[RFC]: add `blas/ext/base/gtriu`

[kgryte]

Description

This RFC proposes an API to copy the upper triangular part of a matrix A to another matrix B.

API signatures:

gtriu( order, M, N, k, A, LDA, B, LDB )
gtriu.ndarray( M, N, k, A, strideA1, strideA2, offsetA, B, strideB1, strideB2, offsetB )

The implementation will be similar to lapack/base/dlacpy.

See

stdlib/lib/node_modules/@stdlib/lapack/base/dlacpy/lib/base.js

Line 255 in ad17191

function copyUpper( M, N, A, strideA1, strideA2, offsetA, B, strideB1, strideB2, offsetB ) {

where we copy all of the upper triangular part of A to B.

In this implementation, however, we will support a k parameter, which, similar to the Array API, specifies a diagonal below which to ignore.

• k = 0 is the main diagonal.
• k < 0 is a diagonal below the main diagonal.
• k > 0 is a diagonal above the main diagonal.

where the main diagonal is defined as the set of indices {(i,i)} for i on the interval [0, min(M,N)-1].

Hence, if k < 0, the functions will copy the upper triangle and one or more sub-diagonals below the main diagonal (i.e., part of the lower triangle). If k > 0, the functions will copy only part of the upper triangle.

As a consequence, the loops in

stdlib/lib/node_modules/@stdlib/lapack/base/dlacpy/lib/base.js

Line 255 in ad17191

function copyUpper( M, N, A, strideA1, strideA2, offsetA, B, strideB1, strideB2, offsetB ) {

cannot be used exactly, but can be used as a starting point. More specifically, the initial conditions for i1 and i0 will need to be updated according to the resolved diagonal.

And similar to dlacpy, we should copy in cache optional order (i.e., row-by-row for row-major and column-by-column for column-major).

Related Issues

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Questions

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