diff --git a/SRC/chbevx.f b/SRC/chbevx.f
index 439d85a70..8ff2aa2fe 100644
--- a/SRC/chbevx.f
+++ b/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.
diff --git a/SRC/chbevx_2stage.f b/SRC/chbevx_2stage.f
index c05adc455..9398baf1f 100644
--- a/SRC/chbevx_2stage.f
+++ b/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.
diff --git a/SRC/cheevr.f b/SRC/cheevr.f
index bab9353f8..c8d8179d4 100644
--- a/SRC/cheevr.f
+++ b/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.
diff --git a/SRC/cheevr_2stage.f b/SRC/cheevr_2stage.f
index 5bd16f449..f2ac021c7 100644
--- a/SRC/cheevr_2stage.f
+++ b/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.
diff --git a/SRC/cheevx.f b/SRC/cheevx.f
index 54324830e..15d24ce64 100644
--- a/SRC/cheevx.f
+++ b/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.
diff --git a/SRC/cheevx_2stage.f b/SRC/cheevx_2stage.f
index 5b93c5aab..cde12aa1d 100644
--- a/SRC/cheevx_2stage.f
+++ b/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.
diff --git a/SRC/chpevx.f b/SRC/chpevx.f
index 7bf5510b3..428084bf3 100644
--- a/SRC/chpevx.f
+++ b/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.
diff --git a/SRC/cstein.f b/SRC/cstein.f
index 1040fe888..974b79040 100644
--- a/SRC/cstein.f
+++ b/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
diff --git a/SRC/dsbevx.f b/SRC/dsbevx.f
index 6b29432e0..20ea91e78 100644
--- a/SRC/dsbevx.f
+++ b/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.
diff --git a/SRC/dsbevx_2stage.f b/SRC/dsbevx_2stage.f
index 233a7121e..b54675f35 100644
--- a/SRC/dsbevx_2stage.f
+++ b/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.
diff --git a/SRC/dspevx.f b/SRC/dspevx.f
index 6eaff9b17..11c71990f 100644
--- a/SRC/dspevx.f
+++ b/SRC/dspevx.f
@@ -257,7 +257,7 @@ SUBROUTINE DSPEVX( 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, INDIWO, INDTAU, INDWRK, ISCALE, ITMP1,
      $                   J, JJ, NSPLIT
       DOUBLE PRECISION   ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
@@ -364,8 +364,11 @@ SUBROUTINE DSPEVX( 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 DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
@@ -458,14 +461,8 @@ SUBROUTINE DSPEVX( 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 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.
diff --git a/SRC/dstein.f b/SRC/dstein.f
index 02de3a0b3..bb7eb0eb3 100644
--- a/SRC/dstein.f
+++ b/SRC/dstein.f
@@ -88,6 +88,8 @@
 *>          the first submatrix from the top, =2 if W(i) belongs to
 *>          the second submatrix, etc.  ( The output array IBLOCK
 *>          from DSTEBZ is expected here. )
+*>          A negative entry, with which DSTEBZ flags an eigenvalue that
+*>          did not converge, is treated as its absolute value.
 *> \endverbatim
 *>
 *> \param[in] ISPLIT
@@ -233,11 +235,12 @@ SUBROUTINE DSTEIN( 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
@@ -281,7 +284,7 @@ SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
 *     Compute eigenvectors of matrix blocks.
 *
       J1 = 1
-      DO 160 NBLK = 1, IBLOCK( M )
+      DO 160 NBLK = 1, ABS( IBLOCK( M ) )
 *
 *        Find starting and ending indices of block nblk.
 *
@@ -313,7 +316,7 @@ SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
    60    CONTINUE
          JBLK = 0
          DO 150 J = J1, M
-            IF( IBLOCK( J ).NE.NBLK ) THEN
+            IF( ABS( IBLOCK( J ) ).NE.NBLK ) THEN
                J1 = J
                GO TO 160
             END IF
diff --git a/SRC/dstevr.f b/SRC/dstevr.f
index d75afcb37..87548af61 100644
--- a/SRC/dstevr.f
+++ b/SRC/dstevr.f
@@ -326,7 +326,7 @@ SUBROUTINE DSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
       LOGICAL            ALLEIG, INDEIG, TEST, LQUERY, VALEIG, WANTZ,
      $                   TRYRAC
       CHARACTER          ORDER
-      INTEGER            I, IEEEOK, IMAX, INDIBL, INDIFL, INDISP,
+      INTEGER            I, IEEEOK, INDIBL, INDIFL, INDISP,
      $                   INDIWO, ISCALE, ITMP1, J, JJ, LIWMIN, LWMIN,
      $                   NSPLIT
       DOUBLE PRECISION   BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
@@ -450,8 +450,11 @@ SUBROUTINE DSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
          ISCALE = 1
          SIGMA = RMIN / TNRM
       ELSE IF( TNRM.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 / TNRM
+         IF( SIGMA.GT.ZERO )
+     $      ISCALE = 1
       END IF
       IF( ISCALE.EQ.1 ) THEN
          CALL DSCAL( N, SIGMA, D, 1 )
@@ -537,14 +540,8 @@ SUBROUTINE DSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
 *     If matrix was scaled, then rescale eigenvalues appropriately.
