Fix rescaling after a partial failure in the xSTEBZ-based drivers; accept Inf input and xSTEBZ's negative block numbers

SRC/chbevx.f

@@ -296,7 +296,7 @@ SUBROUTINE CHBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ,
 *     .. Local Scalars ..
       LOGICAL            ALLEIG, INDEIG, LOWER, TEST, VALEIG, WANTZ
       CHARACTER          ORDER
-      INTEGER            I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
+      INTEGER            I, IINFO, INDD, INDE, INDEE, INDIBL,
      $                   INDISP, INDIWK, INDRWK, INDWRK, ISCALE, ITMP1,
      $                   J, JJ, NSPLIT
       REAL               ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
@@ -415,8 +415,11 @@ SUBROUTINE CHBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ,
          ISCALE = 1
          SIGMA = RMIN / ANRM
       ELSE IF( ANRM.GT.RMAX ) THEN
-         ISCALE = 1
+*        An infinite norm gives SIGMA = 0; leave such a matrix
+*        unscaled so that VL and VU remain a valid interval.
          SIGMA = RMAX / ANRM
+         IF( SIGMA.GT.ZERO )
+     $      ISCALE = 1
       END IF
       IF( ISCALE.EQ.1 ) THEN
          IF( LOWER ) THEN
@@ -517,14 +520,8 @@ SUBROUTINE CHBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ,
 *     If matrix was scaled, then rescale eigenvalues appropriately.
 *
    30 CONTINUE
-      IF( ISCALE.EQ.1 ) THEN
-         IF( INFO.EQ.0 ) THEN
-            IMAX = M
-         ELSE
-            IMAX = INFO - 1
-         END IF
-         CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
-      END IF
+      IF( ISCALE.EQ.1 )
+     $   CALL SSCAL( M, ONE / SIGMA, W, 1 )
 *
 *     If eigenvalues are not in order, then sort them, along with
 *     eigenvectors.

SRC/chbevx_2stage.f

@@ -357,7 +357,7 @@ SUBROUTINE CHBEVX_2STAGE( JOBZ, RANGE, UPLO, N, KD, AB, LDAB,
       LOGICAL            ALLEIG, INDEIG, LOWER, TEST, VALEIG, WANTZ,
      $                   LQUERY
       CHARACTER          ORDER
-      INTEGER            I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
+      INTEGER            I, IINFO, INDD, INDE, INDEE, INDIBL,
      $                   INDISP, INDIWK, INDRWK, INDWRK, ISCALE, ITMP1,
      $                   LLWORK, LWMIN, LHTRD, LWTRD, IB, INDHOUS,
      $                   J, JJ, NSPLIT
@@ -501,8 +501,11 @@ SUBROUTINE CHBEVX_2STAGE( JOBZ, RANGE, UPLO, N, KD, AB, LDAB,
          ISCALE = 1
          SIGMA = RMIN / ANRM
       ELSE IF( ANRM.GT.RMAX ) THEN
-         ISCALE = 1
+*        An infinite norm gives SIGMA = 0; leave such a matrix
+*        unscaled so that VL and VU remain a valid interval.
          SIGMA = RMAX / ANRM
+         IF( SIGMA.GT.ZERO )
+     $      ISCALE = 1
       END IF
       IF( ISCALE.EQ.1 ) THEN
          IF( LOWER ) THEN
@@ -608,14 +611,8 @@ SUBROUTINE CHBEVX_2STAGE( JOBZ, RANGE, UPLO, N, KD, AB, LDAB,
 *     If matrix was scaled, then rescale eigenvalues appropriately.
 *
    30 CONTINUE
-      IF( ISCALE.EQ.1 ) THEN
-         IF( INFO.EQ.0 ) THEN
-            IMAX = M
-         ELSE
-            IMAX = INFO - 1
-         END IF
-         CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
-      END IF
+      IF( ISCALE.EQ.1 )
+     $   CALL SSCAL( M, ONE / SIGMA, W, 1 )
 *
 *     If eigenvalues are not in order, then sort them, along with
 *     eigenvectors.

