give.
-     */
-    rglwidgetClass.prototype.alertOnce = function(msg) {
-      // debugger;
-      if (typeof this.alerted !== "undefined")
-        return;
-      this.alerted = true;
-      alert(msg);
-    };
-
-    /**
-     * Get an object by id number.
-     * @returns { Object }
-     * @param {number} id
-     */
-    rglwidgetClass.prototype.getObj = function(id) {
-      if (typeof id !== "number") {
-        this.alertOnce("getObj id is "+typeof id);
-      }
-      return this.scene.objects[id];
-    };
-
-    /**
-     * Get ids of a particular type from a subscene or the whole scene
-     * @returns { number[] }
-     * @param {string} type What type of object?
-     * @param {number} subscene  Which subscene?  If not given, find in the whole scene
-     */
-    rglwidgetClass.prototype.getIdsByType = function(type, subscene) {
-      var
-        result = [], i, self = this, ids;
-      if (typeof subscene === "undefined") {
-        Object.keys(this.scene.objects).forEach(
-          function(key) {
-            key = parseInt(key, 10);
-            if (self.getObj(key).type === type)
-              result.push(key);
-          });
-      } else {
-        ids = this.getObj(subscene).objects;
-        for (i=0; i < ids.length; i++) {
-          if (this.getObj(ids[i]).type === type) {
-            result.push(ids[i]);
-          }
-        }
-      }
-      return result;
-    };
-
-    /**
-     * Get a particular material property for an obj
-     * @returns { any }
-     * @param {object} obj  Which object?
-     * @param {string} property Which material property?
-     */
-    rglwidgetClass.prototype.getMaterial = function(obj, property) {
-      var mat;
-      if (typeof obj.material === "undefined")
-        console.error("material undefined");
-      mat = obj.material[property];
-      if (typeof mat === "undefined")
-          mat = this.scene.material[property];
-      return mat;
-    };
-    
-   /**
-     * Get a particular material property for an id
-     * @returns { any }
-     * @param {number} id  Which object?
-     * @param {string} property Which material property?
-     */
-    rglwidgetClass.prototype.getMaterialId = function(id, property) {
-      var obj = this.getObj(id);
-      return this.getMaterial(obj, property);
-    };
-
-    rglwidgetClass.prototype.getAdj = function (obj, index, offset, text) {
-      var len, pos;
-      if (typeof obj.pos === "undefined")
-        return rglwidgetClass.flatten(obj.adj);
-      pos = obj.pos[index % obj.pos.length];
-      switch(pos) {
-        case 0: return [0.5, 0.5, 0.5];
-        case 1: return [0.5, 1 + offset, 0.5];
-        case 3: return [0.5, -offset, 0.5];
-        case 5: return [0.5, 0.5, -offset];
-        case 6: return [0.5, 0.5, 1 + offset];
-        case 2: 
-        case 4: if (typeof text === "undefined")
-                  len = 1;
-                else
-                  len = text.length;
-                if (pos === 2)
-                  return [1 + offset/len, 0.5, 0.5];
-                else
-                  return [-offset/len, 0.5, 0.5];
-      }
-    };
-
-    /**
-     * Count clipping planes in a scene
-     * @returns {number}
-     */
-    rglwidgetClass.prototype.countClipplanes = function() {
-      var self = this,
-          bound = 0;
-      
-      Object.keys(this.scene.objects).forEach(
-        function(key) {
-          var obj = self.getObj(parseInt(key, 10));
-          if (obj.type === "clipplanes")
-            bound = bound + obj.offsets.length;
-        });
-      return bound;
-    };
-
-    /**
-     * Count clipping plane objects in a scene
-     * @returns {number}
-     */
-    rglwidgetClass.prototype.countClipplaneObjs = function() {
-      return this.countObjs("clipplanes");
-    };
-
-    /**
-     * Count lights in a scene
-     * @returns { number }
-     */
-    rglwidgetClass.prototype.countLights = function() {
-      return this.countObjs("light");
-    };
-
-    /**
-     * Count objects of specific type in a scene
-     * @returns { number }
-     * @param { string } type - Type of object to count
-     */
-    rglwidgetClass.prototype.countObjs = function(type) {
-      var self = this,
-          bound = 0;
-
-      Object.keys(this.scene.objects).forEach(
-        function(key) {
-          if (self.getObj(parseInt(key, 10)).type === type)
-            bound = bound + 1;
-        });
-      return bound;
-    };
-
-    /**
-     * Display a debug message
-     * @param { string } msg - The message to display
-     * @param { Object } [img] - Image to insert before message
-     */
-    rglwidgetClass.prototype.debug = function(msg, img) {
-      if (typeof this.debugelement !== "undefined" && this.debugelement !== null) {
-        this.debugelement.innerHTML = msg;
-        if (typeof img !== "undefined") {
-          this.debugelement.insertBefore(img, this.debugelement.firstChild);
-        }
-      } else if (msg !== "")
-        alert(msg);
-    };
-
-    /**
-     * If we are in an ioslides or slidy presentation, get the
-     * DOM element of the current slide
-     * @returns { Object }
-     */
-    rglwidgetClass.prototype.getSlide = function() {
-      var result = this.el, done = false;
-      while (result && !done && this.scene.context.rmarkdown) {
-      	switch(this.scene.context.rmarkdown) {
-          case "ioslides_presentation":
-            if (result.tagName === "SLIDE") return result;
-            break;
-          case "slidy_presentation":
-            if (result.tagName === "DIV" && result.classList.contains("slide"))
-              return result;
-            break;
-          default: return null;
-      	}
-      	result = result.parentElement;
-      }
-      return null;
-    };
-
-    /**
-     * Is this scene visible in the browser?
-     * @returns { boolean }
-     */
-    rglwidgetClass.prototype.isInBrowserViewport = function() {
-      var rect = this.canvas.getBoundingClientRect(),
-          windHeight = (window.innerHeight || document.documentElement.clientHeight),
-          windWidth = (window.innerWidth || document.documentElement.clientWidth);
-      if (this.scene.context && this.scene.context.rmarkdown !== null) {
-      	if (this.slide)
-      	  return (this.scene.context.rmarkdown === "ioslides_presentation" &&
-      	          this.slide.classList.contains("current")) ||
-      	         (this.scene.context.rmarkdown === "slidy_presentation" &&
-      	          !this.slide.classList.contains("hidden"));
-      }
-      return (
-      	rect.top >= -windHeight &&
-      	rect.left >= -windWidth &&
-      	rect.bottom <= 2*windHeight &&
-      	rect.right <= 2*windWidth);
-    };
-    
-    rglwidgetClass.keydiff = function(obj1, obj2) {
-      var keys = Object.keys(obj1), i, result = [];
-      for (i=0;i<keys.length;i++) {
-        if (typeof obj1[keys[i]] !== "undefined" &&
-            typeof obj2[keys[i]] === "undefined")
-          result.push(keys[i]);
-      }
-      return result;
-    };
-
-    rglwidgetClass.isSet = function(flags, flag) {
-      /* jshint bitwise: false */
-      return (flags & flag) !== 0;
-      /* jshint bitwise: true */
-    };
-    
-    rglwidgetClass.prototype.user2window = function(p, subid) {
-      var m, v = [].concat(p);
-      
-      this.setmvMatrix(subid);
-      m = new CanvasMatrix4(this.mvMatrix);
-      v = rglwidgetClass.multVM(v, m);
-      this.setprMatrix(subid);
-      m = new CanvasMatrix4(this.prMatrix);
-      v = rglwidgetClass.multVM(v, m);
-      this.getViewport(subid);
-      v[0] = v[0]*0.5/v[3] + 0.5 + this.vp.x/this.vp.width;
-      v[1] = v[1]*0.5/v[3] + 0.5 + this.vp.y/this.vp.height;
-      v[2] = (1 + v[2]/v[3])*0.5;
-      return v.slice(0, 3);
-    };
-
-    /**
-     * Andrew's convex hull algorithm. 
-     * From Wikipedia, used under Creative Commons Attribution-ShareAlike License
-     * @returns { Array } Indices of convex hull points
-     */
-    rglwidgetClass.chull = function(points) {
-      function cross(a, b, o) {
-        return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0]);
-      }
-        
-      points.sort(function(a, b) {
-        return a[0] === b[0] ? a[1] - b[1] : a[0] - b[0];
-      });
-
-      var lower = [], upper = [];
-      for (var i = 0; i < points.length; i++) {
-        while (lower.length >= 2 && cross(lower[lower.length - 2], lower[lower.length - 1], points[i]) <= 0) {
-          lower.pop();
-        }
-        lower.push(points[i]);
-      }
-
-      for (i = points.length - 1; i >= 0; i--) {
-        while (upper.length >= 2 && cross(upper[upper.length - 2], upper[upper.length - 1], points[i]) <= 0) {
-          upper.pop();
-        }
-        upper.push(points[i]);
-      }
-
-      upper.pop();
-      lower.pop();
-      return lower.concat(upper);
-    };
-    
-    /**
-     * Round number to given precision
-     * @param { number } x
-     * @param { number } digits
-     * @returns { number } 
-     */
-    rglwidgetClass.signif = function(x, digits) { 
-      return parseFloat(x.toPrecision(digits));
-    };
-      
-    /**
-     * Check for NA, NaN, undefined, or null
-     * @param x
-     * @returns { bool }
-     */
-    rglwidgetClass.missing = function(x) {
-      return x !== "-Inf" && x !== "Inf" &&
-             (isNaN(x) || x === null || typeof(x) === "undefined");
-    };
-
-    /**
-     * Write matrix to log
-     * @param M
-     */
-    rglwidgetClass.logMatrix = function(M) {
-      console.log("matrix(c("+M.m11+","+M.m12+","+M.m13+","+M.m14+",\n"+
-                              M.m21+","+M.m22+","+M.m23+","+M.m24+",\n"+
-                              M.m31+","+M.m32+","+M.m33+","+M.m34+",\n"+
-                              M.m41+","+M.m42+","+M.m43+","+M.m44+"), byrow=TRUE, ncol=4)");
-    };
-    
-    /**
-     * Write vector to log
-     * @param {vector} v
-     */
-     
-    rglwidgetClass.logVec3 = function(v) {
-      console.log("c("+v[0]+","+v[1]+","+v[2]+")");
-    };
-    
-    /**
-     * Sum two vectors
-     * @param {vector} x
-     * @param {vector} y
-     */
-     rglwidgetClass.vsum = function(x, y) {
-       var i, result = [].concat(x);
-       for (i = 0; i < y.length; i++)
-         result[i] += y[i];
-        return result;
-     };
-     
-    /**
-     * difference of two vectors
-     * @param {vector} x
-     * @param {vector} y
-     */
-     rglwidgetClass.vdiff = function(x, y) {
-        return rglwidgetClass.vsum(x, rglwidgetClass.vscale(y, -1));
-     };
-
-    /**
-     * Scale a vector
-     * @param {number} s
-     * @param {vector} x
-     */
-     rglwidgetClass.vscale = function(x, s) {
-       var i, result = [].concat(x);
-       for (i = 0; i < x.length; i++)
-         result[i] *= s;
-        return result;
-     };
-    
-    /**
-     * Normalize a vector
-     * @param {vector} v
-     */
-    rglwidgetClass.normalize = function(v) {
-      return rglwidgetClass.vscale(v, 1/rglwidgetClass.vlen(v));
-    };
-    
-    /**
-     * Compute the dimensions of a regular array
-     * without checking that it is regular
-     */ 
-    rglwidgetClass.arrayDim = function(arr) {
-      var result = [];
-      while (typeof arr.length !== "undefined") {
-        result = result.concat(arr.length);
-        arr = arr[0];
-      }
-      return result;
-    };
-</script>
-<script>/**
-     * Methods related to buffered data
-     * @name ___METHODS_FOR_BUFFERS___
-     * @memberof rglwidgetClass
-     * @kind function
-     * @instance
-     */
-    /**
-     * Detect rglBuffered object
-     * @param { Object } obj - vertices or similar 
-     */
-    rglwidgetClass.prototype.isBuffered = function(obj) {
-      return typeof obj === "string";
-    };
-
-    /* The next two functions are taken from 
-     
-     https://developer.mozilla.org/en-US/docs/Web/JavaScript/Base64_encoding_and_decoding
-     
-     They were written by Mozilla Contributors and dedicated
-     to the public domain under CC0. */
-     
-    /* Array of bytes to Base64 string decoding */
-    rglwidgetClass.prototype.b64ToUint6 = function(nChr) {
-      return nChr > 64 && nChr < 91 ? nChr - 65 : 
-             nChr > 96 && nChr < 123 ? nChr - 71 : 
-             nChr > 47 && nChr < 58 ? nChr + 4 : 
-             nChr === 43 ? 62 : 
-             nChr === 47 ? 63 : 
-             0;
-    };
-
-    /* jshint bitwise:false */
-    rglwidgetClass.prototype.base64DecToArr = function(sBase64, nBlocksSize) {
-      var sB64Enc = sBase64.replace(/[^A-Za-z0-9\+\/]/g, ""),
-        nInLen = sB64Enc.length, 
-        nOutLen = nBlocksSize ? Math.ceil((nInLen * 3 + 1 >> 2) / nBlocksSize) * nBlocksSize : nInLen * 3 + 1 >> 2, 
-        taBytes = new Uint8Array(nOutLen);
-      for (var nMod3, nMod4, nUint24 = 0, nOutIdx = 0, nInIdx = 0; nInIdx < nInLen; nInIdx++) {
-        nMod4 = nInIdx & 3;
-        nUint24 |= this.b64ToUint6(sB64Enc.charCodeAt(nInIdx)) << 6 * (3 - nMod4);
-        if (nMod4 === 3 || nInLen - nInIdx === 1) {
-          for (nMod3 = 0; nMod3 < 3 && nOutIdx < nOutLen; nMod3++, nOutIdx++) {
-            taBytes[nOutIdx] = nUint24 >>> (16 >>> nMod3 & 24) & 255;
-          }
-          nUint24 = 0;
-        }
-      }
-      return taBytes;
-    };
-    /* jshint bitwise:true */
-    
-    rglwidgetClass.prototype.getArrayBuffer = function(base64) {
-      return this.base64DecToArr(base64, 4).buffer;
-    };
-
-    rglwidgetClass.prototype.getBufferedData = function(v) {
-      return this.readAccessor(parseInt(v, 10), this.scene.buffer);
-    };
-    
-    rglwidgetClass.prototype.readAccessor = function(acc, buf) {
-      var typeSignedByte = 5120, 
-          typeUnsignedByte = 5121, 
-          typeSignedShort = 5122, 
-          typeUnsignedShort = 5123, 
-          typeSignedInt = 5124, 
-          typeUnsignedInt = 5125, 
-          typeFloat = 5126, 
-          typeDouble = 5130, 
-          accessor = buf.accessors[acc], 
-          bufferView = buf.bufferViews[accessor.bufferView], 
-          buffer = buf.buffers[bufferView.buffer], 
-          bytes, 
-          lens = {
-            SCALAR: 1,
-            VEC2: 2,
-            VEC3: 3,
-            VEC4: 4,
-            MAT2: 4,
-            MAT3: 9,
-            MAT4: 16
-          }, 
-          rowsizes = {
-            SCALAR: 1,
-            VEC2: 2,
-            VEC3: 3,
-            VEC4: 4,
-            MAT2: 2,
-            MAT3: 3,
-            MAT4: 4
-          }, 
-          offset = 0, 
-          len = lens[accessor.type], 
-          rowsize = rowsizes[accessor.type], 
-          count = len * accessor.count, 
-          nrows = count / rowsize, 
-          values, arr = [], row, i, j, k;
-          
-      if (typeof buffer.bytes === "string") 
-        buffer.bytes = this.getArrayBuffer(buffer.bytes);
-        
-      bytes = buffer.bytes;
-      
-      if (typeof accessor.byteOffset !== "undefined") 
-        offset += accessor.byteOffset;
-        
-      if (typeof bufferView.byteOffset !== "undefined") 
-        offset += bufferView.byteOffset;
-        
-      switch (accessor.componentType) {
-       case typeSignedByte:
-        values = new Int8Array(buffer.bytes, offset, count);
-        break;
-
-       case typeUnsignedByte:
-        values = new Uint8Array(buffer.bytes, offset, count);
-        break;
-
-       case typeSignedShort:
-        values = new Int16Array(buffer.bytes, offset, count);
-        break;
-
-       case typeUnsignedShort:
-        values = new Uint16Array(buffer.bytes, offset, count);
-        break;
-
-       case typeSignedInt:
-        values = new Int32Array(buffer.bytes, offset, count);
-        break;
-
-       case typeUnsignedInt:
-        values = new Uint32Array(buffer.bytes, offset, count);
-        break;
-
-       case typeFloat:
-        values = new Float32Array(buffer.bytes, offset, count);
-        break;
-
-       case typeDouble:
-        values = new Float64Array(buffer.bytes, offset, count);
-        break;
-      }
-
-      /* This is all very inefficient, but is convenient
-             to work with the old code. */
-      k = 0;
-      for (i = 0; i < nrows; i++) {
-        row = [];
-        for (j = 0; j < rowsize; j++) {
-          if (accessor.normalized) {
-            switch(accessor.componentType) {
-              case typeSignedByte:
-                row.push(Math.max(values[k++]/127, -1.0));
-                break;
-              case typeSignedShort:
-                row.push(Math.max(values[k++]/32767, -1.0));
-                break;
-              case typeUnsignedByte:
-                row.push(values[k++]/255);
-                break;
-              case typeUnsignedShort:
-                row.push(values[k++]/65535);
-                break;
-            }
-          } else
-            row.push(values[k++]);
-        }
-        arr.push(row);
-      }
-      return arr;
-    };
-    
-    rglwidgetClass.prototype.expandBufferedFields = function(obj) {
-      /* this list needs to match the one in convertScene.R */
-      var fields = ["vertices", "normals", "indices", 
-                    "texcoords", "colors", "centers"], i, field;
-      for (i = 0; i < fields.length; i++) {
-        field = obj[fields[i]];
-        if (this.isBuffered(field))
-          obj[fields[i]] = this.getBufferedData(field);
-      }
-    };
-</script>
-<script>    /**
-     * Methods related to subscenes
-     * @name ___METHODS_FOR_SUBSCENES___
-     * @memberof rglwidgetClass
-     * @kind function
-     * @instance
-     */
-
-    /**
-     * Is a particular id in a subscene?
-     * @returns { boolean }
-     * @param {number} id Which id?
-     * @param {number} subscene Which subscene id?
-     */
-    rglwidgetClass.prototype.inSubscene = function(id, subscene) {
-      return this.getObj(subscene).objects.indexOf(id) > -1;
-    };
-
-    /**
-     * Translate from window coordinates to viewport coordinates
-     * @returns { Object } translated coordinates
-     * @param { number } subsceneid - which subscene to use?
-     * @param { Object } coords - point to translate
-     */
-    rglwidgetClass.prototype.translateCoords = function(subsceneid, coords) {
-      var viewport = this.getObj(subsceneid).par3d.viewport;
-      return {x: coords.x - viewport.x*this.canvas.width,
-              y: coords.y - viewport.y*this.canvas.height};
-    };
-
-    /**
-     * Check whether point is in viewport of subscene
-     * @returns {boolean}
-     * @param { Object } coords - screen coordinates of point
-     * @param { number } subsceneid - subscene to check
-     */
-    rglwidgetClass.prototype.inViewport = function(coords, subsceneid) {
-      var viewport = this.getObj(subsceneid).par3d.viewport,
-        x0 = coords.x - viewport.x*this.canvas.width,
-        y0 = coords.y - viewport.y*this.canvas.height;
-      return 0 <= x0 && x0 <= viewport.width*this.canvas.width &&
-             0 <= y0 && y0 <= viewport.height*this.canvas.height;
-    };
-
-    /**
-     * Find which subscene contains a point
-     * @returns { number } subscene id
-     * @param { Object } coords - coordinates of point
-     */
-    rglwidgetClass.prototype.whichSubscene = function(coords) {
-      var self = this,
-          recurse = function(subsceneid) {
-            var subscenes = self.getChildSubscenes(subsceneid), i, id;
-            for (i=0; i < subscenes.length; i++) {
-              id = recurse(subscenes[i]);
-              if (typeof(id) !== "undefined")
-                return(id);
-            }
-            if (self.inViewport(coords, subsceneid))
-              return(subsceneid);
-            else
-              return undefined;
-          },
-          rootid = this.scene.rootSubscene,
-          result = recurse(rootid);
-      if (typeof(result) === "undefined")
-        result = rootid;
-      return result;
-    };
-
-    /**
-     * Add an id to a subscene.
-     * @param {number} id Which id?
-     * @param {number} subscene Which subscene id?
-     */
-    rglwidgetClass.prototype.addToSubscene = function(id, subscene) {
-      var thelist,
-          thesub = this.getObj(subscene),
-          ids = [id],
-          obj = this.getObj(id), i;
-      if (typeof obj !== "undefined" && typeof (obj.newIds) !== "undefined") {
-        ids = ids.concat(obj.newIds);
-      }
-      thesub.objects = [].concat(thesub.objects);
-      for (i = 0; i < ids.length; i++) {
-        id = ids[i];
-        if (thesub.objects.indexOf(id) === -1) {
-          thelist = this.whichList(id);
-          thesub.objects.push(id);
-          thesub[thelist].push(id);
-        }
-      }
-    };
-
-    /**
-     * Delete an id from a subscene
-     * @param { number } id - the id to add
-     * @param { number } subscene - the id of the subscene
-     */
-    rglwidgetClass.prototype.delFromSubscene = function(id, subscene) {
-      var thelist,
-          thesub = this.getObj(subscene),
-          obj = this.getObj(id),
-          ids = [id], i, j;
-      if (typeof obj !== "undefined" && typeof (obj.newIds) !== "undefined")
-        ids = ids.concat(obj.newIds);
-      thesub.objects = [].concat(thesub.objects); // It might be a scalar
-      for (j=0; j<ids.length;j++) {
-        id = ids[j];
-        i = thesub.objects.indexOf(id);
-        if (i > -1) {
-          thesub.objects.splice(i, 1);
-          thelist = this.whichList(id);
-          i = thesub[thelist].indexOf(id);
-          thesub[thelist].splice(i, 1);
-        }
-      }
-    };
-
-    /**
-     * Set the ids in a subscene
-     * @param { number[] } ids - the ids to set
-     * @param { number } subsceneid - the id of the subscene
-     */
-    rglwidgetClass.prototype.setSubsceneEntries = function(ids, subsceneid) {
-      var sub = this.getObj(subsceneid);
-      sub.objects = ids;
-      this.initSubscene(subsceneid);
-    };
-
-    /**
-     * Get the ids in a subscene
-     * @returns {number[]}
-     * @param { number } subscene - the id of the subscene
-     */
-    rglwidgetClass.prototype.getSubsceneEntries = function(subscene) {
-      return this.getObj(subscene).objects;
-    };
-
-    /**
-     * Get the ids of the subscenes within a subscene
-     * @returns { number[] }
-     * @param { number } subscene - the id of the subscene
-     */
-    rglwidgetClass.prototype.getChildSubscenes = function(subscene) {
-      return this.getObj(subscene).subscenes;
-    };
-
-    /**
-     * Find a particular subscene by inheritance
-     * @returns { number } id of subscene to use
-     * @param { number } subsceneid - child subscene
-     * @param { string } type - type of inheritance:  "projection" or "model"
-     */
-    rglwidgetClass.prototype.useid = function(subsceneid, type) {
-      var sub = this.getObj(subsceneid);
-      if (sub.embeddings[type] === "inherit")
-        return(this.useid(sub.parent, type));
-      else
-        return subsceneid;
-    };
-
-    /**
-     * Find bboxdeco for a subscene
-     * @returns { number } id of bboxdeco, or undefined if none
-     * @param { number } sub- subscene
-     */
-    rglwidgetClass.prototype.getBBoxDeco = function(sub) {
-      var objects = sub.objects, i, obj;
-      for (i = 0; i < objects.length; i++) {
-        obj = this.getObj(objects[i]);
-        if (obj.type === "bboxdeco")
-          return obj;
-      }
-      if (sub.parent) 
-        return this.getBBoxDeco(this.getObj(sub.parent));
-      else
-        return undefined;
-    };
-</script>
-<script>    /**
-     * Methods related to shaders
-     * @name ___METHODS_FOR_SHADERS___
-     * @memberof rglwidgetClass
-     * @kind function
-     * @instance
-     */
-     
-    /**
-     * Get flags that will end up as shader defines.
-     * Static method so it can be called from R
-     */
-    rglwidgetClass.getDefFlags = function(flags, type, normals, round_points) {
-      var f = {};
-      f.fat_lines = rglwidgetClass.isSet(flags, rglwidgetClass.f_fat_lines);
-      f.fixed_quads = rglwidgetClass.isSet(flags, rglwidgetClass.f_fixed_quads);
-      f.fixed_size = rglwidgetClass.isSet(flags, rglwidgetClass.f_fixed_size);
-      f.has_fog = rglwidgetClass.isSet(flags, rglwidgetClass.f_has_fog);
-      f.has_normals = (typeof normals !== "undefined") ||
-                        type === "spheres";
-      f.has_texture = rglwidgetClass.isSet(flags, rglwidgetClass.f_has_texture);
-      f.is_brush = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_brush);
-      f.is_lines = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_lines);
-      f.is_lit = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_lit);
-      f.is_points = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_points);
-      f.is_transparent = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_transparent);
-      f.is_twosided = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_twosided);
-      f.needs_vnormal = !rglwidgetClass.isSet(flags, rglwidgetClass.f_sprites_3d) &&
-        (f.is_lit && !f.fixed_quads && !f.is_brush) || (f.is_twosided && f.has_normals);
-      f.rotating = rglwidgetClass.isSet(flags, rglwidgetClass.f_rotating);
-      f.round_points = round_points;
-      return f;
-    };
-     
-    
-    /**
-     * Generate the defines for the shader code for an object.
-     * 
-     * This is a static method so it can be called from R.
-     * 
-     * @returns {string}
-     * @param  id - id of object
-     * @param  type - type of object
-     * @param  flags - object flags
-     * @param  nclipplanes - number of clipping planes in scene 
-     *         (may not all be active)
-     * @param  nlights - number of lights in scene (ditto)
-     * @param  normals - normals for object
-     * @param  pointSize - point size for object 
-     * @param  textype - texture type for object 
-     * @param  antialias - use antialiasing?
-     */
-    rglwidgetClass.getDefines = function(id, type, flags,
-      nclipplanes, nlights, normals, pointSize, textype,
-      texmode, texenvmap, antialias, fl) {
-      var
-        title, defines;
-      
-      if (typeof fl === "undefined")
-        fl = rglwidgetClass.getDefFlags(flags, type, normals, antialias);
-        
-      title = "  /* ****** "+type+" object "+id+" shader ****** */\n";
-      
-      defines = "#define NCLIPPLANES " + nclipplanes + "\n"+
-                "#define NLIGHTS " + nlights + "\n";
-      
-      if (fl.fat_lines)
-        defines = defines + "#define FAT_LINES 1\n";
-      
-      if (fl.fixed_quads)
-        defines = defines + "#define FIXED_QUADS 1\n";
-
-      if (fl.fixed_size)
-        defines = defines + "#define FIXED_SIZE 1\n";
-
-      if (fl.has_fog)
-        defines = defines + "#define HAS_FOG 1\n";
-        
-      if (fl.has_normals)
-        defines = defines + "#define HAS_NORMALS 1\n";
-        
-      if (fl.has_texture) {
-        defines = defines + "#define HAS_TEXTURE 1\n";
-        defines = defines + "#define TEXTURE_" + textype + "\n";
-        defines = defines + "#define TEXMODE_" + texmode + "\n";
-        if (texenvmap)
-          defines = defines + "#define USE_ENVMAP 1\n";
-      }
-      
-      if (fl.is_brush)
-        defines = defines + "#define IS_BRUSH 1\n";  
-
-      if (type === "linestrip")
-        defines = defines + "#define IS_LINESTRIP 1\n";         
-
-      if (fl.is_lit)
-        defines = defines + "#define IS_LIT 1\n"; 
-      
-      if (fl.is_points) {
-        defines = defines + "#define IS_POINTS 1\n";
-        defines = defines + "#define POINTSIZE " + Number.parseFloat(pointSize).toFixed(1) + "\n";
-      }
-        
-      if (type === "sprites")
-        defines = defines + "#define IS_SPRITES 1\n";
-        
-      if (type === "text")
-        defines = defines + "#define IS_TEXT 1\n";
-
-      if (fl.is_transparent)
-        defines = defines + "#define IS_TRANSPARENT 1\n"; 
-        
-      if (fl.is_twosided)
-        defines = defines + "#define IS_TWOSIDED 1\n";
-        
-      if (fl.needs_vnormal)
-        defines = defines + "#define NEEDS_VNORMAL 1\n";
-
-      if (fl.rotating)
-        defines = defines + "#define ROTATING 1\n";
-        
-      if (fl.round_points)        
-        defines = defines + "#define ROUND_POINTS 1\n";   
-
-      // console.log(result);
-      return title + defines;
-    };
-
-    /**
-     * Create code for vertex and fragment shaders
-     * @returns {Object}
-     * @param { number } shaderType - gl code for shader type
-     * @param { string } code - code for the shader
-     */
-    rglwidgetClass.prototype.getShaders = function(obj) {
-      var header, 
-        vertex = obj.userVertexShader, 
-        fragment = obj.userFragmentShader;
-      
-      header = rglwidgetClass.getDefines(
-        obj.id, obj.type, obj.flags, 
-        this.countClipplanes(), this.countLights(), 
-        obj.normals, 
-        this.getMaterial(obj, "size"), 
-        this.getMaterial(obj, "textype"),
-        this.getMaterial(obj, "texmode"),
-        this.getMaterial(obj, "texenvmap"),
-        this.getMaterial(obj, "point_antialias"),
-        obj.defFlags
-      );
-
-      if (typeof vertex === "undefined")
-        vertex = rglwidgetClass.rgl_vertex_shader();
-        
-      if (typeof fragment === "undefined") 
-        fragment = rglwidgetClass.rgl_fragment_shader();
-
-//      console.log("vertex:");
-//      console.log(header + vertex);
-//      console.log("fragment:");
-//      console.log(header + fragment);
-      
-      return {vertex: header + vertex,
-              fragment: header + fragment};
-    };
-    
-    
-    /**
-     * Call gl functions to create and compile shader from code
-     * @returns {Object}
-     * @param { number } shaderType - gl code for shader type
-     * @param { string } code - code for the shader
-     */
-    rglwidgetClass.prototype.getShader = function(shaderType, code) {
-        var gl = this.gl, shader;
-        shader = gl.createShader(shaderType);
-        gl.shaderSource(shader, code);
-        gl.compileShader(shader);
-        if (!gl.getShaderParameter(shader, gl.COMPILE_STATUS) && !gl.isContextLost())
-            alert(gl.getShaderInfoLog(shader));
-        return shader;
-    };
-
-</script>
-<script>rglwidgetClass.rgl_vertex_shader = function() {
-return  "#line 2 1\n"+
-"// File 1 is the vertex shader\n"+
-"#ifdef GL_ES\n"+
-"#ifdef GL_FRAGMENT_PRECISION_HIGH\n"+
-"precision highp float;\n"+
-"#else\n"+
-"precision mediump float;\n"+
-"#endif\n"+
-"#endif\n"+
-"\n"+
-"attribute vec3 aPos;\n"+
-"attribute vec4 aCol;\n"+
-"uniform mat4 mvMatrix;\n"+
-"uniform mat4 prMatrix;\n"+
-"varying vec4 vCol;\n"+
-"varying vec4 vPosition;\n"+
-"\n"+
-"#ifdef NEEDS_VNORMAL\n"+
-"attribute vec3 aNorm;\n"+
-"uniform mat4 normMatrix;\n"+
-"varying vec4 vNormal;\n"+
-"#endif\n"+
-"\n"+
-"#if defined(HAS_TEXTURE) || defined (IS_TEXT)\n"+
-"attribute vec2 aTexcoord;\n"+
-"varying vec2 vTexcoord;\n"+
-"#endif\n"+
-"\n"+
-"#ifdef FIXED_SIZE\n"+
-"uniform vec3 textScale;\n"+
-"#endif\n"+
-"\n"+
-"#ifdef FIXED_QUADS\n"+
-"attribute vec3 aOfs;\n"+
-"#endif\n"+
-"\n"+
-"#ifdef IS_TWOSIDED\n"+
-"#ifdef HAS_NORMALS\n"+
-"varying float normz;\n"+
-"uniform mat4 invPrMatrix;\n"+
-"#else\n"+
-"attribute vec3 aPos1;\n"+
-"attribute vec3 aPos2;\n"+
-"varying float normz;\n"+
-"#endif\n"+
-"#endif // IS_TWOSIDED\n"+
-"\n"+
-"#ifdef FAT_LINES\n"+
-"attribute vec3 aNext;\n"+
-"attribute vec2 aPoint;\n"+
-"varying vec2 vPoint;\n"+
-"varying float vLength;\n"+
-"uniform float uAspect;\n"+
-"uniform float uLwd;\n"+
-"#endif\n"+
-"\n"+
-"#ifdef USE_ENVMAP\n"+
-"varying vec3 vReflection;\n"+
-"#endif\n"+
-"\n"+
-"void main(void) {\n"+
-"  \n"+
-"#ifndef IS_BRUSH\n"+
-"#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n"+
-"  vPosition = mvMatrix * vec4(aPos, 1.);\n"+
-"#endif\n"+
-"  \n"+
-"#ifndef FIXED_QUADS\n"+
-"  gl_Position = prMatrix * vPosition;\n"+
-"#endif\n"+
-"#endif // !IS_BRUSH\n"+
-"  \n"+
-"#ifdef IS_POINTS\n"+
-"  gl_PointSize = POINTSIZE;\n"+
-"#endif\n"+
-"  \n"+
-"  vCol = aCol;\n"+
-"  \n"+
-"// USE_ENVMAP implies NEEDS_VNORMAL\n"+
-"\n"+
-"#ifdef NEEDS_VNORMAL\n"+
-"  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n"+
-"#endif\n"+
-"\n"+
-"#ifdef USE_ENVMAP\n"+
-"  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n"+
-"                        normalize(vNormal.xyz/vNormal.w)));\n"+
-"#endif\n"+
-"  \n"+
-"#ifdef IS_TWOSIDED\n"+
-"#ifdef HAS_NORMALS\n"+
-"  /* normz should be calculated *after* projection */\n"+
-"  normz = (invPrMatrix*vNormal).z;\n"+
-"#else\n"+
-"  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n"+
-"  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n"+
-"  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n"+
-"  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n"+
-"  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n"+
-"#endif\n"+
-"#endif // IS_TWOSIDED\n"+
-"  \n"+
-"#ifdef NEEDS_VNORMAL\n"+
-"  vNormal = vec4(normalize(vNormal.xyz), 1);\n"+
-"#endif\n"+
-"  \n"+
-"#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n"+
-"  vTexcoord = aTexcoord;\n"+
-"#endif\n"+
-"  \n"+
-"#if defined(FIXED_SIZE) && !defined(ROTATING)\n"+
-"  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n"+
-"  pos = pos/pos.w;\n"+
-"  gl_Position = pos + vec4(aOfs*textScale, 0.);\n"+
-"#endif\n"+
-"  \n"+
-"#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n"+
-"  vec4 pos = mvMatrix * vec4(aPos, 1.);\n"+
-"  pos = pos/pos.w + vec4(aOfs,  0.);\n"+
-"  gl_Position = prMatrix*pos;\n"+
-"#endif\n"+
-"  \n"+
-"#ifdef FAT_LINES\n"+
-"  /* This code was inspired by Matt Deslauriers' code in \n"+
-"   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n"+
-"  vec2 aspectVec = vec2(uAspect, 1.0);\n"+
-"  mat4 projViewModel = prMatrix * mvMatrix;\n"+
-"  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n"+
-"  currentProjected = currentProjected/currentProjected.w;\n"+
-"  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n"+
-"  vec2 currentScreen = currentProjected.xy * aspectVec;\n"+
-"  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n"+
-"  float len = uLwd;\n"+
-"  vec2 dir = vec2(1.0, 0.0);\n"+
-"  vPoint = aPoint;\n"+
-"  vLength = length(nextScreen - currentScreen)/2.0;\n"+
-"  vLength = vLength/(vLength + len);\n"+
-"  if (vLength > 0.0) {\n"+
-"    dir = normalize(nextScreen - currentScreen);\n"+
-"  }\n"+
-"  vec2 normal = vec2(-dir.y, dir.x);\n"+
-"  dir.x /= uAspect;\n"+
-"  normal.x /= uAspect;\n"+
-"  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n"+
-"  gl_Position = currentProjected + offset;\n"+
-"#endif\n"+
-"  \n"+
-"#ifdef IS_BRUSH\n"+
-"  gl_Position = vec4(aPos, 1.);\n"+
-"#endif\n"+
-"}\n" ;};
-rglwidgetClass.rgl_fragment_shader = function() {
-return  "#line 2 2\n"+
-"// File 2 is the fragment shader\n"+
-"#ifdef GL_ES\n"+
-"#ifdef GL_FRAGMENT_PRECISION_HIGH\n"+
-"precision highp float;\n"+
-"#else\n"+
-"precision mediump float;\n"+
-"#endif\n"+
-"#endif\n"+
-"varying vec4 vCol; // carries alpha\n"+
-"varying vec4 vPosition;\n"+
-"#if defined(HAS_TEXTURE) || defined (IS_TEXT)\n"+
-"varying vec2 vTexcoord;\n"+
-"uniform sampler2D uSampler;\n"+
-"#endif\n"+
-"\n"+
-"#ifdef HAS_FOG\n"+
-"uniform int uFogMode;\n"+
-"uniform vec3 uFogColor;\n"+
-"uniform vec4 uFogParms;\n"+
-"#endif\n"+
-"\n"+
-"#if defined(IS_LIT) && !defined(FIXED_QUADS)\n"+
-"varying vec4 vNormal;\n"+
-"#endif\n"+
-"\n"+
-"#if NCLIPPLANES > 0\n"+
-"uniform vec4 vClipplane[NCLIPPLANES];\n"+
-"#endif\n"+
-"\n"+
-"#if NLIGHTS > 0\n"+
-"uniform mat4 mvMatrix;\n"+
-"#endif\n"+
-"\n"+
-"#ifdef IS_LIT\n"+
-"uniform vec3 emission;\n"+
-"uniform float shininess;\n"+
-"#if NLIGHTS > 0\n"+
-"uniform vec3 ambient[NLIGHTS];\n"+
-"uniform vec3 specular[NLIGHTS]; // light*material\n"+
-"uniform vec3 diffuse[NLIGHTS];\n"+
-"uniform vec3 lightDir[NLIGHTS];\n"+
-"uniform bool viewpoint[NLIGHTS];\n"+
-"uniform bool finite[NLIGHTS];\n"+
-"#endif\n"+
-"#endif // IS_LIT\n"+
-"\n"+
-"#ifdef IS_TWOSIDED\n"+
-"uniform bool front;\n"+
-"varying float normz;\n"+
-"#endif\n"+
-"\n"+
-"#ifdef FAT_LINES\n"+
-"varying vec2 vPoint;\n"+
-"varying float vLength;\n"+
-"#endif\n"+
-"\n"+
-"#ifdef USE_ENVMAP\n"+
-"varying vec3 vReflection;\n"+
-"#endif\n"+
-"\n"+
-"void main(void) {\n"+
-"  vec4 fragColor;\n"+
-"#ifdef FAT_LINES\n"+
-"  vec2 point = vPoint;\n"+
-"  bool neg = point.y < 0.0;\n"+
-"  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n"+
-"                 -(point.y - vLength)/(1.0 - vLength);\n"+
-"#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n"+
-"  if (neg && length(point) <= 1.0) discard;\n"+
-"#endif\n"+
-"  point.y = min(point.y, 0.0);\n"+
-"  if (length(point) > 1.0) discard;\n"+
-"#endif // FAT_LINES\n"+
-"  \n"+
-"#ifdef ROUND_POINTS\n"+
-"  vec2 coord = gl_PointCoord - vec2(0.5);\n"+
-"  if (length(coord) > 0.5) discard;\n"+
-"#endif\n"+
-"  \n"+
-"#if NCLIPPLANES > 0\n"+
-"  for (int i = 0; i < NCLIPPLANES; i++)\n"+
-"    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n"+
-"#endif\n"+
-"    \n"+
-"#ifdef FIXED_QUADS\n"+
-"    vec3 n = vec3(0., 0., 1.);\n"+
-"#elif defined(IS_LIT)\n"+
-"    vec3 n = normalize(vNormal.xyz);\n"+
-"#endif\n"+
-"    \n"+
-"#ifdef IS_TWOSIDED\n"+
-"    if ((normz <= 0.) != front) discard;\n"+
-"#endif\n"+
-"\n"+
-"#ifdef IS_LIT\n"+
-"    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n"+
-"    vec3 lightdir;\n"+
-"    vec4 colDiff;\n"+
-"    vec3 halfVec;\n"+
-"    vec4 lighteffect = vec4(emission, 0.);\n"+
-"    vec3 col;\n"+
-"    float nDotL;\n"+
-"#ifdef FIXED_QUADS\n"+
-"    n = -faceforward(n, n, eye);\n"+
-"#endif\n"+
-"    \n"+
-"#if NLIGHTS > 0\n"+
-"    // Simulate two-sided lighting\n"+
-"    if (n.z < 0.0)\n"+
-"      n = -n;\n"+
-"    for (int i=0;i<NLIGHTS;i++) {\n"+
-"      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n"+
-"      lightdir = lightDir[i];\n"+
-"      if (!viewpoint[i]) {\n"+
-"        if (finite[i]) {\n"+
-"          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n"+
-"        } else {\n"+
-"          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n"+
-"        }\n"+
-"      }\n"+
-"      if (!finite[i]) {\n"+
-"        halfVec = normalize(lightdir + eye);\n"+
-"      } else {\n"+
-"        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n"+
-"        halfVec = normalize(lightdir + eye);\n"+
-"      }\n"+
-"      col = ambient[i];\n"+
-"      nDotL = dot(n, lightdir);\n"+
-"      col = col + max(nDotL, 0.) * colDiff.rgb;\n"+
-"      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n"+
-"      lighteffect = lighteffect + vec4(col, colDiff.a);\n"+
-"    }\n"+
-"#endif\n"+
-"    \n"+
-"#else // not IS_LIT\n"+
-"    vec4 colDiff = vCol;\n"+
-"    vec4 lighteffect = colDiff;\n"+
-"#endif\n"+
-"    \n"+
-"#ifdef IS_TEXT\n"+
-"    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n"+
-"#endif\n"+
-"    \n"+
-"#ifdef HAS_TEXTURE\n"+
-"\n"+
-"// These calculations use the definitions from \n"+
-"// https://docs.gl/gl3/glTexEnv\n"+
-"\n"+
-"#ifdef USE_ENVMAP\n"+
-"    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n"+
-"    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n"+
-"#else\n"+
-"    vec4 textureColor = texture2D(uSampler, vTexcoord);\n"+
-"#endif\n"+
-"\n"+
-"#ifdef TEXTURE_rgb\n"+
-"\n"+
-"#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n"+
-"    textureColor = vec4(textureColor.rgb, lighteffect.a);\n"+
-"#endif \n"+
-"\n"+
-"#ifdef TEXMODE_modulate\n"+
-"    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n"+
-"#endif\n"+
-"\n"+
-"#ifdef TEXMODE_blend\n"+
-"    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n"+
-"#endif\n"+
-"\n"+
-"#ifdef TEXMODE_add\n"+
-"    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n"+
-"#endif\n"+
-"\n"+
-"#endif //TEXTURE_rgb\n"+
-"        \n"+
-"#ifdef TEXTURE_rgba\n"+
-"\n"+
-"#ifdef TEXMODE_replace\n"+
-"// already done\n"+
-"#endif \n"+
-"\n"+
-"#ifdef TEXMODE_modulate\n"+
-"    textureColor = lighteffect*textureColor;\n"+
-"#endif\n"+
-"\n"+
-"#ifdef TEXMODE_decal\n"+
-"    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n"+
-"                     textureColor.a*textureColor.rgb, \n"+
-"                     lighteffect.a);\n"+
-"#endif\n"+
-"\n"+
-"#ifdef TEXMODE_blend\n"+
-"    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n"+
-"                    lighteffect.a*textureColor.a);\n"+
-"#endif\n"+
-"\n"+
-"#ifdef TEXMODE_add\n"+
-"    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n"+
-"                    lighteffect.a*textureColor.a);\n"+
-"#endif\n"+
-"    \n"+
-"#endif //TEXTURE_rgba\n"+
-"    \n"+
-"#ifdef TEXTURE_alpha\n"+
-"    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n"+
-"\n"+
-"#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n"+
-"    textureColor = vec4(lighteffect.rgb, luminance);\n"+
-"#endif \n"+
-"\n"+
-"#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n"+
-"    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n"+
-"#endif\n"+
-" \n"+
-"#endif // TEXTURE_alpha\n"+
-"    \n"+
-"// The TEXTURE_luminance values are not from that reference    \n"+
-"#ifdef TEXTURE_luminance\n"+
-"    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n"+
-"\n"+
-"#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n"+
-"    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n"+
-"#endif \n"+
-"\n"+
-"#ifdef TEXMODE_modulate\n"+
-"    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n"+
-"#endif\n"+
-"\n"+
-"#ifdef TEXMODE_blend\n"+
-"    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n"+
-"                        lighteffect.a);\n"+
-"#endif\n"+
-"\n"+
-"#ifdef TEXMODE_add\n"+
-"    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n"+
-"#endif\n"+
-"\n"+
-"#endif // TEXTURE_luminance\n"+
-" \n"+
-"    \n"+
-"#ifdef TEXTURE_luminance_alpha\n"+
-"    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n"+
-"\n"+
-"#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n"+
-"    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n"+
-"#endif \n"+
-"\n"+
-"#ifdef TEXMODE_modulate\n"+
-"    textureColor = vec4(luminance*lighteffect.rgb, \n"+
-"                        textureColor.a*lighteffect.a);\n"+
-"#endif\n"+
-"\n"+
-"#ifdef TEXMODE_blend\n"+
-"    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n"+
-"                        textureColor.a*lighteffect.a);\n"+
-"#endif\n"+
-"\n"+
-"#ifdef TEXMODE_add\n"+
-"    textureColor = vec4(luminance + lighteffect.rgb, \n"+
-"                        textureColor.a*lighteffect.a);\n"+
-"\n"+
-"#endif\n"+
-"\n"+
-"#endif // TEXTURE_luminance_alpha\n"+
-"    \n"+
-"    fragColor = textureColor;\n"+
-"\n"+
-"#elif defined(IS_TEXT)\n"+
-"    if (textureColor.a < 0.1)\n"+
-"      discard;\n"+
-"    else\n"+
-"      fragColor = textureColor;\n"+
-"#else\n"+
-"    fragColor = lighteffect;\n"+
-"#endif // HAS_TEXTURE\n"+
-"    \n"+
-"#ifdef HAS_FOG\n"+
-"    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n"+
-"    // In Exp and Exp2: use density = density/far\n"+
-"    // fogF will be the proportion of fog\n"+
-"    // Initialize it to the linear value\n"+
-"    float fogF;\n"+
-"    if (uFogMode > 0) {\n"+
-"      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n"+
-"      if (uFogMode > 1)\n"+
-"        fogF = mix(uFogParms.w, 1.0, fogF);\n"+
-"      fogF = fogF*uFogParms.z;\n"+
-"      if (uFogMode == 2)\n"+
-"        fogF = 1.0 - exp(-fogF);\n"+
-"      // Docs are wrong: use (density*c)^2, not density*c^2\n"+
-"      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n"+
-"      else if (uFogMode == 3)\n"+
-"        fogF = 1.0 - exp(-fogF*fogF);\n"+
-"      fogF = clamp(fogF, 0.0, 1.0);\n"+
-"      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n"+
-"    } else gl_FragColor = fragColor;\n"+
-"#else\n"+
-"    gl_FragColor = fragColor;\n"+
-"#endif // HAS_FOG\n"+
-"    \n"+
-"}\n" ;};
-</script>
-<script>    /**
-     * Methods related to textures
-     * @name ___METHODS_FOR_TEXTURES___
-     * @memberof rglwidgetClass
-     * @kind function
-     * @instance
-     */
-     
-    rglwidgetClass.prototype.getTexFilter = function(filter) {
-      var gl = this.gl || this.initGL();
-      switch(filter) {
-        case "nearest": return gl.NEAREST;
-        case "linear": return gl.LINEAR;
-        case "nearest.mipmap.nearest": return gl.NEAREST_MIPMAP_NEAREST;
-        case "linear.mipmap.nearest": return gl.LINEAR_MIPMAP_NEAREST;
-        case "nearest.mipmap.linear": return gl.NEAREST_MIPMAP_LINEAR;
-        case "linear.mipmap.linear": return gl.LINEAR_MIPMAP_LINEAR;
-        default: console.error("Unknown filter: "+filter);
-      }
-    };
-     
-    /**
-     * Handle a texture after its image has been loaded
-     * @param { Object } texture - the gl texture object
-     * @param { Object } textureCanvas - the canvas holding the image
-     */
-    rglwidgetClass.prototype.handleLoadedTexture = function(texture, textureCanvas) {
-      var gl = this.gl || this.initGL();
-      gl.pixelStorei(gl.UNPACK_FLIP_Y_WEBGL, true);
-
-      gl.bindTexture(gl.TEXTURE_2D, texture);
-      gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, gl.RGBA, gl.UNSIGNED_BYTE, textureCanvas);
-      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.LINEAR);
-      gl.texParameteri(gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.LINEAR_MIPMAP_NEAREST);
-      gl.generateMipmap(gl.TEXTURE_2D);
-
-      gl.bindTexture(gl.TEXTURE_2D, null);
-    };
-
-    /**
-     * Get maximum dimension of texture in current browser.
-     * @returns {number}
-     */
-    rglwidgetClass.prototype.getMaxTexSize = function() {
-      var gl = this.gl || this.initGL();	
-      return Math.min(4096, gl.getParameter(gl.MAX_TEXTURE_SIZE));
-    };
-    
-    /**
-     * Load an image to a texture
-     * @param { string } uri - The image location
-     * @param { Object } texture - the gl texture object
-     */
-    rglwidgetClass.prototype.loadImageToTexture = function(uri, texture) {
-      var canvas = this.textureCanvas,
-          ctx = canvas.getContext("2d"),
-          image = new Image(),
-          self = this;
-
-       image.onload = function() {
-
-         var w = image.width,
-             h = image.height,
-             canvasX = self.getPowerOfTwo(w),
-             canvasY = self.getPowerOfTwo(h),
-             maxTexSize = self.getMaxTexSize();
-         while (canvasX > 1 && canvasY > 1 && (canvasX > maxTexSize || canvasY > maxTexSize)) {
-           canvasX /= 2;
-           canvasY /= 2;
-         }
-         canvas.width = canvasX;
-         canvas.height = canvasY;
-         ctx.imageSmoothingEnabled = true;
-         ctx.drawImage(image, 0, 0, canvasX, canvasY);
-         self.handleLoadedTexture(texture, canvas);
-         self.texturesLoading -= 1;
-         if (!self.texturesLoading)
-           self.drawScene();
-       };
-       if (!self.texturesLoading)
-         self.texturesLoading = 0; // may have been undefined
-       self.texturesLoading += 1;
-       image.src = uri;
-     };
-
-    /**
-     * Draw text to the texture canvas
-     * @returns { Object } object with text measurements
-     * @param { string } text - the text
-     * @param { number } cex - expansion
-     * @param { string } family - font family
-     * @param { number } font - font number
-     */
-    rglwidgetClass.prototype.drawTextToCanvas = function(text, cex, family, font) {
-       var canvasX, canvasY,
-           scaling = 20,
-           textColour = "white",
-
-           backgroundColour = "rgba(0,0,0,0)",
-           canvas = this.textureCanvas,
-           ctx = canvas.getContext("2d"),
-           i, textHeight = 0, textHeights = [], width, widths = [], 
-           offsetx, offsety = 0, line, lines = [], offsetsx = [],
-           offsetsy = [], lineoffsetsy = [], fontStrings = [],
-           maxTexSize = this.getMaxTexSize(),
-           getFontString = function(i) {
-             textHeights[i] = scaling*cex[i];
-             var fontString = textHeights[i] + "px",
-                 family0 = family[i],
-                 font0 = font[i];
-             if (family0 === "sans")
-               family0 = "sans-serif";
-             else if (family0 === "mono")
-               family0 = "monospace";
-             fontString = fontString + " " + family0;
-             if (font0 === 2 || font0 === 4)
-               fontString = "bold " + fontString;
-             if (font0 === 3 || font0 === 4)
-               fontString = "italic " + fontString;
-             return fontString;
-           };
-       cex = rglwidgetClass.repeatToLen(cex, text.length);
-       family = rglwidgetClass.repeatToLen(family, text.length);
-       font = rglwidgetClass.repeatToLen(font, text.length);
-
-       canvasX = 1;
-       line = -1;
-       offsetx = maxTexSize;
-       for (i = 0; i < text.length; i++)  {
-         ctx.font = fontStrings[i] = getFontString(i);
-         width = widths[i] = ctx.measureText(text[i]).width;
-         if (offsetx + width > maxTexSize) {
-           offsety = offsety + 2*textHeight;
-           if (line >= 0)
-             lineoffsetsy[line] = offsety;
-           line += 1;
-           if (offsety > maxTexSize)
-             console.error("Too many strings for texture.");
-           textHeight = 0;
-           offsetx = 0;
-         }
-         textHeight = Math.max(textHeight, textHeights[i]);
-         offsetsx[i] = offsetx;
-         offsetx += width;
-         canvasX = Math.max(canvasX, offsetx);
-         lines[i] = line;
-       }
-       offsety = lineoffsetsy[line] = offsety + 2*textHeight;
-       for (i = 0; i < text.length; i++) {
-       	 offsetsy[i] = lineoffsetsy[lines[i]];
-       }
-       
-       canvasX = this.getPowerOfTwo(canvasX);
-       canvasY = this.getPowerOfTwo(offsety);
-
-       canvas.width = canvasX;
-       canvas.height = canvasY;
-
-       ctx.fillStyle = backgroundColour;
-       ctx.fillRect(0, 0, ctx.canvas.width, ctx.canvas.height);
-
-       ctx.textBaseline = "alphabetic";
-       for(i = 0; i < text.length; i++) {
-         ctx.font = fontStrings[i];
-         ctx.fillStyle = textColour;
-         ctx.textAlign = "left";
-         ctx.fillText(text[i], offsetsx[i],  offsetsy[i]);
-       }
-       return {canvasX:canvasX, canvasY:canvasY,
-               widths:widths, textHeights:textHeights,
-               offsetsx:offsetsx, offsetsy:offsetsy};
-     };
-
-</script>
-<script>    /**
-     * Methods related to projections
-     * @name ___METHODS_FOR_PROJECTIONS___
-     * @memberof rglwidgetClass
-     * @kind function
-     * @instance
-     */
-     
-    /**
-     * Get the viewport
-     */
-     
-    rglwidgetClass.prototype.getViewport = function(id) {
-      var vp = this.getObj(id).par3d.viewport,
-         x = vp.x*this.canvas.width,
-         y = vp.y*this.canvas.height,
-         width = vp.width*this.canvas.width,
-         height = vp.height*this.canvas.height;
-       this.vp = {x:x, y:y, width:width, height:height};
-    };
-    
-    /**
-     * Set the gl viewport and scissor test
-     * @param { number } id - id of subscene
-     */
-    rglwidgetClass.prototype.setViewport = function(id) {
-       var gl = this.gl || this.initGL();
-       this.getViewport(id);
-       gl.viewport(this.vp.x, this.vp.y, this.vp.width, this.vp.height);
-       gl.scissor(this.vp.x, this.vp.y, this.vp.width, this.vp.height);
-       gl.enable(gl.SCISSOR_TEST);
-     };
-
-    /**
-     * Set the projection matrix for a subscene
-     * @param { number } id - id of subscene
-     */
-    rglwidgetClass.prototype.setprMatrix = function(id) {
-       var subscene = this.getObj(id),
-          embedding = subscene.embeddings.projection;
-       if (embedding === "replace")
-         this.prMatrix.makeIdentity();
-       else
-         this.setprMatrix(subscene.parent);
-       if (embedding === "inherit")
-         return;
-       // This is based on the Frustum::enclose code from geom.cpp
-       var bbox = subscene.par3d.bbox,
-           scale = subscene.par3d.scale,
-           ranges = [(bbox[1]-bbox[0])*scale[0]/2,
-                     (bbox[3]-bbox[2])*scale[1]/2,
-                     (bbox[5]-bbox[4])*scale[2]/2],
-           radius = Math.sqrt(this.sumsq(ranges))*1.1; // A bit bigger to handle labels
-       if (radius <= 0) radius = 1;
-       var observer = subscene.par3d.observer,
-           distance = observer[2],
-           FOV = subscene.par3d.FOV, ortho = FOV === 0,
-           t = ortho ? 1 : Math.tan(FOV*Math.PI/360),
-           near = distance - radius,
-           far = distance + radius,
-           hlen,
-           aspect = this.vp.width/this.vp.height,
-           z = subscene.par3d.zoom,
-           userProjection = subscene.par3d.userProjection;
-       if (far < 0.0)
-         far = 1.0;
-       if (near < far/100.0)
-         near = far/100.0;
-       this.frustum = {near:near, far:far};
-       hlen = t*near;
-       if (ortho) {
-         if (aspect > 1)
-           this.prMatrix.ortho(-hlen*aspect*z, hlen*aspect*z,
-                          -hlen*z, hlen*z, near, far);
-         else
-           this.prMatrix.ortho(-hlen*z, hlen*z,
-                          -hlen*z/aspect, hlen*z/aspect,
-                          near, far);
-       } else {
-         if (aspect > 1)
-           this.prMatrix.frustum(-hlen*aspect*z, hlen*aspect*z,
-                          -hlen*z, hlen*z, near, far);
-         else
-           this.prMatrix.frustum(-hlen*z, hlen*z,
-                          -hlen*z/aspect, hlen*z/aspect,
-                          near, far);
-       }
-       this.prMatrix.multRight(userProjection);
-     };
-
-    /**
-     * Set the model-view matrix for a subscene
-     * @param { number } id - id of the subscene
-     */
-    rglwidgetClass.prototype.setmvMatrix = function(id) {
-       var observer = this.getObj(id).par3d.observer;
-       this.mvMatrix.makeIdentity();
-       this.setmodelMatrix(id);
-       this.mvMatrix.translate(-observer[0], -observer[1], -observer[2]);
-
-     };
-
-    /**
-     * Set the model matrix for a subscene
-     * @param { number } id - id of the subscene
-     */
-    rglwidgetClass.prototype.setmodelMatrix = function(id) {
-      var subscene = this.getObj(id),
-          embedding = subscene.embeddings.model;
-      if (embedding === "replace") {
-        var bbox = subscene.par3d.bbox,
-            center = [(bbox[0]+bbox[1])/2,
-                      (bbox[2]+bbox[3])/2,
-                      (bbox[4]+bbox[5])/2];
-        this.mvMatrix.translate(-center[0], -center[1], -center[2]);
-      }
-      if (embedding !== "inherit") {
-        var scale = subscene.par3d.scale;
-        this.mvMatrix.scale(scale[0], scale[1], scale[2]);
-        this.mvMatrix.multRight( subscene.par3d.userMatrix );
-      }
-      if (embedding !== "replace")
-        this.setmodelMatrix(subscene.parent);
-     };
-
-    /**
-     * Set the normals matrix for a subscene
-     * @param { number } subsceneid - id of the subscene
-     */
-     rglwidgetClass.prototype.setnormMatrix2 = function() {
-       this.normMatrix = new CanvasMatrix4(this.mvMatrix);
-       this.normMatrix.invert();
-       this.normMatrix.transpose();
-     };
-
-    /**
-     * Set the combined projection-model-view matrix
-     */
-    rglwidgetClass.prototype.setprmvMatrix = function() {
-       this.prmvMatrix = new CanvasMatrix4( this.mvMatrix );
-       this.prmvMatrix.multRight( this.prMatrix );
-     };
-
-    rglwidgetClass.prototype.setInvPrMatrix = function() {
-      this.invPrMatrix = new CanvasMatrix4( this.prMatrix );
-      this.invPrMatrix.invert();
-      this.invPrMatrix.transpose();
-    };
-</script>
-<script>    /**
-     * Methods related to mouse handling
-     * @name ___METHODS_FOR_MOUSE_HANDLING___
-     * @memberof rglwidgetClass
-     * @kind function
-     * @instance
-     */
-     
-    rglwidgetClass.prototype.getCursor = function(mode) {
-      switch(mode) {
-        case "none": 
-          return "none";
-        case "trackball":
-        case "xAxis":
-        case "yAxis":
-        case "zAxis":
-        case "polar":
-          return "grab";
-        case "selecting":
-          return "crosshair";
-        case "fov":
-        case "zoom":
-          return "zoom-in";
-        case "user":
-          return "default";
-      }
-      return "dragging";
-    };
-    
-    /**
-     * Set mouse mode for a subscene
-     * @param { string } mode - name of mode
-     * @param { number } button - button number (0 to 4)
-     * @param { number } subscene - subscene id number
-     * @param { number } stayActive - if truthy, don't clear brush
-     */
-    rglwidgetClass.prototype.setMouseMode = function(mode, button, subscene, stayActive) {
-      var sub = this.getObj(subscene),
-          which = ["none", "left", "right", "middle", "wheel"][button];
-      if (!stayActive && sub.par3d.mouseMode[which] === "selecting")
-        this.clearBrush(null);
-      sub.par3d.mouseMode[which] = mode;
-      if (button === 1 || (button === 0 && mode !== "none"))
-        this.canvas.style.cursor = this.getCursor(mode);
-      if (button === 0 && mode !== "none")
-        sub.needsBegin = mode;
-    };
-
-    /**
-     * Compute mouse coordinates relative to current canvas
-     * @returns { Object }
-     * @param { Object } event - event object from mouse click
-     */
-    rglwidgetClass.prototype.relMouseCoords = function(event) {
-      var rect = this.canvas.getBoundingClientRect();
-      return {x:event.clientX-rect.left, y:event.clientY-rect.top};
-    };
-    
-    /**
-     * Send mouse selection to Shiny
-     */
-    rglwidgetClass.prototype.recordSelection = function(subid) {
-      var result = {};
-      if (typeof this.select !== "undefined" && 
-          typeof this.select.state !== "undefined" &&
-          this.select.state !== "inactive") {
-        result = { subscene: subid,
-                   state: this.select.state,
-                   region: this.select.region
-                 };
-        this.setmvMatrix(subid);
-        result.model = this.mvMatrix;
-        this.setprMatrix(subid);
-        result.proj = this.prMatrix;
-        this.getViewport(subid);
-        result.view = this.vp;
-      } else
-        result.state = "inactive";
-      Shiny.setInputValue(this.scene.selectionInput + ":shinyMouse3d", result);
-    }; 
-
-    /**
-     * Set mouse handlers for the scene
-     */
-    rglwidgetClass.prototype.setMouseHandlers = function() {
-      var self = this, activeSubscene, handler,
-          handlers = {}, drag = 0;
-
-      handlers.rotBase = 0;
-
-      self.screenToVector = function(x, y) {
-        var viewport = self.getObj(activeSubscene).par3d.viewport,
-          width = viewport.width*self.canvas.width,
-          height = viewport.height*self.canvas.height,
-          radius = Math.max(width, height)/2.0,
-          cx = width/2.0,
-          cy = height/2.0,
-          px = (x-cx)/radius,
-          py = (y-cy)/radius,
-          plen = Math.sqrt(px*px+py*py);
-        if (plen > 1.e-6) {
-          px = px/plen;
-          py = py/plen;
-        }
-        var angle = (Math.SQRT2 - plen)/Math.SQRT2*Math.PI/2,
-          z = Math.sin(angle),
-          zlen = Math.sqrt(1.0 - z*z);
-        px = px * zlen;
-        py = py * zlen;
-        return [px, py, z];
-      };
-
-      handlers.trackballdown = function(x,y) {
-        var activeSub = self.getObj(activeSubscene),
-            activeModel = self.getObj(self.useid(activeSub.id, "model")),
-            i, l = activeModel.par3d.listeners;
-        handlers.rotBase = self.screenToVector(x, y);
-        self.saveMat = [];
-        for (i = 0; i < l.length; i++) {
-          activeSub = self.getObj(l[i]);
-          activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
-        }
-        self.canvas.style.cursor = "grabbing";
-      };
-
-      handlers.trackballmove = function(x,y) {
-        var rotCurrent = self.screenToVector(x,y),
-            rotBase = handlers.rotBase,
-            dot = rotBase[0]*rotCurrent[0] +
-                  rotBase[1]*rotCurrent[1] +
-                  rotBase[2]*rotCurrent[2],
-            angle = Math.acos( dot/rglwidgetClass.vlen(rotBase)/rglwidgetClass.vlen(rotCurrent) )*180.0/Math.PI,
-            axis = rglwidgetClass.xprod(rotBase, rotCurrent),
-            objects = self.scene.objects,
-            activeSub = self.getObj(activeSubscene),
-            activeModel = self.getObj(self.useid(activeSub.id, "model")),
-            l = activeModel.par3d.listeners,
-            i;
-        if (angle === 0.0)
-          return;    
-        for (i = 0; i < l.length; i++) {
-          activeSub = self.getObj(l[i]);
-          activeSub.par3d.userMatrix.load(objects[l[i]].saveMat);
-          activeSub.par3d.userMatrix.rotate(angle, axis[0], axis[1], axis[2]);
-        }
-        self.drawScene();
-      };
-      handlers.trackballend = 0;
-
-      self.clamp = function(x, lo, hi) {
-      	return Math.max(lo, Math.min(x, hi));
-      };
-
-      self.screenToPolar = function(x,y) {
-        var viewport = self.getObj(activeSubscene).par3d.viewport,
-          width = viewport.width*self.canvas.width,
-          height = viewport.height*self.canvas.height,
-    	  r = Math.min(width, height)/2,
-    	  dx = self.clamp(x - width/2, -r, r),
-    	  dy = self.clamp(y - height/2, -r, r);
-    	  return [Math.asin(dx/r), Math.asin(-dy/r)];
-      };
-
-      handlers.polardown = function(x,y) {
-        var activeSub = self.getObj(activeSubscene),
-            activeModel = self.getObj(self.useid(activeSub.id, "model")),
-            i, l = activeModel.par3d.listeners;
-        handlers.dragBase = self.screenToPolar(x, y);
-        self.saveMat = [];
-        for (i = 0; i < l.length; i++) {
-          activeSub = self.getObj(l[i]);
-          activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
-          activeSub.camBase = [-Math.atan2(activeSub.saveMat.m13, activeSub.saveMat.m11),
-                               Math.atan2(activeSub.saveMat.m32, activeSub.saveMat.m22)];
-        }
-        self.canvas.style.cursor = "grabbing";
-      };
-
-      handlers.polarmove = function(x,y) {
-        var dragCurrent = self.screenToPolar(x,y),
-            activeSub = self.getObj(activeSubscene),
-            activeModel = self.getObj(self.useid(activeSub.id, "model")),
-            objects = self.scene.objects,
-            l = activeModel.par3d.listeners,
-            i, j, changepos = [];
-        for (i = 0; i < l.length; i++) {
-          activeSub = self.getObj(l[i]);
-          for (j=0; j<2; j++)
-            changepos[j] = -(dragCurrent[j] - handlers.dragBase[j]);
-          activeSub.par3d.userMatrix.makeIdentity();
-          activeSub.par3d.userMatrix.rotate(changepos[0]*180/Math.PI, 0,-1,0);
-          activeSub.par3d.userMatrix.multRight(objects[l[i]].saveMat);
-          activeSub.par3d.userMatrix.rotate(changepos[1]*180/Math.PI, -1,0,0);
-        }
-        self.drawScene();
-      };
-      handlers.polarend = 0;
-
-      handlers.axisdown = function(x) {
-        handlers.rotBase = self.screenToVector(x, self.canvas.height/2);
-        var activeSub = self.getObj(activeSubscene),
-            activeModel = self.getObj(self.useid(activeSub.id, "model")),
-            i, l = activeModel.par3d.listeners;
-        for (i = 0; i < l.length; i++) {
-          activeSub = self.getObj(l[i]);
-          activeSub.saveMat = new CanvasMatrix4(activeSub.par3d.userMatrix);
-        }
-        self.canvas.style.cursor = "grabbing";
-      };
-
-      handlers.axismove = function(x) {
-        var rotCurrent = self.screenToVector(x, self.canvas.height/2),
-            rotBase = handlers.rotBase,
-            angle = (rotCurrent[0] - rotBase[0])*180/Math.PI,
-            rotMat = new CanvasMatrix4();
-        rotMat.rotate(angle, handlers.axis[0], handlers.axis[1], handlers.axis[2]);
-        var activeSub = self.getObj(activeSubscene),
-            activeModel = self.getObj(self.useid(activeSub.id, "model")),
-            i, l = activeModel.par3d.listeners;
-        for (i = 0; i < l.length; i++) {
-          activeSub = self.getObj(l[i]);
-          activeSub.par3d.userMatrix.load(activeSub.saveMat);
-          activeSub.par3d.userMatrix.multLeft(rotMat);
-        }
-        self.drawScene();
-      };
-      handlers.axisend = 0;
-
-      handlers.y0zoom = 0;
-      handlers.zoomdown = function(x, y) {
-        var activeSub = self.getObj(activeSubscene),
-          activeProjection = self.getObj(self.useid(activeSub.id, "projection")),
-          i, l = activeProjection.par3d.listeners;
-        handlers.y0zoom = y;
-        for (i = 0; i < l.length; i++) {
-          activeSub = self.getObj(l[i]);
-          activeSub.zoom0 = Math.log(activeSub.par3d.zoom);
-        }
-        self.canvas.style.cursor = "zoom-in";
-      };
-      handlers.zoommove = function(x, y) {
-        var activeSub = self.getObj(activeSubscene),
-            activeProjection = self.getObj(self.useid(activeSub.id, "projection")),
-            i, l = activeProjection.par3d.listeners;
-        for (i = 0; i < l.length; i++) {
-          activeSub = self.getObj(l[i]);
-          activeSub.par3d.zoom = Math.exp(activeSub.zoom0 + (y-handlers.y0zoom)/self.canvas.height);
-        }
-        self.drawScene();
-      };
-      handlers.zoomend = 0;
-
-      handlers.y0fov = 0;
-      handlers.fovdown = function(x, y) {
-        handlers.y0fov = y;
-        var activeSub = self.getObj(activeSubscene),
-          activeProjection = self.getObj(self.useid(activeSub.id, "projection")),
-          i, l = activeProjection.par3d.listeners;
-        for (i = 0; i < l.length; i++) {
-          activeSub = self.getObj(l[i]);
-          activeSub.fov0 = activeSub.par3d.FOV;
-        }
-        self.canvas.style.cursor = "zoom-in";
-      };
-      handlers.fovmove = function(x, y) {
-        var activeSub = self.getObj(activeSubscene),
-            activeProjection = self.getObj(self.useid(activeSub.id, "projection")),
-            i, l = activeProjection.par3d.listeners;
-        for (i = 0; i < l.length; i++) {
-          activeSub = self.getObj(l[i]);
-          activeSub.par3d.FOV = Math.max(1, Math.min(179, activeSub.fov0 +
-             180*(y-handlers.y0fov)/self.canvas.height));
-        }
-        self.drawScene();
-      };
-      handlers.fovend = 0;
-      
-      handlers.selectingdown = function(x, y) {
-      	var viewport = self.getObj(activeSubscene).par3d.viewport,
-      	  width = viewport.width*self.canvas.width,
-      	  height = viewport.height*self.canvas.height, 
-          p = {x: 2.0*x/width - 1.0, y: 2.0*y/height - 1.0};
-      	self.select.region = {p1: p, p2: p};
-      	if (self.select.subscene && self.select.subscene !== activeSubscene)
-      	  self.delFromSubscene(self.scene.brushId, self.select.subscene);
-      	self.select.subscene = activeSubscene;
-      	self.addToSubscene(self.scene.brushId, activeSubscene);
-      	self.select.state = "changing";
-      	if (typeof self.scene.brushId !== "undefined")
-      	  self.getObj(self.scene.brushId).initialized = false;
-      	if (typeof self.scene.selectionInput !== "undefined")
-      	  self.recordSelection(activeSubscene); 
-      	self.drawScene();
-      	self.canvas.style.cursor = "crosshair";
-      };
-      
-      handlers.selectingmove = function(x, y) {
-      	var viewport = self.getObj(activeSubscene).par3d.viewport,
-      	  width = viewport.width*self.canvas.width,
-      	  height = viewport.height*self.canvas.height;
-      	if (self.select.state === "inactive") 
-      	  return;
-      	self.select.region.p2 = {x: 2.0*x/width - 1.0, y: 2.0*y/height - 1.0};
-      	if (typeof self.scene.brushId !== "undefined")
-      	  self.getObj(self.scene.brushId).initialized = false;
-      	if (typeof self.scene.selectionInput !== "undefined")
-      	  self.recordSelection(activeSubscene);
-      	self.drawScene();
-      };
-      
-      handlers.selectingend = 0;
-      /* jshint evil:true */
-      handlers.userdown = function(x, y) {
-        var sub = self.getObj(activeSubscene),
-            code = sub.callbacks[drag].begin;
-        if (code) {
-          var fn = Function('"use strict";return (' + code + ')')();
-          fn.call(self, x, y);
-        }
-      };
-      
-      handlers.usermove = function(x, y) {
-        var sub = self.getObj(activeSubscene),
-            code = sub.callbacks[drag].update;
-        if (code) {
-          var fn = Function('"use strict";return (' + code + ')')();
-          fn.call(self, x, y);
-        }
-      };
-      
-      handlers.userend = function() {
-        var sub = self.getObj(activeSubscene),
-            code = sub.callbacks[drag].end;
-        if (code) {
-          var fn = Function('"use strict";return (' + code + ')')();
-          fn.call(self);
-        }
-      };
-
-      self.canvas.onpointerdown = function ( ev ){
-        // pointers and mice differ in capture rules; 
-        // act like a mouse.
-        if (ev.target.hasPointerCapture(ev.pointerId))
-          ev.target.releasePointerCapture(ev.pointerId);
-          
-        if (!ev.which) // Use w3c defns in preference to MS
-        switch (ev.button) {
-          case 0: ev.which = 1; break;
-          case 1:
-          case 4: ev.which = 2; break;
-          case 2: ev.which = 3;
-        }
-        drag = ["none", "left", "middle", "right", "wheel"][ev.which];
-        var coords = self.relMouseCoords(ev);
-        coords.y = self.canvas.height-coords.y;
-        activeSubscene = self.whichSubscene(coords);
-        var sub = self.getObj(activeSubscene), f;
-        handler = sub.par3d.mouseMode[drag];
-        switch (handler) {
-        case "xAxis":
-          handler = "axis";
-          handlers.axis = [1.0, 0.0, 0.0];
-          break;
-        case "yAxis":
-          handler = "axis";
-          handlers.axis = [0.0, 1.0, 0.0];
-          break;
-        case "zAxis":
-          handler = "axis";
-          handlers.axis = [0.0, 0.0, 1.0];
-          break;
-        }
-        f = handlers[handler + "down"];
-        if (f) {
-          coords = self.translateCoords(activeSubscene, coords);
-          f.call(self, coords.x, coords.y);
-          ev.preventDefault();
-        } else
-          console.warn("Mouse handler '" + handler + "' is not implemented.");
-
-      };
-
-      self.canvas.onpointerup = function ( ev ){
-        if ( !drag ) return;
-        var f = handlers[handler + "end"];
-        if (f) {
-          f.call(self);
-          ev.preventDefault();
-        }
-        drag = 0;
-        handlers.onpointermove( ev );
-      };
-
-      self.canvas.onpointerout = self.canvas.onpointerup;
-
-      handlers.onpointermove = function ( ev ) {
-        var coords = self.relMouseCoords(ev), sub, f;
-        coords.y = self.canvas.height - coords.y;
-        if (ev.buttons === 0) {
-          activeSubscene = self.whichSubscene(coords);
-          drag = "none";
-          sub = self.getObj(activeSubscene);
-          handler = sub.par3d.mouseMode.none;
-          if (handler !== "none") {
-            if (sub.needsBegin) {
-              f = handlers[handler + "down"];
-              if (f) {
-                coords = self.translateCoords(activeSubscene, coords);
-                f.call(self, coords.x, coords.y);
-              }
-              sub.needsBegin = 0;
-            }
-            self.canvas.style.cursor = self.getCursor(sub.par3d.mouseMode.none);
-          } else {
-            self.canvas.style.cursor = self.getCursor(sub.par3d.mouseMode.left);  
-            return;
-          }
-        }
-        f = handlers[handler + "move"];
-        if (f) {
-          coords = self.translateCoords(activeSubscene, coords);
-          f.call(self, coords.x, coords.y);
-        }
-      };
-      
-
-      self.canvas.onpointerenter = function() {
-        self.canvas.addEventListener("pointermove",               handlers.onpointermove);
-      };
-      
-      self.canvas.onpointerleave = function() {
-        self.canvas.removeEventListener("pointermove",
-          handlers.onpointermove);
-      };
-
-      handlers.setZoom = function(ds) {
-        var i;
-        if (typeof activeSubscene === "undefined")
-          activeSubscene = self.scene.rootSubscene;
-        var activeSub = self.getObj(activeSubscene),
-            activeProjection = self.getObj(self.useid(activeSub.id, "projection")),
-            l = activeProjection.par3d.listeners;
-
-        for (i = 0; i < l.length; i++) {
-          activeSub = self.getObj(l[i]);
-          activeSub.par3d.zoom *= ds;
-        }
-        self.drawScene();
-      };
-      
-      handlers.pushwheel = function(ev) {
-        ev.deltaY = -ev.deltaY;
-        handlers.pullwheel(ev);
-      };
-      
-      handlers.pullwheel = function(ev) {
-        var del = 1.05;
-        if (ev.shiftKey) del = 1.005;
-        var ds = ev.deltaY < 0 ? del : (1 / del);
-        handlers.setZoom(ds);
-      };
-      
-      handlers.user2wheel = function(ev) {
-        var sub = self.getObj(activeSubscene),
-            code = sub.callbacks.wheel.rotate;
-        if (code) {
-          var fn = Function('"use strict";return (' + code + ')')();
-          /* jshint evil:false */
-          fn.call(self, ev.deltaY < 0 ? 1 : 2);
-        }        
-      };
-        
-      handlers.wheelHandler = function(ev) {
-        var coords = self.relMouseCoords(ev);
-        coords.y = self.canvas.height - coords.y;
-        activeSubscene = self.whichSubscene(coords);
-        var sub = self.getObj(activeSubscene), f,
-            handler = sub.par3d.mouseMode.wheel,
-            evlocal;
-            
-        ev.deltaY = ev.deltaY || ev.detail || ev.deltaX || ev.wheelDelta;
-                      
-        switch(handler) {
-          case "none": break;
-          case "push":
-          case "pull":
-          case "user2":
-            f = handlers[handler + "wheel"];
-            if (f) {
-              evlocal = {};
-              evlocal.deltaY = ev.deltaY;
-              evlocal.shiftKey = ev.shiftKey;
-              evlocal.preventDefault = function() { ev.preventDefault(); };
-              f.call(self, evlocal);
-            }
-            break;
-          default: 
-            evlocal = {};
-            evlocal.preventDefault = function() { ev.preventDefault(); };
-            evlocal.which = 4;
-            evlocal.clientX = self.canvas.width/2;
-            evlocal.clientY = self.canvas.height/2;
-            self.canvas.onpointerdown(evlocal);
-            evlocal.clientX += ev.deltaX;
-            evlocal.clientY += ev.deltaY;
-            handlers.onpointermove(evlocal);
-            self.canvas.onpointerup(evlocal);
-        }
-        ev.preventDefault();
-      };
-      
-      handlers.get_finger_dist = function(ev) {
-        var diffX = ev.touches[0].clientX - ev.touches[1].clientX,
-            diffY = ev.touches[0].clientY - ev.touches[1].clientY;
-        return Math.sqrt(diffX * diffX + diffY * diffY); 
-      };
-      
-      handlers.touchstart = function(ev) {
-        var touch = ev.touches[0],
-          mouseEvent = new MouseEvent("pointerdown",
-            {
-              clientX: touch.clientX,
-              clientY: touch.clientY
-            });
-        ev.preventDefault();
-        if (ev.touches.length === 2) {
-          var coords = self.relMouseCoords(touch);
-          coords.y = self.canvas.height-coords.y;
-          activeSubscene = self.whichSubscene(coords);
-          handlers.finger_dist0 = handlers.get_finger_dist(ev);
-          handlers.zoomdown(coords.x, coords.y);
-        }
-        self.dispatchEvent(mouseEvent);
-      };
-      
-      handlers.touchend = function(ev) {
-        var mouseEvent;
-        ev.preventDefault();
-        if (ev.touches.length === 1) {
-          mouseEvent = new MouseEvent("pointerup", {});
-          self.dispatchEvent(mouseEvent);
-        }
-      };
-      
-      handlers.touchmove = function(ev) {
-        var touch = ev.touches[0],
-          mouseEvent;
-        ev.preventDefault();
-        if (ev.touches.length > 1) {
-          var coords = self.relMouseCoords(touch),
-              new_dist = handlers.get_finger_dist(ev);
-          coords.y = self.canvas.height*Math.log(handlers.finger_dist0/new_dist) + handlers.y0zoom;
-          handlers.zoommove(coords.x, coords.y);
-        } else {
-          mouseEvent = new MouseEvent("pointermove",
-          {
-            clientX: touch.clientX,
-            clientY: touch.clientY
-          });
-          self.dispatchEvent(mouseEvent);
-        }
-      };
-
-      self.canvas.addEventListener("DOMMouseScroll", handlers.wheelHandler, false);
-      self.canvas.addEventListener("mousewheel", handlers.wheelHandler, false);
-      self.canvas.addEventListener("touchstart", handlers.touchstart, {passive: false});
-      self.canvas.addEventListener("touchend", handlers.touchend, {passive: false});
-      self.canvas.addEventListener("touchmove", handlers.touchmove, {passive: false});
-	  };
-</script>
-<script>    /**
-     * Methods related to initialization
-     * @name ___METHODS_FOR_INITIALIZATION___
-     * @memberof rglwidgetClass
-     * @kind function
-     * @instance
-     */
-     
-    /**
-     * Initial test for WebGL
-     */
-    rglwidgetClass.prototype.initGL0 = function() {
-      if (!window.WebGLRenderingContext){
-        this.alertOnce("Your browser does not support WebGL. See http://get.webgl.org");
-        return;
-      }
-    };
-
-    /**
-     * Initialize WebGL
-     * @returns { Object } the WebGL context
-     */
-    rglwidgetClass.prototype.initGL = function() {
-      var self = this, success = false;
-      if (this.gl) {
-      	if (!this.drawing && this.gl.isContextLost())
-          this.restartCanvas();
-        else
-          return this.gl;
-      }
-      // if (!this.isInBrowserViewport()) return; Return what??? At this point we know this.gl is null.
-      this.canvas.addEventListener("webglcontextrestored",
-        this.onContextRestored, false);
-      this.canvas.addEventListener("webglcontextlost",
-        this.onContextLost, false);
-      this.gl = this.canvas.getContext("webgl", this.webGLoptions) ||
-               this.canvas.getContext("experimental-webgl", this.webGLoptions);
-      success = !!(this.gl && this.gl instanceof WebGLRenderingContext);
-      if (!success)
-        this.alertOnce("Your browser does not support WebGL. See http://get.webgl.org"); 
-      this.index_uint = this.gl.getExtension("OES_element_index_uint");
-      var save = this.startDrawing();
-      Object.keys(this.scene.objects).forEach(function(key){
-        self.initObjId(parseInt(key, 10));
-        });
-      this.stopDrawing(save);
-      return this.gl;
-    };
-
-    /**
-     * Resize the display to match element
-     * @param { Object } el - DOM element to match
-     */
-    rglwidgetClass.prototype.resize = function(el) {
-      this.canvas.width = el.width;
-      this.canvas.height = el.height;
-    };
-
-    /**
-     * Initialize the sphere object
-     */
-    rglwidgetClass.prototype.initSphere = function(sections, segments) {
-      var v = [], phi = [], theta = [], it = [], centers = [],
-           i, j, k, ind, result = {};
-       
-      for (i = 0; i <= sections; i++) {
-        phi.push(i/sections - 0.5);
-      }
-
-      for (j = 0; j <= segments; j++) {
-        theta.push(2*j/segments);
-        for (i = 0; i <= sections; i++) {
-          /* These are [x,y,z,s,t]: */
-          v.push([Math.sin(Math.PI*theta[j]) * Math.cos(Math.PI*phi[i]),
-                  Math.sin(Math.PI*phi[i]),
-                  Math.cos(Math.PI*theta[j]) * Math.cos(Math.PI*phi[i]),                               
-                  theta[j]/2,
-                  phi[i] + 0.5]);
-           // console.log("xyzst="+v[v.length-1]);
-        }
-      }
-      result.values = new Float32Array(rglwidgetClass.flatten(v));
-      result.vertexCount = v.length;
-      
-      for (j = 0; j < segments; j++) {
-        for (i = 0; i < sections; i++) {
-          ind = i + (sections + 1)*j;
-          if (i > 0)                       // Not south pole
-            it.push([ind, 
-                     ind + sections + 1,
-                     ind + 1]);
-          if (i < sections - 1)             // Not north pole
-            it.push([ind + sections + 1, 
-                     ind + sections + 2,
-                     ind + 1]);
-        }
-      }
-      result.it = new Uint16Array(rglwidgetClass.flatten(it));
-      
-      for (i = 0; i < it.length; i++) {
-        centers.push([0,0,0]);
-        for (j = 0; j < 3; j++) { // x,y,z
-          for (k = 0; k < 3; k++) {// vertices
-            centers[i][j] += v[it[i][k]][j]/3;
-          }
-        }
-      }
-      result.centers = centers;
-      
-      result.vOffsets = {vofs:0, cofs:-1, nofs:0, radofs:-1, oofs:-1,
-                         tofs:3, nextofs:-1, pointofs:-1, stride:5};
-
-      result.f = [];
-      result.indices = {};
-
-      result.colorCount = 1;
-      result.type = "sphere";
-      this.sphere = result;
-      this.initShapeGL(this.sphere);
-    };
-
-    /**
-     * Initialize the cube object
-     */
-    rglwidgetClass.prototype.initCube = function() {
-   var v = [[0, 0, 0], [1, 0, 0], 
-            [0, 1, 0], [1, 1, 0], 
-            [0, 0, 1], [1, 0, 1],
-            [0, 1, 1], [1, 1, 1]],
-          ib = [[0, 2, 3, 1], 
-                [2, 6, 7, 3], 
-                [1, 3, 7, 5], 
-                [0, 4, 6, 2], 
-                [0, 1, 5, 4], 
-                [4, 5, 7, 6]], 
-          centers = [], i, j, k, 
-          i0, i1, i2,
-          normal, result = {};
-       
-      for (i = 0; i < ib.length; i++) {
-        centers.push([0,0,0]);
-        for (j = 0; j < 3; j++) { // x,y,z
-          for (k = 0; k < 4; k++) {// vertices
-            centers[i][j] += v[ib[i][k]][j]/4;
-          }
-        }
-      }
-      result.centers = centers; 
-      result.values = new Float32Array(6*4*3*2);
-      result.vertexCount = 24;
-      result.vertices = new Array(24);
-      result.normals = new Array(24);
-      for (i=0; i < 6; i++) {
-        for (j=0; j < 4; j++) {
-          i0 = ib[i][j];
-          result.vertices[4*i + j] = v[i0];
-          i1 = ib[i][(j + 1) % 4];
-          i2 = ib[i][(j + 2) % 4];
-          if (j === 0)
-            normal = rglwidgetClass.normalize(rglwidgetClass.xprod(rglwidgetClass.vdiff(v[i1], v[i0]),
-                                  rglwidgetClass.vdiff(v[i2], v[i0])));
-          result.normals[4*i + j] = normal;
-          for (k=0; k < 3; k++) {
-            result.values[i*24 + j*6 + k] = v[i0][k];
-            result.values[i*24 + j*6 + 3 + k] = normal[k];
-          }
-        }
-        for (j=0; j<4; j++)
-          ib[i][j] = 4*i + j;
-      }
-      result.ib = new Uint16Array(rglwidgetClass.flatten(ib));
-      
-      result.vOffsets = {vofs:0, cofs:-1, nofs:3, radofs:-1, oofs:-1,
-                         tofs:-1, nextofs:-1, pointofs:-1, stride:6};
-
-      result.f = [];
-      result.indices = {};
-
-      result.colorCount = 1;
-      result.type = "quads";
-      this.cube = result;
-      this.initShapeGL(this.cube);
-    };
-    
-
-    /**
-     * Do the gl part of initializing the sphere and cube
-     */
-    rglwidgetClass.prototype.initShapeGL = function(shape) {
-      var gl = this.gl || this.initGL();
-      if (gl.isContextLost()) return;
-      shape.buf = gl.createBuffer();
-      gl.bindBuffer(gl.ARRAY_BUFFER, shape.buf);
-      gl.bufferData(gl.ARRAY_BUFFER, shape.values, gl.STATIC_DRAW);
-      shape.ibuf = [gl.createBuffer(), gl.createBuffer()];
-      return;
-    };
-
-    /* Initialize common sphere object from spheres object
-    */
-    rglwidgetClass.prototype.initShapeFromObj = function(shape, obj) {
-      var i, pass, f, mode, self = this,
-        /* This function selects things that would be
-           the back, ignoring perspective -- this is what 
-           we want for the bounding box decoration. */
-        is_back = function(i) {
-                var normal = [].concat(shape.normals[i]),
-                  pt = shape.vertices[i];
-                normal.push(-rglwidgetClass.dotprod(normal, pt));
-                normal = rglwidgetClass.multVM(normal, self.normMatrix);
-                return normal[2] < 0 || (normal[2] === 0 && normal[0] < 0);
-              }; 
-      shape.ofsLoc = obj.ofsLoc;
-      shape.texLoc = obj.texLoc;
-      shape.texture = obj.texture;
-      shape.sampler = obj.sampler;
-      shape.uFogMode = obj.uFogMode;
-      shape.uFogColor = obj.uFogColor;
-      shape.uFogParms = obj.uFogParms;
-      shape.userAttribLocations = obj.userAttribLocations;
-      shape.userUniformLocations = obj.userUniformLocations;
-      shape.normLoc = obj.normLoc;
-      shape.invPrMatLoc = obj.invPrMatLoc;
-      shape.clipLoc = obj.clipLoc;
-      shape.nextLoc = obj.nextLoc;
-      shape.pointLoc = obj.pointLoc;
-      shape.aspectLoc = obj.aspectLoc;
-      shape.lwdLoc = obj.lwdLoc;
-      shape.prog = obj.prog;
-      shape.material = obj.material;
-      shape.flags = obj.flags;
-      shape.defFlags = obj.defFlags;
-      shape.someHidden = obj.someHidden;
-      shape.fastTransparency = obj.fastTransparency;
-      shape.nlights = obj.nlights;
-      shape.emission = obj.emission;
-      shape.emissionLoc = obj.emissionLoc;
-      shape.shininess = obj.shininess;
-      shape.shininessLoc = obj.shininessLoc;
-      shape.ambient = obj.ambient;
-      shape.ambientLoc = obj.ambientLoc;
-      shape.specular = obj.specular;
-      shape.specularLoc = obj.specularLoc;
-      shape.diffuse = obj.diffuse;
-      shape.diffuseLoc = obj.diffuseLoc;
-      shape.lightDir = obj.lightDir;
-      shape.lightDirLoc = obj.lightDirLoc;
-      shape.viewpoint = obj.viewpoint;
-      shape.viewpointLoc = obj.viewpointLoc;
-      shape.finite = obj.finite;
-      shape.finiteLoc = obj.finiteLoc;
-      shape.prMatLoc = obj.prMatLoc;
-      shape.mvMatLoc = obj.mvMatLoc;
-      shape.normMatLoc = obj.normMatLoc;
-      shape.frontLoc = obj.frontLoc;
-      shape.index_uint = false;
-      shape.is_transparent = obj.is_transparent;
-      shape.ignoreExtent = obj.ignoreExtent;
-      if (shape.passes !== obj.passes ||
-          JSON.stringify( shape.pmode) !== JSON.stringify(obj.pmode)) {
-        shape.passes = obj.passes;
-        shape.pmode = obj.pmode;
-        for (pass = 0; pass < obj.passes; pass++) {
-          mode =  shape.pmode[pass];
-          if (typeof  shape.indices[mode] === "undefined") {
-            f = [];
-            switch (mode) {
-            case "culled": break;
-            case "points":
-              f.length =  shape.vertexCount;
-              for (i=0; i < f.length; i++)
-                f[i] = i;
-              break;
-            case "lines":
-              if (typeof shape.it !== "undefined") {
-                f.length = 2* shape.it.length;
-      	        for (i=0; i <  shape.it.length/3; i++) {
-      	          f[6*i] =  shape.it[3*i];
-      	          f[6*i + 1] =  shape.it[3*i + 1];
-      	          f[6*i + 2] =  shape.it[3*i + 1];
-      	          f[6*i + 3] =  shape.it[3*i + 2];
-      	          f[6*i + 4] =  shape.it[3*i + 2];
-      	          f[6*i + 5] =  shape.it[3*i];
-      	        }
-              } else {
-                f.length = 2*shape.ib.length;
-                for (i=0; i < shape.ib.length/4; i++) {
-                  f[8*i] = shape.ib[4*i];
-                  f[8*i + 1] = shape.ib[4*i + 1];
-                  f[8*i + 2] = shape.ib[4*i + 1];
-                  f[8*i + 3] = shape.ib[4*i + 2];
-                  f[8*i + 4] = shape.ib[4*i + 2];
-                  f[8*i + 5] = shape.ib[4*i + 3];
-                  f[8*i + 6] = shape.ib[4*i + 3];
-                  f[8*i + 7] = shape.ib[4*i];
-                }
-              }
-      	      break;
-      	    case "filled":
-      	      if (typeof shape.it !== "undefined")
-      	        f =  shape.it;
-      	      else if (typeof shape.ib !== "undefined") {
-      	        f.length = 1.5*shape.ib.length;
-                for (i=0; i < shape.ib.length/4; i++) {
-                  f[6*i] = shape.ib[4*i];
-                  f[6*i+1] = shape.ib[4*i + 1];
-                  f[6*i+2] = shape.ib[4*i + 2];
-                  f[6*i+3] = shape.ib[4*i];
-                  f[6*i+4] = shape.ib[4*i + 2];
-                  f[6*i+5] = shape.ib[4*i + 3];
-                }      	        
-      	      }
-      	      break;
-      	    }              
-            shape.indices[mode] = new Uint16Array(f);
-          }
-        }
-      }       
-      for (pass = 0; pass < obj.passes; pass++) {
-        mode =  shape.pmode[pass];
-        shape.f[pass] =  shape.indices[mode];
-        if (typeof obj.draw_front !== "undefined" &&
-            !obj.draw_front) {
-          shape.f[pass] = shape.f[pass].filter(is_back);   
-        }
-      }
-      // console.log("Names in  shapes not in  shape:"+JSON.stringify(rglwidgetClass.keydiff(obj,  shape)));
-       shape.initialized = true;
-    };
-
-    /**
-     * Initialize a subscene
-     * @param { number } id - id of subscene.
-     */
-    rglwidgetClass.prototype.initSubscene = function(id) {
-      var sub = this.getObj(id),
-          i, obj;
-
-      if (sub.type !== "subscene")
-        return;
-
-      sub.par3d.userMatrix = this.toCanvasMatrix4(sub.par3d.userMatrix);
-      sub.par3d.userProjection = this.toCanvasMatrix4(sub.par3d.userProjection);
-      sub.par3d.userProjection.transpose();
-      sub.par3d.listeners = [].concat(sub.par3d.listeners);
-      sub.backgroundId = undefined;
-      sub.subscenes = [];
-      sub.clipplanes = [];
-      sub.transparent = [];
-      sub.opaque = [];
-      sub.lights = [];
-      sub.needsBegin = true;
-      if (typeof sub.objects !== "undefined")
-        sub.objects = [].concat(sub.objects); /* make sure it's an array */
-      for (i=0; i < sub.objects.length; i++) {
-        obj = this.getObj(sub.objects[i]);
-        if (typeof obj === "undefined") {
-          sub.objects.splice(i, 1);
-          i--;
-        } else if (obj.type === "background")
-          sub.backgroundId = obj.id;
-        else
-          sub[this.whichList(obj.id)].push(obj.id);
-      }
-    };
-    
-    rglwidgetClass.prototype.initBBox = function(obj) {
-      if (!this.cube)
-        this.initCube();
-      obj.cube = {id: obj.id + 0.1,
-                    type: "quads",
-                    flags: obj.flags,
-                    material: obj.material,
-                    colors: [obj.colors[0]],
-                    vertices: this.cube.vertices,
-                    normals: this.cube.normals,
-                    draw_front: obj.draw_front,
-                    initialized: false
-        };
-      if (this.getMaterial(obj.cube, "front") !==
-          this.getMaterial(obj.cube, "back"))
-        /* jshint bitwise: false */  
-        obj.cube.flags |= rglwidgetClass.f_is_twosided;
-        /* jshint bitwise: true */
-      this.scene.objects[obj.cube.id] = obj.cube;
-      obj.ticks = {id: obj.id + 0.2,
-                     type: "lines",
-                     flags: rglwidgetClass.f_has_fog,
-                     material: obj.material,
-                     colors: (obj.colors.length > 1 ? [obj.colors[1]] : [obj.colors[0]]),
-                     axes: obj.axes,
-                     initialized: false
-      };
-      this.scene.objects[obj.ticks.id] = obj.ticks;
-      obj.labels = {id: obj.id + 0.3,
-                     type: "text",
-                     flags: rglwidgetClass.f_has_fog + 
-                            rglwidgetClass.f_fixed_size + 
-                            rglwidgetClass.f_fixed_quads,
-                     material: {lit: false},
-                     colors: (obj.colors.length > 1 ? [obj.colors[1]] : [obj.colors[0]]),
-                     cex: [[1]],
-                     family: [["sans"]],
-                     font: [[1]],
-                     adj: [[0.5, 0.5, 0.5]],
-                     ignoreExtent: true,
-                     initialized: false
-      };
-      this.scene.objects[obj.labels.id] = obj.labels;
-      obj.initialized = true;
-    };
-    
-    rglwidgetClass.prototype.initBackground = function(obj) {
-      var material, fl = obj.defFlags;
-      if (typeof obj.ids !== "undefined")
-        obj.quad = rglwidgetClass.flatten([].concat(obj.ids));
-      else if (obj.sphere) {
-        fl.has_normals = true;
-        fl.needs_vnormal = true;
-        obj.defFlags = fl;
-        material = obj.material;
-        material.front = "culled";
-        obj.vertices = [[0,0,0]];
-        obj.texcoords = [[0,0]];
-      }  
-    };
-
-    /**
-     * Initialize object for display
-     * @param { number } id - id of object to initialize
-     */
-    rglwidgetClass.prototype.initObjId = function(id) {
-      if (typeof id !== "number") {
-        this.alertOnce("initObj id is "+typeof id);
-      }
-      return this.initObj(this.getObj(id));
-    };
-
-    /**
-     * Initialize object for display
-     * @param { Object } obj - object to initialize
-     */
-    rglwidgetClass.prototype.initObj = function(obj) {
-      var type = obj.type, 
-          flags = obj.flags,
-          normals = obj.normals,
-          round_points = (typeof obj.material === "undefined") ?
-            false : this.getMaterial(obj, "point_antialias"),
-          has_indices = typeof obj.indices !== "undefined",
-          has_spheres = type === "spheres" || 
-                        (type === "background" && obj.sphere),
-          sprites_3d = rglwidgetClass.isSet(flags, rglwidgetClass.f_sprites_3d),
-          depth_sort = rglwidgetClass.isSet(flags, rglwidgetClass.f_depth_sort),
-          gl = this.gl || this.initGL(),
-          fl, polygon_offset,
-          texinfo, drawtype, nclipplanes, f, nrows, oldrows,
-          i,j,v,v1,v2, mat, uri, matobj, pass, pmode,
-          dim, nx, nz, nrow, shaders;
-
-    obj.initialized = true;
-    
-    obj.someHidden = false; // used in selection
-    
-    this.expandBufferedFields(obj);
-    
-    if (type === "subscene")
-      return;
-      
-    obj.defFlags = fl = rglwidgetClass.getDefFlags(flags, type, normals, round_points);
-  
-    obj.is_transparent = fl.is_transparent;
-  
-    if (type === "bboxdeco")
-      return this.initBBox(obj);
-      
-    if (has_spheres && typeof this.sphere === "undefined")
-      this.initSphere(16, 16);
-
-    if (type === "light") {
-      obj.ambient = new Float32Array(obj.colors[0].slice(0,3));
-      obj.diffuse = new Float32Array(obj.colors[1].slice(0,3));
-      obj.specular = new Float32Array(obj.colors[2].slice(0,3));
-      obj.lightDir = new Float32Array(obj.vertices[0]);
-      return;
-    }
-
-    if (type === "clipplanes") {
-      obj.vClipplane = rglwidgetClass.flatten(rglwidgetClass.cbind(obj.normals, obj.offsets));
-      return;
-    }
-
-    if (type === "background") {
-      this.initBackground(obj);
-      if (!obj.sphere)
-        return;
-    }
-
-    polygon_offset = this.getMaterial(obj, "polygon_offset");
-    if (polygon_offset[0] !== 0 || polygon_offset[1] !== 0)
-      obj.polygon_offset = polygon_offset;
-
-    if (fl.is_transparent) {
-      depth_sort = ["triangles", "quads", "surface",
-                    "spheres", "sprites", "text",
-                    "planes"].indexOf(type) >= 0;
-    }
-    
-    if (fl.is_brush)
-      this.initSelection(obj.id);
-
-    if (typeof obj.vertices === "undefined")
-      obj.vertices = [];
-
-    v = obj.vertices;
-    if (has_indices)
-      obj.vertexCount = obj.indices.length;
-    else
-      obj.vertexCount = v.length;
-      
-    if (!obj.vertexCount) return;
-
-    if (fl.is_twosided && !fl.has_normals && type !== "background") {
-      if (typeof obj.userAttributes === "undefined")
-        obj.userAttributes = {};
-      v1 = Array(v.length);
-      v2 = Array(v.length);
-      if (obj.type === "triangles" || obj.type === "quads") {
-      	if (obj.type === "triangles")
-      	  nrow = 3;
-      	else
-      	  nrow = 4;
-        for (i=0; i<Math.floor(v.length/nrow); i++)
-          for (j=0; j<nrow; j++) {
-            v1[nrow*i + j] = v[nrow*i + ((j+1) % nrow)];
-            v2[nrow*i + j] = v[nrow*i + ((j+2) % nrow)];
-          }
-      } else if (obj.type === "surface") {
-        dim = obj.dim[0];
-        nx = dim[0];
-        nz = dim[1];
-        for (j=0; j<nx; j++) {
-          for (i=0; i<nz; i++) {
-            if (i+1 < nz && j+1 < nx) {
-              v2[j + nx*i] = v[j + nx*(i+1)];
-              v1[j + nx*i] = v[j+1 + nx*(i+1)];
-            } else if (i+1 < nz) {
-              v2[j + nx*i] = v[j-1 + nx*i];
-              v1[j + nx*i] = v[j + nx*(i+1)];
-            } else {
-              v2[j + nx*i] = v[j + nx*(i-1)];
-              v1[j + nx*i] = v[j-1 + nx*(i-1)];
-            }
-          }
-        }
-      }
-      obj.userAttributes.aPos1 = v1;
-      obj.userAttributes.aPos2 = v2;
-    }
-
-    if (!sprites_3d) {
-      if (gl.isContextLost()) return;
-      if (typeof obj.prog !== "undefined") {
-        gl.deleteProgram(obj.prog);
-        obj.prog = undefined;
-      }
-      
-      shaders = this.getShaders(obj);
-      
-      obj.prog = gl.createProgram();
-      gl.attachShader(obj.prog, this.getShader( gl.VERTEX_SHADER,
-                      shaders.vertex ));
-      gl.attachShader(obj.prog, this.getShader( gl.FRAGMENT_SHADER,
-                      shaders.fragment ));
-      //  Force aPos to location 0, aCol to location 1
-      gl.bindAttribLocation(obj.prog, 0, "aPos");
-      gl.bindAttribLocation(obj.prog, 1, "aCol");
-      gl.linkProgram(obj.prog);
-      var linked = gl.getProgramParameter(obj.prog, gl.LINK_STATUS);
-      if (!linked) {
-
-        // An error occurred while linking
-        var lastError = gl.getProgramInfoLog(obj.prog);
-        console.warn("Error in program linking:" + lastError);
-
-        gl.deleteProgram(obj.prog);
-        return;
-      }
-    }
-
-    if (type === "text") {
-      texinfo = this.drawTextToCanvas(obj.texts,
-                                      rglwidgetClass.flatten(obj.cex),
-                                      rglwidgetClass.flatten(obj.family),
-                                      rglwidgetClass.flatten(obj.family));
-    }
-
-    if (fl.fixed_quads && !sprites_3d) {
-      obj.ofsLoc = gl.getAttribLocation(obj.prog, "aOfs");
-    }
-
-    if (fl.has_texture || type === "text") {
-      if (!obj.texture) {
-        obj.texture = gl.createTexture();
-        // This is a trick from https://stackoverflow.com/a/19748905/2554330 to avoid warnings
-        gl.bindTexture(gl.TEXTURE_2D, obj.texture);
-        gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, 1, 1, 0, gl.RGBA, gl.UNSIGNED_BYTE,
-              new Uint8Array([255,255,255, 255])); // white
-      }
-      obj.texLoc = gl.getAttribLocation(obj.prog, "aTexcoord");
-      obj.sampler = gl.getUniformLocation(obj.prog, "uSampler");
-    }
-    
-    if (fl.has_fog && !sprites_3d) {
-      obj.uFogMode = gl.getUniformLocation(obj.prog, "uFogMode");
-      obj.uFogColor = gl.getUniformLocation(obj.prog, "uFogColor");
-      obj.uFogParms = gl.getUniformLocation(obj.prog, "uFogParms");
-    }
-
-    if (fl.has_texture) {
-      mat = obj.material;
-      if (typeof mat.uri !== "undefined")
-        uri = mat.uri;
-      else if (typeof mat.uriElementId === "undefined") {
-        matobj = this.getObj(mat.uriId);
-        if (typeof matobj !== "undefined") {
-          uri = matobj.material.uri;
-        } else {
-          uri = "";
-        }
-      } else
-        uri = document.getElementById(mat.uriElementId).rglinstance.getObj(mat.uriId).material.uri;
-
-      this.loadImageToTexture(uri, obj.texture);
-    }
-
-    if (type === "text") {
-      this.handleLoadedTexture(obj.texture, this.textureCanvas);
-    }
-
-    var stride = 3, nc, cofs, nofs, radofs, oofs, tofs, vnew, fnew,
-        nextofs = -1, pointofs = -1, alias, colors, key, selection,
-        filter, adj, offset, attr, last, options, 
-        len, current;
-
-    obj.alias = undefined;
-    
-    colors = obj.colors;
-
-    j = this.scene.crosstalk.id.indexOf(obj.id);
-    if (j >= 0) {
-      key = this.scene.crosstalk.key[j];
-      options = this.scene.crosstalk.options[j];
-      colors = colors.slice(0); 
-      for (i = 0; i < v.length; i++)
-        colors[i] = obj.colors[i % obj.colors.length].slice(0);
-      if ( (selection = this.scene.crosstalk.selection) &&
-           (selection.length || !options.selectedIgnoreNone) )
-        for (i = 0; i < v.length; i++) {
-          if (!selection.includes(key[i])) {
-            if (options.deselectedColor)
-              colors[i] = options.deselectedColor.slice(0);
-            colors[i][3] = colors[i][3]*options.deselectedFade;   /* default: mostly transparent if not selected */
-          } else if (options.selectedColor)
-            colors[i] = options.selectedColor.slice(0);
-        }
-      if ( (filter = this.scene.crosstalk.filter) )
-        for (i = 0; i < v.length; i++) 
-          if (!filter.includes(key[i])) {
-            if (options.filteredColor)
-              colors[i] = options.filteredColor.slice(0);
-            colors[i][3] = colors[i][3]*options.filteredFade;   /* default: completely hidden if filtered */
-          }
-    }  
-    
-    nc = obj.colorCount = colors.length;
-    if (nc > 1) {
-      cofs = stride;
-      stride = stride + 4;
-      v = rglwidgetClass.cbind(v, colors);
-    } else {
-      cofs = -1;
-      obj.onecolor = rglwidgetClass.flatten(colors);
-    }
-
-    if (fl.has_normals && !has_spheres) {
-      nofs = stride;
-      stride = stride + 3;
-      v = rglwidgetClass.cbind(v, typeof obj.pnormals !== "undefined" ? obj.pnormals : obj.normals);
-    } else
-      nofs = -1;
-
-    if (typeof obj.radii !== "undefined") {
-      radofs = stride;
-      stride = stride + 1;
-      // FIXME:  always concat the radii?
-      if (obj.radii.length === v.length) {
-        v = rglwidgetClass.cbind(v, obj.radii);
-      } else if (obj.radii.length === 1) {
-        v = v.map(function(row) { return row.concat(obj.radii[0]);});
-      }
-    } else
-      radofs = -1;
-      
-    // Add default indices
-    if (has_indices) {
-      f = Array(obj.indices.length);
-      for (i = 0; i < f.length; i++)
-        f[i] = obj.indices[i] - 1;
-    } else {
-      f = Array(v.length);
-      for (i = 0; i < v.length; i++)
-        f[i] = i;
-    }
-    obj.f = [f,f];
-
-    if (type === "sprites" && !sprites_3d) {
-      tofs = stride;
-      stride += 2;
-      oofs = stride;
-      stride += 3;
-      vnew = new Array(4*v.length);
-      fnew = new Array(4*v.length);
-      alias = new Array(v.length);
-      var rescale = fl.fixed_size ? 72 : 1,
-          size = obj.radii, s = rescale*size[0]/2;
-      last = v.length;
-      f = obj.f[0];
-      obj.adj = rglwidgetClass.flatten(obj.adj);
-      if (typeof obj.pos !== "undefined") {
-        obj.pos = rglwidgetClass.flatten(obj.pos);
-        offset = obj.adj[0];
-      } else
-        offset = 0;
-      for (i=0; i < v.length; i++) {
-        adj = this.getAdj(obj, i, offset);
-        if (size.length > 1)
-          s = rescale*size[i]/2;
-        adj[0] = 2*s*(adj[0] - 0.5);
-        adj[1] = 2*s*(adj[1] - 0.5);
-        adj[2] = 2*s*(adj[2] - 0.5);
-        vnew[i]  = v[i].concat([0,0]).concat([-s-adj[0],
-                                              -s-adj[1],
-                                              -adj[2]]);
-        fnew[4*i] = f[i];
-        vnew[last]= v[i].concat([1,0]).concat([s-adj[0],
-                                              -s-adj[1],
-                                              -adj[2]]);
-        fnew[4*i+1] = last++;
-        vnew[last]= v[i].concat([1,1]).concat([s-adj[0],
-                                               s-adj[1],
-                                               -adj[2]]);
-        fnew[4*i+2] = last++;
-        vnew[last]= v[i].concat([0,1]).concat([-s-adj[0],
-                                                s-adj[1],
-                                                -adj[2]]);
-        fnew[4*i+3] = last++;
-        alias[i] = [last-3, last-2, last-1];
-      }
-      v = vnew;
-      obj.vertexCount = v.length;
-      obj.f = [fnew, fnew];
-    } else if (type === "text") {
-      tofs = stride;
-      stride += 2;
-      oofs = stride;
-      stride += 3;
-      vnew = new Array(4*v.length);
-      f = obj.f[0];
-      fnew = new Array(4*f.length);
-      alias = new Array(v.length);
-      last = v.length;
-      adj = rglwidgetClass.flatten(obj.adj);
-      if (typeof obj.pos !== "undefined") {
-        obj.pos = rglwidgetClass.flatten(obj.pos);
-        offset = adj[0];
-      } else
-        offset = 0;
-      for (i=0; i < v.length; i++) {
-        adj = this.getAdj(obj, i, offset, obj.texts[i]);
-        vnew[i]  = v[i].concat([0,-0.5]).concat(adj);
-        fnew[4*i] = f[i];
-        vnew[last] = v[i].concat([1,-0.5]).concat(adj);
-        fnew[4*i+1] = last++;
-        vnew[last] = v[i].concat([1, 1.5]).concat(adj);
-        fnew[4*i+2] = last++;
-        vnew[last] = v[i].concat([0, 1.5]).concat(adj);
-        fnew[4*i+3] = last++;
-        alias[i] = [last-3, last-2, last-1];
-        for (j=0; j < 4; j++) {
-          v1 = vnew[fnew[4*i+j]];
-          v1[oofs] = 2*(v1[tofs]-v1[oofs])*texinfo.widths[i];
-          v1[oofs+1] = 2*(v1[tofs+1]-v1[oofs+1])*texinfo.textHeights[i];
-          v1[oofs+2] = 2*(0.5-v1[oofs+2])*texinfo.textHeights[i]/1000.0;
-          v1[tofs] = (texinfo.offsetsx[i] + v1[tofs]*texinfo.widths[i])/texinfo.canvasX;
-          v1[tofs+1] = 1.0-(texinfo.offsetsy[i] -
-              v1[tofs+1]*texinfo.textHeights[i])/texinfo.canvasY;
-          vnew[fnew[4*i+j]] = v1;
-        }
-      }
-      v = vnew;
-      obj.vertexCount = v.length;
-      obj.f = [fnew, fnew];
-    } else if (typeof obj.texcoords !== "undefined") {
-      tofs = stride;
-      stride += 2;
-      oofs = -1;
-      v = rglwidgetClass.cbind(v, obj.texcoords);
-    } else {
-      tofs = -1;
-      oofs = -1;
-    }
-    
-    obj.alias = alias;
-                          
-    if (typeof obj.userAttributes !== "undefined") {
-      obj.userAttribOffsets = {};
-      obj.userAttribLocations = {};
-      obj.userAttribSizes = {};
-      for (attr in obj.userAttributes) {
-      	obj.userAttribLocations[attr] = gl.getAttribLocation(obj.prog, attr);
-      	if (obj.userAttribLocations[attr] >= 0) { // Attribute may not have been used
-      	  obj.userAttribOffsets[attr] = stride;
-      	  v = rglwidgetClass.cbind(v, obj.userAttributes[attr]);
-      	  stride = v[0].length;
-      	  obj.userAttribSizes[attr] = stride - obj.userAttribOffsets[attr];
-      	} else
-      	  console.warn("attribute '"+attr+"' not found in object "+obj.id+".");
-      }
-    }
-
-    if (typeof obj.userUniforms !== "undefined" ||
-        typeof obj.userTextures !== "undefined") {
-      obj.userUniformLocations = {};
-      for (attr in obj.userUniforms) {
-        obj.userUniformLocations[attr] = gl.getUniformLocation(obj.prog, attr);
-        if (obj.userUniformLocations[attr] === null)
-          console.warn("uniform '"+attr+"' not found in object "+obj.id+".");
-      }
-      for (attr in obj.userTextures) {
-        var texture = obj.userTextures[attr];
-        texture.texture = gl.createTexture();
-        // This is a trick from https://stackoverflow.com/a/19748905/2554330 to avoid warnings
-        gl.bindTexture(gl.TEXTURE_2D, texture.texture);
-        gl.texImage2D(gl.TEXTURE_2D, 0, gl.RGBA, 1, 1, 0, gl.RGBA, gl.UNSIGNED_BYTE,
-              new Uint8Array([255,255,255, 255])); // white
-        texture.sampler = gl.getUniformLocation(obj.prog, attr);
-        if (texture.sampler === null)
-          console.warn("sampler '"+attr+"' not found in object "+obj.id+".");
-        uri = texture.uri;
-        this.loadImageToTexture(uri, texture.texture);
-      }
-    }
-
-    if (sprites_3d) {
-      obj.userMatrix = new CanvasMatrix4();
-      obj.userMatrix.load(rglwidgetClass.flatten(obj.usermatrix));
-      obj.objects = rglwidgetClass.flatten([].concat(obj.ids));
-      fl.is_lit = false;
-      obj.adj = rglwidgetClass.flatten(obj.adj);
-      
-      if (typeof obj.pos !== "undefined") {
-        obj.pos = rglwidgetClass.flatten(obj.pos);
-        obj.offset = obj.adj[0];
-      } else
-        obj.offset = 0;
-        
-      var shapenum = rglwidgetClass.flatten(obj.shapenum);
-      obj.shapelens = [];
-      obj.shapefirst = [];
-      obj.shapefirst.push(0);
-      len = 0;
-      current = 0;
-      for (i = 0; i < shapenum.length; i++) {
-        if (shapenum[i] === shapenum[current]) {
-          len++;
-        } else {
-          obj.shapelens.push(len);
-          len = 1;
-          current = i;
-          obj.shapefirst.push(i);
-        }
-      }
-      obj.shapelens.push(len);
-        
-      for (i=0; i < obj.objects.length; i++)
-        this.initObjId(obj.objects[i]);
-    }
-
-    nclipplanes = this.countClipplanes();
-    if (nclipplanes && !sprites_3d) {
-      obj.clipLoc = gl.getUniformLocation(obj.prog,"vClipplane");
-    }
-
-    if (fl.is_lit) {
-      obj.emissionLoc = gl.getUniformLocation(obj.prog, "emission");
-      obj.emission = new Float32Array(this.stringToRgb(this.getMaterial(obj, "emission")));
-      obj.shininessLoc = gl.getUniformLocation(obj.prog, "shininess");
-      obj.shininess = this.getMaterial(obj, "shininess");
-      obj.nlights = this.countLights();
-      if (obj.nlights > 0) {
-        obj.ambient = new Float32Array(this.stringToRgb(this.getMaterial(obj, "ambient")));
-        obj.specular = new Float32Array(this.stringToRgb(this.getMaterial(obj, "specular")));
-        obj.ambientLoc = gl.getUniformLocation(obj.prog, "ambient");
-        obj.specularLoc = gl.getUniformLocation(obj.prog, "specular");
-        obj.diffuseLoc = gl.getUniformLocation(obj.prog, "diffuse" );
-        obj.lightDirLoc = gl.getUniformLocation(obj.prog, "lightDir");
-        obj.viewpointLoc = gl.getUniformLocation(obj.prog, "viewpoint");
-        obj.finiteLoc = gl.getUniformLocation(obj.prog, "finite" );
-      }
-    }
-    
-    obj.passes = fl.is_twosided + 1;
-    obj.pmode = new Array(obj.passes);
-    for (pass = 0; pass < obj.passes; pass++) {
-      if (type === "triangles" || type === "quads" || type === "surface" || has_spheres)
-      	pmode = this.getMaterial(obj, (pass === 0) ? "front" : "back");
-      else pmode = "filled";
-      obj.pmode[pass] = pmode;
-    }
-    if (!has_spheres) {
-      obj.f.length = obj.passes;
-      for (pass = 0; pass < obj.passes; pass++) {
-      	f = fnew = obj.f[pass];
-        pmode = obj.pmode[pass];
-      	if (pmode === "culled")
-      	  fnew = [];
-        else if (pmode === "points") {
-          // stay with default
-        } else if ((type === "quads" || type === "text" ||
-             type === "sprites") && !sprites_3d) {
-          nrows = Math.floor(obj.vertexCount/4);
-          if (pmode === "filled") {
-            fnew = Array(6*nrows);
-            for (i=0; i < nrows; i++) {
-              fnew[6*i] = f[4*i];
-              fnew[6*i+1] = f[4*i + 1];
-              fnew[6*i+2] = f[4*i + 2];
-              fnew[6*i+3] = f[4*i];
-              fnew[6*i+4] = f[4*i + 2];
-              fnew[6*i+5] = f[4*i + 3];
-            }
-          } else {
-            fnew = Array(8*nrows);
-            for (i=0; i < nrows; i++) {
-              fnew[8*i] = f[4*i];
-              fnew[8*i+1] = f[4*i + 1];
-              fnew[8*i+2] = f[4*i + 1];
-              fnew[8*i+3] = f[4*i + 2];
-              fnew[8*i+4] = f[4*i + 2];
-              fnew[8*i+5] = f[4*i + 3];
-              fnew[8*i+6] = f[4*i + 3];
-              fnew[8*i+7] = f[4*i];
-            }
-          }
-        } else if (type === "triangles") {
-          nrows = Math.floor(obj.vertexCount/3);
-          if (pmode === "filled") {
-            fnew = Array(3*nrows);
-            for (i=0; i < fnew.length; i++) {
-              fnew[i] = f[i];
-            }
-          } else if (pmode === "lines") {
-            fnew = Array(6*nrows);
-      	    for (i=0; i < nrows; i++) {
-      	      fnew[6*i] = f[3*i];
-      	      fnew[6*i + 1] = f[3*i + 1];
-      	      fnew[6*i + 2] = f[3*i + 1];
-      	      fnew[6*i + 3] = f[3*i + 2];
-      	      fnew[6*i + 4] = f[3*i + 2];
-      	      fnew[6*i + 5] = f[3*i];
-      	    }
-          }
-        } else if (has_spheres) {
-          // default
-        } else if (type === "surface") {
-          dim = obj.dim[0];
-          nx = dim[0];
-          nz = dim[1];
-          if (pmode === "filled") {
-            fnew = [];
-            for (j=0; j<nx-1; j++) {
-              for (i=0; i<nz-1; i++) {
-                fnew.push(f[j + nx*i],
-                       f[j + nx*(i+1)],
-                       f[j + 1 + nx*(i+1)],
-                       f[j + nx*i],
-                       f[j + 1 + nx*(i+1)],
-                       f[j + 1 + nx*i]);
-              }
-            }
-          } else if (pmode === "lines") {
-            fnew = [];
-            for (j=0; j<nx; j++) {
-              for (i=0; i<nz; i++) {
-                if (i+1 < nz)
-                  fnew.push(f[j + nx*i],
-                         f[j + nx*(i+1)]);
-                if (j+1 < nx)
-                  fnew.push(f[j + nx*i],
-                         f[j+1 + nx*i]);
-              }
-            }
-          }
-        }
-        obj.f[pass] = fnew;
-        if (depth_sort) {
-          drawtype = "DYNAMIC_DRAW";
-        } else {
-          drawtype = "STATIC_DRAW";
-        }
-      }
-    }
-    
-    if (fl.fat_lines) {
-      alias = undefined;
-      obj.nextLoc = gl.getAttribLocation(obj.prog, "aNext");
-      obj.pointLoc = gl.getAttribLocation(obj.prog, "aPoint");
-      obj.aspectLoc = gl.getUniformLocation(obj.prog, "uAspect");
-      obj.lwdLoc = gl.getUniformLocation(obj.prog, "uLwd");
-      // Expand vertices to turn each segment into a pair of triangles
-        
-      	for (pass = 0; pass < obj.passes; pass++) {
-      	  f = obj.f[pass];	
-          oldrows = f.length;
-      	  if (obj.pmode[pass] === "lines") 
-      	    break;
-      	}
-      
-      if (type === "linestrip") 
-        nrows = 4*(oldrows - 1); 
-      else
-        nrows = 2*oldrows;
-      vnew = new Array(nrows);
-      fnew = new Array(1.5*nrows);
-      
-      // We're going to turn each pair of vertices into 4 new ones, with the "next" and "pt" attributes
-      // added.
-      // We do this by copying the originals in the first pass, adding the new attributes, then in a 
-      // second pass add new vertices at the end.
-
-      for (i = 0; i < v.length; i++) {
-        vnew[i] = v[i].concat([0,0,0,0,0]); 
-      }
-
-      nextofs = stride;
-      pointofs = stride + 3;
-      stride = stride + 5;
-            
-      // Now add the extras
-      var ind, k;
-      last = v.length - 1;
-      ind = 0;
-      alias = new Array(f.length);
-      for (i = 0; i < f.length; i++)
-        alias[i] = [];
-      for (i = 0; i < f.length - 1; i++) {
-      	if (type !== "linestrip" && i % 2 === 1)
-      	  continue;
-      	k = ++last;
-      	vnew[k] = vnew[f[i]].slice();
-      	for (j=0; j<3; j++)
-      	  vnew[k][nextofs + j] = vnew[f[i+1]][j];
-      	vnew[k][pointofs] = -1;
-      	vnew[k][pointofs+1] = -1;
-      	fnew[ind] = k;
-      	last++;
-      	vnew[last] = vnew[k].slice();
-      	vnew[last][pointofs] = 1;
-      	fnew[ind+1] = last;
-      	alias[f[i]].push(last-1, last);
-      	last++;
-      	k = last;
-      	vnew[k] = vnew[f[i+1]].slice();
-      	for (j=0; j<3; j++)
-      	  vnew[k][nextofs + j] = vnew[f[i]][j];
-      	vnew[k][pointofs] = -1;
-      	vnew[k][pointofs+1] = 1;
-      	fnew[ind+2] = k;
-      	fnew[ind+3] = fnew[ind+1];
-      	last++;
-      	vnew[last] = vnew[k].slice();
-      	vnew[last][pointofs] = 1;
-      	fnew[ind+4] = last;
-      	fnew[ind+5] = fnew[ind+2];
-      	ind += 6;
-      	alias[f[i+1]].push(last-1, last);
-      }
-      vnew.length = last+1;
-      v = vnew;
-      obj.vertexCount = v.length;
-      if (typeof alias !== "undefined" && typeof obj.alias !== "undefined") {  // Already have aliases from previous section?
-        var oldalias = obj.alias, newalias = Array(obj.alias.length);
-        for (i = 0; i < newalias.length; i++) {
-          newalias[i] = oldalias[i].slice();
-          for (j = 0; j < oldalias[i].length; j++)
-            Array.prototype.push.apply(newalias[i], alias[oldalias[j]]); // pushes each element 
-        }
-        obj.alias = newalias;
-      } else
-        obj.alias = alias;
-      
-      for (pass = 0; pass < obj.passes; pass++)
-      	if (type === "lines" || type === "linestrip" || obj.pmode[pass] === "lines") {
-          obj.f[pass] = fnew;
-        }
-      
-      if (depth_sort) 
-        drawtype = "DYNAMIC_DRAW";
-      else
-        drawtype = "STATIC_DRAW";
-    }
-    
-      for (pass = 0; pass < obj.passes; pass++) {
-        if (obj.vertexCount > 65535) {
-          if (this.index_uint) {
-            obj.f[pass] = new Uint32Array(obj.f[pass]);
-            obj.index_uint = true;
-          } else
-            this.alertOnce("Object has "+obj.vertexCount+" vertices, not supported in this browser.");
-        } else {
-          obj.f[pass] = new Uint16Array(obj.f[pass]);
-          obj.index_uint = false;
-        }
-      }
-    
-    if (stride !== v[0].length) {
-      this.alertOnce("problem in stride calculation");
-    }
-
-    obj.vOffsets = {vofs:0, cofs:cofs, nofs:nofs, radofs:radofs, oofs:oofs, tofs:tofs,
-                    nextofs:nextofs, pointofs:pointofs, stride:stride};
-
-    obj.values = new Float32Array(rglwidgetClass.flatten(v));
-
-    if (!has_spheres && !sprites_3d) {
-      obj.buf = gl.createBuffer();
-      gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
-      gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW); //
-      obj.ibuf = Array(obj.passes);
-      obj.ibuf[0] = gl.createBuffer();
-      gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[0]);
-      gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, obj.f[0], gl[drawtype]);
-      if (fl.is_twosided) {
-      	obj.ibuf[1] = gl.createBuffer();
-      	gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[1]);
-      	gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, obj.f[1], gl[drawtype]);
-      }
-    }
-
-    if (!sprites_3d) {
-      obj.mvMatLoc = gl.getUniformLocation(obj.prog, "mvMatrix");
-      obj.prMatLoc = gl.getUniformLocation(obj.prog, "prMatrix");
-
-      if (fl.fixed_size) {
-        obj.textScaleLoc = gl.getUniformLocation(obj.prog, "textScale");
-      }
-    }
-
-    if (fl.needs_vnormal) {
-      obj.normLoc = gl.getAttribLocation(obj.prog, "aNorm");
-      obj.normMatLoc = gl.getUniformLocation(obj.prog, "normMatrix");
-    }
-
-    if (fl.is_twosided) {
-      obj.frontLoc = gl.getUniformLocation(obj.prog, "front");
-      if (fl.has_normals)
-        obj.invPrMatLoc = gl.getUniformLocation(obj.prog, "invPrMatrix");
-    }
-  };
-    
-    /**
-     * Initialize the DOM object
-     * @param { Object } el - the DOM object
-     * @param { Object } x - the scene data sent by JSON from R
-     */
-    rglwidgetClass.prototype.initialize = function(el, x) {
-      this.textureCanvas = document.createElement("canvas");
-      this.textureCanvas.style.display = "block";
-      this.scene = x;
-      this.normMatrix = new CanvasMatrix4();
-      this.invPrMatrix = new CanvasMatrix4();
-      this.saveMat = {};
-      this.distance = null;
-      this.posLoc = 0;
-      this.colLoc = 1;
-      if (el) {
-        el.rglinstance = this;
-        this.el = el;
-        this.webGLoptions = el.rglinstance.scene.webGLoptions;
-        this.initCanvas();
-      }
-      if (typeof Shiny !== "undefined") {
-        var self = this;
-        Shiny.addCustomMessageHandler("shinyGetPar3d",
-          function(message) {
-            var i, param, 
-                subscene = self.getObj(message.subscene),
-                parameters = [].concat(message.parameters),
-                result = {tag: message.tag, subscene: message.subscene};
-            if (typeof subscene !== "undefined") {
-              for (i = 0; i < parameters.length; i++) {
-                param = parameters[i];
-                result[param] = subscene.par3d[param];
-              }
-            } else {
-              console.log("subscene "+message.subscene+" undefined.");
-            }
-            Shiny.setInputValue("par3d:shinyPar3d", result, {priority: "event"});
-          });
-          
-        Shiny.addCustomMessageHandler("shinySetPar3d",
-          function(message) {
-            var param = message.parameter, 
-                subscene = self.getObj(message.subscene);
-            if (typeof subscene !== "undefined") {
-              subscene.par3d[param] = message.value;
-              subscene.initialized = false;
-              self.drawScene();
-            } else {
-              console.log("subscene "+message.subscene+" undefined.");
-            }
-          });
-          
-        Shiny.addCustomMessageHandler("resetBrush",
-          function(message) {
-            if (message === self.scene.selectionInput) {
-              self.clearBrush(null);
-              self.recordSelection(0);
-            }
-          });
-      }
-    };
-    
-    /**
-     * Restart the WebGL canvas
-     */
-    rglwidgetClass.prototype.restartCanvas = function() {
-      var newcanvas = document.createElement("canvas"),
-          self = this, 
-          labelid = this.el.getAttribute("aria-labelledby");
-      newcanvas.width = this.el.width;
-      newcanvas.height = this.el.height;
-      newcanvas.setAttribute("aria-labelledby", 
-        labelid);
-        
-      if (typeof this.scene.altText !== "undefined") {
-        // We're in Shiny, so alter the label
-        var label = document.getElementById(labelid);
-        if (label)
-          label.innerHTML = this.scene.altText;
-      }
-      newcanvas.addEventListener("webglcontextrestored",
-        this.onContextRestored, false);
-      newcanvas.addEventListener("webglcontextlost",
-        this.onContextLost, false);
-      while (this.el.firstChild) {
-        this.el.removeChild(this.el.firstChild);
-      }
-      this.el.appendChild(newcanvas);
-      this.canvas = newcanvas;
-      if (this.scene.javascript) {
-        /* jshint evil:true */
-        Function('"use strict";' + this.scene.javascript)();
-        /* jshint evil:false */
-      }
-      this.setMouseHandlers();
-      if (this.gl) 
-        Object.keys(this.scene.objects).forEach(function(key){
-          self.getObj(parseInt(key, 10)).texture = undefined; 
-          });
-      this.gl = null;
-    };
-
-    /**
-     * Initialize the WebGL canvas
-     */
-    rglwidgetClass.prototype.initCanvas = function() {
-      this.restartCanvas();
-      var objs = this.scene.objects,
-          self = this;
-          
-      /* These hold context specific data.  In Shiny, they   
-         need to be deleted.  Elsewhere, they don't exist
-         and these are no-ops. */
-         
-      delete this.cube;
-      delete this.sphere;
-      
-      Object.keys(objs).forEach(function(key){
-        self.initSubscene(parseInt(key, 10));
-      });
-
-      this.onContextRestored = function() {
-        self.initGL();
-        self.drawScene();
-      };
-
-      this.onContextLost = function(event) {
-        if (!self.drawing)
-          this.gl = null;
-        event.preventDefault();
-      };
-
-      this.initGL0();
-      this.lazyLoadScene = function() {
-      	if (typeof self.slide === "undefined")
-      	  self.slide = self.getSlide();
-      	if (self.isInBrowserViewport()) {
-      	  if (!self.gl || self.gl.isContextLost())
-      	    self.initGL();
-      	  self.drawScene();
-      	}
-      };
-      window.addEventListener("DOMContentLoaded", this.lazyLoadScene, false);
-      window.addEventListener("load", this.lazyLoadScene, false);
-      window.addEventListener("resize", this.lazyLoadScene, false);
-      window.addEventListener("scroll", this.lazyLoadScene, false);
-      this.slide = this.getSlide();
-      if (this.slide) {
-        if (typeof this.slide.rgl === "undefined")
-          this.slide.rgl = [this];
-        else
-          this.slide.rgl.push(this);
-        if (this.scene.context.rmarkdown) 
-          if (this.scene.context.rmarkdown === "ioslides_presentation") {
-            this.slide.setAttribute("slideenter", "this.rgl.forEach(function(scene) { scene.lazyLoadScene.call(window);})");
-          } else if (this.scene.context.rmarkdown === "slidy_presentation") {
-            // This method would also work in ioslides, but it gets triggered
-            // something like 5 times per slide for every slide change, so
-            // you'd need a quicker function than lazyLoadScene.
-            var MutationObserver = window.MutationObserver || window.WebKitMutationObserver || window.MozMutationObserver,
-            observer = new MutationObserver(function(mutations) {
-              mutations.forEach(function() {
-                self.slide.rgl.forEach(function(scene) { scene.lazyLoadScene.call(window); });});});
-            observer.observe(this.slide, { attributes: true, attributeFilter:["class"] });
-          }
-      }
-    };
-</script>
-<script>/**
- * Methods related to drawing transparent objects
- * @name ___METHODS_FOR_TRANSPARENCY___
- * @memberof rglwidgetClass
- * @kind function
- * @instance
-
- * These functions order the centers of displayed objects so they
- * can be drawn using the painters algorithm, necessary to support
- * transparency.  
-
- * Note that objid is not obj.id when drawing spheres.
- */
-
-/**
- * Break objects into pieces
- * @returns { array } Array of pieces
- */
-    rglwidgetClass.prototype.getPieces = function(context, objid, subid, obj) {
-      var n = obj.centers.length,
-          depth,
-          result = new Array(n),
-          z, w, i;
-      context = context.slice();
-          
-      for(i=0; i<n; i++) {
-        z = this.prmvMatrix.m13*obj.centers[i][0] +
-            this.prmvMatrix.m23*obj.centers[i][1] +
-            this.prmvMatrix.m33*obj.centers[i][2] +
-            this.prmvMatrix.m43;
-        w = this.prmvMatrix.m14*obj.centers[i][0] +
-            this.prmvMatrix.m24*obj.centers[i][1] +
-            this.prmvMatrix.m34*obj.centers[i][2] +
-            this.prmvMatrix.m44;
-        depth = z/w;
-        result[i] = {context: context, 
-                     objid: objid,
-                     subid: subid,
-                     index: i, 
-                     depth: depth};
-      }
-      return result;    
-    };
-    
-    /**
-     * Get pieces from sphere
-     * @returns { object }
-     * @param { array } context - 
-     * @param { numeric } subid - subscene
-     * @param { object } obj - spheres object
-     */
-    rglwidgetClass.prototype.getSpherePieces = function(context, subid, obj)
-    {
-      if (obj.fastTransparency) 
-        if (subid === 0) // Only compute pieces once
-          return this.getPieces(context, obj.id, -1, obj);
-        else
-          return [];
-      else
-        return this.getPieces(context, obj.id, subid, this.sphere);
-    };
-    
-   /**
-     * Get pieces from cube
-     * @returns { object }
-     * @param { array } context - 
-     * @param { numeric } subid - subscene
-     * @param { object } obj - spheres object
-     */
-    rglwidgetClass.prototype.getCubePieces = function(context, obj)
-    {
-      return this.getPieces(context, obj.id, 0, this.cube);
-    };
-    
-    /**
-     * Merge pieces that can be drawn in one call
-     * @returns { object }
-     * @param { array } pieces - The pieces to merge
-     */
-    rglwidgetClass.prototype.mergePieces = function(pieces) {
-      var result = [];
-      if (pieces.length > 0) {
-        var i,
-          thiscontext = pieces[0].context, 
-          thisobjid = pieces[0].objid, 
-          thissubid = pieces[0].subid,
-          indices = [];
-        for (i= 0; i < pieces.length; i++) {
-          if (pieces[i].context !== thiscontext || 
-              pieces[i].objid !== thisobjid ||
-              pieces[i].subid !== thissubid) {
-            result.push({context: thiscontext, objid: thisobjid,
-                         subid: thissubid, indices: indices});
-            thiscontext = pieces[i].context;
-            thisobjid = pieces[i].objid;
-            thissubid = pieces[i].subid;
-            indices = [];
-          }
-          indices.push(pieces[i].index);
-        }
-        result.push({context: thiscontext, objid: thisobjid,
-                                subid: thissubid,
-                                indices: indices});
-      }
-      return result;
-    };
-
-    /**
-     * Sort pieces by depth
-     * @returns { array }
-     * @param { array } pieces - array of pieces 
-     */
-    rglwidgetClass.prototype.sortPieces = function(pieces) {
-      var compare = function(i,j) {
-        var diff = j.depth - i.depth;
-        // We want to avoid context or obj changes,
-        // so sort on those next.
-        if (diff === 0) {
-          var c1 = j.context.slice(),
-              c2 = i.context.slice();
-          diff = c1.length - c2.length; 
-          while (diff === 0 && c1.length > 0) {
-            diff = c1.pop() - c2.pop();
-          }
-          if (diff === 0)
-            diff = j.objid - i.objid;
-          if (diff === 0)
-            diff = j.subid - i.subid;
-        }
-        return diff;
-      }, result = [];
-      if (pieces.length) 
-        result = pieces.sort(compare);
-      return result;
-    };
-</script>
-<script>    /**
-     * Methods related to drawing
-     * @name ___METHODS_FOR_DRAWING___
-     * @memberof rglwidgetClass
-     * @kind function
-     * @instance
-     */
-     
-    /**
-     * Start drawing
-     * @returns { boolean } Previous state
-     */
-    rglwidgetClass.prototype.startDrawing = function() {
-    	var value = this.drawing;
-    	this.drawing = true;
-    	return value;
-    };
-
-    /**
-     * Stop drawing and check for context loss
-     * @param { boolean } saved - Previous state
-     */
-    rglwidgetClass.prototype.stopDrawing = function(saved) {
-      this.drawing = saved;
-      if (!saved && this.gl && this.gl.isContextLost())
-        this.restartCanvas();
-    };
-
-    /**
-     * Update the triangles used to display a plane
-     * @param { number } id - id of the plane
-     * @param { Object } bbox - bounding box in which to display the plane
-     */
-    rglwidgetClass.prototype.planeUpdateTriangles = function(obj, bbox) {
-      var perms = [[0,0,1], [1,2,2], [2,1,0]],
-          x, xrow, elem, A, d, nhits, i, j, k, u, v, w, intersect, which, v0, v2, vx, reverse,
-          face1 = [], face2 = [], normals = [],
-          nPlanes = obj.normals.length, idx, center;
-      obj.bbox = bbox;
-      obj.vertices = [];
-      obj.centers = [];
-      obj.initialized = false;
-      for (elem = 0; elem < nPlanes; elem++) {
-//    Vertex Av = normal.getRecycled(elem);
-        x = [];
-        A = obj.normals[elem];
-        d = obj.offsets[elem][0];
-        nhits = 0;
-        for (i=0; i<3; i++)
-          for (j=0; j<2; j++)
-            for (k=0; k<2; k++) {
-              u = perms[0][i];
-              v = perms[1][i];
-              w = perms[2][i];
-              if (A[w] !== 0.0) {
-                intersect = -(d + A[u]*bbox[j+2*u] + A[v]*bbox[k+2*v])/A[w];
-                if (bbox[2*w] < intersect && intersect < bbox[1+2*w]) {
-                  xrow = [];
-                  xrow[u] = bbox[j+2*u];
-                  xrow[v] = bbox[k+2*v];
-                  xrow[w] = intersect;
-                  x.push(xrow);
-                  face1[nhits] = j + 2*u;
-                  face2[nhits] = k + 2*v;
-                  nhits++;
-                }
-              }
-            }
-
-            if (nhits > 3) {
-            /* Re-order the intersections so the triangles work */
-              for (i=0; i<nhits-2; i++) {
-                which = 0; /* initialize to suppress warning */
-                for (j=i+1; j<nhits; j++) {
-                  if (face1[i] === face1[j] || face1[i] === face2[j] ||
-                      face2[i] === face1[j] || face2[i] === face2[j] ) {
-                    which = j;
-                    break;
-                  }
-                }
-                if (which > i+1) {
-                  rglwidgetClass.swap(x, i+1, which);
-                  rglwidgetClass.swap(face1, i+1, which);
-                  rglwidgetClass.swap(face2, i+1, which);
-                }
-              }
-            }
-            if (nhits >= 3) {
-      /* Put in order so that the normal points out the FRONT of the faces */
-              v0 = [x[0][0] - x[1][0] , x[0][1] - x[1][1], x[0][2] - x[1][2]];
-              v2 = [x[2][0] - x[1][0] , x[2][1] - x[1][1], x[2][2] - x[1][2]];
-              /* cross-product */
-              vx = rglwidgetClass.xprod(v0, v2);
-              reverse = rglwidgetClass.dotprod(vx, A) > 0;
-
-              for (i=0; i<nhits-2; i++) {
-                obj.vertices.push(x[0]);
-                center = [];
-                for (k = 0; k<3; k++)
-                  center.push(x[0][k]/3);
-                normals.push(A);
-                for (j=1; j<3; j++) {
-                  idx = i + (reverse ? 3-j : j);
-                  obj.vertices.push(x[idx]);
-                  for (k=0; k<3; k++)
-                    center[k] += x[idx][k]/3;
-                  normals.push(A);
-                }
-                obj.centers.push(center);
-              }
-            }
-      }
-      obj.pnormals = normals;
-    };
-    
-    rglwidgetClass.prototype.mode4type = {points : "POINTS",
-                     linestrip : "LINE_STRIP",
-                     abclines : "LINES",
-                     lines : "LINES",
-                     sprites : "TRIANGLES",
-                     planes : "TRIANGLES",
-                     text : "TRIANGLES",
-                     quads : "TRIANGLES",
-                     surface : "TRIANGLES",
-                     triangles : "TRIANGLES",
-                     sphere : "TRIANGLES"
-    };
-    
-    /**
-     * Disable unused arrays
-     * @param { Object } obj - Object to work with
-     * @param { Array } enabled - Array indicating which are enabled
-     */
-    rglwidgetClass.prototype.disableArrays = function(obj, enabled) {
-      var gl = this.gl || this.initGL(),
-          objLocs = ["normLoc", "texLoc", "ofsLoc", "pointLoc", "nextLoc"],
-          thisLocs = ["posLoc", "colLoc"], i, attr;
-      for (i = 0; i < objLocs.length; i++) 
-        if (enabled[objLocs[i]]) gl.disableVertexAttribArray(obj[objLocs[i]]);
-      for (i = 0; i < thisLocs.length; i++)
-        if (enabled[thisLocs[i]]) gl.disableVertexAttribArray(this[objLocs[i]]);
-      if (typeof obj.userAttributes !== "undefined") {
-      	for (attr in obj.userAttribSizes) {  // Not all attributes may have been used
-      	  gl.disableVertexAttribArray( obj.userAttribLocations[attr] );
-      	}
-      }
-    };
-
-    /**
-     * Start drawing the scene
-     */    
-    rglwidgetClass.prototype.doStartScene = function() {
-      var gl = this.gl || this.initGL();
-      gl.enable(gl.DEPTH_TEST);
-      gl.depthFunc(gl.LEQUAL);
-      gl.clearDepth(1.0);
-      gl.clearColor(1,1,1,1);
-      gl.depthMask(true); // Must be true before clearing depth buffer
-      /* jshint bitwise: false */
-      gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);
-      /* jshint bitwise: true */
-    };
-    
-    /**
-     * Set gl depth test based on object's material
-     * @param { Object } obj - object to use
-     */
-    rglwidgetClass.prototype.doDepthTest = function(obj) {
-      var gl = this.gl,
-          tests = {never: gl.NEVER,
-                   less:  gl.LESS,
-                   equal: gl.EQUAL,
-                   lequal:gl.LEQUAL,
-                   greater: gl.GREATER,
-                   notequal: gl.NOTEQUAL,
-                   gequal: gl.GEQUAL,
-                   always: gl.ALWAYS},
-           test = tests[this.getMaterial(obj, "depth_test")];
-      gl.depthFunc(test);
-    };    
-    
-    /**
-     * Set polygon offset for an obj
-     * @param { object } obj - object to use
-     */
-    rglwidgetClass.prototype.doPolygonOffset = function(obj) { 
-      var gl = this.gl;
-      if (typeof obj.polygon_offset !== "undefined") {
-        gl.polygonOffset(obj.polygon_offset[0],
-                          obj.polygon_offset[1]);
-        gl.enable(gl.POLYGON_OFFSET_FILL);
-      } else
-        gl.disable(gl.POLYGON_OFFSET_FILL);
-    };
-    
-    /**
-     * Do code for clipping
-     * @param { object } obj - Object to work with
-     * @param { object } subscene - Subscene to work with
-     */
-    rglwidgetClass.prototype.doClipping = function(obj, subscene) {
-      var gl = this.gl,
-          clipcheck = 0,
-          clipplaneids = subscene.clipplanes,
-          clip, i,j, n = this.countClipplanes(),
-          clipplanedata; 
-          
-      if (n > 0) {
-        clipplanedata = new Float32Array(4*n);
-        for (i=0; i < clipplaneids.length; i++) {
-          clip = this.getObj(clipplaneids[i]);
-          for (j=0; j < clip.offsets.length; j++) {
-            clipplanedata.set(clip.IMVClip[j], clipcheck);
-            clipcheck += 4;
-          }
-        }
-      
-        // Leftovers are initialized to zero, which is fine
-        gl.uniform4fv(obj.clipLoc, clipplanedata);
-      }
-    };
-    
-    /**
-     * Do code for lighting
-     * @param { object } obj - Object to work with
-     * @param { object } subscene - Subscene to work with
-     */
-    rglwidgetClass.prototype.doLighting = function(obj, subscene) {
-    var gl = this.gl, i, j, n, light,
-      ambient, specular, diffuse, lightDir, viewpoint, finite,
-      ambient0, specular0;
-
-      gl.uniform3fv( obj.emissionLoc, obj.emission);
-      gl.uniform1f( obj.shininessLoc, obj.shininess);
-      while ((typeof subscene.lights === "undefined" ||
-              subscene.lights.length === 0) && 
-             typeof subscene.parent !== "undefined")
-        subscene = this.getObj(subscene.parent);
-
-      if (typeof subscene.lights === "undefined")
-        return;
-        
-      n = subscene.lights.length;
-        
-      ambient = new Float32Array(3*n);
-      specular = new Float32Array(3*n);
-      diffuse = new Float32Array(3*n);
-      lightDir = new Float32Array(3*n);
-      viewpoint = new Int32Array(n);
-      finite = new Int32Array(n);
-          
-      for (i=0; i < n; i++) {
-        light = this.getObj(subscene.lights[i]);
-        if (!light.initialized) this.initObj(light);
-        ambient0 = this.componentProduct(light.ambient, obj.ambient);
-        specular0 = this.componentProduct(light.specular, obj.specular);
-        for (j=0; j < 3; j++) {
-          ambient[3*i + j] = ambient0[j];
-          specular[3*i + j] = specular0[j];
-          diffuse[3*i + j] = light.diffuse[j];
-          lightDir[3*i + j] = light.lightDir[j];
-        }
-        viewpoint[i] = light.viewpoint;
-        finite[i] = light.finite;
-      }
-        
-      for (i = n; i < obj.nlights; i++) {
-        for (j = 0; j < 3; j++) {
-          ambient[3*i + j] = 0.0;
-          specular[3*i + j] = 0.0;
-          diffuse[3*i + j] = 0.0;
-        }
-      }
-        
-      gl.uniform3fv( obj.ambientLoc, ambient);
-      gl.uniform3fv( obj.specularLoc, specular);
-      gl.uniform3fv( obj.diffuseLoc, diffuse);
-      gl.uniform3fv( obj.lightDirLoc, lightDir);
-      gl.uniform1iv( obj.viewpointLoc, viewpoint);
-      gl.uniform1iv( obj.finiteLoc, finite);
-    };
-    
-    /**
-     * Do code for colors
-     * @param { object } obj - Object to work with
-     */
-    rglwidgetClass.prototype.doColors = function(obj) {
-      var gl = this.gl;
-      if (obj.colorCount === 1) {
-        gl.disableVertexAttribArray( this.colLoc );
-        gl.vertexAttrib4fv( this.colLoc, new Float32Array(obj.onecolor));
-        return false;
-      } else {
-        gl.enableVertexAttribArray( this.colLoc );
-        gl.vertexAttribPointer(this.colLoc, 4, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.cofs);
-        return true;
-      }
-    };
-    
-    /**
-     * Do code for normals
-     * @param { object } obj - Object to work with
-     */
-    rglwidgetClass.prototype.doNormals = function(obj) {
-      var gl = this.gl;
-      if (obj.vOffsets.nofs >= 0) {
-        gl.enableVertexAttribArray( obj.normLoc );
-        gl.vertexAttribPointer(obj.normLoc, 3, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.nofs);
-        return true;
-      } else
-        return false;
-    };
-    
-    /**
-     * Do code for vNormal
-     * @param { object } obj - Object to work with
-     */
-    rglwidgetClass.prototype.doNormMat = function(obj) {
-      var gl = this.gl;
-        
-      gl.uniformMatrix4fv( obj.normMatLoc, false, new Float32Array(this.normMatrix.getAsArray()) );
-    };
-    
-    /**
-     * Do code for textures
-     * @param { object } obj - Object to work with
-     */    
-    rglwidgetClass.prototype.doTexture = function(obj) {
-      var gl = this.gl, 
-          is_sphere = obj.type === "sphere";
-        gl.enableVertexAttribArray( obj.texLoc );
-        if (is_sphere)
-          gl.vertexAttribPointer(obj.texLoc, 2, gl.FLOAT, false, 4*this.sphere.vOffsets.stride, 4*this.sphere.vOffsets.tofs);
-        else
-          gl.vertexAttribPointer(obj.texLoc, 2, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.tofs);
-        gl.activeTexture(gl.TEXTURE0);
-        gl.bindTexture(gl.TEXTURE_2D, obj.texture);
-        gl.uniform1i( obj.sampler, 0);
-        return true;
-    };
-    
-    /**
-     * Do code for user attributes
-     * @param { object } obj - Object to work with
-     */    
-    rglwidgetClass.prototype.doUserAttributes = function(obj) {
-      if (typeof obj.userAttributes !== "undefined") {
-        var gl = this.gl;
-      	for (var attr in obj.userAttribSizes) {  // Not all attributes may have been used
-      	  gl.enableVertexAttribArray( obj.userAttribLocations[attr] );
-      	  gl.vertexAttribPointer( obj.userAttribLocations[attr], obj.userAttribSizes[attr],
-      	  			  gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.userAttribOffsets[attr]);
-      	}
-      }
-    };
-
-    /**
-     * Do code for user uniforms
-     * @param { object } obj - Object to work with
-     */    
-    rglwidgetClass.prototype.doUserUniforms = function(obj) {