 *
    10 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.
diff --git a/SRC/dstevx.f b/SRC/dstevx.f
index e18c03265..e9ddbd806 100644
--- a/SRC/dstevx.f
+++ b/SRC/dstevx.f
@@ -251,7 +251,7 @@ SUBROUTINE DSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
 *     .. Local Scalars ..
       LOGICAL            ALLEIG, INDEIG, TEST, VALEIG, WANTZ
       CHARACTER          ORDER
-      INTEGER            I, IINFO, IMAX, INDISP, INDIWO, INDWRK,
+      INTEGER            I, IINFO, INDISP, INDIWO, INDWRK,
      $                   ISCALE, ITMP1, J, JJ, NSPLIT
       DOUBLE PRECISION   BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
      $                   TMP1, TNRM, VLL, VUU
@@ -352,8 +352,11 @@ SUBROUTINE DSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
          ISCALE = 1
          SIGMA = RMIN / TNRM
       ELSE IF( TNRM.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 / TNRM
+         IF( SIGMA.GT.ZERO )
+     $      ISCALE = 1
       END IF
       IF( ISCALE.EQ.1 ) THEN
          CALL DSCAL( N, SIGMA, D, 1 )
@@ -427,14 +430,8 @@ SUBROUTINE DSTEVX( JOBZ, RANGE, N, D, E, 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 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.
diff --git a/SRC/dsyevr.f b/SRC/dsyevr.f
index 92166fa1b..caa54cda3 100644
--- a/SRC/dsyevr.f
+++ b/SRC/dsyevr.f
@@ -371,7 +371,7 @@ SUBROUTINE DSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL,
       LOGICAL            ALLEIG, INDEIG, LOWER, LQUERY, VALEIG, WANTZ,
      $                   TRYRAC
       CHARACTER          ORDER
-      INTEGER            I, IEEEOK, IINFO, IMAX, INDD, INDDD, INDE,
+      INTEGER            I, IEEEOK, IINFO, INDD, INDDD, INDE,
      $                   INDEE, INDIBL, INDIFL, INDISP, INDIWO, INDTAU,
      $                   INDWK, INDWKN, ISCALE, J, JJ, LIWMIN,
      $                   LLWORK, LLWRKN, LWKOPT, LWMIN, NB, NSPLIT
@@ -511,8 +511,11 @@ SUBROUTINE DSYEVR( 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
@@ -655,14 +658,8 @@ SUBROUTINE DSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL,
 *
 *  Jump here if DSTEMR/DSTEIN succeeded.
    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.  Note: We do not sort the IFAIL portion of IWORK.
diff --git a/SRC/dsyevr_2stage.f b/SRC/dsyevr_2stage.f
index 180800e26..f09a137b3 100644
--- a/SRC/dsyevr_2stage.f
+++ b/SRC/dsyevr_2stage.f
@@ -405,7 +405,7 @@ SUBROUTINE DSYEVR_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
       LOGICAL            ALLEIG, INDEIG, LOWER, LQUERY, VALEIG, WANTZ,
      $                   TRYRAC
       CHARACTER          ORDER
-      INTEGER            I, IEEEOK, IINFO, IMAX, INDD, INDDD, INDE,
+      INTEGER            I, IEEEOK, IINFO, INDD, INDDD, INDE,
      $                   INDEE, INDIBL, INDIFL, INDISP, INDIWO, INDTAU,
      $                   INDWK, INDWKN, ISCALE, J, JJ, LIWMIN,
      $                   LLWORK, LLWRKN, LWMIN, NSPLIT,
@@ -556,8 +556,11 @@ SUBROUTINE DSYEVR_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
@@ -705,14 +708,8 @@ SUBROUTINE DSYEVR_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
 *
 *  Jump here if DSTEMR/DSTEIN succeeded.