SRC/cheevr.f

@@ -398,7 +398,7 @@ SUBROUTINE CHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL,
       LOGICAL            ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG,
      $                   WANTZ, TRYRAC
       CHARACTER          ORDER
-      INTEGER            I, IEEEOK, IINFO, IMAX, INDIBL, INDIFL, INDISP,
+      INTEGER            I, IEEEOK, IINFO, INDIBL, INDIFL, INDISP,
      $                   INDIWO, INDRD, INDRDD, INDRE, INDREE, INDRWK,
      $                   INDTAU, INDWK, INDWKN, ISCALE, ITMP1, J, JJ,
      $                   LIWMIN, LLWORK, LLRWORK, LLWRKN, LRWMIN,
@@ -549,8 +549,11 @@ SUBROUTINE CHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL,
          ISCALE = 1
          SIGMA = RMIN / ANRM
       ELSE IF( ANRM.GT.RMAX ) THEN
-         ISCALE = 1
+*        An infinite norm gives SIGMA = 0; leave such a matrix
+*        unscaled so that VL and VU remain a valid interval.
          SIGMA = RMAX / ANRM
+         IF( SIGMA.GT.ZERO )
+     $      ISCALE = 1
       END IF
       IF( ISCALE.EQ.1 ) THEN
          IF( LOWER ) THEN
@@ -700,14 +703,8 @@ SUBROUTINE CHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL,
 *     If matrix was scaled, then rescale eigenvalues appropriately.
 *
    30 CONTINUE
-      IF( ISCALE.EQ.1 ) THEN
-         IF( INFO.EQ.0 ) THEN
-            IMAX = M
-         ELSE
-            IMAX = INFO - 1
-         END IF
-         CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
-      END IF
+      IF( ISCALE.EQ.1 )
+     $   CALL SSCAL( M, ONE / SIGMA, W, 1 )
 *
 *     If eigenvalues are not in order, then sort them, along with
 *     eigenvectors.

SRC/cheevr_2stage.f

@@ -433,7 +433,7 @@ SUBROUTINE CHEEVR_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
       LOGICAL            ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG,
      $                   WANTZ, TRYRAC
       CHARACTER          ORDER
-      INTEGER            I, IEEEOK, IINFO, IMAX, INDIBL, INDIFL, INDISP,
+      INTEGER            I, IEEEOK, IINFO, INDIBL, INDIFL, INDISP,
      $                   INDIWO, INDRD, INDRDD, INDRE, INDREE, INDRWK,
      $                   INDTAU, INDWK, INDWKN, ISCALE, ITMP1, J, JJ,
      $                   LIWMIN, LLWORK, LLRWORK, LLWRKN, LRWMIN,
@@ -590,8 +590,11 @@ SUBROUTINE CHEEVR_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
          ISCALE = 1
          SIGMA = RMIN / ANRM
       ELSE IF( ANRM.GT.RMAX ) THEN
-         ISCALE = 1
+*        An infinite norm gives SIGMA = 0; leave such a matrix
+*        unscaled so that VL and VU remain a valid interval.
          SIGMA = RMAX / ANRM
+         IF( SIGMA.GT.ZERO )
+     $      ISCALE = 1
       END IF
       IF( ISCALE.EQ.1 ) THEN
          IF( LOWER ) THEN
@@ -744,14 +747,8 @@ SUBROUTINE CHEEVR_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
 *     If matrix was scaled, then rescale eigenvalues appropriately.
 *
    30 CONTINUE
-      IF( ISCALE.EQ.1 ) THEN
-         IF( INFO.EQ.0 ) THEN
-            IMAX = M
-         ELSE
-            IMAX = INFO - 1
-         END IF
-         CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
-      END IF
+      IF( ISCALE.EQ.1 )
+     $   CALL SSCAL( M, ONE / SIGMA, W, 1 )
 *
 *     If eigenvalues are not in order, then sort them, along with
 *     eigenvectors.

SRC/cheevx.f

@@ -287,7 +287,7 @@ SUBROUTINE CHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL,
       LOGICAL            ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG,
      $                   WANTZ
       CHARACTER          ORDER
-      INTEGER            I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
+      INTEGER            I, IINFO, INDD, INDE, INDEE, INDIBL,
      $                   INDISP, INDIWK, INDRWK, INDTAU, INDWRK, ISCALE,
      $                   ITMP1, J, JJ, LLWORK, LWKMIN, LWKOPT, NB,
      $                   NSPLIT
@@ -419,8 +419,11 @@ SUBROUTINE CHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL,
          ISCALE = 1
          SIGMA = RMIN / ANRM
       ELSE IF( ANRM.GT.RMAX ) THEN
-         ISCALE = 1
+*        An infinite norm gives SIGMA = 0; leave such a matrix
+*        unscaled so that VL and VU remain a valid interval.
          SIGMA = RMAX / ANRM
+         IF( SIGMA.GT.ZERO )
+     $      ISCALE = 1
       END IF
       IF( ISCALE.EQ.1 ) THEN
          IF( LOWER ) THEN
@@ -525,14 +528,8 @@ SUBROUTINE CHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL,
 *     If matrix was scaled, then rescale eigenvalues appropriately.
 *
    40 CONTINUE
-      IF( ISCALE.EQ.1 ) THEN
-         IF( INFO.EQ.0 ) THEN
-            IMAX = M
-         ELSE
-            IMAX = INFO - 1
-         END IF
-         CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
-      END IF
+      IF( ISCALE.EQ.1 )
+     $   CALL SSCAL( M, ONE / SIGMA, W, 1 )
 *
 *     If eigenvalues are not in order, then sort them, along with
 *     eigenvectors.