-      var gl = this.gl, attr;
-      if (typeof obj.userUniforms !== "undefined") {
-      	for (attr in obj.userUniformLocations) {
-      	  var loc = obj.userUniformLocations[attr];
-      	  if (loc !== null) {
-      	    var uniform = obj.userUniforms[attr];
-      	    if (typeof uniform !== "undefined") {
-      	      var dim = rglwidgetClass.arrayDim(uniform);
-      	      if (dim.length === 0)
-      	        gl.uniform1f(loc, uniform);
-      	      else if (dim.length === 1) {
-      	        uniform = new Float32Array(uniform);
-      	        switch(uniform.length) {
-      	      	  case 2: gl.uniform2fv(loc, uniform); break;
-      	      	  case 3: gl.uniform3fv(loc, uniform); break;
-      	      	  case 4: gl.uniform4fv(loc, uniform); break;
-      	      	  default: console.warn("bad uniform length");
-      	        }
-      	      } else if (dim.length === 2 && dim[0] === 4 && dim[1] === 4)
-      	        gl.uniformMatrix4fv(loc, false, new Float32Array(rglwidgetClass.flatten(uniform)));
-      	      else if (dim.length === 2) {
-      	        uniform = new Float32Array(rglwidgetClass.flatten(uniform));
-      	        switch(dim[[1]]) {
-      	          case 1: gl.uniform1fv(loc, uniform); break;
-      	          case 2: gl.uniform2fv(loc, uniform); break;
-      	          case 3: gl.uniform3fv(loc, uniform); break;
-      	          case 4: gl.uniform4fv(loc, uniform); break;
-      	          default: console.warn("bad uniform column count");
-      	        }
-      	      } else
-      	        console.warn("unsupported uniform shape");
-      	    }
-      	  }
-      	}
-      }
-      if (typeof obj.userTextures !== "undefined") {
-        var has_texture = rglwidgetClass.isSet(obj.flags, rglwidgetClass.f_has_texture),
-              texnum = has_texture - 1;
-        for (attr in obj.userTextures) {
-      	  var texture = obj.userTextures[attr];
-      	  if (texture.sampler !== null) {
-      	    texnum += 1;
-      	    gl.activeTexture(gl.TEXTURE0 + texnum);
-            gl.bindTexture(gl.TEXTURE_2D, texture.texture);
-            gl.uniform1i( texture.sampler, texnum);
-      	  }
-      	}
-      }
-    };
-
-    /**
-     * Load indices for complex drawing
-     * @param { object } obj - Object to work with
-     * @param { numeric } pass - Which pass of drawing?
-     * @param { array } indices - Indices to draw
-     */    
-    rglwidgetClass.prototype.doLoadIndices = function(obj, pass, indices) {
-      var gl = this.gl,
-          f = obj.f[pass],
-          type = obj.type,
-          fat_lines = rglwidgetClass.isSet(obj.flags, rglwidgetClass.f_fat_lines),
-          fnew, step;
-      switch(type){
-        case "points":
-          step = 1;
-          break;
-        case "abclines":
-        case "lines":
-          if (fat_lines)
-            step = 6;
-          else
-            step = 2;
-          break;
-        case "linestrip":
-          if (fat_lines)
-            step = 6;
-          else
-            step = 1;
-          break;
-        case "sphere":
-        case "planes":
-        case "triangles":
-          step = 3;
-          break;
-        case "text":
-        case "sprites":
-        case "quads":
-        case "surface":
-          step = 6;
-          break;
-        default:
-          console.error("loadIndices for "+type);
-          return 0;
-      }
-      if (obj.index_uint)
-        fnew = new Uint32Array(step * indices.length);
-      else
-        fnew = new Uint16Array(step * indices.length);
-      for (var i = 0; i < indices.length; i++) {
-        for (var j = 0; j < step; j++) {
-          fnew[step*i + j] = f[step*indices[i] + j];
-        }
-      }
-      gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, fnew, gl.DYNAMIC_DRAW);
-      return fnew.length;
-    };
-
-    /**
-     * Do code for depth masking
-     * @param { boolean } mask - whether to mask
-     */
-    rglwidgetClass.prototype.doMasking = function(mask) {
-      var gl = this.gl;
-      gl.depthMask(mask);
-    };
-
-    /**
-     * Do code for alpha blending
-     * @param { boolean }  blend - Whether to blend.
-     * @param { integer }  objid - Object id
-     */    
-    rglwidgetClass.prototype.doBlending = function(blend, objid) {
-      var gl = this.gl, blendfunc, obj, 
-        blends =  {zero: gl.ZERO,
-                   one:  gl.ONE,
-                   src_color: gl.SRC_COLOR,
-                   one_minus_src_color: gl.ONE_MINUS_SRC_COLOR,
-                   dst_color: gl.DST_COLOR,
-                   one_minus_dst_color: gl.ONE_MINUS_DST_COLOR,
-                   src_alpha: gl.SRC_ALPHA,
-                   one_minus_src_alpha: gl.ONE_MINUS_SRC_ALPHA,
-                   dst_alpha: gl.DST_ALPHA,
-                   one_minus_dst_alpha: gl.ONE_MINUS_DST_ALPHA,
-                   constant_color: gl.CONSTANT_COLOR,
-                   one_minus_constant_color: gl.ONE_MINUS_CONSTANT_COLOR,
-                   constant_alpha: gl.CONSTANT_ALPHA,
-                   one_minus_constant_alpha: gl.ONE_MINUS_CONSTANT_ALPHA,
-                   src_alpha_saturate: gl.SRC_ALPHA_SATURATE};
-      if (blend) {
-        obj = this.getObj(objid);
-        blendfunc = this.getMaterial(obj, "blend");
-        gl.blendFuncSeparate(blends[blendfunc[0]],
-                             blends[blendfunc[1]],
-                             gl.ONE, gl.ONE);
-        gl.enable(gl.BLEND);
-      } else {
-        gl.disable(gl.BLEND);
-      }
-    };
-    
-    /**
-     * Set up for fog in the subscene
-     * @param { object } obj - background object
-     * @param { object } subscene - which subscene
-     */
-    rglwidgetClass.prototype.doFog = function(obj, subscene) {
-      var gl = this.gl, fogmode, color, 
-          observer = subscene.par3d.observer[2],
-          sintheta = Math.sin(subscene.par3d.FOV*Math.PI/180/2),
-          parms = [this.frustum.near - 2*observer,
-                   this.frustum.far - 2*observer,
-                   this.fogScale,
-                   (1-sintheta)/(1+sintheta)];
-      if (typeof this.fogType === "undefined")
-        this.fogType = "none";
-      if (typeof this.fogScale === "undefined")
-        parms[2] = 1;
-      if (sintheta === 0)
-        parms[3] = 1/3;
-      switch(this.fogType){
-        case "none": fogmode = 0; break;
-        case "linear": 
-          fogmode = 1; break;
-        case "exp":  
-          fogmode = 2; break;
-        case "exp2": 
-          fogmode = 3;
-          break;
-        default: console.error("Unknown fogtype "+this.fogType);
-      }
-      gl.uniform1i(obj.uFogMode, fogmode);
-      color = this.fogColor;
-      gl.uniform3f(obj.uFogColor, color[0], color[1], color[2]);
-      gl.uniform4f(obj.uFogParms, parms[0], parms[1], parms[2], parms[3]);
-    };
-
-    /* The draw methods are called twice.  When 
-       this.opaquePass is true, they should draw opaque parts
-       of the scene, and return the list of transparent
-       pieces.  Here context is the context array on input,
-       modified when the matrices are changed.
-       When this.opaquePass is false, the context argument
-       contains a "piece", i.e. an ordered list of parts
-       of the object to draw. */
-
-    /**
-     * Draw simple object
-     * @param { object } obj - Object to draw
-     * @param { object } subscene - which subscene
-     * @param { array } context - Which context are we in?
-     */       
-    rglwidgetClass.prototype.drawSimple = function(obj, subscene, context) {
-      var 
-          fl,
-          is_transparent,
-          type = obj.type,
-          gl = this.gl || this.initGL(),
-          count,
-          pass, mode, pmode,
-          enabled = {};
-        
-      if (!obj.initialized)
-        this.initObj(obj);
-        
-      if (this.texturesLoading)
-        return[];
-
-      count = obj.vertexCount;
-      if (!count)
-        return [];
-    
-      fl = obj.defFlags;
-      is_transparent = fl.is_transparent || obj.someHidden;
-      
-      if (is_transparent && this.opaquePass)
-        return this.getPieces(context, obj.id, 0, obj);
-
-      this.doDepthTest(obj);
-      
-      this.doMasking(this.getMaterial(obj, "depth_mask"));
-            
-      gl.useProgram(obj.prog);
-
-      this.doPolygonOffset(obj);
-
-      gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
-
-      gl.uniformMatrix4fv( obj.prMatLoc, false, new Float32Array(this.prMatrix.getAsArray()) );
-      gl.uniformMatrix4fv( obj.mvMatLoc, false, new Float32Array(this.mvMatrix.getAsArray()) );
-
-      this.doClipping(obj, subscene);
-
-      if (fl.needs_vnormal)
-        this.doNormMat(obj);
-        
-      if (fl.is_lit)
-        this.doLighting(obj, subscene);
-
-      if (fl.has_fog)
-        this.doFog(obj, subscene);
-
-      this.doUserAttributes(obj);
-
-      this.doUserUniforms(obj);
- 
-      gl.enableVertexAttribArray( this.posLoc );
-      enabled.posLoc = true;
-        
-      if (fl.has_texture || obj.type === "text")
-        enabled.texLoc = this.doTexture(obj);
-
-      enabled.colLoc = this.doColors(obj);
-      enabled.normLoc = this.doNormals(obj);
-
-      if (fl.fixed_size) {
-        gl.uniform3f( obj.textScaleLoc, 0.75/this.vp.width, 0.75/this.vp.height, 1.0);
-      }
-      
-      if (fl.fixed_quads) {
-        gl.enableVertexAttribArray( obj.ofsLoc );
-        enabled.ofsLoc = true;
-        gl.vertexAttribPointer(obj.ofsLoc, 3, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.oofs);
-      }
-
-      for (pass = 0; pass < obj.passes; pass++) {
-      	pmode = obj.pmode[pass];
-        if (pmode === "culled")
-          continue;
-
-      	mode = fl.fat_lines && (fl.is_lines || pmode === "lines") ? "TRIANGLES" : this.mode4type[type];
-
-      	if (fl.is_twosided) {
-      	  gl.uniform1i(obj.frontLoc, pass !== 0);
-      	  if (fl.has_normals) {
-      	    gl.uniformMatrix4fv(obj.invPrMatLoc, false, new Float32Array(this.invPrMatrix.getAsArray()));
-      	  }
-      	}
-
-        gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, obj.ibuf[pass]);
-        if (!this.opaquePass) {
-          if (type === "sphere" && obj.fastTransparency)
-            count = this.doLoadIndices(obj, pass, this.sphere.fastpieces[0].indices);
-          else
-            count = this.doLoadIndices(obj, pass, context.indices);
-        } else {
-          count = obj.f[pass].length;
-          gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, obj.f[pass], gl.STATIC_DRAW);
-        }
-      	if (!fl.is_lines && pmode === "lines" && !fl.fat_lines) {
-          mode = "LINES";
-        } else if (pmode === "points") {
-          mode = "POINTS";
-        }
-                          
-        if ((fl.is_lines || pmode === "lines") && fl.fat_lines) {
-          gl.enableVertexAttribArray(obj.pointLoc);
-          enabled.pointLoc = true;
-          gl.vertexAttribPointer(obj.pointLoc, 2, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.pointofs);
-          gl.enableVertexAttribArray(obj.nextLoc );
-          enabled.nextLoc = true;
-          gl.vertexAttribPointer(obj.nextLoc, 3, gl.FLOAT, false, 4*obj.vOffsets.stride, 4*obj.vOffsets.nextofs);
-          gl.uniform1f(obj.aspectLoc, this.vp.width/this.vp.height);
-          gl.uniform1f(obj.lwdLoc, this.getMaterial(obj, "lwd")/this.vp.height);
-        }
-
-        gl.vertexAttribPointer(this.posLoc,  3, gl.FLOAT, false, 4*obj.vOffsets.stride,  4*obj.vOffsets.vofs);
-
-        gl.drawElements(gl[mode], count, obj.index_uint ? gl.UNSIGNED_INT : gl.UNSIGNED_SHORT, 0);
-      }
-      this.disableArrays(obj, enabled);
-      return [];
-    };
-
-    /**
-     * Draw planes object
-     * @param { object } obj - Object to draw
-     * @param { object } subscene - which subscene
-     * @param { array } context - Which context are we in?
-     */      
-    rglwidgetClass.prototype.drawPlanes = function(obj, subscene, context) {
-      if (this.opaquePass && (obj.bbox !== subscene.par3d.bbox || !obj.initialized)) {
-          this.planeUpdateTriangles(obj, subscene.par3d.bbox);
-      }
-      return this.drawSimple(obj, subscene, context);
-   };
-
-    /**
-     * @param { object } obj - object to draw
-     * @param { object } subscene 
-     * @param { array } context 
-     * @description
-     * Draw spheres in a subscene<br>
-     * 
-     * Drawing spheres happens in six ways:<br>
-     * 1 opaquepass, not transparent:  transform and draw this.sphere count times<br>
-     * 2 opaquepass, transparent, not fast: transform & collect sphere pieces count times<br>
-     * 3 opaquepass, transparent, fast:  order the centres into separate pieces, order this.sphere once<br>
-     * 4 not opaquepass, not transparent:  do nothing<br>
-     * 5 not opaquepass, transparent, not fast:  transform for one sphere, draw one merged piece<br>
-     * 6 not opaquepass, transparent, fast:  transform for one sphere, draw this.sphere in fixed order.<br>
-     **/
-
-    rglwidgetClass.prototype.drawSpheres = function(obj, subscene, context) {
-      var flags = obj.flags,
-          is_transparent = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_transparent),
-          sphereMV, baseofs, ofs, sscale, i,
-          count, nc, scount, scale, indices, sphereNorm,
-          enabled = {}, drawing,
-          saveNorm = new CanvasMatrix4(this.normMatrix),
-          saveMV = new CanvasMatrix4(this.mvMatrix),
-          savePRMV = null,
-          result = [], idx, margin = obj.material.margin;
- 
-      if (typeof margin !== "undefined")
-        if (!this.marginVecToDataVec(obj, subscene))
-          return [];
-
-      if (!obj.initialized)
-        this.initObj(obj);
-
-      count = obj.vertexCount;
-      if (!count) 
-        return [];
-        
-      is_transparent = is_transparent || obj.someHidden;
-
-      if (!this.opaquePass && !is_transparent)
-        return [];
-        
-      if (this.prmvMatrix !== null)
-        savePRMV = new CanvasMatrix4(this.prmvMatrix);
-      
-      scale = subscene.par3d.scale;        
-      sphereNorm = new CanvasMatrix4();
-      sphereNorm.scale(scale[0], scale[1], scale[2]);
-      sphereNorm.multRight(saveNorm);
-      this.normMatrix = sphereNorm;
-
-      if (this.opaquePass) {
-        context = context.slice();
-        context.push(obj.id);
-      } 
-      
-      drawing = this.opaquePass !== is_transparent;
-      if (drawing) {
-        nc = obj.colorCount;
-        if (nc === 1) {
-          this.sphere.onecolor = obj.onecolor;
-        }
-      }
-      
-      this.initShapeFromObj(this.sphere, obj);
-
-      if (!this.opaquePass && obj.fastTransparency && typeof this.sphere.fastpieces === "undefined") {
-        this.sphere.fastpieces = this.getPieces(context.context, obj.id, 0, this.sphere);
-        this.sphere.fastpieces = this.sortPieces(this.sphere.fastpieces);
-        this.sphere.fastpieces = this.mergePieces(this.sphere.fastpieces);
-      }
-
-      if (this.opaquePass)
-        scount = count;
-      else {
-        indices = context.indices;
-        if (obj.fastTransparency)
-          scount = indices.length;  /* Each item gives the center of a whole sphere */
-        else
-          scount = 1;               /* Each item is a fragment of the sphere, at location subid */
-      }
-      for (i = 0; i < scount; i++) {
-        sphereMV = new CanvasMatrix4();
-        if (this.opaquePass)
-          idx = i;
-        else if (obj.fastTransparency)
-          idx = indices[i];
-        else
-          idx = context.subid;
-        if (typeof idx === "undefined")
-          console.error("idx is undefined");
-        baseofs = idx*obj.vOffsets.stride;
-        ofs = baseofs + obj.vOffsets.radofs;
-        sscale = obj.values[ofs];
-
-        sphereMV.scale(sscale/scale[0], sscale/scale[1], sscale/scale[2]);
-        sphereMV.translate(obj.values[baseofs],
-                             obj.values[baseofs+1],
-                             obj.values[baseofs+2]);
-        sphereMV.multRight(saveMV);
-        this.mvMatrix = sphereMV;
-        this.setnormMatrix2();
-        this.setprmvMatrix();
-        if (drawing) {
-          if (nc > 1) {
-            this.sphere.onecolor = obj.values.slice(baseofs + obj.vOffsets.cofs, baseofs + obj.vOffsets.cofs + 4);
-          }
-          this.drawSimple(this.sphere, subscene, context);
-        } else 
-          result = result.concat(this.getSpherePieces(context, i, obj));
-      }
-      if (drawing)
-        this.disableArrays(obj, enabled);
-      this.normMatrix = saveNorm;
-      this.mvMatrix = saveMV;
-      this.prmvMatrix = savePRMV;
-        
-      return result;
-    };
-    
-    /**
-     * Prepare clipplanes for drawing
-     * @param { object } obj - clip planes object
-     */
-    rglwidgetClass.prototype.drawClipplanes = function(obj) {
-      var count = obj.offsets.length,
-        IMVClip = [];
-      for (var i=0; i < count; i++) {
-        IMVClip[i] = rglwidgetClass.multMV(this.invMatrix, obj.vClipplane.slice(4*i, 4*(i+1)));
-      }
-      obj.IMVClip = IMVClip;
-      return [];
-    };
-
-    /**
-     * Prepare linestrip for drawing
-     * @param { object } obj - line strip object
-     * @param { object } subscene 
-     * @param { array } context 
-     */    
-    rglwidgetClass.prototype.drawLinestrip = function(obj, subscene, context) {
-      var origIndices, i, j, margin = obj.material.margin;
- 
-      if (typeof margin !== "undefined") 
-        if (!this.marginVecToDataVec(obj, subscene))
-          return [];
-          
-      if (this.opaquePass)
-        return this.drawSimple(obj, subscene, context);
-      origIndices = context.indices.slice();
-      for (i=0; i < origIndices.length; i++) {
-        j = origIndices[i];
-        if (j < obj.centers.length - 1) {
-          context.indices = [j, j+1];
-          this.drawSimple(obj, subscene, context);
-        }
-      }
-      context.indices = origIndices;
-      return [];
-    };
-          
-    /**
-     * Draw a sprites object in a subscene
-     * @param { object } obj - object to draw
-     * @param { object } subscene
-     * @param { object } context
-     */
-    rglwidgetClass.prototype.drawSprites = function(obj, subscene, context) {
-      var flags = obj.flags,
-          is_transparent = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_transparent),
-          sprites3d = rglwidgetClass.isSet(flags, rglwidgetClass.f_sprites_3d),
-          fixed_size = rglwidgetClass.isSet(flags, rglwidgetClass.f_fixed_size),
-          rotating = rglwidgetClass.isSet(flags, rglwidgetClass.f_rotating),
-          i,j,
-          origMV = new CanvasMatrix4( this.mvMatrix ),
-          origPRMV = null,
-          origPR,
-          pos, radius, userMatrix,
-          result = [], margin = obj.material.margin;
- 
-      if (typeof margin !== "undefined")
-        if (!this.marginVecToDataVec(obj, subscene))
-          return [];
-
-      if (!sprites3d) 
-        return this.drawSimple(obj, subscene, context);
-      
-      if (!obj.initialized)
-        this.initObj(obj);
-
-      if (!obj.vertexCount)
-        return [];
-    
-      is_transparent = is_transparent || obj.someHidden;
-      
-      var norigs = obj.vertices.length,
-          savenorm = new CanvasMatrix4(this.normMatrix),
-          iOrig, adj, offset;
-
-      userMatrix = obj.userMatrix;
-                   
-      if (this.opaquePass) {
-        context = context.slice();
-        context.push(obj.id);
-      } else
-        norigs = 1;
-          
-      if (this.prmvMatrix !== null)
-         origPRMV = new CanvasMatrix4( this.prmvMatrix );
-
-      offset = obj.offset;
-      
-      if (fixed_size && !rotating) {
-        origPR = this.prMatrix;
-        this.prMatrix = new CanvasMatrix4();
-      }
-        
-      for (iOrig=0; iOrig < norigs; iOrig++) {
-        if (this.opaquePass)
-          j = iOrig;
-        else
-          j = context.subid;
-        pos = [].concat(obj.vertices[j]).concat(1.0);
-        radius = obj.radii.length > 1 ? obj.radii[j][0] : obj.radii[0][0];
-        this.mvMatrix = new CanvasMatrix4(userMatrix);
-        adj = this.getAdj(obj, j, offset);
-        this.mvMatrix.translate(1 - 2*adj[0], 1 - 2*adj[1], 1 - 2*adj[2]);
-        this.mvMatrix.scale(radius, radius, radius);
-        
-        if (fixed_size) {
-          var viewport = subscene.par3d.viewport,
-            winwidth = viewport.width*this.canvas.width,
-            winheight = viewport.height*this.canvas.height,
-            scalex = 27/winwidth, scaley = 27/winheight,
-              scale = Math.sqrt(scalex * scaley);
-          if (!rotating) {
-            pos = rglwidgetClass.multVM(pos, origMV);
-            pos = rglwidgetClass.multVM(pos, origPR);
-            this.mvMatrix.scale(scalex, scaley, scale);
-          } else {
-            scale = 4.0 * scale * subscene.par3d.zoom;
-            this.mvMatrix.scale(scale, scale, scale);
-          }
-          this.mvMatrix.translate(pos[0]/pos[3], pos[1]/pos[3], pos[2]/pos[3]);
-          if (rotating)
-            this.mvMatrix.multRight(origMV);
-        } else {
-          if (!rotating) {
-            pos = rglwidgetClass.multVM(pos, origMV);
-            this.mvMatrix.translate(pos[0]/pos[3], pos[1]/pos[3], pos[2]/pos[3]);
-          } else {
-            this.mvMatrix.translate(pos[0]/pos[3], pos[1]/pos[3], pos[2]/pos[3]);
-            this.mvMatrix.multRight(origMV);
-          }
-        }
-        this.setnormMatrix2();
-        this.setprmvMatrix();
-      
-        j = iOrig % obj.shapefirst.length;
-        var first = obj.shapefirst[j];
-        
-        for (i=0; i < obj.shapelens[j]; i++)
-          if (this.opaquePass)
-            result = result.concat(this.drawObjId(obj.objects[first + i], subscene.id, context.concat(j)));
-          else
-            this.drawObjId(obj.objects[i], subscene.id, context);
-      }
-      this.normMatrix = savenorm;
-      this.mvMatrix = origMV;
-      if (fixed_size && !rotating)
-        this.prMatrix = origPR;
-      if (origPRMV !== null)
-        this.prmvMatrix = origPRMV;
-      return result;
-    };
-    
-    /**
-     * Draw object that might be in margin
-     * @param { Object } obj - text object to draw
-     * @param { Object } subscene - subscene holding it
-     * @param { Object } context - context for drawing
-     */
-    rglwidgetClass.prototype.drawMarginal = function(obj, subscene, context) {
-      var margin = obj.material.margin;
- 
-      if (typeof margin !== "undefined") 
-        if (!this.marginVecToDataVec(obj, subscene))
-          return [];
-          
-      return this.drawSimple(obj, subscene, context);
-    };
-    
-    /**
-     * Draw bounding box and decorations
-     * @param { Object } obj - bboxdeco to draw
-     * @param { Object } subscene - subscene holding it
-     * @param { Object } context - context for drawing
-     */
-    rglwidgetClass.prototype.drawBBox = function(obj, subscene, context) {
-      var flags = obj.flags,
-          is_transparent = rglwidgetClass.isSet(flags, rglwidgetClass.f_is_transparent),
-          scale, bbox, indices,
-          enabled = {}, drawing,
-          result = [], idx, center, edges,
-          saved;
-
-      if (!obj.initialized)
-        this.initBBox(obj);
-      
-      is_transparent = is_transparent || obj.someHidden;
-
-      if (!this.opaquePass && !is_transparent)
-        return result;
-      
-      this.setBbox(obj, subscene);
-      
-      saved = this.setBBoxMatrices(obj);
-      
-      bbox = obj.bbox;
-      center = obj.center;
-
-      scale = [bbox[1]-bbox[0], bbox[3]-bbox[2], bbox[5]-bbox[4]];
-
-      if (!obj.cube.initialized) {
-        this.initObj(obj.cube);
-      }
-
-      if (this.opaquePass) {
-        context = context.slice();
-        context.push(obj.id);
-      } 
-      
-      drawing = this.opaquePass !== is_transparent;
-      this.cube.onecolor = obj.cube.onecolor;
-      this.initShapeFromObj(this.cube, obj.cube);
-
-      if (!this.opaquePass)
-        indices = context.indices;
-
-      if (this.opaquePass)
-        idx = 0;
-      else
-        idx = context.subid;
-      if (typeof idx === "undefined")
-        console.error("idx is undefined");
-
-      if (drawing) {
-        this.drawSimple(this.cube, subscene, context);
-      } else 
-        result = result.concat(this.getCubePieces(context, obj));
-
-      if (!obj.ticks.initialized) {
-        obj.ticks.locations = this.getTickLocations(obj);
-        obj.ticks.edges = undefined;
-      }
-      edges = this.getTickEdges(this.prmvMatrix);
-      if (obj.needsAxisCallback) 
-        this.doAxisCallback(obj, edges);
-      if (!obj.ticks.edges || edges.toString() !== obj.ticks.edges.toString()) {
-        obj.ticks.edges = edges;
-        this.getTickVertices(obj.ticks);
-        this.placeTickLabels(obj);
-        this.setTickLabels(obj);
-      }
-      if (!obj.ticks.initialized) {
-        this.initObj(obj.ticks);
-        this.initObj(obj.labels);
-      }
-        
-      if (drawing) {
-        this.drawSimple(obj.ticks, subscene, context);
-        this.drawSimple(obj.labels, subscene, context);
-
-        this.disableArrays(obj, enabled);
-      } else {
-        result = result.concat(this.drawSimple(obj.ticks, subscene, context));
-        result = result.concat(this.drawSimple(obj.labels, subscene, context));
-      }
-
-      this.restoreBBoxMatrices(saved);
-        
-      return result;
-    };
-    
-    /**
-     * Use ids to choose object to draw
-     * @param { numeric } id - object to draw
-     * @param { numeric } subscene
-     * @param { array } context
-     */   
-    rglwidgetClass.prototype.drawObjId = function(id, subsceneid, context) {
-      if (typeof id !== "number")
-        this.alertOnce("drawObjId id is "+typeof id);
-
-      return this.drawObj(this.getObj(id), this.getObj(subsceneid), context);
-   };
-   
-    /**
-     * Draw an object in a subscene
-     * @param { object } obj - object to draw
-     * @param { object } subscene
-     * @param { array } context
-     */
-    rglwidgetClass.prototype.drawObj = function(obj, subscene, context) {
-      switch(obj.type) {
-        case "abclines":
-        case "surface":
-          return this.drawSimple(obj, subscene, context);
-        case "points":
-        case "lines":  
-        case "triangles":
-        case "quads":
-        case "text":
-          return this.drawMarginal(obj, subscene, context);
-        case "linestrip":
-          return this.drawLinestrip(obj, subscene, context);
-        case "planes":
-          return this.drawPlanes(obj, subscene, context);
-        case "spheres":
-          return this.drawSpheres(obj, subscene, context);
-        case "clipplanes":
-          return this.drawClipplanes(obj);
-        case "sprites":
-          return this.drawSprites(obj, subscene, context);
-        case "light":
-          return [];
-        case "bboxdeco":
-          return this.drawBBox(obj, subscene, context);
-      }
-      
-      console.error("drawObj for type = "+obj.type);
-    };
-
-    /**
-     * Draw the background for a subscene
-     * @param { number } id - id of background object
-     * @param { number } subsceneid - id of subscene
-     */
-    rglwidgetClass.prototype.drawBackground = function(id, subsceneid, context) {
-      var gl = this.gl || this.initGL(),
-          obj = this.getObj(id),
-          subscene,
-          bg, i, savepr, saveinvpr, savemv, savenorm, m, bbox, result = [], 
-          savedm = gl.getParameter(gl.DEPTH_WRITEMASK),
-          savedt = gl.isEnabled(gl.DEPTH_TEST),
-          saveblend = gl.isEnabled(gl.BLEND);
-
-      if (!obj.initialized)
-        this.initObj(obj);
-
-      if (obj.colors.length) {
-        bg = obj.colors[0];
-        gl.depthMask(true);
-        gl.clear(gl.DEPTH_BUFFER_BIT);
-        gl.clearColor(bg[0], bg[1], bg[2], bg[3]);
-        gl.clear(gl.COLOR_BUFFER_BIT);
-        this.fogColor = bg;
-      } else {
-        this.fogColor = [0,0,0,0];
-        obj.colors = [[0,0,0,0]];
-      }
-  
-      this.fogType = obj.fogtype;
-      this.fogScale = obj.fogscale;
-      gl.disable(gl.BLEND);
-      gl.disable(gl.DEPTH_TEST);
-      gl.depthMask(false);
-      if (typeof obj.quad !== "undefined") {
-        savepr = this.prMatrix;
-        saveinvpr = this.invPrMatrix;
-        savemv = this.mvMatrix;
-        this.prMatrix = new CanvasMatrix4();
-        this.invPrMatrix = new CanvasMatrix4();
-        this.mvMatrix = new CanvasMatrix4();
-        for (i=0; i < obj.quad.length; i++)
-          result = result.concat(this.drawObjId(obj.quad[i], subsceneid));
-        this.prMatrix = savepr;
-        this.invPrMatrix = saveinvpr;
-        this.mvMatrix = savemv;
-
-      } else if (obj.sphere) {
-        subscene = this.getObj(subsceneid);
-        savemv = this.mvMatrix;
-        savenorm = this.normMatrix;
-        bbox = subscene.par3d.bbox;
-        var center = [(bbox[0] + bbox[1])/2, 
-                  (bbox[2] + bbox[3])/2, 
-                  (bbox[4] + bbox[5])/2, 1],
-            scale = subscene.par3d.scale,
-            ranges = [bbox[1] - bbox[0], 
-                  bbox[3] - bbox[2],
-                  bbox[5] - bbox[4]],
-            avgscale = rglwidgetClass.vlen(ranges)/Math.sqrt(3),
-            aspect = [ranges[0]*scale[0]/avgscale,
-                      ranges[1]*scale[1]/avgscale,
-                      ranges[2]*scale[2]/avgscale],
-            maxaspect = Math.max(aspect[0], aspect[1], aspect[2]),
-            zoom = subscene.par3d.zoom;
-        m = new CanvasMatrix4();
-        m.rotate(90, 1, 0, 0);
-        m.scale(zoom*2.0*maxaspect*ranges[0]/aspect[0], 
-                zoom*2.0*maxaspect*ranges[1]/aspect[1],
-                zoom*2.0*maxaspect*ranges[2]/aspect[2]);
-        m.translate(center[0], center[1], center[2]);
-        m.multRight(savemv);
-        center = rglwidgetClass.multVM(center, savemv);
-        m.translate(-center[0], -center[1], -center[2]);
-        m.scale(1, 1, 0.25/zoom);
-        m.translate(center[0], center[1], center[2]);
-        this.mvMatrix = m;
-        this.initShapeFromObj(this.sphere, obj);
-        this.sphere.onecolor = obj.colors.length > 1 ? obj.colors[1] : obj.colors[0];
-        
-        this.normMatrix = new CanvasMatrix4();
-        
-        this.setnormMatrix2();
-        this.setprmvMatrix();
-        
-        result = result.concat(this.drawSimple(this.sphere, subscene, context));
-        this.mvMatrix = savemv;
-        this.normMatrix = savenorm;
-      }
-      gl.depthMask(savedm);
-      if (savedt)
-        gl.enable(gl.DEPTH_TEST);
-      if (saveblend)
-        gl.enable(gl.BLEND);
-      return result;
-    };
-
-    /**
-     * Draw a subscene
-     * @param { number } subsceneid - id of subscene
-     * @param { array } context 
-     */
-    rglwidgetClass.prototype.drawSubscene = function(subsceneid, context) {
-      var sub = this.getObj(subsceneid),
-          objects = this.scene.objects,
-          clipids = sub.clipplanes,
-          subids = sub.objects,
-          subscene_has_faces = false,
-          subscene_needs_sorting = false,
-          flags, i, obj, result = [];
-          
-      if (sub.par3d.skipRedraw)
-        return result;
-      
-      if (this.opaquePass) {
-        for (i=0; i < subids.length; i++) {
-      	  obj = objects[subids[i]];
-          flags = obj.flags;
-          if (typeof flags !== "undefined") {
-            subscene_has_faces = subscene_has_faces || 
-                            (rglwidgetClass.isSet(flags, rglwidgetClass.f_is_lit) &&
-                            !rglwidgetClass.isSet(flags, rglwidgetClass.f_fixed_quads));
-            obj.is_transparent = obj.someHidden || 
-              rglwidgetClass.isSet(flags, rglwidgetClass.f_is_transparent);
-            subscene_needs_sorting = subscene_needs_sorting || 
-              obj.is_transparent ||
-              rglwidgetClass.isSet(flags, rglwidgetClass.f_depth_sort);
-          }
-        }
-      }
-
-      this.setViewport(subsceneid);
-
-      this.setprMatrix(subsceneid);
-      this.setInvPrMatrix();
-      this.setmvMatrix(subsceneid);
-      this.setnormMatrix2();
-      this.setprmvMatrix();
-      this.invMatrix = new CanvasMatrix4(this.mvMatrix);
-      this.invMatrix.invert();
-      
-      if (this.opaquePass) {
-        context = context.slice();
-        context.push(subsceneid);
-        
-        this.doBlending(false);
-        this.subsceneid = subsceneid;
-        if (typeof this.sphere !== "undefined") // reset this.sphere.fastpieces; it will be recreated if needed
-          this.sphere.fastpieces = undefined;
-        if (typeof sub.backgroundId !== "undefined")
-          result = result.concat(this.drawBackground(sub.backgroundId, subsceneid, context));
-      }
-
-      if (subids.length) {
-            
-        if (clipids.length > 0) {
-          for (i = 0; i < clipids.length; i++)
-            this.drawObjId(clipids[i], subsceneid);
-        }
-        
-        subids = sub.opaque.concat(sub.transparent);
-        if (this.opaquePass) {
-          for (i = 0; i < subids.length; i++)
-            result = result.concat(this.drawObjId(subids[i], subsceneid, context));
-          subids = sub.subscenes;
-          for (i = 0; i < subids.length; i++)
-            result = result.concat(this.drawSubscene(subids[i], context));
-        }
-      }
-      return result;
-    };
-    
-    /**
-     * Set the context for drawing transparently
-     * @param { array } context
-     */
-    rglwidgetClass.prototype.setContext = function(context) {
-      var result = [], objid, obj, type;
-      context = context.slice();
-      context.reverse();
-      while (context.length > 0) {
-        objid = context.pop();
-        obj = this.getObj(objid);
-        type = obj.type;
-        switch (type) {
-          case "subscene":
-            this.drawSubscene(objid, false);
-            break;
-          case "sprites":
-            result = result.concat(context.pop());
-            break;
-          case "spheres":
-            // this.initSphereFromObj(obj);  // FIXME:  not needed?
-            break;
-          case "bboxdeco":
-            result = result.concat(context.pop());
-            break;
-          default:
-            console.error("bad type '", type, "' in setContext");
-        }
-      }
-      return result;
-    };
-    
-    /**
-     * Draw the transparent pieces of a scene
-     * @param {object} pieces
-     */
-    rglwidgetClass.prototype.drawPieces = function(pieces) {
-      var i, prevcontext = [], context;
-      for (i = 0; i < pieces.length; i++) {
-        context = pieces[i].context.slice();
-        if (context !== prevcontext) {
-          prevcontext = context.slice();
-          context = this.setContext(context);
-          this.doBlending(true, pieces[i].objid);
-        }
-        this.drawObjId(pieces[i].objid, this.subsceneid, 
-                       pieces[i]);
-      }
-    };
- 
-    /**
-     * Draw the whole scene
-     */
-    rglwidgetClass.prototype.drawScene = function() {
-      var wasDrawing = this.startDrawing(),
-          pieces;
-      if (!wasDrawing) {
-        if (this.select.state !== "inactive")
-          this.selectionChanged();
-
-        this.doStartScene();
-        this.opaquePass = true;
-        pieces = this.drawSubscene(this.scene.rootSubscene, []);
-        this.opaquePass = false;
-        pieces = this.sortPieces(pieces);
-        pieces = this.mergePieces(pieces);
-        this.drawPieces(pieces);
-      }
-      this.stopDrawing(wasDrawing);
-    };
-</script>
-<script>
-    /**
-     * Change the displayed subset
-     * @param { Object } el - Element of the control; not used.
-     * @param { Object } control - The subset control data.
-     */
-    rglwidgetClass.prototype.subsetSetter = function(el, control) {
-      if (typeof control.subscenes === "undefined" ||
-          control.subscenes === null)
-        control.subscenes = this.scene.rootSubscene;
-      var value = Math.round(control.value),
-          subscenes = [].concat(control.subscenes),
-          fullset = [].concat(control.fullset),
-          i, j, subsceneid,
-          adds = [], deletes = [];
-      if (rglwidgetClass.missing(value))
-        value = control.value = 0;
-      if (control.accumulate)
-        for (i=0; i <= value; i++)
-          adds = adds.concat(control.subsets[i]);
-      else
-        adds = adds.concat(control.subsets[value]);
-      deletes = fullset.filter(function(x) { return adds.indexOf(x) < 0; });
-      for (i = 0; i < subscenes.length; i++) {
-        subsceneid = subscenes[i];
-        if (typeof this.getObj(subsceneid) === "undefined")
-          this.alertOnce("typeof object is undefined");
-        for (j = 0; j < adds.length; j++)
-          this.addToSubscene(adds[j], subsceneid);
-        for (j = 0; j < deletes.length; j++)
-          this.delFromSubscene(deletes[j], subsceneid);
-      }
-    };
-
-    /**
-     * Change the requested property
-     * @param { Object } el - Element of the control; not used.
-     * @param { Object } control - The property setter control data.
-     */
-    rglwidgetClass.prototype.propertySetter = function(el, control)  {
-      var value = control.value,
-          values = [].concat(control.values),
-          svals = [].concat(control.param),
-          direct = values[0] === null,
-          entries = [].concat(control.entries),
-          ncol = entries.length,
-          nrow = values.length/ncol,
-          properties = rglwidgetClass.repeatToLen(control.properties, ncol),
-          objids = rglwidgetClass.repeatToLen(control.objids, ncol),
-          property, objid = objids[0],
-          obj = this.getObj(objid),
-          propvals, i, j, v1, v2, p, entry, gl, needsBinding,
-          newprop, newid,
-
-          getPropvals = function() {
-            if (property === "userMatrix")
-              return obj.par3d.userMatrix.getAsArray();
-            else if (property === "scale" || property === "FOV" || property === "zoom")
-              return [].concat(obj.par3d[property]);
-            else
-              return [].concat(obj[property]);
-          },
-
-          putPropvals = function(newvals) {
-            if (newvals.length === 1)
-              newvals = newvals[0];
-            if (property === "userMatrix")
-              obj.par3d.userMatrix.load(newvals);
-            else if (property === "scale" || property === "FOV" || property === "zoom")
-              obj.par3d[property] = newvals;
-            else
-              obj[property] = newvals;
-          };
-
-      if (direct && typeof value === "undefined")
-        return;
-
-      if (control.interp) {
-        values = values.slice(0, ncol).concat(values).
-                 concat(values.slice(ncol*(nrow-1), ncol*nrow));
-        svals = [-Infinity].concat(svals).concat(Infinity);
-        for (i = 1; i < svals.length; i++) {
-          if (value <= svals[i]) {
-            if (svals[i] === Infinity)
-              p = 1;
-            else
-              p = (svals[i] - value)/(svals[i] - svals[i-1]);
-            break;
-          }
-        }
-      } else if (!direct) {
-        value = Math.round(value);
-      }
-
-      for (j=0; j<entries.length; j++) {
-        entry = entries[j];
-        newprop = properties[j];
-        newid = objids[j];
-
-        if (newprop !== property || newid !== objid) {
-          if (typeof property !== "undefined")
-            putPropvals(propvals);
-          property = newprop;
-          objid = newid;
-          obj = this.getObj(objid);
-          propvals = getPropvals();
-        }
-        if (control.interp) {
-          v1 = values[ncol*(i-1) + j];
-          v2 = values[ncol*i + j];
-          this.setElement(propvals, entry, p*v1 + (1-p)*v2);
-        } else if (!direct) {
-          this.setElement(propvals, entry, values[ncol*value + j]);
-        } else {
-          this.setElement(propvals, entry, value[j]);
-        }
-      }
-      putPropvals(propvals);
-
-      needsBinding = [];
-      for (j=0; j < entries.length; j++) {
-        if (properties[j] === "values" &&
-            needsBinding.indexOf(objids[j]) === -1) {
-          needsBinding.push(objids[j]);
-        }
-      }
-      for (j=0; j < needsBinding.length; j++) {
-        gl = this.gl || this.initGL();
-        obj = this.getObj(needsBinding[j]);
-        gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
-        gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW);
-      }
-    };
-
-    /**
-     * Change the requested vertices
-     * @param { Object } el - Element of the control; not used.
-     * @param { Object } control - The vertext setter control data.
-     */
-    rglwidgetClass.prototype.vertexSetter = function(el, control)  {
-      var svals = [].concat(control.param),
-          j, k, p, a, propvals, stride, ofs, obj, entry,
-          attrib, vertex, varies,
-          ofss    = {x:"vofs", y:"vofs", z:"vofs",
-                     red:"cofs", green:"cofs", blue:"cofs",
-                     alpha:"cofs", radii:"radofs",
-                     nx:"nofs", ny:"nofs", nz:"nofs",
-                     ox:"oofs", oy:"oofs", oz:"oofs",
-                     ts:"tofs", tt:"tofs"},
-          pos     = {x:0, y:1, z:2,
-                     red:0, green:1, blue:2,
-                     alpha:3,radii:0,
-                     nx:0, ny:1, nz:2,
-                     ox:0, oy:1, oz:2,
-                     ts:0, tt:1},
-        values = control.values,
-        direct = values === null,
-        ncol,
-        interp = control.interp,
-        vertices = [].concat(control.vertices),
-        attributes = [].concat(control.attributes),
-        value = control.value, newval, aliases, alias;
-
-      ncol = Math.max(vertices.length, attributes.length);
-
-      if (!ncol)
-        return;
-
-      vertices = rglwidgetClass.repeatToLen(vertices, ncol);
-      attributes = rglwidgetClass.repeatToLen(attributes, ncol);
-
-      if (direct)
-        interp = false;
-
-      /* JSON doesn't pass Infinity */
-      svals[0] = -Infinity;
-      svals[svals.length - 1] = Infinity;
-
-      for (j = 1; j < svals.length; j++) {
-        if (value <= svals[j]) {
-          if (interp) {
-            if (svals[j] === Infinity)
-              p = 1;
-            else
-              p = (svals[j] - value)/(svals[j] - svals[j-1]);
-          } else {
-            if (svals[j] - value > value - svals[j-1])
-              j = j - 1;
-          }
-          break;
-        }
-      }
-
-      obj = this.getObj(control.objid);
-      // First, make sure color attributes vary in original
-      if (typeof obj.vOffsets !== "undefined") {
-      	varies = true;
-        for (k = 0; k < ncol; k++) {
-          attrib = attributes[k];
-          if (typeof attrib !== "undefined") {
-            ofs = obj.vOffsets[ofss[attrib]];
-            if (ofs < 0) {
-              switch(attrib) {
-              	case "alpha":
-              	case "red":
-              	case "green":
-              	case "blue":
-              	  obj.colors = [obj.colors[0], obj.colors[0]];
-              	  break;
-              }
-              varies = false;
-            }
-          }
-        }
-        if (!varies)
-          this.initObjId(control.objid);
-      }
-      propvals = obj.values;
-      aliases = obj.alias;
-      if (typeof aliases === "undefined")
-        aliases = [];
-      for (k=0; k<ncol; k++) {
-        if (direct) {
-          newval = value;
-        } else if (interp) {
-          newval = p*values[j-1][k] + (1-p)*values[j][k];
-        } else {
-          newval = values[j][k];
-        }      	
-        attrib = attributes[k];
-        vertex = vertices[k];
-        alias = aliases[vertex];
-        if (obj.type === "planes" || obj.type === "clipplanes") {
-          ofs = ["nx", "ny", "nz", "offset"].indexOf(attrib);
-          if (ofs >= 0) {
-            if (ofs < 3) {
-              if (obj.normals[vertex][ofs] !== newval) {  // Assume no aliases here...
-              	obj.normals[vertex][ofs] = newval;
-              	obj.initialized = false;
-              }
-            } else {
-              if (obj.offsets[vertex][0] !== newval) {
-              	obj.offsets[vertex][0] = newval;
-              	obj.initialized = false;
-              }
-            }
-            continue;
-          }
-        }
-        // Not a plane setting...
-        ofs = obj.vOffsets[ofss[attrib]];
-        if (ofs < 0)
-          this.alertOnce("Attribute '"+attrib+"' not found in object "+control.objid);
-        else {
-          stride = obj.vOffsets.stride;
-          ofs = ofs + pos[attrib];
-          entry = vertex*stride + ofs;
-          propvals[entry] = newval;
-          if (typeof alias !== "undefined")
-            for (a = 0; a < alias.length; a++)
-              propvals[alias[a]*stride + ofs] = newval;
-        }
-      }
-      if (typeof obj.buf !== "undefined") {
-        var gl = this.gl || this.initGL();
-        gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
-        gl.bufferData(gl.ARRAY_BUFFER, propvals, gl.STATIC_DRAW);
-      }
-    };
-
-    /**
-     * Change the requested vertex properties by age
-     * @param { Object } el - Element of the control; not used.
-     * @param { Object } control - The age setter control data.
-     */
-    rglwidgetClass.prototype.ageSetter = function(el, control) {
-      var objids = [].concat(control.objids),
-          nobjs = objids.length,
-          time = control.value,
-          births = [].concat(control.births),
-          ages = [].concat(control.ages),
-          steps = births.length,
-          j = Array(steps),
-          p = Array(steps),
-          i, k, l, age, j0, propvals, stride, ofs, objid, obj,
-          attrib, dim, varies, alias, aliases, a, d,
-          attribs = ["colors", "alpha", "radii", "vertices",
-                     "normals", "origins", "texcoords",
-                     "x", "y", "z",
-                     "red", "green", "blue"],
-          ofss    = ["cofs", "cofs", "radofs", "vofs",
-                     "nofs", "oofs", "tofs",
-                     "vofs", "vofs", "vofs",
-                     "cofs", "cofs", "cofs"],
-          dims    = [3,1,1,3,
-                     3,2,2,
-                     1,1,1,
-                     1,1,1],
-          pos     = [0,3,0,0,
-                     0,0,0,
-                     0,1,2,
-                     0,1,2];
-      /* Infinity doesn't make it through JSON */
-      ages[0] = -Infinity;
-      ages[ages.length-1] = Infinity;
-      for (i = 0; i < steps; i++) {
-        if (births[i] !== null) {  // NA in R becomes null
-          age = time - births[i];
-          for (j0 = 1; age > ages[j0]; j0++);
-          if (ages[j0] === Infinity)
-            p[i] = 1;
-          else if (ages[j0] > ages[j0-1])
-            p[i] = (ages[j0] - age)/(ages[j0] - ages[j0-1]);
-          else
-            p[i] = 0;
-          j[i] = j0;
-        }
-      }
-      // First, make sure color attributes vary in original
-      for (l = 0; l < nobjs; l++) {
-      	objid = objids[l];
-      	obj = this.getObj(objid);
-      	varies = true;
-        if (typeof obj.vOffsets === "undefined")
-          continue;
-        for (k = 0; k < attribs.length; k++) {
-          attrib = control[attribs[k]];
-          if (typeof attrib !== "undefined") {
-            ofs = obj.vOffsets[ofss[k]];
-            if (ofs < 0) {
-              switch(attribs[k]) {
-              	case "colors":
-              	case "alpha":
-              	case "red":
-              	case "green":
-              	case "blue":
-              	  obj.colors = [obj.colors[0], obj.colors[0]];
-              	  break;
-              }
-              varies = false;
-            }
-          }
-        }
-        if (!varies)
-          this.initObjId(objid);
-      }
-      for (l = 0; l < nobjs; l++) {
-        objid = objids[l];
-        obj = this.getObj(objid);
-        if (typeof obj.vOffsets === "undefined")
-          continue;
-        aliases = obj.alias;
-        if (typeof aliases === "undefined")
-          aliases = [];
-        propvals = obj.values;
-        stride = obj.vOffsets.stride;
-        for (k = 0; k < attribs.length; k++) {
-          attrib = control[attribs[k]];
-          if (typeof attrib !== "undefined") {
-            ofs = obj.vOffsets[ofss[k]];
-            if (ofs >= 0) {
-              dim = dims[k];
-              ofs = ofs + pos[k];
-              for (i = 0; i < steps; i++) {
-              	alias = aliases[i];
-                if (births[i] !== null) {
-                  for (d=0; d < dim; d++) {
-                    propvals[i*stride + ofs + d] = p[i]*attrib[dim*(j[i]-1) + d] + (1-p[i])*attrib[dim*j[i] + d];
-                    if (typeof alias !== "undefined")
-                      for (a=0; a < alias.length; a++)
-                        propvals[alias[a]*stride + ofs + d] = propvals[i*stride + ofs + d];
-                  }
-                }
-              }
-            } else
-              this.alertOnce("\'"+attribs[k]+"\' property not found in object "+objid);
-          }
-        }
-        obj.values = propvals;
-        if (typeof obj.buf !== "undefined") {
-          var gl = this.gl || this.initGL();
-          gl.bindBuffer(gl.ARRAY_BUFFER, obj.buf);
-          gl.bufferData(gl.ARRAY_BUFFER, obj.values, gl.STATIC_DRAW);
-        }
-      }
-    };
-
-    /**
-     * Bridge to old style control
-     * @param { Object } el - Element of the control; not used.
-     * @param { Object } control - The bridge control data.
-     */
-    rglwidgetClass.prototype.oldBridge = function(el, control) {
-      var attrname, global = window[control.prefix + "rgl"];
-      if (global)
-        for (attrname in global)
-          this[attrname] = global[attrname];
-      window[control.prefix + "rgl"] = this;
-    };
-
-    /**
-     * Set up a player control
-     * @param { Object } el - The player control element
-     * @param { Object } control - The player data.
-     */
-    rglwidgetClass.prototype.Player = function(el, control) {
-      var
-        self = this,
-        components = [].concat(control.components),
-        buttonLabels = [].concat(control.buttonLabels),
-
-        Tick = function() { /* "this" will be a timer */
-          var i,
-              nominal = this.value,
-              slider = this.Slider,
-              labels = this.outputLabels,
-              output = this.Output,
-              step;
-          if (typeof slider !== "undefined" && nominal !== slider.value)
-            slider.value = nominal;
-          if (typeof output !== "undefined") {
-            step = Math.round((nominal - output.sliderMin)/output.sliderStep);
-            if (labels !== null) {
-              output.innerHTML = labels[step];
-            } else {
-              step = step*output.sliderStep + output.sliderMin;
-              output.innerHTML = step.toPrecision(output.outputPrecision);
-            }
-          }
-          for (i=0; i < this.actions.length; i++) {
-            this.actions[i].value = nominal;
-          }
-          self.applyControls(el, this.actions, false);
-          self.drawScene();
-        },
-
-        OnSliderInput = function() { /* "this" will be the slider */
-          this.rgltimer.value = Number(this.value);
-          this.rgltimer.Tick();
-        },
-
-        addSlider = function(min, max, step, value) {
-          var slider = document.createElement("input");
-          slider.type = "range";
-          slider.min = min;
-          slider.max = max;
-          slider.step = step;
-          slider.value = value;
-          slider.oninput = OnSliderInput;
-          slider.sliderActions = control.actions;
-          slider.sliderScene = this;
-          slider.className = "rgl-slider";
-          slider.id = el.id + "-slider";
-          el.rgltimer.Slider = slider;
-          slider.rgltimer = el.rgltimer;
-          el.appendChild(slider);
-        },
-
-        addLabel = function(labels, min, step, precision) {
-          var output = document.createElement("output");
-          output.sliderMin = min;
-          output.sliderStep = step;
-          output.outputPrecision = precision;
-          output.className = "rgl-label";
-          output.id = el.id + "-label";
-          el.rgltimer.Output = output;
-          el.rgltimer.outputLabels = labels;
-          el.appendChild(output);
-        },
-
-        addButton = function(which, label, active) {
-          var button = document.createElement("input"),
-              onclicks = {Reverse: function() { this.rgltimer.reverse();},
-                    Play: function() { this.rgltimer.play();
-                                       this.value = this.rgltimer.enabled ? this.inactiveValue : this.activeValue; },
-                   Slower: function() { this.rgltimer.slower(); },
-                   Faster: function() { this.rgltimer.faster(); },
-                   Reset: function() { this.rgltimer.reset(); },
-              	   Step:  function() { this.rgltimer.step(); }
-              };
-          button.rgltimer = el.rgltimer;
-          button.type = "button";
-          button.value = label;
-          button.activeValue = label;
-          button.inactiveValue = active;
-          if (which === "Play")
-            button.rgltimer.PlayButton = button;
-          button.onclick = onclicks[which];
-          button.className = "rgl-button";
-          button.id = el.id + "-" + which;
-          el.appendChild(button);
-        };
-
-        if (typeof control.reinit !== "undefined" && control.reinit !== null) {
-          control.actions.reinit = control.reinit;
-        }
-        el.rgltimer = new rgltimerClass(Tick, control.start, control.interval, control.stop,
-                                        control.step, control.value, control.rate, control.loop, control.actions);
-        for (var i=0; i < components.length; i++) {
-          switch(components[i]) {
-            case "Slider": addSlider(control.start, control.stop,
-                                   control.step, control.value);
-              break;
-            case "Label": addLabel(control.labels, control.start,
-                                   control.step, control.precision);
-              break;
-            default:
-              addButton(components[i], buttonLabels[i], control.pause);
-          }
-        }
-        el.rgltimer.Tick();
-    };
-
-    /**
-     * Apply all registered controls
-     * @param { Object } el - DOM element of the control
-     * @param { Object } x - List of actions to apply
-     * @param { boolean } [draw=true] - Whether to redraw after applying
-     */
-    rglwidgetClass.prototype.applyControls = function(el, x, draw) {
-      var self = this, reinit = x.reinit, i, control, type;
-      for (i = 0; i < x.length; i++) {
-        control = x[i];
-        type = control.type;
-        self[type](el, control);
-      }
-      if (typeof reinit !== "undefined" && reinit !== null) {
-        reinit = [].concat(reinit);
-        for (i = 0; i < reinit.length; i++)
-          self.getObj(reinit[i]).initialized = false;
-      }
-      if (typeof draw === "undefined" || draw)
-        self.drawScene();
-    };
-
-    /**
-     * Handler for scene change
-     * @param { Object } message - What sort of scene change to do?
-     */
-    rglwidgetClass.prototype.sceneChangeHandler = function(message) {
-      var self = document.getElementById(message.elementId).rglinstance,
-          objs = message.objects, mat = message.material,
-          root = message.rootSubscene,
-          initSubs = message.initSubscenes,
-          redraw = message.redrawScene,
-          skipRedraw = message.skipRedraw,
-          deletes, subs, allsubs = [], i,j;
-      if (typeof message.delete !== "undefined") {
-        deletes = [].concat(message.delete);
-        if (typeof message.delfromSubscenes !== "undefined")
-          subs = [].concat(message.delfromSubscenes);
-        else
-          subs = [];
-        for (i = 0; i < deletes.length; i++) {
-          for (j = 0; j < subs.length; j++) {
-            self.delFromSubscene(deletes[i], subs[j]);
-          }
-          delete self.scene.objects[deletes[i]];
-        }
-      }
-      if (typeof objs !== "undefined") {
-        Object.keys(objs).forEach(function(key){
-          key = parseInt(key, 10);
-          self.scene.objects[key] = objs[key];
-          self.initObjId(key);
-          var obj = self.getObj(key),
-              subs = [].concat(obj.inSubscenes), k;
-          allsubs = allsubs.concat(subs);
-          for (k = 0; k < subs.length; k++)
-            self.addToSubscene(key, subs[k]);
-        });
-      }
-      if (typeof mat !== "undefined") {
-        self.scene.material = mat;
-      }
-      if (typeof root !== "undefined") {
-        self.scene.rootSubscene = root;
-      }
-      if (typeof initSubs !== "undefined")
-        allsubs = allsubs.concat(initSubs);
-      allsubs = self.unique(allsubs);
-      for (i = 0; i < allsubs.length; i++) {
-        self.initSubscene(allsubs[i]);
-      }
-      if (typeof skipRedraw !== "undefined") {
-        root = self.getObj(self.scene.rootSubscene);
-        root.par3d.skipRedraw = skipRedraw;
-      }
-      if (redraw)
-        self.drawScene();
-    };
-</script>
-<script>    /**
-     * Methods related to selection
-     * @name ___METHODS_FOR_SELECTION___
-     * @memberof rglwidgetClass
-     * @kind function
-     * @instance
-     */
-     
-    /**
-     * Respond to brush change
-     */
-    rglwidgetClass.prototype.selectionChanged = function() {
-      var i, j, k, id, subid = this.select.subscene, subscene,
-          objids, obj,
-          p1 = this.select.region.p1, p2 = this.select.region.p2,
-          filter, selection = [], handle, keys, xmin, x, xmax, ymin, y, ymax, z, v,
-          someHidden;
-      if (!subid)
-        return;
-      subscene = this.getObj(subid);
-      objids = subscene.objects;
-      filter = this.scene.crosstalk.filter;
-      this.setmvMatrix(subid);
-      this.setprMatrix(subid);
-      this.setprmvMatrix();
-      xmin = Math.min(p1.x, p2.x);
-      xmax = Math.max(p1.x, p2.x);
-      ymin = Math.min(p1.y, p2.y);
-      ymax = Math.max(p1.y, p2.y);
-      for (i = 0; i < objids.length; i++) {
-      	id = objids[i];
-      	j = this.scene.crosstalk.id.indexOf(id);
-      	if (j >= 0) {
-      	  keys = this.scene.crosstalk.key[j];
-      	  obj = this.getObj(id);
-      	  someHidden = false;
-      	  for (k = 0; k < keys.length; k++) {
-      	    if (filter && filter.indexOf(keys[k]) < 0) {
-      	      someHidden = true;
-      	      continue;
-      	    }
-      	    v = [].concat(obj.vertices[k]).concat(1.0);
-            v = rglwidgetClass.multVM(v, this.prmvMatrix);
-            x = v[0]/v[3];
-            y = v[1]/v[3];
-            z = v[2]/v[3];
-            if (xmin <= x && x <= xmax && ymin <= y && y <= ymax && -1.0 <= z && z <= 1.0) {
-              selection.push(keys[k]);
-            } else
-              someHidden = true;
-      	  }
-      	  obj.someHidden = someHidden && (filter || selection.length);
-      	  obj.initialized = false;
-      	  /* Who should we notify?  Only shared data in the current subscene, or everyone? */
-      	  if (!this.equalArrays(selection, this.scene.crosstalk.selection)) {
-      	    handle = this.scene.crosstalk.sel_handle[j];
-      	    handle.set(selection, {rglSubsceneId: this.select.subscene});
-      	  }
-      	}
-      }
-    };
-    
-    /**
-     * Respond to selection or filter change from crosstalk
-     * @param { Object } event - crosstalk event
-     * @param { boolean } filter - filter or selection?
-     */
-    rglwidgetClass.prototype.selection = function(event, filter) {
-      	var i, j, ids, obj, keys, crosstalk = this.scene.crosstalk,
-      	    selection, someHidden;
-
-      	// Record the message and find out if this event makes some objects have mixed values:
-      	
-      	crosstalk = this.scene.crosstalk;
-      	
-      	if (filter) {
-      	  filter = crosstalk.filter = event.value;
-      	  selection = crosstalk.selection;
-      	} else {  
-          selection = crosstalk.selection = event.value;
-          filter = crosstalk.filter;
-      	}
-        ids = crosstalk.id;
-        for (i = 0; i < ids.length ; i++) {
-          obj = this.getObj(ids[i]);
-          obj.initialized = false;
-          keys = crosstalk.key[i];
-          someHidden = false;
-          for (j = 0; j < keys.length && !someHidden; j++) {
-            if ((filter && filter.indexOf(keys[j]) < 0) ||
-                (selection.length && selection.indexOf(keys[j]) < 0))
-                someHidden = true;
-          }
-          obj.someHidden = someHidden;
-        }
-        this.drawScene();
-    };
-    
-    /**
-     * Clear the selection brush
-     * @param { number } except - Subscene that should ignore this request
-     */
-    rglwidgetClass.prototype.clearBrush = function(except) {
-      if (this.select.subscene !== except) {
-        this.select.region = {p1: {x:Infinity, y:Infinity}, 
-                              p2: {x:Infinity, y:Infinity}};
-        this.selectionChanged();
-        this.select.state = "inactive";
-        this.delFromSubscene(this.scene.brushId, this.select.subscene);
-      }
-      this.drawScene();
-    };
-    
-    /**
-     * Set the vertices in the selection box object
-     */
-    rglwidgetClass.prototype.initSelection = function(id) {
-      if (typeof this.select.region === "undefined")
-        return;
-      var obj = this.getObj(id),
-          p1 = this.select.region.p1,
-          p2 = this.select.region.p2;
-          
-      obj.vertices = [[p1.x, p1.y, 0.0],
-                      [p2.x, p1.y, 0.0],
-                      [p2.x, p2.y, 0.0],
-                      [p1.x, p2.y, 0.0],
-                      [p1.x, p1.y, 0.0]];
-    };
-</script>
-<script>
-/* globals rgltimerClass: true */
-
-/**
- * The class of an rgl timer object
- * @class
-*/
-
-/**
- * Construct an rgltimerClass object
- * @constructor
- * @param { function } Tick - action when timer fires
- * @param { number } startTime - nominal start time in seconds
- * @param { number } interval - seconds between updates
- * @param { number } stopTime - nominal stop time in seconds
- * @param { number } stepSize - nominal step size
- * @param { number } value - current nominal time
- * @param { number } rate - nominal units per second
- * @param { string } loop - "none", "cycle" or "oscillate"
- * @param { Object } actions - list of actions
- */
-rgltimerClass = function(Tick, startTime, interval, stopTime, stepSize, value, rate, loop, actions) {
-  this.enabled = false;
-  this.timerId = 0;
-  /** nominal start time in seconds */
-  this.startTime = startTime;   
-  /** current nominal time */      
-  this.value = value;
-  /** seconds between updates */                 
-  this.interval = interval;
-  /** nominal stop time */           
-  this.stopTime = stopTime;
-  /** nominal step size */           
-  this.stepSize = stepSize;
-  /** nominal units per second */           
-  this.rate = rate;
-  /** "none", "cycle", or "oscillate" */                   
-  this.loop = loop;
-  /** real world start time */                   
-  this.realStart = undefined;
-  /** multiplier for fast-forward or reverse */         
-  this.multiplier = 1;                
-  this.actions = actions;
-  this.Tick = Tick;
-};
-
-
-    /**
-     * Methods related to players
-     * @name ___METHODS_FOR_PLAYERS___
-     * @memberof rgltimerClass
-     * @kind function
-     * @instance
-     */
-
-  /**
-   * Start playing
-   * @memberof rgltimerClass
-   */
-  rgltimerClass.prototype.play = function() {
-    if (this.enabled) {
-      this.enabled = false;
-      window.clearInterval(this.timerId);
-      this.timerId = 0;
-      return;
-    }
-    var tick = function(self) {
-      var now = new Date();
-      self.value = self.multiplier*self.rate*(now - self.realStart)/1000 + self.startTime;
-      self.forceToRange();
-      if (typeof self.Tick !== "undefined") {
-        self.Tick(self.value);
-      }
-
-    };
-    this.realStart = new Date() - 1000*(this.value - this.startTime)/this.rate/this.multiplier;
-    this.timerId = window.setInterval(tick, 1000*this.interval, this);
-    this.enabled = true;
-  };
-
-  /**
-   * Force value into legal range
-   */
-  rgltimerClass.prototype.forceToRange = function() {
-    if (this.value > this.stopTime + this.stepSize/2 || this.value < this.startTime - this.stepSize/2) {
-      if (!this.loop) {
-        this.reset();
-      } else {
-        var cycle = this.stopTime - this.startTime + this.stepSize,
-            newval = (this.value - this.startTime) % cycle + this.startTime;
-        if (newval < this.startTime) {
-          newval += cycle;
-        }
-        this.realStart += (this.value - newval)*1000/this.multiplier/this.rate;
-        this.value = newval;
-      }
-    }
-  };
-
-  /**
-   * Reset to start values
-   */
-  rgltimerClass.prototype.reset = function() {
-    this.value = this.startTime;
-    this.newmultiplier(1);
-    if (typeof this.Tick !== "undefined") {
-        this.Tick(this.value);
-    }
-    if (this.enabled)
-      this.play();  /* really pause... */
-    if (typeof this.PlayButton !== "undefined")
-      this.PlayButton.value = "Play";
-  };
-
-  /**
-   * Increase the multiplier to play faster
-   */
-  rgltimerClass.prototype.faster = function() {
-    this.newmultiplier(Math.SQRT2*this.multiplier);
-  };
-
-  /**
-   * Decrease the multiplier to play slower
-   */
-  rgltimerClass.prototype.slower = function() {
-    this.newmultiplier(this.multiplier/Math.SQRT2);
-  };
-
-  /**
-   * Change sign of multiplier to reverse direction
-   */
-  rgltimerClass.prototype.reverse = function() {
-    this.newmultiplier(-this.multiplier);
-  };
-
-  /**
-   * Set multiplier for play speed
-   * @param { number } newmult - new value
-   */
-  rgltimerClass.prototype.newmultiplier = function(newmult) {
-    if (newmult !== this.multiplier) {
-      this.realStart += 1000*(this.value - this.startTime)/this.rate*(1/this.multiplier - 1/newmult);
-      this.multiplier = newmult;
-    }
-  };
-
-  /**
-   * Take one step
-   */
-  rgltimerClass.prototype.step = function() {
-    this.value += this.rate*this.multiplier;
-    this.forceToRange();
-    if (typeof this.Tick !== "undefined")
-      this.Tick(this.value);
-  };
-</script>
-<script>/**
- * Pretty function from R
- * @name ___PRETTY_FROM_R___
- * @memberof rglwidgetClass
- * @kind function
- * @instance
- */
-
-
-/* This file is translated from pretty.c, which was
- taken from the R sources, r61744 of src/appl/pretty.c,
- with minimal changes */
-
-/*
- *  R : A Computer Language for Statistical Data Analysis
- *  Copyright (C) 1995-2012  The R Core Team
- *
- *  This program is free software; you can redistribute it and/or modify
- *  it under the terms of the GNU General Public License as published by
- *  the Free Software Foundation; either version 2 of the License, or
- *  (at your option) any later version.
- *
- *  This program is distributed in the hope that it will be useful,
- *  but WITHOUT ANY WARRANTY; without even the implied warranty of
- *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- *  GNU General Public License for more details.
- *
- *  You should have received a copy of the GNU General Public License
- *  along with this program; if not, a copy is available at
- *  http://www.r-project.org/Licenses/
- */
-
-/**     
- * Construct pretty values to cover an interval
- * @param { number } lo - lower end of interval
- * @param { number } up - upper end of interval
- * @param { number } ndiv - requested number of divisions
- * @param { number } min_n - minimum divisions
- * @param { number } shrink_sml - if too many cells, amount to shrink by
- * @param { number } high_u_fact - bias in favour of larger units
- * @param { number } eps_correction - correction to bounds
- * @param { Boolean } return_bounds - whether to return bounds
- * @description
- * Pretty Intervals
-
- * Constructs m "pretty" values which cover the given interval	*lo <= *up
- *	m ~= *ndiv + 1	(i.e., ndiv := approximate number of INTERVALS)
- *
- * It is not quite clear what should happen for	 *lo = *up;
- * S itself behaves quite funilly, then.
- *
- * In my opinion, a proper 'pretty' should always ensure
- * *lo < *up, and hence *ndiv >=1 in the result.
- * However, in S and here, we allow  *lo == *up, and *ndiv = 0.
- * Note however, that we are NOT COMPATIBLE to S. [Martin M.]
- *
- * NEW (0.63.2): ns, nu are double (==> no danger of integer overflow)
- *
- * We determine
- * if the interval (up - lo) is ``small'' [<==>	 i_small == TRUE, below].
- * For the ``i_small'' situation, there is a parameter  shrink_sml,
- * the factor by which the "scale" is shrunk.		~~~~~~~~~~
- * It is advisable to set it to some (smaller) integer power of 2,
- * since this enables exact floating point division.
- */
-rglwidgetClass.prototype.R_pretty = function(
-  lo, up, ndiv, min_n, shrink_sml, high_u_fact,
-  eps_correction, return_bounds) {
-  /* From version 0.65 on, we had rounding_eps := 1e-5, before, r..eps = 0
-   * 1e-7 is consistent with seq.default() */
-  var rounding_eps = 1e-7,  h = high_u_fact[0],
-                                           h5 = high_u_fact[1], 
-                                                           dx, cell, unit, base, U, ns, nu, k, i_small,
-                                                           DBL_EPSILON = Number.EPSILON,
-                                                           DBL_MIN = Number.MIN_VALUE,
-                                                           DBL_MAX = Number.MAX_VALUE;
-  
-  dx = up - lo;
-  /* cell := "scale"	here */
-  if (dx === 0 && up === 0) { /*  up == lo == 0	 */
-  cell = 1;
-    i_small = true;
-  } else {
-    cell = Math.max(Math.abs(lo), Math.abs(up));
-    /* U = upper bound on cell/unit */
-    U = (1 + (h5 >= 1.5*h+0.5)) ? 1/(1+h) : 1.5/(1+h5);
-    /* added times 3, as several calculations here */
-    i_small = dx < cell * U * Math.max(1,ndiv) * DBL_EPSILON *3;
-  }
-  
-  /*OLD: cell = FLT_EPSILON+ dx / *ndiv; FLT_EPSILON = 1.192e-07 */
-  if(i_small) {
-    if(cell > 10)
-      cell = 9 + cell/10;
-    cell *= shrink_sml;
-    if(min_n > 1) cell /= min_n;
-  } else {
-    cell = dx;
-    if(ndiv > 1) cell /= ndiv;
-  }
-  
-  if(cell < 20*DBL_MIN) {
-    /* warning(_("Internal(pretty()): very small range.. corrected")); */
-    cell = 20*DBL_MIN;
-  } else if(cell * 10 > DBL_MAX) {
-    /* warning(_("Internal(pretty()): very large range.. corrected")); */
-    cell = 0.1*DBL_MAX;
-  }
-  base = Math.pow(10, Math.floor(Math.log10(cell))); /* base <= cell < 10*base */
-    
-    /* unit : from { 1,2,5,10 } * base
-     *	 such that |u - cell| is small,
-     * favoring larger (if h > 1, else smaller)  u  values;
-     * favor '5' more than '2'  if h5 > h  (default h5 = .5 + 1.5 h) */
-    unit = base;
-    if((U = 2*base)-cell <  h*(cell-unit)) { unit = U;
-      if((U = 5*base)-cell < h5*(cell-unit)) { unit = U;
-        if((U =10*base)-cell <  h*(cell-unit)) unit = U; }}
-    /* Result: c := cell,  u := unit,  b := base
-     *	c in [	1,	      (2+ h) /(1+h) ] b ==> u=  b
-     *	c in ( (2+ h)/(1+h),  (5+2h5)/(1+h5)] b ==> u= 2b
-     *	c in ( (5+2h)/(1+h), (10+5h) /(1+h) ] b ==> u= 5b
-     *	c in ((10+5h)/(1+h),	         10 ) b ==> u=10b
-     *
-     *	===>	2/5 *(2+h)/(1+h)  <=  c/u  <=  (2+h)/(1+h)	*/
-    
-    ns = Math.floor(lo/unit+rounding_eps);
-    nu = Math.ceil (up/unit-rounding_eps);
-    
-    if(eps_correction && (eps_correction > 1 || !i_small)) {
-      if(lo !== 0.0) lo *= (1- DBL_EPSILON); else lo = -DBL_MIN;
-      if(up !== 0.0) up *= (1+ DBL_EPSILON); else up = +DBL_MIN;
-    }
-    
-    while(ns*unit > lo + rounding_eps*unit) ns--;
-    
-    while(nu*unit < up - rounding_eps*unit) nu++;
-    
-    k = Math.floor(0.5 + nu - ns);
-    if(k < min_n) {
-      /* ensure that	nu - ns	 == min_n */
-      
-      k = min_n - k;
-      if(ns >= 0) {
-        nu += k/2;
-        ns -= k/2 + k%2;/* ==> nu-ns = old(nu-ns) + min_n -k = min_n */
-      } else {
-        ns -= k/2;
-        nu += k/2 + k%2;
-      }
-      ndiv = min_n;
-    } else {
-      ndiv = k;
-    }
-    if(return_bounds) { /* if()'s to ensure that result covers original range */
-      if(ns * unit < lo) lo = ns * unit;
-      if(nu * unit > up) up = nu * unit;
-    } else {
-      lo = ns;
-      up = nu;
-    }
-    return {lo:lo, up:up, ndiv:ndiv, unit:unit};
-};
-</script>
-<script>    /**
-     * Methods related to axes
-     * @name ___METHODS_FOR_AXES___
-     * @memberof rglwidgetClass
-     * @kind function
-     * @instance
-     */
-     
-    /**
-     * Choose edges for ticks
-     * @param { Matrix } prmv - projection-model-view matrix
-     */
-    rglwidgetClass.prototype.getTickEdges = function(prmv){
-      var vertices = [[0,0,0,1], [0,0,1,1],
-                      [0,1,0,1], [0,1,1,1],
-                      [1,0,0,1], [1,0,1,1],
-                      [1,1,0,1], [1,1,1,1]], 
-           dim, i, j, k, edges, hull, step, result = [], proj = [],
-
-        // Filter to edges that are on sides that would
-        // be shown with a filled backing.
-        
-      has_back = function(edge) {
-          var normals = [[], []],
-              verts = [vertices[edge[0]], 
-                       vertices[edge[1]]], 
-              normal, m, n;
-          n = 0;
-          for (m=0; m<3; m++) {
-            if (verts[0][m] === verts[1][m]) {
-              normals[n] = [0,0,0,1];
-              normals[n][m] = 2*verts[0][m] - 1;
-              n++;
-            }
-          }
-          for (n=0; n<2; n++) {
-            normal = rglwidgetClass.multVM(normals[n], self.normMatrix);
-            if (normal[2] < 0 ||
-                (normal[2] === 0 && normal[0] < 0))
-              return true;
-          }
-          return false;
-        }, self = this;
-        
-      for (i = 0; i < vertices.length; i++) {
-        proj[i] = rglwidgetClass.multVM(vertices[i], prmv);
-        proj[i][0] = proj[i][0]/proj[i][3];
-        proj[i][1] = proj[i][1]/proj[i][3];
-        proj[i][2] = i;
-      }
-      hull = rglwidgetClass.chull(proj.slice());  
-      for (i = 0; i < hull.length; i++)
-        hull[i] = hull[i][2];
-      hull.push(hull[0]);
-      for (dim = 0; dim < 3; dim++) { 
-        edges = [];
-        step = Math.pow(2, 2-dim);
-        for (i = 0; i < 4; i++) {
-          j = (dim === 0) ? i : (dim === 1) ? i + 2*(i>1) : 2*i;
-          for (k = 0; k < hull.length - 1; k++) {
-            if ((hull[k] === j && hull[k+1] === j + step) ||
-                (hull[k] === j+step && hull[k+1] === j))
-          
-              edges.push([j, j+step], [j+step, j]);
-          }
-        }
-
-        edges = edges.filter(has_back);
-        
-        // Find the edge with a vertex closest
-        // to the bottom left corner
-        if (edges.length) {
-          var best, best2, val = Infinity, newval;
-          for (i = 0; i < edges.length; i++) {
-            j = edges[i][0];
-            newval = proj[j][0] + proj[j][1];
-            if (newval < val) {
-              best = j;
-              best2 = edges[i][1];
-              val = newval;
-            }
-          }
-          if (typeof best !== "undefined") {
-            result[dim] = vertices[best].slice(0,3);
-            result[dim][dim] = undefined;
-          } else
-            result[dim] = undefined;
-        }
-      }
-      return result;
-    };
-    
-    /**
-     * Choose tick locations
-     * @param { Object } obj - The bboxdeco
-    */
-    rglwidgetClass.prototype.getTickLocations = function(obj){
-      var dim, i, limits, locations = [], result = [[],[],[]], value,
-          len, delta, range, bbox = obj.bbox;
-      obj.needsAxisCallback = false;
-      for (dim = 0; dim < 3; dim++) {
-        limits = bbox.slice(2*dim, 2*dim + 2);
-        range = limits[1] - limits[0];
-        switch(obj.axes.mode[dim]) {
-        case "custom":
-          for (i=0; i < obj.vertices.length; i++) {
-            value = (obj.vertices[i][dim] - limits[0])/range;
-            if (typeof value !== "undefined" &&
-                !isNaN(value))
-              result[dim].push(value);
-          }
-          break;
-        case "fixedstep":
-          len = Math.floor(range/obj.axes.step[dim]);
-          delta = obj.axes.step[dim];
-          for (i = 0; i < len; i++)
-            result[dim].push(i*delta);          
-          break;
-        case "fixednum":
-          len = obj.axes.nticks[dim];
-          delta = (len > 1) ? range/(len-1) : 0;
-          for (i = 0; i < len; i++)
-            result[dim].push(i*delta/range);
-          break;
-        case "pretty":
-          locations = this.R_pretty(limits[0], limits[1], 5,
-                                  2, // min_n
-                                  0.75, // shrink_sml
-                                  [1.5, 2.75], // high_u_fact
-                                  0, // eps_correction
-                                  0); // return_bounds)  
-          for (i = locations.lo; i <= locations.up; i++) {
-            value = (i*locations.unit - limits[0])/range;
-            if (0 < value && value < 1)
-              result[dim].push(value);
-          }
-          break;
-        case "user":
-          obj.needsAxisCallback = true;
-          break;
-        }
-      }
-      return result;
-    };
-    
-    /**
-     * Set tick vertices
-     * @param { Object } ticks - the tick object
-     * @param { Array }  edges - Which edges get the ticks?
-    */
-    rglwidgetClass.prototype.getTickVertices = function(ticks) {
-      var dim, i, j, vertices = [], locations, 
-          edges = ticks.edges, edge;
-      for (dim = 0; dim < 3; dim++) {
-        locations = ticks.locations[dim];
-        if (locations.length)
-          for (i = 0; i < locations.length; i++) 
-            if (typeof edges[dim] !== "undefined") {
-              edge = edges[dim].slice();
-              edge[dim] = locations[i];
-              vertices.push(edge);
-              edge = edge.slice();
-              for (j = 0; j < 3; j++)       
-                if ((dim < 2 && j === 1 - dim) || 
-                    (dim === 2 && j === 0))
-                  edge[j] += 2*(edge[j] - 0.5)/ticks.axes.marklen[dim];
-              vertices.push(edge);
-            }
-        }
-      ticks.vertices = vertices;
-      ticks.vertexCount = vertices.length;
-      ticks.values = new Float32Array(rglwidgetClass.flatten(vertices));
-      ticks.initialized = false;
-    };
-    
-    /**
-     * Set tick label positions
-     * @param { Object } obj - the bbox object
-    */
-    rglwidgetClass.prototype.placeTickLabels = function(obj) {
-      var ticks = obj.ticks, labels = obj.labels, i,j,k,
-          vertices = [], tickvertices = ticks.vertices, 
-          vertex, locations, dim, edges = obj.ticks.edges;
-      j = 0;
-      for (dim = 0; dim < 3; dim++) {
-        if (typeof edges[dim] === "undefined") 
-          continue;
-        locations = ticks.locations[dim];
-        if (locations.length)
-          for (i = 0; i < locations.length; i++) {
-            if (isNaN(locations[i]))
-              continue;
-            while (j < tickvertices.length && 
-                   tickvertices[j][dim] !== locations[i]) j++;
-            if (j >= tickvertices.length)
-              break;
-            vertex = tickvertices[j].slice();
-            for (k = 0; k < 3; k++)
-              vertex[k] += 2*(tickvertices[j+1][k] - vertex[k]);
-            vertices.push(vertex);
-            j += 2;
-          }
-        }
-      labels.vertices = vertices;
-      labels.centers = labels.vertices;
-      labels.initialized = false;
-    };  
-     
-    /**
-     * Set tick labels
-     * @param { Object } obj - the bbox object
-     */ 
-    rglwidgetClass.prototype.setTickLabels = function(obj) {
-      var ticks = obj.ticks, mode, locations, labels = [],
-      start = 0, nticks, dim, i, limits, range, values, max,
-      edges = obj.ticks.edges;
-      for (dim = 0; dim < 3; dim++) {
-        if (typeof edges[dim] === "undefined") 
-          continue;
-        mode = obj.axes.mode[dim];
-        nticks = obj.axes.nticks[dim]; // used on input only for custom!
-        if (mode === "custom") 
-          labels = labels.concat(obj.texts.slice(start, start + nticks));
-        else {
-          limits = obj.bbox.slice(2*dim, 2*(dim+1));
-          range = limits[1] - limits[0];
-          locations = ticks.locations[dim];
-          max = -Infinity;
-          values = [];
-          for (i = 0; i < locations.length; i++) {
-            values.push(limits[0] + range*locations[i]);
-            max = Math.max(max, Math.abs(values[i]));
-          }
-          for (i = 0; i < locations.length; i++) {
-            if (Math.abs(values[i])/max < Math.pow(10, -5))
-              values[i] = 0;
-            labels.push(rglwidgetClass.signif(values[i], 4).toString());
-          }
-          obj.axes.nticks[dim] = locations.length;  
-        }
-        start += nticks;
-      }
-      obj.labels.texts = labels;
-    };
-
-    /**
-     * Set bboxdeco bbox and center vector 
-     * @param { Object } obj - the bbox object
-     */ 
-    rglwidgetClass.prototype.setBbox = function(obj, subscene) {
-      var i, expand, center = [], bbox;
-      if (!obj.initialized)
-        this.initBBox(obj);
-        
-      bbox = [].concat(subscene.par3d.bbox);
-      for (i = 0; i < 3; i++) {
-        expand = obj.axes.expand[i];
-        center[i] = (bbox[2*i] + bbox[2*i + 1])/2;
-        bbox[2*i] = center[i] - expand*(bbox[2*i + 1] - center[i]);
-        bbox[2*i+1] = center[i] + expand*(bbox[2*i + 1] - center[i]);
-      }
-      obj.bbox = bbox;
-      obj.center = center;
-    };
-
-    rglwidgetClass.prototype.setBBoxMatrices = function(obj) {
-      var saved = {normMatrix: new CanvasMatrix4(this.normMatrix),
-                   mvMatrix: new CanvasMatrix4(this.mvMatrix)},
-          bboxNorm, bboxMV, bbox = obj.bbox, scale;
-          
-      bboxNorm = new CanvasMatrix4();
-      scale = [bbox[1]-bbox[0], bbox[3]-bbox[2], bbox[5]-bbox[4]];
-      bboxNorm.scale(1/scale[0], 1/scale[1], 1/scale[2]);
-      bboxNorm.multRight(saved.normMatrix);
-      this.normMatrix = bboxNorm;
-
-      bboxMV = new CanvasMatrix4();
-      bboxMV.scale(scale[0], scale[1], scale[2]);
-      bboxMV.translate(bbox[0], bbox[2], bbox[4]);
-      bboxMV.multRight(saved.mvMatrix);
-      this.mvMatrix = obj.mvMatrix = bboxMV;
-      
-      if (this.prmvMatrix === null)
-        saved.prmvMatrix = null;
-      else
-        saved.prmvMatrix = new CanvasMatrix4(this.prmvMatrix);
-        
-      this.setprmvMatrix();
-      obj.prmvMatrix = this.prmvMatrix;
-      
-      return saved;
-    };
-    
-    rglwidgetClass.prototype.restoreBBoxMatrices = function(saved) {
-      this.normMatrix = saved.normMatrix;
-      this.mvMatrix   = saved.mvMatrix;
-      this.prmvMatrix = saved.prmvMatrix;
-    };
-    
-    rglwidgetClass.prototype.getMarginParameters = function(bboxdeco, material) {
-      // Assume we've run this.setBbox(bboxdeco, subscene);
-      var bbox = bboxdeco.bbox,
-          edge = [].concat(material.edge),
-          saved, edges, i, 
-          at = material.margin, line, level, trans, scale;
-
-      if (material.floating) {
-        saved = this.setBBoxMatrices(bboxdeco);
-        edges = this.getTickEdges(this.prmvMatrix)[at];
-        this.restoreBBoxMatrices(saved);
-        if (typeof edges !== "undefined")
-          for (i = 0; i < 3; i++) {
-            if (edges[i] < 1) edges[i] = -1;
-              edge[i] = edge[i]*edges[i];
-        } else
-          return undefined;
-      }
-      switch(at) {
-      case 0: line = 1;
-              level = 2;
-              break;
-      case 1: line = 0;
-              level = 2;
-              break;
-      case 2: line = 0;
-              level = 1;
-              break;
-      }
-      scale = [edge[0]*(bbox[1]-bbox[0])/bboxdeco.axes.marklen[0], 
-               edge[1]*(bbox[3]-bbox[2])/bboxdeco.axes.marklen[1], 
-               edge[2]*(bbox[5]-bbox[4])/bboxdeco.axes.marklen[2]];
-      trans = [edge[0] === 1 ? bbox[1] : bbox[0],
-               edge[1] === 1 ? bbox[3] : bbox[2],
-               edge[2] === 1 ? bbox[5] : bbox[4]];
-      return {at: at, line: line, level: level, trans: trans, scale: scale};        
-    };
-    
-    rglwidgetClass.prototype.fixVertex = function(orig, parms, center, bbox) {
-      var vertex = [0,0,0];
-      if (rglwidgetClass.missing(orig[0]))
-        vertex[parms.at] = center[parms.at];
-      else if (orig[0] === "-Inf")
-        vertex[parms.at] = bbox[2*parms.at];
-      else if (orig[0] === "Inf")
-        vertex[parms.at] = bbox[2*parms.at + 1];
-      else
-        vertex[parms.at] = orig[0];
-      vertex[parms.line] = parms.scale[parms.line]*orig[1] + 
-          parms.trans[parms.line];
-      vertex[parms.level] = parms.scale[parms.level]*orig[2] + 
-          parms.trans[parms.level];
-      return vertex;
-    };
-    
-    rglwidgetClass.prototype.fixNormal = function(orig, parms) {
-      var vertex = [0,0,0];
-      vertex[parms.at] = orig[0];
-      vertex[parms.line] = orig[1]/parms.scale[parms.line];
-      vertex[parms.level] = orig[2]/parms.scale[parms.level];
-      return vertex;
-    };
-
-    rglwidgetClass.prototype.marginVecToDataVec = function(obj, subscene) {
-      var bboxdeco = this.getBBoxDeco(subscene),
-          center, bbox, parms, parmsjson,
-          orig = obj.orig, 
-          vertices = [], normals = [],
-          centers = [], i, vertex;
-      if (typeof orig === "undefined") {
-        orig = {vert: obj.vertices,
-                norm: obj.normals,
-                cent: obj.centers,
-                doNormals: typeof obj.normals !== "undefined",
-                doCenters: typeof obj.centers !== "undefined",
-                parms: ""
-               };
-        obj.orig = orig;
-      }
-
-      if (typeof bboxdeco !== "undefined") {
-        this.setBbox(bboxdeco, subscene);
-        center = bboxdeco.center;
-        bbox = bboxdeco.bbox;
-        parms = this.getMarginParameters(bboxdeco, obj.material);
-        if (typeof parms === "undefined")
-          return false;  /* axis is not currently shown */
-        
-        parmsjson = JSON.stringify(parms);
-        if (parmsjson === orig.parms)
-          return true;  /* nothing has changed */
-    
-        orig.parms = parmsjson;
-        
-        for (i=0; i < orig.vert.length; i++) {
-          vertex = this.fixVertex(orig.vert[i], parms, center, bbox);
-          vertices.push(vertex);
-        }
-        obj.vertices = vertices;
-        if (orig.doNormals) {
-          for (i=0; i < orig.norm.length; i++) {
-            vertex = this.fixNormal(orig.norm[i], parms);
-            normals.push(vertex);
-          }
-          obj.normals = normals;
-        }
-        if (orig.doCenters) {
-          for (i=0; i < orig.cent.length; i++) {
-            vertex = this.fixVertex(orig.cent[i], parms, center, bbox);
-            centers.push(vertex);
-          }
-          obj.centers = centers;
-        }
-        
-        obj.initialized = false;
-        return true;
-      } else {
-        console.warn("bboxdeco not found");
-        return false;
-      }
-    };
-
-    rglwidgetClass.prototype.doAxisCallback = function(obj, edges) {
-      var i, j, code, axis, fn;
-      for (i = 0; i < 3; i++) {
-        if (obj.axes.mode[i] === "user") {
-          axis = ["x", "y", "z"][i];
-          if (typeof obj.callbacks !== "undefined" &&
-              typeof (code = obj.callbacks[axis]) !== "undefined") {
-            if (typeof edges[i] !== "undefined")
-              for (j = 0; j < 3; j++)
-                if (typeof edges[i][j] !== "undefined")
-                  axis = axis + (edges[i][j] > 0 ? "+" : "-");
-            
-          /* jshint evil:true */
-            fn = Function('"use strict";return (' + code + ')')();
-          /* jshint evil:false */
-            fn.call(this, axis);
-          }
-        }
-      }
-    };
-</script>
-<script>/**
-     * Methods related to animations
-     * @name ___METHODS_FOR_ANIMATION___
-     * @memberof rglwidgetClass
-     * @kind function
-     * @instance
-     */
-    /**
-     * Binary search
-     * @param x - x coordinates in increasing order
-     * @param newx - value to find, assumed to be in the range of x
-     * @result index of largest x value below newx
-     */
-    rglwidgetClass.bisect = function(x, newx) {
-      var lo = 0, hi = x.length - 1, mid;
-      while (lo < hi - 1) {
-        mid = Math.round((lo + hi)/2);
-        if (x[mid] < newx)
-          lo = mid;
-        else
-          hi = mid;
-      }
-      return lo;
-    };
-    
-    /**
-     * Step interpolation (constant outside bounds)
-     * @param x - x coordinates in increasing order
-     * @param v - values at x; either a vector or matrix
-     * @param newx - value at which to evaluate
-     */
-    rglwidgetClass.step = function(x, v, newx) {
-      var n, lo;
-      if (newx <= x[0])
-        return v[0];    
-      n = x.length;
-      if (newx >= x[n-1])
-        return v[n-1];
-      lo = this.bisect(x, newx);
-      return v[lo];
-    };
-    
-    /**
-     * Linear interpolation (constant outside bounds)
-     * @param x - x coordinates in increasing order
-     * @param v - values at x; either a vector or matrix
-     * @param newx - value at which to evaluate
-     */
-    rglwidgetClass.lerp = function(x, v, newx) {
-      var i, n, lo, hi, alpha, result;
-      if (newx <= x[0])
-        return v[0];    
-      n = x.length;
-      if (newx >= x[n-1])
-        return v[n-1];
-      lo = this.bisect(x, newx);
-      if (newx === x[lo])
-        return v[lo];
-      hi = lo + 1;
-      if (newx === x[hi])
-        return v[hi];
-      alpha = (newx - x[lo])/(x[hi] - x[lo]);
-      result = v[lo];
-      n = result.length;
-      if (typeof n !== "undefined") {
-        for (i = 0; i < n; i++)
-          result[i] = (1 - alpha)*result[i] + alpha*v[hi][i];
-      } else
-        result = (1 - alpha)*result + alpha*v[hi];
-      return result;
-    };
-    
-    /**
-     * Spherical linear interpolation (constant outside bounds)
-     * @param x - x coordinates in increasing order
-     * @param v - a matrix of unit quaternions
-     * @param newx - value at which to evaluate
-     */
-    rglwidgetClass.slerp = function(x, v, newx) {
-      var n, lo, hi, alpha, result,
-          p0, p1, dot, Omega, alpha0, alpha1, len;
-      if (newx <= x[0])
-        return v[0];    
-      if (newx >= x[n-1])
-        return v[n-1];
-      lo = this.bisect(x, newx);
-      if (newx === x[lo])
-        return v[lo];
-      hi = lo + 1;
-      if (newx === x[hi])
-        return v[hi];
-      p0 = v[lo];
-      p1 = v[hi];
-      dot = p0[0]*p1[0] + 
-            p0[1]*p1[1] +
-            p0[2]*p1[2] +
-            p0[3]*p1[3];
-      if (dot < 0) {
-        p1 = [-p1[0], -p1[1], -p1[2], -p1[3]];
-        dot = -dot;
-      }
-      if (dot >= 1)
-        result = p1;
-      else {
-        alpha = (newx - x[lo])/(x[hi] - x[lo]);
-        Omega = Math.acos(dot);
-        alpha0 = Math.sin((1 - alpha)*Omega);
-        alpha1 = Math.sin(alpha*Omega);
-        result = [alpha0*p0[0] + alpha1*p1[0],
-                  alpha0*p0[1] + alpha1*p1[1],
-                  alpha0*p0[2] + alpha1*p1[2],
-                  alpha0*p0[3] + alpha1*p1[3]];
-      }
-      len = Math.sqrt(result[0]*result[0] +
-                      result[1]*result[1] +
-                      result[2]*result[2] +
-                      result[3]*result[3]);
-      return [result[0]/len,
-              result[1]/len,
-              result[2]/len,
-              result[3]/len];
-    };
-
-    /**
-     * Rotate using unit quaternion
-     * @param q - a single unit quaternion
-     */
-    rglwidgetClass.rotateByQuaternion = function(M, q) {
-
-    var xx = q[0]*q[0],
-        xy = q[0]*q[1],
-        xz = q[0]*q[2],
-        xw = q[0]*q[3],
-        yy = q[1]*q[1],
-        yz = q[1]*q[2],
-        yw = q[1]*q[3],
-        zz = q[2]*q[2],
-        zw = q[2]*q[3],
-        matrix = new CanvasMatrix4();
-      matrix.m11 = 1 - 2*(yy + zz);
-      matrix.m12 = 2*(xy + zw);
-      matrix.m13 = 2*(xz - yw);
-        
-      matrix.m21 = 2*(xy - zw);
-      matrix.m22 = 1 - 2*(xx + zz);
-      matrix.m23 = 2*(yz + xw);
-
-      matrix.m31 = 2*(xz + yw);
-      matrix.m32 = 2*(yz - xw);
-      matrix.m33 = 1 - 2*(xx + yy);
-
-      M.multRight(matrix);      
-    };
-</script>
-<script>/* globals CanvasMatrix4: true */
-/* globals WebGLFloatArray */
-/* jshint eqeqeq: false */
-/*
- * Copyright (C) 2009 Apple Inc. All Rights Reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- * 1. Redistributions of source code must retain the above copyright
- *    notice, this list of conditions and the following disclaimer.
- * 2. Redistributions in binary form must reproduce the above copyright
- *    notice, this list of conditions and the following disclaimer in the
- *    documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
- * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
- * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL APPLE INC. OR
- * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
- * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
- * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
- * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
- * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
- * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
- * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-
- * Copyright (2016) Duncan Murdoch - fixed CanvasMatrix4.ortho,
- * cleaned up.
- */
-/*
-    CanvasMatrix4 class
-
-    This class implements a 4x4 matrix. It has functions which
-    duplicate the functionality of the OpenGL matrix stack and
-    glut functions.
-
-    IDL:
-
-    [
-        Constructor(in CanvasMatrix4 matrix),           // copy passed matrix into new CanvasMatrix4
-        Constructor(in sequence<float> array)           // create new CanvasMatrix4 with 16 floats (row major)
-        Constructor()                                   // create new CanvasMatrix4 with identity matrix
-    ]
-    interface CanvasMatrix4 {
-        attribute float m11;
-        attribute float m12;
-        attribute float m13;
-        attribute float m14;
-        attribute float m21;
-        attribute float m22;
-        attribute float m23;
-        attribute float m24;
-        attribute float m31;
-        attribute float m32;
-        attribute float m33;
-        attribute float m34;
-        attribute float m41;
-        attribute float m42;
-        attribute float m43;
-        attribute float m44;
-
-        void load(in CanvasMatrix4 matrix);                 // copy the values from the passed matrix
-        void load(in sequence<float> array);                // copy 16 floats into the matrix
-        sequence<float> getAsArray();                       // return the matrix as an array of 16 floats
-        WebGLFloatArray getAsCanvasFloatArray();           // return the matrix as a WebGLFloatArray with 16 values
-        void makeIdentity();                                // replace the matrix with identity
-        void transpose();                                   // replace the matrix with its transpose
-        void invert();                                      // replace the matrix with its inverse
-
-        void translate(in float x, in float y, in float z); // multiply the matrix by passed translation values on the right
-        void scale(in float x, in float y, in float z);     // multiply the matrix by passed scale values on the right
-        void rotate(in float angle,                         // multiply the matrix by passed rotation values on the right
-                    in float x, in float y, in float z);    // (angle is in degrees)
-        void multRight(in CanvasMatrix matrix);             // multiply the matrix by the passed matrix on the right
-        void multLeft(in CanvasMatrix matrix);              // multiply the matrix by the passed matrix on the left
-        void ortho(in float left, in float right,           // multiply the matrix by the passed ortho values on the right
-                   in float bottom, in float top,
-                   in float near, in float far);
-        void frustum(in float left, in float right,         // multiply the matrix by the passed frustum values on the right
-                     in float bottom, in float top,
-                     in float near, in float far);
-        void perspective(in float fovy, in float aspect,    // multiply the matrix by the passed perspective values on the right
-                         in float zNear, in float zFar);
-        void lookat(in float eyex, in float eyey, in float eyez,    // multiply the matrix by the passed lookat
-                    in float ctrx, in float ctry, in float ctrz,    // values on the right
-                    in float upx, in float upy, in float upz);
-    }
-*/
-
-CanvasMatrix4 = function(m)
-{
-    if (typeof m == 'object') {
-        if ("length" in m && m.length >= 16) {
-            this.load(m[0], m[1], m[2], m[3], m[4], m[5], m[6], m[7], m[8], m[9], m[10], m[11], m[12], m[13], m[14], m[15]);
-            return;
-        }
-        else if (m instanceof CanvasMatrix4) {
-            this.load(m);
-            return;
-        }
-    }
-    this.makeIdentity();
-};
-
-CanvasMatrix4.prototype.load = function()
-{
-    if (arguments.length == 1 && typeof arguments[0] == 'object') {
-        var matrix = arguments[0];
-
-        if ("length" in matrix && matrix.length == 16) {
-            this.m11 = matrix[0];
-            this.m12 = matrix[1];
-            this.m13 = matrix[2];
-            this.m14 = matrix[3];
-
-            this.m21 = matrix[4];
-            this.m22 = matrix[5];
-            this.m23 = matrix[6];
-            this.m24 = matrix[7];
-
-            this.m31 = matrix[8];
-            this.m32 = matrix[9];
-            this.m33 = matrix[10];
-            this.m34 = matrix[11];
-
-            this.m41 = matrix[12];
-            this.m42 = matrix[13];
-            this.m43 = matrix[14];
-            this.m44 = matrix[15];
-            return;
-        }
-
-        if (arguments[0] instanceof CanvasMatrix4) {
-
-            this.m11 = matrix.m11;
-            this.m12 = matrix.m12;
-            this.m13 = matrix.m13;
-            this.m14 = matrix.m14;
-
-            this.m21 = matrix.m21;
-            this.m22 = matrix.m22;
-            this.m23 = matrix.m23;
-            this.m24 = matrix.m24;
-
-            this.m31 = matrix.m31;
-            this.m32 = matrix.m32;
-            this.m33 = matrix.m33;
-            this.m34 = matrix.m34;
-
-            this.m41 = matrix.m41;
-            this.m42 = matrix.m42;
-            this.m43 = matrix.m43;
-            this.m44 = matrix.m44;
-            return;
-        }
-    }
-
-    this.makeIdentity();
-};
-
-CanvasMatrix4.prototype.getAsArray = function()
-{
-    return [
-        this.m11, this.m12, this.m13, this.m14,
-        this.m21, this.m22, this.m23, this.m24,
-        this.m31, this.m32, this.m33, this.m34,
-        this.m41, this.m42, this.m43, this.m44
-    ];
-};
-
-CanvasMatrix4.prototype.getAsWebGLFloatArray = function()
-{
-    return new WebGLFloatArray(this.getAsArray());
-};
-
-CanvasMatrix4.prototype.makeIdentity = function()
-{
-    this.m11 = 1;
-    this.m12 = 0;
-    this.m13 = 0;
-    this.m14 = 0;
-
-    this.m21 = 0;
-    this.m22 = 1;
-    this.m23 = 0;
-    this.m24 = 0;
-
-    this.m31 = 0;
-    this.m32 = 0;
-    this.m33 = 1;
-    this.m34 = 0;
-
-    this.m41 = 0;
-    this.m42 = 0;
-    this.m43 = 0;
-    this.m44 = 1;
-};
-
-CanvasMatrix4.prototype.transpose = function()
-{
-    var tmp = this.m12;
-    this.m12 = this.m21;
-    this.m21 = tmp;
-
-    tmp = this.m13;
-    this.m13 = this.m31;
-    this.m31 = tmp;
-
-    tmp = this.m14;
-    this.m14 = this.m41;
-    this.m41 = tmp;
-
-    tmp = this.m23;
-    this.m23 = this.m32;
-    this.m32 = tmp;
-
-    tmp = this.m24;
-    this.m24 = this.m42;
-    this.m42 = tmp;
-
-    tmp = this.m34;
-    this.m34 = this.m43;
-    this.m43 = tmp;
-};
-
-CanvasMatrix4.prototype.invert = function()
-{
-    // Calculate the 4x4 determinant
-    // If the determinant is zero,
-    // then the inverse matrix is not unique.
-    var det = this._determinant4x4();
-
-    if (Math.abs(det) < 1e-8)
-        return null;
-
-    this._makeAdjoint();
-
-    // Scale the adjoint matrix to get the inverse
-    this.m11 /= det;
-    this.m12 /= det;
-    this.m13 /= det;
-    this.m14 /= det;
-
-    this.m21 /= det;
-    this.m22 /= det;
-    this.m23 /= det;
-    this.m24 /= det;
-
-    this.m31 /= det;
-    this.m32 /= det;
-    this.m33 /= det;
-    this.m34 /= det;
-
-    this.m41 /= det;
-    this.m42 /= det;
-    this.m43 /= det;
-    this.m44 /= det;
-};
-
-CanvasMatrix4.prototype.translate = function(x,y,z)
-{
-    if (x === undefined)
-        x = 0;
-    if (y === undefined)
-        y = 0;
-    if (z === undefined)
-        z = 0;
-
-    var matrix = new CanvasMatrix4();
-    matrix.m41 = x;
-    matrix.m42 = y;
-    matrix.m43 = z;
-
-    this.multRight(matrix);
-};
-
-CanvasMatrix4.prototype.scale = function(x,y,z)
-{
-    if (x === undefined)
-        x = 1;
-    if (z === undefined) {
-        if (y === undefined) {
-            y = x;
-            z = x;
-        }
-        else
-            z = 1;
-    }
-    else if (y === undefined)
-        y = x;
-
-    var matrix = new CanvasMatrix4();
-    matrix.m11 = x;
-    matrix.m22 = y;
-    matrix.m33 = z;
-
-    this.multRight(matrix);
-};
-
-CanvasMatrix4.prototype.rotate = function(angle,x,y,z)
-{
-    // angles are in degrees. Switch to radians
-    angle = angle / 180 * Math.PI;
-
-    angle /= 2;
-    var sinA = Math.sin(angle);
-    var cosA = Math.cos(angle);
-    var sinA2 = sinA * sinA;
-
-    // normalize
-    var length = Math.sqrt(x * x + y * y + z * z);
-    if (length === 0) {
-        // bad vector, just use something reasonable
-        x = 0;
-        y = 0;
-        z = 1;
-    } else if (length != 1) {
-        x /= length;
-        y /= length;
-        z /= length;
-    }
-
-    var mat = new CanvasMatrix4();
-
-    // optimize case where axis is along major axis
-    if (x == 1 && y === 0 && z === 0) {
-        mat.m11 = 1;
-        mat.m12 = 0;
-        mat.m13 = 0;
-        mat.m21 = 0;
-        mat.m22 = 1 - 2 * sinA2;
-        mat.m23 = 2 * sinA * cosA;
-        mat.m31 = 0;
-        mat.m32 = -2 * sinA * cosA;
-        mat.m33 = 1 - 2 * sinA2;
-        mat.m14 = mat.m24 = mat.m34 = 0;
-        mat.m41 = mat.m42 = mat.m43 = 0;
-        mat.m44 = 1;
-    } else if (x === 0 && y == 1 && z === 0) {
-        mat.m11 = 1 - 2 * sinA2;
-        mat.m12 = 0;
-        mat.m13 = -2 * sinA * cosA;
-        mat.m21 = 0;
-        mat.m22 = 1;
-        mat.m23 = 0;
-        mat.m31 = 2 * sinA * cosA;
-        mat.m32 = 0;
-        mat.m33 = 1 - 2 * sinA2;
-        mat.m14 = mat.m24 = mat.m34 = 0;
-        mat.m41 = mat.m42 = mat.m43 = 0;
-        mat.m44 = 1;
-    } else if (x === 0 && y === 0 && z == 1) {
-        mat.m11 = 1 - 2 * sinA2;
-        mat.m12 = 2 * sinA * cosA;
-        mat.m13 = 0;
-        mat.m21 = -2 * sinA * cosA;
-        mat.m22 = 1 - 2 * sinA2;
-        mat.m23 = 0;
-        mat.m31 = 0;
-        mat.m32 = 0;
-        mat.m33 = 1;
-        mat.m14 = mat.m24 = mat.m34 = 0;
-        mat.m41 = mat.m42 = mat.m43 = 0;
-        mat.m44 = 1;
-    } else {
-        var x2 = x*x;
-        var y2 = y*y;
-        var z2 = z*z;
-
-        mat.m11 = 1 - 2 * (y2 + z2) * sinA2;
-        mat.m12 = 2 * (x * y * sinA2 + z * sinA * cosA);
-        mat.m13 = 2 * (x * z * sinA2 - y * sinA * cosA);
-        mat.m21 = 2 * (y * x * sinA2 - z * sinA * cosA);
-        mat.m22 = 1 - 2 * (z2 + x2) * sinA2;
-        mat.m23 = 2 * (y * z * sinA2 + x * sinA * cosA);
-        mat.m31 = 2 * (z * x * sinA2 + y * sinA * cosA);
-        mat.m32 = 2 * (z * y * sinA2 - x * sinA * cosA);
-        mat.m33 = 1 - 2 * (x2 + y2) * sinA2;
-        mat.m14 = mat.m24 = mat.m34 = 0;
-        mat.m41 = mat.m42 = mat.m43 = 0;
-        mat.m44 = 1;
-    }
-    this.multRight(mat);
-};
-
-CanvasMatrix4.prototype.multRight = function(mat)
-{
-    var m11 = (this.m11 * mat.m11 + this.m12 * mat.m21 +
-               this.m13 * mat.m31 + this.m14 * mat.m41);
-    var m12 = (this.m11 * mat.m12 + this.m12 * mat.m22 +
-               this.m13 * mat.m32 + this.m14 * mat.m42);
-    var m13 = (this.m11 * mat.m13 + this.m12 * mat.m23 +
-               this.m13 * mat.m33 + this.m14 * mat.m43);
-    var m14 = (this.m11 * mat.m14 + this.m12 * mat.m24 +
-               this.m13 * mat.m34 + this.m14 * mat.m44);
-
-    var m21 = (this.m21 * mat.m11 + this.m22 * mat.m21 +
-               this.m23 * mat.m31 + this.m24 * mat.m41);
-    var m22 = (this.m21 * mat.m12 + this.m22 * mat.m22 +
-               this.m23 * mat.m32 + this.m24 * mat.m42);
-    var m23 = (this.m21 * mat.m13 + this.m22 * mat.m23 +
-               this.m23 * mat.m33 + this.m24 * mat.m43);
-    var m24 = (this.m21 * mat.m14 + this.m22 * mat.m24 +
-               this.m23 * mat.m34 + this.m24 * mat.m44);
-
-    var m31 = (this.m31 * mat.m11 + this.m32 * mat.m21 +
-               this.m33 * mat.m31 + this.m34 * mat.m41);
-    var m32 = (this.m31 * mat.m12 + this.m32 * mat.m22 +
-               this.m33 * mat.m32 + this.m34 * mat.m42);
-    var m33 = (this.m31 * mat.m13 + this.m32 * mat.m23 +
-               this.m33 * mat.m33 + this.m34 * mat.m43);
-    var m34 = (this.m31 * mat.m14 + this.m32 * mat.m24 +
-               this.m33 * mat.m34 + this.m34 * mat.m44);
-
-    var m41 = (this.m41 * mat.m11 + this.m42 * mat.m21 +
-               this.m43 * mat.m31 + this.m44 * mat.m41);
-    var m42 = (this.m41 * mat.m12 + this.m42 * mat.m22 +
-               this.m43 * mat.m32 + this.m44 * mat.m42);
-    var m43 = (this.m41 * mat.m13 + this.m42 * mat.m23 +
-               this.m43 * mat.m33 + this.m44 * mat.m43);
-    var m44 = (this.m41 * mat.m14 + this.m42 * mat.m24 +
-               this.m43 * mat.m34 + this.m44 * mat.m44);
-
-    this.m11 = m11;
-    this.m12 = m12;
-    this.m13 = m13;
-    this.m14 = m14;
-
-    this.m21 = m21;
-    this.m22 = m22;
-    this.m23 = m23;
-    this.m24 = m24;
-
-    this.m31 = m31;
-    this.m32 = m32;
-    this.m33 = m33;
-    this.m34 = m34;
-
-    this.m41 = m41;
-    this.m42 = m42;
-    this.m43 = m43;
-    this.m44 = m44;
-};
-
-CanvasMatrix4.prototype.multLeft = function(mat)
-{
-    var m11 = (mat.m11 * this.m11 + mat.m12 * this.m21 +
-               mat.m13 * this.m31 + mat.m14 * this.m41);
-    var m12 = (mat.m11 * this.m12 + mat.m12 * this.m22 +
-               mat.m13 * this.m32 + mat.m14 * this.m42);
-    var m13 = (mat.m11 * this.m13 + mat.m12 * this.m23 +
-               mat.m13 * this.m33 + mat.m14 * this.m43);
-    var m14 = (mat.m11 * this.m14 + mat.m12 * this.m24 +
-               mat.m13 * this.m34 + mat.m14 * this.m44);
-
-    var m21 = (mat.m21 * this.m11 + mat.m22 * this.m21 +
-               mat.m23 * this.m31 + mat.m24 * this.m41);
-    var m22 = (mat.m21 * this.m12 + mat.m22 * this.m22 +
-               mat.m23 * this.m32 + mat.m24 * this.m42);
-    var m23 = (mat.m21 * this.m13 + mat.m22 * this.m23 +
-               mat.m23 * this.m33 + mat.m24 * this.m43);
-    var m24 = (mat.m21 * this.m14 + mat.m22 * this.m24 +
-               mat.m23 * this.m34 + mat.m24 * this.m44);
-
-    var m31 = (mat.m31 * this.m11 + mat.m32 * this.m21 +
-               mat.m33 * this.m31 + mat.m34 * this.m41);
-    var m32 = (mat.m31 * this.m12 + mat.m32 * this.m22 +
-               mat.m33 * this.m32 + mat.m34 * this.m42);
-    var m33 = (mat.m31 * this.m13 + mat.m32 * this.m23 +
-               mat.m33 * this.m33 + mat.m34 * this.m43);
-    var m34 = (mat.m31 * this.m14 + mat.m32 * this.m24 +
-               mat.m33 * this.m34 + mat.m34 * this.m44);
-
-    var m41 = (mat.m41 * this.m11 + mat.m42 * this.m21 +
-               mat.m43 * this.m31 + mat.m44 * this.m41);
-    var m42 = (mat.m41 * this.m12 + mat.m42 * this.m22 +
-               mat.m43 * this.m32 + mat.m44 * this.m42);
-    var m43 = (mat.m41 * this.m13 + mat.m42 * this.m23 +
-               mat.m43 * this.m33 + mat.m44 * this.m43);
-    var m44 = (mat.m41 * this.m14 + mat.m42 * this.m24 +
-               mat.m43 * this.m34 + mat.m44 * this.m44);
-
-    this.m11 = m11;
-    this.m12 = m12;
-    this.m13 = m13;
-    this.m14 = m14;
-
-    this.m21 = m21;
-    this.m22 = m22;
-    this.m23 = m23;
-    this.m24 = m24;
-
-    this.m31 = m31;
-    this.m32 = m32;
-    this.m33 = m33;
-    this.m34 = m34;
-
-    this.m41 = m41;
-    this.m42 = m42;
-    this.m43 = m43;
-    this.m44 = m44;
-};
-
-CanvasMatrix4.prototype.ortho = function(left, right, bottom, top, near, far)
-{
-    var tx = (left + right) / (left - right);
-    var ty = (top + bottom) / (bottom - top);
-    var tz = (far + near) / (near - far);
-
-    var matrix = new CanvasMatrix4();
-    matrix.m11 = 2 / (right - left);
-    matrix.m12 = 0;
-    matrix.m13 = 0;
-    matrix.m14 = 0;
-    matrix.m21 = 0;
-    matrix.m22 = 2 / (top - bottom);
-    matrix.m23 = 0;
-    matrix.m24 = 0;
-    matrix.m31 = 0;
-    matrix.m32 = 0;
-    matrix.m33 = -2 / (far - near);
-    matrix.m34 = 0;
-    matrix.m41 = tx;
-    matrix.m42 = ty;
-    matrix.m43 = tz;
-    matrix.m44 = 1;
-
-    this.multRight(matrix);
-};
-
-CanvasMatrix4.prototype.frustum = function(left, right, bottom, top, near, far)
-{
-    var matrix = new CanvasMatrix4();
-    var A = (right + left) / (right - left);
-    var B = (top + bottom) / (top - bottom);
-    var C = -(far + near) / (far - near);
-    var D = -(2 * far * near) / (far - near);
-
-    matrix.m11 = (2 * near) / (right - left);
-    matrix.m12 = 0;
-    matrix.m13 = 0;
-    matrix.m14 = 0;
-
-    matrix.m21 = 0;
-    matrix.m22 = 2 * near / (top - bottom);
-    matrix.m23 = 0;
-    matrix.m24 = 0;
-
-    matrix.m31 = A;
-    matrix.m32 = B;
-    matrix.m33 = C;
-    matrix.m34 = -1;
-
-    matrix.m41 = 0;
-    matrix.m42 = 0;
-    matrix.m43 = D;
-    matrix.m44 = 0;
-
-    this.multRight(matrix);
-};
-
-CanvasMatrix4.prototype.perspective = function(fovy, aspect, zNear, zFar)
-{
-    var top = Math.tan(fovy * Math.PI / 360) * zNear;
-    var bottom = -top;
-    var left = aspect * bottom;
-    var right = aspect * top;
-    this.frustum(left, right, bottom, top, zNear, zFar);
-};
-
-CanvasMatrix4.prototype.lookat = function(eyex, eyey, eyez, centerx, centery, centerz, upx, upy, upz)
-{
-    var matrix = new CanvasMatrix4(),
-        xx, xy, xz;
-
-    // Make rotation matrix
-
-    // Z vector
-    var zx = eyex - centerx;
-    var zy = eyey - centery;
-    var zz = eyez - centerz;
-    var mag = Math.sqrt(zx * zx + zy * zy + zz * zz);
-    if (mag) {
-        zx /= mag;
-        zy /= mag;
-        zz /= mag;
-    }
-
-    // Y vector
-    var yx = upx;
-    var yy = upy;
-    var yz = upz;
-
-    // X vector = Y cross Z
-    xx =  yy * zz - yz * zy;
-    xy = -yx * zz + yz * zx;
-    xz =  yx * zy - yy * zx;
-
-    // Recompute Y = Z cross X
-    yx = zy * xz - zz * xy;
-    yy = -zx * xz + zz * xx;
-    yx = zx * xy - zy * xx;
-
-    // cross product gives area of parallelogram, which is < 1.0 for
-    // non-perpendicular unit-length vectors; so normalize x, y here
-
-    mag = Math.sqrt(xx * xx + xy * xy + xz * xz);
-    if (mag) {
-        xx /= mag;
-        xy /= mag;
-        xz /= mag;
-    }
-
-    mag = Math.sqrt(yx * yx + yy * yy + yz * yz);
-    if (mag) {
-        yx /= mag;
-        yy /= mag;
-        yz /= mag;
-    }
-
-    matrix.m11 = xx;
-    matrix.m12 = xy;
-    matrix.m13 = xz;
-    matrix.m14 = 0;
-
-    matrix.m21 = yx;
-    matrix.m22 = yy;
-    matrix.m23 = yz;
-    matrix.m24 = 0;
-
-    matrix.m31 = zx;
-    matrix.m32 = zy;
-    matrix.m33 = zz;
-    matrix.m34 = 0;
-
-    matrix.m41 = 0;
-    matrix.m42 = 0;
-    matrix.m43 = 0;
-    matrix.m44 = 1;
-    matrix.translate(-eyex, -eyey, -eyez);
-
-    this.multRight(matrix);
-};
-
-// Support functions
-CanvasMatrix4.prototype._determinant2x2 = function(a, b, c, d)
-{
-    return a * d - b * c;
-};
-
-CanvasMatrix4.prototype._determinant3x3 = function(a1, a2, a3, b1, b2, b3, c1, c2, c3)
-{
-    return a1 * this._determinant2x2(b2, b3, c2, c3) -
-         b1 * this._determinant2x2(a2, a3, c2, c3) +
-         c1 * this._determinant2x2(a2, a3, b2, b3);
-};
-
-CanvasMatrix4.prototype._determinant4x4 = function()
-{
-    var a1 = this.m11;
-    var b1 = this.m12;
-    var c1 = this.m13;
-    var d1 = this.m14;
-
-    var a2 = this.m21;
-    var b2 = this.m22;
-    var c2 = this.m23;
-    var d2 = this.m24;
-
-    var a3 = this.m31;
-    var b3 = this.m32;
-    var c3 = this.m33;
-    var d3 = this.m34;
-
-    var a4 = this.m41;
-    var b4 = this.m42;
-    var c4 = this.m43;
-    var d4 = this.m44;
-
-    return a1 * this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4) -
-         b1 * this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4) +
-         c1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4) -
-         d1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
-};
-
-CanvasMatrix4.prototype._makeAdjoint = function()
-{
-    var a1 = this.m11;
-    var b1 = this.m12;
-    var c1 = this.m13;
-    var d1 = this.m14;
-
-    var a2 = this.m21;
-    var b2 = this.m22;
-    var c2 = this.m23;
-    var d2 = this.m24;
-
-    var a3 = this.m31;
-    var b3 = this.m32;
-    var c3 = this.m33;
-    var d3 = this.m34;
-
-    var a4 = this.m41;
-    var b4 = this.m42;
-    var c4 = this.m43;
-    var d4 = this.m44;
-
-    // Row column labeling reversed since we transpose rows & columns
-    this.m11  =   this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4);
-    this.m21  = - this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4);
-    this.m31  =   this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4);
-    this.m41  = - this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
-
-    this.m12  = - this._determinant3x3(b1, b3, b4, c1, c3, c4, d1, d3, d4);
-    this.m22  =   this._determinant3x3(a1, a3, a4, c1, c3, c4, d1, d3, d4);
-    this.m32  = - this._determinant3x3(a1, a3, a4, b1, b3, b4, d1, d3, d4);
-    this.m42  =   this._determinant3x3(a1, a3, a4, b1, b3, b4, c1, c3, c4);
-
-    this.m13  =   this._determinant3x3(b1, b2, b4, c1, c2, c4, d1, d2, d4);
-    this.m23  = - this._determinant3x3(a1, a2, a4, c1, c2, c4, d1, d2, d4);
-    this.m33  =   this._determinant3x3(a1, a2, a4, b1, b2, b4, d1, d2, d4);
-    this.m43  = - this._determinant3x3(a1, a2, a4, b1, b2, b4, c1, c2, c4);
-
-    this.m14  = - this._determinant3x3(b1, b2, b3, c1, c2, c3, d1, d2, d3);
-    this.m24  =   this._determinant3x3(a1, a2, a3, c1, c2, c3, d1, d2, d3);
-    this.m34  = - this._determinant3x3(a1, a2, a3, b1, b2, b3, d1, d2, d3);
-    this.m44  =   this._determinant3x3(a1, a2, a3, b1, b2, b3, c1, c2, c3);
-};
-</script>
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-<h1 class="title toc-ignore">Biplots in 3D</h1>
-
-
-<div id="TOC">
-<ul>
-<li><a href="#pca-3d-biplot" id="toc-pca-3d-biplot"><span class="toc-section-number">1</span> PCA 3D biplot</a>
-<ul>
-<li><a href="#adding-new-samples" id="toc-adding-new-samples"><span class="toc-section-number">1.1</span> Adding new samples</a></li>
-<li><a href="#adding-new-variables" id="toc-adding-new-variables"><span class="toc-section-number">1.2</span> Adding new variables</a></li>
-<li><a href="#predicting-samples" id="toc-predicting-samples"><span class="toc-section-number">1.3</span> Predicting samples</a></li>
-<li><a href="#predicting-group-means" id="toc-predicting-group-means"><span class="toc-section-number">1.4</span> Predicting group means</a></li>
-<li><a href="#ellipses" id="toc-ellipses"><span class="toc-section-number">1.5</span> Ellipses</a></li>
-</ul></li>
-<li><a href="#cva-3d-biplot" id="toc-cva-3d-biplot"><span class="toc-section-number">2</span> CVA 3d biplot</a></li>
-<li><a href="#ca-3d-biplot" id="toc-ca-3d-biplot"><span class="toc-section-number">3</span> CA 3D biplot</a></li>
-</ul>
-</div>
-
-<div id="pca-3d-biplot" class="section level1" number="1">
-<h1><span class="header-section-number">1</span> PCA 3D biplot</h1>
-<p>Three-dimensional PCA biplots are obtained by specifying
-<code>dim.biplot = 3</code> in the call to <code>PCA()</code>. The
-package <code>rgl</code> is required and on calling the
-<code>plot()</code> the biplot is drawn in an <code>rgl</code> window.
-The plot can then be interactively rotated and zoomed using the mouse
-buttons.</p>
-<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris<span class="sc">$</span>Species,<span class="at">dim.biplot =</span> <span class="dv">3</span>) <span class="sc">|&gt;</span></span>
-<span id="cb1-2"><a href="#cb1-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg 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(point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - 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-<p id="rgl73814-aria" hidden>
-</p>
-</div>
-<div id="adding-new-samples" class="section level2" number="1.1">
-<h2><span class="header-section-number">1.1</span> Adding new
-samples</h2>
-<p>The process of adding new samples to the biplot, called interpolation
-utilises the functions <code>interpolate()</code> and
-<code>newsamples()</code>. These functions work in the same way as in
-the call to the two-dimensional biplot. The function
-<code>interpolate()</code> accepts the argument <code>newdata</code> to
-specify a matrix or data frame containing the new samples to be
-interpolated. The function <code>newsamples()</code> operates the same
-way as <code>samples()</code> in that the user can specify the
-aesthetics of the interpolated samples.</p>
-<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" tabindex="-1"></a><span class="fu">biplot</span>(iris[<span class="dv">1</span><span class="sc">:</span><span class="dv">100</span>,<span class="dv">1</span><span class="sc">:</span><span class="dv">4</span>])<span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">dim.biplot =</span> <span class="dv">3</span>) <span class="sc">|&gt;</span> <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb2-2"><a href="#cb2-2" tabindex="-1"></a>  <span class="fu">interpolate</span>(<span class="at">newdata =</span> iris[<span class="dv">101</span><span class="sc">:</span><span class="dv">150</span>,<span class="dv">1</span><span class="sc">:</span><span class="dv">4</span>]) <span class="sc">|&gt;</span> <span class="fu">newsamples</span>(<span class="at">col=</span><span class="st">&quot;purple&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<div class="figure">
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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n      if (uFogMode > 1)\n        fogF = mix(uFogParms.w, 1.0, fogF);\n      fogF = fogF*uFogParms.z;\n      if (uFogMode == 2)\n        fogF = 1.0 - exp(-fogF);\n      // Docs are wrong: use (density*c)^2, not density*c^2\n      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n      else if (uFogMode == 3)\n        fogF = 1.0 - exp(-fogF*fogF);\n      fogF = clamp(fogF, 0.0, 1.0);\n      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n    } else gl_FragColor = fragColor;\n#else\n    gl_FragColor = fragColor;\n#endif // HAS_FOG\n    \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true}},"evals":[],"jsHooks":[]}</script>
-<p id="rgl19887-aria" hidden>
-</p>
-</div>
-</div>
-<div id="adding-new-variables" class="section level2" number="1.2">
-<h2><span class="header-section-number">1.2</span> Adding new
-variables</h2>
-<p>To interpolate new variables to the biplot, the function
-<code>interpolate()</code> and <code>newaxes()</code> are called. The
-function <code>interpolate()</code> accepts the argument
-<code>newvariable</code> to specify a matrix or data frame of the same
-number of rows in the data specified in <code>biplot()</code> containing
-the new variables to be interpolated. The function
-<code>newaxes()</code> allows the user to specify the aesthetics of the
-interpolated variables.</p>
-<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" tabindex="-1"></a><span class="fu">biplot</span>(iris[,<span class="dv">1</span><span class="sc">:</span><span class="dv">3</span>])<span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">dim.biplot =</span> <span class="dv">3</span>) <span class="sc">|&gt;</span> <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb3-2"><a href="#cb3-2" tabindex="-1"></a>  <span class="fu">interpolate</span>(<span class="at">newvariable =</span> iris[,<span class="dv">4</span>]) <span class="sc">|&gt;</span> </span>
-<span id="cb3-3"><a href="#cb3-3" tabindex="-1"></a>  <span class="fu">newaxes</span>(<span class="at">col=</span><span class="st">&quot;darkred&quot;</span>,<span class="at">X.new.names =</span> <span class="st">&quot;Petal.Width&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg 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(point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - 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-<p id="rgl36317-aria" hidden>
-</p>
-</div>
-</div>
-<div id="predicting-samples" class="section level2" number="1.3">
-<h2><span class="header-section-number">1.3</span> Predicting
-samples</h2>
-<p>To add the prediction of samples on the biplot, the
-<code>prediction()</code> function is used. The
-<code>predict.samples</code> argument takes in a vector indicating
-either the row numbers of the samples to predict or set to TRUE
-indicating to predict all samples. The argument <code>which</code>
-allows the user to select which variable to predict the sample on. In
-the example below, samples 100 to 150 predictions are shown for
-variables 1 and 4. The aesthetics for the display of the predictions are
-arguments in the <code>axes()</code> function: <code>predict.col</code>
-and <code>predict.lwd</code>.</p>
-<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris<span class="sc">$</span>Species,<span class="at">dim.biplot =</span> <span class="dv">3</span>,<span class="at">show.class.means =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb4-2"><a href="#cb4-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>,<span class="at">predict.col =</span> <span class="st">&quot;orange&quot;</span>) <span class="sc">|&gt;</span>  </span>
-<span id="cb4-3"><a href="#cb4-3" tabindex="-1"></a>  <span class="fu">prediction</span>(<span class="at">predict.samples=</span><span class="dv">100</span><span class="sc">:</span><span class="dv">150</span>,<span class="at">which =</span> <span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">4</span>))  <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
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USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = 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projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 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vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - 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-<p id="rgl53955-aria" hidden>
-</p>
-</div>
-</div>
-<div id="predicting-group-means" class="section level2" number="1.4">
-<h2><span class="header-section-number">1.4</span> Predicting group
-means</h2>
-<p>Similarly, to add the prediction of group means, the function
-<code>prediction()</code> is used. The argument
-<code>predict.means</code> takes in a vector specifying which group
-means to predict. In the example below, only the first group means is
-predicted. Important to note that the argument
-<code>show.class.means</code> must be set to TRUE in the
-<code>PCA()</code> function.</p>
-<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> </span>
-<span id="cb5-2"><a href="#cb5-2" tabindex="-1"></a>  <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris<span class="sc">$</span>Species,<span class="at">dim.biplot =</span> <span class="dv">3</span>,<span class="at">show.class.means =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb5-3"><a href="#cb5-3" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>,<span class="at">predict.col =</span> <span class="st">&quot;darkred&quot;</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb5-4"><a href="#cb5-4" tabindex="-1"></a>  <span class="fu">prediction</span>(<span class="at">predict.means =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef 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projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - 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-<p id="rgl18897-aria" hidden>
-</p>
-</div>
-</div>
-<div id="ellipses" class="section level2" number="1.5">
-<h2><span class="header-section-number">1.5</span> Ellipses</h2>
-<p>Ellipses are added to a 3D biplot using the <code>ellipses()</code>
-function which works in the same way as a 2D biplot.</p>
-<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" tabindex="-1"></a><span class="fu">biplot</span>(iris) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> iris[,<span class="dv">5</span>],<span class="at">dim.biplot =</span> <span class="dv">3</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb6-2"><a href="#cb6-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb6-3"><a href="#cb6-3" tabindex="-1"></a>  <span class="fu">ellipses</span>(<span class="at">kappa =</span> <span class="dv">3</span>,<span class="at">opacity =</span> <span class="fl">0.5</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span>
-<span id="cb6-4"><a href="#cb6-4" tabindex="-1"></a><span class="co">#&gt; Computing 3 -ellipse for setosa </span></span>
-<span id="cb6-5"><a href="#cb6-5" tabindex="-1"></a><span class="co">#&gt; Computing 3 -ellipse for versicolor </span></span>
-<span id="cb6-6"><a href="#cb6-6" tabindex="-1"></a><span class="co">#&gt; Computing 3 -ellipse for virginica</span></span></code></pre></div>
-<div class="figure">
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Vvs68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\nms85vRNvSr+I1g2/WgfxPFf7VL/5Vba+X2QxPY31br/Oute+U3LrvLU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z6Xr0C/EowovwAAAABWnDm/LAUiv0oOiz4K/Ey/cfELv+Lcej73h1O/fTAQvwAAAABADCm/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\nL78LYDK/0/mKvqr8LL9fcy+/+o8vvl1dBb9uEFa/T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qMY+T6XgUo/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\nWWurPiMFKz96hzk/Z9YsPkDHGT/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KG+Kk9ZPx7T8b43ZuC+I8ZDPyYqFr+6EAi+xYVMPw7CIL9T95q+2Is3P7whC7+EJZ2+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\noBWFP38UFz6FvvQ/AyddP9CibD57Z08/ljWpP3DdRb4MuVk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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n      if (uFogMode > 1)\n        fogF = mix(uFogParms.w, 1.0, fogF);\n      fogF = fogF*uFogParms.z;\n      if (uFogMode == 2)\n        fogF = 1.0 - exp(-fogF);\n      // Docs are wrong: use (density*c)^2, not density*c^2\n      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n      else if (uFogMode == 3)\n        fogF = 1.0 - exp(-fogF*fogF);\n      fogF = clamp(fogF, 0.0, 1.0);\n      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n    } else gl_FragColor = fragColor;\n#else\n    gl_FragColor = fragColor;\n#endif // HAS_FOG\n    \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true}},"evals":[],"jsHooks":[]}</script>
-<p id="rgl87803-aria" hidden>
-</p>
-</div>
-</div>
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-<div id="cva-3d-biplot" class="section level1" number="2">
-<h1><span class="header-section-number">2</span> CVA 3d biplot</h1>
-<p>Similarly for a CVA 3D biplot, <code>dim.biplot = 3</code> is
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-<span id="cb7-2"><a href="#cb7-2" tabindex="-1"></a>  <span class="fu">axes</span>(<span class="at">col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span>
-<span id="cb7-3"><a href="#cb7-3" tabindex="-1"></a><span class="co">#&gt; Warning in CVA.biplot(biplot(iris), classes = iris$Species, dim.biplot = 3):</span></span>
-<span id="cb7-4"><a href="#cb7-4" tabindex="-1"></a><span class="co">#&gt; The dimension of the canonical space &lt; dim.biplot sample.opt method used for</span></span>
-<span id="cb7-5"><a href="#cb7-5" tabindex="-1"></a><span class="co">#&gt; additional dimension(s).</span></span></code></pre></div>
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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = 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-<p id="rgl47085-aria" hidden>
-</p>
-</div>
-</div>
-<div id="ca-3d-biplot" class="section level1" number="3">
-<h1><span class="header-section-number">3</span> CA 3D biplot</h1>
-<p>As with <code>PCA()</code>, three-dimensional CA biplots are obtained
-by specifying <code>dim.biplot = 3</code> in the call to
-<code>CA()</code>. Again, an interactive biplot will be drawn in a
-separate <code>rgl</code> window.</p>
-<p>Consider the <code>HairEyeColor</code> example again as discussed in
-<code>Ca in biplotEZ</code>:</p>
-<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" tabindex="-1"></a><span class="fu">biplot</span>(HairEyeColor[,,<span class="dv">2</span>], <span class="at">center =</span> <span class="cn">FALSE</span>) <span class="sc">|&gt;</span> <span class="fu">CA</span>(<span class="at">variant =</span> <span class="st">&quot;Symmetric&quot;</span>, <span class="at">dim.biplot =</span> <span class="dv">3</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb8-2"><a href="#cb8-2" tabindex="-1"></a><span class="fu">samples</span>(<span class="at">col=</span><span class="fu">c</span>(<span class="st">&quot;darkred&quot;</span>,<span class="st">&quot;forestgreen&quot;</span>), <span class="at">pch=</span><span class="fu">c</span>(<span class="dv">15</span>,<span class="dv">17</span>), <span class="at">label.col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
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USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG) || defined(USE_ENVMAP)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n// USE_ENVMAP implies NEEDS_VNORMAL\n\n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n\n#ifdef USE_ENVMAP\n  vReflection = normalize(reflect(vPosition.xyz/vPosition.w, \n                        normalize(vNormal.xyz/vNormal.w)));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\n#ifdef USE_ENVMAP\nvarying vec3 vReflection;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n\n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    // Simulate two-sided lighting\n    if (n.z < 0.0)\n      n = -n;\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i]) {\n        if (finite[i]) {\n          lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n        } else {\n          lightdir = (mvMatrix * vec4(lightdir, 0.)).xyz;\n        }\n      }\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n\n// These calculations use the definitions from \n// https://docs.gl/gl3/glTexEnv\n\n#ifdef USE_ENVMAP\n    float m = 2.0 * sqrt(dot(vReflection, vReflection) + 2.0*vReflection.z + 1.0);\n    vec4 textureColor = texture2D(uSampler, vReflection.xy / m + vec2(0.5, 0.5));\n#else\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n#endif\n\n#ifdef TEXTURE_rgb\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(textureColor.rgb, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*vec4(textureColor.rgb, 1.);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, lighteffect.a);\n#endif\n\n#endif // TEXTURE_luminance\n \n    \n#ifdef TEXTURE_luminance_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, textureColor.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - luminance)*lighteffect.rgb,\n                        textureColor.a*lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(luminance + lighteffect.rgb, \n                        textureColor.a*lighteffect.a);\n\n#endif\n\n#endif // TEXTURE_luminance_alpha\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n      if (uFogMode > 1)\n        fogF = mix(uFogParms.w, 1.0, fogF);\n      fogF = fogF*uFogParms.z;\n      if (uFogMode == 2)\n        fogF = 1.0 - exp(-fogF);\n      // Docs are wrong: use (density*c)^2, not density*c^2\n      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n      else if (uFogMode == 3)\n        fogF = 1.0 - exp(-fogF*fogF);\n      fogF = clamp(fogF, 0.0, 1.0);\n      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n    } else gl_FragColor = fragColor;\n#else\n    gl_FragColor = fragColor;\n#endif // HAS_FOG\n    \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true}},"evals":[],"jsHooks":[]}</script>
-<p id="rgl92485-aria" hidden>
-</p>
-</div>
-<p>We also illustrate the three dimensional CA biplot of the
-<code>SA Crime</code> example:</p>
-<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" tabindex="-1"></a>SACrime <span class="ot">&lt;-</span> <span class="fu">matrix</span>(<span class="fu">c</span>(<span class="dv">1235</span>,<span class="dv">432</span>,<span class="dv">1824</span>,<span class="dv">1322</span>,<span class="dv">573</span>,<span class="dv">588</span>,<span class="dv">624</span>,<span class="dv">169</span>,<span class="dv">629</span>,<span class="dv">34479</span>,<span class="dv">16833</span>,<span class="dv">46993</span>,<span class="dv">30606</span>,<span class="dv">13670</span>,</span>
-<span id="cb9-2"><a href="#cb9-2" tabindex="-1"></a>              <span class="dv">16849</span>,<span class="dv">15861</span>,<span class="dv">9898</span>,<span class="dv">24915</span>,<span class="dv">2160</span>,<span class="dv">939</span>,<span class="dv">5257</span>,<span class="dv">4946</span>,<span class="dv">722</span>,<span class="dv">1271</span>,<span class="dv">881</span>,<span class="dv">775</span>,<span class="dv">1844</span>,<span class="dv">5946</span>,</span>
-<span id="cb9-3"><a href="#cb9-3" tabindex="-1"></a>              <span class="dv">4418</span>,<span class="dv">15117</span>,<span class="dv">10258</span>,<span class="dv">5401</span>,<span class="dv">4273</span>,<span class="dv">4987</span>,<span class="dv">1956</span>,<span class="dv">10639</span>,<span class="dv">29508</span>,<span class="dv">15705</span>,<span class="dv">62703</span>,<span class="dv">37203</span>,</span>
-<span id="cb9-4"><a href="#cb9-4" tabindex="-1"></a>              <span class="dv">11857</span>,<span class="dv">18855</span>,<span class="dv">14722</span>,<span class="dv">4924</span>,<span class="dv">42376</span>,<span class="dv">604</span>,<span class="dv">156</span>,<span class="dv">7466</span>,<span class="dv">3889</span>,<span class="dv">203</span>,<span class="dv">664</span>,<span class="dv">291</span>,<span class="dv">5</span>,<span class="dv">923</span>,<span class="dv">19875</span>,</span>
-<span id="cb9-5"><a href="#cb9-5" tabindex="-1"></a>              <span class="dv">19885</span>,<span class="dv">57153</span>,<span class="dv">29410</span>,<span class="dv">11024</span>,<span class="dv">12202</span>,<span class="dv">10406</span>,<span class="dv">5431</span>,<span class="dv">32663</span>,<span class="dv">7086</span>,<span class="dv">4193</span>,<span class="dv">22152</span>,<span class="dv">9264</span>,<span class="dv">3760</span>,</span>
-<span id="cb9-6"><a href="#cb9-6" tabindex="-1"></a>              <span class="dv">4752</span>,<span class="dv">3863</span>,<span class="dv">1337</span>,<span class="dv">8578</span>,<span class="dv">7929</span>,<span class="dv">4525</span>,<span class="dv">12348</span>,<span class="dv">24174</span>,<span class="dv">3198</span>,<span class="dv">1770</span>,<span class="dv">7004</span>,<span class="dv">2201</span>,<span class="dv">45985</span>,<span class="dv">764</span>,</span>
-<span id="cb9-7"><a href="#cb9-7" tabindex="-1"></a>              <span class="dv">427</span>,<span class="dv">1501</span>,<span class="dv">1197</span>,<span class="dv">215</span>,<span class="dv">251</span>,<span class="dv">345</span>,<span class="dv">213</span>,<span class="dv">1850</span>,<span class="dv">3515</span>,<span class="dv">879</span>,<span class="dv">3674</span>,<span class="dv">4713</span>,<span class="dv">696</span>,<span class="dv">835</span>,<span class="dv">917</span>,<span class="dv">422</span>,<span class="dv">2836</span>,</span>
-<span id="cb9-8"><a href="#cb9-8" tabindex="-1"></a>              <span class="dv">88</span>,<span class="dv">59</span>,<span class="dv">174</span>,<span class="dv">76</span>,<span class="dv">31</span>,<span class="dv">61</span>,<span class="dv">117</span>,<span class="dv">32</span>,<span class="dv">257</span>,<span class="dv">5499</span>,<span class="dv">2628</span>,<span class="dv">8073</span>,<span class="dv">6502</span>,<span class="dv">2816</span>,<span class="dv">2635</span>,<span class="dv">3017</span>,<span class="dv">1020</span>,<span class="dv">4000</span>,</span>
-<span id="cb9-9"><a href="#cb9-9" tabindex="-1"></a>              <span class="dv">8939</span>,<span class="dv">4501</span>,<span class="dv">50970</span>,<span class="dv">24290</span>,<span class="dv">2447</span>,<span class="dv">5907</span>,<span class="dv">5528</span>,<span class="dv">1175</span>,<span class="dv">14555</span>),<span class="at">nrow=</span><span class="dv">9</span>, <span class="at">ncol=</span><span class="dv">14</span>)</span>
-<span id="cb9-10"><a href="#cb9-10" tabindex="-1"></a><span class="fu">dimnames</span>(SACrime) <span class="ot">&lt;-</span> <span class="fu">list</span>(<span class="fu">paste</span>(<span class="fu">c</span>(<span class="st">&quot;ECpe&quot;</span>, <span class="st">&quot;FrSt&quot;</span>, <span class="st">&quot;Gaut&quot;</span>, <span class="st">&quot;KZN&quot;</span>,  <span class="st">&quot;Limp&quot;</span>, <span class="st">&quot;Mpml&quot;</span>, <span class="st">&quot;NWst&quot;</span>, <span class="st">&quot;NCpe&quot;</span>,</span>
-<span id="cb9-11"><a href="#cb9-11" tabindex="-1"></a>                            <span class="st">&quot;WCpe&quot;</span>)), <span class="fu">paste</span>(<span class="fu">c</span>(<span class="st">&quot;Arsn&quot;</span>, <span class="st">&quot;AGBH&quot;</span>, <span class="st">&quot;AtMr&quot;</span>, <span class="st">&quot;BNRs&quot;</span>, <span class="st">&quot;BRs&quot;</span>,  <span class="st">&quot;CrJk&quot;</span>,</span>
-<span id="cb9-12"><a href="#cb9-12" tabindex="-1"></a>                                              <span class="st">&quot;CmAs&quot;</span>, <span class="st">&quot;CmRb&quot;</span>, <span class="st">&quot;DrgR&quot;</span>, <span class="st">&quot;InAs&quot;</span>, <span class="st">&quot;Mrd&quot;</span>, <span class="st">&quot;PubV&quot;</span>, </span>
-<span id="cb9-13"><a href="#cb9-13" tabindex="-1"></a>                                              <span class="st">&quot;Rape&quot;</span>, <span class="st">&quot;RAC&quot;</span> )))</span>
-<span id="cb9-14"><a href="#cb9-14" tabindex="-1"></a><span class="fu">names</span>(<span class="fu">dimnames</span>(SACrime))[[<span class="dv">1</span>]] <span class="ot">&lt;-</span> <span class="st">&quot;Provinces&quot;</span></span>
-<span id="cb9-15"><a href="#cb9-15" tabindex="-1"></a><span class="fu">names</span>(<span class="fu">dimnames</span>(SACrime))[[<span class="dv">2</span>]] <span class="ot">&lt;-</span> <span class="st">&quot;Crimes&quot;</span></span></code></pre></div>
-<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" tabindex="-1"></a><span class="fu">biplot</span>(SACrime, <span class="at">center =</span> <span class="cn">FALSE</span>) <span class="sc">|&gt;</span> <span class="fu">CA</span>(<span class="at">variant =</span> <span class="st">&quot;Symmetric&quot;</span>, <span class="at">dim.biplot =</span> <span class="dv">3</span>) <span class="sc">|&gt;</span> </span>
-<span id="cb10-2"><a href="#cb10-2" tabindex="-1"></a><span class="fu">samples</span>(<span class="at">col=</span><span class="fu">c</span>(<span class="st">&quot;royalblue&quot;</span>,<span class="st">&quot;darkred&quot;</span>), <span class="at">pch=</span><span class="fu">c</span>(<span class="dv">15</span>,<span class="dv">17</span>), <span class="at">label.col=</span><span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
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textureColor.rgb) * lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb, lighteffect.a);\n#endif\n\n#endif //TEXTURE_rgb\n        \n#ifdef TEXTURE_rgba\n\n#ifdef TEXMODE_replace\n// already done\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = lighteffect*textureColor;\n#endif\n\n#ifdef TEXMODE_decal\n    textureColor = vec4((1. - textureColor.a)*lighteffect.rgb) +\n                     textureColor.a*textureColor.rgb, \n                     lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - textureColor.rgb) * lighteffect.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n\n#ifdef TEXMODE_add\n    textureColor = vec4(lighteffect.rgb + textureColor.rgb,\n                    lighteffect.a*textureColor.a);\n#endif\n    \n#endif //TEXTURE_rgba\n    \n#ifdef TEXTURE_alpha\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(lighteffect.rgb, luminance);\n#endif \n\n#if defined(TEXMODE_modulate) || defined(TEXMODE_blend) || defined(TEXMODE_add)\n    textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#endif // TEXTURE_alpha\n    \n// The TEXTURE_luminance values are not from that reference    \n#ifdef TEXTURE_luminance\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n\n#if defined(TEXMODE_replace) || defined(TEXMODE_decal)\n    textureColor = vec4(luminance, luminance, luminance, lighteffect.a);\n#endif \n\n#ifdef TEXMODE_modulate\n    textureColor = vec4(luminance*lighteffect.rgb, lighteffect.a);\n#endif\n\n#ifdef TEXMODE_blend\n    textureColor = vec4((1. - 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diff --git a/vignettes/CA_in_biplotEZ.Rmd b/vignettes/CA_in_biplotEZ.Rmd
index 7da3d98..eb05c8a 100644
--- a/vignettes/CA_in_biplotEZ.Rmd
+++ b/vignettes/CA_in_biplotEZ.Rmd
@@ -34,7 +34,7 @@ frequency table. Numerous variants of CA are available for the
 application to diverse problems, the interested reader is referred to:
 @UB2011, @BehLombardo2014.
 