    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.  Note: We do not sort the IFAIL portion of IWORK.
diff --git a/SRC/dsyevx.f b/SRC/dsyevx.f
index 84dfe289d..ac3bf7d28 100644
--- a/SRC/dsyevx.f
+++ b/SRC/dsyevx.f
@@ -278,7 +278,7 @@ SUBROUTINE DSYEVX( 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, INDIWO, INDTAU, INDWKN, INDWRK, ISCALE,
      $                   ITMP1, J, JJ, LLWORK, LLWRKN, LWKMIN,
      $                   LWKOPT, NB, NSPLIT
@@ -407,8 +407,11 @@ SUBROUTINE DSYEVX( 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
@@ -514,14 +517,8 @@ SUBROUTINE DSYEVX( 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 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.
diff --git a/SRC/dsyevx_2stage.f b/SRC/dsyevx_2stage.f
index 4b5519be9..cdbb7e2c1 100644
--- a/SRC/dsyevx_2stage.f
+++ b/SRC/dsyevx_2stage.f
@@ -325,7 +325,7 @@ SUBROUTINE DSYEVX_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, INDIWO, INDTAU, INDWKN, INDWRK, ISCALE,
      $                   ITMP1, J, JJ, LLWORK, LLWRKN,
      $                   NSPLIT, LWMIN, LHTRD, LWTRD, KD, IB, INDHOUS
@@ -459,8 +459,11 @@ SUBROUTINE DSYEVX_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
@@ -569,14 +572,8 @@ SUBROUTINE DSYEVX_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 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.
diff --git a/SRC/ssbevx.f b/SRC/ssbevx.f
index 313616e7d..c7080f906 100644
--- a/SRC/ssbevx.f
+++ b/SRC/ssbevx.f
@@ -290,7 +290,7 @@ SUBROUTINE SSBEVX( 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
       REAL               ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
@@ -406,8 +406,11 @@ SUBROUTINE SSBEVX( 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 SSBEVX( 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.
diff --git a/SRC/ssbevx_2stage.f b/SRC/ssbevx_2stage.f
index 228839cb5..d70644ca2 100644
--- a/SRC/ssbevx_2stage.f
+++ b/SRC/ssbevx_2stage.f
@@ -349,7 +349,7 @@ SUBROUTINE SSBEVX_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
@@ -491,8 +491,11 @@ SUBROUTINE SSBEVX_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
@@ -597,14 +600,8 @@ SUBROUTINE SSBEVX_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.
diff --git a/SRC/sspevx.f b/SRC/sspevx.f
index 375a6a223..ca602d8c7 100644
--- a/SRC/sspevx.f
+++ b/SRC/sspevx.f
@@ -257,7 +257,7 @@ SUBROUTINE SSPEVX( 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, INDIWO, INDTAU, INDWRK, ISCALE, ITMP1,
      $                   J, JJ, NSPLIT
       REAL               ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
@@ -364,8 +364,11 @@ SUBROUTINE SSPEVX( 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 SSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
@@ -458,14 +461,8 @@ SUBROUTINE SSPEVX( 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.
diff --git a/SRC/sstein.f b/SRC/sstein.f
index 471d31220..72d550730 100644
--- a/SRC/sstein.f
+++ b/SRC/sstein.f
@@ -88,6 +88,8 @@
 *>          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
@@ -233,11 +235,12 @@ SUBROUTINE SSTEIN( 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
@@ -281,7 +284,7 @@ SUBROUTINE SSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
 *     Compute eigenvectors of matrix blocks.
 *
       J1 = 1
-      DO 160 NBLK = 1, IBLOCK( M )
+      DO 160 NBLK = 1, ABS( IBLOCK( M ) )
 *
 *        Find starting and ending indices of block nblk.