SRC/cheevx_2stage.f

@@ -334,7 +334,7 @@ SUBROUTINE CHEEVX_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
       LOGICAL            ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG,
      $                   WANTZ
       CHARACTER          ORDER
-      INTEGER            I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
+      INTEGER            I, IINFO, INDD, INDE, INDEE, INDIBL,
      $                   INDISP, INDIWK, INDRWK, INDTAU, INDWRK, ISCALE,
      $                   ITMP1, J, JJ, LLWORK,
      $                   NSPLIT, LWMIN, LHTRD, LWTRD, KD, IB, INDHOUS
@@ -470,8 +470,11 @@ SUBROUTINE CHEEVX_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
          ISCALE = 1
          SIGMA = RMIN / ANRM
       ELSE IF( ANRM.GT.RMAX ) THEN
-         ISCALE = 1
+*        An infinite norm gives SIGMA = 0; leave such a matrix
+*        unscaled so that VL and VU remain a valid interval.
          SIGMA = RMAX / ANRM
+         IF( SIGMA.GT.ZERO )
+     $      ISCALE = 1
       END IF
       IF( ISCALE.EQ.1 ) THEN
          IF( LOWER ) THEN
@@ -580,14 +583,8 @@ SUBROUTINE CHEEVX_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
 *     If matrix was scaled, then rescale eigenvalues appropriately.
 *
    40 CONTINUE
-      IF( ISCALE.EQ.1 ) THEN
-         IF( INFO.EQ.0 ) THEN
-            IMAX = M
-         ELSE
-            IMAX = INFO - 1
-         END IF
-         CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
-      END IF
+      IF( ISCALE.EQ.1 )
+     $   CALL SSCAL( M, ONE / SIGMA, W, 1 )
 *
 *     If eigenvalues are not in order, then sort them, along with
 *     eigenvectors.

SRC/chpevx.f

@@ -266,7 +266,7 @@ SUBROUTINE CHPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU,
 *     .. Local Scalars ..
       LOGICAL            ALLEIG, INDEIG, TEST, VALEIG, WANTZ
       CHARACTER          ORDER
-      INTEGER            I, IINFO, IMAX, INDD, INDE, INDEE,
+      INTEGER            I, IINFO, INDD, INDE, INDEE,
      $                   INDISP, INDIWK, INDRWK, INDTAU, INDWRK, ISCALE,
      $                   ITMP1, J, JJ, NSPLIT
       REAL               ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
@@ -373,8 +373,11 @@ SUBROUTINE CHPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU,
          ISCALE = 1
          SIGMA = RMIN / ANRM
       ELSE IF( ANRM.GT.RMAX ) THEN
-         ISCALE = 1
+*        An infinite norm gives SIGMA = 0; leave such a matrix
+*        unscaled so that VL and VU remain a valid interval.
          SIGMA = RMAX / ANRM
+         IF( SIGMA.GT.ZERO )
+     $      ISCALE = 1
       END IF
       IF( ISCALE.EQ.1 ) THEN
          CALL CSSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
@@ -469,14 +472,8 @@ SUBROUTINE CHPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU,
 *     If matrix was scaled, then rescale eigenvalues appropriately.
 *
    20 CONTINUE
-      IF( ISCALE.EQ.1 ) THEN
-         IF( INFO.EQ.0 ) THEN
-            IMAX = M
-         ELSE
-            IMAX = INFO - 1
-         END IF
-         CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
-      END IF
+      IF( ISCALE.EQ.1 )
+     $   CALL SSCAL( M, ONE / SIGMA, W, 1 )
 *
 *     If eigenvalues are not in order, then sort them, along with
 *     eigenvectors.

SRC/cstein.f

@@ -95,6 +95,8 @@
 *>          the first submatrix from the top, =2 if W(i) belongs to
 *>          the second submatrix, etc.  ( The output array IBLOCK
 *>          from SSTEBZ is expected here. )
+*>          A negative entry, with which SSTEBZ flags an eigenvalue that
+*>          did not converge, is treated as its absolute value.
 *> \endverbatim
 *>
 *> \param[in] ISPLIT
@@ -244,11 +246,12 @@ SUBROUTINE CSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
          INFO = -9
       ELSE
          DO 20 J = 2, M
-            IF( IBLOCK( J ).LT.IBLOCK( J-1 ) ) THEN
+            IF( ABS( IBLOCK( J ) ).LT.ABS( IBLOCK( J-1 ) ) ) THEN
                INFO = -6
                GO TO 30
             END IF
-            IF( IBLOCK( J ).EQ.IBLOCK( J-1 ) .AND. W( J ).LT.W( J-1 ) )
+            IF( ABS( IBLOCK( J ) ).EQ.ABS( IBLOCK( J-1 ) ) .AND.
+     $          W( J ).LT.W( J-1 ) )
      $           THEN
                INFO = -5
                GO TO 30
@@ -292,7 +295,7 @@ SUBROUTINE CSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
 *     Compute eigenvectors of matrix blocks.
 *
       J1 = 1
-      DO 180 NBLK = 1, IBLOCK( M )
+      DO 180 NBLK = 1, ABS( IBLOCK( M ) )
 *
 *        Find starting and ending indices of block nblk.
 *
@@ -324,7 +327,7 @@ SUBROUTINE CSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
    60    CONTINUE
          JBLK = 0
          DO 170 J = J1, M
-            IF( IBLOCK( J ).NE.NBLK ) THEN
+            IF( ABS( IBLOCK( J ) ).NE.NBLK ) THEN
                J1 = J
                GO TO 180
             END IF