-In `biplotEZ` focus will be places on three *EZ*-to-use versions based on the Pearson residuals (@UB2011: Page 300).
+In this vignette, focus will be placed on three *EZ*-to-use versions based on the Pearson residuals (@UB2011 :300).
 
 Now, the two-way frequency table is also referred to as the data matrix:
 $\mathbf{X}:r\times c$. This data matrix is different from the
@@ -109,7 +109,8 @@ $$
 The return value for the Standardised pearson residuals is `Smat` and the singular value decomposition, `SVD`.
 
 ```{r}
-Smat <- sqrt(solve(Dr))%*%(P-(Dr %*%matrix(1, nrow = nrow(X), ncol = ncol(X)) %*%  Dc))%*%sqrt(solve(Dc))
+Smat <- sqrt(solve(Dr))%*%(P-(Dr %*%matrix(1, nrow = nrow(X), 
+    ncol = ncol(X)) %*%  Dc))%*%sqrt(solve(Dc))
 svd.out <- svd(Smat)
 svd.out
 ```
@@ -167,7 +168,7 @@ colcoor <- svd.out[[3]]%*%(diag(svd.out[[1]])^(1-gamma))
 
 ## Lambda scaling
 
-As presented in @UB2011 page 24, when constructing a biplot representing the rows of a coordinate matrix $\mathbf{A}$ and $\mathbf{B}^\prime$. Take note that the inner product is invariant when $\mathbf{A}$ and $\mathbf{B}$ are scaled inversely by $\lambda$. 
+As presented in @UB2011 :24, when constructing a biplot representing the rows of a coordinate matrix $\mathbf{A}$ and $\mathbf{B}^\prime$. Take note that the inner product is invariant when $\mathbf{A}$ and $\mathbf{B}$ are scaled inversely by $\lambda$. 
 
 $$
 \mathbf{AB} = (\lambda\mathbf{A})(\mathbf{B}/\lambda)
@@ -179,19 +180,19 @@ $$
 $$
 
 The default setting is to not apply lambda-scaling (i.e. $\lambda=1$).
+
 The return value is `lambda.val`.
 
 ## Measures of fit
 
-`quality`, `adequacy`, `row.predictivities` and `column.predictivities' are available for CA biplots. 
-
+`quality`, `adequacy`, `row.predictivities` and `column.predictivities` are available for CA biplots. 
 
-As explained in `biplotEZ`, the quality of the biplot is measured by the ratio of the variance explained (sum of the squared singular values of the utilised ($M$) components) and the total variance (sum of all squared singular values ($p$)).
+As explained in the biplotEZ vignette, the quality of the biplot is measured by the ratio of the variance explained (sum of the squared singular values of the utilised ($M$) components) and the total variance (sum of all squared singular values ($p$)).
 
 $$
 \frac{\sum_{m=1}^{M}\lambda_m^2}{\sum_{m=1}^{p}\lambda_m^2}
 $$
-The `adequacy` refers to the representation of the variables. In `CA()` the factor variable represented in the columns is treated as the variables and is calculated as explained in `biplotEZ`:
+The `adequacy` refers to the representation of the variables. In `CA()` the factor variable represented in the columns is treated as the variables and is calculated as explained in the biplotEZ vignette:
 
 $$
  \frac{diag(\mathbf{V}_r\mathbf{V}_r')}{diag(\mathbf{VV}')}= diag(\mathbf{V}_r\mathbf{V}_r')
@@ -200,14 +201,14 @@ $$
 
 The predictivities provide a measure of how well the original values are recovered from the biplot. An element that is well represented will have a predictivity close to one, indicating that the row or column variable values from prediction is close to the observed values. If an element is poorly represented, the predicted values will be very different from the original values and the predictivity value will be close to zero.
 
-The `row.predictivities` are calculated as follows (@UB2011: Page 299):
+The `row.predictivities` are calculated as follows (@UB2011 :299):
 
 $$
 diag(\mathbf{U}\mathbf{\Sigma}\mathbf{J}\mathbf{\Sigma}\mathbf{U}')[diag(\mathbf{U}\mathbf{\Sigma}\mathbf{\Sigma}\mathbf{U}')]^{-1}\\
 =diag(\mathbf{U}\mathbf{\Sigma}^2\mathbf{J}\mathbf{U}')[diag(\mathbf{U}\mathbf{\Sigma^2}\mathbf{U}')]^{-1}
 $$
 
-The `col.predictivities` are calculated as follows (@UB2011: Page 299):
+The `col.predictivities` are calculated as follows (@UB2011 :299):
 
 $$
 diag(\mathbf{V}\mathbf{\Sigma}^2\mathbf{J}\mathbf{V}')[diag(\mathbf{V}\mathbf{\Sigma^2}\mathbf{V}')]^{-1}
@@ -232,7 +233,6 @@ To construct the CA biplot for row standard coordinates:
 ```{r}
 ca.out <- biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = "Stand") |> 
   plot()
-ca.out$qual
 ```
 
 ## `Variant="Symmetric"`
@@ -242,7 +242,6 @@ To construct the symmetric CA map:
 ```{r}
 ca.out <- biplot(HairEyeColor[,,2], center = FALSE) |> 
   CA(variant = "Symmetric") |> plot()
-ca.out$qual
 ca.out$lambda.val
 ```
 
@@ -274,9 +273,9 @@ The function `interpolate()` accepts a matrix or data frame containing the sampl
 The function `newsamples()` operates similar to `samples()` and enables aesthetic changes to the new samples.
 
 ```{r}
-biplot(HairEyeColor[,,2], center=F) |> CA(variant="Symmetric") |> 
-  samples(pch=c(0,2)) |> interpolate(newdata=HairEyeColor[,,1]) |> 
-  newsamples(col=c("orange","purple"), pch=c(15,17)) |> plot()      
+#biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = "Symmetric") |> 
+#  samples(pch = c(0,2)) |> interpolate(newdata = HairEyeColor[,,1]) |> 
+#  newsamples(col = c("orange","purple"), pch = c(15,17)) |> plot()      
 ```
 
 
@@ -286,19 +285,20 @@ The `sample()` function should be utilised to specify the colours, plotting char
 
 ```{r}
 biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = "Princ") |> 
-  samples(col=c("cyan","purple"), pch=c(15,17), label.side=c("bottom","top"), 
-          label.cex=1) |> legend.type(samples = TRUE, new = TRUE) |> plot()
+  samples(col = c("cyan","purple"), pch = c(15,17), label.side = c("bottom","top"), 
+          label.cex = 1) |> legend.type(samples = TRUE, new = TRUE) |> plot()
 ```
 
 ```{r}
 biplot(HairEyeColor[,,2], center = FALSE) |> CA(variant = "Symmetric") |> 
-  samples(col=c("forestgreen","magenta"), pch=c(12,17), label.side=c("top","bottom")) |>
+  samples(col = c("forestgreen","magenta"), pch = c(12,17), 
+          label.side = c("top","bottom")) |> 
   legend.type(samples = TRUE) |> plot()
 ```
 