 *
@@ -313,7 +316,7 @@ SUBROUTINE SSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
    60    CONTINUE
          JBLK = 0
          DO 150 J = J1, M
-            IF( IBLOCK( J ).NE.NBLK ) THEN
+            IF( ABS( IBLOCK( J ) ).NE.NBLK ) THEN
                J1 = J
                GO TO 160
             END IF
diff --git a/SRC/sstevr.f b/SRC/sstevr.f
index 0b72c2f0e..51dac1c90 100644
--- a/SRC/sstevr.f
+++ b/SRC/sstevr.f
@@ -328,7 +328,7 @@ SUBROUTINE SSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
       LOGICAL            ALLEIG, INDEIG, TEST, LQUERY, VALEIG, WANTZ,
      $                   TRYRAC
       CHARACTER          ORDER
-      INTEGER            I, IEEEOK, IMAX, INDIBL, INDIFL, INDISP,
+      INTEGER            I, IEEEOK, INDIBL, INDIFL, INDISP,
      $                   INDIWO, ISCALE, J, JJ, LIWMIN, LWMIN, NSPLIT
       REAL               BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
      $                   TMP1, TNRM, VLL, VUU
@@ -452,8 +452,11 @@ SUBROUTINE SSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
          ISCALE = 1
          SIGMA = RMIN / TNRM
       ELSE IF( TNRM.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 / TNRM
+         IF( SIGMA.GT.ZERO )
+     $      ISCALE = 1
       END IF
       IF( ISCALE.EQ.1 ) THEN
          CALL SSCAL( N, SIGMA, D, 1 )
@@ -539,14 +542,8 @@ SUBROUTINE SSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
 *     If matrix was scaled, then rescale eigenvalues appropriately.
 *
    10 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.
diff --git a/SRC/sstevx.f b/SRC/sstevx.f
index f84e740ef..51c563109 100644
--- a/SRC/sstevx.f
+++ b/SRC/sstevx.f
@@ -251,7 +251,7 @@ SUBROUTINE SSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
 *     .. Local Scalars ..
       LOGICAL            ALLEIG, INDEIG, TEST, VALEIG, WANTZ
       CHARACTER          ORDER
-      INTEGER            I, IINFO, IMAX, INDISP, INDIWO, INDWRK,
+      INTEGER            I, IINFO, INDISP, INDIWO, INDWRK,
      $                   ISCALE, ITMP1, J, JJ, NSPLIT
       REAL               BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
      $                   TMP1, TNRM, VLL, VUU
@@ -352,8 +352,11 @@ SUBROUTINE SSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
          ISCALE = 1
          SIGMA = RMIN / TNRM
       ELSE IF( TNRM.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 / TNRM
+         IF( SIGMA.GT.ZERO )
+     $      ISCALE = 1
       END IF
       IF( ISCALE.EQ.1 ) THEN
          CALL SSCAL( N, SIGMA, D, 1 )
@@ -427,14 +430,8 @@ SUBROUTINE SSTEVX( JOBZ, RANGE, N, D, E, 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.
diff --git a/SRC/ssyevr.f b/SRC/ssyevr.f
index 6a848bb1c..cbe3e71ae 100644
--- a/SRC/ssyevr.f
+++ b/SRC/ssyevr.f
@@ -373,7 +373,7 @@ SUBROUTINE SSYEVR( 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, INDD, INDDD, INDE,
+      INTEGER            I, IEEEOK, IINFO, INDD, INDDD, INDE,
      $                   INDEE, INDIBL, INDIFL, INDISP, INDIWO, INDTAU,
      $                   INDWK, INDWKN, ISCALE, J, JJ, LIWMIN,
      $                   LLWORK, LLWRKN, LWKOPT, LWMIN, NB, NSPLIT
@@ -516,8 +516,11 @@ SUBROUTINE SSYEVR( 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
@@ -665,14 +668,8 @@ SUBROUTINE SSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL,
 *
 *  Jump here if SSTEMR/SSTEIN succeeded.
    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.  Note: We do not sort the IFAIL portion of IWORK.
diff --git a/SRC/ssyevr_2stage.f b/SRC/ssyevr_2stage.f
index 63f002388..47d82f308 100644
--- a/SRC/ssyevr_2stage.f
+++ b/SRC/ssyevr_2stage.f
@@ -405,7 +405,7 @@ SUBROUTINE SSYEVR_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
       LOGICAL            ALLEIG, INDEIG, LOWER, LQUERY, VALEIG, WANTZ,
      $                   TRYRAC, TEST
       CHARACTER          ORDER
-      INTEGER            I, IEEEOK, IINFO, IMAX, INDD, INDDD, INDE,
+      INTEGER            I, IEEEOK, IINFO, INDD, INDDD, INDE,
      $                   INDEE, INDIBL, INDIFL, INDISP, INDIWO, INDTAU,
      $                   INDWK, INDWKN, ISCALE, J, JJ, LIWMIN,
      $                   LLWORK, LLWRKN, LWMIN, NSPLIT,
@@ -557,8 +557,11 @@ SUBROUTINE SSYEVR_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
@@ -711,14 +714,8 @@ SUBROUTINE SSYEVR_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
 *
 *  Jump here if SSTEMR/SSTEIN succeeded.