SRC/dsbevx.f

@@ -290,7 +290,7 @@ SUBROUTINE DSBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ,
 *     .. Local Scalars ..
       LOGICAL            ALLEIG, INDEIG, LOWER, TEST, VALEIG, WANTZ
       CHARACTER          ORDER
-      INTEGER            I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
+      INTEGER            I, IINFO, INDD, INDE, INDEE, INDIBL,
      $                   INDISP, INDIWO, INDWRK, ISCALE, ITMP1, J, JJ,
      $                   NSPLIT
       DOUBLE PRECISION   ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
@@ -406,8 +406,11 @@ SUBROUTINE DSBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ,
          ISCALE = 1
          SIGMA = RMIN / ANRM
       ELSE IF( ANRM.GT.RMAX ) THEN
-         ISCALE = 1
+*        An infinite norm gives SIGMA = 0; leave such a matrix
+*        unscaled so that VL and VU remain a valid interval.
          SIGMA = RMAX / ANRM
+         IF( SIGMA.GT.ZERO )
+     $      ISCALE = 1
       END IF
       IF( ISCALE.EQ.1 ) THEN
          IF( LOWER ) THEN
@@ -507,14 +510,8 @@ SUBROUTINE DSBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ,
 *     If matrix was scaled, then rescale eigenvalues appropriately.
 *
    30 CONTINUE
-      IF( ISCALE.EQ.1 ) THEN
-         IF( INFO.EQ.0 ) THEN
-            IMAX = M
-         ELSE
-            IMAX = INFO - 1
-         END IF
-         CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
-      END IF
+      IF( ISCALE.EQ.1 )
+     $   CALL DSCAL( M, ONE / SIGMA, W, 1 )
 *
 *     If eigenvalues are not in order, then sort them, along with
 *     eigenvectors.

SRC/dsbevx_2stage.f

@@ -349,7 +349,7 @@ SUBROUTINE DSBEVX_2STAGE( JOBZ, RANGE, UPLO, N, KD, AB, LDAB,
       LOGICAL            ALLEIG, INDEIG, LOWER, TEST, VALEIG, WANTZ,
      $                   LQUERY
       CHARACTER          ORDER
-      INTEGER            I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
+      INTEGER            I, IINFO, INDD, INDE, INDEE, INDIBL,
      $                   INDISP, INDIWO, INDWRK, ISCALE, ITMP1, J, JJ,
      $                   LLWORK, LWMIN, LHTRD, LWTRD, IB, INDHOUS,
      $                   NSPLIT
@@ -490,8 +490,11 @@ SUBROUTINE DSBEVX_2STAGE( JOBZ, RANGE, UPLO, N, KD, AB, LDAB,
          ISCALE = 1
          SIGMA = RMIN / ANRM
       ELSE IF( ANRM.GT.RMAX ) THEN
-         ISCALE = 1
+*        An infinite norm gives SIGMA = 0; leave such a matrix
+*        unscaled so that VL and VU remain a valid interval.
          SIGMA = RMAX / ANRM
+         IF( SIGMA.GT.ZERO )
+     $      ISCALE = 1
       END IF
       IF( ISCALE.EQ.1 ) THEN
          IF( LOWER ) THEN
@@ -596,14 +599,8 @@ SUBROUTINE DSBEVX_2STAGE( JOBZ, RANGE, UPLO, N, KD, AB, LDAB,
 *     If matrix was scaled, then rescale eigenvalues appropriately.
 *
    30 CONTINUE
-      IF( ISCALE.EQ.1 ) THEN
-         IF( INFO.EQ.0 ) THEN
-            IMAX = M
-         ELSE
-            IMAX = INFO - 1
-         END IF
-         CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
-      END IF
+      IF( ISCALE.EQ.1 )
+     $   CALL DSCAL( M, ONE / SIGMA, W, 1 )
 *
 *     If eigenvalues are not in order, then sort them, along with
 *     eigenvectors.