 ## Additional example
 
-Consider the South African Crime data set 2008, extracted from the South African police website (http://www.saps.gov.za/). @UB2011 page 312.
+Consider the South African Crime data set 2008, extracted from the South African police website (http://www.saps.gov.za/). @UB2011 :312.
 
 ```{r}
 SACrime <- matrix(c(1235,432,1824,1322,573,588,624,169,629,34479,16833,46993,30606,13670,
@@ -322,7 +322,7 @@ SACrime
 ```{r}
 biplot(SACrime, center = FALSE) |> 
   CA(variant = "Symmetric", lambda.scal = TRUE) |> 
-  samples(col=c("cyan","purple"), pch=c(15,17), label.side=c("bottom","top")) |>
+  samples(col = c("cyan","purple"), pch = c(15,17), label.side = c("bottom","top")) |>
   legend.type(samples = TRUE, new = TRUE) |> plot()
 ```
 
diff --git a/vignettes/CA_in_biplotEZ.html b/vignettes/CA_in_biplotEZ.html
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+</style>
+
+
+
+
+</head>
+
+<body>
+
+
+
+
+<h1 class="title toc-ignore">CA in biplotEZ</h1>
+
+
+<div id="TOC">
+<ul>
+<li><a href="#what-is-a-correspondence-analysis" id="toc-what-is-a-correspondence-analysis"><span class="toc-section-number">1</span> What is a Correspondence
+Analysis?</a></li>
+<li><a href="#ca-biplot" id="toc-ca-biplot"><span class="toc-section-number">2</span> CA biplot</a>
+<ul>
+<li><a href="#coordinates" id="toc-coordinates"><span class="toc-section-number">2.1</span> Coordinates</a></li>
+<li><a href="#lambda-scaling" id="toc-lambda-scaling"><span class="toc-section-number">2.2</span> Lambda scaling</a></li>
+<li><a href="#measures-of-fit" id="toc-measures-of-fit"><span class="toc-section-number">2.3</span> Measures of fit</a></li>
+</ul></li>
+<li><a href="#the-function-ca" id="toc-the-function-ca"><span class="toc-section-number">3</span> The function CA()</a>
+<ul>
+<li><a href="#variantprinc" id="toc-variantprinc"><span class="toc-section-number">3.1</span>
+<code>Variant=&quot;Princ&quot;</code></a></li>
+<li><a href="#variantstand" id="toc-variantstand"><span class="toc-section-number">3.2</span>
+<code>Variant=&quot;Stand&quot;</code></a></li>
+<li><a href="#variantsymmetric" id="toc-variantsymmetric"><span class="toc-section-number">3.3</span>
+<code>Variant=&quot;Symmetric&quot;</code></a></li>
+<li><a href="#measures-of-fit-1" id="toc-measures-of-fit-1"><span class="toc-section-number">3.4</span> Measures of fit</a></li>
+<li><a href="#interpolating-new-samples" id="toc-interpolating-new-samples"><span class="toc-section-number">3.5</span> Interpolating new samples</a></li>
+<li><a href="#aesthetics-and-legend" id="toc-aesthetics-and-legend"><span class="toc-section-number">3.6</span> Aesthetics and legend</a></li>
+<li><a href="#additional-example" id="toc-additional-example"><span class="toc-section-number">3.7</span> Additional example</a></li>
+</ul></li>
+<li><a href="#references" id="toc-references">References</a></li>
+</ul>
+</div>
+
+<div id="what-is-a-correspondence-analysis" class="section level1" number="1">
+<h1><span class="header-section-number">1</span> What is a
+Correspondence Analysis?</h1>
+<p>In its simplest form Correspondence Analysis (CA) aims to expose the
+association between two categorical variables by utilising a two-way
+frequency table. Numerous variants of CA are available for the
+application to diverse problems, the interested reader is referred to:
+<span class="citation">Gower, Lubbe, and Roux (2011)</span>, <span class="citation">Beh and Lombardo (2014)</span>.</p>
+<p>In this vignette, focus will be placed on three <em>EZ</em>-to-use
+versions based on the Pearson residuals (<span class="citation">Gower,
+Lubbe, and Roux (2011)</span> :300).</p>
+<p>Now, the two-way frequency table is also referred to as the data
+matrix: <span class="math inline">\(\mathbf{X}:r\times c\)</span>. This
+data matrix is different from the continuous case used for the
+<code>PCA()</code> and <code>CVA()</code> examples, as it represents the
+cross-tabulations of two categorical variables (i.e. factors), each with
+a finite number of levels (i.e response values). The elements of the
+data matrix represent the frequency of the co-occurrence of two
+particular levels of the two variables. Consider the
+<code>HairEyeColor</code> data set in <code>R</code>, which summarises
+the hair and eye color of male and female statistics students. For the
+purpose of this example only the male students will be considered:</p>
+<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" tabindex="-1"></a>X <span class="ot">&lt;-</span> HairEyeColor[,,<span class="dv">2</span>]</span>
+<span id="cb1-2"><a href="#cb1-2" tabindex="-1"></a>X</span>
+<span id="cb1-3"><a href="#cb1-3" tabindex="-1"></a><span class="co">#&gt;        Eye</span></span>
+<span id="cb1-4"><a href="#cb1-4" tabindex="-1"></a><span class="co">#&gt; Hair    Brown Blue Hazel Green</span></span>
+<span id="cb1-5"><a href="#cb1-5" tabindex="-1"></a><span class="co">#&gt;   Black    36    9     5     2</span></span>
+<span id="cb1-6"><a href="#cb1-6" tabindex="-1"></a><span class="co">#&gt;   Brown    66   34    29    14</span></span>
+<span id="cb1-7"><a href="#cb1-7" tabindex="-1"></a><span class="co">#&gt;   Red      16    7     7     7</span></span>
+<span id="cb1-8"><a href="#cb1-8" tabindex="-1"></a><span class="co">#&gt;   Blond     4   64     5     8</span></span></code></pre></div>
+<p>The grand total of the table <span class="math inline">\(N\)</span>
+is obtained from the total of all frequencies:</p>
+<p><span class="math display">\[
+\sum_{r=1}^{R}\sum_{c=1}^{C}x_{rc}=N
+\]</span></p>
+<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" tabindex="-1"></a>N <span class="ot">&lt;-</span> <span class="fu">sum</span>(X)</span>
+<span id="cb2-2"><a href="#cb2-2" tabindex="-1"></a>N</span>
+<span id="cb2-3"><a href="#cb2-3" tabindex="-1"></a><span class="co">#&gt; [1] 313</span></span></code></pre></div>
+<p>It is common to work with the proportions rather than the frequencies
+in terms of the correspondence matrix, <span class="math inline">\(\mathbf{P}\)</span>:</p>
+<p><span class="math display">\[
+\mathbf{P}=\frac{\mathbf{X}}{N}
+\]</span></p>
+<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" tabindex="-1"></a>P <span class="ot">&lt;-</span> X<span class="sc">/</span>N</span>
+<span id="cb3-2"><a href="#cb3-2" tabindex="-1"></a>P</span>
+<span id="cb3-3"><a href="#cb3-3" tabindex="-1"></a><span class="co">#&gt;        Eye</span></span>
+<span id="cb3-4"><a href="#cb3-4" tabindex="-1"></a><span class="co">#&gt; Hair          Brown        Blue       Hazel       Green</span></span>
+<span id="cb3-5"><a href="#cb3-5" tabindex="-1"></a><span class="co">#&gt;   Black 0.115015974 0.028753994 0.015974441 0.006389776</span></span>
+<span id="cb3-6"><a href="#cb3-6" tabindex="-1"></a><span class="co">#&gt;   Brown 0.210862620 0.108626198 0.092651757 0.044728435</span></span>
+<span id="cb3-7"><a href="#cb3-7" tabindex="-1"></a><span class="co">#&gt;   Red   0.051118211 0.022364217 0.022364217 0.022364217</span></span>
+<span id="cb3-8"><a href="#cb3-8" tabindex="-1"></a><span class="co">#&gt;   Blond 0.012779553 0.204472843 0.015974441 0.025559105</span></span></code></pre></div>
+<p>Other useful summaries of <span class="math inline">\(\mathbf{P}\)</span> include the row and column
+masses (for arbitrary row and column <span class="math inline">\(r\)</span> and <span class="math inline">\(c\)</span>, respectively), also expressed as
+diagonal matrices:</p>
+<p><span class="math display">\[
+\mathbf{r}_r = \sum_{c=1}^{C}p_{rc}; \hspace{0.5 cm}
+\mathbf{c}_c = \sum_{r=1}^{R}p_{rc}\\
+\mathbf{r}=\mathbf{P1}; \hspace{0.5 cm}
+\mathbf{c}=\mathbf{P}^\prime\mathbf{1}
+\]</span></p>
+<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" tabindex="-1"></a>rMass <span class="ot">&lt;-</span> <span class="fu">rowSums</span>(P)</span>
+<span id="cb4-2"><a href="#cb4-2" tabindex="-1"></a>rMass</span>
+<span id="cb4-3"><a href="#cb4-3" tabindex="-1"></a><span class="co">#&gt;     Black     Brown       Red     Blond </span></span>
+<span id="cb4-4"><a href="#cb4-4" tabindex="-1"></a><span class="co">#&gt; 0.1661342 0.4568690 0.1182109 0.2587859</span></span></code></pre></div>
+<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" tabindex="-1"></a>cMass <span class="ot">&lt;-</span> <span class="fu">colSums</span>(P)</span>
+<span id="cb5-2"><a href="#cb5-2" tabindex="-1"></a>cMass</span>
+<span id="cb5-3"><a href="#cb5-3" tabindex="-1"></a><span class="co">#&gt;      Brown       Blue      Hazel      Green </span></span>
+<span id="cb5-4"><a href="#cb5-4" tabindex="-1"></a><span class="co">#&gt; 0.38977636 0.36421725 0.14696486 0.09904153</span></span></code></pre></div>
+<p>Diagonal matrices:</p>
+<p><span class="math display">\[
+\mathbf{D_r}=\text{diag}(\mathbf{r}); \hspace{0.5 cm}
+\mathbf{D_c}=\text{diag}(\mathbf{c})
+\]</span></p>
+<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" tabindex="-1"></a>Dr <span class="ot">&lt;-</span> <span class="fu">diag</span>(<span class="fu">apply</span>(P, <span class="dv">1</span>, sum))</span>
+<span id="cb6-2"><a href="#cb6-2" tabindex="-1"></a>Dr</span>
+<span id="cb6-3"><a href="#cb6-3" tabindex="-1"></a><span class="co">#&gt;           [,1]     [,2]      [,3]      [,4]</span></span>
+<span id="cb6-4"><a href="#cb6-4" tabindex="-1"></a><span class="co">#&gt; [1,] 0.1661342 0.000000 0.0000000 0.0000000</span></span>
+<span id="cb6-5"><a href="#cb6-5" tabindex="-1"></a><span class="co">#&gt; [2,] 0.0000000 0.456869 0.0000000 0.0000000</span></span>
+<span id="cb6-6"><a href="#cb6-6" tabindex="-1"></a><span class="co">#&gt; [3,] 0.0000000 0.000000 0.1182109 0.0000000</span></span>
+<span id="cb6-7"><a href="#cb6-7" tabindex="-1"></a><span class="co">#&gt; [4,] 0.0000000 0.000000 0.0000000 0.2587859</span></span></code></pre></div>
+<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" tabindex="-1"></a>Dc <span class="ot">&lt;-</span> <span class="fu">diag</span>(<span class="fu">apply</span>(P, <span class="dv">2</span>, sum))</span>
+<span id="cb7-2"><a href="#cb7-2" tabindex="-1"></a>Dc</span>
+<span id="cb7-3"><a href="#cb7-3" tabindex="-1"></a><span class="co">#&gt;           [,1]      [,2]      [,3]       [,4]</span></span>
+<span id="cb7-4"><a href="#cb7-4" tabindex="-1"></a><span class="co">#&gt; [1,] 0.3897764 0.0000000 0.0000000 0.00000000</span></span>
+<span id="cb7-5"><a href="#cb7-5" tabindex="-1"></a><span class="co">#&gt; [2,] 0.0000000 0.3642173 0.0000000 0.00000000</span></span>
+<span id="cb7-6"><a href="#cb7-6" tabindex="-1"></a><span class="co">#&gt; [3,] 0.0000000 0.0000000 0.1469649 0.00000000</span></span>
+<span id="cb7-7"><a href="#cb7-7" tabindex="-1"></a><span class="co">#&gt; [4,] 0.0000000 0.0000000 0.0000000 0.09904153</span></span></code></pre></div>
+<p>In order to obtain the first form of the row and column coordinates,
+the singular value decomposition (SVD) of the matrix of standardised
+Pearson residuals (<span class="math inline">\(\mathbf{S}\)</span>) is
+computed:</p>
+<p><span class="math display">\[
+\begin{aligned}
+\text{SVD}(\mathbf{S}) &amp;=
+\text{SVD}\left(\mathbf{D_r^{-\frac{1}{2}}}(\mathbf{P}-\mathbf{rc^\prime})\mathbf{D_c^{-\frac{1}{2}}}\right)\\&amp;=
+\mathbf{U\Lambda V^\prime}
+\end{aligned}
+\]</span> The return value for the Standardised pearson residuals is
+<code>Smat</code> and the singular value decomposition,
+<code>SVD</code>.</p>
+<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" tabindex="-1"></a>Smat <span class="ot">&lt;-</span> <span class="fu">sqrt</span>(<span class="fu">solve</span>(Dr))<span class="sc">%*%</span>(P<span class="sc">-</span>(Dr <span class="sc">%*%</span><span class="fu">matrix</span>(<span class="dv">1</span>, <span class="at">nrow =</span> <span class="fu">nrow</span>(X), </span>
+<span id="cb8-2"><a href="#cb8-2" tabindex="-1"></a>    <span class="at">ncol =</span> <span class="fu">ncol</span>(X)) <span class="sc">%*%</span>  Dc))<span class="sc">%*%</span><span class="fu">sqrt</span>(<span class="fu">solve</span>(Dc))</span>
+<span id="cb8-3"><a href="#cb8-3" tabindex="-1"></a>svd.out <span class="ot">&lt;-</span> <span class="fu">svd</span>(Smat)</span>
+<span id="cb8-4"><a href="#cb8-4" tabindex="-1"></a>svd.out</span>
+<span id="cb8-5"><a href="#cb8-5" tabindex="-1"></a><span class="co">#&gt; $d</span></span>
+<span id="cb8-6"><a href="#cb8-6" tabindex="-1"></a><span class="co">#&gt; [1] 5.499629e-01 1.806424e-01 7.541748e-02 7.966568e-17</span></span>
+<span id="cb8-7"><a href="#cb8-7" tabindex="-1"></a><span class="co">#&gt; </span></span>
+<span id="cb8-8"><a href="#cb8-8" tabindex="-1"></a><span class="co">#&gt; $u</span></span>
+<span id="cb8-9"><a href="#cb8-9" tabindex="-1"></a><span class="co">#&gt;            [,1]       [,2]        [,3]      [,4]</span></span>
+<span id="cb8-10"><a href="#cb8-10" tabindex="-1"></a><span class="co">#&gt; [1,] -0.3832205  0.7807477 -0.27828196 0.4075956</span></span>
+<span id="cb8-11"><a href="#cb8-11" tabindex="-1"></a><span class="co">#&gt; [2,] -0.3195599 -0.2982325  0.59335474 0.6759209</span></span>
+<span id="cb8-12"><a href="#cb8-12" tabindex="-1"></a><span class="co">#&gt; [3,] -0.1736837 -0.5332073 -0.75320188 0.3438181</span></span>
+<span id="cb8-13"><a href="#cb8-13" tabindex="-1"></a><span class="co">#&gt; [4,]  0.8490333  0.1310737 -0.05635808 0.5087101</span></span>
+<span id="cb8-14"><a href="#cb8-14" tabindex="-1"></a><span class="co">#&gt; </span></span>
+<span id="cb8-15"><a href="#cb8-15" tabindex="-1"></a><span class="co">#&gt; $v</span></span>
+<span id="cb8-16"><a href="#cb8-16" tabindex="-1"></a><span class="co">#&gt;             [,1]       [,2]        [,3]      [,4]</span></span>
+<span id="cb8-17"><a href="#cb8-17" tabindex="-1"></a><span class="co">#&gt; [1,] -0.61837991  0.4547976 -0.14487614 0.6243207</span></span>
+<span id="cb8-18"><a href="#cb8-18" tabindex="-1"></a><span class="co">#&gt; [2,]  0.75797511  0.2307003  0.08963172 0.6035041</span></span>
+<span id="cb8-19"><a href="#cb8-19" tabindex="-1"></a><span class="co">#&gt; [3,] -0.20612962 -0.5898626  0.68015284 0.3833600</span></span>
+<span id="cb8-20"><a href="#cb8-20" tabindex="-1"></a><span class="co">#&gt; [4,]  0.02430218 -0.6260980 -0.71300012 0.3147086</span></span></code></pre></div>
+<p>This is linked to the <span class="math inline">\(\chi^2\)</span>-statistic to determine whether the
+two categorical variables (i.e. the rows and columns of the contingency
+table) are independent. The expected frequencies represented by the
+product of the row and column masses (<span class="math inline">\(\mathbf{rc^\prime}\)</span>).</p>
+<p>Furthermore, since the weights of certain objects might be
+substantially different from others which could result in a distorted
+approximation in lower dimension, the <span class="math inline">\(\chi^2\)</span>-distance, also referred to as the
+weighted Euclidean distance, is rather used to measure distances in CA.
+This is an intuitive decision as it follows from the <span class="math inline">\(\chi^2\)</span>-statistic to test the independence
+between two categorical variables, in this case the independence between
+the rows and columns of the contingency table. (<span class="citation">Beh and Lombardo (2014)</span>, <span class="citation">Greenacre (2017)</span>).</p>
+</div>
+<div id="ca-biplot" class="section level1" number="2">
+<h1><span class="header-section-number">2</span> CA biplot</h1>
+<div id="coordinates" class="section level2" number="2.1">
+<h2><span class="header-section-number">2.1</span> Coordinates</h2>
+<p>In order to construct a biplot in which the distances between the row
+and column coordinates are meaningful an asymmetric display should be
+constructed. This means that the contribution of the singular values
+should be different for the row and column coordinates. (<span class="citation">Gabriel (1971)</span>) The standard coordinates are
+expressed by:</p>
+<p><span class="math display">\[
+\begin{aligned}
+\text{Row standard coordinates:} \hspace{0.5 cm}&amp;\mathbf{U}\\
+\text{Column standard coordinates:} \hspace{0.5 cm}&amp;\mathbf{V}
+\end{aligned}
+\]</span></p>
+<p>The principal coordinates are expressed by:</p>
+<p><span class="math display">\[
+\begin{aligned}
+\text{Row principal coordinates:} \hspace{0.5
+cm}&amp;\mathbf{U\Lambda}\\
+\text{Column principal coordinates:} \hspace{0.5
+cm}&amp;\mathbf{V\Lambda}
+\end{aligned}
+\]</span></p>
+<p>By including the singular values the magnitude of the association
+between the variables are incorporated in the scaling of the
+coordinates.</p>
+<p>In the <code>ca()</code> function the argument <code>variant</code>
+allows the user to choose between three types of CA biplots:
+<code>Princ</code>, <code>Stand</code> and <code>Symmetric</code>.</p>
+<p><span class="math display">\[
+\begin{aligned}
+\text{Row coordinates:} \hspace{0.5 cm}&amp;\mathbf{U\Lambda^\gamma}\\
+\text{Column coordinates:} \hspace{0.5
+cm}&amp;\mathbf{V\Lambda^{1-\gamma}}
+\end{aligned}
+\]</span> The row standard (i.e. column principal) coordinate biplot:
+<code>Stand</code>, results from <span class="math inline">\(\gamma=0\)</span>.</p>
+<p>The row principal (i.e. column standard) coordinate biplot:
+<code>Princ</code>, results from <span class="math inline">\(\gamma=1\)</span>.</p>
+<p>The symmetric plot in which row and column coordinates are scaled
+equally: <code>Symmetric</code>, results from <span class="math inline">\(\gamma=0.5\)</span>.</p>
+<p>The return value is <code>rowcoor</code> and <code>colcoor</code>,
+respectively.</p>
+<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" tabindex="-1"></a>gamma <span class="ot">&lt;-</span> <span class="dv">0</span></span>
+<span id="cb9-2"><a href="#cb9-2" tabindex="-1"></a>rowcoor <span class="ot">&lt;-</span> svd.out[[<span class="dv">2</span>]]<span class="sc">%*%</span>(<span class="fu">diag</span>(svd.out[[<span class="dv">1</span>]])<span class="sc">^</span>gamma)</span>
+<span id="cb9-3"><a href="#cb9-3" tabindex="-1"></a>colcoor <span class="ot">&lt;-</span> svd.out[[<span class="dv">3</span>]]<span class="sc">%*%</span>(<span class="fu">diag</span>(svd.out[[<span class="dv">1</span>]])<span class="sc">^</span>(<span class="dv">1</span><span class="sc">-</span>gamma))</span></code></pre></div>
+</div>
+<div id="lambda-scaling" class="section level2" number="2.2">
+<h2><span class="header-section-number">2.2</span> Lambda scaling</h2>
+<p>As presented in <span class="citation">Gower, Lubbe, and Roux
+(2011)</span> :24, when constructing a biplot representing the rows of a
+coordinate matrix <span class="math inline">\(\mathbf{A}\)</span> and
+<span class="math inline">\(\mathbf{B}^\prime\)</span>. Take note that
+the inner product is invariant when <span class="math inline">\(\mathbf{A}\)</span> and <span class="math inline">\(\mathbf{B}\)</span> are scaled inversely by <span class="math inline">\(\lambda\)</span>.</p>
+<p><span class="math display">\[
+\mathbf{AB} = (\lambda\mathbf{A})(\mathbf{B}/\lambda)
+\]</span> An arbitrary value of <span class="math inline">\(\lambda\)</span> can be selected or an
+<em>optimal</em> value could be to ensure that the average squared
+distance of the points in <span class="math inline">\(\lambda\mathbf{A}\)</span> and <span class="math inline">\(\mathbf{B}/\lambda\)</span> is equal.</p>
+<p><span class="math display">\[
+\lambda^4 =\frac{r}{c}\frac{||\mathbf{B}||^2}{||\mathbf{A}||^2}
+\]</span></p>
+<p>The default setting is to not apply lambda-scaling (i.e. <span class="math inline">\(\lambda=1\)</span>).</p>
+<p>The return value is <code>lambda.val</code>.</p>
+</div>
+<div id="measures-of-fit" class="section level2" number="2.3">
+<h2><span class="header-section-number">2.3</span> Measures of fit</h2>
+<p><code>quality</code>, <code>adequacy</code>,
+<code>row.predictivities</code> and <code>column.predictivities</code>
+are available for CA biplots.</p>
+<p>As explained in the
+<a href="https://cran.r-project.org/web/packages/biplotEZ/vignettes/biplotEZ.html" target="_blank">biplotEZ
+vignette</a>, the quality of the biplot is measured by the ratio of the
+variance explained (sum of the squared singular values of the utilised
+(<span class="math inline">\(M\)</span>) components) and the total
+variance (sum of all squared singular values (<span class="math inline">\(p\)</span>)).</p>
+<p><span class="math display">\[
+\frac{\sum_{m=1}^{M}\lambda_m^2}{\sum_{m=1}^{p}\lambda_m^2}
+\]</span> The <code>adequacy</code> refers to the representation of the
+variables. In <code>CA()</code> the factor variable represented in the
+columns is treated as the variables and is calculated as explained in
+the
+<a href="https://cran.r-project.org/web/packages/biplotEZ/vignettes/biplotEZ.html" target="_blank">biplotEZ
+vignette</a>:</p>
+<p><span class="math display">\[
+\frac{diag(\mathbf{V}_r\mathbf{V}_r&#39;)}{diag(\mathbf{VV}&#39;)}=
+diag(\mathbf{V}_r\mathbf{V}_r&#39;)
+\]</span></p>
+<p>The predictivities provide a measure of how well the original values
+are recovered from the biplot. An element that is well represented will
+have a predictivity close to one, indicating that the row or column
+variable values from prediction is close to the observed values. If an
+element is poorly represented, the predicted values will be very
+different from the original values and the predictivity value will be
+close to zero.</p>
+<p>The <code>row.predictivities</code> are calculated as follows (<span class="citation">Gower, Lubbe, and Roux (2011)</span> :299):</p>
+<p><span class="math display">\[
+diag(\mathbf{U}\mathbf{\Sigma}\mathbf{J}\mathbf{\Sigma}\mathbf{U}&#39;)[diag(\mathbf{U}\mathbf{\Sigma}\mathbf{\Sigma}\mathbf{U}&#39;)]^{-1}\\
+=diag(\mathbf{U}\mathbf{\Sigma}^2\mathbf{J}\mathbf{U}&#39;)[diag(\mathbf{U}\mathbf{\Sigma^2}\mathbf{U}&#39;)]^{-1}
+\]</span></p>
+<p>The <code>col.predictivities</code> are calculated as follows (<span class="citation">Gower, Lubbe, and Roux (2011)</span> :299):</p>
+<p><span class="math display">\[
+diag(\mathbf{V}\mathbf{\Sigma}^2\mathbf{J}\mathbf{V}&#39;)[diag(\mathbf{V}\mathbf{\Sigma^2}\mathbf{V}&#39;)]^{-1}
+\]</span></p>
+</div>
+</div>
+<div id="the-function-ca" class="section level1" number="3">
+<h1><span class="header-section-number">3</span> The function CA()</h1>
+<p>The function <code>CA()</code> requires a two-way contingency table
+as input and will return an object of class <code>CA</code> and
+<code>biplot</code>. As this is not a standard data matrix as for
+<code>PCA</code> and <code>CVA</code>, scaling and centering is not
+allowed on the two-way contingency table and a warning will be given if
+either <code>scale</code> or <code>center</code> is specified as
+<code>TRUE</code> in biplot()`.</p>
+<div id="variantprinc" class="section level2" number="3.1">
+<h2><span class="header-section-number">3.1</span>
+<code>Variant=&quot;Princ&quot;</code></h2>
+<p>The default CA biplot is a row principal coordinate biplot:</p>
+<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" tabindex="-1"></a><span class="fu">biplot</span>(HairEyeColor[,,<span class="dv">2</span>], <span class="at">center =</span> <span class="cn">FALSE</span>) <span class="sc">|&gt;</span> <span class="fu">CA</span>() <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+</div>
+<div id="variantstand" class="section level2" number="3.2">
+<h2><span class="header-section-number">3.2</span>
+<code>Variant=&quot;Stand&quot;</code></h2>
+<p>To construct the CA biplot for row standard coordinates:</p>
+<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" tabindex="-1"></a>ca.out <span class="ot">&lt;-</span> <span class="fu">biplot</span>(HairEyeColor[,,<span class="dv">2</span>], <span class="at">center =</span> <span class="cn">FALSE</span>) <span class="sc">|&gt;</span> <span class="fu">CA</span>(<span class="at">variant =</span> <span class="st">&quot;Stand&quot;</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb11-2"><a href="#cb11-2" tabindex="-1"></a>  <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+</div>
+<div id="variantsymmetric" class="section level2" number="3.3">
+<h2><span class="header-section-number">3.3</span>
+<code>Variant=&quot;Symmetric&quot;</code></h2>
+<p>To construct the symmetric CA map:</p>
+<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" tabindex="-1"></a>ca.out <span class="ot">&lt;-</span> <span class="fu">biplot</span>(HairEyeColor[,,<span class="dv">2</span>], <span class="at">center =</span> <span class="cn">FALSE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb12-2"><a href="#cb12-2" tabindex="-1"></a>  <span class="fu">CA</span>(<span class="at">variant =</span> <span class="st">&quot;Symmetric&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" tabindex="-1"></a>ca.out<span class="sc">$</span>lambda.val</span>
+<span id="cb13-2"><a href="#cb13-2" tabindex="-1"></a><span class="co">#&gt; [1] 1</span></span></code></pre></div>
+</div>
+<div id="measures-of-fit-1" class="section level2" number="3.4">
+<h2><span class="header-section-number">3.4</span> Measures of fit</h2>
+<p>The <code>fit.mesaures()</code> function should be utilised to obtain
+the specific fit measures explained above.</p>
+<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" tabindex="-1"></a>ca.out <span class="ot">&lt;-</span> <span class="fu">biplot</span>(HairEyeColor[,,<span class="dv">2</span>], <span class="at">center =</span> <span class="cn">FALSE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb14-2"><a href="#cb14-2" tabindex="-1"></a>  <span class="fu">CA</span>(<span class="at">variant =</span> <span class="st">&quot;Symmetric&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">fit.measures</span>()</span>
+<span id="cb14-3"><a href="#cb14-3" tabindex="-1"></a><span class="fu">print</span>(<span class="st">&quot;Quality&quot;</span>)</span>
+<span id="cb14-4"><a href="#cb14-4" tabindex="-1"></a><span class="co">#&gt; [1] &quot;Quality&quot;</span></span></code></pre></div>
+<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" tabindex="-1"></a>ca.out<span class="sc">$</span>quality</span>
+<span id="cb15-2"><a href="#cb15-2" tabindex="-1"></a><span class="co">#&gt; [1] 0.9833094</span></span></code></pre></div>
+<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" tabindex="-1"></a><span class="fu">print</span>(<span class="st">&quot;Adequacy&quot;</span>)</span>
+<span id="cb16-2"><a href="#cb16-2" tabindex="-1"></a><span class="co">#&gt; [1] &quot;Adequacy&quot;</span></span></code></pre></div>
+<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" tabindex="-1"></a>ca.out<span class="sc">$</span>adequacy</span>
+<span id="cb17-2"><a href="#cb17-2" tabindex="-1"></a><span class="co">#&gt;        Brown   Blue  Hazel  Green</span></span>
+<span id="cb17-3"><a href="#cb17-3" tabindex="-1"></a><span class="co">#&gt; Dim 1 0.3824 0.5745 0.0425 0.0006</span></span>
+<span id="cb17-4"><a href="#cb17-4" tabindex="-1"></a><span class="co">#&gt; Dim 2 0.5892 0.6277 0.3904 0.3926</span></span>
+<span id="cb17-5"><a href="#cb17-5" tabindex="-1"></a><span class="co">#&gt; Dim 3 0.6102 0.6358 0.8530 0.9010</span></span>
+<span id="cb17-6"><a href="#cb17-6" tabindex="-1"></a><span class="co">#&gt; Dim 4 1.0000 1.0000 1.0000 1.0000</span></span></code></pre></div>
+<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" tabindex="-1"></a><span class="fu">print</span>(<span class="st">&quot;Row predictivities&quot;</span>)</span>
+<span id="cb18-2"><a href="#cb18-2" tabindex="-1"></a><span class="co">#&gt; [1] &quot;Row predictivities&quot;</span></span></code></pre></div>
+<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" tabindex="-1"></a>ca.out<span class="sc">$</span>row.predictivities</span>
+<span id="cb19-2"><a href="#cb19-2" tabindex="-1"></a><span class="co">#&gt;        Black  Brown    Red  Blond</span></span>
+<span id="cb19-3"><a href="#cb19-3" tabindex="-1"></a><span class="co">#&gt; Dim 1 0.6860 0.8630 0.4219 0.9974</span></span>
+<span id="cb19-4"><a href="#cb19-4" tabindex="-1"></a><span class="co">#&gt; Dim 2 0.9932 0.9441 0.8508 0.9999</span></span>
+<span id="cb19-5"><a href="#cb19-5" tabindex="-1"></a><span class="co">#&gt; Dim 3 1.0000 1.0000 1.0000 1.0000</span></span>
+<span id="cb19-6"><a href="#cb19-6" tabindex="-1"></a><span class="co">#&gt; Dim 4 1.0000 1.0000 1.0000 1.0000</span></span></code></pre></div>
+<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" tabindex="-1"></a><span class="fu">print</span>(<span class="st">&quot;Column predictivities&quot;</span>)</span>
+<span id="cb20-2"><a href="#cb20-2" tabindex="-1"></a><span class="co">#&gt; [1] &quot;Column predictivities&quot;</span></span></code></pre></div>
+<div class="sourceCode" id="cb21"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" tabindex="-1"></a>ca.out<span class="sc">$</span>col.predictivities</span>
+<span id="cb21-2"><a href="#cb21-2" tabindex="-1"></a><span class="co">#&gt;        Brown   Blue  Hazel  Green</span></span>
+<span id="cb21-3"><a href="#cb21-3" tabindex="-1"></a><span class="co">#&gt; Dim 1 0.9439 0.9898 0.4789 0.0113</span></span>
+<span id="cb21-4"><a href="#cb21-4" tabindex="-1"></a><span class="co">#&gt; Dim 2 0.9990 0.9997 0.9020 0.8177</span></span>
+<span id="cb21-5"><a href="#cb21-5" tabindex="-1"></a><span class="co">#&gt; Dim 3 1.0000 1.0000 1.0000 1.0000</span></span>
+<span id="cb21-6"><a href="#cb21-6" tabindex="-1"></a><span class="co">#&gt; Dim 4 1.0000 1.0000 1.0000 1.0000</span></span></code></pre></div>
+</div>
+<div id="interpolating-new-samples" class="section level2" number="3.5">
+<h2><span class="header-section-number">3.5</span> Interpolating new
+samples</h2>
+<p>Adding cross-tabulations of the two categorical variables to the plot
+is facilitated by the function <code>interpolate()</code>. Note that the
+additional variables to be interpolated did not contribute to the
+construction of the biplot. This is the reason why <span class="citation">Greenacre (2017)</span> term these supplementary
+points.</p>
+<p>The function <code>interpolate()</code> accepts a matrix or data
+frame containing the samples and variables to be interpolated. The
+argument <code>newdata</code> containing the samples to be interpolated
+needs to have a similar structure to the data set sent to
+<code>biplot()</code>. If <code>biplot()</code> received a data frame,
+<code>newdata</code> can be either another data frame or a matrix
+containing the subset of numerical variables.</p>
+<p>The function <code>newsamples()</code> operates similar to
+<code>samples()</code> and enables aesthetic changes to the new
+samples.</p>
+<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1" tabindex="-1"></a><span class="fu">biplot</span>(HairEyeColor[,,<span class="dv">2</span>], <span class="at">center =</span> <span class="cn">FALSE</span>) <span class="sc">|&gt;</span> <span class="fu">CA</span>(<span class="at">variant =</span> <span class="st">&quot;Symmetric&quot;</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb22-2"><a href="#cb22-2" tabindex="-1"></a>  <span class="fu">samples</span>(<span class="at">pch =</span> <span class="fu">c</span>(<span class="dv">0</span>,<span class="dv">2</span>)) <span class="sc">|&gt;</span> <span class="fu">interpolate</span>(<span class="at">newdata =</span> HairEyeColor[,,<span class="dv">1</span>]) <span class="sc">|&gt;</span> </span>
+<span id="cb22-3"><a href="#cb22-3" tabindex="-1"></a>  <span class="fu">newsamples</span>(<span class="at">col =</span> <span class="fu">c</span>(<span class="st">&quot;orange&quot;</span>,<span class="st">&quot;purple&quot;</span>), <span class="at">pch =</span> <span class="fu">c</span>(<span class="dv">15</span>,<span class="dv">17</span>)) <span class="sc">|&gt;</span> <span class="fu">plot</span>()      </span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+</div>
+<div id="aesthetics-and-legend" class="section level2" number="3.6">
+<h2><span class="header-section-number">3.6</span> Aesthetics and
+legend</h2>
+<p>The <code>sample()</code> function should be utilised to specify the
+colours, plotting characters and expansion of the samples.</p>
+<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb23-1"><a href="#cb23-1" tabindex="-1"></a><span class="fu">biplot</span>(HairEyeColor[,,<span class="dv">2</span>], <span class="at">center =</span> <span class="cn">FALSE</span>) <span class="sc">|&gt;</span> <span class="fu">CA</span>(<span class="at">variant =</span> <span class="st">&quot;Princ&quot;</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb23-2"><a href="#cb23-2" tabindex="-1"></a>  <span class="fu">samples</span>(<span class="at">col =</span> <span class="fu">c</span>(<span class="st">&quot;cyan&quot;</span>,<span class="st">&quot;purple&quot;</span>), <span class="at">pch =</span> <span class="fu">c</span>(<span class="dv">15</span>,<span class="dv">17</span>), <span class="at">label.side =</span> <span class="fu">c</span>(<span class="st">&quot;bottom&quot;</span>,<span class="st">&quot;top&quot;</span>), </span>
+<span id="cb23-3"><a href="#cb23-3" tabindex="-1"></a>          <span class="at">label.cex =</span> <span class="dv">1</span>) <span class="sc">|&gt;</span> <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>, <span class="at">new =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb24-1"><a href="#cb24-1" tabindex="-1"></a><span class="fu">biplot</span>(HairEyeColor[,,<span class="dv">2</span>], <span class="at">center =</span> <span class="cn">FALSE</span>) <span class="sc">|&gt;</span> <span class="fu">CA</span>(<span class="at">variant =</span> <span class="st">&quot;Symmetric&quot;</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb24-2"><a href="#cb24-2" tabindex="-1"></a>  <span class="fu">samples</span>(<span class="at">col =</span> <span class="fu">c</span>(<span class="st">&quot;forestgreen&quot;</span>,<span class="st">&quot;magenta&quot;</span>), <span class="at">pch =</span> <span class="fu">c</span>(<span class="dv">12</span>,<span class="dv">17</span>), </span>
+<span id="cb24-3"><a href="#cb24-3" tabindex="-1"></a>          <span class="at">label.side =</span> <span class="fu">c</span>(<span class="st">&quot;top&quot;</span>,<span class="st">&quot;bottom&quot;</span>)) <span class="sc">|&gt;</span> </span>
+<span id="cb24-4"><a href="#cb24-4" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+</div>
+<div id="additional-example" class="section level2" number="3.7">
+<h2><span class="header-section-number">3.7</span> Additional
+example</h2>
+<p>Consider the South African Crime data set 2008, extracted from the
+South African police website (<a href="http://www.saps.gov.za/" class="uri">http://www.saps.gov.za/</a>). <span class="citation">Gower,
+Lubbe, and Roux (2011)</span> :312.</p>
+<div class="sourceCode" id="cb25"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb25-1"><a href="#cb25-1" tabindex="-1"></a>SACrime <span class="ot">&lt;-</span> <span class="fu">matrix</span>(<span class="fu">c</span>(<span class="dv">1235</span>,<span class="dv">432</span>,<span class="dv">1824</span>,<span class="dv">1322</span>,<span class="dv">573</span>,<span class="dv">588</span>,<span class="dv">624</span>,<span class="dv">169</span>,<span class="dv">629</span>,<span class="dv">34479</span>,<span class="dv">16833</span>,<span class="dv">46993</span>,<span class="dv">30606</span>,<span class="dv">13670</span>,</span>
+<span id="cb25-2"><a href="#cb25-2" tabindex="-1"></a>              <span class="dv">16849</span>,<span class="dv">15861</span>,<span class="dv">9898</span>,<span class="dv">24915</span>,<span class="dv">2160</span>,<span class="dv">939</span>,<span class="dv">5257</span>,<span class="dv">4946</span>,<span class="dv">722</span>,<span class="dv">1271</span>,<span class="dv">881</span>,<span class="dv">775</span>,<span class="dv">1844</span>,<span class="dv">5946</span>,</span>
+<span id="cb25-3"><a href="#cb25-3" tabindex="-1"></a>              <span class="dv">4418</span>,<span class="dv">15117</span>,<span class="dv">10258</span>,<span class="dv">5401</span>,<span class="dv">4273</span>,<span class="dv">4987</span>,<span class="dv">1956</span>,<span class="dv">10639</span>,<span class="dv">29508</span>,<span class="dv">15705</span>,<span class="dv">62703</span>,<span class="dv">37203</span>,</span>
+<span id="cb25-4"><a href="#cb25-4" tabindex="-1"></a>              <span class="dv">11857</span>,<span class="dv">18855</span>,<span class="dv">14722</span>,<span class="dv">4924</span>,<span class="dv">42376</span>,<span class="dv">604</span>,<span class="dv">156</span>,<span class="dv">7466</span>,<span class="dv">3889</span>,<span class="dv">203</span>,<span class="dv">664</span>,<span class="dv">291</span>,<span class="dv">5</span>,<span class="dv">923</span>,<span class="dv">19875</span>,</span>
+<span id="cb25-5"><a href="#cb25-5" tabindex="-1"></a>              <span class="dv">19885</span>,<span class="dv">57153</span>,<span class="dv">29410</span>,<span class="dv">11024</span>,<span class="dv">12202</span>,<span class="dv">10406</span>,<span class="dv">5431</span>,<span class="dv">32663</span>,<span class="dv">7086</span>,<span class="dv">4193</span>,<span class="dv">22152</span>,<span class="dv">9264</span>,<span class="dv">3760</span>,</span>
+<span id="cb25-6"><a href="#cb25-6" tabindex="-1"></a>              <span class="dv">4752</span>,<span class="dv">3863</span>,<span class="dv">1337</span>,<span class="dv">8578</span>,<span class="dv">7929</span>,<span class="dv">4525</span>,<span class="dv">12348</span>,<span class="dv">24174</span>,<span class="dv">3198</span>,<span class="dv">1770</span>,<span class="dv">7004</span>,<span class="dv">2201</span>,<span class="dv">45985</span>,<span class="dv">764</span>,</span>
+<span id="cb25-7"><a href="#cb25-7" tabindex="-1"></a>              <span class="dv">427</span>,<span class="dv">1501</span>,<span class="dv">1197</span>,<span class="dv">215</span>,<span class="dv">251</span>,<span class="dv">345</span>,<span class="dv">213</span>,<span class="dv">1850</span>,<span class="dv">3515</span>,<span class="dv">879</span>,<span class="dv">3674</span>,<span class="dv">4713</span>,<span class="dv">696</span>,<span class="dv">835</span>,<span class="dv">917</span>,<span class="dv">422</span>,<span class="dv">2836</span>,</span>
+<span id="cb25-8"><a href="#cb25-8" tabindex="-1"></a>              <span class="dv">88</span>,<span class="dv">59</span>,<span class="dv">174</span>,<span class="dv">76</span>,<span class="dv">31</span>,<span class="dv">61</span>,<span class="dv">117</span>,<span class="dv">32</span>,<span class="dv">257</span>,<span class="dv">5499</span>,<span class="dv">2628</span>,<span class="dv">8073</span>,<span class="dv">6502</span>,<span class="dv">2816</span>,<span class="dv">2635</span>,<span class="dv">3017</span>,<span class="dv">1020</span>,<span class="dv">4000</span>,</span>
+<span id="cb25-9"><a href="#cb25-9" tabindex="-1"></a>              <span class="dv">8939</span>,<span class="dv">4501</span>,<span class="dv">50970</span>,<span class="dv">24290</span>,<span class="dv">2447</span>,<span class="dv">5907</span>,<span class="dv">5528</span>,<span class="dv">1175</span>,<span class="dv">14555</span>),<span class="at">nrow=</span><span class="dv">9</span>, <span class="at">ncol=</span><span class="dv">14</span>)</span>
+<span id="cb25-10"><a href="#cb25-10" tabindex="-1"></a><span class="fu">dimnames</span>(SACrime) <span class="ot">&lt;-</span> <span class="fu">list</span>(<span class="fu">paste</span>(<span class="fu">c</span>(<span class="st">&quot;ECpe&quot;</span>, <span class="st">&quot;FrSt&quot;</span>, <span class="st">&quot;Gaut&quot;</span>, <span class="st">&quot;KZN&quot;</span>,  <span class="st">&quot;Limp&quot;</span>, <span class="st">&quot;Mpml&quot;</span>, <span class="st">&quot;NWst&quot;</span>, <span class="st">&quot;NCpe&quot;</span>,</span>
+<span id="cb25-11"><a href="#cb25-11" tabindex="-1"></a>                            <span class="st">&quot;WCpe&quot;</span>)), <span class="fu">paste</span>(<span class="fu">c</span>(<span class="st">&quot;Arsn&quot;</span>, <span class="st">&quot;AGBH&quot;</span>, <span class="st">&quot;AtMr&quot;</span>, <span class="st">&quot;BNRs&quot;</span>, <span class="st">&quot;BRs&quot;</span>,  <span class="st">&quot;CrJk&quot;</span>,</span>
+<span id="cb25-12"><a href="#cb25-12" tabindex="-1"></a>                                              <span class="st">&quot;CmAs&quot;</span>, <span class="st">&quot;CmRb&quot;</span>, <span class="st">&quot;DrgR&quot;</span>, <span class="st">&quot;InAs&quot;</span>, <span class="st">&quot;Mrd&quot;</span>, <span class="st">&quot;PubV&quot;</span>, </span>
+<span id="cb25-13"><a href="#cb25-13" tabindex="-1"></a>                                              <span class="st">&quot;Rape&quot;</span>, <span class="st">&quot;RAC&quot;</span> )))</span>
+<span id="cb25-14"><a href="#cb25-14" tabindex="-1"></a><span class="fu">names</span>(<span class="fu">dimnames</span>(SACrime))[[<span class="dv">1</span>]] <span class="ot">&lt;-</span> <span class="st">&quot;Provinces&quot;</span></span>
+<span id="cb25-15"><a href="#cb25-15" tabindex="-1"></a><span class="fu">names</span>(<span class="fu">dimnames</span>(SACrime))[[<span class="dv">2</span>]] <span class="ot">&lt;-</span> <span class="st">&quot;Crimes&quot;</span></span>
+<span id="cb25-16"><a href="#cb25-16" tabindex="-1"></a>SACrime</span>
+<span id="cb25-17"><a href="#cb25-17" tabindex="-1"></a><span class="co">#&gt;          Crimes</span></span>
+<span id="cb25-18"><a href="#cb25-18" tabindex="-1"></a><span class="co">#&gt; Provinces Arsn  AGBH AtMr  BNRs   BRs CrJk  CmAs  CmRb  DrgR InAs  Mrd PubV</span></span>
+<span id="cb25-19"><a href="#cb25-19" tabindex="-1"></a><span class="co">#&gt;      ECpe 1235 34479 2160  5946 29508  604 19875  7086  7929  764 3515   88</span></span>
+<span id="cb25-20"><a href="#cb25-20" tabindex="-1"></a><span class="co">#&gt;      FrSt  432 16833  939  4418 15705  156 19885  4193  4525  427  879   59</span></span>
+<span id="cb25-21"><a href="#cb25-21" tabindex="-1"></a><span class="co">#&gt;      Gaut 1824 46993 5257 15117 62703 7466 57153 22152 12348 1501 3674  174</span></span>
+<span id="cb25-22"><a href="#cb25-22" tabindex="-1"></a><span class="co">#&gt;      KZN  1322 30606 4946 10258 37203 3889 29410  9264 24174 1197 4713   76</span></span>
+<span id="cb25-23"><a href="#cb25-23" tabindex="-1"></a><span class="co">#&gt;      Limp  573 13670  722  5401 11857  203 11024  3760  3198  215  696   31</span></span>
+<span id="cb25-24"><a href="#cb25-24" tabindex="-1"></a><span class="co">#&gt;      Mpml  588 16849 1271  4273 18855  664 12202  4752  1770  251  835   61</span></span>
+<span id="cb25-25"><a href="#cb25-25" tabindex="-1"></a><span class="co">#&gt;      NWst  624 15861  881  4987 14722  291 10406  3863  7004  345  917  117</span></span>
+<span id="cb25-26"><a href="#cb25-26" tabindex="-1"></a><span class="co">#&gt;      NCpe  169  9898  775  1956  4924    5  5431  1337  2201  213  422   32</span></span>
+<span id="cb25-27"><a href="#cb25-27" tabindex="-1"></a><span class="co">#&gt;      WCpe  629 24915 1844 10639 42376  923 32663  8578 45985 1850 2836  257</span></span>
+<span id="cb25-28"><a href="#cb25-28" tabindex="-1"></a><span class="co">#&gt;          Crimes</span></span>
+<span id="cb25-29"><a href="#cb25-29" tabindex="-1"></a><span class="co">#&gt; Provinces Rape   RAC</span></span>
+<span id="cb25-30"><a href="#cb25-30" tabindex="-1"></a><span class="co">#&gt;      ECpe 5499  8939</span></span>
+<span id="cb25-31"><a href="#cb25-31" tabindex="-1"></a><span class="co">#&gt;      FrSt 2628  4501</span></span>
+<span id="cb25-32"><a href="#cb25-32" tabindex="-1"></a><span class="co">#&gt;      Gaut 8073 50970</span></span>
+<span id="cb25-33"><a href="#cb25-33" tabindex="-1"></a><span class="co">#&gt;      KZN  6502 24290</span></span>
+<span id="cb25-34"><a href="#cb25-34" tabindex="-1"></a><span class="co">#&gt;      Limp 2816  2447</span></span>
+<span id="cb25-35"><a href="#cb25-35" tabindex="-1"></a><span class="co">#&gt;      Mpml 2635  5907</span></span>
+<span id="cb25-36"><a href="#cb25-36" tabindex="-1"></a><span class="co">#&gt;      NWst 3017  5528</span></span>
+<span id="cb25-37"><a href="#cb25-37" tabindex="-1"></a><span class="co">#&gt;      NCpe 1020  1175</span></span>
+<span id="cb25-38"><a href="#cb25-38" tabindex="-1"></a><span class="co">#&gt;      WCpe 4000 14555</span></span></code></pre></div>
+<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb26-1"><a href="#cb26-1" tabindex="-1"></a><span class="fu">biplot</span>(SACrime, <span class="at">center =</span> <span class="cn">FALSE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb26-2"><a href="#cb26-2" tabindex="-1"></a>  <span class="fu">CA</span>(<span class="at">variant =</span> <span class="st">&quot;Symmetric&quot;</span>, <span class="at">lambda.scal =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb26-3"><a href="#cb26-3" tabindex="-1"></a>  <span class="fu">samples</span>(<span class="at">col =</span> <span class="fu">c</span>(<span class="st">&quot;cyan&quot;</span>,<span class="st">&quot;purple&quot;</span>), <span class="at">pch =</span> <span class="fu">c</span>(<span class="dv">15</span>,<span class="dv">17</span>), <span class="at">label.side =</span> <span class="fu">c</span>(<span class="st">&quot;bottom&quot;</span>,<span class="st">&quot;top&quot;</span>)) <span class="sc">|&gt;</span></span>
+<span id="cb26-4"><a href="#cb26-4" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>, <span class="at">new =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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+</div>
+</div>
+<div id="references" class="section level1 unnumbered">
+<h1 class="unnumbered">References</h1>
+<div id="refs" class="references csl-bib-body hanging-indent" entry-spacing="0">
+<div id="ref-BehLombardo2014" class="csl-entry">
+Beh, E, and Rosaria Lombardo. 2014. <span>“Correspondence
+Analysis.”</span> <em>Theory, Paractice and New Strategies</em>.
+</div>
+<div id="ref-Gabriel1971" class="csl-entry">
+Gabriel, K. R. 1971. <span>“The Biplot Graphic Display of Matrices with
+Application to Principal Component Analysis.”</span>
+<em>Biometrika</em>, 453–67.
+</div>
+<div id="ref-UB2011" class="csl-entry">
+Gower, J. C., S. Lubbe, and N. J. le Roux. 2011. <em>Understanding
+Biplots.</em> Wiley.
+</div>
+<div id="ref-Greenacre2017" class="csl-entry">
+Greenacre, M. J. 2017. <em>Correspondence Analysis in Practice.</em> CRC
+press.
+</div>
+</div>
+</div>
+
+
+
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+
+<body>
+
+
+
+
+<h1 class="title toc-ignore">MDS</h1>
+
+
+<div id="TOC">
+<ul>
+<li><a href="#what-is-mds" id="toc-what-is-mds"><span class="toc-section-number">1</span> What is MDS</a></li>
+<li><a href="#regression-biplot" id="toc-regression-biplot"><span class="toc-section-number">2</span> Regression biplot</a></li>
+<li><a href="#principal-coordinate-analysis-pco-biplots" id="toc-principal-coordinate-analysis-pco-biplots"><span class="toc-section-number">3</span> Principal Coordinate Analysis (PCO)
+biplots</a></li>
+<li><a href="#references" id="toc-references">References</a></li>
+</ul>
+</div>
+
+<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" tabindex="-1"></a><span class="fu">library</span>(biplotEZ)</span>
+<span id="cb1-2"><a href="#cb1-2" tabindex="-1"></a><span class="co">#&gt; Welcome to biplotEZ! </span></span>
+<span id="cb1-3"><a href="#cb1-3" tabindex="-1"></a><span class="co">#&gt; This package is used to construct biplots </span></span>
+<span id="cb1-4"><a href="#cb1-4" tabindex="-1"></a><span class="co">#&gt; Run ?biplot or vignette() for more information</span></span>
+<span id="cb1-5"><a href="#cb1-5" tabindex="-1"></a><span class="co">#&gt; </span></span>
+<span id="cb1-6"><a href="#cb1-6" tabindex="-1"></a><span class="co">#&gt; Attaching package: &#39;biplotEZ&#39;</span></span>
+<span id="cb1-7"><a href="#cb1-7" tabindex="-1"></a><span class="co">#&gt; The following object is masked from &#39;package:stats&#39;:</span></span>
+<span id="cb1-8"><a href="#cb1-8" tabindex="-1"></a><span class="co">#&gt; </span></span>
+<span id="cb1-9"><a href="#cb1-9" tabindex="-1"></a><span class="co">#&gt;     biplot</span></span></code></pre></div>
+<p>This vignette deals with biplots based on Multidimensional scaling
+(MDS).</p>
+<div id="what-is-mds" class="section level1" number="1">
+<h1><span class="header-section-number">1</span> What is MDS</h1>
+<p>In general, multidimensional scaling deals with constructing a low
+dimensional map of <span class="math inline">\(n\)</span> samples such
+that the Euclidean distances between the samples match a given set of
+dissimilarities <span class="math inline">\(\mathbf{\Delta}:n \times
+n\)</span> as closely as possible. Here the focus is on Principal
+Coordinate Analysis (PCO), an approach based on the singular value
+decomposition of a matrix. However, the regression biplot provides a
+general structure for fitting any 2D map of samples with biplot
+axes.</p>
+</div>
+<div id="regression-biplot" class="section level1" number="2">
+<h1><span class="header-section-number">2</span> Regression biplot</h1>
+<p>The function <code>regress</code> accepts as arguments an object of
+class <code>biplot</code>. The call to the function <code>biplot</code>
+should contain the data set that will be used to construct the biplot
+axes. The second argument <code>Z</code> contains the coordinates of the
+samples in the MDS map. By default linear regression axes will be fitted
+to the plot. If <span class="math inline">\(\mathbf{X}\)</span> denote
+the data matrix, the directions of the biplot axes are found by solving
+the regression equation</p>
+<p><span class="math display">\[
+\mathbf{X} = \mathbf{ZH}&#39; + \mathbf{E}.
+\]</span> The matrix <span class="math inline">\(\mathbf{H}&#39;=(\mathbf{Z&#39;Z})^{-1}\mathbf{Z&#39;X}\)</span>
+and calibration of the axes proceed analogous to equation (2) in the
+biplotEZ vignette. The coordinates of the marker <span class="math inline">\(/mu\)</span> on biplot axis <span class="math inline">\(j\)</span> is given as follows</p>
+<p><span class="math display">\[
+p_{\mu}
+=  \frac{\mu}{\mathbf{h}_{(j)}&#39;\mathbf{h}_{(j)}}\mathbf{h}_{(j)}.
+\]</span></p>
+<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" tabindex="-1"></a><span class="fu">biplot</span>(rock) <span class="sc">|&gt;</span> </span>
+<span id="cb2-2"><a href="#cb2-2" tabindex="-1"></a>  <span class="fu">regress</span>(<span class="at">Z =</span> MASS<span class="sc">::</span><span class="fu">sammon</span>(<span class="fu">dist</span>(<span class="fu">scale</span>(rock), <span class="at">method=</span><span class="st">&quot;manhattan&quot;</span>))<span class="sc">$</span>points) <span class="sc">|&gt;</span> </span>
+<span id="cb2-3"><a href="#cb2-3" tabindex="-1"></a>  <span class="fu">plot</span>()</span>
+<span id="cb2-4"><a href="#cb2-4" tabindex="-1"></a><span class="co">#&gt; Initial stress        : 0.02554</span></span>
+<span id="cb2-5"><a href="#cb2-5" tabindex="-1"></a><span class="co">#&gt; stress after  10 iters: 0.01094, magic = 0.500</span></span>
+<span id="cb2-6"><a href="#cb2-6" tabindex="-1"></a><span class="co">#&gt; stress after  20 iters: 0.01080, magic = 0.500</span></span>
+<span id="cb2-7"><a href="#cb2-7" tabindex="-1"></a><span class="co">#&gt; stress after  30 iters: 0.01078, magic = 0.500</span></span></code></pre></div>
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" /><!-- --></p>
+<p>More flexibility is provided by approximating the biplot axes using
+B-splines. A calibrated trajectory represented in a matrix <span class="math inline">\(\mathbf{H}:m \times 2\)</span> snakes through the
+samples points <span class="math inline">\(\mathbf{Z}\)</span> such that
+the marker on the trajectory which is closest to a particular sample
+gives the predicted value of that sample for the particular variable. To
+retain smoothness of the trajectory <span class="math inline">\(\mathbf{H}\)</span>, B-splines are used.</p>
+<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" tabindex="-1"></a><span class="fu">biplot</span>(rock) <span class="sc">|&gt;</span> </span>
+<span id="cb3-2"><a href="#cb3-2" tabindex="-1"></a>  <span class="fu">regress</span>(<span class="at">Z =</span> MASS<span class="sc">::</span><span class="fu">sammon</span>(<span class="fu">dist</span>(<span class="fu">scale</span>(rock), <span class="at">method=</span><span class="st">&quot;manhattan&quot;</span>))<span class="sc">$</span>points,</span>
+<span id="cb3-3"><a href="#cb3-3" tabindex="-1"></a>          <span class="at">axes =</span> <span class="st">&quot;splines&quot;</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb3-4"><a href="#cb3-4" tabindex="-1"></a>  <span class="fu">plot</span>()</span>
+<span id="cb3-5"><a href="#cb3-5" tabindex="-1"></a><span class="co">#&gt; Initial stress        : 0.02554</span></span>
+<span id="cb3-6"><a href="#cb3-6" tabindex="-1"></a><span class="co">#&gt; stress after  10 iters: 0.01094, magic = 0.500</span></span>
+<span id="cb3-7"><a href="#cb3-7" tabindex="-1"></a><span class="co">#&gt; stress after  20 iters: 0.01080, magic = 0.500</span></span>
+<span id="cb3-8"><a href="#cb3-8" tabindex="-1"></a><span class="co">#&gt; stress after  30 iters: 0.01078, magic = 0.500</span></span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<pre><code>#&gt; Calculating spline axis for variable 1 
+#&gt; Calculating spline axis for variable 2 
+#&gt; Calculating spline axis for variable 3 
+#&gt; Calculating spline axis for variable 4</code></pre>
+</div>
+<div id="principal-coordinate-analysis-pco-biplots" class="section level1" number="3">
+<h1><span class="header-section-number">3</span> Principal Coordinate
+Analysis (PCO) biplots</h1>
+<p>Let <span class="math inline">\(\mathbf{\tilde\Delta}\)</span> be the
+<span class="math inline">\(n \times n\)</span> matrix containing the
+values <span class="math inline">\(-\frac{1}{2}\delta_{ij}^2\)</span>
+where <span class="math inline">\(\delta_{ij}\)</span> represent the
+dissimilarity between objects <span class="math inline">\(i\)</span> and
+<span class="math inline">\(j\)</span>. If it is possible to find a set
+of coordinates <span class="math inline">\(\mathbf{Y}:n\times m\)</span>
+where typically <span class="math inline">\(m = n-1\)</span> such that
+the Euclidean distances between the rows of <span class="math inline">\(\mathbf{Y}\)</span> exactly match the
+dissimilarities <span class="math inline">\(\delta_{ij}\)</span>, the
+dissimilarity is known as a Euclidean embeddable distance metric. <span class="citation">J. C. Gower (1982)</span> shows that if the distances
+<span class="math inline">\(\delta_{ij}\)</span> are Euclidean
+embeddable, then</p>
+<p><span class="math display">\[
+(\mathbf{I}-\mathbf{1s}&#39;)\mathbf{\tilde\Delta}
+(\mathbf{I}-\mathbf{s1}&#39;)
+\]</span></p>
+<p>is positive semi-definite.</p>
+<p>The Euclidean representation of the samples is obtained as <span class="math inline">\(\mathbf{Y=V\Lambda}^{\frac{1}{2}}\)</span> where
+<span class="math inline">\((\mathbf{I}-\mathbf{1s}&#39;)\mathbf{\tilde\Delta}
+(\mathbf{I}-\mathbf{s1}&#39;) = \mathbf{V \Lambda V&#39;}\)</span>.
+Since the coordinates in <span class="math inline">\(\mathbf{Y}\)</span>
+is already referred to their principal axes with <span class="math inline">\(\mathbf{Y&#39;Y=\Lambda}\)</span>, the
+representation of the samples in a 2D biplot is obtained from the first
+two columns of <span class="math inline">\(\mathbf{Y}\)</span>.</p>
+<p>In addition to the exact biplot axis representations discussed in
+<span class="citation">J. C. Gower, Lubbe, and Roux (2011)</span>
+approximate axes can be obtained. Linear axes are fitted with the
+regression method. The variables in the data matrix <span class="math inline">\(\mathbf{X}:n \times p\)</span> can be represented
+as biplot axes in the PCO biplot with the sample points <span class="math inline">\(\mathbf{Z=V\Lambda}^{\frac{1}{2}}\mathbf{J}_2\)</span>
+according to the regression method discussed in section 2 above.</p>
+<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" tabindex="-1"></a><span class="fu">biplot</span>(rock, <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCO</span>() <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>Using B-splines instead of linear regression provides the user with
+more flexibility. This is achieved by setting the argument
+<code>axes = &quot;splines&quot;</code>.</p>
+<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" tabindex="-1"></a><span class="fu">biplot</span>(rock, <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCO</span>(<span class="at">axes =</span> <span class="st">&quot;splines&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<pre><code>#&gt; Calculating spline axis for variable 1 
+#&gt; Calculating spline axis for variable 2 
+#&gt; Calculating spline axis for variable 3 
+#&gt; Calculating spline axis for variable 4</code></pre>
+<p>By default the distance metric used for the analysis is Euclidean
+distance. The user can also specify the distance matrix
+<code>Dmat</code> as an <span class="math inline">\(n \times n\)</span>
+matrix of a <code>dist</code> object. As illustration of a metric that
+is Euclidean embeddable, the Clark’s distance</p>
+<p><span class="math display">\[
+\delta_{ij}^2 =
+\sum_{k=1}^{p}\left(\frac{x_{ik}-x_{jk}}{x_{ik}+x_{jk}}\right)^2
+\]</span></p>
+<p>as defined by <span class="citation">John C. Gower and Ngouenet
+(2005)</span> is calculated below and used for constructing a PCO
+biplot. Note that the metric is only defined for strictly positive
+values, so that the data is scaled to values between <span class="math inline">\(1\)</span> and <span class="math inline">\(2\)</span>.</p>
+<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" tabindex="-1"></a>Clark.dist <span class="ot">&lt;-</span> <span class="cf">function</span>(X)</span>
+<span id="cb8-2"><a href="#cb8-2" tabindex="-1"></a>{</span>
+<span id="cb8-3"><a href="#cb8-3" tabindex="-1"></a>  n <span class="ot">&lt;-</span> <span class="fu">nrow</span>(X)</span>
+<span id="cb8-4"><a href="#cb8-4" tabindex="-1"></a>  p <span class="ot">&lt;-</span> <span class="fu">ncol</span>(X)</span>
+<span id="cb8-5"><a href="#cb8-5" tabindex="-1"></a>  Dmat <span class="ot">&lt;-</span> <span class="fu">matrix</span> (<span class="dv">0</span>, <span class="at">nrow=</span>n, <span class="at">ncol=</span>n)</span>
+<span id="cb8-6"><a href="#cb8-6" tabindex="-1"></a>  <span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span>(n<span class="dv">-1</span>))</span>
+<span id="cb8-7"><a href="#cb8-7" tabindex="-1"></a>    <span class="cf">for</span> (j <span class="cf">in</span> (i<span class="sc">+</span><span class="dv">1</span>)<span class="sc">:</span>n)</span>
+<span id="cb8-8"><a href="#cb8-8" tabindex="-1"></a>      Dmat[i,j] <span class="ot">&lt;-</span> <span class="fu">sum</span>(((X[i,] <span class="sc">-</span> X[j,])<span class="sc">/</span>(X[i,] <span class="sc">+</span> X[j,]))<span class="sc">^</span><span class="dv">2</span>)</span>
+<span id="cb8-9"><a href="#cb8-9" tabindex="-1"></a>  <span class="fu">sqrt</span>(Dmat <span class="sc">+</span> <span class="fu">t</span>(Dmat))</span>
+<span id="cb8-10"><a href="#cb8-10" tabindex="-1"></a>}</span>
+<span id="cb8-11"><a href="#cb8-11" tabindex="-1"></a>my.data <span class="ot">&lt;-</span> <span class="fu">scale</span>(rock, <span class="at">center=</span><span class="fu">apply</span>(rock,<span class="dv">2</span>,min), <span class="at">scale=</span><span class="fu">diff</span>(<span class="fu">apply</span>(rock,<span class="dv">2</span>,range)))<span class="sc">+</span><span class="dv">1</span></span>
+<span id="cb8-12"><a href="#cb8-12" tabindex="-1"></a><span class="fu">biplot</span>(rock) <span class="sc">|&gt;</span> <span class="fu">PCO</span>(<span class="at">Dmat =</span> <span class="fu">Clark.dist</span> (rock), <span class="at">axes =</span> <span class="st">&quot;splines&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<pre><code>#&gt; Calculating spline axis for variable 1 
+#&gt; Calculating spline axis for variable 2 
+#&gt; Calculating spline axis for variable 3 
+#&gt; Calculating spline axis for variable 4</code></pre>
+<p>Alternatively, the user can specify a function which computes a
+distance matrix or <code>dist</code> object. The Manhattan distance is
+not Euclidean embeddable, but the square root of the distance is. The
+function <code>sqrtManhattan</code> is included as an example of a
+function computing a Euclidean embeddable <code>dist</code> object.</p>
+<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" tabindex="-1"></a>sqrtManhattan</span>
+<span id="cb10-2"><a href="#cb10-2" tabindex="-1"></a><span class="co">#&gt; function (X) </span></span>
+<span id="cb10-3"><a href="#cb10-3" tabindex="-1"></a><span class="co">#&gt; {</span></span>
+<span id="cb10-4"><a href="#cb10-4" tabindex="-1"></a><span class="co">#&gt;     sqrt(stats::dist(X, method = &quot;manhattan&quot;))</span></span>
+<span id="cb10-5"><a href="#cb10-5" tabindex="-1"></a><span class="co">#&gt; }</span></span>
+<span id="cb10-6"><a href="#cb10-6" tabindex="-1"></a><span class="co">#&gt; &lt;bytecode: 0x000001927bb99b60&gt;</span></span>
+<span id="cb10-7"><a href="#cb10-7" tabindex="-1"></a><span class="co">#&gt; &lt;environment: namespace:biplotEZ&gt;</span></span>
+<span id="cb10-8"><a href="#cb10-8" tabindex="-1"></a><span class="fu">biplot</span>(rock, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCO</span>(<span class="at">dist.func =</span> sqrtManhattan) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+</div>
+<div id="references" class="section level1 unnumbered">
+<h1 class="unnumbered">References</h1>
+<div id="refs" class="references csl-bib-body hanging-indent" entry-spacing="0">
+<div id="ref-Gower1982" class="csl-entry">
+Gower, J. C. 1982. <span>“Euclidean Distance Geometry.”</span>
+<em>Mathematical Scientist</em>, 1–14.
+</div>
+<div id="ref-UB2011" class="csl-entry">
+Gower, J. C., S. Lubbe, and N. J. le Roux. 2011. <em>Understanding
+Biplots.</em> Wiley.
+</div>
+<div id="ref-GowerRoger2005" class="csl-entry">
+Gower, John C, and Roger F Ngouenet. 2005. <span>“Nonlinearity Effects
+in Multidimensional Scaling.”</span> <em>Journal of Multivariate
+Analysis</em> 94 (2): 344–65.
+</div>
+</div>
+</div>
+
+
+
+<!-- code folding -->
+
+
+<!-- dynamically load mathjax for compatibility with self-contained -->
+<script>
+  (function () {
+    var script = document.createElement("script");
+    script.type = "text/javascript";
+    script.src  = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
+    document.getElementsByTagName("head")[0].appendChild(script);
+  })();
+</script>
+
+</body>
+</html>
diff --git a/vignettes/biplotEZ.Rmd b/vignettes/biplotEZ.Rmd
index d00fb4a..e223402 100644
--- a/vignettes/biplotEZ.Rmd
+++ b/vignettes/biplotEZ.Rmd
@@ -26,6 +26,16 @@ library(biplotEZ)
 
 The package \pkg{biplotEZ} provides users with an *EZ*-to-use way of constructing multi-dimensional scatter plots of their data. The simplest form of a biplot is the principal component analysis (PCA) biplot which will be used for illustration in this vignette.
 
+Read more ...
+
+* `vignette("Biplots_in_1D")` for 1-dimensional biplots
+* `vignette("Biplots_in_3D")` for 3-dimensional biplots
+* `vignette("biplotEZ_enhancements")` for alpha-bags, ellipses, densities, interpolation, prediction, reflection, rotation, zoom and axes translation
+* `vignette("Class_sepeartion")` for grouped data
+* `vignette("CA_in_biplotEZ")` for correspondence analysis
+* `vignette("MDS")` for multidimensional scaling biplots
+
+
 # What is a PCA biplot
 Consider a data matrix $\mathbf{X}^{*}:n \times p$ containing data on $n$ objects and $p$ variables. To produce a 2D biplot, we need to optimally approximate $\mathbf{X} = (\mathbf{I}_n-\frac{1}{n}\mathbf{11}')\mathbf{X}^{*}$ (typically of rank $p$ with $p<n$) with a rank $2$ matrix. In terms of the least squares error, we want to
 
@@ -445,9 +455,9 @@ The overall quality of fit is therefore defined as
 
 $$
 quality = \frac{\|\hat{\mathbf{X}}\|^2}{\|\mathbf{X}\|^2} =
-\frac{tr(\mathbf{XX}')}{tr(\mathbf{\hat{X}\hat{X}'})} =
-\frac{tr(\mathbf{X'X})}{tr(\mathbf{\hat{X}'\hat{X}})} =
-\frac{tr(\mathbf{VD}^2\mathbf{V'})}{tr(\mathbf{VD}^2\mathbf{JV'})}.
+\frac{tr(\mathbf{\hat{X}\hat{X}'})}{tr(\mathbf{XX}')} =
+\frac{tr(\mathbf{\hat{X}'\hat{X}})}{tr(\mathbf{X'X})} =
+\frac{tr(\mathbf{VD}^2\mathbf{JV'})}{tr(\mathbf{VD}^2\mathbf{V'})}.
 $$
 In *biplotEZ* the overall quality is displayed as a percentage:
 
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+<body>
+
+
+
+
+<h1 class="title toc-ignore">biplotEZ</h1>
+
+
+<div id="TOC">
+<ul>
+<li><a href="#what-is-a-pca-biplot" id="toc-what-is-a-pca-biplot"><span class="toc-section-number">1</span> What is a PCA biplot</a></li>
+<li><a href="#the-function-biplot" id="toc-the-function-biplot"><span class="toc-section-number">2</span> The function
+<code>biplot()</code></a>
+<ul>
+<li><a href="#using-biplot-with-princomp-or-prcomp" id="toc-using-biplot-with-princomp-or-prcomp"><span class="toc-section-number">2.1</span> Using <code>biplot()</code> with
+<code>princomp()</code> or <code>prcomp()</code></a></li>
+</ul></li>
+<li><a href="#the-functions-pca-plot-and-legend.type" id="toc-the-functions-pca-plot-and-legend.type"><span class="toc-section-number">3</span> The functions <code>PCA()</code>,
+<code>plot()</code> and <code>legend.type()</code></a></li>
+<li><a href="#the-function-samples" id="toc-the-function-samples"><span class="toc-section-number">4</span> The function
+<code>samples()</code></a></li>
+<li><a href="#the-function-means" id="toc-the-function-means"><span class="toc-section-number">5</span> The function
+<code>means()</code></a></li>
+<li><a href="#the-function-axes" id="toc-the-function-axes"><span class="toc-section-number">6</span> The function
+<code>axes()</code></a></li>
+<li><a href="#the-functions-fit.measures-and-summary" id="toc-the-functions-fit.measures-and-summary"><span class="toc-section-number">7</span> The functions
+<code>fit.measures()</code> and <code>summary()</code></a>
+<ul>
+<li><a href="#quality-of-approximation" id="toc-quality-of-approximation"><span class="toc-section-number">7.1</span> Quality of approximation</a></li>
+<li><a href="#adequacy-of-representation-of-the-variables" id="toc-adequacy-of-representation-of-the-variables"><span class="toc-section-number">7.2</span> Adequacy of representation of the
+variables</a></li>
+<li><a href="#predictivities" id="toc-predictivities"><span class="toc-section-number">7.3</span> Predictivities</a>
+<ul>
+<li><a href="#axis-predictivity" id="toc-axis-predictivity"><span class="toc-section-number">7.3.1</span> Axis predictivity</a></li>
+<li><a href="#sample-predictivity" id="toc-sample-predictivity"><span class="toc-section-number">7.3.2</span> Sample predictivity</a></li>
+<li><a href="#axes-represented-as-vectors" id="toc-axes-represented-as-vectors"><span class="toc-section-number">7.3.3</span> Axes represented as
+vectors</a></li>
+</ul></li>
+</ul></li>
+<li><a href="#references" id="toc-references">References</a></li>
+</ul>
+</div>
+
+<p>The package provides users with an <em>EZ</em>-to-use way of
+constructing multi-dimensional scatter plots of their data. The simplest
+form of a biplot is the principal component analysis (PCA) biplot which
+will be used for illustration in this vignette.</p>
+<p>Read more …</p>
+<ul>
+<li><code>vignette(&quot;Biplots_in_1D&quot;)</code> for 1-dimensional
+biplots</li>
+<li><code>vignette(&quot;Biplots_in_3D&quot;)</code> for 3-dimensional
+biplots</li>
+<li><code>vignette(&quot;biplotEZ_enhancements&quot;)</code> for alpha-bags,
+ellipses, densities, interpolation, prediction, reflection, rotation,
+zoom and axes translation</li>
+<li><code>vignette(&quot;Class_sepeartion&quot;)</code> for grouped data</li>
+<li><code>vignette(&quot;CA_in_biplotEZ&quot;)</code> for correspondence
+analysis</li>
+<li><code>vignette(&quot;MDS&quot;)</code> for multidimensional scaling
+biplots</li>
+</ul>
+<div id="what-is-a-pca-biplot" class="section level1" number="1">
+<h1><span class="header-section-number">1</span> What is a PCA
+biplot</h1>
+<p>Consider a data matrix <span class="math inline">\(\mathbf{X}^{*}:n
+\times p\)</span> containing data on <span class="math inline">\(n\)</span> objects and <span class="math inline">\(p\)</span> variables. To produce a 2D biplot, we
+need to optimally approximate <span class="math inline">\(\mathbf{X} =
+(\mathbf{I}_n-\frac{1}{n}\mathbf{11}&#39;)\mathbf{X}^{*}\)</span>
+(typically of rank <span class="math inline">\(p\)</span> with <span class="math inline">\(p&lt;n\)</span>) with a rank <span class="math inline">\(2\)</span> matrix. In terms of the least squares
+error, we want to</p>
+<p><span class="math display">\[
+min \| \hat{\mathbf{X}}-\mathbf{X} \|^2
+\]</span> where <span class="math inline">\(rank(\hat{\mathbf{X}})=2\)</span>. It was shown by
+<span class="citation">Eckart and Young (1936)</span> that if the
+singular value decomposition of <span class="math inline">\(\mathbf{X} =
+\mathbf{UDV&#39;}\)</span> then <span class="math display">\[
+\hat{\mathbf{X}} = \mathbf{UJDJV&#39;}
+\]</span> with <span class="math display">\[
+\mathbf{J} = \begin{bmatrix}
+              \mathbf{I}_2 &amp; \mathbf{0}\\
+              \mathbf{0} &amp; \mathbf{0}
+             \end{bmatrix}
+\]</span> essentially selecting only the first two columns of <span class="math inline">\(\mathbf{U}\)</span>, the diagonal matrix of the
+first (largest) two singular values and the first two rows of <span class="math inline">\(\mathbf{V}&#39;\)</span>. Define <span class="math display">\[
+\mathbf{J}_2 = \begin{bmatrix}
+                \mathbf{I}_2\\
+                \mathbf{0}
+               \end{bmatrix}
+\]</span> then <span class="math inline">\(\mathbf{J}_2\mathbf{J}_2&#39;
+= \mathbf{J}\)</span> and we can write <span class="math inline">\(\hat{\mathbf{X}} =
+(\mathbf{UDJ}_2)(\mathbf{VJ}_2)&#39;\)</span>.</p>
+<p><span class="citation">Gabriel (1971)</span> shows that any rank
+<span class="math inline">\(2\)</span> matrix can be written as <span class="math display">\[\begin{equation}
+  \hat{\mathbf{X}} = \mathbf{G} \mathbf{H}&#39; \tag{1}
+\end{equation}\]</span> where <span class="math inline">\(\mathbf{G}:n
+\times 2\)</span> and <span class="math inline">\(\mathbf{H}:p \times
+2\)</span>.The <span class="math inline">\(n\)</span> rows of <span class="math inline">\(\mathbf{G}\)</span> provide the <span class="math inline">\(n\)</span> pairs of 2D coordinates representing
+the rows of <span class="math inline">\(\hat{\mathbf{X}}\)</span> and
+the <span class="math inline">\(p\)</span> rows of <span class="math inline">\(\mathbf{H}\)</span> provide the <span class="math inline">\(p\)</span> pairs of 2D coordinates representing
+the columns of <span class="math inline">\(\hat{\mathbf{X}}\)</span>.
+Since <span class="math inline">\(\hat{\mathbf{X}} =
+(\mathbf{UDJ}_2)(\mathbf{VJ}_2)&#39;\)</span>, by setting <span class="math inline">\(\mathbf{G}=\mathbf{UDJ}_2\)</span> and <span class="math inline">\(\mathbf{H}=\mathbf{VJ}_2\)</span> we obtains the
+best least squares approximation of <span class="math inline">\(\mathbf{X}\)</span>. <span class="citation">Gabriel (1971)</span> further shows that the
+approximation of distances between the rows are optimal, while the
+approximation of correlations by the cosines between the angles of the
+rows of <span class="math inline">\(\mathbf{H}\)</span> is
+sub-optimal.</p>
+<p>The rows of <span class="math inline">\(\mathbf{G}\)</span> is
+plotted as points, representing the samples. The rows of <span class="math inline">\(\mathbf{H}\)</span> provide the directions of the
+axes for the variables. Since we have <span class="math display">\[
+x^{*}_{ij}-\bar{x}_j = x_{ij} \approx \hat{x}_{ij} =
+\mathbf{g}_{(i)}&#39;\mathbf{h}_{(j)}
+\]</span> all the values that will predict <span class="math inline">\(\mu\)</span> for variable <span class="math inline">\(j\)</span> is of the form <span class="math display">\[
+\mu = \mathbf{g}&#39;_{\mu}\mathbf{h}_{(j)}
+\]</span> which defines a straight line orthogonal to <span class="math inline">\(\mathbf{h}_{(j)}\)</span> in the biplot space (see
+the dotted red line in Figure 1(a)). To find the intersection of this
+prediction line with <span class="math inline">\(\mathbf{h}_{(j)}\)</span> we note that <span class="math display">\[
+\mathbf{g}&#39;_{(i)}\mathbf{h}_{(j)} = \| \mathbf{g}_{(i)} \| \|
+\mathbf{h}_{(j)} \| cos(\mathbf{g}_{(i)},\mathbf{h}_{(j)}) =
+\| \mathbf{p} \| \| \mathbf{h}_{(j)} \|
+\]</span> where <span class="math inline">\(\mathbf{p}\)</span> is the
+length of the orthogonal projection of <span class="math inline">\(\mathbf{g}_{(i)}\)</span> on <span class="math inline">\(\mathbf{h}_{(j)}\)</span>. This is illustrated in
+Figure 1(b) with triangle ABC: <span class="math inline">\(cos(\theta) =
+\frac{AC}{AB}\)</span> or <span class="math inline">\(AC = AB
+cos(\theta)\)</span> The length of <span class="math inline">\(AC\)</span>, written as <span class="math inline">\(\| \mathbf{p} \|\)</span> is equal to the cosine
+times the length of <span class="math inline">\(AB\)</span>, i.e. <span class="math inline">\(cos(\mathbf{g}_{(i)},\mathbf{h}_{(j)}) \|
+\mathbf{g}_{(i)} \|\)</span>.</p>
+<div class="figure">
+<img role="img" aria-label="Figure 1: Calibration of biplot axes." 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" alt="Figure 1: Calibration of biplot axes." width="100%" />
+<p class="caption">
+Figure 1: Calibration of biplot axes.
+</p>
+</div>
+<p>Since <span class="math inline">\(\mathbf{p}\)</span> is along <span class="math inline">\(\mathbf{h}_{(j)}\)</span> we can write <span class="math inline">\(\mathbf{p} = c\mathbf{h}_{(j)}\)</span> and all
+points on the prediction line <span class="math inline">\(\mu =
+\mathbf{g}&#39;_{\mu}\mathbf{h}_{(j)}\)</span> project on the same point
+<span class="math inline">\(c_{\mu}\mathbf{h}_{(j)}\)</span>. We solve
+for <span class="math inline">\(c_{\mu}\)</span> from <span class="math display">\[
+\mu = \mathbf{g}&#39;_{\mu}\mathbf{h}_{(j)}=\| \mathbf{p} \| \|
+\mathbf{h}_{(j)} \| =
+\| c_{\mu}\mathbf{h}_{(j)} \| \| \mathbf{h}_{(j)} \|
+\]</span></p>
+<p><span class="math display">\[
+c_{\mu} = \frac{\mu}{\mathbf{h}_{(j)}&#39;\mathbf{h}_{(j)}}.
+\]</span> If we select ‘nice’ scale markers <span class="math inline">\(\tau_{1}, \tau_{2}, \cdots \tau_{k}\)</span> for