    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.  Note: We do not sort the IFAIL portion of IWORK.
diff --git a/SRC/ssyevx.f b/SRC/ssyevx.f
index 9528c66fc..857e61da0 100644
--- a/SRC/ssyevx.f
+++ b/SRC/ssyevx.f
@@ -278,7 +278,7 @@ SUBROUTINE SSYEVX( 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, INDIWO, INDTAU, INDWKN, INDWRK, ISCALE,
      $                   ITMP1, J, JJ, LLWORK, LLWRKN, LWKMIN,
      $                   LWKOPT, NB, NSPLIT
@@ -408,8 +408,11 @@ SUBROUTINE SSYEVX( 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
@@ -515,14 +518,8 @@ SUBROUTINE SSYEVX( 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.
diff --git a/SRC/ssyevx_2stage.f b/SRC/ssyevx_2stage.f
index 8a1fc2798..a0338bac8 100644
--- a/SRC/ssyevx_2stage.f
+++ b/SRC/ssyevx_2stage.f
@@ -325,7 +325,7 @@ SUBROUTINE SSYEVX_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, INDIWO, INDTAU, INDWKN, INDWRK, ISCALE,
      $                   ITMP1, J, JJ, LLWORK, LLWRKN,
      $                   NSPLIT, LWMIN, LHTRD, LWTRD, KD, IB, INDHOUS
@@ -460,8 +460,11 @@ SUBROUTINE SSYEVX_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
@@ -570,14 +573,8 @@ SUBROUTINE SSYEVX_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.
diff --git a/SRC/zhbevx.f b/SRC/zhbevx.f
index 22487eb27..938789384 100644
--- a/SRC/zhbevx.f
+++ b/SRC/zhbevx.f
@@ -296,7 +296,7 @@ SUBROUTINE ZHBEVX( 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
       DOUBLE PRECISION   ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
@@ -415,8 +415,11 @@ SUBROUTINE ZHBEVX( 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 ZHBEVX( 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.
diff --git a/SRC/zhbevx_2stage.f b/SRC/zhbevx_2stage.f
index a22b589f5..bfc6e542a 100644
--- a/SRC/zhbevx_2stage.f
+++ b/SRC/zhbevx_2stage.f
@@ -357,7 +357,7 @@ SUBROUTINE ZHBEVX_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
@@ -500,8 +500,11 @@ SUBROUTINE ZHBEVX_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
@@ -607,14 +610,8 @@ SUBROUTINE ZHBEVX_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.
diff --git a/SRC/zheevr.f b/SRC/zheevr.f
index 038738ec8..cf77d1c2b 100644
--- a/SRC/zheevr.f
+++ b/SRC/zheevr.f
@@ -398,7 +398,7 @@ SUBROUTINE ZHEEVR( 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,
@@ -548,8 +548,11 @@ SUBROUTINE ZHEEVR( 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
@@ -699,14 +702,8 @@ SUBROUTINE ZHEEVR( 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 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.
diff --git a/SRC/zheevr_2stage.f b/SRC/zheevr_2stage.f
index 0ba5a2953..4553203a7 100644
--- a/SRC/zheevr_2stage.f
+++ b/SRC/zheevr_2stage.f
@@ -433,7 +433,7 @@ SUBROUTINE ZHEEVR_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 ZHEEVR_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 ZHEEVR_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 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.
diff --git a/SRC/zheevx.f b/SRC/zheevx.f
index f7f58932f..29699b8fb 100644
--- a/SRC/zheevx.f
+++ b/SRC/zheevx.f
@@ -287,7 +287,7 @@ SUBROUTINE ZHEEVX( 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
@@ -418,8 +418,11 @@ SUBROUTINE ZHEEVX( 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
@@ -524,14 +527,8 @@ SUBROUTINE ZHEEVX( 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 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.
diff --git a/SRC/zheevx_2stage.f b/SRC/zheevx_2stage.f
index 1b0a22d27..a9a7e5929 100644
--- a/SRC/zheevx_2stage.f
+++ b/SRC/zheevx_2stage.f
@@ -334,7 +334,7 @@ SUBROUTINE ZHEEVX_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
@@ -469,8 +469,11 @@ SUBROUTINE ZHEEVX_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
@@ -579,14 +582,8 @@ SUBROUTINE ZHEEVX_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 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.