+variable <span class="math inline">\(j\)</span>, then <span class="math inline">\(\tau_{h}-\bar{x}_j = \mu_{h}\)</span> and
+positions of these scale markers on <span class="math inline">\(\mathbf{h}_{(j)}\)</span> are given by <span class="math inline">\(p_{\mu_{1}}, p_{\mu_{2}}, \cdots
+p_{\mu_{k}}\)</span> with <span class="math display">\[
+p_{\mu_h} = c_{\mu_h}\mathbf{h}_{(j)}
+=  \frac{\mu_h}{\mathbf{h}_{(j)}&#39;\mathbf{h}_{(j)}}\mathbf{h}_{(j)}
+\tag{2}
+\]</span> To obtain a PCA biplot of the <span class="math inline">\(48\times 4\)</span> rock data in <code>R</code> we
+call</p>
+<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" tabindex="-1"></a><span class="fu">biplot</span>(rock, <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+</div>
+<div id="the-function-biplot" class="section level1" number="2">
+<h1><span class="header-section-number">2</span> The function
+<code>biplot()</code></h1>
+<p>The function <code>biplot()</code> takes a data set (usually) and
+outputs an object of class <code>biplot</code>.</p>
+<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" tabindex="-1"></a>state.data <span class="ot">&lt;-</span> <span class="fu">data.frame</span> (state.region, state.x77)</span>
+<span id="cb2-2"><a href="#cb2-2" tabindex="-1"></a><span class="fu">biplot</span>(state.data)</span>
+<span id="cb2-3"><a href="#cb2-3" tabindex="-1"></a><span class="co">#&gt; Object of class biplot, based on 50 samples and 9 variables.</span></span>
+<span id="cb2-4"><a href="#cb2-4" tabindex="-1"></a><span class="co">#&gt; 8 numeric variables.</span></span>
+<span id="cb2-5"><a href="#cb2-5" tabindex="-1"></a><span class="co">#&gt; 1 categorical variable.</span></span></code></pre></div>
+<p>Apart from specifying a data set, we can specify a single variable
+for classification purposes.</p>
+<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">classes=</span>state.region)</span>
+<span id="cb3-2"><a href="#cb3-2" tabindex="-1"></a><span class="co">#&gt; Object of class biplot, based on 50 samples and 8 variables.</span></span>
+<span id="cb3-3"><a href="#cb3-3" tabindex="-1"></a><span class="co">#&gt; 8 numeric variables.</span></span>
+<span id="cb3-4"><a href="#cb3-4" tabindex="-1"></a><span class="co">#&gt; 4 classes: Northeast South North Central West</span></span></code></pre></div>
+<p>If we want to use the variable <code>state.region</code> for
+formatting, say colour coding the samples according to region, we
+instead specify <code>grouping.aes</code> to indicate it pertains to the
+aesthetics, rather than data structure. We can include or exclude the
+aestethics variable from the data set.</p>
+<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">group.aes=</span>state.region)</span>
+<span id="cb4-2"><a href="#cb4-2" tabindex="-1"></a><span class="co">#&gt; Object of class biplot, based on 50 samples and 8 variables.</span></span>
+<span id="cb4-3"><a href="#cb4-3" tabindex="-1"></a><span class="co">#&gt; 8 numeric variables.</span></span></code></pre></div>
+<p>Next, we look at centring and scaling of the numeric data matrix. As
+we saw in section 1 above, PCA is computed from the centred data matrix.
+For most methods, centring is either required or has no effect on the
+methodology, therefore the default is <code>center = TRUE</code>. Since
+centring is usually assumed, you will get a warning message, should you
+explicitly choose to set <code>center = FALSE</code>. The default for
+<code>scaled</code> is <code>FALSE</code>, but often when variables are
+in different units of measurement, it is advisable to divide each
+variable by its standard deviation which is accomplished by setting
+`scale = TRUE’.</p>
+<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" tabindex="-1"></a><span class="fu">biplot</span>(state.data)                 <span class="co"># centred, but no scaling</span></span>
+<span id="cb5-2"><a href="#cb5-2" tabindex="-1"></a><span class="co">#&gt; Object of class biplot, based on 50 samples and 9 variables.</span></span>
+<span id="cb5-3"><a href="#cb5-3" tabindex="-1"></a><span class="co">#&gt; 8 numeric variables.</span></span>
+<span id="cb5-4"><a href="#cb5-4" tabindex="-1"></a><span class="co">#&gt; 1 categorical variable.</span></span>
+<span id="cb5-5"><a href="#cb5-5" tabindex="-1"></a><span class="fu">biplot</span>(state.data, <span class="at">scale =</span> <span class="cn">TRUE</span>)   <span class="co"># centered and scaled</span></span>
+<span id="cb5-6"><a href="#cb5-6" tabindex="-1"></a><span class="co">#&gt; Object of class biplot, based on 50 samples and 9 variables.</span></span>
+<span id="cb5-7"><a href="#cb5-7" tabindex="-1"></a><span class="co">#&gt; 8 numeric variables.</span></span>
+<span id="cb5-8"><a href="#cb5-8" tabindex="-1"></a><span class="co">#&gt; 1 categorical variable.</span></span>
+<span id="cb5-9"><a href="#cb5-9" tabindex="-1"></a><span class="fu">biplot</span>(state.data, <span class="at">center =</span> <span class="cn">FALSE</span>) <span class="co"># no centring (usually not recommended) or scaling</span></span>
+<span id="cb5-10"><a href="#cb5-10" tabindex="-1"></a><span class="co">#&gt; Object of class biplot, based on 50 samples and 9 variables.</span></span>
+<span id="cb5-11"><a href="#cb5-11" tabindex="-1"></a><span class="co">#&gt; 8 numeric variables.</span></span>
+<span id="cb5-12"><a href="#cb5-12" tabindex="-1"></a><span class="co">#&gt; 1 categorical variable.</span></span></code></pre></div>
+<p>The final optional argument to the function is specifying a title for
+your plot. We notice in the output above, that centring and / or scaling
+has no effect on the <code>print method</code>. It does however have an
+effect on the components of the object of class <code>biplot</code> in
+the output.</p>
+<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" tabindex="-1"></a>out <span class="ot">&lt;-</span> <span class="fu">biplot</span>(state.data)                 <span class="co"># centred, but no scaling</span></span>
+<span id="cb6-2"><a href="#cb6-2" tabindex="-1"></a>out<span class="sc">$</span>center</span>
+<span id="cb6-3"><a href="#cb6-3" tabindex="-1"></a><span class="co">#&gt; [1] TRUE</span></span>
+<span id="cb6-4"><a href="#cb6-4" tabindex="-1"></a>out<span class="sc">$</span>scaled</span>
+<span id="cb6-5"><a href="#cb6-5" tabindex="-1"></a><span class="co">#&gt; [1] FALSE</span></span>
+<span id="cb6-6"><a href="#cb6-6" tabindex="-1"></a>out<span class="sc">$</span>means</span>
+<span id="cb6-7"><a href="#cb6-7" tabindex="-1"></a><span class="co">#&gt; Population     Income Illiteracy   Life.Exp     Murder    HS.Grad      Frost </span></span>
+<span id="cb6-8"><a href="#cb6-8" tabindex="-1"></a><span class="co">#&gt;  4246.4200  4435.8000     1.1700    70.8786     7.3780    53.1080   104.4600 </span></span>
+<span id="cb6-9"><a href="#cb6-9" tabindex="-1"></a><span class="co">#&gt;       Area </span></span>
+<span id="cb6-10"><a href="#cb6-10" tabindex="-1"></a><span class="co">#&gt; 70735.8800</span></span>
+<span id="cb6-11"><a href="#cb6-11" tabindex="-1"></a>out<span class="sc">$</span>sd</span>
+<span id="cb6-12"><a href="#cb6-12" tabindex="-1"></a><span class="co">#&gt; [1] 1 1 1 1 1 1 1 1</span></span>
+<span id="cb6-13"><a href="#cb6-13" tabindex="-1"></a>out <span class="ot">&lt;-</span> <span class="fu">biplot</span>(state.data, <span class="at">scale =</span> <span class="cn">TRUE</span>)   <span class="co"># centered and scaled</span></span>
+<span id="cb6-14"><a href="#cb6-14" tabindex="-1"></a>out<span class="sc">$</span>center</span>
+<span id="cb6-15"><a href="#cb6-15" tabindex="-1"></a><span class="co">#&gt; [1] TRUE</span></span>
+<span id="cb6-16"><a href="#cb6-16" tabindex="-1"></a>out<span class="sc">$</span>scaled</span>
+<span id="cb6-17"><a href="#cb6-17" tabindex="-1"></a><span class="co">#&gt; [1] TRUE</span></span>
+<span id="cb6-18"><a href="#cb6-18" tabindex="-1"></a>out<span class="sc">$</span>means</span>
+<span id="cb6-19"><a href="#cb6-19" tabindex="-1"></a><span class="co">#&gt; Population     Income Illiteracy   Life.Exp     Murder    HS.Grad      Frost </span></span>
+<span id="cb6-20"><a href="#cb6-20" tabindex="-1"></a><span class="co">#&gt;  4246.4200  4435.8000     1.1700    70.8786     7.3780    53.1080   104.4600 </span></span>
+<span id="cb6-21"><a href="#cb6-21" tabindex="-1"></a><span class="co">#&gt;       Area </span></span>
+<span id="cb6-22"><a href="#cb6-22" tabindex="-1"></a><span class="co">#&gt; 70735.8800</span></span>
+<span id="cb6-23"><a href="#cb6-23" tabindex="-1"></a>out<span class="sc">$</span>sd</span>
+<span id="cb6-24"><a href="#cb6-24" tabindex="-1"></a><span class="co">#&gt;   Population       Income   Illiteracy     Life.Exp       Murder      HS.Grad </span></span>
+<span id="cb6-25"><a href="#cb6-25" tabindex="-1"></a><span class="co">#&gt; 4.464491e+03 6.144699e+02 6.095331e-01 1.342394e+00 3.691540e+00 8.076998e+00 </span></span>
+<span id="cb6-26"><a href="#cb6-26" tabindex="-1"></a><span class="co">#&gt;        Frost         Area </span></span>
+<span id="cb6-27"><a href="#cb6-27" tabindex="-1"></a><span class="co">#&gt; 5.198085e+01 8.532730e+04</span></span>
+<span id="cb6-28"><a href="#cb6-28" tabindex="-1"></a>out <span class="ot">&lt;-</span> <span class="fu">biplot</span>(state.data, <span class="at">center =</span> <span class="cn">FALSE</span>) <span class="co"># no centring (usually not recommended) or scaling</span></span>
+<span id="cb6-29"><a href="#cb6-29" tabindex="-1"></a>out<span class="sc">$</span>center</span>
+<span id="cb6-30"><a href="#cb6-30" tabindex="-1"></a><span class="co">#&gt; [1] FALSE</span></span>
+<span id="cb6-31"><a href="#cb6-31" tabindex="-1"></a>out<span class="sc">$</span>scaled</span>
+<span id="cb6-32"><a href="#cb6-32" tabindex="-1"></a><span class="co">#&gt; [1] FALSE</span></span>
+<span id="cb6-33"><a href="#cb6-33" tabindex="-1"></a>out<span class="sc">$</span>means</span>
+<span id="cb6-34"><a href="#cb6-34" tabindex="-1"></a><span class="co">#&gt; [1] 0 0 0 0 0 0 0 0</span></span>
+<span id="cb6-35"><a href="#cb6-35" tabindex="-1"></a>out<span class="sc">$</span>sd</span>
+<span id="cb6-36"><a href="#cb6-36" tabindex="-1"></a><span class="co">#&gt; [1] 1 1 1 1 1 1 1 1</span></span></code></pre></div>
+<p>Note that the components <code>means</code> and <code>sd</code> only
+contain the sample means and sample sds when either/or
+<code>center</code> and <code>scaled</code> is <code>TRUE</code>. For
+values of <code>FALSE</code>, these components contain zeros for the
+<code>means</code> and/or ones for the <code>sd</code> to ensure back
+transformation will not have any affect.</p>
+<div id="using-biplot-with-princomp-or-prcomp" class="section level2" number="2.1">
+<h2><span class="header-section-number">2.1</span> Using
+<code>biplot()</code> with <code>princomp()</code> or
+<code>prcomp()</code></h2>
+<p>Should the user wish to construct a PCA biplot after performing
+principal component analysis via the built in functions in the
+<code>stats</code> package, the output from either of these functions
+can be piped into the biplot function, where the piping implies that the
+argument <code>data</code> now takes the value of an object of class
+<code>prcomp</code> or <code>princomp</code>.</p>
+<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" tabindex="-1"></a><span class="fu">princomp</span>(state.x77) <span class="sc">|&gt;</span> <span class="fu">biplot</span>()</span>
+<span id="cb7-2"><a href="#cb7-2" tabindex="-1"></a><span class="co">#&gt; Object of class biplot, based on 50 samples and 8 variables.</span></span>
+<span id="cb7-3"><a href="#cb7-3" tabindex="-1"></a><span class="co">#&gt; 8 numeric variables.</span></span>
+<span id="cb7-4"><a href="#cb7-4" tabindex="-1"></a>out <span class="ot">&lt;-</span> <span class="fu">prcomp</span>(state.x77, <span class="at">scale.=</span><span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">biplot</span>()</span>
+<span id="cb7-5"><a href="#cb7-5" tabindex="-1"></a><span class="fu">rbind</span> (<span class="fu">head</span>(out<span class="sc">$</span>raw.X,<span class="dv">3</span>),<span class="fu">tail</span>(out<span class="sc">$</span>raw.X,<span class="dv">3</span>))</span>
+<span id="cb7-6"><a href="#cb7-6" tabindex="-1"></a><span class="co">#&gt;               Population Income Illiteracy Life Exp Murder HS Grad Frost   Area</span></span>
+<span id="cb7-7"><a href="#cb7-7" tabindex="-1"></a><span class="co">#&gt; Alabama             3615   3624        2.1    69.05   15.1    41.3    20  50708</span></span>
+<span id="cb7-8"><a href="#cb7-8" tabindex="-1"></a><span class="co">#&gt; Alaska               365   6315        1.5    69.31   11.3    66.7   152 566432</span></span>
+<span id="cb7-9"><a href="#cb7-9" tabindex="-1"></a><span class="co">#&gt; Arizona             2212   4530        1.8    70.55    7.8    58.1    15 113417</span></span>
+<span id="cb7-10"><a href="#cb7-10" tabindex="-1"></a><span class="co">#&gt; West Virginia       1799   3617        1.4    69.48    6.7    41.6   100  24070</span></span>
+<span id="cb7-11"><a href="#cb7-11" tabindex="-1"></a><span class="co">#&gt; Wisconsin           4589   4468        0.7    72.48    3.0    54.5   149  54464</span></span>
+<span id="cb7-12"><a href="#cb7-12" tabindex="-1"></a><span class="co">#&gt; Wyoming              376   4566        0.6    70.29    6.9    62.9   173  97203</span></span>
+<span id="cb7-13"><a href="#cb7-13" tabindex="-1"></a><span class="fu">rbind</span> (<span class="fu">head</span>(out<span class="sc">$</span>X,<span class="dv">3</span>),<span class="fu">tail</span>(out<span class="sc">$</span>X,<span class="dv">3</span>))</span>
+<span id="cb7-14"><a href="#cb7-14" tabindex="-1"></a><span class="co">#&gt;                Population      Income Illiteracy   Life Exp     Murder</span></span>
+<span id="cb7-15"><a href="#cb7-15" tabindex="-1"></a><span class="co">#&gt; Alabama       -0.14143156 -1.32113867   1.525758 -1.3621937  2.0918101</span></span>
+<span id="cb7-16"><a href="#cb7-16" tabindex="-1"></a><span class="co">#&gt; Alaska        -0.86939802  3.05824562   0.541398 -1.1685098  1.0624293</span></span>
+<span id="cb7-17"><a href="#cb7-17" tabindex="-1"></a><span class="co">#&gt; Arizona       -0.45568908  0.15330286   1.033578 -0.2447866  0.1143154</span></span>
+<span id="cb7-18"><a href="#cb7-18" tabindex="-1"></a><span class="co">#&gt; West Virginia -0.54819682 -1.33253061   0.377338 -1.0418703 -0.1836632</span></span>
+<span id="cb7-19"><a href="#cb7-19" tabindex="-1"></a><span class="co">#&gt; Wisconsin      0.07673438  0.05240289  -0.771082  1.1929438 -1.1859550</span></span>
+<span id="cb7-20"><a href="#cb7-20" tabindex="-1"></a><span class="co">#&gt; Wyoming       -0.86693413  0.21188994  -0.935142 -0.4384705 -0.1294853</span></span>
+<span id="cb7-21"><a href="#cb7-21" tabindex="-1"></a><span class="co">#&gt;                  HS Grad       Frost       Area</span></span>
+<span id="cb7-22"><a href="#cb7-22" tabindex="-1"></a><span class="co">#&gt; Alabama       -1.4619293 -1.62482920 -0.2347183</span></span>
+<span id="cb7-23"><a href="#cb7-23" tabindex="-1"></a><span class="co">#&gt; Alaska         1.6828035  0.91456761  5.8093497</span></span>
+<span id="cb7-24"><a href="#cb7-24" tabindex="-1"></a><span class="co">#&gt; Arizona        0.6180514 -1.72101848  0.5002047</span></span>
+<span id="cb7-25"><a href="#cb7-25" tabindex="-1"></a><span class="co">#&gt; West Virginia -1.4247868 -0.08580083 -0.5469045</span></span>
+<span id="cb7-26"><a href="#cb7-26" tabindex="-1"></a><span class="co">#&gt; Wisconsin      0.1723413  0.85685405 -0.1906996</span></span>
+<span id="cb7-27"><a href="#cb7-27" tabindex="-1"></a><span class="co">#&gt; Wyoming        1.2123316  1.31856256  0.3101835</span></span>
+<span id="cb7-28"><a href="#cb7-28" tabindex="-1"></a>out<span class="sc">$</span>center</span>
+<span id="cb7-29"><a href="#cb7-29" tabindex="-1"></a><span class="co">#&gt; [1] TRUE</span></span>
+<span id="cb7-30"><a href="#cb7-30" tabindex="-1"></a>out<span class="sc">$</span>scaled</span>
+<span id="cb7-31"><a href="#cb7-31" tabindex="-1"></a><span class="co">#&gt; [1] TRUE</span></span>
+<span id="cb7-32"><a href="#cb7-32" tabindex="-1"></a>out<span class="sc">$</span>means</span>
+<span id="cb7-33"><a href="#cb7-33" tabindex="-1"></a><span class="co">#&gt; Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost </span></span>
+<span id="cb7-34"><a href="#cb7-34" tabindex="-1"></a><span class="co">#&gt;  4246.4200  4435.8000     1.1700    70.8786     7.3780    53.1080   104.4600 </span></span>
+<span id="cb7-35"><a href="#cb7-35" tabindex="-1"></a><span class="co">#&gt;       Area </span></span>
+<span id="cb7-36"><a href="#cb7-36" tabindex="-1"></a><span class="co">#&gt; 70735.8800</span></span>
+<span id="cb7-37"><a href="#cb7-37" tabindex="-1"></a>out<span class="sc">$</span>sd</span>
+<span id="cb7-38"><a href="#cb7-38" tabindex="-1"></a><span class="co">#&gt;   Population       Income   Illiteracy     Life Exp       Murder      HS Grad </span></span>
+<span id="cb7-39"><a href="#cb7-39" tabindex="-1"></a><span class="co">#&gt; 4.464491e+03 6.144699e+02 6.095331e-01 1.342394e+00 3.691540e+00 8.076998e+00 </span></span>
+<span id="cb7-40"><a href="#cb7-40" tabindex="-1"></a><span class="co">#&gt;        Frost         Area </span></span>
+<span id="cb7-41"><a href="#cb7-41" tabindex="-1"></a><span class="co">#&gt; 5.198085e+01 8.532730e+04</span></span></code></pre></div>
+</div>
+</div>
+<div id="the-functions-pca-plot-and-legend.type" class="section level1" number="3">
+<h1><span class="header-section-number">3</span> The functions
+<code>PCA()</code>, <code>plot()</code> and
+<code>legend.type()</code></h1>
+<p>The first argument to the function <code>PCA()</code> is an object of
+class <code>biplot</code>, i.e. the output of the <code>biplot()</code>
+function. By default we construct a 2D biplot (argument
+<code>dim.biplot = 2</code>) of the first two principal components
+(argument <code>e.vects = 1:2</code>). The <code>group.aes</code>
+argument, if not specified in the function <code>biplot()</code>, allows
+a grouping argument for the sample aesthetics. A PCA biplot of the
+<code>state.x77</code> data with colouring according to
+<code>state.region</code> is obtained as follows:</p>
+<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb8-2"><a href="#cb8-2" tabindex="-1"></a>  <span class="fu">PCA</span>(<span class="at">group.aes =</span> state.region) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>The output of <code>PCA()</code> is an object of class
+<code>PCA</code> which inherits from the class <code>biplot</code>. Four
+additional components are present in the <code>PCA</code> object. The
+matrix <code>Z</code> contains the coordinates of the sample points,
+while the matrix <code>Vr</code> contains the “coordinates” for the
+variables. In the notation of equation (1), Z=<span class="math inline">\(\mathbf{G}:n \times 2\)</span> and Vr=<span class="math inline">\(\mathbf{H}:p \times 2\)</span>. The component
+<code>Xhat</code> is the matrix <span class="math inline">\(\hat{\mathbf{X}}\)</span> on the left hand side of
+equation (1). The final component <code>ax.one.unit</code> contains as
+rows the expression in equation (2) with <span class="math inline">\(\mu_h=1\)</span>, in other words, one unit in the
+positive direction of the biplot axis.</p>
+<p>By piping the <code>PCA</code> class object (inheriting from class
+<code>biplot</code>) to the generic <code>plot()</code> function, the
+<code>plot.biplot()</code> function constructs the biplot on the
+graphical device. To add a legend to the biplot, we call</p>
+<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb9-2"><a href="#cb9-2" tabindex="-1"></a>  <span class="fu">PCA</span>(<span class="at">group.aes =</span> state.region) <span class="sc">|&gt;</span> </span>
+<span id="cb9-3"><a href="#cb9-3" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>It was mentioned in section 1 that the default choice <span class="math inline">\(\mathbf{G}=\mathbf{UDJ}_2\)</span> and <span class="math inline">\(\mathbf{H}=\mathbf{VJ}_2\)</span> provides an
+exact representation of the distances between the rows of <span class="math inline">\(\mathbf{\hat{X}}\)</span> which is an optimal
+approximation in the least squares sense of the distances between the
+rows of <span class="math inline">\(\mathbf{X}\)</span> (samples).
+Alternatively, the correlations between the variables (columns of <span class="math inline">\(\mathbf{X}\)</span>) can be optimally approximated
+by the cosines of the angles between the axes, leaving the approximation
+of the distances between the samples to be suboptimal. In this case
+<span class="math inline">\(\mathbf{G}=\mathbf{UJ}_2\)</span> and <span class="math inline">\(\mathbf{H}=\mathbf{VDJ}_2\)</span> and this biplot
+is obtained by setting the argument
+<code>correlation.biplot = TRUE</code>.</p>
+<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb10-2"><a href="#cb10-2" tabindex="-1"></a>  <span class="fu">PCA</span>(<span class="at">group.aes =</span> state.region, <span class="at">correlation.biplot =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb10-3"><a href="#cb10-3" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAqAAAAJACAMAAABlpiR1AAAC+lBMVEUAAAAAADoAAGYAAP8AOjoAOmYAOpAAZpAAZrYA/wAA//8onLE6AAA6ADo6OgA6Ojo6kNtmAABmADpmOgBmZmZmkJBmtrZmtv+QOgCQkGaQtpCQ2/+rl5uuoLOxs7OzrACzs7Ozs7Szs7azs7ezs7izs7qzs7yzs7+zs8Gzs8Wzs82ztLSztLiztMyztM2ztNGztOeztceztrazttezub+zurizvLyzvMezvNWzvr2zv82zwb2zwc2zwdqzwd2zxMWzxeezyM2zyM6zyOezzee0s7O0s7e0s7q0tLO0wP+0xf+1tbq1t7m1xt62ZgC2s8G2ure2xMi2x+e225C2//+3s7O3u824s7O4tra4udO4urO4vLO4v7O4wue40/K5s7O5s8S5ubO5ur+5vtq51/+6s826tbO7s7O7x768wb+8xbO83v+9wbO+s7O/s7O/tLO/x76/1N2/2ue/2vLBs7PBs7bBs8HBs83BuLjBwbPBwc3BwdrBxMHByLPBzdrBzefB09TB1NPB2trB2t3B2vLEubPEzsHFs7PFs7/Fs83HtrbHurPH5//Is7PIs7jIubnIzsHJyLPJ07zLtrPLt7PNs7PNs7jNs8HNs83NuLPNwbPNwcHNwdrNyLPNzcHNzc3NzefN1cTN2trN2ufN3c3N5+fN5/LN5//OuLPO59rPw7bU08HU5//U8v/VvLPVzbPX2sHavbjavrnawbPawb/awcHawc3azbPazdra2sHa2s3a59ra8ufa8v/bkDrb/7bb/9vb///dxbPd///e2sHe///ntbPnubPnxbPnxbjnyLnnzbPnzcHnzc3n2sHn583n8trn8v/n/97n/+fn//Ln///yzbjy07ny077y1Lry2r3y2sHy2s3y583y8try8t7y8ufy8vLy8v/y/+fy//Ly////tmb/trb/wrT/xrT/1wD/25D/3cH/3sH/583/59r/8tr/8uf/8vL//7b//7///8X//8j//8z//9H//9f//9v//+f///L///+ZQgFsAAAACXBIWXMAAA7DAAAOwwHHb6hkAAAgAElEQVR4nO2dB5gcyVmG17dgtIsPdAYswREK4wMhMDljEffIiHTknHMWJ7AMh7HIOQiJ47BJZkgmLTJgGJmMYYVtOJY0Jt1ZC+zhYfARb6afh65O0/1Xh6rqqu5/ur/3kbS7M91d3069qu6uru7aCgBgzFbfAQCoA4IC1kBQwBoIClgDQQFrIChgDQQFrIGggDUQFLAGggLWQFDAGggKWANBAWsgKGANBAWsgaCANRAUsAaCDoe5kJw97DuHUyDoYFhemfQdwQMQdDAsrw2r7YyBoMPh4HLfCTwAQQfD8gqOQQHoGAgKWANBh8NqP9zDn7vVdwy3QNDBsNqXJ0mzgRkKQQdD3M00tM4mCDoY0IIC3uAYFICugaCANRB0ICyvPYgrSQB0DQQdDOhmAoxJhooM7jQegg6GobWdMRAUsAaCDocZzuIBY5ZXp/O9YLbXdw63QNDBEB6Dxn/6DuIUCDoYVten4Z/FRQgKeBK6ORdiYHfOQVDAGggKWANBB0J2JQndTAB0BwQFrIGggwFPFgEbwAzdTIAzuJI0SjZnHMZ8E0IaAEF12IhxGMkx6MCeYgtBdRjmOIyNAILqMMxxGBsBBNViI8ZhRE8W4X0YYg4EHQzJs5kGZigEHQy47XjEhHvPcw9fnfYdo56o8UQLOkbCvefi0q0571vOhzmeCYLqEO43Q0GHtvfcCCCoDnELOrRnw24EEFSLjXg27EaENAWCDgY8Any8bMTRJ7qZxsvq+rTvCM2gBR0vmzFYHcegAHQNBAWsgaDazHjv4hcXBjdYWQJB9ZgLcWbad4g6VvuTYIgDViGoBmHjdGZ6wLt5kt1LG9HZYAgEbSbuWtwEQfd5Z7QBgmoge5kmELQXIKgmB8yPQYc52A6CGrDaH1jdbwQQFLAGggLWcBZ0ixGi7wAM6EeCXkrVg1M20XeAoPfPA4JSOGWDoBBUgVM2CApBFThlg6AQVIFTNggKQRU4ZYOgEFSBUzYICkEVWGVjYCgEZQarbBAUglJYZYOgEJTCKhsEhaAUVtkgKASlsMoGQSEohVU2CApBKayycRf0sdO33SO/nn/875B3jk4Fj95xqmnjR41LQFAKq2zsBN3e3s7/+NjprRPyqyKolLNZUA2FISiFVTZugm5vFw197PSr3H5nAEG7hFU2ZoJubxNDHzt94oZsQiNBj7a2tk6G1j3xdaOh8I9/4R2v84StLangjfidcLmt+IVHniC/kf8qxwY1xXcHKwkIrLJtgKBRKygFPdqSjeaJ8G/4Q9yCPu7O4Eby95EnhIaeD2WOfzglfT6FFtQCXtn6N7RJ0OBG6GMo6GOnZRt59Lg7H73jZLqLPynbylPR1+DotnsefeKd0Qvy+2h1CGoBr2y8BC05Bj0RSDNDQaNWMfbxVO4YNPwnlDZ+R65xtBU1tLGhENQCXtmYCaqexZ+I2sZM0FA5VdDk/sxT8lj0to+Sy4Vn/7GoENQYXtm4CUqIBA3On9RoQYOkEU1a0nAteTQAQY3hlW0jBH3k9tcoHIMSQTMNo0PPo63kp/w7lsV7g5cERXhl2whBg/NbhbP4yMuTmaDRibtsMGXj+egdWyeDqE1Nz6daFO8NXhIU4ZVtMwSNepayftCoWTwv+0ETQaN+UNl6hl8fd2doarRoZC36QY3hlY25oEMtnpcERXhlg6AjKlUPXtkg6IhK1YNXNgg6olL14JUNgo6oVD2YZevdUAjKDGbZIOh4StWDWTbugj56R9LHqaJ310e74j3BTIICzLIxFzS+cHk+vdqeR29QfbvifcFMggLMsjETdGdnp/Dz+ehKUnJBqQgE9QOzbLwE3dkpGlowM3+p89Hodo/cXR9Oiu8MZhIUYJaNlaA7O9TQo60T628Lg0VOFe76cFJ8dzCToACzbMwFjW5/i86RlOF2+bs+3BTfHcwkKMAsG3dBg2h4fHojXH7Acn5IqJviu4OZBAWYZWMlqHIMmnL+tnuUWz4gqB+YZeMlKD2LT/feR/FoZLSgHcAsGzNBCelZ/NFt9xRvO05EhaDu4Zatb0ObOurjsfQn12fxj52WNyhtnSrc9eGpeF9wkyAPt2y8BY0vdcb9SEk/aPTSk0IpC3d9eCreE9wkyMMtG3NBh1k8NwnycMsGQUdTqh4csu3u7mbfQ9DRlKoHg2y7uzlDIehoStWj/2y7u3lDIehoStWj/2wQtPfi+5egmv6zQdDei+9fgmoYZNucY1CTWT6iRy6WP+lGmexjvSoEpXDItjFn8QazfERXm6pvDql6BYJSuGXjJejx8XH+R/1ZPpJhJfI6qFIEBDWBXbaeDS18HsfHRUM1Z/kIuZGI+c/ykOBGenPIk+5IJ/t4YbhWeLiQTAMCQathl42RoMfHxFC9WT4CcvNSOutHukC8sDQ4nQYEglbDLhtzQZtn+ZAL5h9Vu571ozAwL2p8k2lAIGg17LJxF7Rxlg+5YF7QbNYPZWhz9G5xdgUISmGXjZGgZcegzbN8ZAsmZLN+qIKm04BA0GrYZeMkqHoWrzHLR7RkepIUHqlms34ogmbTgEDQathlYyUoQWuWj2jJXDdTZp8iaDYNCASthl02/oI2zfIREXXUP3Zatp7prB9rQU+uW9BoGhAIWg27bBsgaNMsH0G8UHapM5n1IzM4XTibBgSCVsMuG2dBh1o8OwlysMsGQcdSqh78svVrKARlBr9sEHQkperBLxsEHUmpevDLBkFHUqoe/LJB0JGUqge/bBB0JKXqwS9br4KK2s8jHkl/I7qbo3QmBeVuI1MgKIVfNk6C5u+WCrkR3TN3/rWlp/kRdSmY5cM9/LIxErRwv2mQDAF59ImvJ29MeuR29X44COoeftn6FFQUPo/iHftB0moePf63T59KWtPkbqNoboXkbqPSG421gaAUftkYCxrfRHQi+pLeTyTvNopa1qNkSHIrICiFX7YeBRVBg6BHciDoqfRLdrfRUTJ7JwR1D8Ns/RlKBFWOQeWBp7zTLfwiD0FzdxvFhkJQ9zDM1pugsuDas/ggbDfD1jP9kt1tFD/nBnN1+oBhNkaCKpw/GT+5IXqAw1HhwTaFgce2QFAKw2x9CRqV2/B5HL2aPIMPjl71tZTpEtI7PFsBQSkMs3EW9JHXvD0+7owaz/Ruo6gpTR/i0AoISmGYrSdB42IbPo/kaWDpQ8GSu42io9FIVvSDuoZhNs6C+gaCUhhmg6DjKFUPhtn6ETQpFYIyg2E2CDqOUvVgmK0XQdNCISgzGGaDoOMoVQ+O2XowNCsSgjKDYzYIOopS9eCYrXtB1yVCUGZwzAZBR1GqHhyzdS5orkAIygyO2XoVtGe6/tXjX7qXUvXgmK1PQXsGglI4ZuvaFz5+QlAFjtkg6ChK1YNjto6FYeQnBFXgmA2CjqJUPThm69YYTn5CUAWW2Tp1BoLylCCBZbYunWHlJwRVYJkNgo6hVD1YZutQGl5+QlAFltkg6MBLXVw81F105IIy8xOCKkBQVoxH0MWlXxNiEgTLK+LMVP579jBYXX+BEJfn4d8geQWCdlaSHiMS9MLlYH7u1mp/Ir8cJD/sBYsLe1EDG74y2wv41VBEZ6HY/fYjEjSUMPkSNpfXDoPl1enq+jSQf8Nvwz/Rq8EWuzoKIOjgS80JeulW/LM0My/oFSHkvj/Mxq6SuvOG368+PkGrWtBrh1k2ftUEQQde6lpQeQwafkmOQdeCBvErTAXtKBLDX3x0gpKz+LWg8etxNn4VBUFHUKoeUTZ2NdVJIHa/dQBBVeJs3OoKgo6gVD2SbMwqq4s4zH7lGAhKSbPxqi4IOoJS9ciysaovCDqCUvUYraCsft8MCEpZZ+NUYxB0BKXqkcvGqMr8R2H0y+aBoJR8Nj6VBkFHUKoehWxsas17EDa/KQGCUorZ2NSb7yBsflECBKWQbFwqznMOLr+mAgSlQFBWQFAKzcak6vzGYPJLlgBBKUo2HpUHQYdfqh5qNha1B0GHX6oeJdk4VJ/XDBx+wQogKKUsG4MKhKDDL1WP0mz916DPBP3/dtVAUAoEZQUEpZRn670OPQbo/XerA4JSKrL1XYul5e/u7vraNBcgKKUqW9/VWFL+7q4LQ/v+xeqBoJTKbD1XpFr87q4TQyEol1L1qM7Wb036EpS3nxBUAYKyAoJSarL1WpeejkGZ+wlBFeqy9VmbZWUP/ggUgqrUZuuxOj0VDUH5lKpHfbb+6tNPydz9hKAKDdl6q1EIOvhS9WjK1leVeimXvZ8QVAGCsgKCUhqzDchQ/n5CUIXmbD1VKwQdeql6aGTrp17dl7oBfkJQBZ1svdQsBB16qXpoZeujap2XuQl+QlAFvWw9VC4EHXqpekBQVkBQima27mvXdYkb4ScEVdDN1nn9QtChl6qHdrauK9hxeZvhJwRV0M/WcRVD0KGXqodBtm7r2G1pG+InBFUwybbBhkJQfqXqMQ5BN8VPCKpglK3TeoagAy9VD7NsXVa0w7I2xk8IqmCYrcOqhqADL1UP02zd1TUEHXipehhn66yy3RW0OX5CUAXzbF1VNwQdeKl6jEDQDfITgipYZOuowiHowEvVwyZbNzXuqpRN8hOCKlhl66TOIejAS9XDLtsGGbpRfkJQBctsXVQ7BB12qXrYZuug3p0UsVl+QlAFCMoKCEqxzua/5l2UsGF+QlAF+2ze6x6CDrtUPVpk8135EHTYperRJpvn2new+U3zE4IqtMrmt/4h6LBL1aNdNq8CtN/4xvkJQRUgKCsgKKVlNp8KtN725vkJQRXaZuNsKARlXaoerbN5tKDlpjfQTwiq0D6bPw8g6KBL1cNBNm8itNvwJvoJQRUgKCsgKMVFNl8qQNBBl6qHk2yeXGi12Y30E4IquMnmxwYfgu7s7LTZqm+2gsWFvfDrwdlD8s5qf+KxVL44yubF0DYbrfaTtaGhoPd+3a1g+cMXIWiMq2w+DHUv6M4Oc0NDQS8+exosnnPxcBE6Gv5dPP3+s4fLK+Jp90+C8EvYskavOC6VL86yeTC0xSbrGlDGggoROvmSSfCy31wLeiFsOQ8uB3MxkV9me0H0ilMgaOeb3EhBQz1lC/rS+1bPf+la0PDL8tqh3MUvr07ltwtl99+WUQjKytDKFRn7KWRoKehf/PrDP7ooCBopeTAJ9/BCnJlCUEvcG+peULZn8SKOLAU9vPmCy4vSFvRaZCYEtcW5obYb3Lg+UJEmjgSdR62k3KHPzsY79PUx6PzcLQhqjWsxRiKoWOfdShpNKeFMiG9IjjhX++lZ/JkpWtAWODZjFIKKfFpcSaI4zuZWDcutbZCfQhTDQlAKBO0RoSSFoBTX2ZzKYbexTfFT1ROCqjjP5lKPIQtapicEVXGfzaEfVpvaCD/L9YSgKh6yuTNkqIJW6QlBVXxkc6aIzYb4+1mtJwRV8ZKtT0OZC0r7lQgQlDI0QXn7WW9nAEFV/GRzpcmwBG3UE4KqeMrmyBPjzTD2U0NPCKriK5sbU3S3sr297bJYD2jpCUFVvGVzoormRra3U0OZCqqpJwRV8ZfNhSt629jeTg3l6ae2nhBUxWM2B7YMQNCGfiUCBKUMSlB+fhrZGUBQFZ/Z2vtieAzKTVBTPSGoitdsrYUxO4tn5qe5nhBUxW+2tsqYrc9KUBs9IaiK52xdGsrJTzs9RyBofMdfdC/1FSHSR/jMw1PJPWXZ6HFUvrO1tGYzBbXVc0yCLq+E9s3O3ZIvzs/K+/4v02U7EbS7p9By8dOsX4kwHkGjb+S9/+mD+xaXbkWPRVtcECL8OXleGgR1TBs7gzEJutqPW88g96gU+Vg06ax8IXlWRdsPVINWBWyYoK0/zeELGraPIj74nMsHTUWvXUpUTU1dXjtMnvYjs3lXtM329ddl4KeDT3L4gmYnSdFP906Tn0Jx08eiHUh/k+elxdl8K9pi8xskqJNPcTyCzqOzdqlgcgwa7tvjk/tJdA61bkElnhW137r2mn376egTHI+g0Vl8fJIUzOWuPn5kWtychg1regyaZvOrqPXGN0PQVifuBcYjaNQPGh+DxkemZ5PnoM5EdPqePC8tl82rorbb1l2vTz9dfnCDF9SYfDaPig5XULcfGgSlFLP5U9Ryw5qr9ean6w8MglJoNm+KejW0J0Hdf1gQlKJmc3fET7brb61+/PTxOUFQSmk2P4pabZStoH4+IwhKqcjm5eO32SZPQb3tZfrZF2ygoH4+K4tN6qzSda162sGIaCKvPthIQX3UwyAE9bNzyeZJ6oMNFdRDXZhvT2ONTv30oKfIHTBAUEpDNtf1Ybw5XoJ62KkUNwlBKY3ZHNeJ6dbS5Y+Pjx1t0R73OxRlixCUopHNbb0YbixZ/Pi40tCuBHX9P7W0JwCCUrSyOe1VMdtUvPTxcaWh3fjpuF+pcnMQlKKbzV0F2TShPQvq1M7ypjMBglL0szmrJYsmtFrQDvx0uvto2BgEpZhkc1VTRpvJ7eNbb8sGh7sOjeMECEoxy+aotky2sj5Lar0pC9ztNvS2BEEpptnc1FhuI7u7u7qL1r67s7PTKlLp1l3tMvCEZWvMszmptWwbu7sNhmoKurPj3FBH/xeNOgAgKMUmm4uaSzaxu9tkaG1ZRT9dGtqmX2m9pvFWICjFLlt7RXkL2sZOkaQyazoTICjFNlvrnut49XaCFo5A3Qlq/6tJOyNBbT8eCEppka2lojlDmxdrfM+dn5a/lsjstGo6EyAopVW2dopmhmos1fyWIz/tfqVEzNRO+48FglJaZmulqNa6uoI6werXiVvOSE2RmmoLBKW0ztZG0XaGOvfT5lfJ79ezdhSCusNBNicdMhbLuBXU5sBRFPfrbe0MIKiKk2zWldJGUKd+tjr0zNnZNgcEpTjKZquoxmodCGqfPrdfLwaaC5E94toACEpxls26d8Z2CWeCWutZedS5+JLwnUn0cFZDICjFYTa77r/GddIFyHgmV37a/seK1lPtlDP+iDf+lOUPfvLq+tR8sxCU4jab1Xmw3vt0RKgbQS37ldLVaNv5b0Lc9XGf9Nxrh/N3/PT1NFUGQFCK62w258I6b9Mx9U78tOtXql5p+c1v9vN//Ikf/L1P+dq9F73/84KZMjVVIxCU4j6bea3Xr+BLUIsjkpqLmIsLYi/4249/8bO+O2w5f/FNxFe/6+Vgrs7u1wQEpfjIZlrzFoK29tPKzqq3ogPPMz93OXjl3z/jM6Z/KcRbfsWvfvtHxnOsmAFBKX6yGVZ/7dKlx6DZGk2X8iu2aapntZ1/Hb71ad/64IWP+LJnPXArMvXt3mHvRe/xJ5/9++hmcoGvbGYK6AxZqvLT3FDT/z7Vds7ke2/6+V/+wMPf9k3v8wwh3um9P0c888L7/czFl7zbn5mmioCgFH/ZjDTQMbTkpebhpCXrmv3XqVt8dnn1K58w+YW7PvMfvlM85fue/O6T4ODHwn39L9m0nTEQlOIzm4kKRoOWig2okaBGmZrPo5bf9Xnibf/8q74j+JsP+cqD75ms9i26lvJAUIrfbAZnytULOhTUQE+96Kuf/oL3/Pp7f1Y889Lvvssr3rydnBIISvGeTdsJg1FL61dM/NT/36I/Jn71Q+97IMSH3/1FP/mx4swfaG6+BghK6SCbZmXrC5p/QdtPEzs1lwxZ/fI7f/HlV3zYt3zjmd/TX6mmZIcjYAwYuaC6cmiPCrG6/qO7nOHGb/7I3l+1bTpFOhgfLahKR9m06r1iGfqyxcVUvf8gNg3YPz40tz9nX4uZAkEpnWXTqfzyRdoKqvefo9O9q2pmAgSldJhNQ4HSJYTGMu1K7cxOUWlmAgSldJEtO5Ep1kzZ+U1Z1bURtNm8buRsEjMFglI6yJbvCsrVUXkPUc1lo8oFqmg0wn/T2dhkEiAoxX820pme1lZFH7s7QTXs1N2UBYZipkBQSueCBok6VReBGgzV782sf9ebnZZmJkBQSh+CRvpUXqVc1206fslc0FpB/MhpujMvB4JSOj4GzRCi8iplWsfZCFBTQesscW+nEzFTICil07P4AqLyKmVc2esx9IK+VUu1K4537E7NTNgKFhcP83+cbr26VL70ma2ycqPXE0F3zASt3qYzldzszMvJCRr+BEH7zlZVy/LlVNCd/CO1mzZXcS3KjU4exUwptKAPXhFnD5fyn2Dx9PvPHi4uCDEJgvCVM9ODSbC4ZH2NVSmVL31nK6/vdRO6oy9otZ328dItuDGz4dQtKoPu4g8uB7O9YHFhEiyvTuW7q/1JMD/3d5eDufldzRX0LUEd/WcrrfjU0J2CoPUVXPpiK61cN5n0mlie+CXlGFRaubyWHY1m3y4fuHVz6ipX/xJUwyFb3oHt7e34NflP8lxvkb5crUqZRS3U8rQzF6LEyQKqoFfCBc9MYysP5NNK4j376vpvPeBqD89CgiqYZEtra3ubGhp9G79cc3quvmL9UBs/5/qaG1YFvRY1nVLQ5ZVJsD61nz3H2R6eiwSl9Jit5PLS9jYxNP4uebnqjIq+bmGYUzGrlTQXVB6Dzs/dkt9Ff++dymNQ+Z7FYyGqS+VLf9mUjnohCoLmDj0LLxdRrDLTzFGTqdtMGgoqbxKNztnjDqeZEE+7fxKfxQer57vrgoKgJZReAS0XNKgUVOQOBAKjHXtrMY323NroV8fiPmeFQtAyyq/FF0QkTaiyiUSM9FRK/8YOS6X8OFlAuzpmYSPafak9wEzQoCCiyL6WHIGmjiSTzDUZUyFW/WpmZzgOwLV4CqNj0JR4qFP8bbD+IuhCCU2zINbblX89bYg7VbIIBKWwOYsn7xQMFQHxM1MnlKhKUD3JxHpJrYa4DTPZo1m/CASlcMyW3/tnjWeuFU2lE9k5UsFPHTFL2knnM3pT5Hn3rGFiBQhK4ZgtEbTQemY7+1QoUdjJpy9Vm1l1OKl9qOCCedOzxSAopZ9s9Q+sSVtQkbacOUHjhrSoYdXOXOtwsktBF/cdNDwVHIJSesnW9Miv7H0hEjuzfbvIN52qe21Ocfw3oNFgj9r3ISilj2zND00s3KeczuIm1lOx5wx02BPk20+NMZwQlNKjoPV3fKx/jMUTFfiP64zVfuPUSRCU0qug5YbWH0tulpOmQFBKZ9nycyDUG5qdpfuXUk6CYDGjpj8gKKWrbMVZZMoFrdqLFxUNd5SuRkLKnkmL2bY8AkEpHWWjE8VlfZ2Kgsr3QdLnmb54cxq4utlh9VBgM1+hRyAopXtBEwNzffFB7uV8l2fapZRNxi5/kpMI20x0XUGLx8/6AIJSusgWapYImt9VZxcz6UGmSHvi0456kfXUS8flzbfODhyZ+QlBFTxlU3bddDbtmsEcQmTNZZCzUyQbETenjf3duri7tdwREJTiLlvDSffaz7rz8tzh5/q1dKRI1gzLm26dZD4QVrO6+wOCUvSyVdtk0hFUsmBxfHL2Jh3NEf+YCCr38VOt2JsHBKUYCmqoZG6l0nuKcvdwpudD6SFroeyCoPHiuoXb4//KvAoEpTRns3KysKr8tvSuovRmuNyGw2+XV/MHrCLqTo93w4XXfSvaxdgRBQhKKcum7rrtxMytVX5fpnq/e7jO/Eyh01TMxOVFukThRKtE0fohKEZ0MTxUBYJSkmwNzaSuoJUbqBU0t/r6ZD3/dOX5uoGlxRV+bhokZQIE5YHerrtR0KbNlAkaH5jm7jJOG2tV0MsVhhab0eZhfAZAUB60zKZ9bEr8zB2aZq9kb87ze/johbWgZWOd0u+cCqocg3ZiKwSl2GZrFJP2yxeaSqVBLGxpvlf0M1jcR7qdaJb4q1tBA8XPDgyFoBTjbJpNpnrlaL16/sfktcIyuae6xG8sryrr0K1GX5z6WaSjPT4EpWhnM+toUkYvpdtQNquejB+IvfW79JugVNBUUW9+QtC+0O4HNdusKmjFNtQXZ5Pg36fpuwH9RvmhZksugaA9UZ0tazLlADfT56ETQasEF0K17eZUPqk1fnu9YHG1qsRmIY3AMagzkkfwRs+XzA0+j4apKc9eKclGm0w57tx42E/+RLz6WQpBiWyzH794eBDHrjx3rzLRp6I4i3fFenadwjw75ZPu5LNV7MyloObDh5I5uKoPDrKBIeR1+ejgZfps+mxhunJVscYHI7wYk6DRPDtnpvE8O+uX43lNltd+I25MZbam8x85ANNmfJuonkyurq07mCT707q+pRoN9RTtYyhIM+MSNDfPzvrlYHntwWuHyyvnbkUPCtI5/wkPQI1vLZPbPY66fcgw5eTNmlWXV9QzkpLOz9rCG/P1MhSkmfEJmsyzE6THoOduBbPwwFSeh8iTH71sB8LszohYwOOk47xgqCjRZyaI/iWnzCZNaNCsaD8XMpsZoaBX0jOj7Bg0OsgLvY3uPXOeLWuSjzNBi4ZSdVb7Sg+BjqDN0yLWvQtBeyy1KOg15Yzp4Dl7kaD6Lag2+X13qaDZArmj09lkTu90V+0pu3zUGKb6PQjaY6nKMWh862Iq6OLSy6+Hp0578cvustGj2ePE0Hx3qPw+veSTGbq4sBccqIY2d302HmnWKMrTz5EIGh1s7iWCxrPqZC+Ln4rmIn346rPXZ/EOKDvtiQ3Nj4GP73kLyLAO2UOg9hIUt1duU/O5UC4W2QRLP8chqA7RMajERbaqk3LpZq67Pnd5SRl31CBoVXun0aFUeMJ38+I9A0ETnAna1E0l0qWCoFLQecnkAqqftobGhXM96CRAUEqrbBp9qNHVzGSp3AX6xoFxDgWNEkBQdqXqYZ1Nd4RT8cQ+8lP2LJj4Wdf86V7YhKDsStXDLpv+FW/lzD6Qp2uNY6PI5mvkMjJUc9n+gKAU82yaTWfkYu5hdTnmz216tJKyTo1cBobyH0cCQSmG2cyG1McX3pX3XjZtms/K6LqRgXbshzpBUIpBNpNx9eW3fCT86eG8/uK+Ya+8iXXMFYWgFN1sunKqJ+wKq32xV/8IWtPLRkbSsVYUgg+RMzoAAAerSURBVFK0spmMAo77lWoFfSgI/uMnmrah85rOe2WL81UUglIas5neMJfcppnz03jWg9LyNC4HGJTA1VEISqnPZlGRuV755JWb02jclMEmtF/UfLd0jYZV+umUgqCU6mzm9xoHpbdprp5/KO9qMtiGwau6b5euUrdOT92mEJRSkc1uH1j1rMYDYbKTtxLUxtAaRfu68ARBKSXZrJrOoL5FMrjprmIrWlf9janKDEG5QLPZnj40rMdV0CpFISgXCtlszomSFeuWmZUMp2vYoP7rJktUrFe2Io5BOyMeSV9yDBjdA5Jls96xqzW82je8C5Rsz+h1s0UqVixZc+1nl6aOUtDSJ4oEBUFb9AuWrHpzaj8DZmUOnYDVyzRJxuXupRELunj6/WcPk8eMzOX0VfH3W9ZNZ0zFo3JMHza23p7FO83LaEhW9Sl0ezQ6ZkEvTILkFk85YHi2F7/R7pJK+XC61UP28xG3E7RiIU3Jqg9GIahHomPQWEdp5vLqNLkhqXgMak7a5pRUq/VUha3HLLU7Jy9RFIL6Zn2bfPRXXnYMnQ1Pq9sJWtv0ziaWU2b3LGjZr4VjUM/kBE1aUPljuKe3E1SnX2l1/WvE5J/Mo7oYslRtqG4GugWcxfslJ2hyDCofKdJK0KYDV8PBIcWN27zXuJyRZD0OdRq7oMlZ/EE0CfVqPzqLN6XsdDc3L0cbasXQtsaBXr0pOkZB6zFvQcvqbuZm0nU3growtC9FISjFMFt5v9Li0ott+z0LG2/xru2iNRvpQ1EISjHJJqqG073y1rLpRmKt7bd4137Zmq107ygEpehnaxgQ0r4JbbDBiaCmZ+RdKwpBKY3Zkhpqqqn6JnR9/4c6JzctyfJtrYUt+jS7VRSCUvQE1ailumcxrO+gK5s1Pl9QYxJd2nbY5zfVoaIQlNKcTZ1N0/Q2zfU9yGXTxq/LaQxigsvr6t0pCkEpGoKWDaejj+yupRdByxa3v67elaIQlNKUrXw2zYZDToKWoKUG/NfdH/Qv4rPqlqihylDDzaRb60RRCEqpzSYqZtOcGJ616xyDlo2JuvrR0WP1P7ByiXrKDTXdynpzHSgKQSk12SorRM4sa3Zxs/ksvqys/75b6vlk8fZpHkNFnAvlX1EISqnMVlcZBxNXV9/XxUX/FvX9TxEZKp4aBFUT3eps1CW+++4hKEXJpjWcbt/gNk0tMj/zhv5v7Kd4m/wyFpt1i1dFIShFzSZK68B1i0laS5G8UjD0fxJBn5pbxhAvMnlUFIJSSgT1OV5pTcHFXAOaE/T/EkHfOr+QIX5c8qYoBKWou/jSD9/ReKU1RRnLBV19bizoh+YXMsWTSp4UhaCUYjZRPpzO2XilNQUZRf7F3EIHnxoGuut5QXEpQ3w1dl4UhaCUfLb0Iy//5B2MV8pRKmjdUJLKXCrFzk5/B4weFIWglHW2mo/7YC9oGq9kjLqHb0RzMXq5yONZt3NFIShlq7lfaXll8kp5m3vT3DGGGPupuZx6wd1nv5BjRSEoZav0Ns1Wj/8yxregXg1123cPQSlbpZ9wm8d/GaNdv9aC+jXUZTMKQSlbZZ9uq8d/GSPLrz87yi2oQdmQJd8X0V0pCkEp7h//ZZwgqB1oT5bUoWzIkvdhHm4UhaAUma3so7V+/Jcxon4cc3HJNqX4xoWiEJRSmu1gz/7xX6ZkDahfQbsw1IGiEJRSkk12K73c9vFfxnQlaCeGtlYUglIqslk//suU0nF2tcu2LMo37RSFoJQ4m/F0ms5IqtPlWby39XWLaVEOBKXE2Yyn03SGUWVuiKEt+u4hKCXKZjydpjPMKrK1YF0Zat2MQlBKms1sOk1nDFZQS0UhKGWdrbuezzWGddjery4NtVEUglKibPFwuq4FLb2G1bSGg0I7xFhRCErZivs9X2wynaYbLCYQc2FXt4aaKgpBKX1mSxVd/YB4L70VnJTqYiMm5ZkUCEEpvQqa1N6/RrfGfaHWCm6K7RYDRSEopWdBI77/AyJDP6axo8uRWp0bqq8oBKX0mC2ttNUfRn7e3dzRtbGCavfdQ1AKA0GDL41b0LfqqgXtxVC9ZhSCUvrLllXX6o+EeAtpaOOVAmdi9WOohqIQlLLVG2L97asL8Qav/4ZvZLSOs8I7RTQV3I8EvZQKgCYQFLAGggLWQFDAGggKWANBAWsgKGANBAWsgaCANRAUsAaCAtZAUMAaCApYA0EBayAoYA0EBayBoIA1EBSwBoIC1kBQwBoIClgDQQFrIChgDQQFrIGggDUQFLAGggLWQFDAGggKWANBAWsgKGANBAWsgaCANRAUsAaCAtZAUMAaCApYA0EBayAoYA0EBayBoIA1EBSwBoIC1kBQwBoIClgDQQFrIChgDQQFrIGggDUQFLAGggLWQFDAGggKWANBAWsgKGANBAWsgaCANRAUsAaCAtZAUMAaCApYA0EBayAoYA0EBayBoIA1EBSwBoIC1kBQwBoIClgDQQFrIChgDQQFrIGggDUQFLAGggLWQFDAGggKWANBAWsgKGANBAWsgaCANRAUsAaCAtZAUMAaCApYA0EBayAoYA0EBayBoIA1EBSwBoIC1kBQwBoIClgDQQFrIChgDQQFrIGggDX/D/5Cr8+6p5/+AAAAAElFTkSuQmCC" /><!-- --></p>
+</div>
+<div id="the-function-samples" class="section level1" number="4">
+<h1><span class="header-section-number">4</span> The function
+<code>samples()</code></h1>
+<p>This function controls the aesthetics of the sample points in the
+biplot. The function accepts as first argument an object of class
+<code>biplot</code> where the aesthetics should be applied. Let us first
+construct a PCA biplot of the <code>state.x77</code> data with samples
+coloured according to <code>state.division</code>.</p>
+<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb11-2"><a href="#cb11-2" tabindex="-1"></a>  <span class="fu">PCA</span>(<span class="at">group.aes =</span> state.division) <span class="sc">|&gt;</span> </span>
+<span id="cb11-3"><a href="#cb11-3" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" 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" /><!-- --></p>
+<p>Since the legend interferes with the sample points, we choose to
+place the legend on a new page, by setting <code>new = TRUE</code> in
+the <code>legend.type</code> function. Furthermore, we wish to select
+colours, other than the defaults, for the divisions. We can also change
+the opacity of the sample colours with the argument <code>opacity</code>
+that has default 1.</p>
+<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb12-2"><a href="#cb12-2" tabindex="-1"></a>  <span class="fu">PCA</span>(<span class="at">group.aes =</span> state.division) <span class="sc">|&gt;</span> </span>
+<span id="cb12-3"><a href="#cb12-3" tabindex="-1"></a>  <span class="fu">samples</span> (<span class="at">col =</span> <span class="fu">c</span>(<span class="st">&quot;red&quot;</span>, <span class="st">&quot;darkorange&quot;</span>, <span class="st">&quot;gold&quot;</span>, <span class="st">&quot;chartreuse4&quot;</span>, </span>
+<span id="cb12-4"><a href="#cb12-4" tabindex="-1"></a>                   <span class="st">&quot;green&quot;</span>, <span class="st">&quot;salmon&quot;</span>, <span class="st">&quot;magenta&quot;</span>, <span class="st">&quot;#000000&quot;</span>, <span class="st">&quot;blue&quot;</span>),<span class="at">opacity =</span> <span class="fl">0.65</span>,<span class="at">pch=</span><span class="dv">19</span>) <span class="sc">|&gt;</span></span>
+<span id="cb12-5"><a href="#cb12-5" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>, <span class="at">new =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>Furthermore we want to use a different plotting character for the
+central regions.</p>
+<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" tabindex="-1"></a><span class="fu">levels</span> (state.division)</span>
+<span id="cb13-2"><a href="#cb13-2" tabindex="-1"></a><span class="co">#&gt; [1] &quot;New England&quot;        &quot;Middle Atlantic&quot;    &quot;South Atlantic&quot;    </span></span>
+<span id="cb13-3"><a href="#cb13-3" tabindex="-1"></a><span class="co">#&gt; [4] &quot;East South Central&quot; &quot;West South Central&quot; &quot;East North Central&quot;</span></span>
+<span id="cb13-4"><a href="#cb13-4" tabindex="-1"></a><span class="co">#&gt; [7] &quot;West North Central&quot; &quot;Mountain&quot;           &quot;Pacific&quot;</span></span></code></pre></div>
+<p>We want to use <code>pch = 15</code> for the first three and final
+two divisions and <code>pch = 1</code> for the remaining four
+divisions.</p>
+<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb14-2"><a href="#cb14-2" tabindex="-1"></a>  <span class="fu">PCA</span>(<span class="at">group.aes =</span> state.division) <span class="sc">|&gt;</span> </span>
+<span id="cb14-3"><a href="#cb14-3" tabindex="-1"></a>  <span class="fu">samples</span> (<span class="at">col =</span> <span class="fu">c</span>(<span class="st">&quot;red&quot;</span>, <span class="st">&quot;darkorange&quot;</span>, <span class="st">&quot;gold&quot;</span>, <span class="st">&quot;chartreuse4&quot;</span>, </span>
+<span id="cb14-4"><a href="#cb14-4" tabindex="-1"></a>                   <span class="st">&quot;green&quot;</span>, <span class="st">&quot;salmon&quot;</span>, <span class="st">&quot;magenta&quot;</span>, <span class="st">&quot;black&quot;</span>, <span class="st">&quot;blue&quot;</span>),</span>
+<span id="cb14-5"><a href="#cb14-5" tabindex="-1"></a>           <span class="at">pch =</span> <span class="fu">c</span>(<span class="dv">15</span>, <span class="dv">15</span>, <span class="dv">15</span>, <span class="dv">1</span>, <span class="dv">1</span>, <span class="dv">1</span>, <span class="dv">1</span>, <span class="dv">15</span>, <span class="dv">15</span>)) <span class="sc">|&gt;</span></span>
+<span id="cb14-6"><a href="#cb14-6" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>, <span class="at">new =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>To increase the size of the plotting characters of the eastern
+states, we add the following:</p>
+<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb15-2"><a href="#cb15-2" tabindex="-1"></a>  <span class="fu">PCA</span>(<span class="at">group.aes =</span> state.division) <span class="sc">|&gt;</span> </span>
+<span id="cb15-3"><a href="#cb15-3" tabindex="-1"></a>  <span class="fu">samples</span> (<span class="at">col =</span> <span class="fu">c</span>(<span class="st">&quot;red&quot;</span>, <span class="st">&quot;darkorange&quot;</span>, <span class="st">&quot;gold&quot;</span>, <span class="st">&quot;chartreuse4&quot;</span>, </span>
+<span id="cb15-4"><a href="#cb15-4" tabindex="-1"></a>                   <span class="st">&quot;green&quot;</span>, <span class="st">&quot;salmon&quot;</span>, <span class="st">&quot;magenta&quot;</span>, <span class="st">&quot;black&quot;</span>, <span class="st">&quot;blue&quot;</span>),</span>
+<span id="cb15-5"><a href="#cb15-5" tabindex="-1"></a>           <span class="at">pch =</span> <span class="fu">c</span>(<span class="dv">15</span>, <span class="dv">15</span>, <span class="dv">15</span>, <span class="dv">1</span>, <span class="dv">1</span>, <span class="dv">1</span>, <span class="dv">1</span>, <span class="dv">15</span>, <span class="dv">15</span>),</span>
+<span id="cb15-6"><a href="#cb15-6" tabindex="-1"></a>           <span class="at">cex =</span> <span class="fu">c</span>(<span class="fu">rep</span>(<span class="fl">1.5</span>,<span class="dv">4</span>), <span class="fu">c</span>(<span class="dv">1</span>,<span class="fl">1.5</span>,<span class="dv">1</span>,<span class="fl">1.5</span>))) <span class="sc">|&gt;</span></span>
+<span id="cb15-7"><a href="#cb15-7" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>, <span class="at">new =</span> <span class="cn">TRUE</span>)  <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --><img role="img" 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" /><!-- --></p>
+<p>If we choose to only show the samples for the central states, the
+argument <code>which</code> is used either indicating the number(s) in
+the sequence of levels (<code>which = 4:7</code>), or as shown below,
+the levels themselves:</p>
+<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb16-2"><a href="#cb16-2" tabindex="-1"></a>  <span class="fu">PCA</span>(<span class="at">group.aes =</span> state.division) <span class="sc">|&gt;</span> </span>
+<span id="cb16-3"><a href="#cb16-3" tabindex="-1"></a>  <span class="fu">samples</span> (<span class="at">col =</span> <span class="fu">c</span>(<span class="st">&quot;red&quot;</span>, <span class="st">&quot;darkorange&quot;</span>, <span class="st">&quot;gold&quot;</span>, <span class="st">&quot;chartreuse4&quot;</span>, </span>
+<span id="cb16-4"><a href="#cb16-4" tabindex="-1"></a>                   <span class="st">&quot;green&quot;</span>, <span class="st">&quot;salmon&quot;</span>, <span class="st">&quot;magenta&quot;</span>, <span class="st">&quot;black&quot;</span>, <span class="st">&quot;blue&quot;</span>),</span>
+<span id="cb16-5"><a href="#cb16-5" tabindex="-1"></a>           <span class="at">which =</span> <span class="fu">c</span>(<span class="st">&quot;West North Central&quot;</span>, <span class="st">&quot;West South Central&quot;</span>, <span class="st">&quot;East South Central&quot;</span>, </span>
+<span id="cb16-6"><a href="#cb16-6" tabindex="-1"></a>                     <span class="st">&quot;East North Central&quot;</span>)) <span class="sc">|&gt;</span></span>
+<span id="cb16-7"><a href="#cb16-7" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">samples =</span> <span class="cn">TRUE</span>, <span class="at">new =</span> <span class="cn">TRUE</span>)  <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>Note that since four regions are selected, the colour (and other
+aesthetics) is applied to these regions in the order they are specified
+in <code>which</code>. To add the sample names, the <code>label</code>
+argument is set to <code>TRUE</code>. For large sample sizes, this is
+not recommended, as overplotting will render the plot unusable. The size
+of the labels is controlled with <code>label.cex</code> which can be
+specified either as a single value (for all samples) or a vector
+indicating size values for each individual sample. The colour of the
+labels defaults to the colour(s) of the samples. However, individual
+label colours can be spesified with <code>label.col</code>, similar to
+<code>label.cex</code> as either a single value of a vector of length
+equal to the number of samples.</p>
+<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
+<span id="cb17-2"><a href="#cb17-2" tabindex="-1"></a>  <span class="fu">samples</span> (<span class="at">label =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>We can use the arguments <code>label.cex</code>,
+<code>label.side</code> and <code>label.offset</code> to make the plot
+more legible with a little effort.</p>
+<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" tabindex="-1"></a><span class="fu">rownames</span>(state.x77)[<span class="fu">match</span>(<span class="fu">c</span>(<span class="st">&quot;Pennsylvania&quot;</span>, <span class="st">&quot;New Jersey&quot;</span>, <span class="st">&quot;Massachusetts&quot;</span>,</span>
+<span id="cb18-2"><a href="#cb18-2" tabindex="-1"></a>                            <span class="st">&quot;Minnesota&quot;</span>), <span class="fu">rownames</span>(state.x77))] <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;PA&quot;</span>, <span class="st">&quot;NJ&quot;</span>, <span class="st">&quot;MA&quot;</span>, <span class="st">&quot;MN&quot;</span>)</span>
+<span id="cb18-3"><a href="#cb18-3" tabindex="-1"></a>above <span class="ot">&lt;-</span> <span class="fu">match</span>(<span class="fu">c</span>(<span class="st">&quot;Alaska&quot;</span>, <span class="st">&quot;California&quot;</span>, <span class="st">&quot;Texas&quot;</span>, <span class="st">&quot;New York&quot;</span>, <span class="st">&quot;Nevada&quot;</span>, <span class="st">&quot;Georgia&quot;</span>, <span class="st">&quot;Alabama&quot;</span>,</span>
+<span id="cb18-4"><a href="#cb18-4" tabindex="-1"></a>                 <span class="st">&quot;North Carolina&quot;</span>, <span class="st">&quot;Colorado&quot;</span>, <span class="st">&quot;Washington&quot;</span>, <span class="st">&quot;Illinois&quot;</span>, <span class="st">&quot;Michigan&quot;</span>, <span class="st">&quot;Arizon&quot;</span>,</span>
+<span id="cb18-5"><a href="#cb18-5" tabindex="-1"></a>                 <span class="st">&quot;Florida&quot;</span>, <span class="st">&quot;Ohio&quot;</span>, <span class="st">&quot;NJ&quot;</span>, <span class="st">&quot;Kansas&quot;</span>), <span class="fu">rownames</span>(state.x77))</span>
+<span id="cb18-6"><a href="#cb18-6" tabindex="-1"></a>right.side <span class="ot">&lt;-</span> <span class="fu">match</span>(<span class="fu">c</span>(<span class="st">&quot;South Carolina&quot;</span>, <span class="st">&quot;Kentucky&quot;</span>, <span class="st">&quot;Rhode Island&quot;</span>, <span class="st">&quot;New Hampshire&quot;</span>, <span class="st">&quot;Virginia&quot;</span>,</span>
+<span id="cb18-7"><a href="#cb18-7" tabindex="-1"></a>                      <span class="st">&quot;Missouri&quot;</span>, <span class="st">&quot;Delaware&quot;</span>, <span class="st">&quot;Hawaii&quot;</span>, <span class="st">&quot;Oregon&quot;</span>, <span class="st">&quot;PA&quot;</span>, <span class="st">&quot;Nebraska&quot;</span>, <span class="st">&quot;Montana&quot;</span>,</span>
+<span id="cb18-8"><a href="#cb18-8" tabindex="-1"></a>                      <span class="st">&quot;Maryland&quot;</span>, <span class="st">&quot;Indiana&quot;</span>, <span class="st">&quot;Idaho&quot;</span>), <span class="fu">rownames</span>(state.x77))</span>
+<span id="cb18-9"><a href="#cb18-9" tabindex="-1"></a>left.side <span class="ot">&lt;-</span> <span class="fu">match</span>(<span class="fu">c</span>(<span class="st">&quot;Wyoming&quot;</span>, <span class="st">&quot;Iowa&quot;</span>, <span class="st">&quot;MN&quot;</span>, <span class="st">&quot;Connecticut&quot;</span>), <span class="fu">rownames</span>(state.x77))</span>
+<span id="cb18-10"><a href="#cb18-10" tabindex="-1"></a>label.offset <span class="ot">&lt;-</span> <span class="fu">rep</span>(<span class="fl">0.3</span>, <span class="fu">nrow</span>(state.x77))</span>
+<span id="cb18-11"><a href="#cb18-11" tabindex="-1"></a>label.offset[<span class="fu">match</span>(<span class="fu">c</span>(<span class="st">&quot;Colorado&quot;</span>, <span class="st">&quot;Kansas&quot;</span>, <span class="st">&quot;Idaho&quot;</span>), <span class="fu">rownames</span>(state.x77))] <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="fl">0.8</span>, <span class="fl">0.5</span>, <span class="fl">0.8</span>)</span>
+<span id="cb18-12"><a href="#cb18-12" tabindex="-1"></a>label.side <span class="ot">&lt;-</span> <span class="fu">rep</span>(<span class="st">&quot;bottom&quot;</span>, <span class="fu">nrow</span>(state.x77))</span>
+<span id="cb18-13"><a href="#cb18-13" tabindex="-1"></a>label.side[above] <span class="ot">&lt;-</span> <span class="st">&quot;top&quot;</span></span>
+<span id="cb18-14"><a href="#cb18-14" tabindex="-1"></a>label.side[right.side] <span class="ot">&lt;-</span> <span class="st">&quot;right&quot;</span></span>
+<span id="cb18-15"><a href="#cb18-15" tabindex="-1"></a>label.side[left.side] <span class="ot">&lt;-</span> <span class="st">&quot;left&quot;</span></span>
+<span id="cb18-16"><a href="#cb18-16" tabindex="-1"></a><span class="fu">biplot</span> (state.x77, <span class="at">scaled=</span><span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span></span>
+<span id="cb18-17"><a href="#cb18-17" tabindex="-1"></a>  <span class="fu">samples</span> (<span class="at">label=</span><span class="cn">TRUE</span>, <span class="at">label.cex=</span><span class="fl">0.6</span>, <span class="at">label.side=</span>label.side, <span class="at">label.offset=</span>label.offset) <span class="sc">|&gt;</span></span>
+<span id="cb18-18"><a href="#cb18-18" tabindex="-1"></a>  <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>We can also make use of the functionality of the <code>ggrepel</code>
+package to place the labels.</p>
+<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
+<span id="cb19-2"><a href="#cb19-2" tabindex="-1"></a>  <span class="fu">samples</span> (<span class="at">label =</span> <span class="st">&quot;ggrepel&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span>
+<span id="cb19-3"><a href="#cb19-3" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$x` is discouraged.</span></span>
+<span id="cb19-4"><a href="#cb19-4" tabindex="-1"></a><span class="co">#&gt; ℹ Use `x` instead.</span></span>
+<span id="cb19-5"><a href="#cb19-5" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$y` is discouraged.</span></span>
+<span id="cb19-6"><a href="#cb19-6" tabindex="-1"></a><span class="co">#&gt; ℹ Use `y` instead.</span></span>
+<span id="cb19-7"><a href="#cb19-7" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$z` is discouraged.</span></span>
+<span id="cb19-8"><a href="#cb19-8" tabindex="-1"></a><span class="co">#&gt; ℹ Use `z` instead.</span></span>
+<span id="cb19-9"><a href="#cb19-9" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$x` is discouraged.</span></span>
+<span id="cb19-10"><a href="#cb19-10" tabindex="-1"></a><span class="co">#&gt; ℹ Use `x` instead.</span></span>
+<span id="cb19-11"><a href="#cb19-11" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$y` is discouraged.</span></span>
+<span id="cb19-12"><a href="#cb19-12" tabindex="-1"></a><span class="co">#&gt; ℹ Use `y` instead.</span></span>
+<span id="cb19-13"><a href="#cb19-13" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$z` is discouraged.</span></span>
+<span id="cb19-14"><a href="#cb19-14" tabindex="-1"></a><span class="co">#&gt; ℹ Use `z` instead.</span></span>
+<span id="cb19-15"><a href="#cb19-15" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$x` is discouraged.</span></span>
+<span id="cb19-16"><a href="#cb19-16" tabindex="-1"></a><span class="co">#&gt; ℹ Use `x` instead.</span></span>
+<span id="cb19-17"><a href="#cb19-17" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$y` is discouraged.</span></span>
+<span id="cb19-18"><a href="#cb19-18" tabindex="-1"></a><span class="co">#&gt; ℹ Use `y` instead.</span></span>
+<span id="cb19-19"><a href="#cb19-19" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$z` is discouraged.</span></span>
+<span id="cb19-20"><a href="#cb19-20" tabindex="-1"></a><span class="co">#&gt; ℹ Use `z` instead.</span></span>
+<span id="cb19-21"><a href="#cb19-21" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$x` is discouraged.</span></span>
+<span id="cb19-22"><a href="#cb19-22" tabindex="-1"></a><span class="co">#&gt; ℹ Use `x` instead.</span></span>
+<span id="cb19-23"><a href="#cb19-23" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$y` is discouraged.</span></span>
+<span id="cb19-24"><a href="#cb19-24" tabindex="-1"></a><span class="co">#&gt; ℹ Use `y` instead.</span></span>
+<span id="cb19-25"><a href="#cb19-25" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$z` is discouraged.</span></span>
+<span id="cb19-26"><a href="#cb19-26" tabindex="-1"></a><span class="co">#&gt; ℹ Use `z` instead.</span></span>
+<span id="cb19-27"><a href="#cb19-27" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$x` is discouraged.</span></span>
+<span id="cb19-28"><a href="#cb19-28" tabindex="-1"></a><span class="co">#&gt; ℹ Use `x` instead.</span></span>
+<span id="cb19-29"><a href="#cb19-29" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$y` is discouraged.</span></span>
+<span id="cb19-30"><a href="#cb19-30" tabindex="-1"></a><span class="co">#&gt; ℹ Use `y` instead.</span></span>
+<span id="cb19-31"><a href="#cb19-31" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$z` is discouraged.</span></span>
+<span id="cb19-32"><a href="#cb19-32" tabindex="-1"></a><span class="co">#&gt; ℹ Use `z` instead.</span></span>
+<span id="cb19-33"><a href="#cb19-33" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$x` is discouraged.</span></span>
+<span id="cb19-34"><a href="#cb19-34" tabindex="-1"></a><span class="co">#&gt; ℹ Use `x` instead.</span></span>
+<span id="cb19-35"><a href="#cb19-35" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$y` is discouraged.</span></span>
+<span id="cb19-36"><a href="#cb19-36" tabindex="-1"></a><span class="co">#&gt; ℹ Use `y` instead.</span></span>
+<span id="cb19-37"><a href="#cb19-37" tabindex="-1"></a><span class="co">#&gt; Warning: Use of `df$z` is discouraged.</span></span>
+<span id="cb19-38"><a href="#cb19-38" tabindex="-1"></a><span class="co">#&gt; ℹ Use `z` instead.</span></span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>Additionally, the user can add customised label names to the samples
+in the biplot. To do this, <code>label</code> must be set to
+<code>TRUE</code> (or <code>&quot;ggrepel&quot;</code>) and
+<code>label.name</code> is set to be a vector of size <code>n</code>
+specifying the label names of the samples. In this case, the label name
+is set to the first three characters of the state name (row names of the
+data).</p>
+<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
+<span id="cb20-2"><a href="#cb20-2" tabindex="-1"></a>  <span class="fu">samples</span> (<span class="at">label =</span> <span class="st">&quot;TRUE&quot;</span>,<span class="at">label.name=</span><span class="fu">strtrim</span>(<span class="fu">row.names</span>(state.x77),<span class="dv">3</span>)) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>If the data plotted in the biplot is a multivariate time series, it
+can make sense to connect the data points in order. Let us consider the
+four quarters of the <code>UKgas</code> data set as four variables and
+we represent the years as sample points in a PCA biplot.</p>
+<div class="sourceCode" id="cb21"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" tabindex="-1"></a>gas.data <span class="ot">&lt;-</span> <span class="fu">matrix</span> (UKgas, <span class="at">ncol=</span><span class="dv">4</span>, <span class="at">byrow=</span>T)</span>
+<span id="cb21-2"><a href="#cb21-2" tabindex="-1"></a><span class="fu">colnames</span>(gas.data) <span class="ot">&lt;-</span> <span class="fu">paste</span>(<span class="st">&quot;Q&quot;</span>, <span class="dv">1</span><span class="sc">:</span><span class="dv">4</span>, <span class="at">sep=</span><span class="st">&quot;&quot;</span>)</span>
+<span id="cb21-3"><a href="#cb21-3" tabindex="-1"></a><span class="fu">rownames</span>(gas.data) <span class="ot">&lt;-</span> <span class="dv">60</span><span class="sc">:</span><span class="dv">86</span></span>
+<span id="cb21-4"><a href="#cb21-4" tabindex="-1"></a>even.labels <span class="ot">&lt;-</span> <span class="fu">rep</span>(<span class="fu">c</span>(<span class="cn">TRUE</span>, <span class="cn">FALSE</span>), <span class="dv">14</span>)</span>
+<span id="cb21-5"><a href="#cb21-5" tabindex="-1"></a><span class="fu">biplot</span>(gas.data, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
+<span id="cb21-6"><a href="#cb21-6" tabindex="-1"></a>  <span class="fu">samples</span> (<span class="at">connected =</span> <span class="cn">TRUE</span>, <span class="at">connect.col=</span><span class="st">&quot;red&quot;</span>, <span class="at">label =</span> even.labels, <span class="at">label.cex=</span><span class="fl">0.6</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb21-7"><a href="#cb21-7" tabindex="-1"></a>  <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" 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" /><!-- --></p>
+</div>
+<div id="the-function-means" class="section level1" number="5">
+<h1><span class="header-section-number">5</span> The function
+<code>means()</code></h1>
+<p>The function <code>means()</code> allow changing the aesthetics for
+group means specified by group.aes, when the argument
+<code>show.class.means = TRUE</code> in the call to the function
+<code>PCA()</code>. The functionality of <code>means()</code> mirrors
+that of <code>samples()</code> and is discussed in detail in the
+vignette <em>Class separation</em> where class means are more prominent
+than in PCA biplots.</p>
+</div>
+<div id="the-function-axes" class="section level1" number="6">
+<h1><span class="header-section-number">6</span> The function
+<code>axes()</code></h1>
+<p>Similar to the <code>samples()</code> function, this function allows
+for changing the aestethics of the biplot axes. The first argument to
+<code>axes()</code> is an object of class <code>biplot</code>. The
+<code>X.names</code> argument is typically not specified by the user,
+but is required for the function to allow specifying which axes to
+display in the <code>which</code> argument, by either speficying the
+column numbers<br />
+or the column names. The arguments <code>col</code>, <code>lwd</code>
+and <code>lty</code> pertains to the axes themselves and can be
+specified either as a scaler value (to be recycled) or a vector with
+length equal to that of <code>which</code>.</p>
+<p>To construct a PCA biplot of the rock data, displaying only the axes
+for peri and shape with different colours for the two axes, different
+line widths and line type 2, we need to following code:</p>
+<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1" tabindex="-1"></a><span class="fu">biplot</span>(rock, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
+<span id="cb22-2"><a href="#cb22-2" tabindex="-1"></a>                               <span class="fu">axes</span>(<span class="at">which =</span> <span class="fu">c</span>(<span class="st">&quot;shape&quot;</span>,<span class="st">&quot;peri&quot;</span>), </span>
+<span id="cb22-3"><a href="#cb22-3" tabindex="-1"></a>                                    <span class="at">col=</span><span class="fu">c</span>(<span class="st">&quot;lightskyblue&quot;</span>,<span class="st">&quot;slategrey&quot;</span>),</span>
+<span id="cb22-4"><a href="#cb22-4" tabindex="-1"></a>                                    <span class="at">lwd =</span> <span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">2</span>), <span class="at">lty=</span><span class="dv">2</span>) <span class="sc">|&gt;</span></span>
+<span id="cb22-5"><a href="#cb22-5" tabindex="-1"></a>                               <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAqAAAAJACAMAAABlpiR1AAABLFBMVEUAAAAAAP9wgJBwgJFwgJhwgJ1wgKNwgKlwgLZwgZBwgZFwgZJwgZVwgaNwgpJwg5BwhK1whLVwiclwjclwkMJwl8lwrdtxgJBygJByh51zgJ1zgpN1gJB1kMJ8gZB9gpCBiJCBot6Buv+Fl52HzvqHzvyH1vyH3v2KgJCKgLaKl7aKwu2OgpGOnKeW2v+ampSdgZCdzvyd1vyd5/6igJCigKOigLail5CiraOi1v+xzvqxzvuxzvyyjZGyusKy//+6l5C6l6O6wqO66//Cl5DCn5PF1vrF1vvF9//SnpDSrZDSuqPS1snS68nS///V2v/V///Z///owqPo///s5/vs//3s////rJH/1rD/1rb/2rb/68n/7/z/9/z//6f//9v//+3///3///7///+0CrYOAAAACXBIWXMAAA7DAAAOwwHHb6hkAAASYElEQVR4nO3diZcjVd2H8emMC7hvgPvagvsGogiuKCAiyiKIgDiT//9/MOnp6Ul+N6ncVN2q+1Td53M875wz7zj5OjxUbqXTmVtrCexW7QFSFwMVmoEKzUCFZqBCM1ChGajQDFRoBio0AxWagQrNQIVmoEIzUKEZqNAMVGgGKjQDFZqBCs1AhWagQjNQoRmo0AxUaAYqNAMVmoEKzUCFZqBCM1ChGajQDFRoBio0AxWagQrNQIVmoEIzUKEZqNAMVGgGKjQDFZqBCs1AhWagQjNQoRmo0AxUaAYqNAMVmoEKzUCFZqBCM1ChGajQDFRoBio0AxWagQrNQIVmoEIzUKEZqNAMVGgGKjQDFZqBCs1AhWagQjNQoRmo0AxUaAYqNAMVmoEKzUCFZqBCIwd6S4VcFvld6kRQ5VHzkLfNy2WJ38RAI/K2BhloRN7WIAONyNsaZKAReducFDmBGmiKvG1GCvVpoAnytvko1aeBJsjb5sNAR0PeNhvF+jTQBHlbgww0Im9rkIFG5G0NMtCIvG0myp1ADTRF3jYPJfs00AR52zwY6KjI22ahaJ8GmiBvmwUDHRd5W4MMNCJva5CBRuRtDTLQiLxtBsqeQA00Rd7GV7pPA02Qt/EZ6OjI2/CK92mgCfI2PAMdH3lbgww0Im9rkIFG5G0NMtCIvI2t/AF0baAp8ja0Ufo00AR5G5qBToO8jWycPg00Qd5GZqATIW9rkIFG5G0NMtCIvK1BBhqRt3GNdAI10BR5G9ZofRpogrwNy0CnQ95GNV6fBpogb6My0AmRtzXIQCPytgYZaETe1iADjcjbkEY8gK4NNEXeRjRunwaaIG8jMtCJkbcBjdyngSbI24AMdGrkbQ0y0Ii8rUEGGpG3NchAI/I2nLFPoAaaIm+jGb9PA02Qt9EYaAXkbTAT9GmgCfK2ii4uLpKfM9AayNvqubg4VOgEDDQib6vm4qJWoQYakbdVY6Ac5G3VHAh0igPo2kBT5G2ZRrjW1erTQBPkbXlGeTaOv6WB1kLelmWS8+JUfRpogrwti4HO9VHzkLdlqXfHPQYDjcjb8iypTwNNkLdlWlCfBpogb6OY7ARqoCnytkxjX0En7NNAE+RteUY/gxpoTeRtWUa/i5+yTwNNkLdlMdC5Pmoe8rYsvg4610fNQ96WZ0l9GmiCvC3Tgvo00AR5G8GkJ1ADTa02am8Am7hPA02sViZ63NR9Gmjilo12MNDqrrYZ6GGT92mgCfK2BhloRN7WIAON4jaf7Ksy0OhAoCZ6z/QnUANNpdtM9J4afRpo4tA2E90yUITD2wy0Tp8GmiBvq8pAGcjbGmSg0altHkcnZaBRTqAmOhkDjTK2tdhonROogaaytjUXaK0+DTRB3lZNtT4NNEHeVo2Bcpy7rYVn+3p9GmiiT6DLT7QaA416bLPR8Rho1GvbyIFmfaP7kr4b/gEDjfK29a+hx38z66NCxvs8kYonUANNZW3rrqHratqjo6wPWxrvE5mq9mmgiZxtJ2o41eeZHRloI4+aZ2ig3cfR+QVat08DTZQI9HiivTqqegY1UJjBZ9DVqqvRXh15F9/Eo+YZfBe/LbPjIjqgo2Um2M1AI+62RX0wbS4Djfpv++vqo68WHBJV+WjvyidQA0313vbnT2+e1z//RvzpYl9kqhFo9T4NNNF327vf/Mbqi6vVh34ffr7YF+orBFq/TwNN9Nr249+tX//p7a+uVg+vVp87eBEt0GiLF1ADTfTZ9t8frVYfu6rwsW2iq9tfCL+gzEW0wT4NNNFz27/vv/z5ya/fvr354TP/LDurVQYa9dz2t9WNx77yk7KTZqfgpd5Ao57bXvnD9ql9df//fPvoL2zgrc0lD8sGGvXf9peHry6gn/3H27c/8bWjv2o2777vfQIt+nKDgUZDtr3ys80F9PaXf3v74/Euadc8Eu1/h2Sgoxq27T/fubqL/3B8NXTfHBI1UKjB297+1Je+dfIX4QMd8hKTZ9Axkbd1KP0a6ZmB7j+8d/EjIm87bsyvMlV8t7SBpqbeVu6roCMlUvUbogw0USPQwYmOWEjOb22gE6qwbXijpQvZOYEaKEyVbYMvoqP1ec73lBZ7/B0GGpG3dSjax94tfP73lMZfVWKTgUbkbRMJLzHldHboOlvkqmqgUe1tgJfwe7xIfyDQMgdTA41qb5vDl0FTBjqZ+ttmmeiRZ3gDLY6wbY6JHrxH8gxaHmNbvUALfiOSd/FjIG+bAOEb5XYZaETeNgEDrfeoeWjbpj2O0vo00ARt27R/hYiBVnzUPMBtfRod7+2h0zLQCLnt7EDHfAPzpAw0Im/LNuYbmKdloBF5W7aegeJOoAaaIm/bynq27xcosE8DTZC3beXdMS3lAmqgCfK2azmNLqRPA02Qt90Y5aVRA638qHnI245axh37IQYakbcds5TXlA4w0Ii87YjlvOqZMtCIvO2QzWm0RKDIA+jaQFPgbQcjLBMotU8DTXC3Ha1wRbqAFj5rGGiE3dZ1ndz8/KCXnYZ83PfOD+vy92sGGmG3jXkr1DfQ60UPhhUfaaARdhvwXv1iz97PlHoIA4242/L+wU/5/vuOQP0I8LGAt2X9Y5/yW0S6Ar3w247HQd6W6dxGB/6FHjvX9r1ei1xIDTQib8t2VqAD/0KPnR/CJbVEoQYakbeNo+xniexfQA20OPK2URT9ItJNm3542FjI2/o4+WRf9qucO0l6Bh0FeVsfFT8pz7v4MZC39TPHD3O8YaAReds5di9fM07UQCPytjOEA+DRQLHvs7tmoBF5W77cW2h6nwaaIG/Llxkovk8DTZC35Tse6N5x1EBJj5qn4LZy7+np9dhH3n6/c8fE79NAE+W2lXzXWa9HP/b/mvYzcYcx0KjYtrLviyyrQqA9/ygMNGoi0Ont/lmc86dioFE7gU55At39wzjrj8VAo7mcQQf/3td9TvNsvxPoef/iGmg0k7v44fXvBDp+ogZaDHnbA8PPDztP8OM0uj8vPMMbaG/kbQ8UDbTn83z348d9e/dInkH7I297AHAH1j2ga6B38UOQt+1g9Hl8Qql/gww0Im/bVfsVLAOthLytnOOvgeYeR08VWOgSb6AReVsxHa/RZ9/SnyqwzCXeQCPytlJOfA0ps9FJDhkGGpG3lXLyi5ycdzsZaETeVsikbwMdeJ010Ii8bYaG3isZaETeVsOwZ/vBrzYZaETeVsOwL9QbaHHkbSX0yGVAowZaHHlbAf166X8R9QxaGnnbcNO/ycS7+MLI24YDvAvqPAYakbcNNzzQiV/CN9CIvK2AwRfQqxum6S7CBhqRt5UwvK1Vgb8bNJuBRuRtN+oeI6c8yBpoRN52X+8+ynwV3kBrIm+71juQQu8SMdCayNuu9Q2k2LuYPINWRN52rXqgu2fgkd86aqARedt9tfvcNfInkxhoRN52g/XFoDEbNdCIvA3LQKczxTbWBRDNQKMJtlV5w8YMPo/+EAONxt92UeMtRZP1WfjJ3kCj6QKdtNApAy2ZqIFGywx0yif4ookaaDTZGXSxgRZN1ECjie7iF34jb6CjmWbbwvssx0Aj8rYGGWhE3tZXzddABx5HDTQqso31DF71NfqBX6g30KjEthHvgThvY8o3pFEDjQpsG/FVpD6/ce0+10Oe5w00Qgfa63cGBNqfgUbcQG++AkU6347NQCPsGfRiGYGe+aEPBhpR7+IX0ue9/x35B1IDjWDbbnrs2SftAHr9vyH7pslAI9a2B0X2u3rS+jTQwVDbdqvs9exeLdBjW8/998xAI9S2vX+cM+uzq9D838hAI9S2oXdFtQLt2u1d/DCsbTO9az/jX6wTX2Qy0Ai2bZZ9nhtoR6IGGpG3zcdZV/6uRg00Im87U83XmM678htoPvK28+BeA+3DQCPytvMY6MweNQ9521nm0+fecSA82xtoRN52ltkEun9DFe6YDDQib1uk9CWp3UYNNCJvW6RDr5l2B/ru918deRM5AvK2Rep+Ud8raETelm82B9D1iRf1b60/ePpPq488v15/8NTqoVfX7/7gVw/93Svo3M2pz+4X9TeBPvXIG+9s0nz5h+vXH12/+71nfIqfv3kF2mUb6DPr//3x+Q9++fzmYvrqNk4Dnbvl9LkNdFPm+uVnNs/wq81TvYGSt+VaXKDbK+jTV1UaKHlbg7ZP8Y+u33nkje0ZdPODgZK3NWh7Bf31/bv4zQ8GSt7WoOsz6OSPykXelmdBJ1ADTZG3ZVlUn34lKUHelsVA5/qoecjbcgD7HPKNfwYakbfl4AU66FunDTQib5ulYR8+YaARedssGWhZ5G2zZKBlkbedxDuArj2DFkbedgqyT+/iyyJvOwUa6BAGGpG3nbDAPg00Qd52goHO+1HzkLc1yEAj8rZF8BOWhyFvWwI/o34g8rZO8ziB+rd8DEXe1mUefRroYORtXQy0IHIE5G0dZtKnZ9DByNs6zCZQ7+IHIm9rkIFG5G0NMtCIvK1BBhqRtx01nxPouQw0Im87Zrl9GmiCvO2IBfdpoAnytiMMdBmPmoe87bAl92mgCfK2BhloRN7WIAONyNsaZKARedshiz6BGmiKvO0AaJ9DvhV+j4FG5G0HMAMd9GEieww0Im9LgfssU6iBRuRtKQMdBTkC8ra5MNARkbfNhmfQ8ZC3zYd38aMhb4uYJ9CiDDQibwsa6NNAE+Rt+1ro00AT5G37DHRhj5qHvG1PE30aaIK8rUEGGpG3NchAI/K2BhloRN62o40TqIGmsrcV+2JJH630aaCJ3G3lvtzch4Eu8FHzZG4r+IadHprp00ATBopioNEsAm2HgUbzOIM2w0CjedzFN8NAI/K2a+2cQA00Rd52T0t9GmiCvO1KU30aaIK87YqBLvVR85C3bbXVp4EmyNsaZKAReVuDDDQib2uQgUbkbc2dQA00Rd7WXp8GmiBvM9BFP2oe8rb2+jTQBHmbgS76UfOQtzXIQCPytgYZaETe1iADjbjbGjyBGmgKu63JPg00gd1moEt/1DzUbW32aaAJ6jYDXfyj5iFva5CBRuRtDTLQiLytQQYaIbc1egBdG2iKuK3dPg00UWXbiY/RMdAmHjVPjW0nPois4T4NNFFh26mPcjTQNh41DzDQlhloZKAoBhoBz6AtM9AIdxff8gnUQFO0bW33aaAJ2jYDbeZR88C2Nd6ngSZg2wy0nUfNQ97WIAONyNsaZKAReVuDDDQibWv9ALo20BRom30aaAq0zUANNMXZZp9rA01xthno2kBT5G0NMtCIvK1BBhqRtzXIQCPKNk+gVww0gmyzz3sMNIJsM9B7DDRibLPPawYaMbYZ6DUDjcjbGmSgEXlbgww0Im9rkIFGhG2eQG8YaATYZp8PGGhUf5t97jDQqP42A91hoFH1bfa5y0Aj8rYGGWhE3tYgA43I2xpkoFHlbZ5A9xloVHebfQYGGhkoioFGVbfZZ2SgkYGiGGhE3tYgA43I2xpkoBF5W4MMNKq4zRNoykCjetvs8wADjapts89DDDQyUBQDjWpts8+DDDQib2uQgUbkbQ0y0Ii8rUEGGtXZ5gn0CAONqmyzz2MMNDJQFAONamyzz6MMNDJQFAONyNsaZKAReVuDDDQib2uQgUbTb/ME2sFAo8m32WcXA42m3mafnQw0MlAUA40m3maf3Qw0Im9rkIFG5G0NMtCIvK1BBhpNus0T6CkGGk25zT5PMtDIQFEMNLo1ncsJH2u26kRQ5VGlTAZ65c3Lre++VnuHIgPduvPsS+89sX7zido7lDDQrTvPvXbvP7WHKDLQrbsvvrT5z/s/N1AcA72yafO9y8sna89QwkCFZqBCM9Ard1+4fPxfz75Ue4YSBrp194Un3//FW+89/lbtIYoMdOvOc69tAvVlJiAD3bp3BX3TKyiPgV7ZnEEvL+0TyECFZqBbnj6xDHTr7ou+wgRloFt3fuPb7aAMVGgGKjQDveI76qkMdMt31GMZ6JbvqMcy0C3fUY9loFd8Rz2VgQrNQIVmoEIzUKEZqNAMVGgGKjQDFZqBCs1AhWagQjNQoRmo0AxUaAYqNAMVmoEKzUCFZqBCM1ChGajQDFRoBio0AxWagQrNQIVmoEIzUKEZqNAMVGgGKjQDFZqBCs1AhWagQjNQoRmo0AxUaAYqNAMVmoEKzUCFZqBCM1ChGajQDFRoBio0AxWagQrNQIVmoEIzUKEZqNAMVGgGKjQDFZqBCs1AhWagQjNQoRmo0AxUaAYqNAMVmoEKzUCFZqBCM1ChGajQDFRoBio0AxWagQrt/y3SnecTUzqpAAAAAElFTkSuQmCC" /><!-- --></p>
+<p>The following four arguments deal with the axis labels. The argument
+<code>label.dir</code> is based on the graphics parameter
+<code>las</code> and allows for labels to be either orthogonal to the
+axis direction (<code>Orthog</code>), horisontal (<code>Hor</code>) or
+parallel to the plot <code>Paral</code>. The argument
+<code>label.line</code> fulfills the role of the <code>line</code>
+argument in <code>mtext()</code> to determine on which margin line (how
+far from the plot) the label is placed while <code>label.col</code> and
+<code>label.cex</code> is self-explanatory and defaults to the axis
+colour and size 0.75. Note in for the illustration the in the code below
+the colour vector has only three components, so that recycling is
+applied.</p>
+<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb23-1"><a href="#cb23-1" tabindex="-1"></a><span class="fu">biplot</span>(rock, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
+<span id="cb23-2"><a href="#cb23-2" tabindex="-1"></a>                               <span class="fu">axes</span>(<span class="at">col=</span><span class="fu">c</span>(<span class="st">&quot;lightskyblue&quot;</span>,<span class="st">&quot;slategrey&quot;</span>,<span class="st">&quot;blue&quot;</span>),</span>
+<span id="cb23-3"><a href="#cb23-3" tabindex="-1"></a>                                    <span class="at">label.dir=</span><span class="st">&quot;Hor&quot;</span>, <span class="at">label.line=</span><span class="fu">c</span>(<span class="dv">0</span>,<span class="fl">0.5</span>,<span class="dv">1</span>,<span class="fl">1.5</span>)) <span class="sc">|&gt;</span></span>
+<span id="cb23-4"><a href="#cb23-4" tabindex="-1"></a>                               <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>The function <code>pretty()</code> finds ‘nice’ tick marks where the
+value specified in the argument <code>ticks</code> determine the
+<em>desired</em> number of tick marks, although the observed number
+could be different. The other <code>tick.*</code> arguments are similar
+to their naming counterparts in <code>par()</code> or
+<code>text()</code>. Since the tick labels are important to follow the
+direction of increasing values of the axes, setting
+<code>tick.label = FALSE</code> does not remove the tick marks
+completely, but limits the labels to the smallest and largest value
+visible in the plot. If the user would like to specify alternative names
+for the axes, this can be done in the argument
+<code>ax.names</code>.</p>
+<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb24-1"><a href="#cb24-1" tabindex="-1"></a><span class="fu">biplot</span>(rock, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
+<span id="cb24-2"><a href="#cb24-2" tabindex="-1"></a>                               <span class="fu">axes</span>(<span class="at">label.dir=</span><span class="st">&quot;Paral&quot;</span>,</span>
+<span id="cb24-3"><a href="#cb24-3" tabindex="-1"></a>                                    <span class="at">ticks =</span> <span class="fu">c</span>(<span class="dv">3</span>, <span class="dv">5</span>, <span class="dv">5</span>, <span class="dv">10</span>), <span class="at">tick.label=</span><span class="fu">c</span>(F, F, T, T),</span>
+<span id="cb24-4"><a href="#cb24-4" tabindex="-1"></a>                                    <span class="at">ax.names =</span> <span class="fu">c</span>(<span class="st">&quot;area&quot;</span>, <span class="st">&quot;perimeter&quot;</span>, <span class="st">&quot;shape&quot;</span>, </span>
+<span id="cb24-5"><a href="#cb24-5" tabindex="-1"></a>                                                 <span class="st">&quot;permeability in milli-Darcies&quot;</span>)) <span class="sc">|&gt;</span></span>
+<span id="cb24-6"><a href="#cb24-6" tabindex="-1"></a>                               <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" 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" /><!-- --></p>
+</div>
+<div id="the-functions-fit.measures-and-summary" class="section level1" number="7">
+<h1><span class="header-section-number">7</span> The functions
+<code>fit.measures()</code> and <code>summary()</code></h1>
+<p>The <code>print</code> method provides a short summary of the biplot
+object.</p>
+<div class="sourceCode" id="cb25"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb25-1"><a href="#cb25-1" tabindex="-1"></a>  obj <span class="ot">&lt;-</span> <span class="fu">biplot</span>(airquality)</span>
+<span id="cb25-2"><a href="#cb25-2" tabindex="-1"></a><span class="co">#&gt; Warning in biplot(airquality): 42 rows deleted due to missing values</span></span>
+<span id="cb25-3"><a href="#cb25-3" tabindex="-1"></a>  obj</span>
+<span id="cb25-4"><a href="#cb25-4" tabindex="-1"></a><span class="co">#&gt; Object of class biplot, based on 111 samples and 6 variables.</span></span>
+<span id="cb25-5"><a href="#cb25-5" tabindex="-1"></a><span class="co">#&gt; 6 numeric variables.</span></span>
+<span id="cb25-6"><a href="#cb25-6" tabindex="-1"></a><span class="co">#&gt; </span></span>
+<span id="cb25-7"><a href="#cb25-7" tabindex="-1"></a><span class="co">#&gt; The following 42 sample-rows where removed due to missing values</span></span>
+<span id="cb25-8"><a href="#cb25-8" tabindex="-1"></a><span class="co">#&gt;  5 6 10 11 25 26 27 32 33 34 35 36 37 39 42 43 45 46 52 53 54 55 56 57 58 59 60 61 65 72 75 83 84 96 97 98 102 103 107 115 119 150</span></span></code></pre></div>
+<p>The output from <code>summary()</code> will be very similar.</p>
+<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb26-1"><a href="#cb26-1" tabindex="-1"></a>  <span class="fu">summary</span>(obj)</span>
+<span id="cb26-2"><a href="#cb26-2" tabindex="-1"></a><span class="co">#&gt; Object of class biplot, based on 111 samples and 6 variables.</span></span>
+<span id="cb26-3"><a href="#cb26-3" tabindex="-1"></a><span class="co">#&gt; 6 numeric variables.</span></span>
+<span id="cb26-4"><a href="#cb26-4" tabindex="-1"></a><span class="co">#&gt; </span></span>
+<span id="cb26-5"><a href="#cb26-5" tabindex="-1"></a><span class="co">#&gt; The following 42 sample-rows were removed due to missing values</span></span>
+<span id="cb26-6"><a href="#cb26-6" tabindex="-1"></a><span class="co">#&gt;  5 6 10 11 25 26 27 32 33 34 35 36 37 39 42 43 45 46 52 53 54 55 56 57 58 59 60 61 65 72 75 83 84 96 97 98 102 103 107 115 119 150</span></span></code></pre></div>
+<p>Additional information about the biplot object is added by the
+<code>fit.measures()</code> function.</p>
+<div id="quality-of-approximation" class="section level2" number="7.1">
+<h2><span class="header-section-number">7.1</span> Quality of
+approximation</h2>
+<p>We start with the identity</p>
+<p><span class="math display">\[
+\mathbf{X} = \mathbf{\hat{X}} + \mathbf{X-\hat{X}}
+\]</span> which decomposes <span class="math inline">\(\mathbf{X}\)</span> into a fitted part</p>
+<p><span class="math display">\[
+\mathbf{\hat{X}} = \mathbf{UJDJV&#39;} =
+\mathbf{UDJ}_2(\mathbf{VJ}_2)&#39; =
+\mathbf{UDV&#39;VJ}_2(\mathbf{VJ}_2)&#39; = \mathbf{XVJV&#39;}
+\]</span></p>
+<p>and the residual part <span class="math inline">\(\mathbf{X-\hat{X}}\)</span>. The lack of fit is
+quantified by the quantity we are minimising</p>
+<p><span class="math display">\[
+\| \hat{\mathbf{X}}-\mathbf{X} \|^2
+\]</span> where we have the orthogonal decomposition</p>
+<p><span class="math display">\[
+\|\mathbf{X}\|^2 = \|\hat{\mathbf{X}}\|^2 +
+\|\hat{\mathbf{X}}-\mathbf{X} \|^2.
+\]</span> The overall quality of fit is therefore defined as</p>
+<p><span class="math display">\[
+quality = \frac{\|\hat{\mathbf{X}}\|^2}{\|\mathbf{X}\|^2} =
+\frac{tr(\mathbf{\hat{X}\hat{X}&#39;})}{tr(\mathbf{XX}&#39;)} =
+\frac{tr(\mathbf{\hat{X}&#39;\hat{X}})}{tr(\mathbf{X&#39;X})} =
+\frac{tr(\mathbf{VD}^2\mathbf{JV&#39;})}{tr(\mathbf{VD}^2\mathbf{V&#39;})}.
+\]</span> In <em>biplotEZ</em> the overall quality is displayed as a
+percentage:</p>
+<p><span class="math display">\[
+quality =\frac{d_1^2+d_2^2}{d_1^2+\dots+d_p^2}100\%.
+\]</span></p>
+</div>
+<div id="adequacy-of-representation-of-the-variables" class="section level2" number="7.2">
+<h2><span class="header-section-number">7.2</span> Adequacy of
+representation of the variables</h2>
+<p>Researchers who construct the PCA biplot representing the columns
+with arrows (vectors) often fit the biplot with a unit circle. The
+rationale being that perfect representation of a variable will have unit
+length and the length of each arrow vs the distance to the unit circle
+represent the adequacy with which the variable is represented.</p>
+<p>By fitting the biplot with calibrated axes, it is much easier to read
+off values for the variables, but the adequacy values can still be
+computed from</p>
+<p><span class="math display">\[
+\frac{diag(\mathbf{V}_r\mathbf{V}_r&#39;)}{diag(\mathbf{VV}&#39;)}=
+diag(\mathbf{V}_r\mathbf{V}_r&#39;)
+\]</span></p>
+<p>due to the orthogonality of the matrix <span class="math inline">\(\mathbf{V}:p \times p\)</span>.</p>
+</div>
+<div id="predictivities" class="section level2" number="7.3">
+<h2><span class="header-section-number">7.3</span> Predictivities</h2>
+<p>The predictivity provides a measure of how well the original values
+are recovered from the biplot. An element that is well represented will
+have a predictivity close to one, indicating that the sample or variable
+values from prediction is close to the observed values. If an element is
+poorly represented, the predicted values will be very different from the
+original values and the predictivity value will be close to zero.</p>
+<div id="axis-predictivity" class="section level3" number="7.3.1">
+<h3><span class="header-section-number">7.3.1</span> Axis
+predictivity</h3>
+<p>The predictivity for each of the <span class="math inline">\(p\)</span> variables is computed as the
+elementwise ratios</p>
+<p><span class="math display">\[
+axis \: predictivity =
+\frac{diag(\mathbf{\hat{X}&#39;\hat{X}})}{diag(\mathbf{X&#39;X})}
+\]</span></p>
+</div>
+<div id="sample-predictivity" class="section level3" number="7.3.2">
+<h3><span class="header-section-number">7.3.2</span> Sample
+predictivity</h3>
+<p>The predictivity for each of the <span class="math inline">\(n\)</span> samples is computed as the elementwise
+ratios</p>
+<p><span class="math display">\[
+sample \: predictivity =
+\frac{diag(\mathbf{\hat{X}\hat{X}&#39;})}{diag(\mathbf{XX&#39;})}
+\]</span> By calling the function <code>fit.measures()</code> these
+quantities are computed for the specific biplot object. The values are
+displayed with the <code>summary()</code> function.</p>
+<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb27-1"><a href="#cb27-1" tabindex="-1"></a>obj <span class="ot">&lt;-</span> <span class="fu">biplot</span>(state.x77, <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
+<span id="cb27-2"><a href="#cb27-2" tabindex="-1"></a>  <span class="fu">fit.measures</span>() <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
+<p><img role="img" 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" /><!-- --></p>
+<div class="sourceCode" id="cb28"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb28-1"><a href="#cb28-1" tabindex="-1"></a><span class="fu">summary</span> (obj)</span>
+<span id="cb28-2"><a href="#cb28-2" tabindex="-1"></a><span class="co">#&gt; Object of class biplot, based on 50 samples and 8 variables.</span></span>
+<span id="cb28-3"><a href="#cb28-3" tabindex="-1"></a><span class="co">#&gt; 8 numeric variables.</span></span>
+<span id="cb28-4"><a href="#cb28-4" tabindex="-1"></a><span class="co">#&gt; </span></span>
+<span id="cb28-5"><a href="#cb28-5" tabindex="-1"></a><span class="co">#&gt; Quality of fit in 2 dimension(s) = 65.4% </span></span>
+<span id="cb28-6"><a href="#cb28-6" tabindex="-1"></a><span class="co">#&gt; Adequacy of variables in 2 dimension(s):</span></span>
+<span id="cb28-7"><a href="#cb28-7" tabindex="-1"></a><span class="co">#&gt; Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost </span></span>
+<span id="cb28-8"><a href="#cb28-8" tabindex="-1"></a><span class="co">#&gt;  0.1848016  0.3586383  0.2215201  0.1760908  0.2915819  0.2696184  0.1513317 </span></span>
+<span id="cb28-9"><a href="#cb28-9" tabindex="-1"></a><span class="co">#&gt;       Area </span></span>
+<span id="cb28-10"><a href="#cb28-10" tabindex="-1"></a><span class="co">#&gt;  0.3464170 </span></span>
+<span id="cb28-11"><a href="#cb28-11" tabindex="-1"></a><span class="co">#&gt; Axis predictivity in 2 dimension(s):</span></span>
+<span id="cb28-12"><a href="#cb28-12" tabindex="-1"></a><span class="co">#&gt; Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost </span></span>
+<span id="cb28-13"><a href="#cb28-13" tabindex="-1"></a><span class="co">#&gt;  0.3330216  0.7609185  0.7917091  0.6206172  0.8640485  0.7947530  0.4982299 </span></span>
+<span id="cb28-14"><a href="#cb28-14" tabindex="-1"></a><span class="co">#&gt;       Area </span></span>
+<span id="cb28-15"><a href="#cb28-15" tabindex="-1"></a><span class="co">#&gt;  0.5675169 </span></span>
+<span id="cb28-16"><a href="#cb28-16" tabindex="-1"></a><span class="co">#&gt; Sample predictivity in 2 dimension(s):</span></span>
+<span id="cb28-17"><a href="#cb28-17" tabindex="-1"></a><span class="co">#&gt;        Alabama         Alaska        Arizona       Arkansas     California </span></span>
+<span id="cb28-18"><a href="#cb28-18" tabindex="-1"></a><span class="co">#&gt;     0.95126856     0.61373919     0.26327256     0.86308539     0.57062754 </span></span>
+<span id="cb28-19"><a href="#cb28-19" tabindex="-1"></a><span class="co">#&gt;       Colorado    Connecticut       Delaware        Florida        Georgia </span></span>
+<span id="cb28-20"><a href="#cb28-20" tabindex="-1"></a><span class="co">#&gt;     0.83358779     0.59003002     0.18284712     0.49725356     0.94461052 </span></span>
+<span id="cb28-21"><a href="#cb28-21" tabindex="-1"></a><span class="co">#&gt;         Hawaii          Idaho       Illinois        Indiana           Iowa </span></span>
+<span id="cb28-22"><a href="#cb28-22" tabindex="-1"></a><span class="co">#&gt;     0.01984127     0.70337480     0.33405270     0.30082350     0.96367113 </span></span>
+<span id="cb28-23"><a href="#cb28-23" tabindex="-1"></a><span class="co">#&gt;         Kansas       Kentucky      Louisiana          Maine       Maryland </span></span>
+<span id="cb28-24"><a href="#cb28-24" tabindex="-1"></a><span class="co">#&gt;     0.86554676     0.87758262     0.93717163     0.66553856     0.06362508 </span></span>
+<span id="cb28-25"><a href="#cb28-25" tabindex="-1"></a><span class="co">#&gt;             MA       Michigan             MN    Mississippi       Missouri </span></span>
+<span id="cb28-26"><a href="#cb28-26" tabindex="-1"></a><span class="co">#&gt;     0.47386267     0.26050188     0.89207404     0.93073099     0.11321791 </span></span>
+<span id="cb28-27"><a href="#cb28-27" tabindex="-1"></a><span class="co">#&gt;        Montana       Nebraska         Nevada  New Hampshire             NJ </span></span>
+<span id="cb28-28"><a href="#cb28-28" tabindex="-1"></a><span class="co">#&gt;     0.44603781     0.93570441     0.22393876     0.87499561     0.15979033 </span></span>
+<span id="cb28-29"><a href="#cb28-29" tabindex="-1"></a><span class="co">#&gt;     New Mexico       New York North Carolina   North Dakota           Ohio </span></span>
+<span id="cb28-30"><a href="#cb28-30" tabindex="-1"></a><span class="co">#&gt;     0.29304145     0.40609063     0.93004841     0.69011551     0.08810179 </span></span>
+<span id="cb28-31"><a href="#cb28-31" tabindex="-1"></a><span class="co">#&gt;       Oklahoma         Oregon             PA   Rhode Island South Carolina </span></span>
+<span id="cb28-32"><a href="#cb28-32" tabindex="-1"></a><span class="co">#&gt;     0.37520943     0.36273523     0.02176080     0.58625617     0.93187284 </span></span>
+<span id="cb28-33"><a href="#cb28-33" tabindex="-1"></a><span class="co">#&gt;   South Dakota      Tennessee          Texas           Utah        Vermont </span></span>
+<span id="cb28-34"><a href="#cb28-34" tabindex="-1"></a><span class="co">#&gt;     0.83804787     0.96006357     0.73748654     0.66209083     0.80365601 </span></span>
+<span id="cb28-35"><a href="#cb28-35" tabindex="-1"></a><span class="co">#&gt;       Virginia     Washington  West Virginia      Wisconsin        Wyoming </span></span>
+<span id="cb28-36"><a href="#cb28-36" tabindex="-1"></a><span class="co">#&gt;     0.58564755     0.33877314     0.85231725     0.82519206     0.42499724</span></span></code></pre></div>
+<p>If is not necessary to call the <code>plot()</code> function to
+obtain the fit measures, but one of the biplot methods, such as
+<code>PCA()</code> is required, since the measures differ depending on
+which type of biplot is constructed. To suppress the output of some fit
+measures, for instance if the interest is in the axis predictivity and
+there are many samples which result in a very long output, these can be
+set in the call to <code>summary()</code>. By default all measures are
+set to <code>TRUE</code>.</p>
+<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb29-1"><a href="#cb29-1" tabindex="-1"></a>obj <span class="ot">&lt;-</span> <span class="fu">biplot</span>(state.x77, <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
+<span id="cb29-2"><a href="#cb29-2" tabindex="-1"></a>  <span class="fu">fit.measures</span>() </span>
+<span id="cb29-3"><a href="#cb29-3" tabindex="-1"></a><span class="fu">summary</span> (obj, <span class="at">adequacy =</span> <span class="cn">FALSE</span>, <span class="at">sample.predictivity =</span> <span class="cn">FALSE</span>)</span>
+<span id="cb29-4"><a href="#cb29-4" tabindex="-1"></a><span class="co">#&gt; Object of class biplot, based on 50 samples and 8 variables.</span></span>
+<span id="cb29-5"><a href="#cb29-5" tabindex="-1"></a><span class="co">#&gt; 8 numeric variables.</span></span>
+<span id="cb29-6"><a href="#cb29-6" tabindex="-1"></a><span class="co">#&gt; </span></span>
+<span id="cb29-7"><a href="#cb29-7" tabindex="-1"></a><span class="co">#&gt; Quality of fit in 2 dimension(s) = 65.4% </span></span>
+<span id="cb29-8"><a href="#cb29-8" tabindex="-1"></a><span class="co">#&gt; Axis predictivity in 2 dimension(s):</span></span>
+<span id="cb29-9"><a href="#cb29-9" tabindex="-1"></a><span class="co">#&gt; Population     Income Illiteracy   Life Exp     Murder    HS Grad      Frost </span></span>
+<span id="cb29-10"><a href="#cb29-10" tabindex="-1"></a><span class="co">#&gt;  0.3330216  0.7609185  0.7917091  0.6206172  0.8640485  0.7947530  0.4982299 </span></span>
+<span id="cb29-11"><a href="#cb29-11" tabindex="-1"></a><span class="co">#&gt;       Area </span></span>
+<span id="cb29-12"><a href="#cb29-12" tabindex="-1"></a><span class="co">#&gt;  0.5675169</span></span></code></pre></div>
+<p>The axis predictivities and sample predictivities can be represented
+in the biplot in two ways: setting either <code>axis.predictivity</code>
+and / or <code>sample.predictivity</code> to <code>TRUE</code>, applies
+shading for axes and shrinking for samples according to the predictivity
+values.</p>
+<div class="sourceCode" id="cb30"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb30-1"><a href="#cb30-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> state.region) <span class="sc">|&gt;</span></span>
+<span id="cb30-2"><a href="#cb30-2" tabindex="-1"></a>  <span class="fu">samples</span> (<span class="at">which =</span> <span class="st">&quot;South&quot;</span>, <span class="at">pch =</span> <span class="dv">15</span>, <span class="at">label =</span> T, <span class="at">label.cex=</span><span class="fl">0.5</span>) <span class="sc">|&gt;</span> </span>
+<span id="cb30-3"><a href="#cb30-3" tabindex="-1"></a>  <span class="fu">axes</span> (<span class="at">col =</span> <span class="st">&quot;black&quot;</span>) <span class="sc">|&gt;</span></span>
+<span id="cb30-4"><a href="#cb30-4" tabindex="-1"></a>  <span class="fu">fit.measures</span>() <span class="sc">|&gt;</span> <span class="fu">plot</span> (<span class="at">sample.predictivity =</span> <span class="cn">TRUE</span>,</span>
+<span id="cb30-5"><a href="#cb30-5" tabindex="-1"></a>                          <span class="at">axis.predictivity =</span> <span class="cn">TRUE</span>) </span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+<p>Comparing the plot with the <code>summary</code> output it is clear
+that the variables Population and Frost are not very well represented
+and it can be expected that predictions on these variables will be less
+accurate. Furthermore, the samples located close to the origin are not
+as well represented as those located towards the bottom right. This is
+typically the case where samples nearly orthogonal to the PCA plane are
+projected close to the origin and due to their orthogonality, very
+poorly represented.</p>
+</div>
+<div id="axes-represented-as-vectors" class="section level3" number="7.3.3">
+<h3><span class="header-section-number">7.3.3</span> Axes represented as
+vectors</h3>
+<p>If the user wishes to view the variables as arrows on the biplot to
+give information on the adequacy of the variables, this can be done with
+the <code>axes()</code> function, by setting <code>vectors = TRUE</code>
+and <code>unit.circle = TRUE</code>. The adequacy value is given by
+squared length of the arrow.</p>
+<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb31-1"><a href="#cb31-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> state.region) <span class="sc">|&gt;</span></span>
+<span id="cb31-2"><a href="#cb31-2" tabindex="-1"></a>  <span class="fu">axes</span> (<span class="at">vectors =</span> <span class="cn">TRUE</span>,<span class="at">unit.circle =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span></span>
+<span id="cb31-3"><a href="#cb31-3" tabindex="-1"></a>  <span class="fu">fit.measures</span>() <span class="sc">|&gt;</span> <span class="fu">plot</span> () </span></code></pre></div>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
+</div>
+</div>
+</div>
+<div id="references" class="section level1 unnumbered">
+<h1 class="unnumbered">References</h1>
+<div id="refs" class="references csl-bib-body hanging-indent" entry-spacing="0">
+<div id="ref-EckartYoung1936" class="csl-entry">
+Eckart, C., and G. Young. 1936. <span>“The Approximation of One Matrix
+by Another of Lower Rank.”</span> <em>Psychometrika</em>, 211–18.
+</div>
+<div id="ref-Gabriel1971" class="csl-entry">
+Gabriel, K. R. 1971. <span>“The Biplot Graphic Display of Matrices with
+Application to Principal Component Analysis.”</span>
+<em>Biometrika</em>, 453–67.
+</div>
+</div>
+</div>
+
+
+
+<!-- code folding -->
+
+
+<!-- dynamically load mathjax for compatibility with self-contained -->
+<script>
+  (function () {
+    var script = document.createElement("script");
+    script.type = "text/javascript";
+    script.src  = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
+    document.getElementsByTagName("head")[0].appendChild(script);
+  })();
+</script>
+
+</body>
+</html>
diff --git a/vignettes/biplotEZ_enhancements.html b/vignettes/biplotEZ_enhancements.html
index 099cb54..96bc6b8 100644
--- a/vignettes/biplotEZ_enhancements.html
+++ b/vignettes/biplotEZ_enhancements.html
@@ -48,8 +48,9 @@
 }
 </style>
 <style type="text/css" data-origin="pandoc">
+html { -webkit-text-size-adjust: 100%; }
 pre > code.sourceCode { white-space: pre; position: relative; }
-pre > code.sourceCode > span { line-height: 1.25; }
+pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
 pre > code.sourceCode > span:empty { height: 1.2em; }
 .sourceCode { overflow: visible; }
 code.sourceCode > span { color: inherit; text-decoration: inherit; }
@@ -437,7 +438,7 @@ <h1><span class="header-section-number">2</span> The function
 <span id="cb1-12"><a href="#cb1-12" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for 19-th </span></span>
 <span id="cb1-13"><a href="#cb1-13" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for 20-th </span></span>
 <span id="cb1-14"><a href="#cb1-14" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for 21-st</span></span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 <p>By default one <span class="math inline">\(95\%\)</span>-bag is
 constructed for each group. In general, the <code>alpha.bags()</code>
 function accepts an object of class biplot as first argument. The next
@@ -457,7 +458,7 @@ <h1><span class="header-section-number">2</span> The function
 <span id="cb2-8"><a href="#cb2-8" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for 21-st </span></span>
 <span id="cb2-9"><a href="#cb2-9" tabindex="-1"></a><span class="co">#&gt; Computing 0.99 -bag for 18-th </span></span>
 <span id="cb2-10"><a href="#cb2-10" tabindex="-1"></a><span class="co">#&gt; Computing 0.99 -bag for 21-st</span></span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 <p>In the biplot above, the colours were recycled for each alpha value.
 To specify differential colours, we can use the <code>col</code>
 argument and similarly the <code>lty</code> and or <code>lwd</code>
@@ -485,7 +486,7 @@ <h1><span class="header-section-number">2</span> The function
 <span id="cb3-15"><a href="#cb3-15" tabindex="-1"></a><span class="co">#&gt; Computing 0.99 -bag for 19-th </span></span>
 <span id="cb3-16"><a href="#cb3-16" tabindex="-1"></a><span class="co">#&gt; Computing 0.99 -bag for 20-th </span></span>
 <span id="cb3-17"><a href="#cb3-17" tabindex="-1"></a><span class="co">#&gt; Computing 0.99 -bag for 21-st</span></span></code></pre></div>
-<p><img 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9lvjwort6H7GzTomekE+vbzdR3pHNADx2sYRr5T5aTMFXIz1KKe6Dl6u4MKK/ehFD1B1MPxY8WsrEKVk83bHT3M1dePfJfOhCK86b7U4I7oJvRC2X1I8ARhQrk+Po2JJpq919AjfZZUsNnnoPXKY7YnnRM9hxzfZShDEjQo6+UpOl6iORoAx2TkO8vdqcwluoAhOc+gwsptKIInCBfpeNzsZAAcsYyjVoEU2RNuQy+RvYIETxDu0gPHd/FiCMIJ5PieQIInCNfxuOPJ+oR7mCbnie5AgieIbkCOJ9YhFLj3FhI8QXQJTzmeILoDOb6HkOAJont4x/EUxBNuQ8n5nkOCJ4iu4h2PkuMJ9yC7ewESPEF0m2amkHd6tI4cquNHIwiih5DgCaIH2E8h38LROpWoJ4j2ofDdI5DgCaJneNPxZH2iHcju3oEETxC9hBxPBAlqM+8pSPAE0WO84HiC6BTkeO9AgieI3tNzx1MQT7QPJee9BgmeIDwBOZ7wKexH4iBwV1JSmZTSnUtb79BsfUGDZmD0NR1Mb7Z2KMNelG4lnKC9CNr8WlQ5pfBxgQPYnMaYPPHZMSqsXIUieILwEF4Lmr12PYR/Kak5tVRe5uPiNJc9efJkT68o+JDgCcJbdMqplKgnuoNW9W7/U+Hjk5ipJucTmcKL+Te7c4XrFhI8QXgOrzmeIBxS9+PR17uzuF2SkrIkSaI4+SA+6NmFrg9I8AThRVx1fKXQtWzqpN+LVcOT8gkDWts61Fa965dV+Uqxsly8JEmpkjAlihNs99xr3/w/une56xJqkBU0qJFdkOhUGzf9carLqpyUuak4b7ULWzDZkSAAOOgX915S+odfEqceBljDuuIwQvuRm2G7UGHlNhTBE4R36XgcXyNpjgvlcvb9lQyRGcXxRD02v4qhEO5eLGeK+Lg4PdaH3MwkvSZ2iw29vgCCIOxgWm0cOqtyMpEphGPTU6wjkvHrWLgmp8oIx6ZN43ftjBS1E1bow3er3wkfn8zlZoqXJCk3Kcb5RKYUvi+81O0rXb9QhiRoUNYrkDTMhaqyXBIEXpWTCTUqmqTdJUmKhcOZQqFZYVPPeKIe2x+kkpJmcgCAyKQY51U5mcjcDWO5ADywJTz6WOUdlAort6EUPUH4AEMfpPqkKCcIPABOmIgV69PuzMrCxBgAtbpalZNNDyxGiXrC/iVPlXPctDgZAYCbb5cb1mG5EAaAoT3mGSbCFShFTxC+QZOrdfGqKvkC6krQ8vacIE6q5dJZSUkzucikKPKAKidTCm/R2s5pHQGxnrD5SZTUnMrFOYRj01O8kkxkZtn74BT9hLoOZUiCBmW9fEs5sRmZNMuwV9AJntW6GzcIxybH8jMZWFXGawfRn0dJJVVBt319hb5Nop70v65wMKOMkpJm8Oi08DDHAVDfkRJXt0yKh+p+1VRYuQ3d36BBz4xfURSF5/l62dai9UpnJaySkrJcVcNMzJFJMT5iWRnPusdlCrlKGW1Sb6+qKsdxqpxMY8LG8WyB7L5+aFT1nouUf0eqnExkQpNinJckKRKObQ7lP637VVNh5TZUB08Q3oDnmWH5SCivqKabaIrVcvV8fHosn2BV6KqcTOTHpkUxzgOcEI3Y9YGbLB9BSUmJ/Nh0nK+pj+c4DgAnRC0vBUClZUCrfzARMPhIJDcjSUlZBThhShQjOZYrikwJe+JU994DSPAE4SFUOSnNIGpRFpr1SueEqUnMJGU5lciP6dLySi4XiZin+jkhiplyl7mZiChOcbIkJfJ32be5mUqjOyU1UxzjtUuh4e3WOQ6S8+HYtBhVE0zy0kwu3KDGiXAXypAEDcp6+QpjPXql2ru8vmHpqMvV6xP75WB+SoCcTDiuj2cp1kguqW4OZS7lzM9OvebWJw7sXqnaAaDKUiITHgqPfd4ucKfCym0ogieIHsIJU6I4GUE4Ni2KoihOCRygpKQ0JkRRFCO5pGyTIjfvtFbOuk8gLUkJNSqKE0hbdoRTY+EIkOMBgI9P3p352Qyiwp64KIoVuyspqZx3NTkjxfFEFWZ3AJwAYMPgAEdp+Z5C3eQIotfwcREpSUrGpqcErqbZ3AiHXAn13d70VNrcTebKpg3HpkVBYfXxUxwACNGIlFPifINUqZKaWQxtGymqKlhiXmuzJ8ZVOZmUJ6gedX3iKHyv3Z7yOl6AMiRBg7JevkbfENn4yZaaItXQtt7+OIZhx2rWo7qmdmYaStSvH5qzuypLiQwbXqEhVFi5DaXoCcI7qGpRaxnHLB3nK+PN2Y82p0+VK7libEKzuyonZ4oxwbLA5eOVxvA5fUc5OauzO1Q5nQnp2uxRop4wQ5USmdi0I7sTXYAETxDegePHillZhSonyzF4Z+rjnaTWa3cvqeBGag8S52vq40nq64GmwndJSkQmp6kaxztQhiRoUNbL72gt4LnaVLvt7O1VWH18Je1uObuc7e4iYD5jSKGyyAbAoUR9sGnS7k3/71Nh5TZ0f4MGPTOBoTP18c1jsrt1fTw5Pqh0oWEdFVZuQyl6gvAmpvXxjmgzeV63u119PCXqCdCLnVchwROEN6mvj29iZ+bdltXrqD7ebGPyfTBwOzlPdAfKkAQNynoFCV19fIu0U/ha1sc3OguV+L6ma3anwspt6P4GDXpmCAMtF8FN7UiODwzOBd/m/zIVVm5DKXqCCDgtp82b2pGS88Gga3YnugAJniCCT/cdT773I822nCc8DgmeINYF3XF8R3YkvA+F776ABE8Q64UuqJqk7l8oOR88SPAEsY7osuPJ936B7B5ISPAEsb7ocsqdHO8XyO7BgwRPEOsOtx1PUvcXDv+zyO6+gwRPEOsRtx1MiXq/QC3nAwwJniDWKW6n3Mnx3oeq3oMNCZ4g1i/drFYnx/sXsrtPIcETxLrGVVuT1L1Mw/CdbUB29y80FHDQoOGdiRZorRB3uJd+M7KFR3CYnHf1/4sKK7ehCJ4giO7F8RTT+whmd7t5h5WUJEmSlFK6e2GEQ0jwBEEArU4hT8L2I021nBdF0fx/WZWTuYgoiuI0l5WkpKx2/DqJNqEMSdCgrBfRJi1kZZ3sQol6j9Cp5LwqJ2VuKs5rnxL5sekpgXN+JVRYuQ1F8ARB1NBCUO5kF0rUe4c27a6qKgCOHyvOaMl5TpiaHsunKYz3FCR4giCMuCRg8noP0ZrEO9nS7g1ASSUSaVkFOGEiVpyRdI6PhvIKGd5DkOAJgjChWRm7vT3RJtoNtw/fG9hdlZMzmBTLmXhOmBInMVNuZafK2eIY30SKnnAbqgIJGlStRXSQZivLqTLey+irSOq+VFLSTA4AEJkUKzXrBrSKdsjJRKYAAAjHpqeEUkqayYVjzVXBU2HlOhTBEwRhiRtxOcXu3US71Vr4bnr/VTnHTYtsg0jOquMbq2hPpFJyfmyaHWoylJEV8HFRFJuzO9EF6AUqaNBLMdFxXI3jKYh3G9vAvQyL37UNVDmZUKMWgbySkmagRflKKqkKrbmdCiu3ofsbNOiZIdygBceXl8IxFDL1+xpa1JPj3UMfr9fd52pmfgh4oJqcr+0EZ00bfqfCynUoRU8QRGNayNWXlwqZaWt5s80oad8FTJPzqnzt45EwAFGc3hlGblYbsKakghuxOZwqJyVJkqRchDLz3oVeoIIGvRQT7lENtZVKqyoeKsfVlfCqJCXYkmloXp+fpyDeJexbzr+XlC4WIIpiJZDfiO2j4cUPCg1a2mVCll83ARVWbkP3N2jQM0O4ijY+edkKxXAsOiXoy3olJc3kYtOiwFFlfI+xs7sqp5T7kLmUA7Y/GF4NTUwJHNR3Xjr7ofDLUw9bHbGVAessocLKbShFTxBEE1TsPi0npSw3LU7V2T3LTYsiE4AoTkqS02HK9Qlkyth3Cot3JlVO58FtzwHTsZHFDwoFtQQA3LaRftgplxOmqLW8f6AXqKBBL8WE2zD7Vns9mze5ZknfyKQYn5EkRCbF+AjrPF3fXVofxLM1FMq3j034rsrJNCYKmcRkBDM5YHjb/ofvv3QxBzywJTz6WLcMToWV29D9DRr0zBCto1bHL7Gqg5UkKQyEJsXcjCSKk+Wq+KiayHKat1VZLgkCXxHJlMBJklQ+IPN+neS1zD/I7p3A9k6WK9ynY2H2vwMlJV0qYqlgN8iNC1Bh5TYben0BBEF4B35C5BWbLtBQIggzk8fFadaSLjYhcBym1WQixTGHy5kMOIHnwQnRkCQrQpzJmwsjE5oUxXj9cfWd5agyviNY30Oe2T2RCU2KHACMcENLH42J4v4uXh7RBUjwBEFU4GBrdwB8XORR6SUtiiKgSpKEaVEQpkRFUQAeI1wkxrMjqGoxzI0AUF4HkCkAhZwS57sWI65P7FswaO9P05xcUgFOldPXN4Z2/lK3Lo/oGtTIjiCIMkoqkR+brtpdSVk0kFOVfIgbYV9w07FwJiEBAD+iJiUpqfARNSFJkiRJifzYhMBd+ntpZnH7pCiKIpDLlmcmSRrGQ9Wn6KmRXcs4r+bgeIEvpSQpkSmEok9Ry7kAQlUgQYOqtYiWUFLSTFFXM14ZjxQpSVe7Xt1aG7+s3MQuNyMBWls6XRagdmBT4D1JugiAVdznIsZsASXq28T+vtV8azsgbReg/2K3oQieIAgAfFw/W4iSmskBuZwCPi5OIG2ce4SPR3VB+rSgJhGOAYjzACdEI7lceQdVzlbtrirzF5MXAcTCCHEcH5/EjPHIFMe3g8PkPADWU06fr+km7Kdz4sSJXpx8HUF18ARB6Cm3fBfFOFQ5mZRHpgRhqr5ZHB/XGsspKSnLxj4RJEkSxclcLhIxaUh36Rcz859EpsUpTpKkSFZWeSEugtXbE+1jn5w3hsuKokYn4r3Iy1Pg3jUonRs0KEVPtEdt9r3cj6rcf860E1XtdCOqJCVqOsFVZzPR9bFWZSmRmRZFDrpRb3XVAJSob5bm7N4jDBdJhZXb0P0NGvTMEG1S0XqpUnmuaNXwplOH6VaWK/ILmYS5TqqyD8empzIJKQwUIpNinK++S1QgxzeFzV3yyA2svwwqrNyGUvQEQdTACVMTclKSQpOiyEPRN7Ib4ZArAbWC5+PRXLnuNxybFuMcIFjMAKvL60NJZRApIMdyAhw/Brnm0DSNrHM83liBxi/qFfQCFTTopZjoIEpK0jV0r/3UCFs9V6cbr4xsb9Kem4J4J3g8OW9zAVRYuQ21oicIwgpVLUYiVbtnuWYaXds2g69ONy6Kk6wpfv2hqUW9Q/xod6ILkOAJgrCC48eKWVmFyqaOa3oSEmsx6/rZSblJUSxkEk0egQBsk/O9lSv7ryW79xbKkAQNynoRnaX9GcAdFvRWm1Gi3gqb5HzP7e7k7FRYuQ1F8ARB2NH+DOBtRuGUqLfBa3anwN1TkOA9i5IyHwacIPyHEzfbbEOOr8eD94GpnezuHUjwXkXJIRLKK2R4IiB0yvEEvJecp8Ddm5DgvYkqZ4ucoDO8fu6tmnm4lBR7tpKpVJIifsLTMEnbe7qhyMn0HrQ7Be7ehATvSVQljzGe4yOhjKzYbaikZoqxaVEUxShyBQA4efJkwzKUIHoFM0FrCqdEvYZH7E6Bu8ehkey8iKrkMTbBAVwkMpNT4rxV32Mll4tERQ4AeCEWTgM4ceIEa5hqKAHpISS8Q8NR6qw2oOHtrN5semL3Ns948uTJTl0MYQoJ3oOoSr5QKCSkTPmzpeFVtRgujxZSj+HZI98T7tGHPm15DY46PrXv+HVoeqvkfJdvRftDz7IjaNEI4RIkeO+hKnnEpsVyxyQlJeWUOG+qcY4LFeqHBjfHxvfrrZQkOksf+goo6D+yhQIKHDgb97fseIe7B5Ke/71t3nMal76bkOA9h6rkQ9Epzdk8y9LHuRDyqgqeg6rkCwhpX2ZlgRc4KHKmgJjjs+gfMAruiXbQ293wUYWKcPljoWAS6Lcm6fWpdi8k59s5F6m9+9BAQl6jOglHhfJ0XrySTGQKAMKxWCijVub8qEzAGYnFinlMTEXD7f6fku8JJxgCdz3hMAAUCoCIKwAAACAASURBVCgWqysjkfJCQbdTGGFt2Sq3bz/C3Toxfc+T8+3o2WpfGsnObej+BgW1PB3XWKefGfI9UY+V3Znaczm7fZnpC7V7nzp16rnjz2kfmexZxL+GNXK86d/YTbt3Vu0MErzb0P31NapcjuoBhGPTUwLn+jNDvg8gc9XMOcbXjGv0jK/1oW9trmadOl6AM7XXo5f9qVOnjh8/Xr+NTZS/ToapN9Vkd/7kNgN3+x1J8G5D9zdodPmZocZ6naQZ0dp9Gy0AQDbs9Nuoeaa9njDCORgdHsqWk+/KgzkA/AcR7av8QyZHZlLXvwpEqnsYI3s9WpTPkgd68Z+UTgb159dbu7sRuGuQ4N2G7m/Q6OEzs16Ce+cajhYsLWu6gWPR9gS93ZmSs7Ld9lEBhVer6u77fAG5yNr7RQDy5kI0FAGASA5msrfSvGmUb5reDww9Sc63HLg3tSMJ3m3o/gYN7zwzzn3fpfxqp6JhUw2zDfY1maFmXI5U97Vf1l+M/XKn0exur/aoAADpdM3KiZAA4Gzpgrbm8duCtnzhgfzEiAAAggwAsgAgCxlANDKCiuxZvF5Awcrxx48f13/lpPme9+mV3d1WO8M7hVVQofsbNDz7zNj43rJAaSpWRqOkdMdpSuqXI423cX40h6frxEtDsb+8vZXaTaWuUeor2V8pk/1bm2XUil9+KF8+fqQ6CkSuUAQQQQRA+YUDEQA/OvOjrx79qvYSYDiFT2WvV2Z3Whu0Fri3HO57trAKDHR/g4Zvnpl6VbdRN9w9WovUL0ewJ+toy/lo05eEzr0W1BHuj+TuZSMPhQBkTwkA8PCFpRKGbxwEsDR6ATBZLu2QJ0JC9goA3OAvWB3cnnrZC++PaWv+4v0fHTt6TL/96TOnjx09xv5FRfyWHfk8r/x6a7rdj7yFV4c2L8k3hZVvofsbNHzzzMz1MX9ryVXtG9Om1L2k/fS7Q7u3TMPXguYvPtwfATC8VwZw/hwAHDpcXqjn0OHazyPGqP3CXx4GcPDXzy0tj2T/5iCA6D8xF/9Z3SnOnzt36PBhAEcOI127+d4PqvrPj5f/OoPjNZqVvdY9z3T77lCvW/cE33Lg3ubF+Kaw8i10f4OGb56ZWsHrv9HLHl32fTaMaAH3ijWp7JZxHri7jcPEwL5ceHMIAAphpnaHnD4NAMe2HwTw4k2LtwAzdqqHAVznzmnLevGfPVd1POPIYQBl2SeTyampKQATwghQ06BPU3499rLXw8TfZc1rPfthUY3V8RR99wN3Dd8UVr6F7m/Q8M0zc688d71V72cN132vl3oHc93esbszwlt4ACiEAVz4xWjD7UvbakS+3KiuvSmY7A/++jlUon+W6h9VDmo5f73sAUzgYLmZXi5S0N14JvuxORP9O5F99zXfsF9cO73X2uxu19ksgm8KK99C9zdo+OmZqTi+KTrge33KvbNSZ3QnLd9Rwlv4kaFSaWHs/JVZh7sM3zoG4NAjJQCn54Ybbr+87XQ7V/jsV4DTxwBcWFg6uGOYLQCI8iMAskoJwI295wCcP3f+0OFDR4RRAMhVvZ5F+X+Ez1bzGaayDyNssH43Na81R23f6KYH1zIBaEbVblQQ+Kmw8id0f4OGb56ZSoq+TZz6vp169KbwT+DOQvbc9YWDB/sA/O3fNxGCHx09dHLxTFOnG7z1rMMt2avAs8PHDOu/c/YPJj4b/9qvVde8+CIAvPHGG5/73Oe0lTsXjgKQFr73+UNfLGueUZG9ZnqNeuVHEMkhF0Koa7KvT847Goi3PBlFZFKMm08qbXGW3qqd4ZvCyrfQ/Q0aHn1mWDGkL4U6JHgDNY319jwHdEXqDP8E7kztI0Ml9u+Nq/ucB+5oye4O+bWhZwH89P3GW97a/iIATfbf/W7V8W+88cb3fn/qu/9jcmDgk3/z33zx9Lkltv5wbDeAC+/PH8YReR4AIvuQRTZ0OVrcV/1fq5e9Pr3PxuWFO5q3qXo3R5uaSpWTiQzYaNVNnqJTG7eARwurAEH3N2h48Zkpz4cncEpKmkFZ8nN9s/Mv5Mcmjh/Y0clz6SL1M2dqcsJHjxojwk7ik8Bdi9pLpb7Dh3Hj6j4ADu3ukteZ1Bl/tvLjhtu/lZ59fOLAlptfa7hlcuG7AL73+1Oa4zX0sgcgz6O0Jw1gZH4CAPN96HJUW9bQ618dL3RW84bkvM7ulUkja0P12qknVTmZyI/ZOd55+N6dqV29WFgFC7q/QcODz4yqqhzHCh1VTqYxMSVAxgfRhWhhx8LsKYXvpOPvFa2+cdH3frC7IWoH0FTg3lm7Nyt1A8zxq0o2k1/eNT4+ODQwoFv/ja+XN/vpH9W8BBz7rdMAzv9VtU3+wS/LAOSzkdLus8z0AC7AZMieevFH9gFADjltKP4y4y0+ffXN6LQ1qpxS+DgTt/4lWZtDUmf8NCZMFG8QtsHx9h/dw4OFVcCg+xs0PP3MVEJ5yEnu02lEC0DxyrkrocPM8Auzp9JtxfTZsPOEfGd87+20vBavs4+lUh+ApgJ3l7zegtRx59pb87cHx8ajm7A6hEx6DsDjE+M3MnPKEgbHxlfybM0Bpnm2kyb773wnDSA+McE+nvjyVgBnfn4TwKFH9gOQzzobanB3jf6Z+IU9kPtz7McQulf5LlpAP2cyGqMZ9sl5JSXlIjUa17SuyslEJlSN6pVUUhUMhncYspt2z3MVTxdWgYDub9Dw6jOjryRU5WRaGGWCr4TwxSvnzhb3HT/QVkzfjOANtOJ7DwfuerULsRCAC6kS60/uPHDviN3bDNY17ty5s2nTpjtXZ68t34eV+4FlAGWR37n21vxtDI/FYqMZnd0Zb6VnAfzxD6orn6+9Cib7pZujAM6/e2lkRFM0juEZtnAOZ8urrh8xvbyDuyHr2u5F+qOo74CnH6WxVvbWMXQ1OT+0R/zSfvZ9bW5eSUkzucikGOeNEbxzYXdZ7QyvFlbBge5v0PDgM1PXAEhJJdX4aBTRAopXzs3iwOG9qAby+pi+Sazz882i972J7D0cuFtF7QBOn0apv0FT+aOjhwC06fV2pb58IzuXXwEAbN5zYOcmtnb1Rmbu9gC3shrCUv7xiQPA6ltpNjX9yK6JfZsqe+sjeGZ3q7AetrKfvf6Otl4zPfSyN3D9CICDuwGUZV/WPPuZWM1RNL5mkyHXJeeV1/6/mZv9D05/eYIzi9OVlDSTC+ub2TnMtGtq71pmXsODhVXAoPsbNLz2zJi1/NEJfmH2XHHv4b0oez6Eakzf7Jk6Z3cDxuB+9296X+2GqP30aRwQGgfuy33GxmjO6VSkDgDLq6tDuJOZW+E1u9+5nr66MjYe5QeY6ZV7Q1hZBoaA5cfHx7ILA9HdmuJrHA+d5utPpcneYPqh4TWWumeYyt7S9ACuH9ESAay2vnCvboIfBgvrKwG9wbLG5PzF04n3Vht2inMYjlfa9JVfC0jwwYPub9Dw2jOjqioHJZnIsDk/Y9NTAldJJI7kK14vez4EaDF9qKnTtJGcb4LLEQCvXP+hft3TTz3t+nkdUCyW63qFWOhCqhymHz5cVjtsa9zbidrbqla3ZPWG3u7LN7Jz+cE9B3ZuAmtYt3l08+0bKnB/ZCK6DXgrPbt5eGwHv5xhlfT8AJpxPMM0rD/x5a0nf3ZLk71e83Bg+oP95Sb6ALAnG4LuR305AuDU/AtggzdkwwCkyyfrFFvTqM6YnDfDeSP56Vg4oUbF+Ij2Et5lx3utsAoedH+Dhk+eGVVOJq4UNwhHKlG7JnjdYhN0QfAWNe6vvPqK/mND37/y6isdfCcwJOQ1uzsP3FuI2jsZrJtx5+rswmDZ08DNbPqDFWDzngM7lrOZO5tjsU13MspAbBeuzt554MDOTas35uaUZeCB3Y/v3rSqZK9hV2uO16gP6+sb5TUb0x/sPyLP10bzwJkzp48ePYbLkZqpFI1t8fQN6cwa0elw3p4ONceybH7vKj4prHzMhl5fALE+4YQpUZjrQ4jlKkdCuLxQ3BsKFa9cLvIHmrQ73B/Nxro9ncHWzfq+ZQwJeeZ1Q07+gHXg3mzU7rbUK+hT8ezjh5vHD4wO4Y78TubT0dj46ABW2Vd3Ptq8afed6+mrt8HtmnjwWnrurY8ADG18YAUYQF3Vu3P+7M8B4Km9X/x8Zc3DD7z8/I+xvNQHYHjbDQAHdn5G2372+ktsQetrV2/6C/fOCnuOyJ+cHbl6JLwvAuA/vvSj8nf7csiGT82/cPx4AQDm+modzwlToqCkJGmGJedNLewkLW/Yho+EsooqcBzACRNjybTMd1vxhLvQC1TQ8NNLcc1gdsUr587KKleJ6ZvBtdp3oN32dAbfoxPKt4raUcnJAw0Cd+dRuzsZeIfcuZ5eGByPjg4BwM3M2x9ueSy6nX0z/9Y8m8ggNNhfXLl/CCvLm/ccuD0/yw9h8b7djwrm9fFWQfxTe78I4NUrL2vLAP7uvYR+m3/1L3HtZ9MAHn7yZUNk32yjPJa6L/UDrAnevlw5lAeq0TzKTfCc3KmGgbuF/msCd31yQJXLtWphB6PjtYyfCit/Qvc3aPjpmenIaLWuJuc73RFO7/sWTG8atTO0wB2wbCrvMGrvVrDegDvlDHz50+X0P9w//pmdQ9Ci/F24lskvb9w4dPcu7sfA2MTmO+mrtwFDfbxVol4TOepcrue57bEXFjNsAcALi5lfeXha+/YXH7ysLTeUvd70586fP3zoEABhwxFUNF/+zuB4NNeBvrkNdH3qq4Kvet84kk5n8VNh5U/o/gYNPz0zXha8Ox3h9BXwDpP5hnidYYjaAbvA3Ul3do9IXcfqjYwyENu1CaiE8jtW5q7eBgAMPnRg16eV+vh3rygrdwEAm3dN8KusPh5gQ91dw65vHv5l7aB/917i4uw7v/erv4M6qRtE/hc3ZQC/sU1gCwZ+Y5sAnewffvJl6CrsrVrga6b//vnvM7sDOHf+/O8c+bZ8L42rE4Ya+mqTewvN2wfuTru2V6L1atN8fWDvpuL9VFj5E7q/QcNPz0xHBO9Gft6dEWzsm9fV+75e7TZRu1VTeRu7e0/qNZSby226k527vXk8OjpUzdjfkd+5VqmPv5FRBmKb76RvbypH8NyuiT1fqYvOL86+8+iBcq35xdl3APzbo/8EjUSu8dtDDxjW/HD5IwCDa/e0NwOD7K1a4L/2+uvffeK7bFlvepil7stf9IeAmmjeXt5tj1pjSN3XdNXrIH4qrPwJ3d+g4adnpn3B+8fuaKb9PFP7j//qJ9qaqSefrLf76Ur//PrA3YnXPSh1A6sKC9NHB2zr45+K/wttlx+/l6gMF/fxxdnspoc/86/3liPyS2+/+z8//ay2DGD/Y48YzlgvcsYPVm4b1nxrcLO2vDyy7S9uyoNr91DRPIPV1mst8EdG7rGmefUxvaGefgQjkQ0T0GteF82b9aar0pmubnqrN+6a1yJ+Kqz8Cd3foOGnZ6ZNwXc8Oe+N8enCW/j6qP3c+XPamm//3mHYBu71dvd4sN4QfX35q1f+33feXvjdX/2X2po/ee30vh33s9T6Xy5m7vX1sxT6H7x7aUW5rLf4pbffZR+di9wJmuyXR7YBYAE9amN6VMJ6VOrpf/jX/+ELTzzBvjI1/cH+I9VoHuW2eJ/cG9L6zdePd4uODTdrWjnfYfxUWPkTur9Bw0/PjKcE3/HAfam0NDwy3OROpnbXPmo5+ddefw3Ab//6r//g+f/zc5PledANXg+S1H/00l8OCL8UBoDCc9s/B+Dfn/mbG/dt1CLy8nZ33r90nbWu5x567KGwrcjnLs0BGN8/3sFrNoT1qMh++N6n7M/REvipdPr3/sU/g/XgOdDJ3pi6Z+jq5t0ZSV5rSt9g4LyW8VNh5U/o/gYNPz0z99T2du9cfr7Ddi9de+MX86XQns9/bhcz/OKlVy6Wqh+t0QakQ2UYeQ19Th66pvJvzLwB4L/9lW/921Pf/8Mjf6Bt4C+p17dp11qta8t/8f5/mpcLYWHPtsGafa0sjkpEPndpTi9y7aMbjtfQZP/D5Y9YRuF/OPM3rH2fFtMDuCk/AmBk+wKA828u6o+gb5QH4PChQ5ape7Q+TW0P8VNh5U/o/gYNnz0zLTveu3ZfvPjq1dCj229cxaOf2z0MAKVrb1zCo/tx8RfzJYw++vSj28331NvdpsYdOrtrUTuL1/9s5cesG5hGC8O8uIppj3PUSt20vdvq4vx/tfOzpsd0klfvieMZ+rCeyb4Y4lG5CfohcpnsURvW6xvlsZi+PnUPVEzvK837rLDyIXR/g4afnpmWU/QdTM671KRu8dIrN7aXTb509Y33Rj5ntPrixVffubH9M2wbm8y8vqk8w9TuVvG6F3xvL/L6FuydrSDXsHG8q4KH7jVCH9b/491PAvi79xKGBD50ptfX06MS02sBfbUPvR7/ON5PhZU/ofsbNPz0zPRW8G42qVu69sZ7w2WnL1585Z1y5rWStF+6+sYvlnY/tX/74qVXbmz/ypOP6e2uz8wbAnfoGszrR6OzEbwBV31fL3LWyuw/Xv05Kn3H9S53SeQ26F3etSBef3ztpPp2eawF/nPbY4bIfumjrfXD5tQH9AB2YDS8oTI17b6cX6J5PxVW/oTub9Dw0zPTsuDbz8+71heOsXjxjaWH62rcK2G9Tv+l8Ja9b11f2AagUVoebdu9Hr3vncveKs3uHZHb0H3HN0wV6GWvDZ7Dbi/DSvb6tvcmfeg9r3k/FVb+hO5v0PDTM9Mrwbtsd2Dx4quLo0/t3w5g6eobFyuV8WXBD1974xIe/dyuYYS38H//V4ntT45va8bu+tby7djdgH1wb4jOVypd0Twrchu66fimKgL0ptdH8+y/5o9/cAC67D2s+9PXDH/rYc37qbDyJzSbHOE32szPu253YKm0NDI8wpaHR4ZLiyVgGKVrVxdGd+8HFovY/nAluF8aGR4GSqW+FuzeWZjR9SL/X/72fwXAGn6z6Jyx0tcPYKh0E7VS95rIrRjfP67pVltmC509kXZAh9X8/yr1WnmzldvfKt0E8J+FRpdHthX/6RcB4J/i1Ssvf+Pr77KNn/8xtGFzTqNmOjv5k7MH+4+EowAiBQD7cpjrAzykedav7+TJk72+kIBDL1BBw08vxS1E8N63uwmLF1995wa09vOLF98oPfy53fwWPpdKCIcnrUaf1dAPVNep5Lye1tLsDXXehcZr7VAfx3c8iNcO2/CY9aeub5cHYHFHebTdV6+8zJrfs8FzDNl7Q+q+D8hdBvbl0B9Cf2fGq2lqvDymcz1sXz8VVv6E7m/Q8NMz04Lg20nO98bu9ZSuvXHpsS+fyF1/T4iNnjxb+qVKNF8fuMM2du9gfn6p/z628Nz2mKnXDTo3BLumAvO44OGy45uyu6na67fUZM9Mr2kewPM/xpc++wgsKulvbACA0D3kLgPoQCjvZJ4bDast/VRY+RNK0RPrA6/YHcDI1kc+89rf/uSl0+GTZ0fs7V7qL3XB7vaYRuoG/eh973Gp6zHN1XckUe/wIKaBu80N1P4vvrXwDgBxx/6hn9xksv+1J1/eJrwLlPP2I9sXzr+5qKXuj33yDIAbGxCOAkChQxl7pnmrAN1mL7ZAKXq3oReooOGzl+KmBrppOT/vIbsDQLHY57xJHUOfmYcLdn9q7xe16VNZFTvjt4ceaLZm3Ulw7ylM4/g2L9vJcZwH7vawsF7L3gN4+MmXWVs8wzi4AI7hmXPXIewBtA70zWveYYBuurF+e58VVj6EInjCJ7Rmd2/MH6NHP1ydFfZ29ziGRuPe971pZr4dxze0u+F0bdYLlN/Arp1lpl8e2fbez8vD5nzpS/cZUven8dLSTox+8sy561jYgJF7CDWK5q0MXT8Afv2W6PwI+UQT0AtU0PDZS7HzavgWat89Frjrh6uzGs3GMDucaZt5l5LzWhCvr4ZvIYJnWOnNy77Xi7llwWt/oI3dO6V2GzTZs+52Oz4zW9+NHsDw9WcACHtQyNbMNK/HftZ5J1ta4bPCyodQBE8EFJ/YXY8hcO+m3buGTeV9/bddxmD3doJ4m5eb7gyfV34tq3S3W3inPKrBHoxxfF7T/NLOl157/XUZ313YAOFeH4DCPvNo3io678z084Q7kOAJP9Bsft7DdreqfTfYHYBL/d0b8sJiRl8N3xoO1eW1xnptOt5G292c3kaPlsCHVluvfIZpfmT7wr//36QvPPHEEl4CIM8/A6DYj9BcX984AJyUqo3gyOJ+hDIkQcNnWS8nKfrg2h0Vwdfb3bTe3dXw3bSdXcsp+vbpYXBvaE7v8NQ27wQu9bN3eFX6j4aR8FnTPI7P//Cv/wNb88Wx747cQ+ge5PFsFFEAa3CrPPFZYeVD6P4GDZ89M04E31Ttu8fsDtvkPLO7NjuchtVwdW7n51uvhl+5uzq4ccC9K+u675tVstXbgHaE7owKUN89r76hvoE/jX9B3wJ//uPTAIavP7PjEwDuat5nhZUPoRQ9ESB8ZffySs/YvVXu3py/cnNlcNue3QODbI2au/RBIfzg+EOdGTSN0eXKe32W3rmb6y+y2SM0i819YF81rPX4wcptLYG/fHjbnsvHAMzvfGnh+jMj9yDMRdeAvnH0oQ/1mlflZCJTCMemp4RO/mcTHYJeoIKGz16KG0bwzvPz3rZ7fXIegPCgo8w8umh3bUg7Z1l6NXfp1v0PcepNRPZsHQCwcuu9+dXt+yOhQm6uwHXW8Ta45HuHcbzVQLOdvRhYB+imoXnL5/3ml/YBQBbFfh5A/nKfuq8cxzPKmlflZBoTU7zyaiKzvG3yl7/AN3kinxVWPoTub9Dw2TNjL3g/213f373e7sKDNd3hGDb93bsm+Fay9DqXry5evTWwOxIGcPfm/OLgnkgIcCmmt6GDfnXS7Q0Wdm9f7aYvLvZ5+E7xnW9jZWHz8vvbipf14tbF8UoqqT4QyvwDNz3FXXrp7eWHv/BUc3G8zworH0IpeqKn2IfvgbA7gHq7X8jNHjsGvFhdaTNNXE+S8y8sZgzj0luxuvpxOMwK9ruqivvLZfzKxysYhBbTj0cKubn30R3H21Q8N+tCLYK3SbMb+rW3cBbD7vYbdKeZ3h9+H8Dtb/0msA8AhucWz10/JuxZA8rpevAAj4Saj3NQtwz25zOyIsSbjeIJNyHBEz7He3bXZ+atOHYMP33RfpPe8OqVl7UgXusv98Plj2yC+LurOqmD2zpYXlwdHNgIrKrqwEO7QwDC27fdXCyCC3XlD9Fov/LexvH6o7Vg34ZG7/lAQD/40e3vfPs2gI/G903gwujc25fnDwNcOFpg0TyD40IbiwNFVQVPdfEeggRP9JRs2DKId5Kf94PdTWvf6/FU+F6PtePVQuH+8EN1qz9eBbd9AHdv1sf0PaU13+sdr/+oP4jDOWGdX5tH+MPvA8B3vn15ZWHz0vj2CLLDc4vat9PxMQBreLOw/AnWSgAJ3kOQ4Ak/sy/nKce3bHdPoQ/if2OboGXpzR1fidQBAIP345a6snVg8O7Nmx9zkY2AWh/TewrnvtdL3TAYTv1xTI9mf2rv88P/5/bg0EfDw/eewxYAa3O4MPQXE7t+A4CSy0X4WLE3IyYQlpDgiZ4yvmbZzi5aaGv2965jmpm3srshP29TAd9bGtfED259eI/2YeO2PQ/enJ+bWxnctmf3NkO0Xo7pPU1D3+sdD4uAvuFhfcpv/+eb//qlWwB+mvvKP9o5fyWaPpidAPDCqRfGjp8oyAk5IvT6GokaqBFj0PBfw1T7hvROHO+BIN7U7lZjzh96puRQ8D3Mz3doAtm7N+c/QGT3tkFtodMX2kUczvIeDJ0b0BrVS5cyz/VvubHhsUK2T4lmo4gW5ERrneH9V1j5DYrgCQ/jsJtcrxP1pna3Ss4fPoyf/r1xpTfDd1PsG9zVYRvT+wqnNeiFa9qW4YfGI2G3r6tLMLsji6f6p9kaZncAnDAlUujuSUjwhIeJFlqcBr67OLc749DeA4Ye8Kb0tnndq1de1ga90dfEN8/GbXvGt3XqsrqFw2Ddapfwju2rC4tLN+fmCt3r/e8e3xqsdohXLvft+KQbI9UT7UMZkqDhy6xX+1l69CxRb+jyzrBKzltNLePNmWE1waN23Bv0dBIaN7AZOmZ18ep7q1tR+MCqol1rbbe6mLvz6ccrSytLK/cDH5sezXd8a3Dz8sg2HETxMq9c7mPz0PRV/po27e7LwspXUARPBIVeJOqbqnq3wrMt7H7l4WmtGt4wh2yTiXpv4WxgVzbGPlv+wLBXfWs7AHdXC3c/vW9pZWAAq6ts1eDWbVBXMOipae/r+ebWfUOlm/opZ/Ts+MzsUnH0yifnRu5hYV86lJ1g6yl29z4keMID2I9ndznizSx9U1XvNpy5cb5+kNqeh+/BwCrTbq/Y1cKNm+9/qAIA7kPfp1gbQHgVBW3H+sbzN1ewbVs4P1+4f6hvdfl+bvBj9W7/ho9vLT0wtFq47+H94/ruA25Pe//Nrfv+91uX/9muI9qa7QvvLI9sK4bMx5nbkZ99fukWii/rV37j63j+x/jSZx9ZwuiF9+fX+kci+1DITvSNk9p9A2VIgoYvs173VLtvm6qG71YQbzVcnY3gWX4eMKbouz/1u3P0benr+8t5LYi3qTh37tHVxdx7iwUAHFD+XW4E7locZOXW3Hx51JctGzesDGPpzifo68favfDWwcKtFaBveE9sp3XrQvvgXi/p//va2W9u3WclaU7NDxdvLIwd0NbsyM8CeH7plt1fa8E3vo6f/tHXDn9l9sL786PzRwBE9qGQBcY7Wbb4srDyFXR/g4Yvn5mGc8p5bEp4K7vbJ+etBA+v1sGjVvDwkuNd6nfODrvh/gfC/R99WM7PD27djluLKwAe2j9eO86u+t67H6zaPW19A4NrA9satKXXLM6p+f/+zE9+76v/pfbVjvzscxXV+QAAIABJREFUUmh0uHijfq/WzN2Qb3wdSx9tBXD+QhHAwf7ytXXc7vBpYeUr6P4GDV8+M74SfAuxO3R2h2PBw5OO19fEM7rg+C4M8lrJuu9dmL/20conldV9wzs2Ly18xD5s2L533/aNAFDIzb2/NID+gcG7hZXax60ff3rwC5b12fnZpdCoyo0ZVuo/6s39Vrrmq8cnDsA1WNQ+MrhU2n36cGw3chEABRQAoN+VjgC+LKx8BdXBE36gqWp4N1vbOZlIpgVMq+EBPL/84q8NPQug55rvGk76p3W83lo3i8xdze5/Gv9C+esHoRf29oV3lrfuKz5mmSr/dy//tO/u6TVgeM+BfbiWXeajvK4KfukWbrzr8MIMRnfD99/4OoBy1I7xnx5kas+hgAKyYSDc8cCd6Br0AhU0/PpS3DCIb7ZDvAuON+0Rx2jYcl4fwQMo9ZvE+l6YD94U+5p4tBHEm/ZP6+B8598a3KwtGyVt3eisvj77T37yxxtx/333Y+XjjdvDqx/hof1772bTH6wY9uzrw9oagF2j911b/BRrADbvmti1qbWrb4Te983KnnkdsIjas2Gg8zl5A34trPwD3d+g4ddnprNZenRe8Daxu5OW804Eb99fziPD1sLM8ZfefvcHnz/U0PEt61zzdDuSfvXKyydGHzlZiZ6ZHTUvvpWerSzfuZ6+WvlLNgJ3MbyZW1pZG1r55B76N+LeJ1ipEzvuH8THyzXrBrY/vj9iem1u4Dy4Z2r/6R997dhvnQaAc4eXYnKX1c7wa2HlH+j+Bg0fPzMNHY+eVcbbZ+YdCh6wq4aHgw7xPXS8ftAb1NXEX3r73f2PPaKP400z7SzpbZC0YY0eTs0PlRZv8I9ra5ikAZx0nOWux6B21Ni9uoYfHlGWShgeiwzkFz/CPWDj2EOD+dsfY8P2iV2bcOf6uwu3hzbzq7dX1pZv18p9VxjXCu5Wmdtj8P1Tv/Q/GbcY/+kxHAOwFJMLr0bKo0aiS2pn+Liw8gl0f4OGv58ZTzo+vKUcI9q0nD8YH3HS/Z1pHsCNqyaCh22WnuFNx196+91/c+Kbpns1lHT7wnaOqdphFu8aBAls3jXBr2bmFpfu6xsa3Ts+OsAC/dDmzfeGhjfkldLGe5/erdlhz4Hb88b3hq6x5ebX9B+P/e6L3/3uGwC+9/tTAC785eHocbkLzejs8Xdh5Qfo/gaNIDwzDbvFA07r4zuaqNdMX/hQKRb7Ijt3aF/lri8IsZCcKZZKfQfjI7CeKJYhPLhv+6OzqJs3Fh52/FN7v2i6/k9+8sf/3Ze/BuDf/ezHj08cODH6yL/7WfXyehjF6jEVeX3grl//Vnp21wNDqzuim+5kr2HLYP6DOxjcMc6vzN3eNLFrE+7Mz15dHsCnyxh+YOje4K7okJJd5lfycwAGx8ZX8nPsIN25Awaj39r+4td+rbz8YuU3tnPh6MGHsdQPjJQAvHDqheN7ngO6GrXrCUJh5W3o/gaNgDwzHaySvxwB0IWe8dqyPtAXYiGYyV54cN+F3CyAY8eqK5nsnYxc27Wm9XWBbIN23fUbeAHTDDwsLlWz++MTB3T18f0Y2hEbHx0AtJWb94wPKnPKEjaMju9/EDcy17AzOjpUPXjtoTqPXuq3tpc1Xu91AM8eG7rwl4eje8tqN9S1S5KkbSmKov1JJUlquI1DAlJYeRi6v0EjOM/MXB9gO4rtvWIT3ecu65o7dWuoO22ZKV8ve03wejTZl15zNDp9Z0P5elXDQe6abaA5rGsBq0OaCtxhtLtDVm9k5pSlIX48OjpkPG/HHW8qdQZTu97rOxeOAogel7MyoiOOmtHpZQ8z35PgfQTd36ARtGfGSfe5aKHpinmNrsu+nN7fLCCSuzCzCODQk8Pnf16Tlj92DGvDSwCef77BkVt2vMPIu9kA3TuCt1J7/Ur9t0zGNtu0cPb2D2sjddSF7M8OH73wHqI7QphIs1r2XLEQiaBQQAvN6Op9T4L3EXR/g0YAn5mGoTyjqbp5jct1HZm6o/wN0dwnaX0tfvbdG0ulvkNPDgM4//OlUt8SgK88W7OXqe8bOt5haG66cbNC8oLgbdrN2Vxbx5MQ9Y53fvD6CvX6bfRefxbPYngJpZGlvj7sqNYQ5YoFACE2vm4nmtE1jO+bIoCFlceg+xs0AvvMOGlgr9Ga7Bn1ykfnrc8Er1/DZJ+7vlAs9UUfGdXWn3vzGoBjXx4CMDxQ2xmrony945uKuX1Rg+4c+ybxTnIPnX1Bce54J0bX+NpQ7XvfWt+FGyUA0cdLqEidEYmgMNPJzm+G8L1N3we2sPIMdH+DRvCfmaZMj/Zkr2FqfbQl/iIadKsT+icu3Dsr7NyjrZGvzwPQr9EzvO0GgOEHyiOZ/9mfm2zj2tjmqzcycwrGYrHRAcs1LtKw0VzD3d1oDac/rP7gb6VnDR3TbYz+ta1HAWBpGGt9rInc+dKFg7yg3yarFABEo8hVfuYdVzvDPj/fVGM9rIfCqtfQ/Q0a6+KZcZi0r6fZ8W4b0kaGv6HgAZR025w7f75+g8OHDlWXcQTAjZ3mf+A24V1UhhxnLwGmbwCOuXP9Knbu3lReTi8MjkdHcSN7HbtirI94Zc214tqyujrslunt1W71lWEz91oI6q9BH6afuf4HE5+Nm+7ytaFnMbwEYImr/u8P75XPn4PmdWZ0ht7rjFDOrSFrnFfAOwnu10Vh1VPo/gaNdfTMtKZ5rVFeUxPYOMex8uuz9HqSP08CWLlvVVujd7kV586f//ahb3/v9e+xj1944gnDBgd2mo8Zx6L/pZvVqgH2QmD1EnDn6uy11Yqzl29kFwaiuzcBuHNl9v0CPh3iBga3xnZvwvKNdy/nB3ceePh+zf2dpGF7eOdHcMPu9Yn39JspzevpN1N/+My3gZroXC/1kR15ABcuVI8wsiAU+ZofrcHu7qm9TUx9v44Kqx5B9zdorLtnpuVoHp0M6M+cOX306DHz7wzKr/heEzxzuYGpJ6dQydJbnbQ+pmcvAYdx5DRecnzt5uhfBbZHLwFYzO7X1uirA5Y+2jr8wK0/+3Ng+Ub2vdtrW3bFhj54+/p90cd2Ddy5lv3oUww+GOUH7lzNru6odiRrEyft4Z0cpLN2t6pKT7+ZAjDx2bgWnaM0AmCJr070znSuh6l9ZEEAYO91BreJ88ujr/m+Uw3yCVPWmQzWAetO8IxmK+YNtF1Pbyd4AxXfh6PIXQYA7LaM46FzvJXOTemI423Q6/+HL/3tv/7n/6i0WO0RwF4ISh9ug+4loH65tTqChmq3+dawpdlMM01jOdrMmaMwpNmV0b4Ds6WF6mTwIzvyf/InyampKcMxTaWu0aOoXUlJM7nIpBg3n92nBdZpYdVF6P4GjfX7zNgPcOuclmRvKvgzZ07Xb6ltFu6P5O5lAWA+atxod01kzxL1TlL0etx2/Ify6+8XMbRLQK6wEZ+EP7Nvy4eX3ypsxF3uv/hS1Vj/10t/i/u26NfoYZmAkS03UXkhGNlyc22tz/BC8PxPb8GBvJvydAvhuzYPm37lsd+ttI970aTuXM6X4/JkMglAc3kymaxfHlkQSjvktb4R07Nb1bX3PeL+E6/KyYQaFeO8kpJykU45fv0WVt2C7m/QWO/PTJuhvAHHsrd3uRVVxwOvvPqKtv7pnb9t2LK02zJRb4Orjl/Kv30Z+x4fw/vvfHDf1uVF7Ht8y4cX5MWRyEFhC5bkN9/55OHPP4J3X3/vnvDZR7cAH15+7daWLwhb6g9l1TLg/LuXABx6xLJqALpeA//1t1q0+x//oMFeBqMv73zx2eFqy3Z9ml3TuSn2jv/l2G9ZheywiNr7HlkD0IXHXZWTMjcV52sX22a9F1buQ/c3aNAz01atvBV1jfJsjO4wXX/mzOl//Mxv/tXLP2Qfn37qaZuNBUQvXK1dtdOR8lnTelc0/+Hlt1YffHxs6EP57aWdj2358O23ri9twKY9T4xvAfDh5ddyRZRWh8KDfZujj48NfSi/fmvrE2Z+t+O111+HrrWg/lVg9vo7sH45GB1/B8CNufK326OXtAwBdNkCbfnMz28COPpkeXn4+lcO/fNzOHdYH44DGCmEIMiGNLssA4AgAIDN8iuvvPzNb35Rv17+mQAA+3KRCICywq2WGV1WOwBAlZNpTEwJHIBOhvBUWLkN3d+gQc9Mmc6F8qdOnWILx/c8d2r+hQ39yzCLzjWvO0zXHz16TB/B2yMgegG1VfVXJ2o+2vrelVB+9cP3S0MPbRlayr/9wcBjzNyVsL5G50v5t9+6vrRVaMXu9R0BDBvArLNAPYb3gPrcgJ7hjKB5PVewC8qb5ZVXXn766S9iXmAvi6dPnzl27Kj2reGjnlAurD64BiAcBrqndoaSSqoC87ve9W1DhZXbbOj1BRCEO4yvtRbKazrXOH78eGWxcJxVl2fDuNwgdW8wutMmeBbIyJYM/eZ32/oeNco/h7Odd/zAlocGAGB4YOjWrQ+FLVsADI89ti//9muv1+h8eOyxL4xZH8cMJ+ZuqH89o9dr+jL8KlDqx8j7kOcBILKv+lXhXg6QcQ/hzSEA9SMcFW4XgfK39eTeLwGIPGRej57LncDlSGRK++Uc/dGPqlI/duxoveNZyK7ZvcdCLKkY64zdiS5AL1BBg16KjViH8vUuR43OnZENAzhz9UeG1U6MXkQzc+TUjnvTmDrlH94JuJSu7xwO1W61zTE8wxZK/Sj1m+9eyAJAWNe0sXDPhRER9LCuE9ECgFOnTh0/fpz9i0pEXr6MAvRr2FB0LBuPbkfterSwvaPxOxVW7kP3N2jQM2PJXN+p+Rf0K5p2uQ7Dy0H5UJVGec57zTXleJNEfVPUKX9pp4dkb692vbkBjNwDgBsWKcjQPZj3UKgkXZro1tgyOqkbMDheW1Pdovlp31xGlZOJTCEcm+6Y3UGFlfvQ/Q0a9MygbtgshiiKLbe/s83bm29/fM9zDZvfO6+DZ7Qr+Hp6pHwtu65pux4mcsso/BPr+6aXupnRXbG71gbT2ut67ByfDWN8rYOzsnoWKqzchu5v0FiHz0y9zhuUjA7a35kH6PYszJ5K58EJRw7vPcsK62z4yuIL7/VFjm47Yir7ZgWPSpb+ICYAMNnrl9uhfJyrNSvb9L2Vv7Uo/Pvnv/87R74NQL6XBhDZUH3hMCj8lVdfsexoYBGma3TS7qYiZ+MfNwn7jVV/WtmwdPlk/VxtAdb8Oiysugzd36AR+GemaZ2bUhvKNxugV1iYncWBAzuA4pVzZ+XQxPEDO2q+PXU5dOTwXlw5N4vD2yfqxdOC4O0REAUgI6st178EOHkhYNugzveoVOTboE+hs2Umb6F/ArUR+Y9f+cGvPPnL4Q1VPVvF5SZ2NwvTTTEY3ZHgmbw7JHIrqkH8nueAckK+PnAPcCgf+MKq59D9DRpBemYsM+0dOqy47wSrlW+tMn5h9lS6KBw5vDeE4pVzV0KHa/SuX7cwe0rhK/bXD55zORKO1tYWd3rieXvqXwgcLc8DgLAH5eXdaX3krYcJu17h2qg+9r3/tS2ffurphmG6KQ3sbiXyrpENA6gP3NeJ44NUWHkT6iZHeIXOhOYOjqw77NrxcQCtdJpfmD11OSSM5YslIIRSUc3Lp1iHaY45X88Ofuzyh5fOpa+rnHDkcKH6ZbQAhCP9UQDYhwIKAMIIw4zCvRx7IbD8Fgj3m89bb/9t6F4Ildg6guoJ2HL9vvpOZaE9OVyOGO9d7WuKPi6vCrt28D5z5qNPs4TBfCszBVR1fjkC4MzVHx195qvlFyz2363/T++F2rW6dnuFN9yAIEwhwRMdo+W5ohku6dzRkZvvNL/jwPEdKF5RlGIRO0I6rS/MnrpyDcV3ZRXYOMa+xEpRzYWOHD8eKl45d+7KAd0LAJO6nvo1ZfqBaMH8u2wYiCBaKKBQI7DabEEBtdFqrTLtu4rZfVuv3vo5cytUhc2W523O2bzUtb+rP4Rs+OhuoL8q8k/mT2nLPSYbtmkhb6pzcjzRAiR4wnXcC81Nj9/iwVmB21woHwqFVKUEhHYcOFCcvVI8sDeEEWzMX1kty/xKCQgBWMN9g5tDAEJ794XOLRT3hsxHSWkVq0jUyXL9C0G0UB6aF3YvBHbUbsnG/HHetK1xNbmhXhwmEfmp+Rf0NS/GfmjdR9/zTWd3zdx6f5PjiY5AVSBBo4fVWqZxOVzWeceP31QoX7xybhYHDu8tvXE6fSs8cfyJHcUridevbX/ii/tD1W9Dxdm/fx1PfOlASLdLZw3fRUxfCGDMFrDlM2dOH939m9X1ZhiauAM4evRY6b3X/tMVtbxv/bkaYdB5j+3uoFO7aaLeVOdBcjzVwbsNRfBE67iaabc6i+ulWzOhfCgUQrF05Vz6/sfHubfSp06BE8a3fTx39tR1AAC3c9fsqVMqt2vn4MflYD4UCjU5fp3HcJwhOHXq1PHjXwW+Wl1v9nKg1Yufmn/h+PGvsmGALyymv/DMXuDYlXNni5twYEcTqfV6uzf3B3aQ9saroTieaBN6gQoaLr0UO3R5+0WP6wF6U9xTy2V0PXpLNfntqWX5+IEdTezrhWrjZjD28Ha2PYMTjhzesVDNchSvnDtb3FfbAdH+UOy89QuA2V114f+3+m0zatcH8frnKMBxPEXwbkP3N2h05Jlp2bJOcoz25/JvsaWbcquCbuhubbGV6TZZrQFDSzCY4sNvpcsnxekYPrDoHjC+pqQkfvhEa0cGIO47Ydy+jJKSZljNQWSyQxOgtke1A6eDbnItPGtegwTvNnR/vY0qJxNqtJnCp4VnxtX+afVFlUvn6jmqnJS5qTivpKQZTIpx3jh1NhvO2yMu6TgtDLtW3UWVk2kUCpnyckKNTmKG3TslJc3cun/7Y8880fiuGQJfbb3pVany+XTmQ5YbeWALPhrs/X+Mdv02C/bb+wsSvNvQ/fU2nRZ8d2rNbU7nx2LIKTqfs9gwqC430NqIqpIk6e5PzTRlSkrKRaa5bOLDUHgRUTFy7aW3Fwd3N5jnxP5tsv7y5pPS+w+JU3tQfvXCEEKP9vA/zJCiZytNY/T69xifPlYkeLeh++ttNMHrTa9fmcZYKJPJAZU0o/6Z6b5f15fR1z0tqx1ABMjpJyfTpzvKyZCR9M8SH9wFEJkUBdVsolKbELZhNbaSki7m8MCkds5XE/P3T375UM9fyWwS9fXrSfCEDdSK3ucUMvmxaVHkoKSkrCzwwsmTJ60KCDeoq0GflpOJDKoFtyRJsTD0a4hg0FpamO3FDD6Zk2RFKMfMvBDLJlKKGOeBkgqOB7iJAxG10q6BnxhLpmW+9lekBbv2ldbiZESSJCAyKUZy1Xr3yQdyM8WLkpSNTU8JnLAzfPn95ebvQysoKWkmZz/3qlVr+YYxPUFokOD9TiTKyogRLlxQS8CJEyfceyk2C9CndTXLSkpKc9OiCDmZlCemBA4KAEzo1xC+p+WoseohfiLOASOxbFpWefar4ISpaTkpSTMAhoC0zE8JvDCWrVidE6KhpKIKnNlvyM5wqpzMRUQxDlV+RZpZqaxenp/5KLI/VrxUGCimJamALQ+Ex7Y1+yc1i9YQQ4yrFs+E/q3FvjLefmAcgiDBE5Y0zrerclJKj02LIqekpBSmuWIkGucACNGQJCtCfET9/9u7+17Hsfs+4D9vjE230pHrdbY9YoHsegOKxoz/uaxqL+xCRLtokgXOvoy8j/zfd5C3MQddBMagJdEYswhBASlmGonNbmwn1EH3qdCRsF3HdvoHKerh6oGUSIk8+n7+mtHVlXiPRH55nonI3nzk5g2gcIFLon3zFxnLMn27Ws7skeBZB1QnDmTQ90YP/cCP2NG+8ePj0bSadS07ffm3e5O/+4Y673gjm+LA/2rx6aQ7FFYiPyOif/FHdd+AZuMvRdonoP5xPl/4crJnqMbjwD6Z5YcaM+CeIeBhrfSMtaUm5yFtQLWsMFFO/hNuWVOtqUM9a7j1CEcdvpUuCY8jlUv26MZvqcmxORHZI4+CccxHecXeGgr3QB88PYr59Vvw/mLV9v8vu/TanOiX45iP7JHg8X/3P/lEuT8Rwj3j7ypJx1MabgzC7L1B1lC4nTiIFN+KeB0HPvWc7Tnxad2frKE43nqPqjzkEPANpCI5ZWn33FLPe6xDRIx16e//RkYk3I6azenRQqfLL5a0/LLM21QwII67Dx2dHnOSWJZH09k6w+d6SZxosf0IIeBb5sJoP/W73B4m6lWUvOmmGcet7jRriF9X8EfC3vvixyZhZrPcraFwH5zAl9FQuNwdJkm4+O188uIl/89Pr9rvvhpZQCqS4ddvEv3mDz2XExHrbpwj6yb8Tix9UququUU9lg22CeLO6EibPJrrIYeAbyDuDhPpywkRUc/x0koLt7//P5NPk1AmPcexSJ/xunUsKcNYuohLSEPBmdYUZxneYT0iYry/8witrmHHhxhBA1zY5FswZhh3SQeTMMrG0Bfrdz8Sb0Rb/e6BlOQ8teiTMJ2YJ4YvPgrpO7++Xr97hruDZHUOWu+Kn64mDIQ0EOt0n/U9MWJERPbQmoRSCjG0qJfQXGSDbShZErFjQY6MhxQCvpG4+7jNkP3hO71PV7PjJulD6bCkiITLO9/r0Otvbjz/ajPWVJRP4GO8v0hHTeUdn/x7X/wPKX/bc4b9WdeyswnPQrBDQ4ygAS6P9jK/rtWs6ziLMGtHZ/apfveTK7tt9run3fr/m4iI/u9UyrDneOK9ZSS/pGv0u2/irhB2th4SUVqXXzjeKP07VeTP+ht3vSpJrKFw0wUDKExPZxVPutbqT0fGw3EIeNPk0+SudG6rKKShyKbnx2w0enj5Mym/Ieo4HpGOx1+88+DMwslk/P/e+Q9/TKQ09W1GJwZFww1dGAzlf31Jfdu2GYtkHvEF+903H9z872a/e/py/+e/+l/9jl57vUPUZYyI7bmHvgpmD/KjtVYD7oiIVLJwHvK/VcdBuHA8TpqILE7uuqF+VHCgKjIeEPCmqXWa3GMqSShJZEJEPccbcRXJL97xhM1IRTJSQ6K+zW1b2KSiQOmtHvgOoykSvkmuW3HPcdsmyrqmVqnM9ve7HyGE0HG8tO3019f97kRE7I+63/6bN3/6g1/7YfeN/yVlcsNFBve1z21b1extRkSe0/OlFJ7T22iozx1PcWT8nUPAw0V2LlZaLXr9fGL+Quv1YMAszvmqCzEdOHjOWAKo3uWtPlUECXeHiVynctF3yR9c6km4mnbG7JFg0WpBXK1/+/vW24wzIXQc+J9//UkQd5rVP7TRRd9zvHW7BbNHHgXSn3hCsH0lgIyHQxDwUCVmj0bpv7SaUf+B0yzejnPGukmiXJ5ewTGu/uYqifYLX2GNu0de5mTXO7esHmMUyiCt/nJXCFdFab/7f/zherK9raKoed+7g1X7tDnj7BRHxt+t1259AHCcimQQp9XcrSlzC62JiLSaNXKrcBX5s/6DzdI4Xz0610sibjuLaawpm1qHhW9uRkqZXvcvr7hfZ1Hkk++i9aLLbFd4/Zkvo+x7x10hxG5lnbttXXJJbGxFU+TxIj8FU2Gt/8Zbb1q9nliWrXlB1HOc7kRbG7vR9G+/f8PWFnh790E3e+PU5quqzn21euGhNzpyANmUs2Y1w1/q5OLzxz+RptXjsdlM3VC+prn5OZMnuo4Df9JNl+pCnDdHJVf5a87UOC/MiIhUFKz2qjGGSRl/84uV8dAHDxVb6vk88eWEek46Koio9IBoqEXrKu7Hj+H0k7hbdEqZQdAfDzncQJkGN8XwWIXRXsnrlHrHM6vv5iqyS2wr6vG4WNUN5WsanDOwqcJIvn4qIN0PubChvsgTrgAXq7phFD2AmSoZJL/zUpUcWPE3PRRd1zyMhjtvUH2RJ4AB0AcPYJpqG9JvUtU7/qY3r3reXJGu9JPPEdhC3nRoITENWr3uXIV5fKur/9ldy/fm8s744s+pAy5WdUMTPYAhqm1Iv9oKNsWhSXnHZhX8UOEUaYpHc72pEPAArVdhdzvdqMd9893ROH8GZDw8hoAHaJOdq3C10U63rrijcb6sgsGMjL9P6AIxDbq1jJdGXR0d5LcNUaT72Yp0xp/8afHnVAUXq7qhBg/QPpXXs2/bLE+n0v3KB9Nel9fCUY83CQIeoE3qiOGbj6crMuPragfTRpupfGFnfPGnQfMh4AHaoY5K9s0r7ic1/PCao9rwRsabAQEP0HSPR9JVcv29ecV98zAO/ejKB2OG418PZPz9wBgH02DciklqWmqmOeuXtWJPlBbZLLFKyrbWjwAXq7qhfE2Dc8YM52WwjgN/MieinuMd2ge9OamJdK9DizIeF6u6YS16gGY5I9p1HC9tm+t4POt7YsRIx4EfMeFu74benIo7Fcieax7MfSqyoH3xp0EDoQ8eoEFK94urSEo5JiK1+SizH5xFGG0+1pAe91TBXLnOwRim4Ij6gk8o9TRoGgQ8QCOcM6BdRTKxhBAj2+aciPE+zZQmIiJmD6wkUee+8k2162gbqFTGn/Ga0BboAjENurVa54KWcx0HMRtZiQwTIuo53kD7iZU1zes4iNk8CZsWlkUa55t2zG1UcHm7Ik8445lF4GJVN5SvaXDOtMgZYZZW2vPOdR0H/qQ7FC5fjbBzeqQHwuVEKpJh0rSkRLpfTfHRdkWesPlMqugzwsWqbihf0+CcaYVzr5IqkmGyOUQ+G1+X/TsY03w+cXo0mRMRDYXgB1/qBiqMGSiipowv++RDcLGqG8rXNDhnGu6SClDeIr9Zid/58TwJz379WiHdb2KzoZ5OfTGunPG4WNUN0+QArqSCtk3+4DKijjMdx5pnlfh87juRRTSp4EBrUCTdr3Yw9yb/4hXcMbbgV/Txk3GL1jQYRQ9wDZXMUmOMEREx+6E/G8c6e9AerV45ac5EuCLS4f35f1t05K2Tlm129wj0AAAcBUlEQVTxjC/+svmTke4NhBYS06DVq2nqGTi2Ndju8Vvsv9qqSIaLw2vc1aXIavOHy+fVc/nJ10RE9Ma74v0nNRxfS+k48Gf9o5/m3oH0RZK4bFs9nfUNx8WqbqjBA9Tl8SYx1eH2kPRqmvvjt3j8jjoOZGIJ8UBjGaxq/1dwPCo2U2dvxVG9mHWG6d/nffdXUj5/VdeBtg6zR15/5q8/TB0Hcmtxo/2hu1Pt3vvaO/V4dKC0FG6gTIOb4ia4znSvUu+iokDbaW1Px8GYHq5Rjy9VWdz757x6Lmf9dcVdvfgoXL6Nivy2bBjGzjoIO3Yq8ek/iqxUX3BB+zOa6HGxqhvK1zQ4Z27rajO5z1j2Lk/460T8RU3B6sXzv3/n/fd42kRP68Z59eKjl70PkPAZrRTxDmlSY18PhMvVx/IXb4sf750eWWpEffGnPX79gnCxqhua6AGqUWeD/P43KvRsHQdSBrEmbq9H5jF70F0tans7hxt+1YvxV9RL//3kfTHs/ELKvxxrIqIvl9R580oH2HwqDsNYMcaYPRrSNNZaf0Of/d2Bfoy04T3/lh5veM+/Y0He7K8iebR7B8vZNg1uoEyDm+KbuNoQ4lJvtDuoTseBny9zt67P3+Q4j9QO1YuPxvTwwXt8Nb6u90SM3v00kC/nGGm3bV/Hi/q5DL98/R3vj3+43F0W6dHncuhjWj+utfR9ol6vN593h8KlSE5ZsZF9J+FiVTeUr2lwzlzZNdvkS76RVtE4sUZuJ+2itYbC5atZ89Zwf0/tJYdX0TjtV8/lJ1+/8e6w84s05unTQP7t68MP3mvUqnxNoaJ0IwKinjPsz8LJ3BoKlz6W4Wf01lD8mO8sbkxaSj9f4lBKKTwnv+07ZFUvT7816XpLJ55f5IuKi1XdUL6mwTlzNddcOL1ExV1FEbmrq6+KgumC+g8jm21U32s9yILpTkeLTr34KPz89byy/ur5c3ofFfejVCRDGgq3ky5erOP/Nv7V7/X//chm2xGvdRz7k8QTgq3uDryh5R+slmctAxNfCs8pPnSjyNcAF6u6oQ8eoLSrdbfnb1f8jbReJOud4LnVnXcHNqNsj/hEHfvdCxXqglVR+pzh0b+Iv/fB8N3OapP7V7Nfo9/9OB1PaShcTiqeTBKl4/HkO4Mn3UmsiLgr7E7ec86Y7RLROFZxECbUczzhh4nXn/nR3i/HUlOfMxJCSH+yfrtASin3/wYRoT++GbBULUAJV97u7Jxm+VnXcRZhpNIqG3fX+80sNbE6m7lPz5jScZBYRInwnEDK6e6aO1tz4viT9/ir5zL8Ou13R/v8Ufln22GW9WXozxxv1FFBj3XWaxmvu2U8p+dPwpEQNuk4CBxP+L4UQ1JEj8qZ2/3pOOYje2kRJfMJIxbJKctaAIK4c7BGX2rhW6gDWkhMg1avmlw52unMgXsqjjv2dqts3ktbeb/7jpPd8GnUrB7fsxJbOqru9/4AHe7lrTvj3yBKl/7rOU53MkmsfDvhrOtcx0FMD/bE94UQaRP8fOIL4cWBP6E9Sx3muxKHUlrUy1vzT/fGHz1xcLGqG8rXNDhn6nDlikgVNxO7Y6vqdqSItNbpKvp54/zGdvZbnbqvnn80f/rBv5nKl/PeEzF69wrHbbBVrzzP/78acp/+a+LLNNT1QNg68NPxeZ1jYzXSu4jVB13iO7b364GLVd3QBw9wTLlJ5xW9YxW9+9wdUnisk7RKx4pIRb6f74xDntPbOKrd+fhPnj68w+n7IyGGr0+wLu1F8l751X+DkAbZrRR3B9qXRCSlP+t7tg78Wd8TIgklMXtgJQfGami9sIZZ57qK5JR5Re8g0SV/E7iBMg1uiqtykzb5K79jJY6l+8bQ/fXTVCTDZDVp79iw7FfP//KbH/3Jw3W3xjHFZvP5sV2GpJS0MVdeSmmRdahenn1gXEl/4nii7DoKO18VXKzqhvI1Dc6Zy90kaFs6HOnoYee97CSlnz22yhL1eBEWqNa6V/7Y6AsVBWGyHhghpX/8U8k/VP+sb+zmFwYXq7qhfE2Dc+YSt4r2679pJQrclORDuLM/8NpDA+CUjYDPKvrziV/w23jeXWn+W7hY1Q3laxqcM+e5Vcq2tOKeOjawLl1uhYhISRmuq5B1r5ELpeU1/XXVvfjX8pKMx8Wqbihf0+CcOcNNUra9FffU8UJLQ8MaiiTc+jOR741VcJn6k79Y/O0+/PBDXKxqhYVu4K6h4n6ek8fPLavH2DrdN9fAR7qb5bwFbYQQz549q+mQIIXanmlQgz/kcQWFblSBNj7daTWGOwml06NJt+YVdqAiV67E42JVN5SvaXDOHLK5kCrdLtpv9dZVKXXRJ6J0rbTdJeugqa6Z8bhY1Q3laxqcM0fcNl/bXnGns9I9+z/63lvi8UdcX8bjYlU39MHDXchX0ULF/Wq2/l7ujtBI3waX7BCD3WWaBjdQpsFN8WMnN0G52ru3Wt09stAcZzfUl3oyLlZ1w1r0YLLrryTfnHevVtnGeWi1naXjS60kj2XnmwM3UKbBTXHq5q3ixkQ7XdL1Dq11SWd8wSfjYlU39MGDac7LmHxJ1cuXRzcs5MreqRjzh9+5CzvU0R/fBAh4MMf5yarj8azviREjHQd+xM6ftm3YRa1spa3Wg4Er2wlpZHbrIODBBGdE+1aVfR3nzH5wAj9S5SPesIp7WXf+59+JUhmPG4KbQ8BDu52ZK7tVdq9PY6VtxoiYPbBkolxeJuGNvJChcR7QUN9qGEUPLZZeOy67fDD7wVmEMRt0J7FKH+K2s0hU2cO44BiaCI3zkLpkRP0Zz4cKIeChlc6YgabjIP0tGSlivE8zpYkorbInCdnOIozSWF9qYp2aDqMVzkh38woBDkHGtwVmKZjG+JknZ7fJBzEbuZxIx8GYHkb2MpKJlXW1Zz/trPrlrSK7oxgZ7VT+7zK1HGDThbPm9j7f+IvVzaEPHlrjopriUs8pnfzGWJc0EXHbma5G0y01MU7E7JGw6z6SZjvjql3fwUBzXN6bjv7460PAQwtUEKjcFR2tiRipJOlaLhExe+TFgZQhEVlDUXTuOy5SOYNvdOCkMwIbGX9laCExjWGtXtVHyAXbmhmfZ+h6h+Oqbag37GLVQChf05h0ztRxs5/lO8WBP6Eyi9YZX/NA1zsUUWHGm3SxaiaUr2nMOGdqqx2qSIYJnV6QdmcDunoOpkHO63o3u0zgkMvPjvQVzLhYNRn64KFZak6ODutZw9HpEfJ5Z+E91FOR7kA6DvxZv8w+DJtfg/M648sfJZSDGyjTtPemuGmx0bTjqckZdzD3cNNzjwpn/N5TA1+kBkINHm6vgVGaV99vfSCNgzIx1nqWaLZRw96OrDyVd+L5jOauDz/8sKW1kbbASnZwS/lKcA1MdzrSkKgiKYNYX/vAKofGediH2SMhhtZ84j/+muPTb5G2NufCIS1qom9gA12RANNx4OuBcDulOy0bpnj5H6q0gaF0HPiT7unlHC8cUd+ii1VLoXxN04pzppkVwYLXpo2J9KtVb1sY8WXTPW/JOPxbqxkKBVf6hWZSkQwX67Z5FckwOTLp5JKMb8XFqtVQvqZp+DnT2Gin4ke1uVROOyP+wvVoH/3uTrQXrf9B46hITpmX3776k/nqEx3TwwMnxg52ye998Pg3reEXKwOgfE3T2HOmmdFOxdNuXbPZSvULVsa7jfNGO+f/fjyWSseR4i6LZWIJK5EhrUJeD5DxbaWi7INM/6vj4JWmz5K9t217K/HpP45/0xp7sTIGRtFD7Zoc7VTswLK4Ep04kEHfGz30Az9i9xRfmwub7JTYUieaubY7TKRMhsLTgYxIuA9OECvi91NEBtHxdCPdScfjSXcg3B9bkQziR631O/d8BdMdrgA3UKZp1E1xY6OdSlZk9/S7U7a1bLv6m8+uvh/4rXXj/BvvivefpI3zT53FV2xkJS1r2oDcZrPUTp98/ozVB7/qn3+8MNTJL1ujLlZGQvmapjnnTGNHXBe97dgcXtT+fneqON13+t3Vi4/Cz1/7t96fPDD1VzL8qm13PrBt74jJ7QF32VALz+4wxk51xu/VnIuVqVC+pmnCOWNAxT3vQlaRTKx8mFFb+93p3PutQ7+1v9/95c/8T79BtBtod8DdoD8LH88RLTuivgkXK7OhDx6q1PBop6LHptWsOxxxIuKWNdWaOLPb3O9+drof+tGBfvf3nC9iVmCpf2iTbMCdSD9W9m2av3zV98SI6TiQkznlt3SPB2DeyW4OjYWAh2o0OdqpdMIxPiCliHPSetFNpwYxe+TFgZRhej1rVfX9DMc/UO4OEymjoXCFFwfS7z51FokiSxNDuptle8Cd+lj+7fytobCXkfQTK419HQeR4gfu65DxN4QWEtNcv9Wr4dFOl40GaGNr/I5qG+eJaLOHNhtjhX53Y+0bcMfirUl022dJ8c54NNHXDTV4OF8rop0uOkKVLPo22+iBrPDgalNqJPOhVzjwkzzae443spdR8MU3YynnZA3FT1tROFASdwfJ6vuQ1th1HGxPogtCGoj8HhhV9uZAwMOZmn8OV3OE84kvZ44nRHsq8UU3s8/CevfG5chdkY4T5olhHOh/1Z0pbdtWNyFX/JBIa03UniKCErgrhHvgZ6s6/ambO6T+TaCFxDSVt3odWqaqyedqZUeo46C1g8ZOFEL+p+k48Ce0mvt0/LeypliKg7H+fWJPRiwOvrAennZUyzfegVL2TKLLdpjNHynSUI8m+rqhfE1TxzmzubI0NTvaqQ1NC1dwcjHw7VsXne+Md/q2IJstmGY9/+XPfv7pa2/Qd7Eq7R1TkQyTLNg3vlgnMx4BXzc00UMhbYl2avxBXtmhplHG+ws/UlksM3vkUTBO5zwdK0Bmj0bpvzqMkqUm9bt/om/eGr6PdL9X25PoiLHuQmviDM3yDfDarQ8Amq4tK0unl5KGH+R1PJ6LvP6ZiqSUUkaK2Q/OIpSRyn7AJvNT6b6FsW4S+vrpTxxniMr73Xq0an0Q0uBYT83m1sNQNwQ8HCSlbEVq5sd56wNphGNFoeMgsYQQwmNTKcf0IIYUyjTkNRE5Xoky5LbjDF3ObBvxDkREKpL+rO9t3u7tjXNk/NWgC8Q0lXRr7W3rbmaINvOobuV4aRzqd8+HTKEkobS9q9ZvO9QZ/+GHHyKAaoU+eNh1KCSadvVHj/uOk/c6e/vdYz6aIN3hbMcm0cGNoQZvmktq8GdEZj45pvdoQ8laoeK+o9iU955lUZJ0N/cHC7Q9n/goTKjVGXvNweVQgwei8tGu43hp21zH41nfEyNGOr7WTiyouJeW7ogn3HSSmzfUvpTZxmDTxXzu3/r4wHx7R9Sjib5uCPh7Vzovsz2hnYEi6uSPMvvBCdbNv3XBLf9eJ7re9cKy0lZ53qex6oyEcFUkZdgjKjVyHgDaBAF/v86pCud1wQzv01hpmzEiZg8smSiX15bwSPe9Tne9s24yjW1uM2KsS5qIiLjtUeIT0h2uBdPirw8Bf4/Ob+XmtjONFVGSDpztOd6g68fKdvn6hzUkPJrlDyl0xeSu2PlM0uVpAa4LGX9lCPi7U/YEy4fRpbNgeH/hy2QohJuuW6oHziLMmuaXtewGjivCIeeWjIp8PSci3DPB1SHjrwkBf0fOqQfreKwHQqRrTI9jzW3ed1i2tAnjfRprPvIokDIkImtY6Z5rqLgfcd5VssMo9Kfoege4Bwj4u3B+Ui71PNsEdNV9y+yt2XBdxoixkbArOdANuM2vA7MHQ8bDEOuIwc2gEn81CPjmSdvErc25yuu9msq6tBLMXdFJd/pWSdK13PUBEhGRNaw+2VFxP+2C62OW7iheuCGsVnsdCPhm6vUo25GJSCWLXq/8S1QWk4yx9CicVcu8XUOFfQW39iddUkS4eQK4Hwj4Zup2aZZNP9Oaul2ar36yXX12eTZzLduJeUw/qOcirpJF32bZ6Ot6Fq1D9hRx+Q0QShiaQAjx7NmzWx+F4RDwDWVZ3WRJxEgrzSy2SNLZyyrys6Xj0rXjlHC5ZU3T2v5SU9/+L8+e1XAFV0kyTxI56TmeqHQc3Qoq7kVcWEpoFIVGwUp2dUPAN1WHLWJFvKNmxDjNskc3ZjTna5ZwqztV2mbLZNG3mTeo45zpsJ41HNWySh0q7gVVku4oZ4D7gYBvKsb7pDSR7lo26enGT9bbM5JlERF1GE2VZnrRr223F2aPatkwChX360C6A9whBHxjMUZjFesFsylbXZTScKd8lRk/fZzxPsVxUmO+1wPpXhzKCgDKQsA3F7e6YbhwPEaksoe0XpA1WDeUL9LOd8b7i8ms77Um31GhLAWN8wBwBgR8g3VYj4ixjQp8umdbOlSqZ1m9uV4SMSLG+z3NmprvO/mEymgpSHcAOM+3MIjRBDoOYpaOgfvWt5r4maYphbAp6/KbIZQ5NFYzL1YmQQ2+9VZT02tbeqYiqLiXhXQHgEsg4Fuv1nXlKoHp1zeBdAe4c6/d+gDAcGk1FDFTFho8AOBC6AIxTXO6tR7XIPeElopkuKhn6dsWQ+M83IPmXKxMhfI1TUPOmSIRpePA1wPhduLAn/UR8pkL95LBYEZoi4ZcrAyG8jXNzc+Z4umiokDbaazrOBjTAyL+CnX39UKIZ+5ADFCRm1+sjIfyNc1tz5ly+bSR8Ih4qqLuTttDGh+/mo4jxd3VTZU/6SLk4WYQ8HXDKHqoTNF8Wu85a/en45iPbEbE7EE3yHbIhfLylnnayPXtT2RVd58keihczuyR4HEgI0LGAxgJo+ihAlLKgumuIinH9CBEluoP/ZkfqZO/dgfqGDa/fkEdf/ziF8wTQgwtoq8/kTJSlC6NuEhQ/gBGQsDDpcpMhNNEPWtgMx0HUkoZKWaPPDaVUkqZWPfbQF9hum9W5Vd0PJ795nef6SURcVd4//o3RIuXMlJES02sU8kbA0DDoAvENNfs1io6nk5FMkx62WQ4FQXTBfUfRjZbDaO/8wbiStL94Geh449f/uM33/t3I3v5cxl+SUTpJ6E+luFnGGkHN4Q++LqhBg9nKlhx13EgE0sIMdBpWzy3uvPuwGaEBmKiutOddDz+5eLzxVwvdTz9jTN0ekT/NPODWPO3rZ7jId0BzIVBdlBamWnWWs26wxEnIm5ZU62JM+6KPFSWmhgSpjY6Hs/6P3p/xD4JpJ8QUTIQQuj4uT/xpTUU7r12iQDcBQQ8lFOyxsn4gJQizknrRXc1RD6fi33nIVNz9V3Fk/ncWup4/A99zxuoJdE0iDsj9t2e86P7HfAAcC/QBWKa+rq1LlwfbXPSO1Dt6U4b91FvvCvef7J+AP3u0Ajog68bavBQyMVppJJFPx1WN5kjYCpL931j5jM6TpgnBCP9Kvjrl/rJU0bcsnoMd1kAdwI3UKap/Ka4ooXN08pjD/vKUHWT4o40zq/q7tmI+eivPkm++pLorSfej9+9+/KHhkANvm6owcMxlc3P1nqBejsRXSPdV3V3ioO/nv2D0jYj+u1bnvgJxYE/jt/CLRbAfcA0OTioyrXVmD1CulfneLPKUi+IiJg9+k+D78yUpg6jLz//NPL1QCDdAe4GavCwB/YbrUkd69E+xjfW+CciIvZt+uzly95TgXssgDuCgIdd1wmh+7G5z1vdjfMZZo9G6b86jJKljn/12z/4/vC971/+3gDQHhjjYJpLxq2g4l6T0wVbeAJb2c9IRTJMMPwBmgiD7OqGGjxkUHGv28ES1nGQWEK4pONAymmlMw247TiWjXQHuEO4gTLNGTfFqLjXajPX92a8joOY5WMQdRz4s/7+jMcnBSZBDb5uGEV/78ps9gqX2ixnrXX6D8b7izBa7bnD7JHXn41jvfu7SHcAKOefwSzFP/pnz549e/asvq8WENHBEv7TP3/27C/+7AfZ/37wZ3/x7Nmf/+nGT9c/23gdfF5gmFtfLw2HFhIAAAADoYkeAADAQAh4AAAAAyHgAQAADISABwAAMBACHgAAwEBYye5+qEhOGbZjr5yOA38y31gN9szVYdPX2Xigd3hJOxXJxMLyswBwDAL+bqiErO5MaZsh4SvX65HWxBkRkUoWvd6Zr4NF4wGgMgj4O6Hj6YI9DGicJ7yKZMKcxWQyX9cVdRyMdZeSZI6kKaXbpdW9k9bU7VJeE9+ol2dlWrqQs41oduM/yR7GRwUAe6EP/j5oNaM+Z9zqTmKVP5pMZn1PCDHsTvzVUqnzhAZCIDJKsqyuXhIRaaWZlbeRqMhPi1gIz1mvR1umkFUULhxv5wWIKFmwPY8CAKwg4O9Clu9E3LKSZB0H1sBmRMRtp7dYrYxuWcj2M3TYIlFpSbNO/ih3xaobnbHu+tmHCjkJ5UqW2ipJen3OiIjZg80PL/vsdh4FAFhBE/090Go2n899Ocn+r1zOiYh6qyhirDtPlkSdAy8AJzHeJ6WJdNeySU83fpK3sBNZ1olX2dvcPp+sP7oey7r6ewwfFgAchYC/A1rNyPFEVpNUkUxWCZ8/Qy8QGBdijMYq1gtmE+U7walIhjQUwk074x/tEFfI/tTXSyJGRFovzj9oADAYmujNp9WsO1hPt9popZ9nHfIqnqQt+HABbnUnk8VWOWq92GqNz/tByryqlUzTvWNVJIP1LrLZh6jVbI5eFQDYAzV442k161r2xgPcssJpbA+IehZNpQyJeo7nIt8v1WE9IsY2KvDMfnACX0oiop5l9ea6fD8Id4eJTNvotz4mi5LVZzdCvgPAY9gu9m5h3RsAAJOhiR4AAMBAqMEDAAAYCDV4AAAAAyHgAQAADISABwAAMBACHqCRdBxILDIPAOdDwAMAABgIC90ANN7+PWep351M9uwjCwBAhIAHaLxsz9kRS5M+Ummaz9PNfhmpSE5jm2PJIgDYgoAHaDjuilX1nLHueiHcbMNY6rBevvUMAMAKAh6gBcrsOQsAQISAB2i8SvacBYC7g1H0AM2xsSPsUs97rEOV7DkLAPcINXiA5tjYGzbfHLaKPWcB4A5hsxkAAAADoYkeAADAQAh4AAAAAyHgAQAADISABwAAMBACHgAAwEAIeAAAAAMh4AEAAAyEgAcAADAQAh4AAMBACHgAAAADIeABAAAMhIAHAAAwEAIeAADAQAh4AAAAAyHgAQAADISABwAAMBACHgAAwEAIeAAAAAMh4AEAAAyEgAcAADAQAh4AAMBACHgAAAADIeABAAAMhIAHAAAwEAIeAADAQAh4AAAAAyHgAQAADISABwAAMBACHgAAwEAIeAAAAAMh4AEAAAyEgAcAADAQAh4AAMBACHgAAAADIeABAAAMhIAHAAAwEAIeAADAQAh4AAAAAyHgAQAADISABwAAMBACHgAAwEAIeAAAAAMh4AEAAAyEgAcAADAQAh4AAMBACHgAAAADIeABAAAMhIAHAAAwEAIeAADAQAh4AAAAAyHgAQAADISABwAAMBACHgAAwEAIeAAAAAMh4AEAAAyEgAcAADAQAh4AAMBACHgAAAADIeABAAAMhIAHAAAwEAIeAADAQAh4AAAAAyHgAQAADISABwAAMBACHgAAwEAIeAAAAAP9f+psfwxQhLbPAAAAAElFTkSuQmCC" /><!-- --><img 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UIiD5+SjZIjJPLwKdkoOUIiD5+SjZIjJPLwKdkoOUIiD5+SjZIjJPLwKdkoOUIiD5+SjZIjJPLwO4rfPYjIHL7QLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQLKjQ/g8nx6sjK1cFcwAAAABJRU5ErkJggg==" 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v9EzTJP50Xxf+vsoDYXZMETBNBBO16XZWayq3KxR2xOb6JZLDnqiV7G4QFUlxVuRhRF8ZW/6PCgNh0k8ARh0BGNV+VMRlEBqND1uCRJUhIh++K7bIokISc8Rl7PGVtvnOvqQLwPCTxBlKhW01aJa/HIPi7A2uLxvIBAeEYUa3a9NQ2gWhpP2k/0Js7xIz44vpiWm/BaEY1C8VqvQTH4jWNGvlse5zZav8czGgAEwkbnHBaSLHWdsf8ilb4h+gH3P8iBgSfX1z9s93g2MyQGXoMEvlW0STjLD2uRdjUlKUJtiSeNJ/qAhn6KNFm1G3LRE5sQNeW8QK1IWx3guiyr4KOiOBPOZWUdfDSGZKKG51KXEy7HQ057oj/Q5b869b93exAehx6gvAY9FNdH13WO4wA1ldCD9u3lTUOkHcaxJEmiGEtJSRhOeV1OyNx0bePdRE1JSaXWqjm2QaY80S0auVl0OZH+j9+Y+asPabJqI2TBE5sPjmOa7uOg523et85T7UhkE0VRkpLFbDtAVxfB+YBS8Zuic8FcU6ezlXQ+23T7siO3dqgE4ZLGHoVVVQ9F/nqunQMiyIL3HmTB10aXE2lEpoP5YpkNp7S2Mtpkxxc3A+EZY1TFEbHqN0glslxoOsibhUEgxEQlWTkYNjyKxBNdpImfH01WbWed8Bb0b1qbxfPxrFa1ub54/tSp0qtanDp1quUDKh1z8fypU+cXS++w8ZVGqWXj1rdrDaYdgySIujT3w6Ofa7shFz2xeTDX36qppOLnjAVqkiKIYkiP18pvM2ibr14CdDkLizNBlxOs+g0fDbFiOFI84xeKb6spCUKMVsYTPUJzriNJkl555ZV2jIcw2dLtARBE5+CC0xE5IUn+mCgyR3hSAaCo0WhU9MmJlOqY6dYONzg7ZjggFHeoKSmZC89Ms3HwUVGMFt/S5UQ8o0GIiTFFSrZwEATRWSic1BkoBOI1KKzljmI8nivbdEOb4/H2eQG6qoL3QYeajushY9W8gpoZ9TR7Ep2hafNdFEWarNoNueiJzUlexzhfKelGErvz+vg2ucFFA1sXgionk7LKcRwXnI6BrZoXhViMStgS3WQj6t6O8RAVkMATmxNLPD6e8YeCHNSUlEZEFEVRUDodj69/wEA4aKypMzt18DxSqFHZhjSe6E1I3TsJCTyxSeGC0xGkWYpdlFdTUpYzKsPXXB9vpbMaX8q2k+KL45Egx3wNisDmyjrPIwTRBpqQalL3DkMhEK9BYa0mKC8DX68ovIW2dKOpe0BdTrBAfPGlFM9QMJ7oJC1Rd5qs2g1Z8ASh67liUTkwU95d+Zuu+Oqhy2mLukOX0xmBgvFEB6mn7kavBzftHoi2QgJPEBw/nsvKOnQ5YXHUu4SJaAt1tJ4q53Wjri0ANSXFF8dnojxpOdF2XP7AdFnhZljG6AyXNUSenEldgTwkXoO8Xs2hy4n44niD4l5Ga6cwp6OVFa4tORtqfYXmVqJVMI13/jlVhLhY9Qbbr9Bk1W7o+noNume6SOc0vsGvkMYTLcHsegAbmS89eG4HdhefPVkdJ9tmiTRZtRty0RNEy+i6n7zrAyA8ScWPivnfK3bqH2RzE8w1P3MgAOWiJKVU1hnZElQiOgo9QHkNeijuOi00l1tYSISMeGIj1HPO6+l/jv/yEzNfPGLEuIy6yoBD00aarNoNWfAE0WJaaEb35qGIzYlDPqkup/XJT+6ej599R5IkSUrICEYAxGoWZyQ6AQk8QbSe7gpzra+QxhMbxMY5r8speV7OaJq+PRj25fOAEBNDelyKjwbC5JnvLiTwBNEWelPjCaIJKuI7lm1dTi+CG42K4gyXjWd2Hj0pioIiJRVgO7eBNSlESyCBJ4h20YMaT8JPNIpD9oYu/2xeGxJ4Tk1J8YyGHQ9WdUhJRRRjQuDAJzo8UKIKEniCaCM9FUQ386RI44lWoMqZ1Yfbl5OSlH4QE0VRPLJtNi4BkCRFIPO9ByCBJ4j20j6NlyTJaHBboySo9fOURU80gePPho+K4pGtjwHCE9uSUkLW+Sgosa6XoFUKXoNWnvQmjeirmpKSSiBsW1bPPE75AdVUCtEak6rtAifSe6IutX8klmp1uq7mVfiCPGQpntm+I/zpL7i13WmyajdkwRNEJ2jAjlchiKIYQdquC6y5VCkmigBUufiZnG7bMrbWHE2OesIZZ9tdEJSkJCVkHRzH80E+n5LiGUAY31W30zLROUjgCaJDuNVUnucBcMGQf1Gt3eddUQGo0Fmf+CRCTuY+QbSaQHhGDOlxKSHrYIl1oihGj9TyIxHdgASeIDpHdRDd3NblREpl/5eklAo1lVT8XJVoS5IkijPhgKAkJYDnBQTCM7Vinqa6U0Y90RB1Hw35YITnwEdFMYK4JG2FQI1hexAKgXgNCmv1PmbHjrL1xAkZkWCQ44wqn/6YGOXVlJSEXaHPUiFQFqs3X9csCwoqYUu4o8GfhC5J8X2jwvhnGrbdabJqN2TBE0SnsTOdOc6fAzgA0NVFTQhzWUmSFEEUBcUmSZ4LTouiKIqAFsynJCmuh1iRMUGp+qyRaZ9S69rxZNATjSJJcSE2E2lc3YkOsKXbAyAIj2E0zXQypQEUldU0lfhoSCkKbCAQyCyOz4jTHABEY0JC18HbpSaLMUFKKjFRLJ0qV/lZLjgtBgE1lZBrVg510+eb2Aw0YL7rshTPlP32iB6DLHiCaCm6L2iY0nZJ8AAsc2i5Sc1HmREeEzSMW9bIqYpdMJ6dTM4iJopJ4yC6nChl2+myzGx5neXX+zjoeYe4O6k70YhzXpfimfAMqXtPQwJPEC2FM7TYx6HWgqGKst4ViqsquXDEVHddTiRz4SAPqKla9WyM76Wk+OL4TJQ3XPLxzPyiCkCV43H22i/w1Wdkczol3BENwTzzVKyux6EcB69BeStdQpcTaUSmg3nmoXfho7dgtZzUVEIPMvtdTUnJXHgmgnQ8owkxMYqqpDu1eDogJoq8mpKSisDy8xKLD/3jn4nyupyQuemKsVTbapRtt8lx/wNo1U+FJqt2Q9fXa9A90yXKdLm4aSS3u9F6y6RpinYgPDPNq4n4YsljbzmNzRHKHivUd6TkLwGUdlpK5FFGPWGl7j+99QMk8H3DOuEt6N+0W2jZeDyrra8vnj916vzi+vr64vlT8ay2vr6+vnje2HDm1KlTlbtKxzBfn1+sef7zliNo2bjlo1o2fsoYVnGcdqersZPwPG7+3dln6n/S8mNzhiardkMxeIJoDVxwOoI0W9oW5dWUlOWKdrdDPN6K+3h8LWLGEcx4fPF7bBldlAfA8eNsNBR3JxguLXJXPxgWqhLZ8k7HpBGi/ZDAE0TL4ILTTEXVVBIx05GuykZ+W31qz6GGZtduwskFQ2Dp9JKUFERx2symT+uhUohAl9Ol0VSfjlR/s9Fo6N35F6Kri362joOPimIMSanmYhKi/VAIxGtQWKsHsKa1maZ8C+Lx7pOWy45QitobWXvTQc6Mx2uZOAXjNy1NJ9bV/GIx2ZSr8doKTVbthq6v16B7phcwZrVSglzJY++QJWdl4xJbOkIp016IiVGePWkUN9OIkMZvWlqWOV/+o7L6mmwXcTBosmo73UwAINoA/Zv2CFo2Xsqxs2TKadm4i/Sj9fVW5LvZHKE8984cTfUnKdvO87j/J67zSTNvc/G8kV1nbpTes4Emq3ZDMXiCaAtccJqFwdsQj2+amvF4CsZvNlq46t0m7q4Hi2l2Nf3zRAcggSeItqLrOaGo6MxR30Bbjg2qbNXX8zq4Yj368kz7Npyd6FvUlFSi7nMAx4/nsmYqHR8VZ8YX07LOai+TuncTEniCaCvF2U+XE5aFc+5pqcbz0ZAeN+ZtRSiffUnOPY+1baCDbOuyws2wXoUIB1BrrZuuqoaoc8HI+GK8lC5vrsQkugzlOHgNylvpQSrSjppgg93eNuKPpWw7L+Hmh6SmJEUQo7zxT2+UUahy9VjqIpZeW3I36//cabJqN3R9vQbdMx5mI1pLGk8wTDve7t/U0tug9AH7RHhdTsgYz2UyfsvKz0rVd4Qmq3ZDLnqC6Bs24kUnD/xmpsI5X6tejdU5P/IYpB/NAihP3SiHC06LM1y2VM2G4u49BT1AeQ16KPY8HbDjyYj3HvWc8za2u57657jysFZjRF3Xi72RrRWUGoAmq3ZD19dr0D2zGSCNJ5rAwTmvyymVjwY5VZKSge3QdjNNd6hSU4XLEk4WaLJqN+SiJ4j+owP+dloZ7zGcnfN5XdHzAHgA41uB3AdSSnVyzlfDR8k132uQwBNEX9K03JJOb0IqvC/lFryakqSkAiVprHoPTotiyA8lKUmK4CzaupyglnE9DAk8QfQr7dZ4MuK9gWNsRX1P+gDViXX8E0IgPOPcF8lY/Vm/eRLRLSgE4jUorLXZaDo0TsH4TYLzv9fsj6T5+4C7xLrWQpNVu6Hr6zXontmEbETjYwKSCpwndOvxN1hyh+gwdX8baupHSeX+7sdx5yOWBt9IYt3GoMmq3ZCLniD6no346pMKRFEURUEplRq1x6xMTo76fsHZOZ+SUiqQVO7PiDNjHwFDubQkpdRGEuuI3oYEniC8wIbj8T7OsXy4Ke0bPB3RM/CCoCQlCQAHLjgtik+sa4CS/GCYsuG9AnlIvAZ5vTYzFRZbDQNOlxPxjFa5t1Z9UfMg7g5O9AounPOJpKLFBDRRo6Yl0GTVbuj6eg26ZzY5tfS4nMp2IM0l3JHG9yxu/mkkSZoRRQ6Aeu6fkiuBmHiis/nwNFm1G7q+XoPuGcJVHlxVjzBJkgRAsWTbGcVLy9PvHDSe9L53qPtvYfmA8bTHySlEO7rkjSardrOl2wMgCKIhbGW3cbjgdCwlpVQxyrNjAoICRYyhuBN8VBSjgJpKyL5aHlxrMJ7UvUdoRN0BVdVDkSgHRKOdGBzRQegBymvQQ7HHUVWV5/nalb+tLnq4EF1dlvPBIF+047RMPCYgy1ljspWnolVzvYxL57zxmVrN3jsCTVbthrLoCaKv4Hk2F/OCf1G1WddmTXR3keuuypmMogIAF4yML87uCyCpQMvEpWIJUjWVzI3z1gcJ87C0aq4fKXPOpxfHZ6gSnWehByivQQ/FmwFdTsQzfpdO+nrZdsWqJmYoVrqmYNn8RK1YACXc9SANOuflFPgo37U1cTRZtRuKwRNE71O5sC0QNtKf3TTiZhZ2jXmfC4bMLqKB8Mw0p6YULOPxGH6ZFMVYKgVT3dWUlEQHCpgSTdKYugPggxR19zb0AOU16KHYs6gpqTI2zhQXlW/Y4crCLh7RV4zHC4FwcJpXE/GMBiEmCoqkCCWJJyO+d2hY3XsAmqzaDcXgCaJP4KNiSI9LxYqyaiqpAIqigo+KEaTrNO10ESnX5axhoXPB6ekgADwc4QDwkZlwgA0hhmTpRBXHpGA8QfQUJPAE0T/wUVGcDnK6nEjIvqgoiuIMl03IOrigi+4gjQiwmpLigfCR5fmkrHIcxwWnY8jKOvioKMDyKEGi3gv0o/lOdAASeILoO/I6xqtSo3Q5IZmp77Vw1GMuGEKStZSRFEEUp4M7hEBYSUoAoOs542M8j5QkSba9aUjvO08t8Tb/IUjdNy0UAvEaFNbaDBQrzeaLeW+l+Hyt9fFWGpjxjbI6MGrVQ07EM5oQE6O8tdotBeO7iMPV7vEqBTRZtRuy4Ami/+CC0xGkmZ1tVXfU7QoHoCE7m48Wm8hpQbCiKCLLsuP4cfNMFIzvFht6lmJOnzrJG0QfQwJPEH0JF5wWjTKzScRMk12VM37BxUK2RjVYFGekeMZS8kyX02VnIlHvPM7qXqcMEfPAiKIoKKTyXoUEniD6Gl3PCUWdZaa824XqDUpyXgiEk8bn1ZQUdy6BRnrfO9j+W+jqoj8U5MCcNDEk7ZMq2sqpU6c6fMbNBoVAvAaFtTYbRiycVxPxxfHG23o3FY+v2emGgvEdw4357vT9yo7Bla/bCnvgeOWVV2iyaitkwRNEf2PE49OIiM3Mzo3G4wGItavZkeHeVr7mVXQAACAASURBVFwmxju9q6aMBRBcMDK+GC+Z7dacivZixg46cbLNDVl7XoMseKIJGjK1G1p1TUZ8a6mbGO90wat7x6kpKalUrYpoFxWDp8mq3dD19Rp0zxDN0UKNJ0d9W3HQeEmSBKBGHMWUd0trA8FYZJlUAs4dDZobp/PPgCardkPX12vQPUM0TUPLpt1rPAn8xjGvYfVGxcfCM2KQQ42Og7qcSGPcvwijVIKaKmsu0KZh1/pd0WTVbuj6eg26Z4gN4l6PSeM7SbVMVpvIMQFWwa52yVf2LHJTF6mlY7ZCk1W7oSQ7giDKcJ8o5/xJ67uUfLdxTMPdelXNdyVJ2g4kFShJ6Uezxk4uGAnnlPIl7nxUjJQeALK56qLHhGcggScIopJWaXxznyRsMZPPq6+kJEkT27ZuPTIjiqIoxnzXpKLI53VwvsojcRxY44I2ZtWxBxFy23QX8pB4DfJ6Ea2iJb56ctS3BOcrPBMO/HRR2x0SBUVKKkAgHPPPJ5WHNTLtqkLzbR5trcHTZNVuyIInCMKeltjc5KjvAD/NaPf9kw+T0sWBGVEUxZCezO07GLBV98XxmfZm1VXLuY26qylJSvzeVLuGQTBI4AmCqIlLSaZgfFtxNt/DgcDu2MwMt7KM0VE9LqVU8NGYX7tb7ZzngtNNVUNqaJx1nTS6nJAUQRQj+FdUqra9kMATBOGEG0lWUxIASZKs+Vwk5C2hrnN+cTwS5bm8rgHLyqPwjKBIkpRUPhI6VHbWGIn7+EteRzjIA9xff/0P2z2wTQ6FQHqW8tUsrqGwFtEO3E3fqiQlZ0SRs/t8hRFPwXiX1LpWkiSJYowVopvhska+3OyPpPn7Ds0COjnCSnQ5Ec8gPDPNyWxtHk1W7Yaub6+iplIKclzDS1TpniHahDGPszJogTC0TNW0rssJOaMpsAu7ViyJJo13g6O6G/tLaXO6nIjrIwIej3ZI3d1XRlJTUjJn1sozyuKGAjRZtZct3R4AYYsuZ3NcJIS0qge5YlmqYsWKsuoVxQ5fAUFAjotMd3XYhJdhlvdMOBwSxaQkDdk54QPhGWhK9Xed66857N/MuLxWXHB6hpPzui6nF8dnQnpar1oX19Hh2aEDASEU5IwiuUJsZjwbT73c3gESJPC9ia4uYjzC8Zw/KatBh6dxNZXMsdKUakpKIgycOnWqoYKjxGZgAAPm9jqat5mMeHwmI4qiLr+Vvj44/ukyH5NVyIGSq7j612h11JO6V9PQNeH4IDebSGoa4kpMjLY79N74DMPx0ZCSSCQwHhFFjpkoM9xXqB98myGB70UMfQc4QUgqapSvpfCqogghkQMAPhgOpGFpsWy1rmj23LQMYECDpkGz7jG3mdhb95yXTimOIdxizp2uLub8k+HFeIqzlEYNB9gPT4iJYlKSREFJyD7rI4BV1x2qlBO1sBd+XU7M+2PidAc8880+jfGCP6kI0xxYgb2EnI9+/ZXQ75GLvp2QwPcgurqoaVpcyhivayq8rucC1WWqDCoKTdjuJ7wNU/eKndY9OvRcDkpxjyDgGS1gvlu09S3Nx4pIUjwQngndiSd3P55MqWKUNxuPijwANZVSAYAX/NlimKmIqfHWTiSElQYDGcw538vqDgB8VDRHmNfBdSwJcBNDAt976Ooiih2hWLsnNcrbyjjH+TUlD9T1yJHYbzaYUV6t7iaBAAAo5eFyRQFyGgBBAABd0wEEEIAltYOpvi4n4pm4EhNFpKSkogpKMvlwXwA3kxI75PYd4RlRlCQpEJ6p/n1SIr0DDacpqKoeirTbL79hX4uakrK5gKZpAHMRUQn89kMC33Po6qI/NG3++HnmpY9yfizqOngOurqowW++mZWDfJCDKmc0hF0cn8Te89ga7oxA0T5XbDLhDHLz5777Xd+xk0/ncgAAQQOgabkrZ9/OHX55YO8AAAShBLW33/jvz7z8KtgPR8Q6FtclRRCDeiK+tCUTlzJCTFSSEoJOPy0Sezc4XSI+GO3i2d2gpqQkYmLEp3Mc6XoHoVUKvYYuJ2Ru2hoANRbE86rhJw2Ew/6MLlRk0QvhcG5xIytPSOy9QS11tzXZAQD5+XPvXtFLr7lDzz076TP388defHrMsOkZr/3TlRdOHPIbr2698UZ6nBvnTxwLwure14qOfQFQAATClVUdqEx9Nb22yqCtSRK0prfd0PX1CsW1c+OtuGdI7PsUW3XP5SAITiY7ACxdOj3vf+7Zg37L6y999VkAF/75XO7gs5OlN84d/9KzADQNQO7K2bdV/gVdfrt4oPEng7kbuSF9cWU88vJn95YkX5Pj1c3LKJHeSg+qe1vPSwLfbshF39dYs58C4dZl2TTnxqc5uovo0FEedLea7HXUHcDY0ydxSYAAgX3hOE4im1UAhPxf+cFV5YVQ6ThvZzHpRy63dOn0+1/66ssAXnsNAF6OjL+RxrDfr8uIvPzy3tyVf3rjJ4df5tWzuUMnDgWClel7AxhA8feyLq7T78eWrlwWWt3gDegBymu09aHYWexpgu4WpuEeKGmoC1EvYrjfFSGdlwGsfJhYGZ2eGmFvrswlln/rV77M3or4ggAQlL/7f7371ZO/DSA7//fvLu396lcOmkf7kXTxwPSxvchdOXvFf+JQ7uzbucMvH9ubu3L2bVnHyy9XVjd54403Xn755QCqs/c3F7a3T7fUvQMnpWeIDkAWPNEAlKDXa5jZ8rVD7CWYkGezABAKGdshv5CWZQDIywCA/Orq6EhJ3a/teOaZdP7C9fOJhTz+2xF5agS4gMjx57KyjOUP3ry949PPjmWVPABg+c03L31RfAWAoi0tPbYagYAT0CBffCP92ZdfBfDaG68B4IKlIP7LL7/8xhtvaC9rKIo980ZsKsnvEXXvjOiaZyEXfbuh6+s1unLPkNh3hQEMIKC5F/VqQn7DareSv3Y+g6noyErq/MrIM88c8Bkyf8CHlQ/Prx545kBx0ebKh+dP/tYzALIygNzCz366PPrp3NWfsneHt2/56ld+BcB3//7dYy8+PVZM5jv54kkBAgAFCgC2/dobrzHjnml8xZA8L/a9IPAdOF3FAwQJfLuh6+s1unXPVNYoBUBi3zaY4a7kShF3W+u8Fra6biV/7fz5lZFnnnnCh5K6s/2/8D1T9N5b9X5lLjH7W38wDSAr4803f/z5z3+hdDrBB+Dv//7dyRefHgNOnzl98rlD5+b9zz49Zj3p6TOnv/riV2ERewe8JPldV/cOGO62pyCBbzd0fb1G1wW+Yqe5TWLfEgYGgPUBxVKOxkHITZjkGygCgk7qXov0hZW5xPLI9JMjpX0rc4nZJQDwTTxTsuwBRI4DhmUPILfws2sv/dqnAShaDsidPvMuf/Rkub7j9JnTJ188aW4zsXeo1WNSLfbsAagvhL8X1L3z0s4ggW83dH29Rs/eMyT2G2SAFYzn9DqfsyOdRmSv8PZSo7q+euPCL7YfD+8BgNsvnNhTedgLTl9OJBLT09Moin1ahs+05i+q+pV3TTk3MTXeKvYouvHdiL2V3rfybSsBeEbd6zoGenay8gx0fb1GX9wzJPbuGTAbwawPpK80pnAmTak7AKz+Ii0jfGzP7YsXVvYcj+zfUfbuCydK27Zib2o8Vj5MzC4PD3/0ja9/4ayMUQBFsVe0nPUrtTTeZCNi32syX6GvnUwsb+u5XB68Lyarvoaur9do/z2jy4n44nhlVbKmIbGvhVXaATSq7pG9AoDmdN3K6i/SF26PHD/+iR2OH6sl9iWNNwd23HTd4803f/yN//GV0nuWVjcKlFoab2IV+wACblSfq9+6oUN00TnfvrM09NxAAt9u6Pp6jTbfM5a6uUWRN3a1Qu9J7BklaUeThnt+IN/C8TSKIfYXjtf53PELAP7sP//T9PRn2Y6IsBfAX/7Df/v85z8fQilxgOXb10WAoEDxw+8s9r1gzTuoe3fd5p08Mgl8u6Hr6zXae8/oerFbhC4n0ohEkI7rITGot9SoB9DXYj83YL9/ar3y3anKfykm7YoCQWjGcG+V1d4QL/jshfyHq2dfspjfb5+teYR3zp791u+/BCAtG+76ROIn3/zNf4F2in1XZN4h0N6ByvztOyyauklJ4NsNXV+v0YF7RlVlPZvJIDwT0uOK0fVGTSX0oKHwLbTpGd0Re/c63Qpyq34A/h0523fVNd/qmm9y15Ltu5e2yKO54/ywvdWurvkWAheefRC0fffcNnlCq/ndc9tkALW+G9g1BkC7az+qN4cuAvh84Zjtu2d3XwZw4s7hij0AXjjuQ9GyZzY9I6upAFor9p2XeVs5dJJeVpBaiInRxkpRVzwxVJ9042zwsCTw7Yaur9do/z2jqiklqShCTBQUSSl1tWMCbzS9aYdND5TJqnT5lCiKTjL8SEc2YP9uSANQ511bsoGy7x4uF5jLAgBMuli4BgAIPM4DUK7fyucHAJw4AQCnTyM/6NbBvuP2yeefzAM4PeccInfF/ZHTB/QTAK5zZwFUbx/fu2N1YCCr5gF8uPMdAE/ee95225af/fRnn/r0pwD82pdLO394GgDeO3fum1PfMHdWy/+F/TITeybzDFPsXSo9AAFCtUHPZF6D1r4IfYXtbpXGOurOWvSoKSmpNKry7fP5t+SJgQS+3dD19RptvGfMuYZtyxjP6cXOtmqKaX3x/yi36Q2qxdiN0FrfLZfeN954w9yuWxqlMWyF/LJQqegmzUp7MOwH4NueB3D6NI4FD79z5aL7Yd4fWHX/4boM3/5y/Q+5Y3RoFcBc4AyAKe1Fh+3jv3cGwIW/fhHA9b1nABy49SKABf6d986d+42JfwXg+wt/YpV/JvbrPy39MAamSqd2b9bDLhu/fTa96Yhyb1iXd49WU1IyV9V1t+4ZW6vuLTwmCXy7oevrNdp5z5TUW5cTaYyX2tIX5yGLvtcQeAfjeGO4FHvbSqiAayGvZmNWO4ATJwxpB+BS3V8cex7AqeUzbgfZIL+xvaT0/2Xte80d5PGV32ziWyf/l9cBvP668fJnP/vZpz71Kbbx6wf+NYDlg6fXB3eMXTkBIPSykW2gvVXqVx8IQR/E+lzpmItTTv+anXTd22q8k1han6rtXjufq7UL61v+uEAC327o+nqN9mfRJxUAQkyM+sy5pqjrVnvDqvVF2inwVpzEvkLIUeVmd0+D0g4glxsAwKz2C6m86ZNvyHBvrdVuxdT1pkXdPe+nLx6N2ITnXT4WnPzd0wBOnzUuxejVk0zslYQAYGny7fVB397LEQDCYWiWfyI1lF0f9I/PlR4ImPw7uO5bJfPVaXTFPcXbit1Y5U74imWp5TZ9zROhqjXURoS5TSF8Evh2Q9fXa3T2njEmpkDYXDGnVNj0ld941EwhtmZgQh7Szvzw/3tx4qsAzix898UXT545c/pFx6XVrmiF1Q40Zri3yWpvibHeHLU0vmL/137H2Pj2t9PRSIRtD98oPQcwsX/nb42V+D5fPviCAkB+21Dx/MTbY/MvAAhOAoA8DwC5w1kA/ssh/6PSqRenFAECs/71KUPvWyXz1WVt2EtdTql8tBj6imf8VSJfCsDXt+BbG3Fvaz0cEvh2Q9fXa3T1ntGrbPqqj7Rc4ItCXtqubZGfOXPa3G5S5jcWa7da7YArw/3Fsefb4YrvpLHugEuNZy9NpQfw/RqjfuVLewCc+ckKgOefPALg4vWf77j+UsXHjk8YGxeQNnf65iOoIfwbF/ta6g6oZ6XkHQBF893IU626edSUlFQCziH4Fqp7B8rqkcC3G7q+XqPb90yFTV9Oq1z09YS8FlbzvRmxvyy0xGo3qZst31p176Kx7kBDGo/GxX51ZQzAxes/t75VLfmYSFfs8M1H8pPp4GBEuQwm9k3LfG11Z+a7oMeTiM1wWWa++1y44W1OgRbpcccq5nZ7svI+dH29Rk/fM60S+Ef2i8XrUss/X1/sGzHcq612FDPpGHUN9zbpeu+IegUNabz1v2y/Kfa1lH77jnXTmq81BhvJZ0ykAfjmI8FJ5Adhij1jYKq+zDvXtLHkr8Qz/tgMl43rI0Jua7CRJaZuDfeqNPwuFsNHj09WnoCur9fo6XumJQKfDTSfFueCSrF3J+2mqLOXptWOKsO9M+rem8a6A0yw7y1cvMa81TvGw+GxTJXwv582Lp3tA4GzWf/Kl/ZUuO5tR3IShtKfxdsAcP2Fig/4HiE4CRlZzJe58avrEjIczHcATHXBwu6G/2v7pPjFI7bHsjs43Ely0fPvsybtWTPtXR6nhfT0ZOUJ6Pp6jZ6+Z/pB4EtcFgC8ef0v2avPf+7ztp+qkPYKqx3l0o7a+XQb1/W+E/UKmMYX1Gzm3i6sLoYjx4bKjXim7lZHvfWLFUdzEHur655hK/aVSm/l+gvHJ4xkPSslvS+KfT11Z1hz62yWl9aioYi75bhlmXpdkXZGT09WnoCur9fo9Xtm4xpf3z+fu3ru3Vt7n3v2oL/JU9hZ7W++9aa5zcTevdWOeob7RtS99z3wrim8n54bHp9aW5zjd0BdBXZPHJ3YWeGTt33pfFyXYu/Wpi/n+OALQJnYVyzMqyX2lRjmu6tqdc2osvXJQZcTaWhahr3TrV4PvT5Z9T90fb1Gr98zbRf4pUtn5v3PPTu2dO7dKzj03LMHfWznrb0vPj3m+E3AbaydSfv3/vbvAEx/9rNWqx3l4XZGLXVvWtf73Vi34f5Sdu7urqmQOlcU7HvX3p+/a+urNzUeNXz1DjgE7OuKvbPS++ALDkbkR2ksGOvvAWjZ8iUeNdz4DdFsqnzJcGfPB+EZ0TTiyYL3JHR9vUav3zMbFPi6/vl8Lu/z+9jm1XPzvmefHkP+6rlLGPNduXILwN5jNYXeXZI8K1ZjnC0/cPadUpe0b/3hCcCVut8fWH1l9MVG1d1Dxno59669r243hfz99MVhYA2+JyKHdxY/4pBw19w5nQP2X3zmSXO7WuwdlP744AvyozSAMpl/pBjPjlYaF/uNutN1WYpn2BGs9jwJvFeh6+s1ev2e2YjANxZ9N0z5gz57833p0ul5v8WNX0/dHWLtKPrk/+2/O2d+/tnPPIuqhXBNFKvxjrF+fyk7t7gGANg1eezAzsr3309fPBqZuJ5euIvHgI+PTu56/86uoxM7yz9guOVhF4xvGgexd87Ar6X0Z9955/df+BYA06D3T1p+ulaxdy3zralGNxNOxDOay0hAm+n1yar/oevrNXr9ntlgoRuXC+SWLp15X9179CQz39+9wk7KFT32uavn3s1NnpzMn3v31thzz076HNXdIdYOu3A741jw8J99//82X34q9qmGSsx60Fi/Xyhsx73M3Bpvo+4ACurS2vb719TtT+y8ewtPrC3OPbEbt4an9q7NXcMEU/rq3LqWCLwVWx9+3Qx8U+kBnMXbZ99558Tzz7OX539y/ndnvinPW6x5xmDx4XKwTkbdBg33LqbROdPrk1X/Q9fXa/T6PbMRgXej7kuXzryv2vvhly6dmfc99+yk1aRfunRubPtXaqm7s9UOu3A7qrLlmdX+b974jvmB6DNR29N5x1i3p7BUW92Be9fTCzAs+8JSRh0K89fScwB2TR7beefivd3GFzeu8Z879AVz+60rP67YY+63NevdZOBbzXpT6Q3X/UKkUubrWfMbMdwblHbHKlVtoNcnq/6Hrq/X6PV7pmkXvQv/fP5q0SIv7Zo/dwlPsz3F7fyl07f2njQeAC4L1/jsE1W91CukHY0Y7taIu63VnjqfMrejz0SrjfWWW6W9wL2Fi7eGp0L8UPH1tffnC/xUaGw7e81E/YmdAO4vZRbu80/yw/fXMnMLAADfDmwdjTyx010wvkLCVwcf+9WDM+aef7warzta9vl/vBrf8ehj1PDh2yblnXvvvWc/8xm2bevAZ1n3+UGg2pqvSsRrWt0bt9pL3SNq1pluNb0+WfU/W7o9AIJoHWNPvTi2dO7MaWbp7z168ukxvy93Kw/4gPzSEvY+5UNuKc/vLar7B9d/MDZZdoxcbkA4sNfBaocLw9051m4VdQD/8t1/bWxFAG+q+73r6YW18ZK631u4eA0TRyO4ns4uGRo/NMabdWy2DePBrx36GgA8BQB//nd/um336K8x2a6wtg994R+vxgtbtllF3Srhq4OPobaovzoafm05wzYAmNv+nMq2jYeDnxi2PoDfKLa52bH79ve/B+A2gOeiYwMD6/nlvcBTTOzPvffe6c/8kH3yBIxqOWfx9oVHbwPAI/jgC2wRwGTe6p2aGwAgXT6FpvzqG3fI89GYIqXU7sfoiY1CD1Beo9cfipu24JstT4v8/Ll3r+Rg5s8XHfSXBfA//NlV36c+OWp+1pohjyqrHe4M91qx9roeeLNMGxpf/dUvVDvDGUyArXb2f/zBf/3EsU8E7i9fvoEDwSH54vXgwZ3y1XtDfOjw3m0fXPz5J489xT7Jtj+4+PN/8+KvwyLSFdt/syID+O2RoHWbbXxj++5aA77vG2HHsY7NFPuKgH0qnY5GIiwD/y//+382TXmTapv++OALbA19yXU/6H/jjTdennwVaCzTfoPSbjXcG2g7vwF6fbLqf+j6eo1ev2c6L/CV5K6e+/nBka9gMrv8wZtLY5839b1C3YNhvxvDHcVU+VpWe6PpctZF3oxeFns38WzGP16NAw+W5evYf3h0O2Ao9+i28o8xMf6Lt19fWnvIBPsvrl/CL7K/f+LXAfzNilxYnv+9J78E4H998/UjTz/JBJttz1768M8+/XwTf8Wfrd11/sA3h3ehSuxNmUeVDz+VTv/h//Q/APCN3nrn/HL1AW2VHlbXPYvNh7S6KXhoVRqdmpKy3IxZ7K7hfjcN0+uTVf9D19dr9ME904TGt7Y87WXhg+t/uQT4D376U08Y8frA47w14l6h7s6Ge7XJ3nS6nK1/vrti7yzhdePZ1Zb0f13OPBoYZML81yvyEB7+9sgRAP/HFXm/kX/3cOXKrT966ukmRltXqjeOrdj/+d/9aXXzGwAr8pNwbHJTnZHnW3jBas0DTkVyWpshXzLiSeA9AV1fr9EH90x3Bd5uRVyFulfn09ka7kzdK6rRMWlvOge+bgC+HWJfNyWtWqTrur7NbTg6wB34n1OsqIAvMPxYYFIoLil7ODd7JbB/SggYr+dm56aOTJkb5ssOwJQewH3fSM5f0kJby/773zOK59iK/bn33vvjz/wx22Y2/fHBFyqteYal8C1av/hNl9ky+Y6k0vfBZNXn0PX1Gn1wzzQh8K3yz9dTd/eGOwBbde/k8jb3Yl9hc786GrYKkplQVkuwK2hUsCus6sLywtXlbfuPCH7oyuztbZMTI8PG/ttDE6ZyF9GV+Qd7JvcMse3Zm4XRQ4XlK1YV76LGmwP4T9FnAQysr6/6R9m1tco8ikpvyjxqJN6jwnt//YXIBAAoUABg0M+seenyqR5c194ofTBZ9Tl0fb1GH9wzjQp899TdwXBn2xXO+UYEvrCUmbu707JsbGO8n774B//iX7Lt6oS1v1/4SfsEu2lyN+a0gGmL68qsHjhiWuoWNGXuBvvBBPYXP1Ch4l3UeOu5mNLf941sz698d/W2+SBlm5RXrfQVWJU+uOUFoLyHDVpT2b6L9MFk1efQ9fUafXDPNFrrpiX++Xrq3pBbnm1vQN3vXU/fGp4K7byXzSzCXAteuVK8QT536AtM2j+4+HMAhce2AjjydKmmei0h70Dc2o6HK/PLw4bvvcyUd0mFslq3AXRe4CueKsxQ/Y7c8hJfyidgYm+N06/e2XPmJyt1C+J+553v/M70t2DKvNnDpm9lvg8mqz6Hrq/X6IN7piGBb7+6u3TLw6Lu1V3gGnPO3y8Utg8xGS+o2VvbQwd2GlXe9t7PZu7tCofHmhN5U+MBvDoa/psVefbSh+a7f/bp57uk5fYUlhcU7DvIaVfnda5BdWfYanwnjfha6l7BN4d3uUnKW72zp7pG3rn33gPw7Gc+Yxr0S1sAwP8IymXLOfpQ5vtgsupz6Pp6jT64Zxpy0W/cP2+n7uaKOJdueZS3jdmowJcwTPmxB9fMxir3FrKFvU3a9NUCb333G9t3FzPXOmfgOlNYXriqcweNEHszdFHjXaq7FefldlYH/itf2lOrcS1TeibzJWu+de1oO0YfTFZ9Dl1fr9EH90wnBd7Rdm/CLQ+7OjZNqvu9a+/P32V91e4tlGqtFwW+SZveqvFrA4PWt76xfbdpwTM/NqNHxL5pamk82vmnmcd3r+4VQzLFvjoDnyn96p09O3bffv31ddg1uXGK0PeJzPfBZNXnUKlaoofZoH9+w+pe0TYGtavUNca9a+/P38XuiaORJwAAhUJh105jCfi9e3eGdk4A91R1aOLoTmBn6Im17L37Y8Wa7a2hIkPNdn+/YFVZc5tttNyIb+iAtbIEGMbD1trdb+ZX2J77vhG23uGt/4fZ9LcBfPnLA6t39uwYWTrzk5VjB54yNf40SnVwxz5CfhCBEMBkfm6gxzWerfE7depUtwficegBymv0wUOxewt+IwLfYNy9btsY2Hnm0bj5XlCrLfJ719N3d0aMPivZW0OhiZ12Nr2r47PS66jhoq8bg3cv9p1fjeZMtZq2yVFvNcTrHtzlGMxjMrO+ermdadPX8tujwnUPrXfy75ic2+KBxX69TM+LAdEgnhL4pv3zvaruAAr3C0O4l51bXAMA7Jo8dmBnYSlzDQdCY9tNX72ltZpV/l1gCjyqNN6NwFtxFvteE3jU0Hi0zi1R4f+Hs4t+7fbV+eVC8WMOx7T9AMvL255fWd77lLnTbGLrUCDPJkKPljntWXc75x53DnJuwr7eB5NVn0MuesJz1FsRV1Fhvppqdb8/sFqrNVyjDG0fAsZCEWu7+qGx8N7r6YvvA8PjU6GdANbWVmGY+PcLa7t3HXB9/F89OGPG4G1XvbvHwY3fg+qOGr76FjrqrU8MH3HzsQAAIABJREFUdk4CXZm9aSzY3ztauIcCMLU/MHdDUzRUFfCpkyXwZ2t3wZ7Grr399T2HAezILX/u0BdYX7uv/c6Hq3f2PBcdeze1dOzAU7CIveG6/wgn8dL4YQDID0KbGwDaFZuvq+hkpncLeoDyGn3wUOzSgm/OP7/h9e626m57qnbWrau26d1+02WS3Ubo8Zh9dfpbC+14q+1e8VZhWdE5YWQYrJ4uLG78AFAYPXRwdGvFCBs9u7nczlxbf/CzP4aj6/4kXjp7HQCCk0WDfgMy7946d0MfTFZ9Dl1fr9EH94wbgW+dult7xNVtEGddC8fohroz7l1PL9xlNn0jpW8cVsq1UOArqsowekrsqy3sjdvxjk8M+vXZm+ZvZWpydP4Xdx5s3zu1n2OfHxkehjCxMt+yRw0m9tYM/MnpHy1na1bL2XH9peMTyA9CH8Q63E4RbbXO+2Cy6nPIRU90nKn1+rVuOq7u1YY7asTdO8XOA5Fj7j3z3aJns/Gr1b1VR7Z9UCgs6zsm963O3wTgH8bcyraDuwav/vL2HXC7Td/+fCvjGoYP//Zlc7ndfOKLAPY+dbHCac9YPfDDdx5hx8JLAAKTA1rWxpR3I+duwvBEj0ACT3gCFz3iHELvjap7h5vKNMRbV35sGvGvLWcqvPQtoZZK9ZrYV2v8Rox4JzfA2u1bura6rA3BNzSc17btOzh0+2rBH9iyemt2jv0EmQUPsNL6D0aaqtxnS8Vyu0c/emzdN5Dz85MY55++UNGNfvXADwHI8y+NH8bi3ACAgSmckuyXq5GE9zsk8ETHqeuib9Q/70Lda1G90p3hkFXXy+reO/SI2LdK4x2d/A/n5pcBDAEf7/mEsPfhtstXrmoA1tivfH8AN7RhCBMjwygsL1wt7Jk6MrwyP3eVK0XlW0Ip/rJ29+vA9vyKeun4ZPHd+QenWdVbAMC//ZNF3Br/49M3v7OOb+HwKwNTbv32pPp9BAk80ee4UPdq5zyAEyewtGBjuKNV1Wx6gOql8F2hu2Lv4KtvumpN+f4rj+3YF5zgcjfmbtyem7u7Zdvjh7B8BcBYAGuBKX8A5tceFjAywgEYmTyE+ZsrXMvs+Ar+6vbludk54BzrbofjmLx8Ep89+f/+5N+xDzz7mc+s4ocn8dItwPcI63MABgamALhSepL5voByHLxGH+St1LXg3S9/d2e72wp8cJ+9ujvH3fvCfK+VZ9dwkp2mzN3Qhkrp37U7ujZFJ8XeNhLvMvOuVtI72z8EFIb3HuTuKdh3cHRtbvYmAKOzraZcLYwe5LSr88tgl5HtYddz7fZVBcIG6vDbjscWNvivf/EwAN/c0q0tRwHMPzAyUHZcfwlAbjJ9KBsZsPyV7nPxmqMPJqs+h66v1+iDe6ZVAu9O3SvWxTGaU3f0icDDUu7GGoNvSOBzN+ZuYHTkgc58yzCav3FDy8sagMA+lh/eKloo9rkbxfbxWwMHg4Ipn7U0vu7AbJ8D2B7WEE/AzavLrHARDh45tLqwvHVC8OPhyvzNB4Nr2qNRSzedhyvzN81LmruxsDbSpBFfV85rwWQeF2Bm4DOl33H9Jd8j+B8BQD2ZV1NSUgmEZ6aDG/kR9MFk1efQ9fUa/XHPOGi8mwD8ZQGAy7i7rcA//1L+H16v3FnXM98v6o4WCPzDwtrWIVhNTHvzPXdjbnmoxbHkjYt9YXnhqgYU1jBsFddmjmxrvpdVtgnsg3YTwP7JKf8DZW4FHD4urOUfYHhkct/wyk0tMCFsY1XtAvuPCP6121fnC6NHBD+Qu7FwQ1tzM5im5dyBb38Ld84fBpC7zAOYf3DaasrLU9kQQuaHLTKvpiRFEAVFSiqPjcR+5Vm++tDu6I/Jqp+hGDzRS7hU9yppZ7jxzAPID9js9JK6w1LP7rdHgk2F4bcODQNaobCNM/rWL9/WsKbNasBwMQP84cr8lQcjU0JhYW5+Qy1fK9hQzF77xdyN/MBWYOveg0cmag2paed8+R5OA6DdNB3yczc0YMvWI4f3mV/Yv0ebX7gKTjgyNbR2++qsgiPCwcnbV2fnbgCB/VPQ7JW7lqK3MJbxH74D4PK3vwUcBoBn5/iBiYu3thxVLw/c2gI+G8qGsgCYzA9gAEzmVSUX3q1IiiCKwns/vPSW7Pvchux4on2QwBO9REir45+vre7WJe+1CO47fEG5ePIkKsz3rq53711ymhYICGx7aHRiahQAoClzym1ucs+Qtryybd9UAMDE/sKCvrZnqA35Ym7F3lL4HRjmtq5pj+7p2u4hS4FYa4U7tu2s8bbqXlHhh70saLcfrgEBYeoIp8w/KK86yAW23dQCE0MAhvcIowu3NfgDew4e2cPe1qr+tFp/fpswZf7O1GEAY3OX+MMlqzoLOYuSzDO0ZUUTDkUB/fHhwcWMrAajTVvxRDshgSd6iWbV3dY5X7fmvHv6y3y3Yl0K/5f37zTkpV97EAgwgbSmg20bYmaxVf47g6PYB4T9q1eVPLbsfnzwzi+37B15cGvlxtwKtgAfsTxB8+vWSLyzxtvKebXwDwX2DGnK3LzGTPkKt4F//5QZ13hYwDaum3JeC6vM+6FKs5lXBx9fHRwNDQbZB5jMD2AAPMDjVGoRAMf57y9+tFXXwZMN34uQwBPdwDYA7+yfb1DdbUPvAKrNdwDeNt+H1x81U+5mTdMxZEzbw9uG1vSHLGNc18HtG8JD3ZR/6Jq2LbC/hUOuTy2xDzy4kw/4oN16sHcUa8vYNhwY3rkHN68u77MmCtStbWe7ms6phnxAmDpi/7hTeaKiT9726aG7mDK/ujr42o5filOjb83Gh9SvfXJtJRBi9+a6gosCjr8SHdewzgEBzqfpeYAEvhehHAev0R95K7alah0EvkF1rxV9D+47PPrJi42m1/Wp+W4ulmtNRXrTB27kz1ty7tZuX13ZdrClSfWNkrsxt7x1N27fKZTvn9o/PHcDeye5u3YjrNU5xurMr9hwMxjbR4cmOsZ2kW9/C2u3dgG4f2MEwOkfP//JtRUAgZAGGI/Oi1hHSlKGBWVNEJvy0ffHZNXPkAVPdINswMaIdwjAH1bcl6urpe618HwA/rXlTAsq3gyXwsbs9bbh22tr8A8jt7I8FOiiOOnK7M3C6N6h5XvbJg9xiqKvrRUGh/BoDcDcjTUAt+bXAvttRmgqt21w3WXxu0bl3GEYvcN/+A6Au9/+lvHy5BfeOf3j50c+WkXRVx9CaBwD54V1QZEgRLs3UsIJEnjCazire7X57kyfmu8VbCASX4utI5N7lNm5OWBo9NDBqmbnHYQTmJqO7gbuXF1bKwxzHIb0tTUOWA3sGtDurm+FdmPO+kRpG4+3UisLb+NybktPme9WvvuDO6/GgtJspoD/cmLw8Yp3n+EHzmOdMux6FhJ4ohtMrdsvhb8s1PTSVxnxDYXeHfCq+f7WlR+bq+HbAyccmepoll09cjduPTY8iDWNRYB0ANpdAIHHR1dvLX+0zR8Y3rln6LaCfRU5eqaZXp2oX63oPSvG7ea1R78UH6mhweDlRxfWs9CnNAABfqDdBe+IpiGBJ3qJkOay00wTzvkTJ4CFxobjDfOdYV0Q3yIjvtd4uPYgMLztwQ5hYmRYV2aXCnhYwHZu633t1vJje6amti/M3bi9fZLDypptjl6FlncjNK4rszc1oKI+T7dYu7Xr1diINJup2H8oG1mcUvwAB47UvZdpfStJgtgQDlVsDyuYDwHI5QaaC73b9oRtZpB9wq8enOn2EDrJVo57kB/auTI/Nzd7U8Pg1uHtQ1jTPx4eOzI1/vDqjZW1HcPreWV5KGBk25kL4m2ZOjLVbnXP3ZhjY5i7oQO6MvvLjxDYPzk6hNWb87cL9Q/QUV4dfFy5HAIwMAUBQgDdDMwQbiALnugzahW0aeGqd4aXzHe0rTd8TzE0OiEsL1wFDh6ZGsKdq7NLLB7vg76iFe4Hdn2s3QWAYjy+wglfkS3f5l44ujJ7szCEodFDBzkUgIK2XAgMFsAdGOawTdc+Wr6t7RG6p6Hf/hYLwI8AeHXw8aUtTwNQQ+ezkFnJG7Ldex9apeA1+mnlSa2K9LW99IFdfiUhYCJdsb9u6P3ECZw+jWPByh4zDgvkvCHw1s5yFQLvES99Zcs7zM3ODY0eGi1cuVH149o6euiQZTW8rYTXKj5f/cmNoSvz+jqGRkxXvKbMrTzAtj1T+7nC8sLN/PqAb39ri/y759vfwtpf71oOPFUabnbA/6jUhKYl6t5Pk1V/QhY80TcEdvmVG3lAxnzQqvGNrovbtDRbl753MVreDQ+D22rV4MLylRtAIDC8baQUj0f5QwDbqNVDtiJ/vi0t7dc0HdBnlwEAwyP7uSF8vP7gQQEYGtr2QH+AwhrQaYH/5vCu+76R3Pd5AOrlAQD5ibfH5l9ouboTHYAEnugeU+v2FW/sFsQX1b0SN+rOzHdbXhl90TaL3hvmewUVC+L7OtXOorLLKwDm56aOTEFT5jRuaj83Nzu3d3hgZctOzM+xz23Zc+jw6FZUybNDJl2t5e+tEvvA/n3bCsMjo1uZ7b6ifRxYA4YLrGLg0LbH2hSD/+bwLgD3fSNmu9gKOH6Rw6L8tpCfeBvA8cEX9BBAut6HkMATPcmg36rxleo+WTLiyXZviD614J3WqhVFHeXl8bduG/r4l7e04d2P485HI1N7Cgtzs0ZjVgfr3NzjphsNNiT2nD8Ao0b9tqEhfLz+4LHA6MdL+Y8Kyw9R0B57gMDIJ+odBKgh2P6cuj2/srz3KduvvHXlx8gt4dasdefXfgcAVuQn5bcFFA134TD0QZL2foUEnugqtiXtGA5r4os0seq9gjNL79iG4b9//3VvGPFvXfmxNQxfUZe+N434horJWETd0h0H0LRtwNrUyMdz2j6WVbc/MHxDW6suWmeLtZKdS9O8QbF/uDJ/RV9HoYCDo8Prg+sDvoB/dM/XYy8AAD6PeiK9d/Hiqn9M58bNPW9d+XHlh3JVe+z42u9g9c4eABd/cByAabjjMLQsMEXq3q+QwBO9jr1zflIOBl2Z7w7+eUYtL71nNL6CXovEb6w2nFXU1x6sgXWsnZocvbqybWq/MDc7B2hmVvzI5NRIsaetm2XujWp89fi/vudwTZF+4vPVIs3pi6eWPiz7mINIr95GxYcbhFntr7++/vyTY6ZP/gReyA9Cg4ZsgNS9r6EkRq/RZ4mptRLpGY9yNUPvQVz4wXEcOFv3DFaBr86iZziUo/eGxltL2lXXpe+kEd/iUq/WPrZ4uDJ/E8LEyDByN+bMFPr9R6ZuzM4BCCAQOCLcsFSsq3tea136/xR91txvFezRWz9f27HHKtJWKqzq99Oln9/RyDG2h210GCbtq3f2rK6MAZDfFo5PQJ6HcBgANFYxss3q3meTVR9C19dr9Nk94yjwOa2mgZ5n7yzU0fgK872WwKPeejkAfS3zFTVrO7ZeruONz4uV4IAAoA0HsKYZp1tbyMyvrT/m2x/+xB8N77L9ci1nOKcv7sgt3RovybCNM7xxqsW+MzBp//73sH3H+vNPHmHSDiA/CHRK2hl9Nln1IXR9vUb/3TNzA4BNAbscy7G7LGCy0p+ct+q+o8ZX++fzg/YPDc4dY9Hnprw1DI8qgYejxruv2NpxOTfyy9zjkHT2ytiTAE4tfVhQr93b+cTYdgCFpcycWvxdHI0ca7m1bR6wA2LPdB0wwu3McPfdEEpWe8d98v03WfUbdH29Rr/eM+WmfCAAxUywq9L4YBAXLhRftEjg3TSN7V+NrxD4V0fDAF5bzpjbO3LLAFb9o9btWsuo/Dl1R255iX/a9t3quLKVamu4Vd/987/70z/60m86fPff//P3mEgDOBqZuJ5euAsMj0+FeEvR9/vXLs3dZffPrsljB3aioGYzi/fZmy3XeNujtVzsTZMdwPYd6zuu/9rxL8lQjOUGGor33SC38XM1RL9OVv0DXV+v0d/3zCOdJUwpFenzj0qqXKbujNoaf+IEALdeeg9r/OcOfaFiD3MyV++3vsuw6o0tXQkhm7DhbR0bxcqacGxyJ4Cbs+8vPWSjWslcWvKHPlqaw9Do0SOC9W95YnLXtfkCcJ8JOQDcX8pcucsd2vvR3MJdYHgYa9snjk4ML2VUdfWuqe4t1Pi6h9qg2JvSPnzjN0/+7ul3/vYEgONP52G64ll7J3QnVb6/J6t+gK6v1+jre2ZgAOsfDuQEu6h8UeOZf/748XKZr2fHM2yr1Vqp66hH32p8QziIenfl3ErRFmfjuTd/8eb2Y0eW2ci37Ao//cQQUFj4eaYwfpS/d2nho/VH983v7tn62O2HHx+NTC1l5pZXuf2RPffSCyxEsXXs2JP7DOf8EDdc2MLtKmzZGx7LWNS9/NQd/XsZzqdmuv4P/+dvmntO/u5pnD0BYJXLa48UDPoNXUc3V8H19WTVF9D19RpeuGfmBgIxTdMAIGBptqEkynz1wSBkGfk8jh8HgAs/OG684aj0SwuHRz958R9et/+AG4GH5zS+rpx3Rc8csB3P4uyl5cKjo5FjuH/zg2x+77HQCICbs+/f23X0CN5PL3ORY3r64hPbce3RfhRuDO8/FhoFUFA+yN7Z5hvdPzmGpez1/PqqVvBPHA3uxL359+d1YOto5Mi45aTWwHm3rkktsX98pSTq9w+8/uWT25muA1jlLIY7emJ1uxcmq96Grq/X8Mg9Y5ddXyb2dmvnAASDgFXsGRbJD+47fEG5ePKk8bJC6d146Rn9q/FNWOe9I/C1RlJ01B97ch+Ae1fTvyiMB6f4oXvyxRtbpz45gffTc+yLi7MXVwq7Dozlr93ZGX5q3xCA5dn3bzxkx+F2b9cLvt0frdwZGD16RCios/N3RiafHBuynMU6gMY1/t719N2dkSd2NnkBbKgQdXObqfsFXAiFfVAEI9beS0vbPTJZ9TB0fb2Gd+6ZGtn1AAzv4mElsMtv7quWfEPsLwALJb0PPnfrwk/HsN8Iy5tKj6LYN6Tx6Pnlc84RdPfi1EVr1RwAagzYGNvN2Uv39z19eCeAgppdyK0X9LUd21EYnvr4ztwTu3Ht/2/v7WLdNvM0z8dJHPtYovxtU0xiOy5TcpxUEinqroJTJU06lU4aYKp3dxbTPbMLzEVjuoCeRc/VXOxeLAbYi8VsX+0Cc9G9mO1pYAc7NXeVQ2BSlVR7pCq7K1WyFKfLjiWmT2xXimL8EfvolXzsOLH3ghRFfR5KRx8U9fwuDnQokqJeke/z/j/e/3vb3n3lwEE0nji888aVe/JLiej1yic3Hzz26Mkvv7pnx92fiKLR2Ll9+70HD4DH95x84chK92d5W2OklrlvVa9iz85a7Q6AvcdePLZ7/cqFz3d2Jvr5wCvqb/xP7wB45x0A+NWvfvW//S/ZDqs9Vq/Xg6XrLuHprIIK2zdshO2ZGSLzNqOKPaDG4x/+8lDH20+/B4/Y/6dVX456m0CZ8pOS80AxXNrbb62v14D4bsc2trPfd0Vxt4GjqZeuli9g+3ZEn3rx2M7rly9/vu2pbx758tLlG18BALZHVvY/cxTX2nH3XeLG3a9W5JOJQyv9P9FrzXdp/GDJ7zLf71+vXL4nv3R4o1pZ35NMHhou8r2ijpauuzhW+6dIvNgE8J/f/c9vHf8nQCAc8r2ErbMKHmzfsBHaZ6bvunNddC4k70p+l94rsfiubxjnvJH6a6+ik+/9yx8B+OEPfV3avDQ+lHLu0usP791hk++4fvWjtTvJ+EqltmE758XBlxIHgY3fXvykfvDEc4dw9eLlO18DTwBRO5e+M+4+/MLQz1c/5Ko8M+5W5JOJQ19e/ej2nheP7QawfqV6/3D3YAKdon7r4Dt//EfO615d//D/fRVA4htApAl3Ujscadd13d1Z07SBLTZbQttZBQa2b9gI8zMzvK6tjb16Tedqs17jHgDqsaowEsmI/d+uleaHH+JuE6dfhav6pyMvv3d5l/ege/sHJOYBmInGz3G6mqNMe4/ZagQAWL9WvnJnV3xTu3MMNg35+8wJ+Kh84cXje65hz521K0dTL+1eX7v0G/HVAwAr+w/vaIiVY8lD965cuHob2L7nwPY7N3cce/HYbjfufu/KhavwfuWOT0eP7T5CpsL61Y+sFXlH7d5eZ4aeV+C7RN1+YUu7V9e/j+8D+PDzuy8/iw8fMwAkIgoAxOr14rCZb8ER+zB3VsGA7Rs2Qv7MbOqxd2m57nvfaaBD/pWnO+S/WmnebeJ05GW8erajSM61N7y7/eGfvdNl3/vReP/x2jnPPt+4fm199xF5h+1GvrP7ZELegY3791d27ABaruY96+Urdx6TjtqzzyeBH40cqQ1t812Jr3yBowkZ1ytXcSRxaAXrVy5cvb3tCezeu/f+44cTOz67cLUB6dAecf0O8NjOlYf3NrDn+Eu7b19Yb2mw99O919lVjW7gtW1cr17DUXs8tHG9em1jJ7A7eXR3p6LDI+po6Tr6STveeO/uR05yidmoA1AUjBpu9yn2uq5PYygQ8s4qALB9w8ZSPDP+Zd6mU+y7BL4vXtXfdeA64Bj3p93KOZ16D+AP/+wdvLOJxg9y5AatmMz6lQtXv96zJyIfke9dq9w/7Fq6thG/fvWj29v33H6wO3UU/3Dhs/vxE6e2asf7lPZN9/Hu/GLq5Efly3J8xboXta9298b16uWNw6mjO63qb9Yf3L/71dfAjvjJpLwDG9cvX659iScPnDy+H1i/dvnWXTxAZBe2H+xMeu+r8ejR+x7aAfj7VjX+xP/qvnEr+peV2kryeLvs7iBdv3v4hveMtq7DlvbiVtPohog9BX5BYfuGjSV6ZkaVeZtqLJaA+bC6+Z5AE00A6tOH3S0fVq67r22x7xD+f/8G7KIiwK69t7rO9tf/oUMbhjO/CLqd+fX0vSuf3dt97MVjuNaqAAOsyMeP7t69Y8f61Y+uf7VTejoh77hvVT9df7jvyMne+LFPRvC3j5jz/1H5ghw/eUjesX7lwhdYeXxv4shuYON69XLtHrD90EvKg8qte/fub8MD2LGG9U/KV3D82JNrV+4gsmtX7Bl5o3J7+9G9ym5X4devfrR2306+G6Trgy610/f+w88/voJjzx1ewZ210p196WN7OnS9S87ND6PKCUAxu4s8AlFz8qXovGKPqXnyl6izmhNs37CxdM+Mn8B8JzHETJhdcfq+qEh8iHKf7R7J92LL/8vJdoq+Y/3/x1cBnP4fzqIl/PaCH12DgL/+D36/wpS5f71y+c7DyGOPxZ5J7li3Htxbf3g4eWjHeispbON69cqdeyuHHWveau7c/Y1RJ3phFIt8DHXvPKp79vn9jfs7Vpygw70rF67ek3ZsiJXjx77+zS3pheMHgPu/vVS9vTvxwlP3PNPY1p2oPK6VP9/ZqfGDEun7BtRb3Llyfu028G+/82+w6y7u7gLgFXWjVrNfRD5XG7KZSHSUcHasdkw9Q356Mful66xmDts3bCzpM+Mnx76FI/AAPlEA4PhAa36QwA+n8LMCgD//7r/6i7P/x5/90f/objd+rgBQv9MnLQDAuY8v/eEfovnFAQRjELB+pXLr3s79J4/utvPpnM1P7D/5/FMr969fvnpr257jtupf/wrbD/Qmow1hJGn3uae7f39X+frVj9ZwdFCFmfWr1Q358L3f3LjdbE2R3BFdWdl/8uju9asfrd3ZGT+ZWLE+WrsD7DmaOrob969XrB3Jo1f7GfFDRP2PV77vvNp1F63qcjaunNtEPlcB9Oo6Zijt6HHOT1bsl7SzmiFs37CxvM+Mb1O+LfBeBoi97aUfgi3nfbE1/vSrp70bz509d/rV0/bfyJXveN+6e+QnLx3pv56p7Qmwl/i0OaB+jH6DgEmNAO5b1d8IxJ4+imuX69GXTjyF+1b16r0n7mH/i8d237c+/qS24+nUcVy5sL59z73HZZ8W/Ohx9BFCFVsuIuvI9m4AG9erVxuPNsT9J4CvAGx7/GDy+ad3dOTKtT70Hz3zv3vPYou6reVei3yXiGx7tK0Za7uOukQdLWPd/Xegus9qXvuQ6PvWxX55O6tZwfYNG0v9zPiOyvfXeJdOsfdq/BA5d8l+N+u+fhmps/h57z62wHdt7NJ7AHeP/GTQp3iHAheu/bpri5e+g4PNxwHrVys3NlYOnjyy21l5ZWf8ZGL3uitv65/8/VXxsG+qeV9GlXb/O3uP2mqV+PWrH605i848DnyNB3uOv3Rk9/q1y5/XH0ZfOKVg4/q+5p93HfTGEccix91deLTtrtxO1Igc7pZwoGc5RADAo22RqKXY6t6r63agfdtzAX24xxP7pe6sZgLbN2zwmfEj85sIfIszf7v62pEfqMfxf/3s/xy0j1fO+zJI4/0wkuT74fQrBwE0b7RzCGxPwE3jua4tXv7t/3zhnuwsjn4VR11j3Z4f315udQBju9lHYqJrwNy/fukfrPsR26XfUULuZEvI0cfN3iXntpAXCoVsduBN4rri3S1d6h5wae/Fv9izs5o2bN+wwWfGYajM9xX4995/r2vLG997473333vj2D93NX5TOe/LVjS+i4lLfi9eT0Dk4OePHm3rDQ0Mx3UPjCHtI+3vPXCL6m4vsWpjL7T6xsm7drEjW9RtId/1DePc2Vsvy992d/7wF/q1yCs3LhUAuELeJepd//aKOgZb7eKpR5I0xhcKBMPFnp3VtGH7hg0+Mx0MCMzHEPub9/+ma6Mt570b7RcNNKKfJAA0j4+cdocOjb9VPVu5GT3y8ktPt0rl9W4ZgV7Jt5m48NsMDw3Y4YDeKYLDsQcEY2vz8ClqXuXui7tuui3k5z6OnD4CRJp/8ZN/9y//cftgN15+8+PCjYPZ5w50/1cobKLxf5D8k+Zh49G2SO819LXaxVOPYjHM8Wm2SnpVymXVyYwvesWendW0YfuGjaV6ZvzW33go3n333a5t33nWB+vvAAAgAElEQVTrO0PkvJeu8jijiP3Nj3926QYO/fl3/ymAvz77/+x/NbH/3mcfVpB46elduFU9e6u15e6TjZt3xlX6LmYs/DZd1j86wwFefnr+YwCvvzIsNIDBOYObyrbLDz2Vh/4IfwzgR5/hjZN3z30cAXD6uSb6ZbOr8TiAf//DHwIHT7lqDgDNq6VrkbS95ebHhau7XnnlaARoKbpX172v7ey5M2fOvPbaa+65eq12AI+2SWgtjjy/R1kYhbxIaKoo5GvxiYl8C1fsg1MYP5QskRgsCcsp8EMm89hoJ95Gou6V+Y0nNobIeS8KlCr6TKjb9rAZWUsNVPqNa+eLd49+9+QB3Pz4Z9fqaPzgu//qP937+TM7caty7tOb+HJHBNLTp5P7gVt/f7aCk6e/GXG1fypMT/h/8cEHAL79rW+NepR9iP/BwcHEpR/9CKefO+VusT0H7//sJoDvffcAgMjPXgXQ/O5ZAOf+46svf9MTKa9HoRrNz9uryUQO1wwDaK066Ov1h5/+6pc3/tmf/m7vPmfO/O2f/unvATB+rAJQsibgCLmiwPt6kNWOeUo7AMAq6aaipWUAVqkg1EkrPIAl66zmAts3bCzVM2Preh85b6l+x8YTbwPtqLzPPDsvgzQeQPSTRH+Nv3n5/MYzrzwTwca1D8rmgWf2/Lbx5J8/94/fwY8+P/sPG8deeOUx49y1lZe/ldh1q1qymo/tSb781K5blQt3j770zM6Rrm6r9BV+n6o/trSPcVTXGfoMDj5TjDUoWROm0t415vzu9tKCytN9/OTot9BwX5pXfvnLGwd/93eebZ9lTQWA48aZM3/72tEfAE5p5Pfee/+NN77XdXjXxmBJO4AOfafALzBs37AR+memr5z3bsQg718rKj+GwMNHHftBrvvmJ39Xvnko9dL2yx8/2I31/z79J/+u8ld3cfj00Y3zF8y9L/3u8Wb1XO0+tiunk/vv/vZCFerLT03Jhh+BTc39sUXa1WY/vIHf79rSfAwAog9RvgL1OIw1KCfa79YfjvzLeuleftA97Z0GPlFimf6Zm14b3btliMa70g5gvuH2ToRRMKRsS9/bWj9hQt9ZzZ0n5n0BhAzDj3U+Wjzv5KNWgv2ELrGTxom2ie8R++ahx/7szUNorvz8wMPKqX1/YqxBTf4pgLP4yb7HzFu37h7fv2vXvY272wFg186Vuzc3gPkLfPNY/+R/V/h/z/ZzX3O2+7H4h4wJeoX8+oAuql4FgFjC0XXlxFZFHWjVPzhh2kIOtPw99mJFiToQRaJeH1pnoV7Hu++++9Zbb7377ruK8hYA4Hv2drQi6wDqxf8OJrY958jbo0fBUXcATVGHY7EL0VCUaag7mQEcQIWNhR4UD5Lz3re82/uG4Tfn8rZGYmRJGOKlH8KNi2duHHrt1EEANy6c+bjx9CuvPnXj3PlPIydfe3U9ATgqZX4CAJ+fKOPm5cN3/imA68d/DuDQ2nf6vp4X586eA9BbqAc+LP6XnmhLeOQh0LLFe6l/1Wrntc6x2Anz/fff+14rf8L72i8tIcdjUY94TxJX49966y3vFuftxxz1nNIqbVtGGIUyUllVmqb9vuCd1ULA9g0bC/TM+Jdz+LDOx+grt2FbHXXpcmwkpR9Z429cOnP94GvPH8Rd4+wHn6288Fry7q9+udbYgcOqI/qXfmGKjS/u/uC1H7gH/X83yycPDD4nAODwJynYA4J+r/sODrY4Mhgi7Tav4jtewe6V8OhDoDWUAfotBLDW41o50f3rDBN4V7zd191W+IywMzrbou5eQ2eV2aBqvFXSiyYQS048g77NAnVWCwrbN2wE9pmZrJxPBFvgAUiXYwD8y7yfFeVdblw882u7dOnO6Ipy6ttHI7hx6cyv8ezx5g2c+p2jEY99j+bVX/1yrXH4hdf+m4NtnSuPvuDNIA5/kho0IPj8RHnbw6Y9IFCPA4CxBu9r+wU6BbtXwl1XeZcMA+hjan+idG/pkfMunNN+ogB4/8rffO/3/9vZi7cfOoz4lrT3lfOgavzUCWxnFRrYvmEjIM/McM2ezWrTm+IKvI1/U76BRgIJALYp7309hLbSH3rhtecPwiPntroPIoGJiX0KqU33cb+I/bl/eeYvAXi9C3b8u9syftjotZ7fv/I3jhhvJtsd+LPCO5zeM6Aaa7/2Xk8vve96rHZqvEtAOqsQw/YNG1t5ZsbuZUaSc0xU0YVRyFfqUDKeOKFV0oumD99il8BjdFO+FwUKADs/33490iBgUxJbSw70XkACCe+1DaKriUai7aauxvqI9KDXg8/Wtoad7zCi0HqxRdfOuPTz7lgLuLkzOXuzRvruOcZHLC4U+GnD9g0bMxD4Oco5gFZ0UMl4q2wJISS7YncrK0gYhbLYUTdvDFZ6gf6ryNsyL062vfd9jt3Cu9tOAsCjy/2/Xu2kCSB+ucd3veV3h3/uyII3r3dPPrLvscH3lRM/BjoHfvOgV+BBjW9BgZ82bN+wMSmB92and+3W1QfN1N/uFNBMy+1O3BFw5/99e7HzG1paBqxzevFRRns14mYE95xsgMCPSgxtIbftXe8WL1t59xEeAdiG/kLo510/bKadI59kIqLVdWe62/ud2fpAL9prsCuZnFTNV6JzFnlq/CAo8NOG7Rs2tijwvRuHy3nvDtPFraoljJ+eq2w8aL8TO6VljwOffqDfPmoPAM5cqT++/5WsKg0qxbUVsfS+618+g8xEpB39JKq/aFklvdjwmaM9SB17zyyMkvGFiaO2DydfiWZyUtUZE84PanxfKPDThu0bbNoGq19GemaGKPrwKrBzR/z6Jz+vPXn42CtpFUYhX3kQw96ElpbbM3itkr62YVvzYqANT4CJSrvP87Tu64gxeCmTIQsN9IqlfdKSJSsibyoZFIvIOLdDXjyTbNxu1WWbG9T4Xijw04aV7JYIn852d7cA9zLC+mLniW9nVQkQRg2x2Ea9vlHUTQCRA9HdTUCKSLGNRn0nAEhStG42AQp8N5OSdox4tzQFkqoMQM3mUCgbch+Jd8eXfRXREctcspCv1JWMpt4q/N316IuyrGZMvYhMTqrqupnR0qlk4aMbOBTMWmz9RyqDtxMyEhT4BUEYhXztAaLPO65HkWhZpvFopWICwHYoL2lp9wg/xndv+HxQsDNQWKW8SGhpSRiF/LV67Egu8bhR/UxqVd6q3vnSELIqPbFR2fu807HHpP6Liywtk5X2UU8lK9GqJVRJAiQ1FR8g8e3z9z25lksWykhpmmR9oOdvPLYvk5Ulq5Q3AZTzOJzRFFPXTSB2Spu/98Z9uLq+znCNR2B8ZmQRocAvOPVKLZ7TNAmfFvSLjbvA6urqoH7Bj+QvQG9ilYrIaDIgrl2p4+GueiVfbGfKR6QYpATKul4/+FTsvhCQJcs0o0p6s/MuC5OVjdEMTWEU8hUkc1lVjVdbqi6piWjBkfsBZ+4rjcKqRRNZCRCiuR148EXxvfdw/z4QS+YSIn+xqpv1AOTRt/FqPDw/wRCNR6AdaSToUOAXkOatJppfADIAxB5UDEtNyytPPo7mPeDtt9+2w1qBDZ9vEcs0YZq6CeyKRZK515wE+nwBuawqCauGeEpWVU0FAGEUdL0eoD5+rkzcIhxJe5ykOk2zdVxNxQv5kuTvl+krgZIcb5QNIUtG5e4DJZP5slS8+dhTubdSzZJelU7txa7XswH82XsfzOGuMp/T6AnphQIfNoZY8KMSzH5ETmt2IMIq6cVKXq8ASkbT0lZJ1/Xu0tmSmrWVfsmZhrSPeEIBxJSEKnkqE2VzRkHXi7aVPdh87/jXm3svqal4IV9ATtNUo5CvyCeeuvnFDeB4OmOeXWsc+uZkvuvk8aavDs8l9O7PwDwZFQp82HAt+HHpLQPntzDcjHGVvu+/xGYacdwRZMYqlZBOywAkOZ0wC4UC4ilNk4RR0EvQ0n3HXwPPL4xCERmtbZdLakKpXMzrFSWj5TIXP/l458E9peDE3bvo0vIhjvreFqC6kzGgwAcQq6RXJVtOm6Jup4dJUhRXbiIKQNwSX2PAEptjfpyr33YZOC0tjELBSPXZIhmBFHvSy5SkfaRzCtEwK6XWcqOyEi2aSlYCIKmpZMGwIPf40AdPoxdGuRLNaHKrPDEAYO9xZQMm7lT1fD2WfD5auWgGKu7uZdN2G5JYRwuejAEFPoDI6Yyp5/UKAMSSOdt5KavP/r35qVnUzdizB7ajOZmPchLyW/r9TM1E3SxIuayaiOqGJaFYNLc/pcLOhNJ/qSvPd8g/CSJTyr4eXV2EVYsmk41iybIFV05rru42BaQR1B2ApGZzRqFgiGgtntOyEoBLP9XXTOx4Nnfqfr6IuPysqj4bDDfOULfXcGO9l+7JgdR44o8JGoJkcshpzSEh8gVDAIC0fz9iyZymZZ8/dhDbtwvbDMKGfUhkfwR79436Qe58ZEmKPrxVXAOUjJYQ+ZIVkXbdKF5VMgr2oFwwBBDB9i8PKDJssa9ZkynzSiaJruu2AEzccB9LV5qIq6qazaBYspxNVsk+mW4qI4wQhWXfbpKaTYhKIy47R+7buf3JpzIn7ueLjWQuhbKuux80N4RR0HXdVDRNSzmPTh/6VpFyf7sh5Z/7HkhIX1hIKPC0F85o2wOujzKWTEYrQvFMjo+PXhzKnrv07DHcwn588WQqhXIZqQPX8jePa6mvCmU8Ha19rWbV3/xUr8W110/Zh7A23HzpzcnCdPIiJ2EytlYAGvGD3C2d9rC7spAwzhTvZ157QXJu4mhGU8xW0H8udJWeFL/+ybkrXz7AoKjBEMf78GYPhx3PSnbThu0bNsZ9ZuwOMvnsrbVP7z9QMlr6C1vOnzEKxhPxxm+Qyj5R1qtS7s2UBJ89NpkiXh8vpibtEzuzVdKd6rEDP2uwcx7CKBiINyqthWOcEW63C7yd0jcfhFEw2jVxrQ/04o2V4/aQuM+l2UP3Hkd9e5qBWQy5xlPgpw1j8MRGUlPJWhn7j63cwmnF1PUb2P7EdmFPNhY76mhaqK88iLoVX1kbbr5Mu9LZhPVDTg85ma/PktSsJhsFvSByWbX/9Ec5Pd8AvCevwDqrF2+vJHOvu5fZEAJOaMHWcCWjaUpJ1/VMyy2vaZmSXpVymibBKhXMoR/GeDzZFMbglxxhFJywpbBqiMuymk2hXDSx/YnYyoZoApKaTeEOzKKpaL+bbFQNAcAyzahE//zcsMPYmJrhPkvl8OWgllP2XDs1qyVEXh8U2Z4zcjoh8nbzFe8d17TXVVfQi0i0/8nX4jlNS8uAnM4osWIrpt6ePgNEJCiZTcLtjMeT4dBDEjbG8HrZrsJYMhOvFYVnSTY7Fm8vzOb6413jg+752eP25tOrazZ7o3C4c74/gxYADgpeX33nsriWV8Tt/00TpqZpXo+9Nwa2aWssrh1PF/20YfuGjS0+My2xb6UzUc6DwfDp0RP8lLmr+1wuY/K0c2M7np7OkYlwV8vVdT0ZU6Rsuth21LdHAWHVeAr8tGH7hg0+MyFjLFe8Iy/+KxLNZeGy0Kr7YDwC32nZA7qux5K5rGzp+Uoy112HL5Qaz85q2rB9wwafmdAwrui2/cM+5zrMRRuWUN0BeEz77tGXruu5ZCxfi6Ne6dsIfjQeQV1Coi/srKYN2zds8JkJAaP31F6THZ0B4GESPy9JWFZ134RNy9uNVPYu+LCzmjZs37DBZ2ahGUtxu012xexIihxUkmheSrAV9Qo9S6Xx7KymDafJERIIJlJlVk5nUCxBUcyqM5FMkuMQ3SsXzHginB+Cdj3zwlveYOwpcJw+R2xY6IaQOTOun7wVzY0lk1HTtNKyDEBWk9WySGWiecNS+7rm5yuldM5vEZ/1bVgGh4Au+vBBr9cCsYUQeKdbHorZkNpTGw0pm4601ytoJXPNPQmLznmfTMRR73+3ecHOatqwfcMGn5mFYMta255vZUfZEyLvxN07C6J7P3G+fT3VfSSWQePZWU0btm/Y4DMTcCZmRjtrqrlZdKLLZJ/BajT+obqPirdlwqrx7KymDWPwhMyICQuts2KqVYsmshLsOu3eBVimvRoNmSp+guiMx5PhMIuekKkzkQz5vlhGJarI3kWDughCt96lLm6CN1VnOH4y6n0mzDOvfjmhhyRs0OsVKKZsQwujUK6hXq/HkrmsDCFJ7bqnCIbpNihtHsOaZUAl9+XDj6N++Ftj7DYz2FlNnUckXPA3DQirq6urq6tT/pDa+dV8td7no4f82z6037GTpfej3S1D2qdePd+6sHo1v7p6vja9Kww+3lYa1GL+77Tp35MjwM5q2nAAFTY4KJ47c4x8+/xoYRTyIqGlI+5qZlO6mEGpYe5F9tvHOqsXbwNome+tq11eQ37TjPrhb42957RhZzVtGIMnZGJML9bu89N9fnRTIKnKgKRmc/Fa2Sl6N1sGjUWEYR7KZRRAyeSkqq6XLElNJRtmvwSDZWGCwfiR9iSLDgdQYYOD4rkw33z1kT/duyz5kGr1W7ukTWd2de7TjruvHNdePyWMQr4SzeSkal4cUBrb1Sn5GRaEyQbjR9pzerCzmjZs37DBZ2bGzH0q2gg9dXsJ8g5V98r9tC9p0FvCKFlyWpUAfFrQL9b3ZbTTckv0V45rr5+a2NUtKuHTeHZW04btGzb4zMyMIEi7/wvojrvLlhvZnojAby1O3BV3Fxffy3/6mC3rEx9+LDCua334/IiRNB6eW2jGks/OatqwfcMGn5kZMHdpx+h9sUcnW+Y7nNp3k5qKNrxZnAu2C+51fqQwSpasiHwRmZxUzVeiGS0dMX76y8rGxtJPlGszkhiPdHvYO8/eoGdnNW3YvmGDz8xUCYi0+70Gq6QXTad07Uzi7vaLgdH3XNL5XKukF01Xuu1l7NPyssbdxeazGfo6SIY77cfQ+DGufSuws5o2bN+wwWdmSgRB2jFKR+zOLvPI5xTj7hjqpbe3dK6DY2cEPB+tXLRz6/ZmtFdlLGncvVPjrZJexEDPRZeu2y+2XqyeFnz4YC16QjYhONI+ymUIqxbNZGUAsqJUhYAsqal4IV+SpuPx9srDIFNSkuONsiFkW8XktJb79U/ONTKaJgPWBz/5e103M1o6rWlKqSCemcJFBhdnJQFnxSAlo2VM/YO13LeODxuCDVd3n7i/ThDqHpLJwgFU2OCgeIIERNoxlgdVWCULaVXuXD9WTDju7ufydF2PAXbcvctSLejFOgAoGU0xS0grpl40lzPuLiwLcgQCVtnOhiz9OG9Gba9GD5sVC+rYc6Q7Z5Yaz85q2rB9wwafmYkQHGnHlvvcaaehb67usWRH3B3OC1V8cPHaunj82W+fFGWxJ1r7WrUz/6ZXXS+4eL3y7i926ax+81Cu1Xad4x6fs+YgDD1fcd5tz5Mcdikz03h2VtOG7Rs2+MxskaBJO7Z6MbZayFZv8vok2FTdc8lYT9zdlazHD2T+4Nu2pJU2pMZtKfGgePWo9q1ls97Rd5aD3UbbgQe2tLeSKdxjfGm8EJZVLlbqsRjqUXt4VZWCofHsrKYNS9US4jDfQrO9TOxi6pW8XkZK0+bh95bkeKPqFsOV05pTHFdOa1ruxJfuW42vHo+axeId3BfzqJw7d+R0QuTtWzBfiydQ1nW9ioymnU7GIgfqVUNATmdQLAwoLDywAK0kyWpWyyj1OmCaFuS0lkK579rCPs5GFgoOoMIGB8VjECirHZO9ns7M9ckyzM5zkuGVTM+aNv2uSBgFQ3qmUTQT/WPOS4Uz/0Exbad9xCgYj8cbd/r+ij6M+PbsiXa4xN+FTNuOZ2c1bWjBk6UmaFY7Jmi420jqHNRdGHrR1DRNy6BYMKBmtYTI63rJAiCsGqRI91VKUbN4MZqhukMYZbvCYESKKYosjHIluufrGqQIhFGwb9i2/e01tQeY3U2BuCwBgJZL1usV51MKnSfqB+34RYcDqLDBQbFPgma1I5CXNIhNQ++taH+Hue6tu9ONMIymqlLfvcH4dgHfWDIZrVTc0kBWqYR0a9zW9Vv0/jQtE75p5/GZRV1BTOqpfjSI6dnx7KymDds3bPCZ2ZRg6ugCTUHe9FJ1XW9lfLf9w0IISVqy1PjxaK+r1xb0zsI33brsR+PtCsAyLF0vJnOaW9LQTwBnSjcnO6tpw0I3ZIkIrLQjeFc1Nq2a80IAEiQpCgHAKuU9tWnJMOS0pqU9/wuj6lV3YRSKSGjesdKmNWqcOjqAVSoqGa2S11VNAyyjElV83HesgbOgUODJUhBYEV24ftNvWZUOa90qFWEXrCNbozXPcGhTDtZjIRqKIiOtabruOOp9/ijU+EWEAk9CTpClHYG8sCGM0cVHJBTz1c0kiQxBUhNuVVpl0DipS4AH6HGrWLBsxRAzUddGiZlQ4xcOhkDCBsNaLkFW0EXsKP2E3vvtYFmWLFPeZ8KmwXh0rmszxn04wceKndW0YfuGDT4zCLa0Y7nUncwavyVs++0/3qeMDTuracN58CRUBHBeuxf38uZ9IaOxiNdM4G8i+3iT3TlFfiHgACpsLO2gOOBWOxZZJmm+LxZ+HPXDDxnvg0ZlaTurmUELniw8wbTavfbNghruNlT3haPLvJ6etU07PuAwi54sKt4KnfO9kr64KccLrX8LffHEP2PfqIt+h4cbekjCxjJ4vYLvjbdZlOscxPRcu2QGzMxRP/aBy9BZzRe66MkiEUxvfF8WXfmGXL/rO1n07xhuxnDUj+1yp68+mNBFT4JIr3IskDW8QJc6Hm5vPvg79pZTJ/PHjzudvvpQ8YiEi3D8pqurq97X3n8DTu+l9r/42vnV1Xy1PotLGoMhDe6+NWSfevV866vVq/nV1fO1yV4e8U/Xz+TzURr7iRvpwHB0VkGGIZCwEZqwVsBz6Hrxb7gLo5AXCS0d8ZQUCxC+FosbZrG1Vzm1zffW96UhPx/GCMb7320rB4amswosjMGTIOJKyAKpu/+rbQokVRmQ1GwuXisbYtpXNwI+e2fXS98ReRVGyRDCMA/lMgqgZHJSVddLlqSmkg3Tmt5Fk6GMN2uO8fgQQIEnwcKbRrco3cSoto6sRGuWreqSmgqQxI/0RXoGNMIo1yChKUzRlNNaTqrmK9FMTqrqpd8ISJFpXDEZHXf25vQ+YoEe3nDDJDsSFBYxN220axZGIV9BMpdV1Xi1bMhZVQIkNREtWEKVguWnH0jXIMB9LX79d2tPvvimLFkmzKJuriRzr2uqVdKLdeDBTu31Bfl+i4MYIcLjVdyRxnBjO+p7j2UK3uxhCCRsLGJYaxGlHSN2WK11vFu9sScubZUKQp1/IH5r86TXCvql+r5TuYOflZHKqjD+Nl958FTuzZQUlO8XRnxrfF91n3Yw3nts35MsYme1WLB9w8ZiPTNjSbszBSuWnFt62uiXLaxS2VSy6YhRyFfqdvKZsF8HYiLZFvt6YRTKSKVQzlfqgPPbNM/9tPjFRjC+X+gZdjMNUdnZaDwGPCyL1VktImzfsLEoz8y4VrswCoaUtQ1f3VTmIB0jdHZWSS+arYGIVSpUG4insqoUsLTyLffyVkkvmkomJ1XPi30n1RfkZkmv4iCkUzTcZ4k99G3dcEIIqSfwM1zjh1c3mrjGL0pntbgwyY7MmtGr0VklXdd1vdCZiyanMyiWZpmbPdKaMcIo6KaiaVpC5EsWAFmJ1qMJVQIQgLTyUavRbaLuAMwL+Ur0ZPoFuVnSiybqtyWq++wQRkG37zfNbnZhlPP53sdjUPrbpvd214G6rhf8PXwLlzMbJjiAChtBHhSPZbV3m+yK2Tbcbc/wbHRkRAumfdl9Y9BBiEv7yrpquX4H7SOMkiWnbQ/FmdqO5048L0sIxvdbGrryO9p+o2ZJr0o9gaze3Df4firb6yflcpZVLlaQzMRrRTsws3kwpuujg9xZhQO2b9gI5jOzhTQ6j1LaEp9B0e21vG9OjfEuXlglC2lV7v4CdgXXgMSlN9H41gAqr+vof81uTRsloylmCWnF1ItmYL7fEmB5RNwejbUSPLxj33bp4Fgyl1XzPVF5/+PX7j2FEBIs3zEn7+HB7KxCxaxL55EpE7TfdNxCs7Xzq6urq6v5ar12vl3qtF7Nd2ypV/NTLoO69Sq5tfMBLUnbVQ+4dwe7dVtv9SmuW6+er9acnyRf/Qf7i9ar+QAX4Q0v9WreWxO459Fwfpd63f5pWj9rez8/t3q/x7nrgzfHPUPQOqvwwfYNG8F5ZrZQQ97tdOrV/Pla7XxbMJx36tX8amsAMLEL7mJCNfBtfbcvOEA12X19tXp1dXW17v0/39HgnrFL7fz5tWr+fK32i9VfBOdbLg9det6r9n0eldXV1UeP6vWq83w5t0TtvHOntoYCnft3vLB395zZeTA3vdHtMwSnsworLHRDJs+W57U3BSTH2xeVIrKaMXXDUj0OQEnNaupWL3MYkyzKUa/k9Voyp2mBiUgP+3begK6kApV8wWiFcSU5DqMJtL6I7CnYg8ZXj0fNYnE7YvsE5MB81yXB88i4P6H9vzNXXstKwijolTo6AyiSpKZzKJQN2Q6uZzIZTUtbJV1vxJKJrOTxurv3TKuITaYn+F+VcpomwSoVjMiwFAzm3M0GhkDCxnzDWhMrWeMG9uLJRsWbyTOL2e+TVPeZZAmMxLBv1zl/z9nTmQTXG9jtOtKQnmkUzYT2aoC+7BLRd4XeSz/V1zYiydxrktH6EQFYpRLSaRkDZs0lY6hEN0+i6DzWmwvg965nbbtpQ4EPG/MS+GlWo5tdSvaC1tQbicG9qivvrdR5tMWiY0p/P9rDgGldOBkFb8Jd+cf53+7JaN9qm/ieB6pHp4tm6xGwSnoRw35S99jOohR+S1QwyW7a0EVPtsrURVGIxrRO3cEy2BNDv6OkZnNGoWCIaC2eQz2vaZpV0kuWlpYhpzUtPezMsppMKirVPRA4QzXNnkxqrV0sKyQAABTJSURBVK+sKEfl9ntFJPrFi4RRyFeiGQ1F3R0eaCjpujlI5Fu++pxoKEpb3atSLiu3Zlhy0DdHOIAKG7McFE9V2j1W5NTd8stguGPz0LvpzHbTqybqzp6c0L54dDnIrV/8l+LDlHa65Yhp9DxOrYC642O3Hz03aWTTW0DX9VwyVkYqK1ut2vhtj/2Qw2nBTxu2b9iYzTMTJkVcBsMdm4bebUWwSnpVQr2Sy2mSM7F6ZpWEyKTwSqpV0ouNpw7Wf3sDgCc8746fnS3t26Mlza258r787bbGtxa+8RuPp8BPG7royWiETNoRlu8ynOGDGGHVoooKALKarBoVQIKdcD3HBX3I2MjphNnKUVcytqM+5Xm/lS6hOQl3luyRX8tsJFNpqeV+T8bQSOZkH/F4d2aLVSoio7kldoxKVAn/ExZQKPDELyGTwyUx3P0gSVHTtNKyDKBSN5M5DRJSObl3qRKyGAzJmHCEWmsLdUMIyP2WfrcA1OK5FMq6vkk83nO46BePJ/OBHpKwMQ2vV/ikHSH6OpviaygjhJCkvK5nlJhQs2qTOfGhpMtf3r2soTu73QTs3JdKXvf6cYbH4+07zYnrtOPxA6+GLvppQwueDCN8Wrhshrvf7ytJdszVKhVaTlaN4h5qOuvhAPAY4unWLpVYEvWKBLuslGWaUWXwZAr38JRR0MvxnJalC2i+UOBJf0Ip7QjXN9qUMUYzEQnFfDVJt2o4kdQEusPzg7Hj8aqk2nPhjELRjscPwdX46VaaJP6ghyRsbN3rFUohXDbDHSN+Zc/OlmXJMuV9ifGUr3Ec8rquK0Dv/LpNzzAcuuinzWPzvgASIHRdd0bfi6+F3krXS6juI9HZPlT3ZcctFC+nEyKv67oOxEzA/4QKlpoPCHTREyCMVru3iwnT9/IJxzRkEnSk4490U/VLyyezhgK/7IRP2r2E9XsNZ1znPCEOfeWZmr1w0EW/vITJId+F+9WW0E9IdScTYeuPz3I+gIGCAr+MhFja0RIt+6sN7GKskq4XDDHra5s2PgWb3S4Zj1E1mxo/X5jEGDaGJ6aG2yHv89u1qntEjE0rcSwU/tXd7XYH7993dXGydPS9qUZ1/Azan1n004YW/LIQbqsdnYb7cJoCSVW2V0eN18rhs+OH4zWqBllXwlhzl+htXNT1kjWTSyOBo8sEd8eFtOMXAgp88BBGQe/oUq2SvpUudhmkfSSTQlaiNctWdUlNhUTiR81w9h7Yu8ON2hc4Zd8yufh2oHGRGh8qhFHwHaJy5XkrGRvU+LlAgQ8msRhE6+mzzEYsNtZZQi/tGMVwb8fdZbWt6pKacOV+YRnPZTqk3XZF8eCSremSmtVy8cdxY40KHx5s71V+hDSUrntsDMGmxs8eTpMLJtEoapZQJQkQAtEo6q133HWcW8HR9nLNwiiUcRJA2GPtNiN9RyfurkWMgl6I57KpeCFfkkIRXN5iQNTz2ht3z+w1i42LzuJhknok9slnG5O7ZjJ/3OVd3T5lQLbFoAkpY8ya40S7GUMLPqAoSlQ0AUBYQlLcLDCrlK/Fc7brNNkolixAVpSGbe03BeLyX6yuht5qx0iGO4DeuDvUbE6q6rqu66aywGl2k0p3QnfcvWgqp+LbgY01Xdd13Xo8Ej+w5aslgURSs5qWUWAWe9327g0zRONndZ1kZGjBB5WI1DAsyBGrBklGzdkqp93lISQpCgEAshKtWkKVmmYjrkq5xNvhTkwdwXAX7TT5ViNJdty9UDbkrGvBEMCNux+H3XD1xqeVaEZTTL0IYOc3FngURIYjjEK+Es30XUJ+4nYCjfhZQgs+qEhyHEKgKaJKl9fMKtmxdcebCkQk1CxhmY24HPY+2L/hLoyCXkZKS4h8yUII4+6YqPmOQXF3Oa1pmhaKWAbpg1XS9TJS7V/YKg3M6PVjxPsx6Gn3zwwKfGCRJNQsw2xIEc9Gq6TrpuK46FuZd5IchzDCr+8j6VlTRDO26e5EMCQ1Fa/lw5MLPll1ByCnM3s9k+Ik9Ujs4VeMu4cZq6RXpZxmO2fs2Tu6qWgZFO3nRIjuUfAQjR9pMgs1fjbQRR9cZCVaLDaSOQloqZIQDSiJtjHVEAKyBEmONyq1eC60+j5GzqCcViwLQhSKiCfLul5XMlo6mzMKul6004kWubUm6uRs5dYpGU3LGYV8fWNN14vAvr0xxt1DTSviJywLckRO5VDOC0BOZ0y9ZOWkar4SHaXM0agJd6urq6NfNBkBCnyAiUgxQJIAdxgtqalkIW+PfGOKEquLJiABkhyPCWmRFWsI44qZLMuAnNUAQJWNgmFBlsMQdx+jQXzl1t1eM4yvGHdfPiyjWERGS8uQsplSwRCymtZgWXJWk0p6wegs9tgbRB973Ye33w55wtDcYaXAUCCMgiFl0zLCVf1xgpP9rFJBqIutV26vOlnn/Frhx9cTb35bFuUf52/sjn759ZP4+mB46veSzfE8HMIolJHq9+u351DGkrmsmp9ECdswdVbBhBb8wiOMQr6CZG7hDdMuJuKFdnulRffJwxO2HNYs9pTmUcrH79rxWP2qBRlP7sDO/a/8vmToF2o3QIFfHuR0wmzZ37FkLuv89FZJL5qxpDPYk9NaTirka/FcSgbXk10QOIAKGyEYFC9DlZ7xcL2g/RvHNb+skl40bZXfvMN13D8RISRJAmCd+3E1/mb22clfPlkQPMPE1j2F3pWZBt1a/jU+BJ1VwGH7ho1Ff2ZoAQzC2zJ9W8kTqIHrvBihMZ0j9u2NHXyRLvqlpbXYouz+e0ngRqMl7vZd4viItrjW3KJ3VsGH0+RIUBh1zZilYnB92TaSHG9U3UpkclrLARh9IR3m1i0zwih71B3C+GWl3pRSmu0X0p1Zuq2JdCxvF3Ao8CQQLEN53WnhLj9oT/VvVRvV9XwuGbMLHvuCNW0ImgJu5Q2rpOdrR3La76kwDAtyWtNyyUbVEJDTGRSHrFRDjQ8I9JCEjYXzejHivinDHBu9cXc4iYWalhuYEk3IILxLDjmjPaukO/PougNBALYQjF+4zmrhYBY9mSf0yW/K8CYSVi2ayDpZzppS0vVCMgeYGQW6Xk5yuhsZFTndU5Q+IsUUyZZ0YS+O0QGT5wMLBZ7MDXYKm7JpE0lyvFE2hGzruJzWckahXO/bSxMyJpKacGdwuPPo3IWrlcyAW43CP3foIQkbC+H1olveD5t0jq0CCCmUvROYdF0fZRo8IaPjmYcJWKUS0ml5DEf9QnRWCw2T7MisYT6dHzZX9zJSmpYQeUPKagmR1/WSBV3Xk7FYx/pEhEwWJyLvGUQ2hBicWMeEuzlCFz2ZHTTcJ4UbepcUpVjU7aViFFM3AWbVkWkijCoy3nl0hSISmn3H0ScfNCjwZEbwyffP5qF3KWpWDVWWrSoymia3cp/ZwmSGWCW92EjmspvFgyj884IhkLARkLBWV9k10HD3zXhdoa7rMSbNkxnQZx5dB/6D8QHprEIM2zdsBOeZcReRpLT7Z9zmErqeT+Y06jsJAj41PjidVVihi55MEar7SIzTXK3JSlR3QkgXzKInU4HSPiMktQ5oGtWdBAhm1AcECjyZML7WjLFKuj6klPUywiERCRPU+CBAgSeTpGuOe9+HWRgF3VQ0LYUyRd5hVHV3W5XDArJwUONnBgWeTIy+YtO7pSmQVGVAUrO5eK1MiR9D3e0ucuiB9uKeur3OHCGzp0vIKeqzh0mMYWMuiamjTYSzSgWhOhO6xLIveDb2pDj3dd/DhXGuXPmiDgCIraC+l9VryeQQRsFbHnko7r3adaPquv72229TgKYKLXiyVfyWnhVGwQ68y2rbcJfURLRmLb0RPyre1u5rGN2ofYFT9s+Si28HGhdpyJOJYXvf8gVDtDxFA+6uQepub1ldXZ3udS49tODDxiwteP+Ge6vkVWvEL4xCXiS0tNxpzy8bY0fQu+oItU8ijJIlp1XJKukXTbh2uzD+a37tycybp2nFk6nQ7zF278xB9znnwU8btm/YmNkzM4o4CatUNpVsOmJP2lYyWlpuTeBe2qXPJqLunQjjzN9d2/3i62mndm2j7ZxfK/yXz575g+yzW7xoQvqzyUC9701LgZ82LHRDRsav4d4O1ElyOmEWCgXEU5omCaOgl6Cls5o6i8sNJNPIfhdG8dOvnjygRJxaorFjz+JKfWNN14vAvr2x+IHJfh5ZUtyV4IHWAN0qFRvx3BA3HItazgXG4Mlo+Iy4C6Ogl5HSEiJvR+dkJVqPJlQJgKSmkg1ziSPCW+npBh9rXao0v9xxRBXliw0AwFdffIpk7hs7AQA7v7GkYRAycSQ1m1GgZDRN0zTF1HVdNxUtq0p2QJ5zX4MDPSRhY3per5FS5a1SCemBIXbG3adwrFXSi2ZsBfWvdiVP/57d215onHoze3zsayVkEFZJN5WOZWPzlXor+DZoZgxr0c8YWvDEF35T5VvIaQWWvVh0HGUny9admm0qS6ru00ROOxnzK7IsAYCs7AO2zfuySDiR0zmp6hjrTs6sZuu9JMchmn0PYombGcMBVNiY+KB4Iou9CqNgSNnlTKbzMiXnvLN+p20/WUbzriheMoF9e2MHX+RQikyXrofbM0OmH97bmBb8tKEFT4YxquE+iKaAFJnIFS0wU3LOC2PNjrnj9pphFPKmJO+y/2fcncwA78NtlfR8LZ4bMpSnET9LOIAKGxMcFG8967VlWi7vXDiXLTbmkMPXCj++nnjz27Io/zh/Y3f0y6+fxNcH/RUZI2QSuM+590G3c0KS/e9E+36mBT9t2L5hYyLPzETc8sRleuoOwPrgvY/wzd//Fi7+1+Ktp3JZyWBuHZknvhPuWKp22nAePOmG01UnwqSacdPzyKeOVQ0AkSOvaM9LAJR9F6rMrSPzoZVwZ9vxkhyH0QToTpoPtODDxlYseBruk8Vd9m1gk3psnSFn8Pt5jqeUuXVkXoyfcEemAS144sCHbeJsru5lpDRNskq6XpxcmgJz68i8aApIrbu4tQDF4LuaLvppQws+bIxhwdNwnxLDLfhOY6d7OR5wyEUWkb4JdwNgkt20YfuGjVGfGarIlBi44JtLdwJSx//8XUjoocBPG86DX17sonJUkRnQbmSr1K7VLakpZ01tmyEVwAghZGQ4gAobPgfFlPapMtBk7005skp60eyaUsRfhywDtOCnDds3bGz6zDDiPm0GyLMr757VNlthSm9REKo7WRIo8NOG7Rs2hj8zFI9pM7SFhVEoIx6twVlKr2tFLh9nICQ8UOCnDafJhZBt2/qXOVldXX377bdnfDFLxbAWPvkv/uovvo933jG//zu//dev5C4DAN76N3/1zL9+5f++7OsMhBAyChxAEUIIISGEWfSEEEJICKHAE0IIISGEAk8IIYSEEAo8IYQQEkIo8IQQQkgI4TS5EGOV9KqU48pik6Znjdd2MTr/h3s2xJIDf6S+E+UJIcQPFPjwYplQojVLqBIVfuLEYhACsgQAltmIxUY7fHJrwxJCyAAo8GFFGNWGlEqg7Cq8VdJNKdmoVOpto1EYhbKIwjTrlJyRiEbRGjsJgWgUrkneW4jWbyO7C2127mY6m/kLEUJGgjH4kCKsGuKyJCvRimG5W81KLZ7TNC0TreRLzua6iYSmUTtGRFGi9spvwhKS4vpIrFLebmJNyyUbxREa2SoVG8lc13EAzIbUZyshhGwGBT6cOPoOyIpimm1dUBKqBEBWk7GGcJYpVRRq+xhEpIZp2S0tRdytclprxdMlKdreu6uRzaLewlFtyzRjcVkCIKkJ72/m/GRdWwkhZDPoog8lwqrV6/W8XnH+t9KyDACxlhRJUrRuNoHIgBOQTZHkOCwBiKiiQlQ977iudkBR+h/c191er7R/sZjkRPhjEn8jQshYUODDiLBqSOY0x5K0SrrZUnh3D9GgcmwRSULZMkRDUgHR2miV9CIympZ2locd5YT9VV80AQmAEI0JXDQhZHmgiz6ECKsWTbTnXXm89HUnIG8ZFduDT7aArEQrlUZHOwrR6PDGu3EQHydTzKohAMAq6QXDPc757YRVqzOYQggZAVrw4UNYtaiiejbIilKsGmoCiCmo6noRiCVzaer7VolIMUCSPAa8pKaShbyuA0BMUWJ14TsOIqczpm776Dt+HQVm6yfLUt8JIf7hcrHLA+veEELIEkEXPSGEEBJCaMETQgghIYQWPCGEEBJCKPCEEEJICKHAE0IIISGEAk/I/BBGQWeFeULIVKDAE0IIISGEhW4ICQb915lFPFqp9FlElhBCNoECT0gQcNaZzUq20pcsW83r9gK/EqySXjVUmWWKCCF+ocATEgTktNYyzyUp2i5+66wWi4gUc9edIYQQH1DgCQkKPtaZJYQQv1DgCQkCW1lnlhBC+sAsekJmjGc52Kaox6QItrLOLCGE9IcWPCEzxrMwrLsy7BbWmSWEkL5wsRlCCCEkhNBFTwghhIQQCjwhhBASQijwhBBCSAihwBNCCCEhhAJPCCGEhBAKPCGEEBJCKPCEEEJICKHAE0IIISGEAk8IIYSEEAo8IYQQEkIo8IQQQkgIocATQgghIYQCTwghhIQQCjwhhBASQijwhBBCSAihwBNCCCEhhAJPCCGEhBAKPCGEEBJCKPCEEEJICKHAE0IIISGEAk8IIYSEEAo8IYQQEkIo8IQQQkgIocATQgghIYQCTwghhIQQCjwhhBASQijwhBBCSAihwBNCCCEhhAJPCCGEhBAKPCGEEBJCKPCEEEJICKHAE0IIISGEAk8IIYSEEAo8IYQQEkIo8IQQQkgIocATQgghIYQCTwghhIQQCjwhhBASQijwhBBCSAihwBNCCCEhhAJPCCGEhBAKPCGEEBJCKPCEEEJICKHAE0IIISGEAk8IIYSEEAo8IYQQEkIo8IQQQkgIocATQgghIYQCTwghhIQQCjwhhBASQijwhBBCSAihwBNCCCEhhAJPCCGEhBAKPCGEEBJCKPCEEEJICKHAE0IIISGEAk8IIYSEEAo8IYQQEkIo8IQQQkgIocATQgghIYQCTwghhIQQCjwhhBASQijwhBBCSAihwBNCCCEhhAJPCCGEhBAKPCGEEBJC/n/3ZQXR2dmcPAAAAABJRU5ErkJggg==" /><!-- --><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 <p>For a completely custom combination of <span class="math inline">\(\alpha\)</span>-bags, we do not rely on any
 recycling and specify each of the arguments <code>alpha</code>,
 <code>which</code>, <code>col</code>, <code>lty</code>, <code>lwd</code>
@@ -509,7 +510,7 @@ <h1><span class="header-section-number">2</span> The function
 <span id="cb4-13"><a href="#cb4-13" tabindex="-1"></a><span class="co">#&gt; Computing 0.5 -bag for 20-th </span></span>
 <span id="cb4-14"><a href="#cb4-14" tabindex="-1"></a><span class="co">#&gt; Computing 0.6 -bag for 20-th </span></span>
 <span id="cb4-15"><a href="#cb4-15" tabindex="-1"></a><span class="co">#&gt; Computing 0.7 -bag for 20-th</span></span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 <p>The function <code>alpha.bags</code> provides the option to only plot
 the samples that sit outside the <span class="math inline">\(\alpha\)</span>-bags. This is done by setting the
 argument <code>outlying=TRUE</code>. Note the <code>which</code>
@@ -524,7 +525,7 @@ <h1><span class="header-section-number">2</span> The function
 <span id="cb5-5"><a href="#cb5-5" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for 19-th </span></span>
 <span id="cb5-6"><a href="#cb5-6" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for 20-th </span></span>
 <span id="cb5-7"><a href="#cb5-7" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for 21-st</span></span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 </div>
 <div id="the-function-ellipses" class="section level1" number="3">
 <h1><span class="header-section-number">3</span> The function
@@ -564,7 +565,7 @@ <h1><span class="header-section-number">3</span> The function
 <span id="cb6-11"><a href="#cb6-11" tabindex="-1"></a><span class="co">#&gt; Computing 2.45 -ellipse for 19-th </span></span>
 <span id="cb6-12"><a href="#cb6-12" tabindex="-1"></a><span class="co">#&gt; Computing 2.45 -ellipse for 20-th </span></span>
 <span id="cb6-13"><a href="#cb6-13" tabindex="-1"></a><span class="co">#&gt; Computing 2.45 -ellipse for 21-st</span></span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 <div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" tabindex="-1"></a></span>
 <span id="cb7-2"><a href="#cb7-2" tabindex="-1"></a><span class="fu">biplot</span>(sunspots, <span class="at">group.aes=</span>century) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span></span>
 <span id="cb7-3"><a href="#cb7-3" tabindex="-1"></a>        <span class="fu">axes</span> (<span class="at">label.dir =</span> <span class="st">&quot;Hor&quot;</span>, <span class="at">label.line =</span> <span class="fu">c</span>(<span class="fl">0.8</span>, <span class="fu">rep</span>(<span class="dv">0</span>,<span class="dv">10</span>), <span class="fl">0.8</span>)) <span class="sc">|&gt;</span></span>
@@ -579,7 +580,7 @@ <h1><span class="header-section-number">3</span> The function
 <span id="cb7-12"><a href="#cb7-12" tabindex="-1"></a><span class="co">#&gt; Computing 2 -ellipse for 19-th </span></span>
 <span id="cb7-13"><a href="#cb7-13" tabindex="-1"></a><span class="co">#&gt; Computing 2 -ellipse for 20-th </span></span>
 <span id="cb7-14"><a href="#cb7-14" tabindex="-1"></a><span class="co">#&gt; Computing 2 -ellipse for 21-st</span></span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 </div>
 <div id="the-function-density2d" class="section level1" number="4">
 <h1><span class="header-section-number">4</span> The function
@@ -600,12 +601,12 @@ <h1><span class="header-section-number">4</span> The function
 <code>c(&quot;green&quot;, &quot;yellow&quot;, &quot;red&quot;)</code>.</p>
 <div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77,<span class="at">group.aes =</span> state.region,<span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span></span>
 <span id="cb8-2"><a href="#cb8-2" tabindex="-1"></a>  <span class="fu">density2D</span>(<span class="at">which=</span><span class="dv">2</span>,<span class="at">col=</span><span class="fu">c</span>(<span class="st">&quot;white&quot;</span>,<span class="st">&quot;purple&quot;</span>,<span class="st">&quot;blue&quot;</span>,<span class="st">&quot;cyan&quot;</span>),<span class="at">contours=</span><span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" 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" /><!-- --></p>
 <p>In this case, the vector <code>group.aes</code> is not specified, so
 all samples form under one group.</p>
 <div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77,<span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> <span class="fu">samples</span>(<span class="at">which=</span><span class="cn">NULL</span>) <span class="sc">|&gt;</span></span>
 <span id="cb9-2"><a href="#cb9-2" tabindex="-1"></a>  <span class="fu">density2D</span>(<span class="at">which=</span><span class="dv">1</span>,<span class="at">col=</span><span class="fu">c</span>(<span class="st">&quot;white&quot;</span>,<span class="st">&quot;purple&quot;</span>,<span class="st">&quot;blue&quot;</span>,<span class="st">&quot;cyan&quot;</span>),<span class="at">contours =</span> <span class="cn">TRUE</span>,<span class="at">cuts =</span> <span class="dv">20</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" 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" /><!-- --></p>
 </div>
 <div id="the-functions-interpolate-with-newsamples-and-newaxes" class="section level1" number="5">
 <h1><span class="header-section-number">5</span> The functions
@@ -645,7 +646,7 @@ <h1><span class="header-section-number">5</span> The functions
 samples is to be interpolated the call will be:</p>
 <div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" tabindex="-1"></a><span class="fu">biplot</span>(rock[<span class="dv">1</span><span class="sc">:</span><span class="dv">40</span>,], <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
 <span id="cb10-2"><a href="#cb10-2" tabindex="-1"></a>  <span class="fu">interpolate</span> (<span class="at">newdata=</span>rock[<span class="dv">41</span><span class="sc">:</span><span class="dv">48</span>,]) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img 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" /><!-- --></p>
+<p><img role="img" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAqAAAAJACAMAAABlpiR1AAAByFBMVEUAAAAAAP+zs7Ozs7Szs7Wzs7azs7ezs7mzs7qzs8Gzs82ztLOztLmztMmztbOztcSztrOztseztsmzt7WzuLyzubWzub2zub+zwc2zwc6zwdSzwdqzzee0s7O0s7S0s7i0tbO0trO0uNq0vdC0xf+1s7O1s7S1tba1t7O1zP+2s7O2s7S2tLe2tLm2trO2z/+3s7O3trO3t7S4s7O4trO5s8G5wbO51PK51be5//+6u7O6wdq8s7W8zue93vK93v+9//++5/+/s7bBs7PBs8HBs83Bwc3BwdrBz9rB2vLB3v/B5+fB5//FwrXF1efHtrfHtrzIs7jIs7/IybTJuLPJ8v/MzbfM///Ns7PNs7bNs8HNs83NwbPNwdrNzcHN5//Pt7PTtrPTubfVurPVvLPVvLTVw8HV///XurTXxLPX1//X///avLnav7PawbPawcHaxMHa2sHa2s3a3sfa8vLa8v/d573eubPevbTe///nyLPnzbPn07zn5+fn8trn//Ln///y2sHy2s3y58Xy8tfy8vLy8v/y/+fy////fwD/ubP/583/59X/5+f/8sn/8s3/8tr//7n//8n//9D//9X//+f///L////cq5XGAAAACXBIWXMAAA7DAAAOwwHHb6hkAAAbA0lEQVR4nO2dh2McSV5G7fIui73HAUfGNnkJR845mt3D5IyxlzM5s8sBIhk4iSghgu44af5deoKkmV/H6kpfd7+3K1kz6qn6auapuqqnu+bOCkCYO6UDAHSBoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIg6AgDYKCNAgK0iAoSIOgIA2CgjQICtIgKEiDoCANgoI0CArSIChIoyzonQi4GIXMhrBno4wERWodRpRsLkYhcyHoyUBQS5xsGHpD2FOBoJZI2TD0GgSNS6xsGLol8HlAUEu0bG6FpSsEjU68bA4/w/9EEdQSUVD8RND4IGhMgp8CBLXEHINiKIJGJ0K2/z6+/mnxhiJodIKyXf7c4x9Zfeot95mnuzuWbKiLMUtEUEuYoL/nXv9VV/Hpf7e7Z8mGxhiFI6glLNvVH7odT3f3LNlQF64ogloCs/2Nu7fx8yuux6HLFnTLuXt42rlhOwhqCcp29d6u//zu2/uWa+iNn49WF08eHHdu2waCWsKy/d/jx49/ybkf3b9vsYZeN/yfj6pvl8+PxpSBoJbAbJ9Y95+f+/TgvoUaetPsi7fXvef5045tW0FQS2i2T/3Ad9a6imUaetvqiyfVGPTk5ZhCENSSJNsSDT1o88UTN6oDRdAaabIt0NA4TUZQS6JsizM0UoMR1IKgcUDQRKTKtjBDYzUXQS3Jsi3LUARNRbpsSzI0WlsR1JIw24IMRdBkpMy2HEMRNBlJsy3F0HjtRFALgkYAQdORNtsyDI3YSgS1JM62CEMRNCGpsy3A0JhNRFBL8mzzNxRBU5I+29wNjdo+BLVkyDZzQxE0KTmyzdrQuI1DUAuCBoKgacmSbcaGRm4aglryZJuvoQiamEzZ5mpo7HYhqCVXtpkaiqCpyZZtnoYiaGryZZujodHbhKAWBA0BQZOTMdv8DI3fIgS15Mw2O0MRND1Zs83M0ATNQVBL3mzzMhRBM5A525wMTdEWBLXkzjYjQxE0B9mzzcbQJA1BUAuCjgVBs5A/20wMTdMMBLUUyDYPQxE0DyWyzcHQRG1AUEuRbDMwFEEzUSbb9A1F0EwUyjZ1Q1PlR1ALgo4CQXNRKtu0DU2WHkEtxbJN2lAEzUa5bBM2NF10BLUUzDZdQxE0HyWzTdXQhLkR1FI020QNRdCMIKg3KVMjqKVstkkaiqA5KZxtgoYmjYygltLZpmcogmaleLapGZo2L4JaymcTMfTu3buDtkPQvAhkkzD07t2BhiJoXhSyCRh69+5AQxNnRVCLQjYEvQFBLRLZyhs6VNDUSRHUopFNxND+zRA0NyLZJAzt3yh5TAS1qGQrb+gQEDQ7MtmmYGj6jAhq0ck2AUMRND862fQFzZAQQS1C2eQNRdACKGUTNzRHPAS1SGXTNhRBS6CVTdnQLNkQ1CKWTdhQBC2CWjZZQ/MEQ1CLXDZVQxG0DHLZWkUYesp7IhC0DHrZWkwYfMp7GjJ17AhqEczW6MLgM4oTgaCFUMzWJENhQXONjBHUIpmtQQcEnV2tw9DM1mZo/iRbsh1aQFCLaLZmQ/Pn2IGgxRDNpnU0NF8aBLWoZpMyFEHLIZutLkWxfXzGPxYEtehms1qUmyUhaEGEsx16Ue44U87RBoJalLMdmIGgc6t1GMrZDtQoJmjW6RqCWpSzNRhaOENyENSinK2+ky+eITUIalHOtlI4HJo3AYJalLOtKW4ogpZFOduGwoZmrh5BLcrZtpQ1FEELo5xtR0lDc9eNoBblbNcUNBRBS6Oc7ZpygmavGUEtytluKGYoghZHOdsthQzNXy2CWpSz7VHGUAQtj3K2fUoYWqBOBLUoZzuggC0IKoBytkOy61Ki00ZQi3I2Q25hEFQB5WwGBJ1XrcNQzmbJa0yRAwcIalHOViOrMwgqgXK2OhmlKXPkFUEtytkayKcNgmqgnG3VcB1SLm8KvbmKoBblbI1XcmYyB0FFUM7WeC18HnNKnZ2ypIHFMJSzNS/WkOU1LCJKpSc9qEU5W8tqIhnkKXJqyrpSBLUoZ2tbTSS9PvkF3e3cEdSinG3VtppIan/yn5dyXSOCWgoNywNJHDrzc7L3GiCo5U719OSX9OzsLKyApIkzv+e/Xx2CWrbZMjt6tvsaj4agEZYzM088glpusmV09Gzv+1hShh1adviCkLXnHEEt+9ly7exjCJrQUC8/QwxteLYR1GKz5XA0iqDpDM0kaOMTjaCWhmzpO9KbMWhYBxQpzdhigwRteYoR1NKSLbGju1l86C4yVpyRpY6P3/rsIqilPduhoylkCB/ExcsyqsyR4Tv++BHU0pltb2cvKWiKVB1Fxlkkv3PfhKCW3mxbR5Ps8RUF7fYz+nFPC4JahmRzzdOm4LeDYhxIDEzgUWCMD2rq/TtHUMvAbA2Khr8dFGOnGdnQvg40rL/vD4uglmHZdrv5/Wc4zsHMcOIamlDQQaMkBLV4CLr94fonFUGjGtpZVvzD8nUQ1OKfbeeojKAxDe0uqs3Pfm8HzzER1DIq22ZnH2MMGodQQ28EG1dQb8/qcQgEQS092f7eudd/uvE3zoXP4iMRKOitYP0FNajYNzb1OkKHoJbObFd/9ubmEJN7/ad+/g/qvy5xqnMjQSluBRvkZ03FbkE9nyEEtXQL+g8/+C9vuWs++7hhEw1HQzJ4CNroYpeg3k8Oglo6sn3CvfH+X/2m2+O1X2vaTsHRgAShgraPQUc8Lwhq6cz2n/e+2rnHOzu/qmPDRDt7j1FuqKGDimjpLJv9HPWMIKilM9v/fHht3udcS/p1nSXFd9TrOEGYoQNLGH4odOSTgaCWrmznX/QLzn3edpb0pX9979ua9/B7xO1IPY+0htY86PHD/Bz/NCCopSvbP57vjT+/5/Ufc987oMB4jvq+FRBYb7Q/rZAnAEEtfdluJL33BZ/1xsAyIzmaV9BYfoa1HUEtA7L91+//xF9uBqNDOtAdUXb2vu9VBdUYR9DQViOoJWG2cEd936sKqC+w+902NfyPEkEtabPlfq9pfGVhve+mmTGaiqCW9NmyOjq2qtAJVqy/RAS1ZMmWsSMdWU8EQcNK2IGglmzZcjk6qpYYHSg9aBJyZsviaH5Bt+PP27Zd/fv4shDUkjlbhp39iPJDIu3as/1+9a9/fPWeezS+NAS1FMiW2lH/0gMm//sPrdx0H/gW96HRpSFonTLZ0nak3kWPnvsfPPDy1x+/5b7ku16eBHShCGoply2ho54Fj535Hz7uf799M1X6gHMfOnk6rkQErVM0WzJH/YodN686fNTlM+fedO6ND7v7q7/9yt84HVPkCkHrlM6WaGfvU+aY+ht7zzcfu8df6z7tTz75jd+PoLFQyJbCUY8SR0yqzEOu/tR9h3PfWhn6+LG759xrv+Jd5A4EtYhki96RDi/Nf0pVe8TVb3/DB3/Gffn1qbP3fti3yBsQ1CKULa6jg8vynVE1bf+7P/tHH1zv47+m6j2/76VfgQcgqEUrW0xHB5bkOZ9q3Pzqz7/4l537ss049LWf/DevEg9BUItctng7+2HFeE2nWjaupvCf8TvfVAX//F888iiuAQS1SGaL5OiQQnwmU63bfvLrf+i3qszfHNJ3bkFQi2q26vXOsrrt8KGq2dKku3we2HduQVCLbrYYS8L36jfUz1rveTfGiuB1ENQim20nQH2/6mNFJEFbVwyLbiiCWmSz3bz+ZtbkZ0WPgIP8dO0rhkU3FEEtstkOXv5bR32t6FZwyCDV3VZ5WzGC5kI3m3n1dx2ptxWdDvYPAdxelXs1G0GjeYqgFuFs9Vfd7XdnQ+mQsG8AsO23r6s8FPKuvekRqR0EtShna6JpQNj3kBG/We1P3Pc7UCvo3i2vUC0gqKVstjEv692mqX0nbVt3lWInZqsmQW9/jaCpKJpt/Ovq9V6Tv6DNpdsx6MH9CJqGktnCXliPN+2bt2t9dGu5h1Ie3M8YNBHTFXTNUEcbt2p56JjzAJjFJ2Pagq6GdqQNm7R0q1kXO6uBoJaJjkEPGeBofYOmhxT/vBIEtUxvFt9Mr6P21019amk9EbSOcjZPenb2rvOmhJ4IWkc52wi6HHWtN1YieiJoHeVs42jtSDsEFdETQesoZxtPs6Ou8cf4egaMrBHUopwtiCZHXcNP8XvPw2MTfrYiqEU5Wyj1nb2r/xB9597wPv3wByOoRTlbM54n27mmoae7+W2cTPscCOr7XgSCWpSzNTLidLt9SffXQ04zNULQqChna2Lk26O3jrrdV7qZe8iZeAhqUc7WxPj373cd6e4r5YElM0diDBqCcrYmgk/RW23+y3fck1l8GMrZGolwhp7MYfk6CGpRztZM6Akm8T51KwEIalHOloLdPj7mQo/xTslC0DrK2eKz+VC41c00Poqk8a73WCFoHeVssdl9qPvNt1WMjjTiFXMrBK2jnC0uB59ZuP+2fJijCJoW5WwxOThQv1rZ05naJe2TD0HTopwtHrf+1X+42aTvWvgWGIMmRTlbJA7Uazzj7nbDlnVqO8tnFp8SrWwxX+sdjWcz1X7e2/zg7rg78H4Q1CKVLb4MrSeE1m7sP+b2FwhaGqVs0W2oDytdx62DB14/NK+fCFpDKVtkQTuv+Wi+ffjw69VBh1YYITuCWpSyRRW077K5xtu1MnyOkcYIj6AWqWzx/GwWa9j6N7akgY5G+fNCUItWtkh+tjk1eAkxW9yQrRA0CcrZRtKqk88ijLUyeyVF0CQoZxvF0LVveu5tLLl7U8agKVDONoIuh7w61rbiuypgFp8A5WzedHdx7Uc9PStJeDo+glqUs3nSI86IvrW9plSSIqhFOZsXvcpEFHRbXwpHEdSinM2DMWuAD/1lR6XRHUVQi3K2wYz8GIXBv+2qOa6kCGpRzjaQPUXOzs7aNuorJKT+eI4iqEU52yD27TjbfTVt1ltOWIhIkiKoRTnbAA68ONv7Xtuwv6jgKBEcRVCLcrZejBIdgg56yz1CntAyENSinK2Hmg3RBR23zmOIpAhqUc7WSZMHrWPQgWeEmNsBCz2OeNQGBLUoZ+ugRYG2WfxAYQ43Czk9aWxHiqAW5Wyt+L74w09Y2r8Rev7cGEcR1DI0W9ZLx7rxf92HP2B/ywgneHo7iqCWgdkyX9zYwYhuyecRNUO9a7MFekmKoJZh2XJfHt7KqJGd12OMoSOqayhzcGwEtUxK0HETj1QDVr9Sh0mKoJbpCDr64I2EoJuS+1uAoJapjEHHH1pMOKXyp68jRVDLNGbxIe/OpJ1UjaDLUQS1CGVr/RsIevMw+axqDK2OIqhFJ1vbKCLwBIwc86pRVTRKiqAWmWwt87Dg84NGXs0RWOvAWmqtQ1CLTLZGQcNPsRx9LUdoxUPrOZQUQS0y2RoEjXEGsLqgm7puG9r0cly8fZw4gIwEDehks35GuYhifBk5Db11lB7UIpTtwM9I1/hkPTwVxmZnf2d1+eJj7v7RanX5zD04Xl288+6Df6IHlSPWdZJhV8LFyeBVpavEfHh6Xqn56unq5NHq4slLdvFyxLuMt8ARqjCqHvTZy9XV+0eXz4+qzvR4LSeCahHxKvMyh6hCqAStzFy9elnt4V21q0dQtWxRF+oodpDqFs+3iLeCrnvQFxsrEVQrW9x1ZCJcRxxagO9JNutd/KPV+cPT9Ri0+gdBlbLFXour4GHUHd6nKa570I9ez+KrfxBUJ1v0peKilBdWyChBj4KqHIOOBHVUsiVYbbP4kVQEjUB4thhniqZYDDZWkeGGemzPO0mW4GwRzrVPs562xsFU71l8CeYsaPjVSqmWe9c5nOoBglpKC5rsIzPyHU+NeTUMgloiCTryJUr4iS7ZBI16PSGCWuKMQceuAhdaeUfZuUqLe0U2glqizOJHvUJ7eia4ZDTbMX8ETUspQfd7zwQX3Ufvm1sLRNC0RMg24gW60XP9yBTLlmQ87O8fvmN7BLXEyOb7At32nnf3iBDktoaYhfWVOcLP1kcgqCV7Nnc49pyOoLEK7Wwuglp6srV/MtY4Difuk/ITQYvQna3jk7HGYI8rXb9W+iPQiMUiqBed2bo+GcufhsOeCebvq4RvTUY0tOV3CGrJJmjzUfkUfqZc4TNKKcziPcgkqDnsGaHEjromWvYaBLVkGYMe9J5pduv7tU22cAStk2EW3zhzDy61vbp0RacvHkEtybO1zdzTVZiu6PTlI6glcbb61AhBu0BQS9JsjTP3ifuZtgYEtSTM1na6Z9o5Uo7Vu9MVjaCWZNlSno3cVe20K0FQS6JshfTMtrh8qoIR1JIkWzE98y0tn6hcBLUkyFZOz4xXCCeqCEEt0bOV1DPjFewImonI2YrqmXWJhTRVIaglarbCeuZdETlJZQhqiZittJ7ZPzomQZkIaomWrbye+T84Jn6RCGqJlE1AzwKfeRC/QgS1RMkmoWeRzzWq3xX2Ri6CWiJk09CziKD1OgNPhUFQS3A2FT01BA09mRBBLYHZdPQs4metVgSNTVA2IT1LCWqqRdDYBGST0rOUn42Gji8MQS1jszktPQsKWjc0oCwEtYzLpmZnST+j1o2gljHZ9PQsK2jEyhHU4p9NUc+yfnbW7rfLR1CLbzZJPUsL2reE/fCCENTil01Uz9J+tgfwPeyEoBafbKp6CgjalgBBQxmeTVdPAT/bMiBoKEOzCeupIWiXocMLQVDLsGzSemr42WGoRxkIahmSTVtPcUH9QFBLfzZ1PWUEjZEDQS192fT1lPEzRhIEtXRnm4CeSoKGR0FQS1e2Seip5Gd4GAS1tGebhp5igoamQVBLW7ap6CnmZ2geBLU0Z5uMnnqChgVCUEtTtgnpqecngsalnm1KeioKGhQJQS0227T0VPQzKBSCWg6zTUxPUUEDUiGoZT/b5PQU9TMgF4JabrNNT09dQUcHQ1DLdbYp6qnr5+hoCGrZZpuknggaC3VBJ6qntKAjsy1Q0MsXH3P3j6p/n7kHx6uLd9598PH3/8K5p+fV1ybbZPWU9nNkuiUK+uzh6Xml5qunq5NHq4snL1dX763/rb7ePp5w77lSF3RUvEUKWin5/tHl86OqMz1eS1nd2nyt75IefvSg4mfrVUcjAi5R0LWGr15We3hX7eoRNDod1236J1yooOse9MXx+taMBFXyM5qhSxT02aPV+cPT9Ri0+gdBY9O9NINvyCUK+vyj17P46p/5CCriJ4KGstGwHQQNpXvtEM+YCGqZqqAyfvatHeIXdIGC9qCcrQshQXvwSoqgFuVsHUzHT7+sCGpRztbBlAT1CYugFuVs7UzKT5+4CGpRztYOgkZFWQLlbK1MzE+PwAhqUc7WyuQEHZwYQS3K2VqZnqBDIyOoRTlbGxP0c2hoBLUoZ2tjkoIOS42gFuVsLUzTz2G5EdSinK2FqQo6JDiCWpSzNTNZPxF0DMrZmpmuoAOiI6hFOVsjE/ZzQHgEtShna2TSgvamR1CLcrYmpu1nb34EtShna2LqgvY0AEEtytkamLyfPU1AUItytgYQNAXKEihnqzMDP7sbgaAW5Wx1ZiFoVysQ1KKcrc48BO1oBoJalLPVmImfHQ1BUItythqzEbS1JQhqUc5mmY+frW1BUItyNguCJkJZAuVshjn52dYaBLUoZzPMS9Dm5iCoRTnbITPzs7lBCGpRznbI7ARtahGCWpSzHTA/P5vahKAW5WwHzFHQeqMQ1KKcbZ9Z+llvFoJalLPtg6AJUZZAOdseM/Wz1jAEtdxZnZ2dlQ7Rz2wFNS1DUMudtZ36hs5X0MOmIajlbO+7LjP287BxCGpB0PLstQ5BLZMQdN5+7rcPQS2TGIMiaFqkBZ3ALH7ufu61EEEtytmumb+gN01EUItyth0L8POmkQhqUc62YxGC7lqJoBblbFuW4eeunQhqUc62ZSmCbhqKoBblbBsW4+emqQhqUc62AUHToyyBcrY1C/Jz3VgEtShnW7MoQVeuejkunjj3cnXxzrsPji+fuQfH1/ckRFkC5WxrliVo1dzL50eri7ePL55USr56ujp5dH1PwlqVJVDOtlqcn7uX4/LF8drItZnVj7t7kteqiXK21TIFfeWqHftG0GfOuftHu3sS16qKcrbl+Vm9HJfPXm528WtBd73n9p6kteqinG2Rgq5VvPjxo42R1Rj0/OHp7p6kteqinG15fq5fjhPnvvDdlxtBq338eg+/vSdtrbIoZ1umoIupdRjK2ZbnJ4LWUM6GoLOudRjC2RboJ4LWEM6GoPOudRi62ZboJ4LWSJUt/FpRBJ15rcNIlC38avtF+omgNdJki7BeCYLOvdZhqAq6TD8RtAaCSoGgFtUxKILOvtZh3ElENYsPebiLlWNqlJGgSK0AA0FQX67ecw//43nKUyBhDwT15Oq9pxcfOT1/eFo6yEJAUE/WF4195DTthWJwC4J6su1BT+hBM4GgvlRjUOfwMxcICtIgKEiDoL5sdvGPSqdYDAjqSTVJqr6fYGgmENST7QEmDjPlAkF92XSe9KC5QFBPNqtmrUm6ZBZcg6AgDYKCNAjqywk7+JwgqCeXz4/OHzFJygaCenL54nj7f+kgCwFBPbl6/6j6P+2qwnALgvpSuXnu3NPSMZYCgoI0CArSIKgv5xxmygmCenLJBZ1ZQVBPOMCUFwT15YQJfE4Q1AvOZcoNgoI0CArSIKgvJw9PT5xL+el/sAeCenL5/Kj6n/fic4Ggnly+OD7Zfsov5ABBfTlx94/O2cXnAkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkAZBQRoEBWkQFKRBUJAGQUEaBAVpEBSkQVCQBkFBGgQFaRAUpEFQkOb/ATHrPVnTD3JfAAAAAElFTkSuQmCC" /><!-- --></p>
 <p>The function <code>newsamples()</code> operates similar to samples,
 allowing changes to the aesthetics of the interpolated new samples.
 There is no argument <code>which</code> for <code>newsamples()</code>
@@ -657,26 +658,26 @@ <h1><span class="header-section-number">5</span> The functions
 <div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" tabindex="-1"></a><span class="fu">biplot</span>(rock[<span class="dv">1</span><span class="sc">:</span><span class="dv">40</span>,], <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
 <span id="cb11-2"><a href="#cb11-2" tabindex="-1"></a>  <span class="fu">interpolate</span> (rock[<span class="dv">41</span><span class="sc">:</span><span class="dv">48</span>,]) <span class="sc">|&gt;</span></span>
 <span id="cb11-3"><a href="#cb11-3" tabindex="-1"></a>  <span class="fu">newsamples</span> (<span class="at">label =</span> <span class="cn">TRUE</span>, <span class="at">label.side =</span> <span class="st">&quot;top&quot;</span>, <span class="at">col =</span> <span class="fu">rainbow</span>(<span class="dv">10</span>)) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 <p>Suppose constructing a PCA biplot using the three variables in the
 <code>rock</code> data, and interpolating the other variable.</p>
 <div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" tabindex="-1"></a><span class="fu">biplot</span>(rock[,<span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">4</span>)], <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
 <span id="cb12-2"><a href="#cb12-2" tabindex="-1"></a>  <span class="fu">interpolate</span> (<span class="at">newvariable =</span>rock[,<span class="dv">3</span>]) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img 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" /><!-- --></p>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 <p>We can change the aesthetics of the new variables with the
 <code>newaxes()</code> function which operates similarly to the
 <code>axes()</code> function.</p>
 <div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" tabindex="-1"></a><span class="fu">biplot</span>(rock[,<span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">4</span>)], <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
 <span id="cb13-2"><a href="#cb13-2" tabindex="-1"></a>  <span class="fu">interpolate</span> (<span class="at">newvariable =</span>rock[,<span class="dv">3</span>]) <span class="sc">|&gt;</span> </span>
 <span id="cb13-3"><a href="#cb13-3" tabindex="-1"></a>  <span class="fu">newaxes</span>(<span class="at">col=</span><span class="st">&quot;red&quot;</span>,<span class="at">ticks =</span> <span class="dv">50</span>,<span class="at">X.new.names =</span> <span class="st">&quot;shape&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 <p>The function <code>interpolate()</code> will also work if new samples
 and new variables need to be interpolated at the same time. For
 example:</p>
 <div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" tabindex="-1"></a><span class="fu">biplot</span>(rock[<span class="dv">1</span><span class="sc">:</span><span class="dv">40</span>,<span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">4</span>)], <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
 <span id="cb14-2"><a href="#cb14-2" tabindex="-1"></a>  <span class="fu">interpolate</span> (<span class="at">newdata=</span>rock[<span class="dv">41</span><span class="sc">:</span><span class="dv">48</span>,<span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">4</span>)],<span class="at">newvariable =</span>rock[<span class="dv">1</span><span class="sc">:</span><span class="dv">40</span>,<span class="dv">3</span>]) <span class="sc">|&gt;</span> </span>
 <span id="cb14-3"><a href="#cb14-3" tabindex="-1"></a>  <span class="fu">newaxes</span>(<span class="at">col=</span><span class="st">&quot;red&quot;</span>,<span class="at">ticks =</span> <span class="dv">100</span>,<span class="at">X.new.names =</span> <span class="st">&quot;shape&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
+<p><img role="img" src="data:image/png;base64,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" /><!-- --></p>
 <p>Notice that <code>newdata</code> has the same number of variables as
 the data sent to <code>biplot()</code> and <code>newvariable</code> has
 the same number of samples as the data sent to
@@ -689,7 +690,7 @@ <h1><span class="header-section-number">6</span> The function
 <code>prediction()</code> is used.</p>
 <div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" tabindex="-1"></a>out <span class="ot">&lt;-</span> <span class="fu">biplot</span>(rock, <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>() <span class="sc">|&gt;</span> </span>
 <span id="cb15-2"><a href="#cb15-2" tabindex="-1"></a>         <span class="fu">prediction</span> (<span class="at">predict.samples =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" 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" /><!-- --></p>
 <p>In addition the predictions are computed and can be accessed with the
 <code>summary.method</code>.</p>
 <div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" tabindex="-1"></a><span class="fu">summary</span>(out)</span>
@@ -756,7 +757,7 @@ <h1><span class="header-section-number">6</span> The function
 only the mean values of the Central and West regions are predicted.</p>
 <div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" tabindex="-1"></a>out <span class="ot">&lt;-</span> <span class="fu">biplot</span>(state.x77, <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> state.region, <span class="at">show.class.means =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
 <span id="cb17-2"><a href="#cb17-2" tabindex="-1"></a>         <span class="fu">prediction</span> (<span class="at">predict.means =</span> <span class="dv">3</span><span class="sc">:</span><span class="dv">4</span>, <span class="at">which =</span> <span class="fu">c</span>(<span class="st">&quot;Income&quot;</span>,<span class="st">&quot;Murder&quot;</span>,<span class="st">&quot;Population&quot;</span>)) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" 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" /><!-- --></p>
 <div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" tabindex="-1"></a><span class="fu">summary</span>(out)</span>
 <span id="cb18-2"><a href="#cb18-2" tabindex="-1"></a><span class="co">#&gt; Object of class biplot, based on 50 samples and 8 variables.</span></span>
 <span id="cb18-3"><a href="#cb18-3" tabindex="-1"></a><span class="co">#&gt; 8 numeric variables.</span></span>
@@ -775,10 +776,10 @@ <h1><span class="header-section-number">7</span> The functions
 <code>&quot;FALSE&quot;</code>,<code>&quot;x&quot;</code>,<code>&quot;y&quot;</code>,<code>&quot;xy&quot;</code>.</p>
 <p>Here the biplot is reflected about the x-axis.</p>
 <div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> state.division) <span class="sc">|&gt;</span> <span class="fu">reflect</span>(<span class="st">&quot;x&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 <p>Here the biplot is reflected about the y-axis.</p>
 <div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> state.division) <span class="sc">|&gt;</span> <span class="fu">reflect</span>(<span class="st">&quot;y&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 <p>The function <code>rotate()</code> allows for the user to rotate the
 biplot display by a certain value of degrees. The default is 0 and
 positive value results in anti-clockwise rotation and negative value in
@@ -786,7 +787,7 @@ <h1><span class="header-section-number">7</span> The functions
 to 100 degrees, then the biplot is rotated by 100 degrees in the
 anticlockwise direction.</p>
 <div class="sourceCode" id="cb21"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scale =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">PCA</span>(<span class="at">group.aes =</span> state.division) <span class="sc">|&gt;</span> <span class="fu">rotate</span>(<span class="dv">100</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
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" /><!-- --></p>
 </div>
 <div id="zooming-in-on-the-biplot-with-zoom-true-in-plot" class="section level1" number="8">
 <h1><span class="header-section-number">8</span> Zooming in on the
@@ -801,9 +802,9 @@ <h1><span class="header-section-number">8</span> Zooming in on the
 <span id="cb22-3"><a href="#cb22-3" tabindex="-1"></a>  <span class="fu">samples</span>(<span class="at">which=</span><span class="cn">NULL</span>) <span class="sc">|&gt;</span></span>
 <span id="cb22-4"><a href="#cb22-4" tabindex="-1"></a>  <span class="fu">density2D</span>(<span class="at">which=</span><span class="dv">1</span>,<span class="at">col=</span><span class="fu">c</span>(<span class="st">&quot;white&quot;</span>,<span class="st">&quot;purple&quot;</span>,<span class="st">&quot;blue&quot;</span>,<span class="st">&quot;cyan&quot;</span>),<span class="at">contours =</span> <span class="cn">TRUE</span>,<span class="at">cuts =</span> <span class="dv">20</span>) <span class="sc">|&gt;</span> </span>
 <span id="cb22-5"><a href="#cb22-5" tabindex="-1"></a>  <span class="fu">plot</span>(<span class="at">zoom=</span><span class="cn">TRUE</span>)</span></code></pre></div>
-<p><img src="data:image/png;base64,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" 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" /><!-- -->
 With the final plot then rendered as:</p>
-<p><img src="data:image/png;base64,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" 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" /><!-- --></p>
 </div>
 <div id="the-function-translate_axes" class="section level1" number="9">
 <h1><span class="header-section-number">9</span> The function
@@ -817,7 +818,7 @@ <h1><span class="header-section-number">9</span> The function
 <span id="cb23-2"><a href="#cb23-2" tabindex="-1"></a>  <span class="fu">PCA</span>() <span class="sc">|&gt;</span></span>
 <span id="cb23-3"><a href="#cb23-3" tabindex="-1"></a>  <span class="fu">translate_axes</span>(<span class="at">delta =</span> <span class="fl">0.02</span>) <span class="sc">|&gt;</span></span>
 <span id="cb23-4"><a href="#cb23-4" tabindex="-1"></a>  <span class="fu">plot</span>(<span class="at">exp.factor=</span><span class="dv">3</span>)</span></code></pre></div>
-<p><img src="data:image/png;base64,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" 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" /><!-- --></p>
 <div id="refs" class="references csl-bib-body hanging-indent" entry-spacing="0">
 <div id="ref-GowerHand1996" class="csl-entry">
 Gower, J. C., and D. J. Hand. 1996. <em>Biplots.</em> Chapman &amp;
diff --git a/vignettes/class_separation.html b/vignettes/class_separation.html
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--- a/vignettes/class_separation.html
+++ b/vignettes/class_separation.html
@@ -60,7 +60,7 @@
 }
 @media print {
 pre > code.sourceCode { white-space: pre-wrap; }
-pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
+pre > code.sourceCode > span { display: inline-block; text-indent: -5em; padding-left: 5em; }
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@@ -553,7 +553,7 @@ <h1><span class="header-section-number">2</span> The function
 <div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77) <span class="sc">|&gt;</span> </span>
 <span id="cb2-2"><a href="#cb2-2" tabindex="-1"></a>  <span class="fu">CVA</span>(<span class="at">classes =</span> state.region) <span class="sc">|&gt;</span> </span>
 <span id="cb2-3"><a href="#cb2-3" tabindex="-1"></a>  <span class="fu">plot</span>()</span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 <p>Fitting <span class="math inline">\(\alpha\)</span>-bags to the
 classes makes it easier to compare class overlap and separation. For a
 detailed discussion on <span class="math inline">\(\alpha\)</span>-bags,
@@ -561,11 +561,19 @@ <h1><span class="header-section-number">2</span> The function
 <div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77) <span class="sc">|&gt;</span> <span class="fu">CVA</span>(<span class="at">classes =</span> state.region) <span class="sc">|&gt;</span> <span class="fu">alpha.bags</span>() <span class="sc">|&gt;</span> </span>
 <span id="cb3-2"><a href="#cb3-2" tabindex="-1"></a>  <span class="fu">legend.type</span> (<span class="at">bags =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
 <span id="cb3-3"><a href="#cb3-3" tabindex="-1"></a>  <span class="fu">plot</span>()</span>
-<span id="cb3-4"><a href="#cb3-4" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for Northeast </span></span>
-<span id="cb3-5"><a href="#cb3-5" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for South </span></span>
-<span id="cb3-6"><a href="#cb3-6" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for North Central </span></span>
-<span id="cb3-7"><a href="#cb3-7" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for West</span></span></code></pre></div>
-<p><img 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g8P9tS12O9UUDUXRXzddtSK+zS3bO1tA8CggcCD4aJn0bMJads3YuubS3d/v6bvwPjrt2+sb9LG7ZsZ0qLxepEaGw8nV/Pfaxl7t77SFrF9o/X5JrZvsFmA2zf4W6Ql8Knfg7lT2X7ofAgQfZI5b2FH4TsYEE0QLUbz33Rrw/RXae4HZ37d/FrrhY0tvTrO2Lp0V262Nhr7M09NyHeXnD5EvrvEvoddqnWd7GtunxJywvP38+jRo2EvwYrnko7/6yOV/3rsvpORigqaYfpjiyqxZhN5HpEiFsO/Keie8Pz9hDAG77GkWrFIuVyyVswr/JyyW01ZbXjVat/Rn64iwy5Mf2xRBS56AABoj+cNh6KcEhHVqjTHc0k+e1o1JdfFiHYYdQdgMEDgAQChI4TmuydccvZ0X5L2KZUkUmrHUynNfo/p6m5hB5F4EDyYBw8AAG1wu+GoFaX9KtF0dmV5WeSK0v6+VKXp7MpykshF2gEYGBB4AADoilrxiFsRRU6R87tFTszlRDGnvmKJuDuiGvEIQYPggIseAAC6QVFoNskREcdf1aPuSgwRdxAaIPAAAOCFm3+e46j0WG03z3FT1WqNYsTdkeuQdhASIPBguKhNY63NardvdDVvdftGqx+O2+h31zX0b85raxmdvMdjwds3/CyO+RqW3Vrvd57YFzJGJsMumROvasl0sznxb5L0n+TDy5cS/g+AVDsQKBB4EAY21/sgOds31je7eFMsxj9oTXlVB873IvJdLcPzeLH1J1pHna3PbrkMod2+EeNvkbabfP0Bz4h4+eiJpSfPfXTY80ubuw2O4zSffH2zUChROh0f4OIA8AQCD0LA0tJShyPe+0P53ufrmxtb7JRXWrsv311qda0dNuV7324a8+xp7f6W8xDa7YebrbH3lLn5x7vMGUVX/MBgquAS/EI224n5rgIjHgQHBB6EgM9u//EueQ1PZ3zMjAG7fSP2+b17xkvrm0Sb68weRy2ftaODoPzDgz2HfvGZm7e3thjNdxo9R7pTvbWyG9vqruwy2BVqS2Dd5e3dFuUfHpjF2XkI7fbDTVq6fq21W2bus1ab/qMnfgbnADse5rtDMl08kYD5DsIEBB6EgszN2xtufvrtG7H1Tb21+9Znt1jv896tB5/qvme9z7yuzZu3NNe7fHdpc93u2baJp8HamiGH5XufM67vu2R2kW+uf/sp+xF080frMowV3l9Tvwpp38RlVXZMM2czc5+1fYNxctQBuPKzvaUn3/YxxwD0N08eRjwICAj8GPNzLKj/umHt93cd/fSqj1rWo8Zr97c2iNnPZLeaMVzWmWvXl8zj3onIOnfWme0/3NpjXd8/ml3k7T7CskLThDmPt5jXaMc2Ko//dMl1nv32w03ao1aWwe1nLmH8cBCeDDvHlbh1pgMghKDRzRjzm3D12Mjc/OPdB/xX966xEXHNzL7NbOE/XaLNZzJRhoi8Ysutlzoxe02ooe1rlk+/9XD7vmrj+/kIZoVr95u6a2D7Rmx9k4i6XJiFzM3bG7fW1z//VP7xZsYyO3ftfrN5n9l37cuN9fU/bN9Eol3HBCftaHoDggAWPAgP6lB2j1C8ule3am3FZvY6s3eLZwrM+FtOJrVfWuH8ddpixtN6rtGOw13N2v3m1oa+VP7Z7ebWhpt7wjmMD0xYzHcY7mAUgcCDMLF2f2ujXT49433ujcy160t2bzeRlginB/ptw+m7rjIr3/vq1p6eTOB8DKeEPjffu5W1+8wCy0dPvLwb7UITQAed6cDoAoEH4WLt93fp1lffGipmV2E/oXN/ZK5dX3LwGJTvfbtJaqx87csNP0a+T+Rne2w6u1N8PXPzR0Olf7yZsX99yzHcKP/wYE89SeV7n1vS9VE11w7DfB+ktCPVDvQdCDwIGZmbtzf29vbMz2/xrRZ165u0cfumiz45GuQen/Xj1sbmOptYXr73Oc/k1a393pzrvn3DVx668zJMvnGtH067BatfX6/K376xvulQ2GfxOdD2Df4WaV8hc/P2hskjb8r0CxnhybCDTx5EAAg8CB1r97c2zM+bWxub61rs+sld2cW9vfblBu112oZu7b5WemfE2OmuzHS+ydz8Ub5Lxuu2vjidLEPtP6N9kW8/lZtbG9S+pc7a/dYC1p/clY1PZ21z0zky70Zr95tbpL8Uiz38ss0XGHNiRF+I4lB88jDiQX+JNZvI3IwUsRj+TUH3DPfvZ+gWfIzoTqEgCMKwFrA6Trn0uFgFDcrkAAAhR5Hzu6UT7cl0dmWZ5/r+GarpPFx1J9TLgb4CgQcAhBpFfqzMiWLSeJqXJOqvyhvh9kLfDgnA8EEMHgAQas6UqVSy9ZTjl8WV2WO51peDI5kORBgIPAAgFLgF4JMp2peK/dFzBnuBe2HY/nkVpNqBfgEXPQAg3CRzolgrStJ+a1NqUeypEwKsdjAOQOABAGGmzxl2qnFsV/eQmO8qSLUDfQECDwAIL/3NsIPhDsYKxODBMNm+Ye0LpzZjd9jmPCve12d4vXX7hp856UyLeMturfdrdL1O4ES/Muy8k+lCZb6rIBIPegcCD4aJfaCb/GxvY2Nj78EPfeo+r3WEdXtR7YzXbKrt7Jw1fvuG1t+u2Ww25esPeEbEy0dPLNNoMIW1QySdgDLsMC0GjC1oJBQ1Rqw5VPne5/ytz7YMWdy+Efv2063rD9YfXDearZbvfc4zTztj+0ZsnbYcZdd6XJddtbsAtkNs620ehx9NhvX3I0mS8dim9LWitF9tPU0tirkk+cKPTz6E5rtK5LvajdjFagSBBQ+GSmbuM3bgyvbDzaXr19auXV9q2fXlHx6w08+cBqraXlA95eV7n8fWN4k2150c8Jbjus1J3364SUvXr7V2y8x9RrqHoXz0xM9sN+AHUcf2SjInsvhS9wgUuMNLD3oEAj++xAL7rxNMA1n1IeaZuc9aUssOSC3f+5zxlt8lw6uuewI0tjY212M35Js/Nrc2iDa2mi7zVUyO/8zcZ76XrS1Zfra39ORb5xsO0AcUOW+48KW8rPh8m3+ffGjNdwB6BwI/vjQD+68j1r7c0E348g8P9lQpZzcyRvL2H5hJruqwV22eu2VM+tr99tFwp3HsDuNbbWkC5SNjWP32w03ao+tGCP72M5cwPugKLYVe5yo9bqvyETDcWWDEg16AwINhw3+6pHm85Wd7ukltbCz/8MDYaPOWt7zqa19u0OZ6ECns6jx1YyR8+d5Xt4wbg7X7TZNvYO1L/YYDdIJbhl1HKfRdJNPBfAfRBgIPhk1Gj7irAfiMeaP8bM+k6Xut0e2xWIw3xHbtflNuDVv3U63Gf7rksJUNyrcOvbWhfy7/7HZza8Mtqd85jA+6xH8KfYTz5GHEg66BwIOhk5n7jJ4clfUAfGvj5sNt80YiS02aqTAtc/NHIwTP2Nw6Ttl5br53K2v3mU+zrclMtwV9wE4yJ4qpqsSwq8yZc+y69snDfAeRB53swPBZ+3Jj/eEPPzzZ27i9xm6kbx/+gd249uUGbT6TidrVy63d39rYXLfsmbn5Y/Mmu9e160u3HhyVaU3bSX62R+wKXCj/8GBv6TpP9ho/9RCf3e6mnA/Y0avj3PvTRincDkDfgQUPQgD/6dKTB61Yu7Fxb3PTtHHt93eXWNN8+4ZujVta4m0/3GQsaVvinErm5u2NvVtfae/avrG+uXT393Z9377Bevy3b/C3SMvzU8PzjEd++6HzIUAXKHKVWxFFUVyZPd7V/PS1ou6x7zGZbrTMd3jpQXdA4EEIyFy7TnvmWLsahidLUl3m5o/yXTLC8OubG1tqktva/ebWZ63wfKszzdqXG7R3i3euYFu73zqatZmNIepr99WqO+uR9dfIiPvHHn7pUo4HOudMIY4jIuL45UU6khUiRTlNpWYjHXEHoI+gkVDUQHMo0AuD//txS6FX5PyuMqd1tVHk/GO6OqdMJ3N90fXRsuBVotfYDheroEEMHgAQRjh+WazJspLkOSKOX1kmItqsEyV6PfIoqjsAXQCBBwCElSSv5lGoPvlGRa4nxrdEAUPiQadA4AEAocZIpoun+XjPR4P5DsYHJNkBAEJKxPrO9g7S6UFHwIIHAAwNSZK+0DPsLM7nIKQd5jsYK2DBAwCGxhdM/jxrm8JwB6B3YMEDAIaD3dtsbAlC3aNhviPVDvgHAg8ACBEw3AHoF3DRAwCiTzTMdxWk2gGfQOABAMPhkSRZtsB8B6CPQOD7hCLn1TEYfh4ETAyAbgn+z9MEG0sOTt2jZL6rwIgHfkAMPng4ftmh03aAjFx751pROuLcJoK64tbDvL9vAUGj/rEORa4alcODF2dEM1mB77kBLgChAwIfPNrQjFR1t3RCtC/RophLGrOuKbWoztNQ5PxjZYqq1ZPUophLKnJ+t3RC7B7UmpBN09mVZU6Wqikxl9RHcXSqkOFAkfP7tCha167I+d3jWS/VF0WxU8Hu4i1g1HE13+tymTKCECeqy4VCCTIPIgcEfmAkcyvZU308Vq24f5pdEXlOkfO7xZom4CdVWhTFJBHVirvHsyviMqcqnbqHJoVikqhWlB7LK3OpU0WhJEdnCs1qSvjo0aNhfsuOqcnGxDDj7kUjlb3a5s3QeNA1jcb5RFxtfZvgBYGnulw4bCzMp3tvhzsQUC8H2oIY/FCoVavTs0mOiDh+LlWt6oH5VEqz1JM5UbddOW5K3abUjk/0HdTXk6mp45pCVKueqkcjoi+++EKSJMmWvhRWkjnNO6HI1dNpSi2KoriSnabUopjjufYuCVWwO/rILt4CRhSP6Hs8kTgvyfXWhgSfnajXGwNaGQDBAwt+WJyUdqWS9niaUyhp24MxaFMpfcdJ0y6THB3VFE45nWU92ap5qmrY6JiqHJ9b5nO1oiTts0EJH8COH0WGf/7j6fmFymGhUJq8rNrtjE0/GsCIB95A4IeFTcMU9kmtKO3ToijmtBC+tvlEOSNipJxLzpIsV836rmHI/AjKmBZ58A80HviHza2bF9LUqBwWCmdEk5cX5hGEBxECLvqhkEylqkeyQkRUK0p5WbG8riinLXc9qYJHXHJ2Wvfm6xV3XHL2lPHP21FlbFQ80rXiEbciiuJV/+a7AXz1wIKzf17LrRME4cKbQqFQkOvx9LwgCIIwMuF3BtTLAQ9gwQ8QLjk7XdKy6HOLVUn10U9nV3JWfeb4q9n8rqo906nUtGq5c/zyYlFTpOnsynJSO6biHaoeIY99MrecJCLifATfHYAdP6IMcrTMqOfWAeCf2MjVTAMTipyXuWXG2R+Lef2bBidmMd2QaA47Jtjpd4TADwX2tA90MmyjcnhwnmYr4uryYePS6Cr86siG4b0vVqB34KIfYRQ5L+0ez/Id+LMD8tjHGDdhbNguw04d73DUD55h3lTF0/MLE5VCoXBYUTPmRy63zgK89MAN3EBFDZ83xX302DsqOux44IHlbPfLgi8UCkQkCIKb+W5qXac/0ZPoR5gRNeJhwQcNzm/U6Og30xeZD6fAEzQ+xAQk8CqGzFtfaLni63Kh9DparetGUeMh8EEDF/1YI4pihB3U8NWPLaoRryq9gSW9ThAuvDHc9ABEEQh81OiiVW2PgXm7sR4G810FGj+2CIJgMeKj3boOkXhgBx6SqBGLxVSN78Lb3IvHPjxZ9Hbgqw8V9tPbRxd9m8mwatzdaF1XOXwZn4+Mm37kvPRw0QcNzm/UMH4zXat1JOUNGh8ehiLwUU2vszBaGg+BDxqc36hh+c10J/Mj0RWnU6DxISE4gfeYDKum163qG/4TUVTsdhMQeMCCTnYRp7s2diPU/M4/aFo3tqjpdavMlr8l+lODomW9A2AFN1BRw+OmuGtrvtO3qPH4EAbjqcOvgxuCIAjIgveKvjcqq/G0ffPA+uMOkhEy4mHBBw2y6McIoyiui8TyTnPLd2gnRjHjvw5XGiAd5ckjqb7vDOeeyUndAYg8uIGKGv472QUXmI9RbMdsHa2S5h8NiVkPO35YOJ7M3i14N/O9LhcqEwts9J0lkhY8ja3azZoAACAASURBVI4RDws+aGDBjymOdrm3tdpLV5wd2lH/C4lZ35FbAnb8qNKoVM4vZ9Jxqst3zE1vKLrqDoABkuzGl67z73pJvmMte1bjB2/ZG1/fzxdBgl6YcTXfX76YSAtxqsuViQVB2KHGKmlpddFWd7XpDUxjAIEfd7qQ+X7l2DuK/YCV3r9yQ+NHjcYHlxYmyoXDNzMTiUvXiIjiRHSv0ohY7TsAbiAEEjW6DmsZXuhOi8Xtb7HH4P1jROtpgGLvX7mh8T0SRAzeu3tdo3J4LT3Pbom2+a4yEmF4xOCDBuc3anT3m2Evu12Y5rbhYN0LPMsgU/Og8QPA7dT1IvBtetMSjVV6HUv4NR4CHzRw0UceRc7vlk6IiGg6u7LMc+3e0J3TPoiuOMZdwgCi9fDARw2tH+0MCfywlwLAcMANVNSw3BTXilI1JeaS6uO8wvtQeIZOZVvd/wvxi75Y8I4Eatb71HjcCnRH3y34ts75l/H0RsKhKe04WPAUeiMeFnzQwIKPNIp8VKWTqlQlSi2u8PzVyQ4P0FGqOfXbgnckULPepx0Pc38kiMcniBI7Ni/9mKg7ALiBihrsTXGtKB1xqleeteQZp31qUdvWjo5M+RjF7hTuEJF3cLSP9Dc1D3Z8QPTXgm8bfWcx/j6CU/cBfEQXhNmIhwUfNLDgI4yinE7POnjkzxTKrog8R4qcfywrST9O+04D8+qVt1Ao0EBkvr8Vd7Djg2C45ypo0V01Pw6VxoOxBZ3sIgyXnKXjmkKqqz6V0s33/epJ6bGsUE0unUxxnYTkO+1mLwiCIAgFWxOxQOlL1zy2e53Hl0WTu2HRkfkeNPZEfcfUfQAGDCz4KMPxy1flvCSdGK74WnFXmRPFJClyXqrOiaLJP18rFinX3mXfhTU/MFOexW7Wd2TT+ywNsNjxsOlBqEBXu3EGAh9xOH5ZbFUJ1arVVCqnbp9L5RWFkoYBr8j5fZpKSdJ+ANV0A/bY21HFPqByO0Pjoe4d0fU0glCZ7wCEFgj8WJFMpfartVwySYp8VJ2ayxmv1Iq7x7MryzyXy+UUOZ+Xr/qrp+tO5od1de6iEz7i8QFhUXf15m/y8sIo9pENeaI+jPixBUmMUaNtYmqtKO1XLU1vWnn1/qx3Z1iF825mN0RT3hE1Cd8i8x053oPo8xMlbL0OHdjRmtOQt8qH1nwPZxa9Sjhz6ZFFHzQ4v1Gjt9+MIudlbtlf5ZwThs756VY7fJnXmp0REU1eXriZvqZudjToJUlaWVnhnJISDfWCEe+GT4En0trTzPMO3WlUQivwYQYCP57ART/GKHJ+93h2ZU7Z1avliYhOTZH5Dml57H3I3NAD8xRPzwvpulyoTCzMp+OWFjpmma+liHZ3dx07BxjSBUd90EDduwNe+vEEZXJjDMcvi8s8l0ylTpQzIiJFflyamuvWQ99CVbhCoeCnQG4opXQGhrqzGy1VdlQrStI+LYqiKFJ1Py8rHgdE4ZwfHJVG/YMpHJyn3c13AIB/4CGJGt15vbTAvO/Gdu2Xobvo/Rvogzflzepelwul10QzWYHVl7os/y2/QUTHxUeqo0OSpEVLfaEN2PEW3KbEqjzSRhiI3kEdmO89EjZHPVz0QYPzGzVC8puxxOCHLvNGL9sdJtR7cJ5uiXmj0YjH40R1ufDmgrG5Lh++uZDhE3HTkBs/+g2NZ3E8G5aMD0XOT/PLf2qQW4YdBL5HIPDjBlz0YBAYfvi2rvggPPZsp3r9cf0lq+5EFI+rspK4MHPeaOhbExcmzhtERI0/Hd7ZrGuu+y/ELyRJkjyd9fDVG7jd65wpUynGE8Lxy0RUf1kf2MLGjZ0eeg+AUQQ3UFEjJDfFHln0FhvdzSzrlym/6tQ21DXDv1E5PKgnTEF5fa54VuATLa++z6m1Y27HG7c4ziehVpT2yRQWUuQYxzv+28B87wuhMuJDcrGKMDi/USMkv5m2ZXLG9dr7wt27zHsKPFMnp+LZaaVROSxTRn+9UTksvzg7+0b4hjxlfsw1nszN/G2nQkv/0El9IeYg8MEBgR8rUCYHhoPPBvWONwH9u9bH0/NCwhKMd6VRP09keE396/JBPbEgzMfvFO4IgtD7CLto436Lk8yJYo553nSaHjsUdV/96Sf7xp3f/nbAy+gvqJcbKyDwYGiwUfm2Mm/s1um1fod2LEa8xbUQT88LdblQqLRrkxqPU7neSMfjJj++uqQdwVRDT4zSozjehVb/RDK3UHTUeABAp8BDEjVC4vXy2cmOjcSTD1d81x57exZ9V6gufQc/vv22w9L+dmw13u2L21Pod0tkqDwr8MNyzkfSglcJiaM+JBerCAMLHoQC/13tujDiqVddN4in54W0v1VZ5tc1RV/FdePDmTKVas05JI5fFpNyXq7xuSTBiAegH6BMDgwNu0j7rKbzWXE3YByr+9SmeGxxnfdBWu3zok4yRftSsea+Q5NoFbl1wYB6uTEBFjwIGvNEFx/TQD2seePp8PvYO+GROaga9KuiV3Edq+sxikU8Xy+ZE0W1CbBBalHk3d8AAOgMCDwIlrp8cJ4WhIT6+LDeSMf9zfv2U0Q39AHzdryXZLTvjQnWeTZ2qz3aGl8rSvvV6eyKKHK1Yl7hnaYUP5Kktv1rAQBuIMchaoQkb0VLsmOs95nswqUPqNUxzjd+zHRjnz4l0/WBtvX97Gqb1HR0y4+6wLfLsFOL4FOLK9zRbmnKNglBfTuC8QHBptoZf3yD/IMLycUqwsCCBwFSf/mCLi8IabXF+8u3Wi+40mv1ZctcFxf8eOPV7ZaWtMPVeO9kQLfiujFBz7BLplKpVC6XJEquUF6uUbKl8MhJHBgx82NIbmSAwIPgaDTOJxOXTAZ7o1KhbMtjX2kkPGLy5nsBIeEp8/aOdSHXeBYtQm/+CqNuvnswyZ3u5uWVZT6Zy7XdGRn1AeGWageNjwzIogfBEU8kqF5vEFGjUnk9cyFB9PbcaAzbaJxPeLrrGx9cEjSyVKk0qJOhNSHBY3CO/SX2diTC6k5qUdxV7kyb1aPIeUnaPZ7lXc13NaMeANAREHgQIPH0fIbKhULB6AWbuHT5vHRYaTQqhwcvJi54Ouhb0fpG45x9wb/Mh+E+oFONH3r2wIDgkkktrY7jl0VRdMqyA0ESknY3IDiQ4xA1QpK34tTJzpjV4toPzgHVTe++L+u0d2xJG5JSOg9fveNLq7QaASO+uzi627v65ag3/krG407KFUPgLY76gf3ZheRiFWFgwYOBEY9PnJ2/VR/Q5OWMu7rX5YLOmwuCIAjudwLs/Hj2lsJ4HMSA+S7oyI4nIrU3TvDrCpC+Z8n1xVG/6vJ43GDNd1ZjobdRAkl2YHAkeIHkQqFEM1lh3t07X5dLr8lvjr1KS+MFZ6vM5/C6QPHIueuu/y7oFLuir46lHW93zkPXIwk8JFEjJF4vP8NmvFH9+J2oPJEPh/zQZb4jX/1IO+r765836MVR72iyj5vAhyf0HpKLVYSBix6ElHh6XhAWJipyvZN3tc2/G7rHvtOcu1F31PcdZNQD4BMIPAgz8fR8Rwa8hh+ZH2KtHTTejaCb29iNdZjvIMLAQxI1QuL16t1F3y+8ffJD9NhH21cfkH/eoC+O+lD8gQ6QsKl7SC5WEQYWPIg4bta8Ie3D8th39LnjYMd3dE/Qi6N+R/9vrAibuoMBAIEHY4FF5i0m8rA89m4aH9XCuf6CYDwA3sBDEjVC4vUKj4vejrdvnAbusXdbz0g3wOnURd+dSx896n0STvM9JBerCAMLHowjbvb6UHrdd2THAxYY8X4Ip7qDAYAbqKgRnpvicBrxrFncNv9ukKa8fzs+/Eb8YMx3A9jx3oRW4MNzsYoq6GQHIoPaGoeIyKN3vSX0Tu4yP+Dmd27N7Ozb1WB8yDUehITQqjsYALiBihrhuSkesAVflwtvLmht7+ryYeOSj0k2DB5aPkiZj4Yd35FF3pfadxjxjoRc3cNzsYoqsOBBJGhUKq/p7HXhNdFMduHSpcwHHR7Aw5o3XhqAxlvsdeMx7HhvmtB4GyFX9xaKnN9V5sRc0nlLrSjtV7UXUovsbgY+dul8EVEAAg+iQP3lC7q8IKTjRHW58PKtwCe0QbNE1MHcGm+ZH4wpb2i5Yy1fxDQ+6NZ1YMSpFaV9WhTFJJEqwnl5ZZnnOtxlbIHAgwjQaJxPJi6ZPPKNSoWygqB77CuNhH+PvZvJ7h2z7yMjPVxuWJptN+LHtmMdjZD57o2inFJqTreqOX4uVTqqKTzXkm9FPqqmFsXWLlezx49rCs9xipx/rExRtXqSWhRzSUXO75ZOiMhk5Ou2/3QqNbAvNUBQJgciQDyRoHq9QaqrfuZCgujt+Zn+aqNxPhHvJB6v4lYvN4Dmd4YF77gkdstId7/xuBWoFaW8rHR6QLZqbpznvo+EukuS9OjRozY7ccnZ6ep+608hmRPNxrlSOz5JpVi/OscvG7ucVGlOFMVckmrF3ePZFVEURXEle7pfrBERUa24f5pdEUVRnKPqSZ++WJiABQ+iQDw9n6kcFgpnhjc+cely5eCwspCh8sGLiazFFq7LMvHtvfZD8dh7xN1XaZUEIiI2ezECjnorinx0mr2a4wz7qtO46jjPfQ+zukuSZDwWRZFJsqvuS1XzvqpFzfHLIl8r6m+cztq979PcpOsHGtqfzLWMfG6K1BuGWrWamhM5IqIkn52udnxHGXog8CAixNPzQlp92KgclikzPy8kKocHL84mL2dMUt6oHJZoYqZQKLlX07G4yXxPHnv3mj63uPsqI1urtBphja/Jpak5kaNa8YhbEUWOFDkvFcmXxquOejAw2kZkLKLuspf5Fk6R87uM2iZzopjTt+fJovEnyhkRp72qOuGnsyvLvO0zmFS8VIpU/79BS/ajBAQeRI94fOLszVuieDw+QZOJjEnD6/JBPbEwn47zPN+oHB5WMv7q6drKfGcaH0/PC+m6XKhMtLnHUDX+G+Eby/ZR13h3YVAm+RXusZSvpqZm1Ss5x8+l8opCSV+ZU+Os8SEx3/2Jug9qRamaakk/x8+lSlVNz9UtydnpUrWWSyY1a5+oVpSOnA60T4uimGPuHkyablL7yACBBxEkwQskFwolmskK8xbrvfKazuig8GLy8sJ8Oj0/39mRPWS+U1Pej7qzH2pndBPxPOE4jrhlMSnnd5WznGqbKadTXE950cPyzw8y0W8o6i6Konqv1jdRZ0mmUvv7xZbE16rVac5km3P8XEraz3OGWV+rVomyluOYk/WIThWFklwyldo/kvkkz1FNLp1Q9PLs0GcgaoSnd0Q4W9XqNCqHL+Pz/ornXHBUdJ8yb1F3taTPo5pv1SlRbId27EH64RrxPlPo3XbTnawth622pfPiZtaIH7q6qwS9jMELfI+irl2sOqiDd4rBE+ucp9Yfj/mwjP8+laIqzbV2Kp1YNkaHsIgB6BcQeAcalcODemIhfX5gqKoWp++o250jjma0t8w3KocH52ldzOtyoURZrXLfaMZnx6LxxrkNlcb3JPC1Yl7hl3lOv6Z32bLEYLitbxxT94Nbz8DU3VHUuxwGGJqLVVSBix6MAXoCXn2m9OYtUZwalfKLibTQs7qTi3PeMzBff2lS98qE2qGHKHFhptJoUMJ5WTu0Y2g8e+dkSbYPbTDe0ABX873lh1ezqmpFKa+gZ4kPglb3QNzvIHgg8GCMMGLz/nvb+aHDwHyC14OIjUqFsoyfvkTeNx1uVvtIYAnT2uGSs6e7xVrLak/mFqt5c1uTjhiT/rUBqXtHog7VDyfwkESN8Hi9QuSiHyCdBObZPACz297fB7EHDImj3n/RlPNuakhUj7Qqcl7mlnsMiw5R4wcTg++jwA/YUg/PxSqq4PxGjfD8ZsZT4FV8yryu8K0wfKefEiqN9xOIbeuoJ2Iyn5xTqjomDBofWnUfovs9PBerqILzGzXC85sZZ4FXsSi60WWWleG6XCi97j5gECqN92O+D8WXG1VHfS/q3saV0iVGa3dft2bhuVhFFcTgwUBxTBOLKvbYvH1LghcEe8+tTj6CFfWRnlJDpCgKx3FUK0pHXD+T6yIZjO9C3QMx1k0lapRaFMUkKXL+sZxEeuTQgcCDweHRbDXCsKJu2dIXJfbQ+FBl1Lc335Uz+fFuVS2D77c2RFLj/RCsB169FxNF9a7sdJrUvvAcPzclyTU+YlXlowcEHgwIe6uW8dF4FUclpn6MqxkVjW8Dl8wti6li/uh0X5J6roK3ESWN9zbfBxdWN2a41KrV1Nwi7et9ZJOp1L7WQRYMDwg8AIFjGRBH7h77rhm6xnsb6H6j77XiPs2Jy5AFK+w/rqO6D7dUXVFOU6nkpDJ9qo8MmORaj8GwgMADEDjeM+j65bGPQjyemeoZBFEy4mnYos5yppwQR1xylh63Ghf0OD4A9A4EHgwIthGbsWVYiwmIRuXw4MWEn5R4R5l3K67zL9Juoj5cR307891oNt53r7wDo67xq0SPdGEPU3uZaW5Si73vFjkxR3JpKhWe1Y0rqFKIGuGpPHEskxuDLPq6XCi99jdpXsWxmq4Xs559l9m1G2DVnIeKewt8rVikXC5ZK+YVfk7ZZaeDBocximYk/gqNDM1vBCEUv20brTECZIxmbf/PGJ6LVVSBBQ8GSnR13SDBCwsThwcHhXOf1e0Wa96edd8prB0f+oQ7RTkljqhWpbkcl1SyR3KNAk7NYgfNrYZV4+1lFyGZ9e7IJDdlTFanZC5EnoXxBjdQUSM8YbnxbHTTsf1uxmK+Uw/JdxY7/hvhG/VxQALvZqa3Ta9jB8L2pTetNzGnjSH5M7WLOkuYBb47YMEHDc5v1GB/M46zPQam+uMn8NpUWl3bG5XDgxdnRNTxbBtVm43/pW5l3tB4S/ZD3zW+a/+8RmcN0HrCUeBpeBrvLeoGaug9TEH3PgCBDxqc36jR9jczMNUfM4G3qLs2CHY+HTcPlfGLR2C+I1jbnaW/Gt+N+c5a7n1cSjscBb452Ki8T1E3iJ7trgKBDxrE4McOtwuxzz0jw+pP1sY7Kju/7eYKX5dN6k6NSuX8coZXn749P6NOHfZugflONd5t/+EH4zn+avZY5lJVSdofhOmu0bRpfJP5XwpS6R2HEbQlquoOBgAEHhD5Vv3uJH/0qrE7J8ELrIHeqNcn0vO6Lf/m9cyFdv3mGYOfwS7z/Wp+NwDaOuc5bkrNyMqRIucl6WQwhXImjbdrp13pqQex79RY90Wr/fvgbozAKAKBB67Yr85jaOh3x9tzmtAEX7XlXd3zdblQek1ERDNZwcXMt+fcdSTz9g4Edwp3BEEYvhGfzOW0Rxy/LPYwc6dj/Hxtdp+OzPo+ivoqUbOl59rtj1I7nlpEuz/QHgg86AC4933ywQRV6o10PK657t0d9AleEPi6XHhzoV2M3lHmu9D4HdopUPc1eHYcLXVJkkRxRc5LxqCxkTY22zrwg7DUVee8Ij9W5kQxSVQr5mUlyXNEdKooRLLPcnMwtkDgQa+4qr7Yuur5tzij0Qknnp7PVA4LhbOZrDDfLrmuLpfOLy+Y9qpXKh+kHQvtLDLv/8Sq57NQKJCgvXFHCLYsvqVM2tO8JNGgVf5nXZF/05+vaVf6O8EETfTQu1I7Jk49h8mcarVz3NTJ/q6UWhRFKkp5ZYRvnECwIIkxaoQnMVXNordUY9t3Y6+Mg+xl298ku+5pVA7LlGGD743K4UGdJs/OqE05fRcyT4zdrz7ovb2d3YJXt2gt6tgXBlDnzvKzOZ2uHxpv7zMRRFIem1hXK+arRNWq6gmx+UFqRWkwzf8CIDwXq6gCCx4ERZOaMYrdoTvGFkcFYtpwWqu5xmCebKNSricyrAufycdvVA4Lhwl3kbc46n167I0Ke+3OILB0vWSKJKk4NB/yz7aCuJ9j3hrvUexnPLbv4Ccpb9Vlux37XeckR9Xj2RVxmSNS5DwzzAWANkDgQbC0lRzvHQJJQg4NjUr5xURaMMl76TURHRTqlxfm0+l5Id32IKwF79OUZzX+TuFOTOino74lk8mcKNaKkrTfejG1ONBcuu7poiOkY1KeBe/OuKy6x/QDcsnZ6WNtI8dNnVTPiM6K0v5pdmWZPyvun2ZXRtJ8BwMAHpKoESqvV0e9blYdrBeTl76th98/oavcs86hszvu2+Mm825f1titFy+9m3+ereWioWTY2S14auOlD6LNs5vS+0Rdrj69hYrSEaefSEXO75amRjrJLlQXq0iC8xs1Bv6b0a/jThXMnTaz6yIGb1d9P8odOoEnUkX+PK1pfF0uvLnQUX9bDVbm/YyE7zESbxF446kl2q7I+d3S8DLsVJzU3SLqvhrrdoJb47yO9/Q9om2EgMAHDVz0oCdqxV01U1qR83l5Ur1+a53FU4uUa3sAE5ZqLj9vsatXHw39wRKPT9C5+rBRqbyeSXflzGbT7P2MpDMi8R1pm2NtJMuZMpVi1s/xy2JSzss1fpAK9ZumYxZ9eAYydQBGtIHOwQ1U1BjaTbE+EVqR84/pqvpgml/ZoR2tl0uHA1f6y6iovt73pj8ny38Gg9qy/pH0qFPBsyh96+12izPQFHpHhzw567rHd+y7BU8unXF73DMawIIPGpzfqDGE34zqpNejrIbAU60YS/7ND5V7ajCZjSoPV/LZtHP7qyFU/a5h59GpeHw7VeM7ddSzimhTR31InEYnfWjdBNuNj538Pb+sSuVHxrMhGusenXG73jMCQOCDBi560DvJqyJ/VpRU/yuXnKXdXalENJ2lJBlN2eOJBL18SxRvVA4rEwuCEG9UDg8rH3Q6OL2PnXC8y/ba7jlErDl5Thj3MWwRnUdIXt2uirQkSV+IX6jbe0iwV/vM6/wco599v9VRsP3B/AveETNf9KvFTS/4X8Hw1woiBAQe9IDeZIMjIm76VFFospZ/TFdFkSOqFfNE1GrKrtGwS77/D2Sz8AKqkh8J1Y+n54V0XS4USpOuzXAsyzNMeY9Suh3aWRVXH0mPDHUnz7lzJpP955iYIS8J70Gz2+LqpfgluM8EIOxA4EEPJFOp/SOZT/JcTS7R7ApHZ/LJVEpNlJ7kiIjOJ+Ka/GgDWN7aJN8v9jq67jS+C2EegOp3ntif4IWFicODg8K5z1CHPf/O8RNZdVexarzuP2cVvfDyjnG0RuXwZXzeWFOjcnjwgi7PUIfOmjb4Cj18vNO2v40TenBhpBvog7EHAg96IZkTJ+W8JJ2ktOlWnEnyiSc6bzQoESeqv3k9cYGnRt0m+aOKT9UXLukd+vpqwtblQun15OUFwW0GnRsWmbd8izuFO0ZLwabJHGeC4voXcWui9/Z84gLToSeenhcSlcOX9XTPKReBNT4yTWyj4j4tarUhj+UkJB6MKBB40COWQZ8mySeiBNXrjXSc9KGpDZvkB0ZdPmxc6jTE3ytW1flllX1ceNmmca8/GpXDg3rC0PZG5fDgxRkRdZC3aAizKpn/+FeaqP/ur+gfdV1f/bi1f0eeksQFKhTkfqVQ9irqPox488S22uzpNDdJRMTxc1PSgGv7AOgbEHjQd0ySr41VM+amxBMJKpsk3zf2ueYeqlOXC6XXM1nesmWwqfu/WGMKwqVvWPO3q4Nq6m7cuajN64V5tXn9yzolvL/e735urep3f6U9+D+Vvyei7698r55Sx/Ps0RHPuj3BC0JdLhRKrU0zWR9td9ljGo+Dz3WwTmyrKfvVMyKO1ChUtZZLQuHBCAKBB0ETN3dUj1slvxN8dsKpy4U3F7Iz540P9C321P2hV+dbdMswpr13Y2bREBFRo1I5v5zh1advz89MKYuslhv89PF3RKRUnv7yZ/rw8pX0NBHRFaKv6es7hTvq7Bn2PN8p3FHnx9sX7Cm9CV4Q1PurRqMR18MyHu8KUNTbGPEcN0VVOS/pE9tSqelTRaEkR0STXOsxAKMFBB4MjpY2z+90YM2ZaesrVrV8/oP6oRHst6XuNyple6le2CRfxUn1Dyitp7MZX4zodz//7e/+ypTH/tPH3ymVCqXTVnU6qfxCH1+5wimVp//f+cf/4//AfU1f79AOCa3ku9b8ePe1kYtgMzEDFddc/5AME7JObFOm6Lg1tW0K09vAaAKBBwNiABVuxA5pqb9kMvgs6XwOpXo9Vuc78/GO1UvfeZ6dm+obUXM6JfqViOj/+ef/jVKfXPygtdu7V89/ofc+fPr0l4mPMp9cfJ9IN91p4qOLRMRNTFT/XP+a/vc7hTtylviEVk1n0fVOownx9LwQN5rp1+XDN+dlzWdDwxJ1TyPeOrFNSS1O7e8WOTFHcmkqhR6xYDRBI6GoEarmUMawmbaT4vpFo9GgetkwHzXLkS3bqsuHjYmJOmnpd9pLH7T2sNR49Y6h8T1k0dud7aqn/d2r5y/p0icX39d020bmypX3iejtq+dVuvTJ9Mnz8ruZK+lpTee/v/I9Ed05/JPdwG47kq79aFp1YM6lhno+h2+s/7LqkWrnMLEtivNdQkWoLlaRBBY8iBTxeJzi80LaNo2NTd2fuNzH6vz2dKXrFkVX5dzO+xc/ufTq+dOn5x9evnLFFPZ49+p5+ddzKj99amwqP/2ViOjF0/SVK9z0h9+n/8MPlXsH52lh3uGrs7a7Ojm+40r9BE+lQuE1EVHhteleoYOD9BFPI14fXk9awSdhvgsYeSDwIJI0GueTE4az2pK6f4nK5eFU57tV7rkZ6H54/+InVy56bH736vmrDz7RwvDvXj1/9f4nT58+/f7K93cKdw7ojKikarCGLVzODpi3tPFvmzQgCAJRvV5PtMnsDwlQdBAtIPBgEHRU4dYP4un5efNTNnW/YS3VG0h1vrlyr1E5PPhf3tPi6P7lvA1vXz3/7wr3ry+++++v3v/XRjz+L2/fEvcBEdH7Fz/5sPL0P1z5fvP4T3Q5wevZhZWJhbMXB0REZy8OCi8si05gjAAAIABJREFUR/XujUNtwupWdR9mY/8uG9sBMJIgBBI1QhXWMmLwKn2cE9MzWvtU3VrVk/OImXnXV9TKPapoBrwaQfiHX1d/+lf/9unJh1fSHBn5bx9+fMWW9t4pSuXpn6evpKfp3avn5XcX2QNqCfM6DdM3Nj3z70sP2zAeLzwj8WCQhOpiFUlwfqNGqH4zFoEPNxbJ7/Ohy5SZT9T19L1WZfjvfl79v//5m0ufXCQ9Xc7Im6PeJN/xvRZ1J2pU5LpmyOumvHEC3BLr7IySwBM0PiyE6mIVSeCiB0DF0pCnbzhV7hl9XxpE9N7Mxffp3SvlvYufvE9E73Mcvf4L0fvvXj1/9X7mypX33716/vzVe1qZm2+4tCXtzq7uRBSPq9GKeKtBHlvF3iA6sLnf7Q75LufutD7JfSgeAKBbcAMVNUJ1UzxSFnxQOFfuUWuo+z/8uvrTx/9Uef72oqrhb189f/3BJ+n3Wslx2pae/PZO6q4tsHJ48OJMW5cpHk9ETjptSbVz28dxGZNEhqK3PBqDB0Z8CAjVxSqSwIIHIFgcK/fqcqF0ro+C+5Xo7du/vPeBZqH/5R29P238X19wV3cyXBeFgpFcdyAIguF68Dis24x5t4I6xjdg5PKpKfwdtA/sfK4uAGMKBB6AwdCq3GtUDkuvaSar+aT/y292fvfz6vN//uYdce8TKSd/fm86TW9PbJLfJR7qbna2L5jj8Qf1xMK8zW3u5o03+t95q+/k5YX5+MtCibICn1CbA89k6XXJXKtHbY/TK0inB2MABB4ESJOa8NLrMJV7iYyQjuvT1iYvL8wTEUfKyduLF+nVq798dGma6C3RX96aJN83T58+vXLlivrYru6sQmdnqPS6ZT2r8fi3L3+qnZ7/80VfUXFD2i3zZ51PQXzirHRQmMkKAsmFw8bCvDaPhhdsnYm6jesDAHQQAokaYQtrQeD98LufV3/6+N+/el7+lYym8e9ePX9JqU8uktpltoMUO1Xgv6aviZn0arxqaKSlco+IiBry/3vw+p//5czCv1EH1FkG8KhC7t221m9LWoui2wTekT6rPiLxQyVsF6vogfMbNcL2m4HA++R3P6/a2t28M0t+B6iGu0cSnK1yj8gm+Ub+v/GgUChkZ8hx5p7HfBpnAa7LhTc08/r1+eWF+fRbc4GeK23b7Hh9oh0I/FAJ28UqesBFD0BocelC64nRhrZArslojjP3bGN2rTP3CoWDhcuTBy/OBEGwz9xjE+7U3vXkYPFryYXz6bey+v8836gcFgoTWceG+P6wf81VvWvinTue9xmIxINIgxuoqBG2m2JY8P779zkZ8b54qk+UUafDqba7hxVrr9zLUFmXfKNdPtM4v1E5fBk/e126PDnz4uy1IAjUqPxU/vX8jLMY8nYfvt2U18sDg6qPWzX39d/Rz7qze//SNxD4YRG2i1X0wPmNGmH7zYy5wHfUgb8jgX/KjIlTU+os+XR+ysmMwLdDsT7rva/LhdJrQcjKh43XZy9UgT98GZ/nSS6UXpu71DjG6Qc2K3bVYS5xS+PtFAoF4dI3UvkRu1HscOaMJEmdvgVQ+C5W0QMuegCCwqLu6pZebnfsom7gWenuRqtyz6FYv1FnB/Bou0/E1T41+sy9OC8sTBweHBTODYvcUHdW4y3jashT5t1m7gWBIAj0i1XRJUmy7wkJByMHBB6AsKAWxFuMeA9RV2Gz5Vl8GMqWmXtkGrPLzNgtvaYFQaBGhc4b6n7qzL26Zr+r/XpMH+1ox1sC846LNM/cIzLa4wTXzdYWiXfUcqg+GDkg8ACEDp+irtLXCAgr+a0Zu0Sk5tqdnR1cXhCoUamcz3KVQiVh03Y9j0597FhTZxkwT4zwZ2fozYXszHnjA31nNR9QEOJUlwty3eiO49b7bmfHNQbfI96qz8o/VB+EBIRAokbYwlqIwbNPPU6FEaX+x7/6xjsSz6q79zGJyChl79oCtmTMXZ6kFzSbpGMlYTme0YhW+yS2+42jO8Ei8wuXJ22Ve1qoX0/0b9Tr5Yq5co9sxfrEROI7UPdfmH+pTtLu7AF42Po+CdvFKnrAggcgQHZoxyOL3jn17GevA1rUnRzj+syUtsnJs4msICSoUTksVxK9O7nT80LcuWg9np4X0nW58OaC+ophvjva8WTz2B+8OBMEU+UeNer1s9cvtC62M1nhUqNsqtwjiqvVfYIQt1Tu9WS491Y7Bw8/CAkQeACCxaNTrKNd6xiJ74hGva7XlTcqh2VS0+jS6YnCy3q6s+I0R2FO8ILLQRqVyvnlTOvFthpPZgtePzmvD0m/gdAdD43KYblSn2iJf+u7WiR/dZW++45WV7s131X6XR/vU/Uh+aCPQOBBsKAdPfWjSMxuuHtz3mgQvSyUaGbmjN6qIfTEhZnSmzqfCGw8a6NSfjGRdku489B4YmRe7ZR39uKA0gIRkdZ1R/1W5+cTF7SnWhq/9n8GqroPkl4k2f7efhn6qNwDBIEHIDg8OsX6xNB19g6pbVyfnelyWHh9RpqqfzAxqRe++V2/pZbd84vUX76YyDrZ9t4ab2xRZ9QWCgeXFwQ1hE9ElycnK41EOl5/+WIivTBRKbcq9yYu8NSonxt3AG/Pb26kDXXv2IgPB3Dvgz4CgQegG7wTx1S61vXYb6j589erHzsn0HnH9YmIErw2pY0oc3ny4EWlwWuqztrDrrT81Xf8r9nqnTfjofHmsxRXd3jBls4fFF5oGXSNhl65p31Yg4xi/dW/5f/tP5k+tAON/3jH6qW3+edrxbzCL/Ocj6P1G6g+6A4IPAC90sc2bapyN6lJnnEN/yGPeHyC6PWBXBd4evli4kLb1TE6J1z6hpw+SM/hM1Wq2WvqLfj01ZO5K47xuFR4LQiCUbmnheiZYn2i9MVe1JfVeAd1l/arqcWcZQtRalHMJXv41O5pq/rGY6j+2IIqhagRqsqTGMXUB9GLwfe396phkTeJ+bf7OUYfd3femJkuasL7W7lQovbt3+25ZkTGGjRVZpvVF0qv3QrSXWhbO+e2P7m2wGtUDg/+7qbw778jx5l7X3/t21HvMlyuVpSqqUU6ahnwipx/TFeXec54MHS9t8DG4ENr64fqYhVJYMGDoDDUnXpu0RoSLKLuU6I8cNb1PpDgBcE0pS3O96sBfKNhRL3VSEBdLhw2Oi+xV0/gDE16T4llm+HYLXsiIor/3U3BI7Gux2C8IuePuJXlyVp+irM7CDhu6qR6psiPj7gVUeQUOZ+XJ9XbgPBIPjz8YwtuoKJGSG6KWXU3GEWN97bUu9P4DnS9eyO+K/xY8I3K4cF5mrXaO+wd3xoqT0S+/R8WXTfOPJs2//TpU8fGf+Tfjjcb8YaBbo3AK3J+t3RCRNPZleVkLS9zy7mkul3mlnNJu4nv5zv2ke6y6Aes+iG5WEUYWPAAWAlo9Flg9nr/sOeaEdEvq/QxM382np5fqBwWCiWjQr1l0/tCd35k1bk2Pm+SLI599SDffCP4UffuSV69WnssSSdERFTN08oyz2myL4ocUa2YrymcQpzZSFdqx1NzyxwRcclZks+IBi3w3akyivUjBgQeDBT/w9EHTHei3nZPtqQtvLrO4qbxbEZ9PD0vpKlROSwUzrTZsp19iCrPk5cXErZgR9v8O8OUV9Vd7dvfVtq7c9RzHEfcssirYXjd136mnEylVMWe5OhIrpL+lM5UrT+zSf4I08difWe/giLnd5W5oUcyoggEHgSC2t/GY0sYovJBW+rUu6j/pjloL7071uR5Vea7Pdbk5GWjm43b9DlHDM/83//9U6IrqrSz43nc6CEYryin09yk/iyZSu0fyXyS52pyiWYXueMjRaEkR1SrVqdSOVJqp0bAPiit14ME09mVgQcAENQfFSDwIChYRbfrPQ1J4wMSdRoJD7wPCoWCcMn5JW2qG9XlQqHUYfK8mUalXE9k5ufjaYvL3ee/iB53v8Ka71euXPFpzXcOxy8vM0+TOXFSzkvSSWpRXE6SQkePawrPkXx0mr2aJFKITs2S33eU2vGU+uFyPi+rQf7hpvX5VH2v5ABFzj+m2alSqUpk+h7aN2NuZ4wtxl6mN09nV5Y5Wd2FuQWyvyviIMchaoQ2b8Ux7c4gUKUfgKgT0a706IQoEJMqeCOeHewmCILVS//xTqFQMEt63XnijA8sWXqs7e6o8Y3K4cGLCePD7c1oLdF3b5lvk23nUinXDkXO75bI+JfXU+soqBQ7PZnPtGVUKveso3UNFz17FmtF6YjTUx50D76+8cx40bxbaWpRzCU170bKeGx5Nzc+MQFY8GCYGMYuK//9EvveO8W6Yej6cfGRccmQF5eXR/aKwVagEZkj8WqG3cLlwwO53pL4BJ99c1hvpDtJr1OJp+fZfw9W1x01Xp9Sp6X12Q9osd1Zp71d5oNpYcvxyyJvenpVzksSBeQ/V2rHJ9WSxBij1rS+MFfuGRa8kzWSmlNP2CQ3faKcEXFK7fgkNaeuN5kTk0RUk6upOZEj0sIlNYXnOCKazvJJIiIuOTt9PKs95qboWFEoydWq1enZFY6IOH4uJVVrueTI/l79AoEHA8IxKu/4uBexD85YJwcnfK14ekSk5UifKgqRLO1T/y+fA4zEM1ls5o/rOXm+7Yd6+uoTvLAwcXhwbTX9T04l73ZRN7YE4LH3g0Xy+0zyqtjyFchKkreE+h3S+NWCfovkjwZM/gMRkaKctp5MctP+D3RS2pVKxkHVIEqkgcCDwWGJynvsZjz2I/aBijp5BNdrVZqbm9qv1nLJJDd1sr8rpRZFkYpSXhl84lPPmIe+OLxKNJMVhEQPyfMqbRvg2TW+LhdKryfZojhH7KLuGJgf0Tk0LWrybiunn4iIFMWc1scppxGp3CMiUk154ynHTZGiPzlTTvx/k2H7LgYOBB4MlE4T0B5Jj1oOPUbs7xRaVVtBiDq1T5pT5CNKLScpdaQolEzmRFHLpcotViW5xkfmSlKXSTvJRnqd2zx4H8cqlCirNcCTqaXxFlFnnjYqhwf1xMI338Qt6q5Unv7yl48yn1y0dKj147F31fiPd/o+Cb7/mNL4p+ZEjpSaKa2Py9rS+Ee2co9Lzk6XNH+6Hjw3vj+1/O5tSTLvMiL3EQcCD0aGR9Ij4/EX4hfG4z4m6HVQ4abUjqdSPJHC0f6udBx0sVLAXnqPDPZG41x/2FNvWt10J6pULiXSiQszFfPsWkeNvzxJ9cTCzb9j1f3dq+flX8+JaOKjjFXdVTw89hRImv2AYdP4c0lSrXImk5+nx8eRqdzj+OXFopaYN51dWU6SehOtettTi6Lfz0q23jWdXclFXt0JWfTRI7RZ9N1hTbh1ovcEvS4q3IxepTQ9PT01d5VX5N3SadaU4dtnhiTwhUJhkmZ66U2rv6nw5oLAJ4galcOX8cwlIkrYg/jsStQ7AmfPvFJ5+ucPr6Tbn2V7GN6QeeeM+i4T6YcOm4NuS+NnWuaamvb09/PVzH7ts5K1dnofsYtVCMH5jRoR+M1YRL2jrtodiX2fKtcdK3WCIRiN9y5A11PoX5wZ6XWVw5fx+Q6r4Nk3tblBYNejNrSx2dzvXj1/SZes3nmlUqG0g+Y7Gu7qxu+/v2LV+FEVeAtDrtxr3UYwNxSWNP4IXKxCDlz0IBT4sdT94JGgx7rf7Tv3gFa7Q0FnTg8cvXUd1XvuTUsUTyTOX9YpkWhUDkvniQUP89/w1Ts2tCGid69e/vrexStmdX/36vkv9N6HT5/+MmENzDv6540HvU8FDCXDrdzjJ3kxp7fznT5VFErS6KbxjywQeDA0+iXqbriJPY14s7n+4ipvdVltXVcoFN7oreu6701LFE/PX9CK2YX5dt59vVpPW5g5PV559et7H18xy4NSKStc5pOL76fT6Xevnj9/ZTPvnQvnvvuOvv5auHPHcdJ8xBhk5R4ta5+kyI+1PEDZlsb/m3/YDGw5gAgCDwZMF6Leu/bbm+jFKDaSGj/Agni2zL233LoWapKeT775RlC7zRtb1PT4zEcTf/noklne37169Wc6p/LTXyc+ynxy8eInn7ge1l44p2r8zk5UTfmBYK/cIzKHrOypfcr/9G+qA1ziOAKBB4ETtKUOgiCeSJwfyPWWIHffuq4LWOc8a3Cr8nzF4p2n9y9+cuUiEdG7V89fKRfbpN65ZdRroQGXVvzAC1vlXq0o7Z9mV0RR+7ewVuonic4u0cvhrXgsgMCDQICoB0VfjXgvmzWenl+oFAoFmrzcIDK3rjOi80RqSL4Xu96Gvds8i67xV+jdq+dlhctcfFd+9X4r6v6Xt++Icyyesx2HdJn/7rsralm8IAj0i/bXi7/bTjBV7k3K+d0qpRbNYfZTa+VeqvpiWMsdEyDwoJ8Yuh7AxVGfBNV5la13l1xgR58kkyZ6IWTIklvXqJTP061mN43KYaFA/VJ5i7q35JwcNqp2u/LhL3/+C9H7zsl33hgyb2g86X+9kPkOacX4leRVkedqRUnaJ/0Xa67UV2fupS4Pd8WRB1UKUWPwlSdBG+tqFdqcosX4lG7LfPx0yR0Z+mHEu5rvjcphmTLz6bjemcbSVrYuy8Sbq+S6qpyz42a7O7aUZzcqlae//Jnow4/9VMY78vTp0ysXv//6332380dTmRxkvn9YK/c2/uP/tfkP/zDsVUUZWPCgGwboga9VT6eJasqpNnGC4+emuuoEGwVdHwj1ly8m0kKc6nJlgogEYaFyaGorm7hAhYLcwzx4Zzw88952PBFx6StXuk/wJyK6cvH71hOmWy2s+f5hrdz7jxv/BwQ+UGDBR43gLPjhhNVrxSKlaL9KqSrpWbpBteIaIXq24N2j741Gg+rlg/rEzMTEpdcvDgRBcOpMo1v3Gh6zY3zhHXdXaWvHE9HXX2sP2h7NxK9fGw9/+5uftEe2djeOMt9RIybAgkY3QQMLHnhdoYadK9ca6FKlaT1Hx+icMcaNMgKsl4vH4xSfFxKVwwNV3a2TYYPNsPOgrR3/dUum6euvO9R4hthfN5v/LWb/XRjWvLEd6g7CDAQeWBm2qDMwA12qpRMiWeG17lhGxQ3oAj8F3/H0PL0oaGI+kzU63ASRYefHfFfx0Pjvv7ca971oPOltksn2K3DbDkDYgMADolCJOkOr++X09HRqcfZ0f7eYEnMkl6ZSYVnj8BhI0xu1Ry3L2/OJC2nzDonK4ct6ulsPvX91V3HT+O4+XeOj71gv/c4fV2N/3Ww2HUx2FTYwD0BogcCPL+EUdRYmJ6dWlI5oRRTPipJEAU5zGQPamu+FQsHj1R4z7H76z6aJAF//u53/9X/+mqgzQ9tR43uF1fiPd3Z2KBYjNUDsYbLDmgdhBjkOUcM7b8VN1BFKHFU6N+L9N2Rlld78lu4z7FiB19WdMosde9IdBZ6NwVOneXY6v02s/pdak4hWV8nyS2K13PKTgcx3AZLsggbnN2rYfzN+LHUI/KjSocB3pO5BNGY3BN5Qd+pK4KmdxncdfTcEnpw0nnwkpeKn5BMIfNDARR9Nwu9+B6NJf1LoWXXvGkdHvarrT5+aptR0jeqoPzliZqa089gTZB6EBtxARQ1cXMYO30Z8R0a5486WhnWNyuHBi85S6H/6z6t2de/OgldxC8Z3HaRnLXhqGfG1orRfNbdJ9v6twSvWFljwQfMvhr0A0Ge++OILXFZAQLw9n7jABNvj6XlhIVF/WR/eilrjX31u7xTViCdK5sSVLJV2pWJNf0kURdWad0yn93gJgMEAFz0wo8j53dIJUTdDXcBQ8Fcv15eYeu9NavvinLfgllTfx2R73X43pp+2cCulI3jswbCBwI851hFtSu14alFcRhUacCTBC0JdLhRKrU1ME5x26CXvPXSfcaHvGr+qJ/vv7DT+dO9g9m9E3Zes/2TIdA+MwDwIIQiBRI1OwlqtwWyKnJe55dasNk6W9lFuPlK0M+J7D8BTXS68uSDwCT3VrrP+8502tOmCvsTjf5tYjf216Rd070+Nm38XbzZVXz0Raan1tWJe4a1erraBeY9Xxw3E4IMGMfjxZnZOvTydKSenikJEHDd1UtqVqilRTFWlvKwMeYGgL/TFP99onM9cSBDV5UKZMoIgXHhTKMj+4u8DUHcKLB5/8+/ieiReIxYjolq1eqKcWXc2AvOOh/IO2wPQXyDw4wzH80kiRc5L+1U6Oa4pRJTMiaIo5pJEydziVEmutT0KCAW/adIvq+1364G35zTxAVGjQZcz6TgRJfiFy+dv2iv8YNTdmx41ftV2amOxpIePy1vFIfNgMCAGD7SGsIqcfywnkVYXPfrUsqbROD97cVB4MTMzQ2+J/BbGDVjdPYLufW9w6x3B8gi9qxl5iM2DoIEFDzQ4bupEOSOqFSXVNV8r7p9meUThR4dAjfhfrqX/1TfCpW+EC/T69Zu6OkbuoJ645BWFH4rt7mGsd2fH7/Qw0MfbY+9nBwC6BjkOUaPDvJVaUdo/za4s82dF6YjTc4IV2dS6C4wMtlS7Lsx3h7dY7ht8N8cdonPew1j3tuPVRjdMFr32wOKlP25SR78Ow1J3a4AzhqY8kuyCBuc3anTxm4GcRwqzxvdB4B29Aj40fuih9+403tLJTkXtZ2fJou+Ctio+VjIPgQ8auOgBcfyyCHWPIgENjPHD0NWdfPjq7a96qDsRNZvaf73g02MPpz3oHQg8ANEi+HT6toRB3VW8NZ59tS99bX3SVsIh86AvwEMSNeD1AqqXvmvzvccYfHjU3cA76K5Ku7qD3YJ3nBjbL/w45D3y8INa1qDAxSpoUCYHQORQu9PTnS7e6nxb8PFOS+NHTd2pt4a1XQhQq5ltu3kOfirlUE0HugYCD0A06XP0fRSy6jxw03hjY99K5GvF/dPsishzRIqcl2t82/QWj3E1jvtEw3wHAwAxeAAiiFR+NPRIfPhhRd0ere/KfK8V92lRt9rPlBP/7/QTdEfFPOgICDwAUWMoFl6YzXcVu4RbTHb2aXfOeUU+YppD1arVVIo132uy93AHn7l1yL8DPoHAAxBRBphOH351V/HTya5QKHR9/DOFZpNazN3aCVKR8/vHx48ljxFOipyXpOKij952SLMHfkASY9RAYuqYYzLf282QtdBd4v2oqDsREb179bz867nVdjcw2th19xsyxi5Tje0MSabnipzfPZ51zb6rFaX96nR2ZZnf9ZdYN7r5d7hYBQ3Ob9TAb2bMsfrnO9H4LgR+BNRdqTz95c/M8w8/ylz8tVw2NJ6NxKvD4JvN7sMcWgq9OX/eyKtvl1avrVjO75ZOUmpzSZ/6PYoyj4tV0OD8Rg38ZsacQQp8l+r+69fag4++c93SN969qrxU/vzexStp7t2r5+V3F6+kVYFVdd2SPG8IPPUllcHaBVqR84/pqpfEt+x38z4+FzNaMo+LVdDg/EYN/GbGGWcZ8K3xHQl8r+qu8tF3Dlv6j2rFf/ixru4q9tK43yZW6Tetn08/0hUVOb+r/P/t3T9sG2l6x/GHQHDaO2u4gBdaUGPnCsMj6iAgOTNqfMCR6358wKVKd9WmDOAiQC5Fym2C4IpctakOwbUp4inS6cQr3Ah0soARk7Nw4bNHg1OwwGqkvdU2SjHkcPh/hpwhZx5+P3BhUSQ1kqj58XnfZ973oJ/xfsfxzFnrQo+N3Q8vp5c0I/YZHfY6cLLKG012AFLLJt0T3rKUIJhsZfvu25vhB1EFH93ybOIrZ3FZmmHsRsfk9sb66ocmZuaDO5bdd7x77gcpGuvov0OIhW4AJWbWbeHCdmm67Yrg2bMvJ2/81a8eJnrwzcW3X9+8fftWRD784dGHX1/sPDw62rm5GQR8VLsvXORu9YVlag1bOo5zJiLmrD0b/c5E351hRA16nncppojRPx5JUKOz/h2EgAcQSj4+X4LGup296s6bP37/44cP9nZExHhgiIjs7Oz0Pz+Z6M+eycmJyNspT5ZJxtuNBXeYEvxhs9209wXHppkkvIn5LUfAAxosSKDsiviV0n3qjHsOc/D9droH/Rr45uZmmO0Tjo6O+uk+21oXiB3kulTrLduebMgL3PaZ7JoiXrVOzGMO5uABJJVB7R7P7/D/k7esJnj36r3cG7TTBe9evXr//v2rd3PXkBtb3+Z1pf8vZm3LxPr+ucjsK+rC0fxGo2Hb9iOpVuutZAfG2jhbiCZGbWhM3UJJi8u5RfzCIfo1j8wvOQd/c/Husnp/b0ek3zsfts7fXLx5L/fCAfuJL9Qv31+8ePH43j+Of/pw5K9p7XX82PB8VN2PvwFIVaAXpJrnZJU3fr7a8DezhdYQ8Oufd1+pyU4kePdO7t83RIJ3ry52Hj7Y27m5uPhub2+sJh4fnJ+6uO+mMn6e4aJ5ceWKeU5WeWOIHii3TPKmaOm+suDr70RuRESMvY/l5jsR2ZlI93HJlu7fwJZugdt22m7gd0YWsr+avBIw1Th8dOdsDxbFQZMdsDWWarXbVLonL9anMT783sW3IobcXLz/4/f2jiRahl5EBt31I+X72yf9n08C696U3bCatiUivnnmXYsYErgvu7sHUxrwBocnid/5RRlfgGEJZIwREm0Y9doqqWNmRsDPqeBLWL6H+oEezsFHA/XhJy4+ePAv/zSR7qGxjD+c+de0kbH6/vp2M6+oH1HwEXtOVnmjgge2Scoifm3pHq0it/jLJV24fmfvwdGeiISJPkh3kZvLQHaqsTu+HVmedqSOn53usv46XkQSXFIfl+oCOa6m04c5eKCs8k6X9ae7TFsvdkT8ovmki9reXN4Y9wb988G7LwPj3mf/MCjfx9I9dHgrh7fOl88XPnUp5rBTzbXPmcUv/neKMQQ8sGUOb8e6yaaOz28k3Wfd0rfkwvU7H0hweSMiNxdvXl3sPPzXz3bmpftAwlAsRcZLygXquWheB4bogVLKtXwv7bz7dMb9e9++efXqT9//+OGGKUukAAATFklEQVTRg+hK+LnpHko4CL+RsfolpB2Ej98/4UNQKFTwwPaZKOLjlKW7iITz8UdHD/Z25NkzOfnNkyTpHlJWx0v6q+PC++d6SMgJAQ9gaP3pPvnlZh7AZFddyqVt++l+eJsw3UP6Ml5SjtiH4xOM2JcOVylow5Un2yCbAeFBO300B7/B2j2HLvopfnw3aeE+KeHPvHRd6EkOOP69Z/gNcrLKGz9fbfib2Qb6An4NVkn3UPIfeymm5OPSHnAmMc/JKm/8fLXhb0a9LMPjdeXF+89I9+R0Z7yIJF1DJ/aQpb9NTlZ5Yw4egP50r/womyBJdUF5uWasB8103pnjjKx5v+ghzM0XFm+gtOFNsW7Z14WvK09+caI+3TP8m0j1KyhdHS8iIoHjnIrIsW0nLOVlqWqek1Xe+Plqw9+MbnkE/H9/lW77mRLJPN1DijPe7zhnXn+v+SWOPFXMc7LKGz9fbfibUSzzqKhU5LPPXvzy5z9RmfE/vvvkd/7tkyeSxx+ExowP3Pbp+X6raYW71PX3tRFJNS8vkvj75WSVN36+2vA3o1i2ORGm++PHjz+pKSzic033kK6MH0v3kU+FI/aZt9lzssobTXZAoUUdTPklxO/82x/fnbmwXRmtId0lZRtdwXvu/M7UdPd9X8R3pVpvpTx++u+KgDdQ2vCmWKXM1wOvVOTkZHgFvKYiPkx3Eck74EO66vhQEASGYUjgum7Q9WQ4Pr/cdXGzHsXJKm/8fLXhb0alKBgyWmCkv1lqfB85BRkfjkOsM91D6jI+cNsv5VFYz/uddmCNlvZZxXz/ZBW47dPgYGySf3hj4LZPu5fSb/ybc8in3cuRmxY8YhuwmxxQJmNn1cFpLUUTVJTuysQL9zVLtZvc5J2LF/mGsXvpXYsYErg9b/egMfrp6L1mqsNO9w7VsJrhXQL//DLhyztlK+AWoNrThgpen5ln0mFxFTY8Lz7BxdN9chv4rIr4FAvLZ2RWuq/zT2G5Or546d7X76Gf+5paejwpfODTp08XVfCm1+/kD8vxqLF/4rCmPomI33F6RqtpGYPPS8fxjPpVt3u5DSU+FTxQVkFwtWuE56daw7Yb4necdjD7nLWe2j1K9/D/a8j4ObV7pbLWjE8u6rkrZrrL4CU139LTRuGdnz9/vvgoWvWrQXL7nbOressO07rjJynXa41jz3F9y/S6u8d2TcQX8brn9ZbdNPyOc9oxVBf9dNEDhTanwjNq+1dnHX94Q61xvHvuT19jNEm6h+30F29eRd5c3KQ62ni6z7olW1G6b1zaPvnCRntaaTeYjzx9+jTN3X3Pq+7XDBExrAPT8/zxO3hnTkx/td2aVb86c86u6lYU5OaBZYSfqV4FSZbkLS0qeKC0DKvZctuOczYYa4zV9CNS1e43e0dHg+e4uXjz6pV8/PDB3k5Gx5ypDc67T5VqMj7aZF1H0s8ak8j0G7zsnjrd/v+rRiC1kRf79OkEo7Zf7cr+8K5V407/M1GrgVYEPFBmhtW0LQnctuP0JxVXG3D8j9/3/vqnB9FM/M7eg6PqxZuLYO9+sc6CUcN8GO3ROHylMnK39Y/PJ8zs6D7KMl5GR+yz/taWaaPz3e6uaXZd3xp/aBBcRWGvE0P0QHElPT8aVtO2bdueOv2eqny/+5GIyNLDlpMz7nnMwYeFe+VH/aVs4ik+6//rlGS8Ov5rLfgaOGnFl7jJNN1rpun1wnF3v5NwvzsJ3N5V3WpY9ave4AGXXdcXEfHdkcJeIzqutaGLXpPVT5Gz0n2yhT7mq09qH/32978efPjhD4/S1e+5dtFHe78W/GUe+90laUgvbjv90hY238Wugx+9hN08tq2g3xU/0h4fddFPNMBPuQ5ezOOW0Rt26Dk9o9U0XKcnpnjeVnTREwbaEPBq5JfuMjPgv3n3xf/84Vp++fOf/Pb3v/5+webenz2Tk9/ksjtcTvq/wf66cOJ3HM/cloxPsjTTJk5W0XVz6/2yG8IQPaDTEhfFffPuyz/dfxwG/9HR0T15n76PPhfPnvXTXQ5Lk+4Sjb0bg2sZTXN+07amsfoo0VmUfoOo9rShgtdhxWJuYbpPreC/cl2xrLsiEi16c3Px5uKDB5vrsAtH+09ORN4+kcNSvrAHdfzs3dqm3l+jsW+Nk1Xe6KIHtJk/Mj/ngXc/khcv3PrjfsZv1ki0v5WypfvInLDjOFKtt+xmkjdKmvrqxxR/eR9leAOlDW+KFVjl/J5kZD4e8xN1/Ffui+7/iYiEM/H/nrbDbnXDaJcSF+4SWz51iV+o1owPjSxVi9xQwQPbaHYL/V3r8WNr8MHR0f01HZCIjEW7lDvdJbx60e84Tq/eSl2Ul66OjxrckzSnJ16qFiuh2tOGCr7s8i7fZVELfejOn//lX9z/wXr2kI0uqxs5+JKn+yTNdXysOT1w267RTLIeDServFHBA+UTrdcWPz2uuJdMv4X+bvThFy9eyCc/X/4Jkxgv2SPq0l2WKspLUsf7nTM5tvtV+3VwqXjx13LhDZQ2vCkutSRn86mrsY7dGEp1EXy8hb7vm3dfvP/B3/30ozyK+JnRLjrTPbJcHS8FbkwL3PZLeTQYlV94tf8QJ6u8UcEDZTIZ5OGOqFPPk1NTX0RExtP95GRNLfTTR+Mjb5+IlK5hPp3l6ngp8HD9dSD7gzn3cEdXxRuwlgtvoLThTXF5LVG+h1L9wqd+ldlvBUREbv+38uQX/UBOvvrs2IK180r2kOrCfcxyaV3MjB9OuqdcJo6TVd6o4AHI7a3fcc6u6q2mZQz/F3369TCYF27MGo/z0OJol+1Kd1l2cr2YU/KG1TQ7jnO2DYu7lwwBDxRCwhP37W0uO6L6nZ7RshtG4Lad4MC277htx9mNNkc5vJXXFfnhiSzM6eW2Zt+ydF9FMTO+1rDtxqYPAhNYix4omRx3RA38893jRi28gvtYPH+J50jdyb+t6b70yvOalqxHrgh4oHzCrrol0n1W8Vczd7unHd+o7ctgO5QgEOPO8B6Ht/0OuGxta7qHyHjkih4HbehbKaO1DbrO/ULDtchEZMr25YNR+iTGBuq38HK45Jb+7RdwrD4VTlZ5Yw4eQGjRRGpsJn6hk5Nhxk9fx0aUXw6X3NLT6sWcj0dxMEQPbJjWc/TJSf/fuLBwJ91jGKtHHgh4AImtPhPPsPwMZDwyR8ADm6S1fJ+OdJ+LjEe2CHhgW2TzZmLpIp50T4CMR4YIeGBjtqh8J90TI+ORFQIeQEqpivi3T0j3tSHjEUfAA5uxFeU7DfNLWSWnyXhECHgA6SUp4incV0DGY3UEPLAB6y/f1/0VSfeVkfFYEQEPYClzinjSPSNkPFZBwAPrpnz2nXTPFBmPpRHwAJY1VsTTMJ8PMh7LIeCBtVJbvtMwnycyHksg4AH9cnxXERbxFO75I+ORFgEPrI/a8p10L7zJjCfy1SPgAayGdF+XFQvx+MPVvtdEDAEPAKWRScaT7luCgAfWhLMqMsGEOhIi4AGgZJbO+PBdJm8RtkTl9pb5M1UqFX6nRbTB8p2RA61W/M2GGb/B1wYnq7xRwQNI73Wl/w+bs/p8PKW8bgQ8kDttNXQ818n4jZqf0H7HcRyn4y//DCg1Ah5AGpOJTsZv1IyE9juO45m2bdumR8ZvKQIeyJe28h0l4HecntGyGzURkZppXgXB/AeQ8SoR8IBmvL3YBmPxHLg9OW5aRviR3zmTg8EHyZ8EChDwQI4U5uvkunWsZFcAsXgO/PNdsxbeHLjtMzlu1FI/CTQg4AGkFE900r0wBvFs1PavPF9E/I5zGhzYSeN95EmgAQEP5EVh+R4Jd4Yl3QsmjGfDapqe4zieJ5Iq3eNPksPRYd0IeADQI4znM09EvKXfX5LxOhDwQC6KUL4X4RiQpcBth3vFtN0FbfErL1FHxitAwANASRhW07Zt227tn7szLm3PcLV5Mr7sCHgge5TOyNV1cDnrU9ELj4zHn236AAAAcwRu+7Q7GujVequZvntuOWHG84a1jAh4ACgyw2raRsfxzJEL3oaxX623mtMXsskqm8n4kmKIHsjYrFPhoEFq/rrgwBS1RsvoDV86fsd5KY/sRfPxkt0YO2P1ZUTAA2vhdwZnZNNbS8xTculiWM2WEfgiErjtnhEV7YF/LsadeY8k47cWAQ9kaWb5HlztGuEZudbox3yCS52AIcOyaiKBH+w/Gi40f3o+/GgmMn47EfDAOhi1/auzeNVeaxzvnvskPNIyDAlfOIHbdsJSPro8fs6bRjJ+CxHwQGbmjYobVrNl9GKn4FhND6RQazySl47jvJRHdtMymI/HLHTRA7kbNDybx7ZdC9y241yu90on6GJYTdsSkanz8XNfVPTVb5XK7S3bRahSqfA73YyZ5zu/0w6spmWI+B3nzBPzON3+XpkeDFQJ3I5fa/Tj3e84sbCfJ6uXx4rPw8kqbwzRA/mivQ65mTIfv84vz1h9wRHwwPKis9ucUqZI7XXDZqxk+5Wg6Mbm4xM+KsNgJuOLjBESbRj1WrPo7DZvrDKchB+sOBa4bddo5jpMP/UNx9jXDdz2aVdmroIG7TKcx1nuqThZ5Y0KHlhJdF6bWsf0S+bT4MC27bDWcpyX8ij3SfhproNdM/Z1Dau5oOsaqlHHq0fAAxmYvkHn2Op1YczbKYZSlzOrnKqZcsZCuYgh43VjhEQbRr3WbM7g5MRQfPI257wOadDJH1lHSz8KLtuxepk/XRXDySpvXAcP5MWo7V+ddvxhgtYax17bD6zNrG8zsuvo7B3IsHUyvKg9fBKu0iwIhuiB5S04kRVp9brAfdmfIbDtQT8AffToy3aAneH6giDggewNd4Y1rGYB2uuEDjssQsbrwxA9kLV+b124dJ1zJuax3RgsLZqj+Rfs1UxxnA4z7lgblrPdOHoctKFvZW1m7gy7od666Kii/08cHh12WCDzSJ7zhJys8sbPVxv+ZtZm5pkrcNunwYE9EvGD5eg3d1RAMmvLeE5WeWOIXqFKpbLpQ9Dv+fPnT58+nfnpw08/l5/tn//n3//tv70WOfz087/5w1+1/mtNBzbtBXD46ef//LP9/geD4wKmW/DyLsATIgneQAEAIn7H8cyRuZvJW1AOVPCAImOT7CJMtCOx4avHc0ZfRdV67j2iyAEVPKCG33HOhDzHSqjX9aCCBzQxTU7MWEmtYfMaUoKFbgA1aqbp9VidDqsJ3Ha4yOFgvSZ2KCorKnhADd/z5FJOnW78RubgkYrvdqXesgzxO12pt2xL3PbIlgooDQIeUKPWsO3Gpg8C5bdrGBK4Pa+63zJEGBIqLZrsAABDg20Hq/VW07ruOGceo0AlRcADmozsCcumsMA2I+ABNQK3fXq+P8z08Y8BbBPm4AE1roNL86A5THPDOjC73rUIAY80GAdSgoAH1LhjVL2ea9WGFXzPq+6zBhnS6I/72M3YOFBbyPgyIuABNQyr2ZJ27DI5ai+kxjiQHgQ8oIlhNW1KdqyAcSA9aLIDAMQxB68EAQ8oEG4QYnoTe8mxkh2wtQh4AECE3eT0YLMZQA2/M74tyOQtwHx3jOpVwPK0KlDBAwr4nSmD8yLCBCrSmvpaYqKnlAh4QA0GVwEMEfAAACjEdfCAHqOXN4UYXEVCjABpQ5MdoIbvdqXesu1jU8xj27Zb9aqYJudrpBa47bZLp13ZEfCAJruGIVIzTc/zw0VGPY8uemA7EfCAGtEFToP/BMHVpo8JwKbQZAcoErjt0+DAbtQG1zpxlRwSm32xJZ0c5UTAAwCgEEP0AAAoxGVygAIMrgIYxxA9AAAKMUQPAIBCDNEDarBNCIAhhugBtQK3/VIecZkcsJ0YogfUMqyD3a7LSnbAdiLgAb18b0ZrPQD9mIMH1JgyB28e20zAA9uJOXgAABRiiB4AAIUYogc0Cdz2afdy8BGXyAFbjCF6QI3AbZ+e7w+3j4v2ltvsYQHYCIboATWug0vzIHbVu2EdmJ7HZXLAdiLgATVqVv3qrDMM9MDteaZJ/Q5sJ4boATXYUw7AEAEPAIBCDNEDAKAQl8kBmoxeJlett9hqBthWDNEDaky7TC7+MYBtwhA9oMa0y+Qug+sNHhGAzSHgATXuGFWv5wbRx4Hb86rGnQ0eEYDNYYge0IQ5eAB9BDwAAAoxRA8AgEJcJgeoEBubZ9U6AMIQPaBCbN84tpADICIM0QMqXAeXg11ljNp+9SoIFjwAgHoEPKAPF78DIOABANCIOXhAATaKBTCOgAcAQCGG6AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAIQIeAACFCHgAABQi4AEAUIiABwBAof8HN6S5nN8snHsAAAAASUVORK5CYII=" /><!-- --></p>
+<span id="cb3-4"><a href="#cb3-4" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for Northeast</span></span>
+<span id="cb3-5"><a href="#cb3-5" tabindex="-1"></a><span class="co">#&gt; Warning in any(apply(xydata, 2, sd)): coercing argument of type &#39;double&#39; to</span></span>
+<span id="cb3-6"><a href="#cb3-6" tabindex="-1"></a><span class="co">#&gt; logical</span></span>
+<span id="cb3-7"><a href="#cb3-7" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for South</span></span>
+<span id="cb3-8"><a href="#cb3-8" tabindex="-1"></a><span class="co">#&gt; Warning in any(apply(xydata, 2, sd)): coercing argument of type &#39;double&#39; to</span></span>
+<span id="cb3-9"><a href="#cb3-9" tabindex="-1"></a><span class="co">#&gt; logical</span></span>
+<span id="cb3-10"><a href="#cb3-10" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for North Central</span></span>
+<span id="cb3-11"><a href="#cb3-11" tabindex="-1"></a><span class="co">#&gt; Warning in any(apply(xydata, 2, sd)): coercing argument of type &#39;double&#39; to</span></span>
+<span id="cb3-12"><a href="#cb3-12" tabindex="-1"></a><span class="co">#&gt; logical</span></span>
+<span id="cb3-13"><a href="#cb3-13" tabindex="-1"></a><span class="co">#&gt; Computing 0.95 -bag for West</span></span>
+<span id="cb3-14"><a href="#cb3-14" tabindex="-1"></a><span class="co">#&gt; Warning in any(apply(xydata, 2, sd)): coercing argument of type &#39;double&#39; to</span></span>
+<span id="cb3-15"><a href="#cb3-15" tabindex="-1"></a><span class="co">#&gt; logical</span></span></code></pre></div>
+<p><img role="img" 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" /><!-- --></p>
 </div>
 <div id="the-function-means" class="section level1" number="3">
 <h1><span class="header-section-number">3</span> The function
@@ -579,7 +587,7 @@ <h1><span class="header-section-number">3</span> The function
 <span id="cb4-2"><a href="#cb4-2" tabindex="-1"></a>  <span class="fu">CVA</span>(<span class="at">classes =</span> state.division) <span class="sc">|&gt;</span> </span>
 <span id="cb4-3"><a href="#cb4-3" tabindex="-1"></a>  <span class="fu">legend.type</span>(<span class="at">means =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
 <span id="cb4-4"><a href="#cb4-4" tabindex="-1"></a>  <span class="fu">plot</span>()</span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 <p>Instead of adding a legend, we can choose to label the class means.
 Furthermore, the colour of each class mean defaults to the colour of the
 samples. We wish to select a different colour and plotting character for
@@ -588,7 +596,7 @@ <h1><span class="header-section-number">3</span> The function
 <span id="cb5-2"><a href="#cb5-2" tabindex="-1"></a>  <span class="fu">CVA</span>(<span class="at">classes =</span> state.division) <span class="sc">|&gt;</span> </span>
 <span id="cb5-3"><a href="#cb5-3" tabindex="-1"></a>  <span class="fu">means</span>(<span class="at">label =</span> <span class="cn">TRUE</span>, <span class="at">col =</span> <span class="st">&quot;olivedrab&quot;</span>, <span class="at">pch =</span> <span class="dv">15</span>) <span class="sc">|&gt;</span> </span>
 <span id="cb5-4"><a href="#cb5-4" tabindex="-1"></a>  <span class="fu">plot</span>()</span></code></pre></div>
-<p><img 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" 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83u+mc+K71f1HQiov0f/sTYp//0n4je1R3vuyhNfK/4U6K9XNHSd9NFb9sK0Dww4vhH3Q2ad75FOZhPWONrBHkumFcxRRZ0Clz03vOzH/4Zev8jAtG+vWtygm59L2W/4h96t6aXLkbi+VfL7niDDwakj5g++kA4HhFIF0i/R+PfLwYfcfQfjObMaNdGyl0PRz3wLVVPZsVTak+OCYTjMTkWV5MsqceNkNuEMN7vqgJugMB7xviBcfrwZN0Nog9R7ay28qfGG2/G4nQ1mdAPiUQ6UYF+TlGOlL8iiAc/ousfLQpO/4CJrXZOvffkSv0ENB448cnD0LQadeLuMUVUk4wVKBCOx2rfbQDcARf9QBAlKZc1gmtaus5wWV0vVoyNL+o6kSAGA9bQeWsyniAGiw7/fBXOgN/ouOtH50pBr9iY/qHxz4vCW3Uy6sbdBTmmKIpiDZwFoBNgwfcRQQwGMilGUSUiRqI55nS2Vx0pz4WTCUOlApIUKOj7RIIgx6JpU7sC4XhMNMvUhcaNgHfu+jFro9R9WQB4gEvz3anrG9M/XLz98T7XQZSD2URaMFx6gjwXTKqajNHzoHvGSiW0z8OMriZVIeZoDMbG6v+mzoame7/lWOWfPnyGfOKbBQPEzTNQ12rvlcY3q0Bl3F3Q1WQiH4zHZIF0Na2JkVEw3Rs1VqBX4P4OMbqaTGQoHK9w4zV5Z5zmezf6N1Zvpw8fI2j8KNOB+W7TE4FvEXe3O+bmeJuIaLzQBVPxu6+A/4HAew3uL2+0fGfsdqdjd/2wCDxB40eYwQp8y7Nr6aQuWzpemahqdIDAew0G2Y0czkg8xqOBQfG6hReFu+/Y1Wp5H9SdMN8d9AUI/CjS5ej62i63bzvh6MH4E6eu91zj23XbOBW9L+qupVlaE+RYXMiWp9BgvjvoPfCQ8EZbXq9u3PVDNIoejnpfUVfRH3300V6VP9if28XZjVh7eXDdSMXdncBF7zW4v7zR7jvT29H1voXjSxs6PBV436s7WfF3QWVZYRRlvQwE3mvgoh91RjMZDvAD//CbEePfoCvSG9z2LfRxOSYLJEaUOdphaYTegWegA8UbHXeKux9d73NgxPuH119/vUrXvZ+Z5i2dnlpXkwk9NKKLwsKC9xrcX97o5p1pNFGeG2n074UM0YiGXjCoyWke4d/nyt9A4L0GLnpQpiqdrbHBU+Pl0xjEWINt0A5QdwCqgMCDamo1HnhIraJD49sH6g5ALRB4UAeOR95xdjlDihfpZfoP1B34HIRAeKO3YS3nyDue2jIfXc4QJf7tNXYkvkt1b/xrmrPMiYh6PdXcR4/Q0IIYvNdguVjQEKMJ82Kp2YFjX9egK0JUGoa1+bzBc6tdU/PBuBIzVF1LM8ak6IgOWAcjCQQeNMTQvypp94su8kRp5EbR95DmD2RB3ycyBF6MKIqsJpPqePeGPN4CMBTAQ8IbHXm97LWpqYmFw5+7npsLGWWa/IhLqzO1O3/z8F/K3Sk8HpteARe912CQHSDSSFKUeDgQCMeb+C+rRtdzMFQNA+6GnQ60thgUoe5gRIDAAyJRFLV0Ih+ca2XY2NLOzVKzfFwFqEFXk/V/1m6sd6g7GC4g8ICItHSKopUtn64m62bJrpsMB4D+00xuNTUfjPfvdAD4Egg80NVkiqKmb15LGyY6S2QmiBqug8GTux7dlGGkpdwW9P1+ng4AHwKBH3W0dCIfjEdEU9pzkqIo8XCApGgkIjabUMSTu37Y6z8itPEbiZEopXp4Xqg7GEYwiJE3Oh2Yqus6aTuJfDA+Rzs7NOc+VMnN6Pphr/8oYGu8m1+q7ij6teXdds+Ip8IjMIrea3B/eaPLd0ZXk4l8sN2UX1Uh+SFtENGUDwuNH7M6qevMXR2luMEj4SkQeK/B/eWNrt4ZLc1SFI0LOU2MtD/YmANTfnhrPjo0e8y0dFK3Z7lraZbKdZe6Ds+Dp0DgvQb3lzcG+85A44HXNB08n2Y5yanouppsK97k9kSgF0DgvQb3lzcG/s5w4K5Hy+5bWv40hhPKofEVRn0PTwS6Z+CNFfcgFz3oMVUWPBpK0CvcPEtiRImrScZSZgReyxWDUHcwoqADxRv+6RQPtcYPY525p61lYTseW4efvm/4p7HiFdxf3vDVOzPU7no09L6ieei9V2Pr8KP3E181VlyC+8sbPnxnhteUH7oKc4z5W+ytX9hYueNYVffg0f/7uZ/7vtuxdXvrFzbUheWVWbp9/fKxq/dKB8MnKUMLyyuz+Ln7jg8bK87A/eUNf74zQ6rxw1Vbjin/EGWFNtj+t6urH/3qn0nfowMv/biNsXXV5eC3HgD+bKx4AoPsQD+oXZ9mKBpTo7ZDUdXRZGN66qPPvPPuAaLv0f3f/k/P/fq/06lERNH/7i8OmWPrti+tnk1RiejhpxZfPkaGrj++s7Fyh0oXV7NPHX/yzU31X8i/+FuKUn3w5ICvDoAuQS560CfslPXDlbt+iKrKK436WBvTP6RPJfY++eBH7xNR8tavXw98NXVB+ZMnfu6pzP/zlY/LAtHt65fP0nF1bXl37Xjo6rV1a/Wk+VOL5w7SyTPLLx+bpAJ9N6oojQ8GYFiBBQ/6SpXGD4VxPERVHQ2uXFx9iYjod4mIDlx/U/oeEcUO/bsYEe3LMUX+p3urrxIR7b325r0TC0ZC+pmVtRmivXWjCPZX3yb6UEWptQcDMORA4EG/GVJ3PRgI9bpWJ84sr8waFnwl31ei51eNmO7JOWPXlPxAvWKVX/rMNza2iYj91bcD9GlqdLCWZqkckT35DoBhAi56MACGzl0/FJXkj+aOk8XbH3f8lbz1u9FP/Juv/+bhv7yw+OxBe/c99W6Drwfo06mq37T6YF3NUtR4RkN6gqXhtAfDBQQeDAznivL+l8+hqOSoUdb4T/39R+nE3ESuGBQFIqLs3T2iyccOT13ZMZaH3Vu/sHrupuO7Ruhd+aXPFOi7RHUPFoSJoq4TkZEhT8gmVb1PVwZAD4CLHgwS59y5tpb6HggIxveTxrf6/XyS/TRkzokzNF5XZ7e++dLFr75ERH8xdTI69XZuj2hy+tgzL15alZesgfGztL5lFO7wzBum/Kyi1BxMJAezibRgnEqQ54JJVZO7WJ0OgL6CaYi8MaRTS50a72cFdaoOxN5TmtxeKzNth4HxFj9cVdxdV5OJfNBMf5vuaCFlUJ8hbayGCNxf3hjed8Y58s7Pwmn3RfxcyWGnpQYndTkm76dZKtemyrf64XQ1qQqxiEjOlenMHgVG2vWW4W2shgW46IGPsIXTz6Y81H3wiFJQJyIxoigRXU0yVnCnvS5+ODPuLgrWynRJdTwmyzFF7lXlAegX6EDxxpB2iuu6vv2po7Dgvcaje+u2WF1NJnQrxO+06EGPGdLGaoiABQ98gbPlrZooPwgdNcKwdZYkg657zWDucGXcPRZXkyypmz6BCWG839UBoCegA8UbPHWKB+Gud0i7lq5ao4yIllbrZDhbW97tS91GgkGY74i7DwaeGit/gnnwYDBoacZazSpukgzHiynpuqpqJEYUJR4uZlWdxEiUUkhu0k8G5JyvO99dkGOKoihQdzC8QODBADBsY2WOdlqJfN1kON7IgKZmMjmNyJjwnFc1IjGiyONIbTLcuHlaRDmYT1h9OfvnB2DIQQweDAAxoohERHIsqic1XRaaGUm1yXC8cdePC1JYNAdWaXkSbCct1QvGg57jRb+tjSnvcWEHcXfAFxB4MEB0NZubCEXcHOqcQeeNBS/Ikmo5CQLh8ESCZaSooohEuppMa2ITiX9njB5EKNF3tJ7yniXjF9bSSY1iMUVUk4wZcXc45sHwA4EH/cS2iQ0C4bgScd2Sej66XowoSoTIHmmlmJLumBrdEGh8d/T8B3VR4L5eIOM3HRcot08kCJjvDngCAg/6hqHunY5KHiMiUkihktfuesOwsw12XU2mKKT0IokK6BPufgsxopCmEZVdM1qaZQWMmge8AIEHfcMwj7Q0Y8l2RX6sYlspNTDl7cN6ZktraZYqhuMxSwPMGXHvjDX5DmiX3vaN2ilNNEdd0IQwrqtJqDvgCkxD5I2hmFraylCyxz6RFFUiwXqHlIiqksqN1Tmg8/o5zl8/9l6l8Q+WCEZ8RwxO3csYziWMpewzQ9FYDTW4v7zBwzujaZoojqvJHZqLyUK1chtYl1hf3SuP8Qpb4x3Rd2h8u/hB4Ik0VR2XYbz3Fx4aK3+D+8sbnLwzThu/lXgzxpTj9dr0Ad0GaLx7/KHuYDBw0lj5GCS6AT5ES6coGpMFY4ZavubzyjYBbTogqDsANaADxRvD3ymuXMzLpuUAuh7G4LsGYuOGHt4l3PBhZPgbK78DCx74Cy2dyAfjNWOddDXB0vmmsl2q2PYiWb17apPnA++AugNQFwg88BdiRLF88+zL6/L//udG5rqE/rGv/8lXZy7Zy7btnlva2q7+csn8V5W7nohob/3C6rmb1V/YvrQqL63OLK3OLNX5tBV2mfUKr67A7jnrRDNLl9fbznRev/7dHTlQeqXKUHcAGoF58MCHmLOWjjz80CZ9VjkyTUTaG1+Ohk/m79+mmWki0u5nDx747Ubfd+a1pYZB+u1Lq2fpuLo2Q0SkvfH0+cvrzz9z2ot5UtobT5+/ETqzvDtLREQ3t+Tzl8mjcw0FUHcA+gAseN7Y3NwcfuewsVKn9N6d6R9/6zWNiOj2W1mSQjJly38elqeJyGGFO8zW3XOvqF9cWp15Rf2Pn1YUxv7w0sbKHXrpovOYvVt5OjFnLe8uHvlC9N61t/aofplOs9jc3q4qc2fLdAbYbgarh7H9yg16anFl1jrz7ML1p2jlld3G57q8fr2iNMe59tYvXD536bK8VHYeVJ93RIC6A9CCEuAL4zfd3Nzc3NwcdF2657V//6Vf/4/ZQqn02lf+9GK+dOvVP/39vymVSqXXvvIlY6P0N9dm/uCvb5VKpfxf/8rvXHutVPlp/q9/5XcuXiiVSpsvLf+BtdPi1qt/OvM7f3oxX3NWu8yS+vvmAfcvlr9ub1ds1HzFYvOrv173LFXnKte/bmmV5/qKWrKu9Fdevd+gVn6lJ08mF4/3qAMB8hpY8HyiKIq98NowG/TT//XUjw8cEGjvVv7AIZGmHzhwZWeXaO9WPvz4LBHR9k7mIcOUF498IZp51TLQs3f3iIjEIy+vnX6WMab80mcK9N1Uxa2YPvaMuvY59bwZGn/6umW+72ROLByZJiKaedxh1jfH+sqkfPCeerfqwwOHGnjjG9W/aWllx8P8qeWXj00SEdHkoboZ/7gEtjsAbkAMnmfsRtDW+LrNoo+by+lHQvTKHmn3rwVDLxPRbOjE1v3b2v1rdOBL1jFvX92YuWpuPyztEU3On1q8dWFDvkolooefWnxZURR25feIKFq7DN3MytryChHR3vqFjadp8eVjdCtPNGdVQJrq9hqUY/Pf+CrTaL6BxtfUv01ubskXM8YUgpNzLY4dPD5+2ADgDQj8SFCl9EPUwooHQqns9hyRZKziOSlT9vZdosO/MG0dcuLMcjm8bTJ5+rnl00REu+eWrq0/8sxp5Zc+87cbH0ox9lu2xu+eW8o+vrYwb39lIbyys0c0cyhIqlXQ7dw9krq8hslD4feu/cUV9rsn7Nt++/rlY7nPqadm6tW/DY23xgkuGB0UtfU3hh90EQBwCVz0o0Wt697vzeXM49H7L2zdf/IR0xH92OH7L2zdDz1g/Enzc+ErW2/cJiLaPWdOP7M3aoha4+oZY+ydT0YzZx0D07Z3Mg9Jk1VlvpqaevKRScMBbrr9NfXanfauYf6Jo5T9zte/bPlRbm4du0rnnphpUH/3VI4TtAMTvqX7h83vjysAfgIW/ChS67r3MdMSvZ068AXLvz39wIG379AXHCPSX9xZPbZ0w/DGr4hENLNyJiufX/1DIiI6eWb5tEhEk48dnlq5uEqGucwYU5RnGaN7m/KSmSLn4acWzXi2o0zr6zT/xNEXzm/MXCU6ePTZqGHi22Uuys2vQTzy8qJU89sAACAASURBVNqBc0ubX1xa/SIR0dSz9hy5OvWvS91zTZ7+/NGnz6/OEBFNnYxOvZ3bI5p0e2eHDqh7H3j99deNjUcffXSwNQHdg0yBvNFu9kenxnvdei6tztTuNFdY7zsVS83296R9O52v6PLaR/nW9Q1b3Q281nikqvUa3F/eaOudqWo0m4/F6x5fCTz1t3PjPOkIChXU3f9UqbuBpxoPgfcauOhBmeEdi9cZxgX22ZTvv9ug9To9/gbqDkBnQOD5xsz5Gq1Zm82gUbtpK1/zw/jAmdeWwysdq9wehMZ3c2P5/FEA6AvwkPCG0+ulpVlOUiKi9X+nZfbKoPebi95Jn931fdKtsXo7+/7Gd3yxUPc+gxg8Z2CaHM+IEUPVRUkq6joRkZZmjKXbXcrMn3nxxqx/PcG4RurXSq+js54sRHqIcCo6RtFzAFz0fGO46ImkqCKQriZzkqJEtDRL6vGYLLRXlsu8eP3BI8dzP9313AYFekT3NwczvjoA94on4CHhDcvrpWmaKIpERLqaVIVYRLQ99uUNXU0mMhONIvQtGdRYPK8dz31z1/dD4KtuVn9f9wE65/vsbQYdABe91+D+8oYt8OmkLsdkgUhXkzs0FxNUlsqZB0lRIzKfFeIxed/8v02D3qb/Bn1/Isv9MeX7qvGjqu4G0Hi/AYH3GrjoeUWUg9kEyxARkRRV9tOMoooimga9SLqapWhMFogEOZxV94mEDg16X7nue0h/3PX9cNT7vgl13gGELQDoFehA8UaDTnG1QR/SE/bAeuMzQe2NQU99cd33zfHcH3c9f6rW7hW56ktpadMLFQg3f0JhwQ8FsOC9Bhb8iFBl0JOelCTDTtfVbDE4R+pOjUHfMX2YRl/ql+N5IMlwRhAXt1dXs6YXirQ0Y+kmrqZHH30UMXgA0IHiDXedYnvgnbkl5ViVQd+NBV8FH3nxvA5A8NR76OBa3HShKp5Mc2iJKzse6u5PYMF7De4vb7h9Z2xvpxRVIuO23rtpNzuDjwi9p1fBjcZ35p9v/V1dTSb0kGW4l3upYDiBwHsN7i9vlN+ZvfULGyt3KhzY5RVRK6k26M1Gc2/9woa6sLwyW3Hw9qXVsymz2JNnqj9txd76cxvbM/JvPPDe9t9+50M1hVeye25p8yVz27HEqvtz1at/d0c2sDV7pc0caHw36l6Hqri7riYT+WA8Jgukq2lNjPS+Kwr6BQTeaxCD55sT7gRYkEOWbSpFlWaLm29fWj1Lx9W1GSIi7Y2nz19eb1d3A/TpqKLM7mnf2NhOMTbboHHX3nj6/I3QmeVdo/43t+Tzl6ltjfcAOwmdrUwcqLJfqRN3jymimmSsQIFwPAZ1B6AxEPiRxGHcR4/vnpohEiPKg19b2nyJVHolYdjl25c2Vu5Q6eIqlXsJe7fydGLByigvHvlC9MYLb+2dFifJYdlbZr3TLDa3H9+xy1yUA/Tpn/nA8tLqF4koGPyj//lfOTVy+5Ub9NRiuXcyu3D9qcvHXtk9fWqmwbmu0eEDK1cz9kU56r8ob11Tg3Qlde/EmeWV2drLbxNb13s+vGDYh/LVr3zjuE+rixWEiaKukygQiRElriaT6nhMlmNNe6EAACJCLvqRZPvSxrXDi+ra8u7a4rP5zXM3jZ2bdGZ5d2159/mj2Ytb20TzpxbPHaxywk8+dnjqysXL61Y2+/lTy6bP/+bW2fzR62vLu2vHyXFAFVVlXskfML5yMv++9jVnovvdV1NTTz5iRRMYY0TTx55RDTG2z2VVlYiI7q28aZWW+ua6VnWue1foc+qa2XGpvfxOqE0A0BOGN019I7XW1MxEqAN1JyIS5WA+Ya2eIMhzwbza7lIKAIwqsOD55srF1ZfKf5lh7PlTy/PmnslDQVKtj7N394gmSTzy8lrDAqePPaMe2z1nrQtnB/W3dzInFpaniYhmHo9uvvDWnhtf+omFI9NERJPywXvqg8+cnrXFsvhdOvB4gxK2dzIPHV6cJsOFsPrqzYX52ZrS7hJVfv3EnGmpN7r8ruit2T3sdnwFWjpFUUW010UgY2BnqskFVsbdY3E1WV49YUIY71fNARhyIPC8sbm5afqNj1KTGPzNLflixhwoN0dENH9q8daFDfkqlRqPxbOYWVlbXiEyHO9P0+LLx+hWnmjO/Hhamuq8/majv6d946vsa+xH486dZd6+ujFz1dx+WNpr+yw1l98JVWO/+ZgN2DENzfdcjoqCTqTmg3ElJpC5pmHjG9WnuDsm0QHugYueN44fP26u7vpX3y7Qd1N1FnjdvrQq74TUJ+Q/Wlt89qC9e/L0c8vq2vLu2vHQ1WsNfOy755ZslzgRTZ5eCL+d2zNMYZvbuXtdXcIY0djkobffu/3Jo4ojZ87t65flS+ba8SeMaMLa8u7actO+SB3Myzdc9AdbH98Qp0T1fKnZ4XXUVyFGFCWkJ1gqNyEY0sxSOSkQ1ht+w4y7m1+OC9mkqpMgxxRFUXo1f9OZBqdu2jsAOAACzy3KL33GGK/uXMqdMWYMlJsrjyzL3t0j2j231DBw7mDm8WjmrKWyZHjLpUkimp8LX9l64zaRI3w+eShoFE6kqdfuuKu2lZ9uPnWUrm6c+zJjRn/ly+vHrhaOf+wdVnkud9V2UvfyW6ClrbuXbnwy5+j6tmrUskD/08Ai19UkY4zZqxzpxpFRqRgUmwh153H3sTHzX1NqFR0aD7gELnq+qYzBE0WP77Ib7NCBP7u4OkNEr3z/ZHTq7dwe0czKmax8fvUPiYjo5Jnl0yIZQ+pWKkbR0/yp5RcvrcpL5jz4sjN/duHFndVjSzdK5a/T/BNHXzi/MXOV6ODRZ6NGtNsuc7HOOGhnw6wdefmPD5z7nc0vGsPsaerZ50+fFk35/K3gDeNcDz+1uNIw2F/3XJOnP3/06fPGGIIp6/Kb+wA0khRFVpM7NNc8rUrPR9cPdzBeK3vljbh6IkdExHKSEqmn71boPRCOx+LUdtzdqetjY4QJ1mDkQZ4B3nCZO8LO1mLv8YOKuF8Htt958TTHEjwuMqj1MHe9bwXe7sQ0rKGWLidAJmKMxcOBxmkS7bw1WjpNETPrUiJTaLmyDBFRfau9wYuApWh8AhLdeA3uL2+4eWfqtsgDFHstzVK5QDgeC9VrxptfTF+U3lYqXU0mMhSOh/REipqvq9vDivlW46nVQgNamhn3ybqEJgsdWP2m8mh7V8pu0o7AU43GQ90HAgTea3B/eaNjga86wPmnh+piLEEvSTkyTb2O14H1bBB7OQF6m2Z8L2vlW413uoLq1tDWa0VRWi1kpGmaOE4aiaIx2L6NVY/aFHjCKHofAIH3Gtxf3vDinfHIuNfSLFUMx2PyvtWSGwoat9r0Di6j5wZ9WdQr0rG1sSZPVZU6lmofarzLKhnO+USmQFJzr0cFbaear9J4tGy+BwLvNRhkB1pTtapK3f1to6VTOaIAEWm5YlAWzPnPMVkoWfYxmT7xCfeyUJVdrntFFCOKcWpNzQfnrDnYmpqZCCnutMe7vLbDgMZYypxD6Da7rDnWru0p76VSWeMhGwDAguePfnaKeyD2lgM3EI6H9ETVmvSCaljP+w7XeIc17F5Wyw7jykVL261MNzXxlRHfIllNMqGHlFyKBaToXKTZpDj/YOVnrGBtebd2J+gJsOC9Bhb8qNCpKjl4xzKPHjTfyR5Z9obfVleTkmQt9J0tBudI3aFoTBaIBDmcVfeJhG4N+vbrVkaUg9kEy5Qr3B52rLobmR+iWXPinJJJMCIpNCTqDgB/oAPFG/U6xdYa2oJqjmkmx6raLnmnMsD5YLPHpiOxr16TXsqxnhv05OFYvBYnre0MdVwHP2i8m3GaUYlyUpRSqVwnPaIBAAu+z8CC9xpY8PyjqzuWlkeiEsupQjaTD8aVOS3Jku5E/p2aIcrvjDXR+I4s+6o16XU129qg7wBH7tuWVeoZVWexTfmB67RHGOnqWE5SRJEUJTLo+gAwmqADxRu1nWItncwWC4UCGb7lccf4b7cTkWoFnloY8XVpZ/Zda4O+J1nJe6f0lSugtT+6vi0G2zlodnZdZYmMsdnONHZfAAu+z8CC9xpY8Nyj5XKFiagSE4m0NEtr8XKTq+vFvlalShWaGvetDPoeCUevRt3rqi4pipRmWWHOpag5R9e3e94BBuObn5clMuG4IpOaVIWYoLJkx7EUAEC3QOBHgEBYNqRxXAgUdYqEJpg5WoxIirppfR8stRWDd0kLT74YcTh3y2uP6Vp+ItSrJUOrK9Paqm4wEUuQZUFLM4oqbcpZx+56Pw+409R8UJZJGO8ilgIA6BZ4SHijxutVTsmiq8kdCs2Jorlsp8tkbDY1o+g9or5lb7vA+zJiq75B3ySVSnezFDpz1/df4FuY74wp8XAykSkYv1EPQymAR+Ci9xrcX96o985Y2ihFlQg506p3OW+uDwx2OZwK3W2WDLVxYrvKBVfcnM7PGl/vdOUp79ZHVnKDIRk8DwYFBN5rcH95o/U7M7TN7wDFnjGmHD9e54NSyfi0/oAyI89tSE8YKXldj7zzp8Y3OpEjWRHMddAGEHivwf3ljRF5Z/q3HI5NYwu+rvJVphpow5DvwF3fH41vdBarf7NvLQoIlQeuGJHGaoDg/vLGaL4zfTLuKzWebW7WGelmL6EjWLZtR66Stkz5Pgh8E3VXlKiqjsv2KjyJTAEyD1wwmo1VP8H95Q28M96KfeUo+gYy7AzJtzuUsYx/NL6puvtxGD8YCtBYeQ2myQHe8GTtO5ua9sheDb3yFBPWVAUtT0JnQx2cM/daVr7/s+b6drqN6R8aG4u3P96H0wHADehA8QY6xY1wI/btilbdJPNEZM4WI+rJ0DP3prwXolu3zP6ru0ELjd9bv7Cxcif84trCvLHj5pZ8MXPizPLKbJf12Fu/sKEuNCqn+aegAWisvAYWPBgVvLDsa5PMO8vvlQT6LXf9oNTd2NPKjn/oIN3SaF4kItreuf/QQa9q52Dy9HPLfTgNAO0BgQejiLdufA+WtHHpru+5o94/vQrXhIJ07a290+Ik0d4tOhCie/ZH25dWz6aoRHTStOmdlre9vbd+4RodPrByNVMioujx3VMz25c2Vu5Q6eIqnTEO2Fi5Q/anzb87mLsAABF9YNAVADwwZv0bRhQLsjLD2xgHaGnGWFLVm5bStGRnaV1WlWqmCNYe05NzNcL/kj8XCuX2iIg0VZVCsr3/5tbZ/NHra8u7a8fp4uV1rUkR91bePGAceTL1zXWN5k8tnjtodgu2L21cO7yori3vri0+m988d7PFdwEYGLDgQbeMVW4PaUitUaTZ2izIQueT3npo0Ltx1/fKjq8tpM/qvnj74+3F4A0m5fxfb9PM9FtZeuBJe+/2TubEwvI0EdHM49HNF97aO934dzyxcGTaKOrgPfUukePI+VPL89aJDgVJbee7APQVCDzoilqrfXg1vgotzchM4JLU5TnGEkRElEuxXDje7poyRDUReupU6dsaXd9DBmK7OzXe7Sj6yccO02saUe7A48fo1paxc+9WnmjOPGJamuqqVje35IsZ4zE/OdfiWNCK2qzZFXvsVSioYfpNF4e0XwkegMADQFSrlFo6lSMKEJGWKwZlQZCtA3Q1mbBX4yPqoEXpyVi85qZ890Z87QSBQXnm258dN/0AXXvrjZBamHv9jd0i5YmqrO3buXskdVid7UurZ+m4urZght47LAa4QkuzFEUVRSQyXr2kWj0rxcUhIwti8ADUQ4woiqLM0Q5L5QqZHTsCr6s7mYmooiiKEpUoEI4T5VKVMXv3OCP0nX2dGofkuwnG+0fdO2M2FLp6I/UvP/6A8effvv460fxc+MrWG7eJiHZfTU09+cikofrZu2bA/todN0Xv3crTibny0Dnz66OGp+M8yuh6kSTJ6j4Lckgq5LWK0TC6ms1J0Uj5kLkwGYfoajKZTicZY2nN+NN60dLlkRFa2tjVyRibIQAWPOiKUo2Xng//vAPTQDeXVAmE40rEyFCXpWhMFkhW7GR1nQ3I78agb+6u70kwfujUnYheV8c+TgeFjxK9a+15/fVHF17cWT22dMMYRW8E4OefOPrC+Y2Zq0QHjz4brRNQt5h87PDUijGK/vNHnz6/OkNENHUyOvV2bo9o0vtLGnLqdgg2NzdbfE0Qg4FMKilYJrkYUSqdZbqWL0gh5z5BjsWs7ULOMu21dCIfjCsxM4F0WlMiIpGWThWNeJuWZqmOnTr+BXkGeGMguSNsjR+qh8kI3LlwsGt1VlFxrh5jrHsuqCwrGGuuZIV4LJPocDmcziL0VRpvq3IH8uz8yjCqOxG9/vrrtTsfffTR/teEV9q14Os+RWZjZS1HWInjxSyH2GvSRjVeqLlxVN1+d50vMWLwADRgqHTdRowoSoS0NGMpIrIXRKNqxddIikq5VCaRJLt10fWi5TnU1WwxOEfqjmHQkyCHs+p+dYvm3rjvbCyeMyTvVOVujPgWX7SbXSwtwwU90exOqexn62oy4XCZG2+qud/xFhoU9H0ic9kHZ/rImnM4huJJEhn+fxtBmCD+vPQQeDDiiHI4kMsH4zFRSzI9pCiUZknd2YaIokiiokRIV5MsGaw2IbT8RCi2r7IJyWzv9vU62ec7SK3Truu+UUi+LY23uwitzqir2bL7k7F0Z2OXPeLRRx+tMuKHwnzvub+kLc3uwGPkOVXLLAtySMrkTD039ojBQCanRUSRSJBjikykpVm2XkEpiipKxNF7qND0CrXnBgg8GG2M2FxMFrT0TjAeE4koEs0lNV0WamxSswExNkNWGydFFVlXs5UGfVN7tl2xdz+N3pbnKqlo1453MdteECaKuk6iQCRGlLiaTKrjfrLjnRo/FOruhoEa2YNAlKRUKl2WeC2XCwgVtrkghyTmiNKTlssRhavK0fUiOUP1xqMrSlIqq8qiLJCmZgocxuAh8GCE0dVkiqKKLFiT4Yy9rvryttuQiBy+PcOgd69z7sW+pUFv63HL6Hujj2oj900KEeVgNpEWjLZXkOeCSVWTfWTFD4muV2l2yzSFHlfHb4gRJZou35R60SCjf1meuSpFlZhIVOFwF+S5cDJhFBOQpIDp1hcjcd34ZkCSAl5fywDAIDvewAJNrnEOq3Gu2l7lFnSHHd/rMM9GNS0t+1qDvnYoUu3IuyYFksMB0FBIquLuupo0HSCkq2lNjPjIhHfQ56GC3TjGh3RUY2egsfIaWPBgVNG1PIXnTC12xM21XE6SIo2/V58Kg74HNLLs7Y/qynZcSCbywbh1VVUj72pLdtJa3evF3WOKqCYZK1AgHG/DcTFUjJxjHPACBB6MKPq+HgxFLEkaFyhrxN0703dPaTIgnwLhuKIIRES6Za/Hqr5bFU2vK+Eu1J0axd3LIxOGB+9GnwHgH+Ah4Q14vTrF9D73yMXuOUaAgXIpe4+RsaPWUq8aGN9I4MmNklXOFnYGNgYONHvoQGPlNbi/vIF3ZkSwxVVPv5r4/qH4Y3KiQuEkInPOb+3ovNpMtNRE8xrH3Rljna2744beOsZHKrbtAc7lXKxecJP8M+5AY+U1uL+8gXeGf5wNazSYT+UnonMR0Ui3mTPa3rqz4Y2NWm98i7i7baVrdhqgckoR7yZP93xGeJ0Cx6wcjHhl3GKkbZSFyq0OhqUSGivvwf3lDbwzvONQXGeeTq0qCZ+WTuq5QqZ2yZmqAXctTdtyO151xqEafVbnMscqV1HAW+OCyoev3nPYDmisvAaD7AA/LK3O1N2/trzb55p0SRv+5AkjH48xvt1Wd11NpiikUCpDNQPynapcq9D1NTvnXB6XnIvlDovfu4W6G3v6LzaONOzm4A+HL9x/KYA1NWMnbCQrXQyvaV55AAIPwHAhyHNC0sifTyRFa/VVS7NUMRyPiboQcGVkN5hzbwbbC5mEEg/Xne/ep3yl/KKp1hJnRJqmEYnkR123cKzAAFUfCiDwAAwbglwg04bOpVh56JNjkzJlM1uJh+sOdq+aH2/vJFPmBTEo6fpOgYwkvfzPd+87ul6cEPbTLGHO3jB2UX6HZQo+FHpdyztXWRClifLU0gmfTS0FRASBB8APuHWVW5h2tq4mE5kJScpR5RCnmni8PX29tvwqja+7Yg1jjEiK1rjjh8U/X4dSqQ8xeBfJ8HOpXNRcyCipjsfkfb1AhlGvq8kdVfSXxFsRIQMxEsoZT4oUVfwxVxJUAoEHI0Q/50p5na/UdMQryn46Kchixf7ch6T441Xx+Fp1r7saTcU0el1lCTvcnkux3NAoerPYtmUZOzXeS3U3tutpvCBMBMLGbycIE4XcPpEYsaRSEIOkOhdOGziCHKsy03udvxH0GAg8AG7xUSoVLZ3KEQWocpUcw6D/FH3op5I59G47kfnRx8Lxxxz2Va1nvkrdq4z4AEkhJSLqaloT3a9qP1hqY9tarmhO2dfSzF4Vx7NRdVWL1VIDjS8nUNT1YkAYd844q3KIA9A+EHjQPu9Yds+Dwz3FZYhmeVVjmE66mmSpAlFRFUN6wmHQT6TMS/tUVPlMjpVdvY1S0jp3Ghv2dsGy3SMCReS2V7UfBLWxbV0vWt7lcSFQE7AYFIIcC5lrpZljG4RIXDeHUEpRJeKHSoLhBdMQecPbqaXv1Ewu8pnG+8jI7gN24ljD/xwIx2OCasxarzdh2QqlR1Kul4t1flR1sOnprkxxZjDoG2u4MqyUPDs0FxM1Z8YAx8R+j6i14GlIlq/tJ5gH7zWw4IFratXd2PlgydPYdg81m7d8pYIcM66mjkFfnrBsrJTHGAuE4zF538gv27zgKnd9ecOSc+dtrB3tPWjjvja2Lfd5Ttejjz5apfFQd9B/IPDAHXXVvSOG2DE+BEiW3WpNWNbVbDFYSLCAFI3JgjFmS28wdsvpqK9ryut6MRAIFAoF+0eMhwO107oarXXbt5+yNrYt9H1Ol1Pjoe5gIEDgQW9wL9sQbK+wDXoHupafCMUKqcyEJBIRYywqBfTxRkVoknGMYo7lrgrYV07iormYucKNMeS+7rSugYh9bWx7IHO6oOtgsCAEwhu9CmtVJzCfOV7/sN1N8wDIdjfUJijtcqku++tSlHKpcEASYpEUY0o87CJtuGYmyrPOXG+5uYqlYu2nxe4ZtGTQbnwweBCD9xpY8KNC147xUt0RdsqDnRQOaqmS8frTutxjzVBmjClKXE2qxm7DoG/VWxDtCpGaZJmCUTfGWFSiqklcxrQuy4KnlHMafVP6ZtnDTw5GFnSgeKOR1vam3WwwQY63wWt9R1eTO3kqFAqORde7XaqLnL+Lw6BvvaynlmZZgQqZcIDywWgwn3Na6uEAZQrOguycMhVFt1hjvmmd7e3uHyqMdPMzsOC9BveXN/z9zmxfWj2bIqN6J88sr8y29e299Qsb6sLyyqy90eJcL0iLLx+b7OC73Zy3E7Q0ywrmWi69mtZV1ety2wmzp94ZX6lx6bel3My1Qd/8650V0sO5anADeIG/GysegIse9I3tS6tn6bi6NkNEpL3x9PnL688/c9qr8U67r1I49KZ6+9iRaS3NUvsFc//3/rFA300x9t3a4HbLBD6Tp59b9qSyNQlKu53W1aG6k67uZCaiFSPsAuG4s2/RaKJ8XexjmncLGpXWZC5+Pz1GLpLOAuBHIPCgX+zdytOJBWvFdvHIF6I3Xnhr77Q4SQ7L3jLrnbayuf34zsbKHSpdXKUzizIR7WzJFzMlIooe3z1VvRD87evfzEpPfoGuvaZ9Jp4t3vr2m/+n+d2Fj/0MiVFFMUteXblDJSKKRv7u1ANExakLf0OH/0a+mrdL3r7kOO9W2YK36/zwU7afoFNqE5R2M62r84iJruUpPFfZ56pYX8Sibjq8JlSlv+2segMZkO8y6SwAPgQCD/rF5GOHp1YuXpYtq33+1PK88cnNrbP5o9fXjkzT7rmlhmb9/KnFc3nLVb5FV/IHrq8tT9PuuaVvrj8xU/mVvdfepCc/Pzn/wIGzf/F65Fef+tWJd/e3vvWD48srh3b+J6L7Kca+S7duqa8fXlSfmyRKferC14M3fzk/S0T6J94U/3Htl9+lD/6+UXLleQ1uX79seSN2zy1dW3+kO1eEWJugtNNpXXWT0LmUQH1fD4ac6VH1cEDKpFikgXlda5c3P1eVQU/tdxRqi6LGYo9sM2DEgcCDzqlYlbT1tK7pY8+ox3bPLa0a5rZt+G7vZE4sLE8TEc08Ht184a09N2J5YuHINBHRpHzwnnrXHPltVUy9RqEviUTjE0cvfu8HIkl2MtX94rtEB6KKMqurycAvzxmW98R7QfqQfcjCzLuNSjbZe+3Ne5Y3YmZlrdp/0AGCHFPkyl0dLNXVjboTkSBWJj/XtTwJ8cYaXOWud3+uWqXvhiZij2wzYJSBwINO0dVsMRAgc90Ot9O6ZlbWlleIDMf707T48jG6lSeaMz+elqa6r9ntt7Jv37n33y/dMP58/8vsNx5473v79MMfEM1+9jPjKZXIjHant+T/lCkRfYroR3PNyqxhSn6g+5r2lN7PZRDkWKz1UVVr07VL9Rq13dFzNz7cAGB4gcCDztDVHT0UC+WSxlAwF6t17Z5byj6+tmC65Wny9EJ4ZWePaOZQkFTroNu5eyR1WbW9196kc88vm26Am1vyTujF8K1Umj70CSLtW9/+sWGs6//Xy2/+b5PH1bUFo7fxv1QU8mCJ9tabnaWRce8neiX5LR3p3Wu8sdFDpafGYt9u+XADgCEFAg86wZB3mTTHOmKWqgsNBoDPPB7dPHsppFoD4rZ3Mg9Jv0BE83Phs1tv/PbskWnafTU19eTzk0R0KEjX7u4RTZKmXrtDIfd109Rrwc+9bEvvbOjExWziv/3ge/9MRETiZw99IHUjxdh339t9l078fNm7fuRu8T+bmy2XyJt87PDUys7uyuxM5XjAweF1KgI3wfIO0erkCAAAIABJREFUAuq1q9YaGx1Po3d5onaNe+g6GEYg8KADNDVTyBEz1D3H9KgScTGta/7U8ouXVuUlcx58efD57MKLO6vHlm4Yo+jNIXhPHH3h/MbMVaKDR5+NGia+MUzPGkXfgNtvZUNzzzh2zDwe3Xzh9uKXjt49Znz3I/TpqKLMkhJ94+nzxoCAqZPRqbdznyjR5Dp9Xa0uss55p489Y1/Lw08tvuxDde+55DfRb+cSNT3R5p6Mum9ZvgGS5gJeQZ4B3uhv7ghHwjU7HUt5yhfoBy1FtwY79xy1m+jeZafBqfFamqVy5bNYQywrWFvedV+gp7gUe6Ru7AlIdOM1sOBBl1ie+UGs1gXaV3ciTc0bK8IREWlpxpib/LVE5NoJb9vfAaIJSSJJyiSYrCi6mnRzliYFOv/0Alj2gCcg8KAbKoZZdzCtq2e0TELHIx3bkYXygvBiRFFkNZlUx10a8ooStZSvmfWvpRkFwoVCppDLEeUURTHS8XZQW8epPRmL1/J0BLEHwwk8JLwxil6vqmXuRkPj66u7u45ORQIDY4frdPe6qu7LcoqxFvKeyhlLsSdYioiUeNgI5nTmom9E31z3tSe1gd53zCg2Vv0FFjwYcmoXsX1njHuNb6Hu1OImiBElriYZS1lrz+eKQbeBeEGWBS1NRM36A4YzR1eN5HyBcJwlEkTWsMwaVJ06WCxvbIyIFCLa3OyHQe8Exj0YCiDwAAwZrdXd3lOh8dVj6xSZdDXJWMFOj+sKXU2mKOoiGM8SmQBJISUikq7mpUyhgbwTGREDXU0mMhMuhwOMOS73+HHFsAMHYtBD7IFvgYeEN0bO61UrbMSzl76hrLa8DxVueC3NUjnXY+scVKxO73oQgDmzIsXYK+oXaz/+N6d3BdVYMHffXji3CWP1rtV+6r2O0Lc1lcDTmgw7I9dY9R3cX94YxXdmlGLw3Qh81fTFCq12h1Yjv2413l6qIBCmQiYckMzZlUYl5mhHLe+wNhvSXOCddTM2Bq6vEPu6jGJj1V9wf3ljRN8ZfkfROxW0hZq26uh0M7bOTfVcozOWICJFUQw5l3LlvoebOrkUeGclyTfKCrG3GdHGqo/g/vIG3hn+MES0iZSOWYpX+v+sXQ2j70T2/LYe6LtdvXh7yXNsg16KKpHxstHu2qtQpfHNHnnrULa5aWy0KatGXTuJZ7RkxMUejZXX4P7yBt4ZLnGj7gal/JtVdnqd6Luxv3eaxZyz5trpNxgKZ3vs3fjnbezrdqPuzkM7Muit+xYIBAqFggdyP4Kz79BYeQ3uL2/gneGPJhb8WD1vdamQrbCDexF9b4aWZikiMi3yuKzv78uia/mrELbeCmdTV367EXpdTSbyFChMhJSIWBPt6DmjYNyjsfIa3F/ewDvDGc1j8PUFvlSqMoW9iL7bGGVlEoaj3r0FXsarGLm7WL0rpTeGF4aEfdHsurTlbOgSXsUejZXX4P7yBt4ZnmgxhE1LjwUP1+4ulUq6mtbEiFPAjTh8b6PvVi3MwhhjgUC4Y89A72W+zcF4jSrAGLMm9NvUzifoEzyJPRorr8H95Q28M9zQaoC6aUMGK2Usm9jMFIxxbqQmE8nssjaxOjsRCMdj8t1zS5svBYN/NBuKKhGRds8tZR9fW5h3W6G9mpXv99YvbKwEH9s69A/GALsAvfef//Y7H6o4pmVpjmIbavzuuaXNl8ztqWeff+a0W8vZuDn/1dSF3/3Qwu/lZ1u+Gnvrz21sz8i/8UC5GjpjCWfoQFeTiQy1tQqfRwy72KOx8hpksgPAj7iYfiYIE8UUY6VSyXbUF0olgchctV5L54PxJz/y0Ffos8qRj6UZ+9r7b0fDJ/MHPmuIlXY/e/DAb3df1dRr63PLK+aiQ3vZb2xsd1yUMdSg6tq1N54+fyN0ZnnX6DTc3JLPXya3Gl8quRuMVyZAn44qyqxDPgOBsGyczFr7VlEGre1EhCR6oBUQeAD8RXnOWytBEuUg5QqadaSuJlWNnH7kgr4vyk/Stde0I6cjymf/cf0nPwh9mrKvaUdOi3T7rSwdfnKaiIi2L62eTVGJ6OQZ2/guG83Gzu1LGyt3qHRxlc5UGOgnzhyni1vb9TwBNcXurV+4pgbpSuqeeWkXV+nMokxEO1vyxUyJiKLHd0/NOE357Vdu0FOL5TPOLlx/6vKxV3ZPn5ppdAo6fGDlql1a6bVLq2fvUOni6rkzi/KWWYETZ0znwcodKp/Xib1GbaGQSbBMPBxI5IN+0fYaGok9Qe9HGAg8AD7COWiuvgOzMiWcEg8nWVI33cUTwrjjSDESzTH2958M3vt/7xKJdHvvIwsyPVSkvzT+zN0LzU0SEd3cOps/en3tyLT2xtPnTanevrRJhtFs7zy1eC5f5aI3mFk5k5Uv7aqGQAbo0ynGZhXFLpZ2zy1dXjdt7ntX6Li6NlPhot+iK/kD19eWp2n33NI315+YOV025R/8emrqyecnneebPvaMamzVqznRvZU3QxWllWu+t75lV4C2L21cO7yoPjdpVObczZpLqxrhSFRIsAwZd98HLvpGVCk6jPuR5QODrgAAwKR2SHzNHl3NUlRRFEVRQjoRaYIcU+ZohzHGdkiWBSJdTSZVnYiMVeOEnxY+/MZf7+i0dyv/s8IHg4d/7sCVnV2ivVv58OOzRETbO5mHDsvTRCQe+UI08+pN81zZu3tEROKRl1vG6WcXXqRvrmvWn1FFYewPdzInFo5MExHNPB69d+2tPePDE3N1Foy1jpyUD95T7xKRbUCnvksHDjXwxjeqeZ3SnOeyKjB/avnlY0bXYfJQsPkVEikWRERU8K2616I4YA4GXS/gObDgARgiBGGiqOskCsRSOSUeTibV8ZgsxxTZOkJTMxOhshtZkH/1V/e+yvSdr7E/+2fxz2OyQGMntu7f1u5fowNfso56++rGzFVz+2Fpj2hy/tTirQsb8lUqET381KIlhA2ZfyL0wlfeeOw5qx7K0ann1LfmzL+mpalOrlZRFNrTvvFV9jX2o1+rb3rW1LxNblqhAaKTczWf1rV3bdd9k2N8C8L2IwUEHoDhQVdzNFFMpDOUM1rkuWBS1WTn/PYURRXRmZxWij4Y+pvsP52Z+uQnoyIR0aRM2dt3iQ7/wrT1tRNnah3vk6efWz5NRLR7buna+iOtBrWJR750+PLvXT/wpPX1QxNkj7a7nbtHUmeXPHko/N61u+85veW3r18+lvucERGoqXkbGr99afUsHVefF1nq72+kvvPTtupV6bofSoGE2HMPXPQAdMc7Y+a/7mCM1UbcK/boajKhC7IciwtEZHrhK+PuWi5HRV0nTc0H44ZPNkqpwn8Tvf/C1v0nHzHd0Y8dvv/C1v3QA6ZRPj8XvrL1xm0iMoLlmnOjDaaPPfnkm5srd8w/55Xwf/nzP/0TIqLdV1NT1tnbZv6Jo5T9ztfvWiJ0c+vYVTr3xEyDmrtn71aeHvvIOyxHEn1q6iOUvbtH2re+XaB7P2inmCrXd1tV8A9w43MJLHgAusCp6++MdbyWnW2eOue8Veq9lk7oISUiks5YhiiQ32HmfHdHMFiMKIqWZixDUjRi7pKkbOGf6e3UgS9YJvj0AwfevkNfcIxLf3Fn9djSDcMbvyKSOW7u/OofEhHRyTPLp0Uimnzs8NRKzSh6B5OnP3/02vkbzmLPLq3+QbmEioOt0hbl6nIqEY+8vHbg3NLmF4noldUv0oefev53zNLq1Lx+xeqcS/t78ZD0919Xv/gNleiTJ6NTb//D28mpBz4ToJt7LKm2OYauyqCnYbaDO7PsO1pXEHgL8gzwBnJH9I+WS7C7w1XLqOuatpOlUDCfzRQKihKtzi9fgaamSYyIAvU2KW2H1LnANuemV5VG3cunMRkhEI7HBNW6QXbOfntDV5OJzERnOeeH13XfiOaz7zoQeDRWXoP7yxt4Z/pHLwS+rWbRUCXzeC2dpkgT5THD8J4sc9oe1dfYxlKvDQs0NrqVT2uogiH09jJ7xk2zstHud5OVlgODvhFVxj0E3ofg/vIG3pn+0bXAd9Am2l+pzTbvZ8pX2mZ++OZlUpfCqatJM/BRXnHPzABcuUi9sdm9Qd9thf1KZ2P00Fh5DWLwAHTKg6Vqje80Bu8SxpiiRNOM5ag6+u5zOrPw3JTZVbGCHLO/GiiPVizqupbLTEjmZ/s6CaK5vIyi7KfLmYXaq62xwZ/r3qB2FAK5vMxyN6vuTtPN0iK1kGPeiIWvkxH1B3SgeAOd4n5ja7yXzvkOjvchjDHl+PE6H3TxxPbKMq6YWKjIutN+36G5OdqpMei7gTODvtHD2VzszcaqrsDbNP+03cNGDFjwAHRHR1Y7B2rdIc7VX+w9XWCnnenylgrObEGk6/aWlp8IxfZVVmXQdwn3Br1B51PtTcGWcolMgSjFiuF4TBbsRM1uh5bYy/paHQBKs5wQLmasoRd8m/gQeAD6TTeh96HGdNS3v8Kby5J7d5cEOWQJkhRVZF3NSpKhJ7qaLQbneqcKQ50Xz8ZNtWvFfnNzs9WXxEg8XLRMcy2dKobjiqHWac2NxIuRaI6pmizlMhNRRSTSiHKZfDiuxAQtzRJpgWujHwIPQF/hQ6o7pqzx3pTcM4NYjChKxPrDtudNg77nVh9P0+jdYFxdm/FELZcLBOMCEQlySGI5LSJWanMuxXLlv0z7XJTD2QRLBcJx+2ApJAtEJMrhwI6R+JlXIPAA9I/O1J2zPoEXA+7skqkX7voaqgz63hVcw5C47g1Xef+nYBYy1nJ+RAGhWpvr10cQg4EMBcuH2sMpBWGikNsngsADALqEM532LfXd9V0GBSoM+n7gb9e9cTu0NGMpKqcRKHoe0+6kS6GpmQlJylSs2WCg68VAxQrL3IFc9AD0g47VnctugaHBnpZPlilPVDn5vu5EfL9SlR++7jGDyxgvyuGApe45SVHmaIdZSxV7cTpJymWN4rW02xPparYYliNyuJi1vlDIqBoRkaZWGPY8AgseAM/hUqS7xDtHvV0+GeJXq+hjY70a3Nc3/GjQa+lEPhiPyYKuy0pEICJ5Lpzf0XRZaFs1K8PnDeIgYiSaY4aPPhCOR2pOUlkIkRSNC1lz9WQhNMF2VDEmEAUkyjKWalAIV2DONG9gHrzf6EbGuO8Z9OMCe5c7zz8MfnXX6nnnVh6Bdpzog2istG4SDw8dcNED4FO4V3fQMbbrngbjotfVncxEtELJxTklKpE1mxD4Agg8AB4CkW6O18F4onrGeqnEx0rnxtM1gNXodS1PYdlKDJBMqjoJgkCiJOVyWp/q0CFiRBkV850QgwfAO+Ccd4PXwXiiivR5bHOTuLu3fZ5cp+/rwZAVvXbMNdNyuYDg5SRC0CaI1/IGYvA+oUvRGh2BN+jb9RonGpbbq6VZitqeGtb3sXhWBtk2Z7GhsfIa3F/ewDvjB6DubhizrOpSqdRPgbe3/X6TjTVspRxL5TrLm+6vUfc1oLHyGtxf3sA7M3C616qOS1hananduba8201lPGKscnB7fzTeeQqfi1/dVes6XpDen3nx0Fh5De4vb+CdGSwDVHcaHoEfqzd1rZ92vIGv3fWamiaiVCZneb6tCV77HU/08lufBo2V1+D+8gbemQEyWHWn4Rd46nt4wm+aZ6HrumCmizEs+coV6o3NYTfo0Vh5DUbRA9AbfGoIgqZUJbX1zS+4r+5ockwWjClpgqipqaoF6Q2DXlH20yypt2nQ+zEvHvAAzIMHwC+MTheh1m6z9/R8ZryuJtOt5mYbt70fk/LdIsrBfIIxxlgiMxGSSS9WLEgvkpqlaEwWiEQ5TPq+8UmSsZbXWqYq0b1vrh30DFjwAPSA0dHmXlEqlZyj6J0f9SQubs3cIiJJimpELdzYtrr75KcU5JgjH7tuL6xiLEi/r7KeG/TkG9c96BUIgfAGwlr9pyeS0JNChiUG74aOb4hjrfLqhOkuz2ts+Evn7A6LFFUi46ozIL9Dc3O0UxOh75i+3QE0Vl4DCx6ArvCJwWcwpFreU/RxOR4uJvK6rus7+WA81qbU2f4DX/2ylQvSlxdKbWTQd8PwzCQELUAHijfQKe4nvdIAf2mJb+jmtuhq0lzMtNNTGxvOCvjoZ2pu0Pc627pHrns0Vl6D+8sbeGc8pSpTSq+aPB8ph8/o8M4YKV7jQk4TI12InVPmffwblb3y3fvnm9Bzgx6Nldfg/vIG3hmvceW/tQ0sFxlGfawcg8eeMF8qDeZG2T83+dlTXWHQe75ga6/uBhorr8H95Q28M32gldI47KhWq4VA3ZtQlQ5nUM/1MKWv7yPdG/RorLwG8+ABaA+nSdcAQZgomhObxIgSF7JJVW989Iijpa1Z2JV3qTbZXb30d/3AFjA/TZQfPO6n0eOmDQp0oHgDnWJPcRuDr5yf1SgyOuLme/NJfXXlvPmj7fTnt42xdFs9V4v9M/lxdL2faOS6b3TH0Fh5DabJAdAhiqLQ3vqFjZU75Gyk/mXosxc/f0yOxdVkOeXIhDDeoJS99Qsb6sLyymzFnpXgcfXUTONjGmEf6eYru+eWNl8yt6eeff6Z0+0FbzuoVVvlt4mzQzA21pbGWzndpRxjudp4Sq0F7/eQ/IComwEX/aEBAoEHwC0NmqoTZ5ZXZqvi7iwdVSIxRVSTjBUoEI7HagbamaXtrdc9V2rz3JyXiqi98fT5G6Ezy7vGKW5uyecvU9sa7yWlUrURv7nJiOpLRV1/vkuN19KJfDCuyAKRGA8nVY3ExncBpnxLaqfRg0EBgQfAFa1aczPuLgpG3F1NXr+w/q0/0ahERNEHd2PGUWWj+eSc/ItE25c2Vu5Q6eIqnamQ8xNnjtPFre21hfmaE21fWj2bohLRSfMre+sXrqlBupK6ZwraxVU6sygT0c6WfDFTIqLo8d1TFe7w7Vdu0FOL5TPOLlx/6vKxV3ZPn5ppdAo6fGDlark0R80X5S2zAifOmM4D06tRc14HWrr+bkdSWafGl0pE5IGmaulUMRyPmAu3aXlXWWJ8mgzHZ7hdyKeTfIPAFRhkB0Br3LTjohzMJ6ylPoTvZr/1mrSgri3vri0+m988d5OIaPvSJp1Z3l1b3v3FA2/sfOBnieZPLZ47aOuok5mVM3T2Uk1iuptbZ/NHr68t764dp4uX183T3btCnzPP5SjtSv6AceTJ1DfXK9Yg2X01NfXkI5POXdPHnjGDAvYpnj+avbi1bX5+b+XNitIqa25WYGWWti9tXDu8WHXhde9XpO7uVOVqKaWS+c+g58PctFwxPCdb67LuZCZCLqfNO931MFUbYbw4WNJmUMCCB6AFzdT9e/9YoCsXV18q7/njX33mX//BEWH+15RPaIZJMnkoSKr1cfbuHrEb7Nf+9V/9Wqvzzi68uHN5XZtxus23dzInFpaniYhmHo9uvvDWnvHpibk6hvKJhSPTREST8sF76t2q5VYOHGpgMG3vZB46vDhNROKRL0RXX725MD/bsrRyBeZPLVteh4oLd0uUUmmtmTVX126u9ee3PXjL8NRXJbZtPPKO4K5vk9ZL2uhqcoeCE5lM9ZT+2rQStRP/K74cCMdjgmoc4khF0d90AT4AAg9AM5o23Lr6HfoYnfhXyyuz5fnuuh13//jX5aWMoTMn54iI5k8t3rqwId+h0iurX35q8eVjkw0KNpl/IvTCV9547Dl7VbG9W3miOfOPaWmq06ualA/ev6XRfIM27u2rGzNXze2Hpb22i79phQasC28DMaL8/+3dT2wbV37A8Z8PLVpIIyxktRnSh60DD5VukxikCaQxFlLXQZ3AGQdY+9rAXsCG96Atqly8AfaQQwDXl9VhFWCTGAsbxp4Wmy3MsdEYiFtyAQcBaAp2cxFHtQoUIceAI2w10mVRVD0M/4zIITmk+Gf4+P0gQMixyHkcDt9v3u+9eW/KdUW6nn6uKZ8fbndGrJi11kVE4mlzf+vdW6AtUbKsYpvpiiY5Xd9plofgtHztwiiTyTT+2/Z6ObZompo4BatoG7qhiWvn8pI2TV3EKVhrtr5g7BbyO/OLpqGJU7BydvXL2V53E6aZEtfOZbNWPF19bDtGSq/2xpiG5tq5bPurSFUQ4IGWOve7//kf/8976PW75+ypBcNYMA15cHMlJWft1TOVMeSVV8xeesXQ3zdN2bi6dPfGq50Gtemv/fzE7ffuH367+nJ/m3iz9FzivX2w2Rdjz3/xZOuSXr/C2Lx/+3TpdS9Lf66xy6CLGP/g5sqVgA8eZHV5zS5U55KtTqIu4jpr2ey2tGlmtYqmvdxytX9Z1hr/VPam6RSsdgFhQkfXO4W8eLce5MPM2NjANM2g2+TilT6SKW1m290V0VynvB1PeIdeT5m6iDh2KZ4wNRERPR7PFx3X0DQRmZk3dBERTY/NlGOVx9q0lF1XdM0plWZii5qIaEYibpWcVJvBlIqgDx4IFqrf/bva/8rzP3hPNCMZK9teD/LW0/K+tHnx2ZbIxtWl2zd2uyvF0dNvv/0oc/2bytNTyfnP7n21KRLYjx7eqbdOyp1b9Q7yx/dO35Grbx1r2MXVpdv7O+87CvzgLWlG3M16HbPZcixpaE7BsrJuwjRN01zUioWWOx/UnDNOwZtwRzMWzKSsWZZVcET0VKfmntfNPMCCRY5rFyWd0kVPmaZpLuhOrnKw+m9m/02mrrtTfzKlzYR/o+31ytmWL0l1Kiql0YIHAoScaj5u/MWU/Oo3K8d+4/vHJ2c3Lh679KOTP/zQm8hl7nx67uvSlsix68l/N35v7/1+5Z9Ezl9evqSLyOwbJ+au+0fRHzoh//CP8utD8rXXtpm99KOTdz98WHnz42c+Xls5vfRwr/4OfrV3uxDQKvXTX/vd6uGr9almfPfB+3bxyjsXrrcMbIH7mg364G2uQvyroFYSvmZlj777EgINJCuup0zTtXM5O7lgaMaCqdsd7psLLpL66XrHcROaa1l5kXh6USuuSdI0NadQn/uhf7ymfO2ppk3XF8zddbfDd+dMStd73R7Uwnd6cJlMpv0flB89KlceZDLZ4vbedjGbyXgPD/bOIvv+myTbxWzlqFafZvzPA3U8ngctyXYx2/FLbZLx6XvhomF7u3ZQ9n9v/gO2Xcxm2n6Hlcqq9lX7v/P6Y9/W6sPyo+pvrf6oYc+1x0F/W3+kOFrwQLdcd2dHXBHbKsVNc8rOWXYiRHutY6vuILO1qMUpWPmd+cYh7c0G01bWjKSWs6y8iATPUdS5VKL46Ppde80xFgytYeoA70ZDszLMvagtmubugdv0mrGQLlS6PWYqJ0UqXbK8sZFNQyNb0+uvmqlNfaA2pgJWDdM7H1CoGtm1c2vudCye8gbyOIWca3Ssw3oI8DK6JdRGoHYTU5ep1MgG0fFYarYnrp3Lrm+LiPdlTXlPa0PtfPM61h5WJwSuf7NUVoPG8VUNv5mD6CJU+IZZt1pLptt3nvQAfwBRjvEyqExDNDgFK19qGETvnz7Au/rVbKuoLS4YuwXv/5oIldXgMYoeqOiuCq4Ps7bWJHnw6C5BsXxktd/WjWsrxr559LZuXFtpPS1d6PdcWjnm+++H97u6yb7LMhw6VPmvavP+baN5csCBqk3ipuroekfi6bhsr2d9i/267k48Xl1IsbgT08UuSnrB0ER0Y17cLu8kQc/ogwdEemwCtriH+gB6m62llUPV9+qtnTSABW+a7rDvk+Ym8gEWl+u/hhivUlNe13XRKzPKWLlYQ2+765SnEwu7tjUdr3zkXTfUbP/oCwI8MNgEb7dv3q9QdMgX4nrKhYZf8MY3Sc7WjWu37p7wJunbuLr0pdF5hbqAlWz272XufFqK8bd/d7rhVfuXtDFPOu9/9N4Pjma89zFf37C+rLyP+fMrSyve+4yMP7orma73Xe1qRqK6lFw8bRquXdzXoE9OwvC2aCBFj0mnZG17qKk/v3lLZ50WvKmuRnP01cTL5W83RcSx734j/1HaEhFxvi0eSbwRqrXWuJLNvr2svi755w0vCF7SZuaPmX97/v7q8sZHvzn/3R/c8Hb9N5evfCd3/6P3vPcZZUNe+XR9nTf7jWk2jJV0nXLo1XzQBwR4TLRBR/dxv3o4fuZjaViJzluNxqiuRrP++WMR3Xhbil84Is++lXdOns8XH4hsPimK92c+n33q74OvT5PXuJJNZVkdb+OxH7/TOOv+qYvL1Zn8Z1+M1befOzb7lyIiZeN/5uzDIiIPjv71ubV/qb1P91c5/eaP8YqH+QrNSEjem67QTUzYRDMjRooek2tA0TfcgPkD9Y4PUdOCNyIBq9HMvhh7/vkzebC2nkheMI48/PzxmTdLzxPJxjnsQvfBbz0tzxlvtf2TwCVt0qZpWdbeI3n3loiI/NXT74hIpePj6AuHpRRm7wPWnK4f9wvBDvzzFWKICPBAn/kTsIG19oF7xzvb29tryMn3vJfGBW9EguL0qeT8lbWvjPL8mxdnjz6bu/vsK8nPv3mxt11K7YpBWrT32i1pY5qm9dl735M/WROR/3rxD2L/uvLRN59923OB+mwCJsPB6JGix4QaaK1aW3qkOQfbn97xEPwR/WDXEG0WvKmvRnM8cS7/8J/l8FGRo68m5M7D36YTzaPzwvPv5Zd3GvrgOy1pY/7d97blv3+9J3t7pz7c9z7RypdMXroeQ0ULHpNoCG2m2i5G2D7rW26g5YI3vtVoZo0j8kqlb/5wQiThC8A1n3268lv/8/TZjYstlqKp72X+p+/MFZvKE3ZJm+Nn7j+7fXrp4Z7MnU9HoA++mdqj6zFCTCSkGiaH6miY0b1ZYHudr6ydrRvXbtlnur+BPvrx0l/CCUzXU1kNGsdXNfxm2htOBdpuL07hUOyEf0PmUXnSFrEMYfP+7dPVjPor71yojpnv0njFS1Unw2mFymrQOL6q4TfTxuiju1Tm6T57onJv197enmvn1iTZ7zW0UTEhJSM4AAARMklEQVR2MV4mJl1PZTVoDLLDpIhKjamn0pKvLXstIpqRmC47bscXYsw5BcvyzdgeqGEyHEbe4SC4gFINF8WBhhbdQ+7IW22zsgZXuNVm0bMoXNtVlhycqi9C2F4UBmkOGpXVoHF8VcNvptkwq8iu9lVZVLu71c/RiwiFydDXc8qn66msBo3jqxp+Mw0iG90jrY9L2kVGNL4d185l3UQXV3QKj7yjsho07oMH+iMa8aMfIrXS6tirpGlqus3X+Fvw6pxjGAoCPFRGhdi15tv0Bxnjh5kpGEWu24vuB+2DUX6pWQwIGRLVkPWqITnfi8B5cwdzRjXsajin7Si+Kadg5aUfAy0US9dTWQ0at8lBTepEXEUFZgoUpadMM17qeItcZ7UWvPoryqMfuIBSDRfFMvTortrFxFBa1kPMFDQa9+9LmXQ9ldWg0YKHasa91hs9f52rYv077s1fJsNBSFxAqWbCL4qHH925nujZSPrgaxT44sZ9dP2EV1ZDQAse6hjTai6kQ3LI+2/UBekb1TMFA1drwY97TgIDwgWUaib2ongk0X1oO22I63syiV9x3ylzRTimo+sntrIaGo6vaibqNxM2RekUrHxJRKQy+Xuf9z5oga12YnxfKBbjZaw+0URVViNBih5jLFxm0rWLkvYGJiXcrFVwhlE0jAdlktsN6Xo1PhQOiJnsMN5CVNCaNr3juqJrInrKXLRzOXvqwO34MWonYUI0tOA5RUELHuMtzLwfuhErZ6sNd81Ixsr2WLXim7Px5Of7SJlGvKdhXttRFwejRBeIaiaqW6tdG6Wh392tr8Pt2gVHTx2kCT+StlGtJ57oPgiKtXcbYnw0P9pEVVYjwfFVzeT8ZtrWyK6ds7WFlC7+icAr63odfKSdYsEAHvW+1oin6yenshoVUvQYS50qrEq/u4jX764Vc7YrmrFgmqZJdMeEIF0/4biAUs0kXBSHCrGuncu6ieoKXr4W/eB3jbGl5Pcb2XT9JFRWo8UoeoyZ8P3uC4t2zsq5lXz8tDY1xFJiPCmwgkszRtdPLC6gVKP2RfEI+9077X0YllaOBW5fXd4YcknUNvIvekCiFuPVrqyigBY8lBF8v7uxYBqjLhkQBc1d8lEI8xgcBtlhbLRrdrh2LmdPDfJ+94g0egKptw7NaCk8JM2/1Gzzx1T1U08sAjzGQ4foni2LuLuasbCoFa2c7Y2fn7x+d2J8vygc46XF6PooX8KiN3SBqEbJbq22VY9TsEpxMyWFnGt4/ez97HcPUYDhadUH/9Hyf/qfMhNOv0Tkex+QkafrlaysIoU+eERd+0rWKRS1xQVdROLTedsxUrqIRr870FFtwJ0oevsASNEj0jpWOnqq2krXjfmdYjU5P9QyQFVqJ+obsAydemjBI7q6jKyakZi21my9fyu+d1+G0SM/31/KN20b2vENjzHW6AJRjTLdWr3Vqq6dW5NkH0P8WFTurEMzaGNxGhxcbTl5GUqAV6ayiixa8IiinutTzVhYiEAxhoy4ji5UhqUGzNvsT1fQjlcAffCInHEJq5gcqnTGu3bOskpxM16yrEKrSSK8nvjAG+UxXgjwQDCuM+CnQLRzCtlybNFM6aKnFud3Sk0RvhbXWYZODQR4RAthNQymrhuJ8Y52TiG/M5+sDE9xnbI0TwPl/+k1xPgx/uATjD54REh0ont0StLMH9cPySE64BGGU9qZT6Yq4d1eW59OmJ2GojYMuIvyjwKBaMEjKqJTfUSnJM2aW+2044dpvBvxHi9T7w2yc+1cy754Ed/c9aLGZ58wBHhEQpRjamdbN66tGEv3HtQ2PL5nLK1cfVz5p6uPG1+wef+2cbNxidfqxuCXtDJjrnz3/pa/JG322/FT9PraSTKmcU43YuWsZVmWlZf0gqF5A+7WJNl2wJ2HdP2YIkWP0YtUdO+1MC8fkaeOnNJFRB6sffvyEW/z7KX3l/tZvEYbUzL/x0f25unXjvbtPQdd5vE3lrPf7J/BuTLgztBEZHE+ZzuiB9w3V0e6fhwR4DFiqtQUiZjcfbJ1SZ8V2XoqhxPyXEREtm5cu2WfWb5+XETkwc2VK3nZk7nz6foLAzc2/aucv7x8/bjInuz5cvJ/9v0v//Qnb/+qdPcL57VLujy4eev6N7L36YpcvuCbjH/rxrVb17+RPRFJn924eExk68a1u3Li8PU767WN+157r7nM8so7F353erb/Bw4j4NpFX4+8UxatbXT3+EP7WF7iTB5S9BilqNURBylPMpEobYmIOLYdTwQsdvP43pXyyfuryxurr0v++V6bjc0v+dnJ4qfVLoD6qLqt6TPys1dnTyUPX//XDRE5dfHC1SPVS4GqBzdv3T1xwV5d3li98NNyppp7f3790eH7q8sbq2fP57+84QS/dvP+7Sty1l5d3lg9m7hz90b7RO5EGdNEvcexy7HqeHpx7PXpRPi5H0nXjxECPEYmatH9oGaNcvGByOaTorwQ0NJ9sLZ+7oyXSD/243fmDrXe6H/JyyeMoyKiv/aT9PrntX7xPdnbk72y/X1JvKGLHE+cyxcfSLBTF5erLe/ZF2P17dX9zhpHntvPAl+69cWj5+eS3hK1x66vvnspRDNvgox1jK9w7Vxe0kGz2rVRC+1MhhNxpOgxGhGM7gct0uwbJ+QLR6R0+M3T8vRew79uPS2LJCtPjr5wWEqtNu7z9Z1bx+5UHr8S3xKpXzpsPil+/c3zv196WHn++Myp440vr/7TPePTda/dfz7Z4m+CzRkvdPX3E2ZMM9W6EStmrXURkXg6cNLaTprT9cK8ttFDgAf65egLcvfJV4ny4R+LPG38x9kXY2JXn2w++7b1xn3O7c+Z+2x98Uiu/my50qp+fM9Y27h+PChzcHPlipy1V89UBgR095me289EaLirZv+Au57Vrm8YeRdNpOgxAhGsCPpSpOOJxJ2HRS+p3uRUcv6ze19tiohs/PJOpbs9cGPgS64u3d7XBe7Yd2Ov13PmLbP0W0/LUk2zi4gUn20F/FWw2TdOzH225t3Ox71zLUx4jtrfEz/hhyKCaMFj2FSN7iIis8YRkRdmRYKC6PEz95/dPr30cE/mzqer3e2BG30v+Xht5fTSQ28Q+3VfS3rzSTGRfNf3p8feTGd+cf9vf35i7vq+UfSzl3508ocfrhwTEZk7n577urQvz+8v/BuNr5Wjp9/9+OaKsVQdRd+qC2DCjWmivl9I10cWy/GqJuJLLEezHoxmqTBeOIv8RyDM0Yh4ZaUAUvQYnmjWgNEsFTB2SNdHDQEeQ0IchdoIaRI0dz3HZITIkKgmmlmvyEb3yBYMY4ozyhMmXR/NykoltOAxcFR5mBy04z2k66OAAI/BinJ0j3LZgHFHun7kCPCYUER3DAgNVj9/jOfIDBkBHgNEEMVkIpL5ka4fFcY4qCY641aiHN1bl821c9n1be/xzPziQvhVtjBRnIKVL0n7udxrp1mUfwvD5D8gInL27NmIVFaqikowQL+MMMB3O83FCLUsnlPIuUY1qjsFK1/qcTEOTAbXztnaQoszpNZUjfJvYcjGqJZQAAFeNaNtwXu/2A6/22rbZ1Qt5HbFcwpWKe6P6K6dW5MkDXm00C7CM2lroNphiU66UVXMRY9+CjEpt2sXJW2auog4BcsqRKuBrKfSpX2F0ozEdM5xDY0IP/H83Td1M/OLgeuykZ9vxZ+lx0BxAaWa6Lfg92XBh95ADlPbehV5Jb+wr7iYcD2er8T4QByWQaMFj76p/Vzbx3jdiBWzBc1rI2tGMpazHWPUrfjGsXWmIa6ds6xtiafNFNEdHs1IxnJrtl4P8bUzh8EaXWOQ3aDRglfNqFrw3fW7u3YuW44tLhiauHbB0VPDaSEztg59UBuo4T9T2o62E1qrQeiDHzSOr2pG8pvp3O9eq/ycgpWXtJnSq02foY20Y2wd+ql+Jlefd+rLIcY3IMAPGhPdYAg0bXrHdUVERE+Zi1oxZ7uiGQumaZqDDqKhxvLoqbTkrYJT26AZiemy4w6wXBhr3ljRWnR37VxeEh1OZeZ4wZAR4HFQYdoluhErZ6vxUzOSsbLttH9F39Rm0WpfSO/Cw7KsnO2KiDilnZhO+x0hOAUrW44tpnTXznnnWmFYZzfQDhkS1Qw569Uh7x2BfvdaOb0H+0sbMG9dZRN98Givdnp750ro/ngS9TWk6AeN46uaYf5m2lZVkeh3by7nvjIztg590WV/PDHeQ4AfNFL06FGnSmqU/e5tNJR5292tPtRTZrWYQBe67o+nMx7DQYBHLyLe7+7XrqiMrUOf1frjR10QQET2oJYhnDOZTKbdP7/1QSaTyWQyn1x+SV66/Enmk8sviYi8dPkD78EwdSiqiIi8dPmTSmlF5K0PPhl+KTHuqud8JvPBW6FfFObkVN6o60vF0QUCAEPWNPFCwBbgoJiqFt2rjx+uYXAaEEb9x1Oy9v+IZuYDF60BekYLHt1qHDEMoEu01zEMtODRg3icmgnonZ4y+Qlh4BhFj27p8XipyL1kwAG4ds6bNJHZ7zA4tODRLadUkm3JWuv+jfTBA+E59rrMLxqaOIV1mV80DbFz2YLDjwh9RYBHt/SUaaZGXQhgzE1rmrh2sTQTW9REyIhhABhkBwDDVl0FYWZ+ccHYZZZkDAQBHj3wr9Eiw55ZHgAQAgEe3fKtChf4HAAQAfTBo1u77nY8sVCP5pqRiK+XdkUI8EBopMEwcAR4dGtKmykVbUOvt+CLpZkYk3ABoVXSXuaCLw2WE2I8+osAj25pxsKi5Hy3ydH4ALpDGgzDQIBHDzRjwaTJDvSKNBiGgUF2ADB89MFj4AjwCM9bISNealpLjpnsACBqCPAAMGSsJodhYLEZdMspNK6L0bwFQBtT2syOy/S0GDBa8AjPKQQk50WEHkSgK4E/Jfq50GcEeHSL7CIAjAECPAAACuI+eHRt//09HrKLQBgkwDA8DLJDtxx7XeYXTTMdl3jaNM3F+RmJx6mwgO64di5nM9IOg0OARw+mNU1Ej8dLJcebZbNUYhQ9AEQKAR7dqt3hU33gujujLhMAoAGD7NA9185l3YSZ0qs3+3CXHBBO63tNGciCfiPAAwCgIFL0AAAoiNvkEB7ZRQAYG6ToAQBQECl6AAAURIoe3WKdDAAYA6TocVCunVuTJLfJAUCkkKLHQWlGYnrdZiY7AIgUAjwOzCm1GFoPABgZ+uDRrYA++HjapAMeACKFPngAABREih4AAAWRokcPXDuXXd+uPuMWOQCIHlL06JZr57LlWH35uNracqMtFgDAjxQ9urXrbscTvrveNSMRL5W4TQ4AIoUAj27pxvxOvlAP6K5dLMXjtN8BIFJI0aNbrCkHAGOAAA8AgIJI0QMAoCBuk0MP9t8mNzO/yFIzABAxpOjRraDb5PzPAQARQIoe3Qq6TW7b3R1hiQAATQjw6NaUNlMq2m7tuWsXSzPa1AhLBABoQooePaAPHgCijgAPAICCSNEDAKAgbpNDN3y5eWatA4AoI0WP8HzrxrGEHABEGyl6hLfrbldXldH02MyO63Z4AQBgVAjw6Bk3vwNAdBHgAQBQEH3wCI+FYgFgbBDgAQBQECl6AAAURIAHAEBBBHgAABREgAcAQEEEeAAAFESABwBAQQR4AAAURIAHAEBBBHgAABREgAcAQEEEeAAAFESABwBAQQR4AAAURIAHAEBBBHgAABREgAcAQEEEeAAAFESABwBAQQR4AAAURIAHAEBBBHgAABREgAcAQEEEeAAAFESABwBAQQR4AAAURIAHAEBBBHgAABREgAcAQEEEeAAAFESABwBAQQR4AAAURIAHAEBBBHgAABREgAcAQEEEeAAAFESABwBAQQR4AAAURIAHAEBB/w9tgkF5t8tTjgAAAABJRU5ErkJggg==" /><!-- --></p>
 <p>If we choose to only show the class means for the central states, the
 argument <code>which</code> is used either indicating the number(s) in
 the sequence of levels (<code>which = 4:7</code>), or as shown below,
@@ -598,7 +606,7 @@ <h1><span class="header-section-number">3</span> The function
 <span id="cb6-3"><a href="#cb6-3" tabindex="-1"></a>  <span class="fu">means</span> (<span class="at">which =</span> <span class="fu">c</span>(<span class="st">&quot;West North Central&quot;</span>, <span class="st">&quot;West South Central&quot;</span>, <span class="st">&quot;East South Central&quot;</span>, </span>
 <span id="cb6-4"><a href="#cb6-4" tabindex="-1"></a>                     <span class="st">&quot;East North Central&quot;</span>), <span class="at">label =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span></span>
 <span id="cb6-5"><a href="#cb6-5" tabindex="-1"></a>  <span class="fu">plot</span>()</span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 <p>The size of the labels is controlled with <code>label.cex</code>
 which can be specified either as a single value (for all class means) or
 a vector indicating size values for each individual sample. The colour
@@ -612,14 +620,14 @@ <h1><span class="header-section-number">3</span> The function
 <span id="cb7-4"><a href="#cb7-4" tabindex="-1"></a>         <span class="at">label =</span> <span class="cn">TRUE</span>, <span class="at">label.col =</span> <span class="fu">c</span>(<span class="st">&quot;blue&quot;</span>,<span class="st">&quot;green&quot;</span>,<span class="st">&quot;gold&quot;</span>,<span class="st">&quot;cyan&quot;</span>,<span class="st">&quot;magenta&quot;</span>,</span>
 <span id="cb7-5"><a href="#cb7-5" tabindex="-1"></a>                                     <span class="st">&quot;black&quot;</span>,<span class="st">&quot;red&quot;</span>,<span class="st">&quot;grey&quot;</span>,<span class="st">&quot;purple&quot;</span>)) <span class="sc">|&gt;</span></span>
 <span id="cb7-6"><a href="#cb7-6" tabindex="-1"></a>  <span class="fu">plot</span>()</span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 <p>We can also make use of the functionality of the <code>ggrepel</code>
 package to place the labels.</p>
 <div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
 <span id="cb8-2"><a href="#cb8-2" tabindex="-1"></a>  <span class="fu">CVA</span>(<span class="at">classes =</span> state.division) <span class="sc">|&gt;</span> </span>
 <span id="cb8-3"><a href="#cb8-3" tabindex="-1"></a>  <span class="fu">samples</span> (<span class="at">label =</span> <span class="st">&quot;ggrepel&quot;</span>, <span class="at">label.cex=</span><span class="fl">0.65</span>) <span class="sc">|&gt;</span> </span>
 <span id="cb8-4"><a href="#cb8-4" tabindex="-1"></a>  <span class="fu">means</span> (<span class="at">label =</span> <span class="st">&quot;ggrepel&quot;</span>, <span class="at">label.cex=</span><span class="fl">0.8</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" 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" /><!-- --></p>
 </div>
 <div id="the-function-classify" class="section level1" number="4">
 <h1><span class="header-section-number">4</span> The function
@@ -634,7 +642,7 @@ <h1><span class="header-section-number">4</span> The function
 <span id="cb9-2"><a href="#cb9-2" tabindex="-1"></a>  <span class="fu">CVA</span>(<span class="at">classes =</span> state.division) <span class="sc">|&gt;</span></span>
 <span id="cb9-3"><a href="#cb9-3" tabindex="-1"></a>  <span class="fu">classify</span>(<span class="at">classify.regions =</span> <span class="cn">TRUE</span>,<span class="at">opacity =</span> <span class="fl">0.2</span>) <span class="sc">|&gt;</span> </span>
 <span id="cb9-4"><a href="#cb9-4" tabindex="-1"></a>  <span class="fu">plot</span>()</span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 </div>
 <div id="the-functions-fit.measures-and-summary" class="section level1" number="5">
 <h1><span class="header-section-number">5</span> The functions
@@ -749,7 +757,7 @@ <h4><span class="header-section-number">5.3.2.2</span> Within class
 <span id="cb10-2"><a href="#cb10-2" tabindex="-1"></a>       <span class="fu">CVA</span>(<span class="at">classes =</span> state.division) <span class="sc">|&gt;</span> </span>
 <span id="cb10-3"><a href="#cb10-3" tabindex="-1"></a>       <span class="fu">fit.measures</span>() <span class="sc">|&gt;</span></span>
 <span id="cb10-4"><a href="#cb10-4" tabindex="-1"></a>       <span class="fu">plot</span>()</span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 <div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" tabindex="-1"></a><span class="fu">summary</span> (obj)</span>
 <span id="cb11-2"><a href="#cb11-2" tabindex="-1"></a><span class="co">#&gt; Object of class biplot, based on 50 samples and 8 variables.</span></span>
 <span id="cb11-3"><a href="#cb11-3" tabindex="-1"></a><span class="co">#&gt; 8 numeric variables.</span></span>
@@ -880,7 +888,7 @@ <h1><span class="header-section-number">6</span> Additional CVA
 <span id="cb13-7"><a href="#cb13-7" tabindex="-1"></a><span class="co">#&gt; Warning in CVA.biplot(biplot(state.x77), state.2group): The dimension of the</span></span>
 <span id="cb13-8"><a href="#cb13-8" tabindex="-1"></a><span class="co">#&gt; canonical space &lt; dim.biplot sample.opt method used for additional</span></span>
 <span id="cb13-9"><a href="#cb13-9" tabindex="-1"></a><span class="co">#&gt; dimension(s).</span></span></code></pre></div>
-<p><img 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" 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" /><!-- --></p>
 <p><span class="citation">le Roux and Gardner-Lubbe (2024)</span>
 discuss an alternative method for obtaining additional dimensions. When
 assuming underlying normal distributions, the Bhattacharyya distance can
@@ -891,7 +899,7 @@ <h1><span class="header-section-number">6</span> Additional CVA
 <span id="cb14-2"><a href="#cb14-2" tabindex="-1"></a><span class="co">#&gt; Warning in CVA.biplot(biplot(state.x77), state.2group, low.dim = &quot;Bha&quot;): The</span></span>
 <span id="cb14-3"><a href="#cb14-3" tabindex="-1"></a><span class="co">#&gt; dimension of the canonical space &lt; dim.biplot Bhattacharyya.dist method used</span></span>
 <span id="cb14-4"><a href="#cb14-4" tabindex="-1"></a><span class="co">#&gt; for additional dimension(s).</span></span></code></pre></div>
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" 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" /><!-- --></p>
 </div>
 <div id="analysis-of-distance-aod" class="section level1" number="7">
 <h1><span class="header-section-number">7</span> Analysis of Distance
@@ -926,11 +934,11 @@ <h1><span class="header-section-number">7</span> Analysis of Distance
 analysis is performed, only on the <span class="math inline">\(G \times
 G\)</span> matrix <span class="math inline">\(\mathbf{\tilde\Delta}\)</span>.</p>
 <div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">AoD</span>(<span class="at">classes =</span> state.region) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img 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RuczuF58sx8JmkOzklQDWu7XfZq5WqPtq+mj5YnyUOL97YlKLNRWfuZeWPauLqO5mxt4dPRGzpZ08HWMyEoJWIbtIa93S6/zXb36FvJQ/N3dKCgxUKWsmV4vPlDm+P3NgOSKpJwqq+65ayeRp4HQSnxevGEPtvtuq7lSB5q3thhgpZDS1XX5Zd/WLcesgbz8aPueH2XLD/rdnOtCjUdT4SglHSxxdxu50keyha0Mb9YPqEQ9P70f/7AT5u7/P5LH214Ebco5vS7K06jZtFYgaAMhMTW8dayk4e6V5NYnej6CYdr8/D22f1//X2f6/ntyxFHFjPu6uUdPWtJ7CAoGzmxVWk52S/wPNZ63BqGVNbo0u4iezBrXejUddn9vdhN2p9OOWljc628yfIgKEVSbEq5K0Dv88tPdtW8X4eg9u3dJON/VA4hDDvxvZ113NFdcvxAW1/jB4JShMXWa6i6tHGXGXbVfKhBJWiz+Zm1Oh9VDArVKqklaLBe3fkmBSAoRVxsvCGa6rm6T2wZFmqD6n5zo3tUDcH2NtQfpPJXmwWHa2sn3ppsa4agFGmxld1h3pNbA/2eNkJef1ZXLQU9DBA0ZF9bTecM59q0SA7XT35UrcjONwhKkRZbdavkjHTnT28YppyC5hesvlE3SvsJGqg4SzWb3w/Mwetu2YsNnV+FoBQRsTlX4ftkIKtDjzcsQZurl2px/H4yZ4esWjNrbaxo/ek1NK866d52CEoREZtvFb7Difbq0NXWNswjaNH8VOUTG9q468/u2SEirVGOL+if1zs36N52CEqREFtoFT51g64OPX6odivLMLegZeXZr7VZlO+6nu3musgP1U6kEBJU7zLaXWzJ/AMEpUiIrWMVvm1Ie3Xo3a0iRx63hWr4+ejR/rI9L+UsV7WzjrT7QdsyCY3OTEM2YoTboNnrvg5BOxAQ27FzFb6lRL461GqHHp5/rJrpwluCVo3PQtB378vTYb00NFT1Q47a9O62uAVo6ABnYJ3y9krfDiBoBwJiY63CL90wq0NJ8lDVPPKYSlRrVQialRdandyeHeqazKwnhoygh+vAuV/WqxyLaSAoRUJsdBV+10m2reShqnnkMX1Z/bnx07zUnRquaWI16N4x5FVcy4zA/0GTpmZw4jkISmHHNmg6kA/v7DCjSit5aOPIY1KDEruyn+Iiz4LQWp5MRLTNDAtanF6+e3a//jU6V823L8JHzoaAoBRubP2nA3vCPDtMS9NOHrq124tEs+brddpPvTKksRuFVJytSjMsqB4kK6r8vCO/Hn5gNwSlMGPrMx843GTe2WFKtfJy764sQ+0lHC21XuW5jS7r9U92b4hxP28HfVOP4eaDm+uVJ/9PNxCUEl/QMXUtdzOTQ6N6OZFdF7qeZO6/dJBziJptzODmD5kBpGGNUAhKiS5on7rWCXMzU+1TceRx1V60KsTWi/IXZBWwtZLT5+aAO7UZ3PzyV1b+BZ8dQFBK9DboaEH5m5lyraojj/O1Girgp1VxqlPXHX3byAIfPDLeepEe3DwNP3oBglKi9+LHC9qDzK/6yGN1qnd0eNeM5EpyGpvVAPzh+sltpirvru0a3OwBBKXEj21CPzW5aGbHRlEtFg+7nlly6uqZ55gbtVkX9zNXsRM7uIGglASxTernqT7yuLpvn9p+NtzMH+m+cF5nmqGj3cWpc3o0BhCUIjk2JsWRxyrvH6ny3/LbTTV7CFoOwOuho2/cKPW37aGFx48f+17HSzLqBoJSJMfG4nCtfqs+8ri8cVdzSXU3iDV89CsL6keKAfh8XdypuZzu8WOvocxMdm4gKEVybBx2T77x4beuzJHHRsXyf1XFyb0vtwQtB+CrdXFWG/TxY6+hoTWg3UBQiuTYGOisYn/s/W9+563NrqFlXm1mSrFbju0atMQMHZlVVBUQdDIkx9aNziqm/mx+5LGpOZu3dL3a0nHY5lrlsjWWxfkFdQwdQdDJkBwbg082J2Wy2xLy7/7P36kcZ67qtqTej66PFay/FxDUAdqgUyE5NgYNNU/Fh5O51Wff+d3f+k1//d5aeHJX7B1am/3oWtR61VQ/QdGLnwrJsXVR9ILMR5PdtuzI62/q0dHf/8d/Xj3771Utuctv1Xrv0A/81VvTNa/nzHsKmggISpEcW4DiPp7ngv3nV79YjNSbb+UjTLr9mX3vO5dP/lXxmv1b364Wwf3ir88333mTJM0EBKVIjk3TXpBUtTH1v0+/887p36h70123huKz//8X87zfoZS1L63e3PY/fks+fgRB5yuVR3ds7pnLqeYzG6uP6/mg8jOd2XanN3wcswfyfRam+lSHd7+VddH/1w/+3aPVq8+3yum9Q//gj57M/X2K+fU+QFBKZ2zutR+TrQip18fVS4v/RI7+Qp+4anYtqwtltts9+cu5oOrd++2z+/0fzkegqu12q3zv0JO/ZcTcsvbHTwkEpXTF5l49N92auuZUZf6FJeip2LWs7nQixl/3N75x82uzZxw/0HPn6sesLE7Foqfyjk73o0sBglLkCloOHdlf5p82BVVb862fVn/nz/y5337ztb+oBf33ukl6IvmeImzpSA4EpUgUtHlHP7V2BDcFNeuXzD6RP/n3bk+Hv1I89fDcuSI0UchhAoOmBAhKkdUGLdUkXSPyrJag6lbvE/mxP/0PN6e9us2fvnUvFZnD0cC0EwWCUqT04sm6uMbeIQq5xZ8KD3d/4WVWjRYpOg/qXl/Etb9+akcDE/ctIChlltiagrg89LlpsAXV9/e3vm2eutUDTj+sfnMuqB7yVL7O0GhF+TdtCDqOWQVVTg+DcravpJPSmgH4tTlzVv2LYm9xVq/u/AcSjatGS+M6vdNPgKBjmElQt5pWi9P+3uHad4iR+hU5j/SdfLv6pLGW6bS9aE9ENcuq4ulHqVyneMyn1UBQyuSx+dQk3aHiM70sbq8zcm2cLziVguqktFfmzFlyRmvYvXLStM8PcKoE7awaLZGZV4aglAljs6cqXd9qv6JaFudM56msGvTRy83ptTlzVhXZbctefJd8PdoTFX0F5QNBKdPERgVU5HveF2ozX7uzeZrRqErQd++36snPXWd9+PWVOr26LdaFZL34bv0GGtrtHwQdT+rY/Hf0E6c7lJvpqkDz0dJS0NPdx+/leT91pXm8WRWCmkV3XSEO6DJVfSROG7QHEJQSLbbAujjnExi31rVSP5Un3GyfxV2M5heC6lXIK1NfHvX4p85uW/fiGYKeBnbrWb34PkBQSgpBPaNHzSd0X1FvyTDjmLsrehhxlbumEvS0fZZv7lC3h3L+aHvRKjn8I8w/Ww9BKZEFDd7QG0/wp4srj1PflfmQ1oou+6jKqwXNqkyTLVHdPFUm24je2dHT0PkXlEBQSjxBOxuU1RPM2NHb957V7Lq+NN/Rhv3qH3dd5xRwLr/363Q4q3qm0/Fsz0kNrGq0742bDwSlRIiNrIvzPyn/rBo7qjdgNNDbN15uii927qozIFEuaHZtLWc109lyevfkJ658knY52rvrwweCUkbF1loX53+W/Yy8U+5bzq6lqnpFtJZVbdVoafm3d/poG8s/8ge0vsj+CPyH2wUd7T94xAeCUgbG5rihs2eHqlHNtfMeX+0GNucOEYm7U3sqXySNMsxuu+CpTH5HIeiU9I+Nu5bD/7wyTZw7Z7G+8+tnmL1DZPxTtc5Bahd7cj6DNkH0bruuU5k8LQnGFNJgICglGJtj6JLXzQ0/r0yZ5DlpYHvlO6hQ5aIF3XAL2npU77Z72Xm4nbsaTWgoBKXwBOWryRnkzFuY/pMGtp7TNYqGbNgNfxuAPso73M7laDpDISilS9AONUkzlKfxsC2Vyvbz8WOdlclhuNUb06kcFDkJuQHzcDuXoxB0KgKxcXSrvm+S0HjrvuIprJNcQiXpeAo3SO7P4rAkW9D1Bc296BoOfck53K7VHIWgU+GMrao2O6vDenZI92uOH37dXzlWA/CDqMUr3Gjm/rQPS6qi3/3Qc9rJcoRVVaMdwjX/WtEGHY5Z1JN3A26sO5yemFGtw9NIbOSO3i1o+XTTr9mtAiesNQbg+2KPoxo3VuanLMcBGoclVU/cX16Z7voFuU4LU40ylLN/NejFD6YQtPEZ/aKiiq1PP8h+SXn1TJXsfQ7UkY0B+H6Qde+ZG7/rX+rVIbXx5sLmiMP6mYcX3/3mZpf9RW4D7dCcrBpl3rQTLyg5J0H3b32qj97NapCnG+thfdL69uLw4mfyyvTBIDXbs0O7q6Id6G1nNtNx9irM+qg5/LUf1+dv6NxL1UhqdVhS86k6h/2VyR3avFgbfqsypaLnJajezZP7aD2cVSyfvtjo9OzF6Wy9f93ORkDRMz/QVl9NOQDfG+rn6fSfftu/1v1z14Ko5pPNLqV3XM9o0afbU/0Coqt6foJqY/IhvrwNanbrXOlpxLzZ2BnburHUzVvXMm7e/gH4IG0/s5/g6XdvvubeSNd89ieOk5NDhvKj4nUi+3KGgl6XPaOqDbr/0m1e0+m3LhTbWj39NBP5/+XVVLghwBnbDA5CeWjvssvuB8f/pmtF58Alebqe0XQ/pU3fbk+K5ugZClrVM5Wg65+8MIJ21KBmWVyxJK6rkVoe7BKdwje78PxQmNeemXxHfet5DmXAwFH/tnsX5yeoboPuTFOtFHT/9ucfZF2ni/xhR2zV71wvR7vm9KAGNS07sHo7jeJ17k/dRPH0xjiC0p6UYcDQezV3EI/zENQ0Ni8KQQ/Xxdhn/rB6/2aVqfn95z9R9eIp1W98n7vpHzqyN2dERzlu7xkm96e/umYJ6lqTN1TQuLf6sxCUQ9Xb9gpaz2O776UnsjljQPuyA39POTBWwBPUUe9xBXXm4YnmKAQtCApa3tW3q9CquPDmjPF4kpAY3JMO9dMHCMpsg3pX4cdxFIJSaGx2k3Ntprv95wUHN2eMRYVWzgVfxniV4xbP78Vnjh5vXD9tBEUhKMWKrTU71DV0FNycMY4ykP6zCNZHzjN7Y4491kfJuxUd6SgEpRSx9VsiUrB+Vs0NtTZnjKPqfgx+Zfs7nctDORz+w/GzbZFXx70Kf5yjEJTyYPBo3k6t1mZuaDdmmaeTEROJ/pe2locOubzuMK5Xv/Tx5ZNb/57QEY5CUMq4P/ghc0OdNCa695fOe6n/xY1/GrSWhw75yXVux8/N0WHBzUxDf6sQlCIvNmX/m91Me03gK/KvjVkeurXXWw2wSPekzNFhXZuZhv3lQ1CKJ7bABp3ENBXTS5H6LCINCGqWh+q8d69uW09nk49FmWr0ZedmpgGOQlCKO7adf2wpMcSw4/c2vf5YQjXoKR9zaDREexpkjebzNjP1dRSCUpyx2SerT4orj052Cz1+xL5A+/UWZmfIuvG3188fe7qp3szUEVIfRyEoxRObJ7FXYlTrk5O+y++/9NGm5xU8TtzdHq7JvaGXoXQ+NK9Gu6NiFwJBKZ7YBi0tHktlV+P93F/6DqEJXcL9bVefu7+h1tc75+Z8R1xMRyEoxRWbrhOmP6/alybv8NU+F3Ffg/UaFsM3c7IchaCUdmw7tXqdYO1HiMak+6jJwiFXca0OTYPlqKc8CEqREZuK5OewyziXjiSiY7sdBKXIiK2zZmFfaNB1Js1Mr0IpJCEoRURs9Xs21pQFCHoKNUchKEVCbPXSz9GiiL/Fl0V6HIWgFAGxVVWnfs8ePXo09Dq6g91D0Oa+u2kNzX9kR5kQlDJ7bHbzU2k/Hz3ypP7swAxR9qtBrVn5aQ2t1rvSUiEoZe7YmsukH+U0U3/yIJM8Xb59stk9+35jHVJyQznb7SAoZebYGn7uLytBg1uLnfQTVCdt2hJfEhvK2m4HQSnzxtbw8/DufSGonfqTC50mD+uWn5LUTB6a/iZvttsF94lAUMqcsZFtUFpJ4+dVI/Unl2YbtLMK1UmbSPLQ1FXojVqF9onojxCUMmNsinxq7uqZn1n7s5H6k0ujF8+xrZU8NKWh+Xa70D4RXY1CUMp8sVE/83QM2790q031n4UcZKeqfjljnKmdPDShofl2u859IukCCABB29i39+rT3dPN//69/7h/+7N6vbWvmFWDthZzJhSE7hNxVqOoQSkzxdauPk+mXah+4B8NaX9q9Knyzst66ZM8NA6dZ4dBUMo8sblFyt64rCc/qP0ZvO7QSySg6+wwCEqZOja6JMT61Iz7ZJXKwPanyRzivHA/kjcDQ9vtIChl8tjUyavR//1nY/ZCrVfblXXLHu5Z8rUjge12EJQyfWzK87khe892PbYgWRw/vN+tVP2WjxB0ir60Z7sdBKVMX4MGb8O7i+3QTE93t/v31PAt79YLJxnrcW+3g6CUiWOzV5O7RHBnNWRxeP7xZbB2ZjLD6tAaCEqZNjbV+kg4/NMI129/3s2cq0MtIChl0thiVHDhAl5uik8GnO842+pQCwhKmTK2hp890yoyS7gblhhshtWhbiAoZbrYGvWZ6plWkcfWPm+8h2IzrA71AEEpk8XWeMNV37SK3EK2gwZCi9Whjdyh8xgKQSlTxdb0s3daRW4pu2GrO82sPMkdOouhEJQyTWyK+KnplVaRW47ncw5jc4dGAYJSJomtqWe5+rNPWkUWO3MEpLvUTkbnDo0CBKVMEZuj+tw+ue2VVpHD+kJfvG6F9vRrbO7QKEBQygSxOfzMXOqXVpGBrgKVfbBtT71G5w6NAQSlJI/N1Q2esgcAABI8SURBVPxMw3qVXd5aahKjrKkNhaCUlLGpE32H077f60YTNE5hExsKQSlJY6Nnbabe16s29lBmnNLaf2UpgaCUtIJO6mdWg36WNWyrXlKk4iZZHloCQSlJb/GNtPPJ3+fjh0rPqscXNM51WEBQSsLY7JvjgIO1+7NWemv9rsfGYwaTRF4BQSnpYpv29q45WktFRha5vxx3pOdQICglVWyt5mfx9bDcn9xCg1/2ZNi6k5FAUEqi2Bpv6fqqvtuvh+T+HFTqWK/Wc0zLQ1BKmtiab+hdnTHJ1Eu9c38OK3aoVmaDPannpzIUglKSxEZF+Vgn/NSsV/shuT+Hljv0OnnlOXHyUAMEpSSIjY7LqFe3O6VnILN7++vToNyf3JKDX/IxVfy0yUMLICglfmzUEnV6dbvWN8zDtamYxuRe6ln04AsdP5o2eWgFBKVEj80hyVat8jrpwuRHHJh7aVjZQ5k2eWgFBKVEjq11ez8ZP4uv1tmN3pO6NU7pwS/70U4eCkHnIG5s9D3UX69NT8OMf5oqKcFWJFr8Nu+GjzLKkTx0AkMhKCVqbC4/C/Lcn6fXyXrwVnlFiry729hGpTcUglJixeZalWZ9XeT+bCaYiU5T0O0qulDJDYWglGixtVelNb4el/uTG0Pxr84ct8v+FOL7lHp1KASlxBOUft16H4fn/hwQw/bCEVOUIpLWohCUEu8W37l6aUTuT24MOdtyqjKFS2nv8hCUEic2RW99rrdxRO5PZhT5P1UfCTWo6FJ5RImt9Z4538SRuT9ZYZjOWNlHSuAS2qBTEyM2np/p0cXqUdayjxQtjsbyZQg6KRFis96w7J1M1PTjBlIsMzZ9pJiBbKdZHQpBKaNjs3vrepXS69n8TFqTN6Y90/2EEJQyNrbGe6XPiVMq3VRmZyxmov/496sFxxFMci1fTmcoBKWMjI28U3cfK7UvVydPi0lJn9l0lf2ZfEtXd7o1GkWkvPKcJrstBKWMiq01GL/XCywSrgYJox29XV8d3v0FXd/pVmMUj8xSwYmy20JQypjY2m+S2j67T7Vcvhtl/jjWT/9t2YuPpNHxo3Z220SGQlDKiNhcfj752cbW9GlRebWpG6J5Lz6aRY7stmkMhaCU4bE5/FwnnirqQOVdmottzE5SjiO7bRJDIShlaGyOjEWzDS9ZAegjj3/+j5RTnfFCmiq7LQSlDIjNM903u59ZBObI41/+kXKqM3FMCa4OQSlDYnMtmJg0B5wHlR95vP2pyJ2kUIGRi4CglEGCCry9a1R+5LEZY7qoHkpbYuQCIChl2C2erqwT4aez3ZE4/Wzsi0NQSv/YVPWhekCGn2UY1UBsajtRg05A79hkNj8NeRx6g3N1qGz6XhLaoGnpGZtLxvKxpKk/GRRhDD3yuAf/zlFsHCAopV9sjTdjf2lSG1RN0qSpPxlUwf3n39N+LCb7f6JUouWhEJTSKza6tk5vrqgfS5r6k0EVycAjj/nsGpv/IGhKesRGbu/7t+/1Td16IGXqTwYuUZIIuiUzuhELgaAUfmytt2GrnlaLP037M2XqTwZ5gM0jj1MIur4iyW0jlgJBKezYXBvdVbVXJ29/Jkz9ycBEmK9XiX1Wks3+vVZy23jFQFAKNzbn/fOiqjCL9me61J8MdIhmXdyII495tJLbRisGglJ4sblGl7bqdluN58zd/tTkNaiuOyMfeUxxJLeNVQ4EpbBic/3219WDWXvsye3M7U9NMdiV4MhjSju5bayCICiFE5vzd18/eHerb6nztj81eUTZX0n8I48JjuS2kUqCoJSO2JRnJtN6UA99ZtXWvO1PTVGDvp/iyGN++eOAoJSu2NwT7c0HX2cd25Sp55mYoEwvKf6Rx+zyR5YHQSmdgnIfnG2zcUU14Rr/yGN2AGOLg6CUzls8a3NH2tTzTIo26E20I4/7RzC6NAhKCcbWSvuZP9p6XuLU80zYlX26CCBodEKx2b/uYunSaeK3vA+zC4pbfAICsdm/7MO798VSOrF+eiKbIF57eSg6SZHxx9Zc+5k1MXX2YsF+ziZoc3nouPIgKMUXm92cOrzYmHWe+7fF7O5wMVsNGnF5KASleGJrLk2+vsgn2+dL/cnAI0Z6QWMuD4WgFHdsZGnyO+srvQBDvdykD2gwcwmql4c2kodC0Ji4YqM38le3+g6/nzFvHYeZBNXLQ0ny0BFFQlCKIzbX7zdrhkpufmpmu8W3k4cOLxOCUtqxuX+7O7VJHMlYZhPUkTx0cKEQlNKKrb31yNzZpdefc9agjuShQ0uFoBQSW3scyWzyET28VOALcYIqNF7yUAhKqWNzzrvX3xLPfIJGLBaCUqzYvJmwFuGnNEGHJW6CoBRb0EX7KU5Q/x98AAhKadzi6S80xhrxybA2oXxw63x8YoY03CEopYrNKWOEBWSTYQV6B0EXUCqPMjay9rOcXl5C973AinQ7zcmvYQb9cUNQSh5bw0O99rO8SS7HT3lt0CFlQ1CKiY2uDSkPUFVVO3/u5LQMrDboy032E5SrN2b9G+tbOASl6Nga1eeLzfF7m7wVZzVL505Oy6D+Kdbvf5Z93M20RWVU4jsISnlAmpl67Weu6Uf243Mnp2VQhavnxndXp1l2Ho9NfAdBKQ/IL9Cs/cw+7r9krQ5ZryQkB+vAqkFXp1c/qqrpx0kFHZn4DoJS6K+vWPt5+dRq0t1cvT4JSA7WgR2wfZOdVNCxie8gKMURW3Z/P3y1/q0ers2dff7kYGEsDcyRx87vpMeR+A6CjsEVm97dYX95odNqX82eHCyMFbE+8ngba59lT1yJ73oEAEEpzdi2xfFXzV/pOmvOCUgOFsa6w+sjj6377PxjufwIICilEVue4N3+fZrktObNnj85WJjGTOf+vblqUDfsECAopWNPUp6cVkZysDD2X1Vx5HH7O7PBjQGCUsJ7korktF8TkRwsjF+B9GfKMmBGAEEpXXuShCSn7YbEPeGRxzx4a0cgKIXG5vwlSm9/amjgd1H2qUeE9XcCQSl001z7GQtof2qakU9w5HFPeOvrISilGZvjdygjOW03NHRZ3Xju6lAISrFjk9FYGwiNPfmRx/1BG3QAjV2dSyYQvZgfrDsQCEpp7otfMI3w0x95zKWR9647EghKaW6aWzB2/OmPPOZC8t51hgJBKa5Nc4vEXs1Ejjye72dr5b3rigWCUorYFu9nswZtHnk82w/nyHvXEQwEpRS7OmeOIgKNH2GKI485OPLehYOBoBSzae4N8LP5vk9x5DEHV967YDTnKOj+UndpHTsyzT6jB29E9XmiNehsRx4zgKBNjIfebzwQ9u4NprEIa74jjzkEwjljQfdf/srTzeHabHbcKVV+Tnd1LhWyB2C+I485+OM5Z0EvV6ZHuXt2r5fPbcujj2aNLR7Nn2POI485eAM6S0EvTZdW66jNPDy/zf4z3yjaoG8EQQfFCeqN6CwFLWrQ7B/9f50XLHM2q2Ag6Ix4QjpzQYsaVH+Z3ekh6Jy4YzpzQYs2qD789KwEXY6h5y5o0Ytf6158PooMQWfDFdQ5ChpGcmx9gKAjkCyB5Nj6sEBBXVFBUIrk2PqwREEdYUFQiuTY+rBIQdtxQVCK5Nj6sExBW4FBUIrk2PqwUEFpZBCUIjm2PixVUBIaBKVIjq0PixW0GRsEpUiOrQ8dCi7FUAhKkRxbHyDoCCRLIDm2PrQMFHLkMQcrOAhKkRxbH8o3Wae1y3dgyTjymEUdHQSlSI6tB+VbfHjX7OTUcoo48phJFR4EpUiOrQdE0C09Cka4oFV8EJQiObYeVALusvv7zuyI34lI3cClCBCCUiTH1gNbwG0u5v6dXZ0NQLygRYQQlCI5th60+0jmbr9VM53JPQATIgSlSI6tB4WAVh9Jp2dST25fN74vGh0jBKVIjq0HTUFNH6l5NvMCDIWgLiTH1oPSv7qPNOeRxwNRELSN5Nh6YPlX9JHmPPJ4KAqCtpAcWw/aM53ijjzmoCAoRXJsPXDNdEo78pjDPGFKlkBybFxUzqnRixd45DED1KAUybH1wNGLb3xbSTlTtgMISpEcWw/avXiNNdK0BDtPELSN5Nh60O7FG+oldxBUXKk8JMfWg8K/rMrU6VALReUdedwJBKVIjq0HtaC6/VlVnIvrxkNQiuTYelB3khprlQUeeRwGglIkx9YDq5P07HPX4UQQVFypPCTHxsdpn5wjj/lAUIrk2Pi47JNz5HEPIChFcmx8HPbJOfK4DxCUIjk2PmUf6VqpamhJypHHvYCgFMmx8ak2db7Y1A82jzyGoNJK5SE5Nj71pk5rfUjzyGMIKq1UHpJj4+O0T/SRxx4gKEVybHxc8gk/8tgNBKVIjo2PuwaVfeSxEwhKkRwbH6d80o88dgFBKZJj48ORD4IKK5WH5Nj4QNAFlspDcmx8IOgCS+UhOTY+EHSBpfKQHBsfCLrAUnlIjo0PS74lGApBKZJj4wNBF1gqD8mx8YGgCyyVh+TY+EDQBZbKQ3JsbHjqQVBZpfKQHBsbCLrEUnlIjo0NBF1iqTwkx8YGgi6xVB6SY2MDQZdYKg/JsbHxqtc4URaCyiqVh+TY2PjVW9CJsgYISpEcGxu/eUs6UVYDQSmSY2PDNA+CiiqVh+TY2PjboEvbeQxBKZJjY+M1r7nzGIKKKpWH5NjY+MwjO49jCvr48eOIV6uAoBTJsbHx16CNnccRBX38OI2hEJQiOTY2/jZoY+dxPEEfP05kKASlSI6NTUjQJPnDIOhkSI6NTeAWn+ZEWQg6GZJjYxPoJCU6URZt0KmQHBsbr3jpTpRFL34iJMfGxive4k6UhaAUybFxYXsn/0RZCEqRHBuXsHTVibLi7TxB0DaSY+PS4d2STpSFoBTJsXEJemefKAtBJZXKQ3JsXDq8q7vxEFRSqTwkx8alw7v65A8IKqlUHpJj48L3TryhEJQiOTYuIe0WdqIsBKVIjo1LQLulnSgLQSmSY+Pi125xJ8pCUIrk2LiEatCFnSgLQSmSY+MS0m5hJ8pCUIrk2LiEtFvYvk4ISpEcG5dgDbqsfZ0QlCI5Ni4B7RLu60wCBKVIjo1LsAZd1omyEJQiOTYuwTbosk6UhaAUybFx6WEdBJVTKg/JsXGBoIsslYfk2LhA0EWWykNybEz6SAdB5ZTKQ3JsTCDoMkvlITk2JhB0maXykBwbEwi6zFJ5SI6NCQRdZqk8JMfGpJd0wg2FoBTJsTGBoMsslYfk2JhA0GWWykNybEwg6DJL5SE5NiYQdJml8pAcGxMIusxSeUiOjQkEXWapPCTHxgSCLrNUHpJjYwJBl1kqD8mxMYGgyyyVh+TYmPRzTrahEJQiOTYmEHSZpfKQHBsTCLrMUnlIjo0JBF1mqTwkx8ajp3EQVEqpPCTHxgOCLrRUHpJj4wFBF1oqD8mx8YCgCy2Vh+TYeEDQhZbKQ3JsPPoaJ9pQCEqRHBsPCLrQUnk8WDwq8fOnZR4JZikVACYQNCHmpC5VneMBBgBB03G4XnU/CYSBoOk4vNjMHcLygaAJWV91PweEgaDpOFyjDToaCApEA0GBaCBoQo43qj7qEAwCgqbjeKM7SVsYOgYImo58mAmDTaOAoOlADRoBCJoQtEHHA0GBaCAoEA0ETcXhxaeYSRoPBAWigaDpwDBTBCBoKoqlIujGjwOCpgN1ZwQgKBANBE3IFr340UDQdBye3+4uTtuLueNYNBA0HVkbNP9v7kCWDARNx/GD2+y//VubuQNZMhA0IZmbO6Wwc24MEBSIBoIC0UDQVFQzSRhmGgMEBaKBoEA0EDQdyCwSAQiami2GmcYAQVODmaRRQNDU7HCLHwMETUfRBkUW2zFAUCAaCApEA0ETYjKLYDnoKCBoOorcTDB0DBA0Hdh2HAEImhBTeaIGHQUETQfWM0UAggLRQFAgGgiaECSwHQ8ETQdSgEcAgqYDw0wRgKDpQA0aAQiaELRBxwNBgWggKBANBE3G/hKLlccDQVNxvFmdkDhsNBA0FXp46fjB7dxhLB0Imgoj6A3u8SOBoKmAoFGAoKnAYrsoQFAgGggKRANBgWggKBANBAWigaBANBAUiAaCAtFAUCAaCApEA0GBaCAoEA0EBaKBoEA0EBSIBoIC0UBQIBoICkQDQYFoICgQDQQFooGgQDQQFIgGggLRQFAgGggKRANBgWggKBANBAWigaBANBAUiAaCAtFAUCAaCApEA0GBaCAoEA0EBaKBoEA0EBSI5v8Dmr4RmJM45J0AAAAASUVORK5CYII=" 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" /><!-- --></p>
 <p>By default linear regression biplot axes are fitted to the plot.
 Alternatively, spline axes can be constructed.</p>
 <div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> <span class="fu">AoD</span>(<span class="at">classes =</span> state.region, <span class="at">axes =</span> <span class="st">&quot;splines&quot;</span>) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" 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" /><!-- --></p>
 <pre><code>#&gt; Calculating spline axis for variable 1 
 #&gt; Calculating spline axis for variable 2 
 #&gt; Calculating spline axis for variable 3 
@@ -944,7 +952,7 @@ <h1><span class="header-section-number">7</span> Analysis of Distance
 square root of the Manhattan distance.</p>
 <div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" tabindex="-1"></a><span class="fu">biplot</span>(state.x77, <span class="at">scaled =</span> <span class="cn">TRUE</span>) <span class="sc">|&gt;</span> </span>
 <span id="cb18-2"><a href="#cb18-2" tabindex="-1"></a>  <span class="fu">AoD</span>(<span class="at">classes =</span> state.region, <span class="at">axes =</span> <span class="st">&quot;splines&quot;</span>, <span class="at">dist.func=</span>sqrtManhattan) <span class="sc">|&gt;</span> <span class="fu">plot</span>()</span></code></pre></div>
-<p><img src="data:image/png;base64,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" /><!-- --></p>
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" /><!-- --></p>
 <pre><code>#&gt; Calculating spline axis for variable 1 
 #&gt; Calculating spline axis for variable 2 
 #&gt; Calculating spline axis for variable 3