diff --git a/SRC/zhpevx.f b/SRC/zhpevx.f
index 3a60e8fd6..a3a5bcfe9 100644
--- a/SRC/zhpevx.f
+++ b/SRC/zhpevx.f
@@ -266,7 +266,7 @@ SUBROUTINE ZHPEVX( 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
       DOUBLE PRECISION   ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
@@ -373,8 +373,11 @@ SUBROUTINE ZHPEVX( 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 ZDSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
@@ -469,14 +472,8 @@ SUBROUTINE ZHPEVX( 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 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.
diff --git a/SRC/zstein.f b/SRC/zstein.f
index ca408fe70..a00c088c1 100644
--- a/SRC/zstein.f
+++ b/SRC/zstein.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 DSTEBZ is expected here. )
+*>          A negative entry, with which DSTEBZ flags an eigenvalue that
+*>          did not converge, is treated as its absolute value.
 *> \endverbatim
 *>
 *> \param[in] ISPLIT
@@ -244,11 +246,12 @@ SUBROUTINE ZSTEIN( 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 ZSTEIN( 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 ZSTEIN( 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
diff --git a/TESTING/EIG/derrst.f b/TESTING/EIG/derrst.f
index 94018743f..3662873a9 100644
--- a/TESTING/EIG/derrst.f
+++ b/TESTING/EIG/derrst.f
@@ -86,6 +86,7 @@ SUBROUTINE DERRST( PATH, NUNIT )
      $                   E( NMAX ), Q( NMAX, NMAX ), R( NMAX ),
      $                   TAU( NMAX ), W( LW ), X( NMAX ),
      $                   Z( NMAX, NMAX )
+      DOUBLE PRECISION   RINF, RZERO
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAMEN
@@ -439,6 +440,49 @@ SUBROUTINE DERRST( PATH, NUNIT )
          CALL CHKXER( 'DSTEIN', INFOT, NOUT, LERR, OK )
          NT = NT + 4
 *
+*        A matrix that holds an infinity must come back from the
+*        drivers that scale it, instead of reaching XERBLA with a
+*        scale factor of zero.
+*
+         RZERO = 0.0D0
+         RINF = 1.0D0 / RZERO
+         DO 50 J = 1, NMAX
+            D( J ) = DBLE( J )
+            E( J ) = 1.0D0 / DBLE( J+1 )
+            DO 40 I = 1, NMAX
+               A( I, J ) = RZERO
+   40       CONTINUE
+            A( J, J ) = D( J )
+   50    CONTINUE
+         D( 1 ) = RINF
+         A( 1, 1 ) = RINF
+         E( NMAX ) = RZERO
+         A( 1, 2 ) = E( 1 )
+         A( 2, 3 ) = E( 2 )
+         SRNAMT = 'DSTEVX'
+         INFOT = 0
+         LERR = .FALSE.
+         CALL DSTEVX( 'V', 'V', NMAX, D, E, RZERO, 1.0D0, 1, NMAX,
+     $                RZERO, M, X, Z, NMAX, W, IW, I3, INFO )
+         IF( LERR ) THEN
+            WRITE( NOUT, FMT = 9997 )'DSTEVX'
+            OK = .FALSE.
+         END IF
+         D( 1 ) = RINF
+         E( 1 ) = 1.0D0 / DBLE( 2 )
+         E( 2 ) = 1.0D0 / DBLE( 3 )
+         E( NMAX ) = RZERO
+         SRNAMT = 'DSYEVX'
+         INFOT = 0
+         LERR = .FALSE.
+         CALL DSYEVX( 'V', 'V', 'U', NMAX, A, NMAX, RZERO, 1.0D0, 1,
+     $                NMAX, RZERO, M, X, Z, NMAX, W, LW, IW, I3, INFO )
+         IF( LERR ) THEN
+            WRITE( NOUT, FMT = 9997 )'DSYEVX'
+            OK = .FALSE.
+         END IF
+         NT = NT + 2
+*
 *        DSTEQR
 *
          SRNAMT = 'DSTEQR'
@@ -1427,6 +1471,8 @@ SUBROUTINE DERRST( PATH, NUNIT )
      $      ' (', I3, ' tests done)' )
  9998 FORMAT( ' *** ', A3, ' routines failed the tests of the error ',
      $      'exits ***' )
+ 9997 FORMAT( ' *** ', A6, ' called XERBLA for a matrix with an ',
+     $      'infinity ***' )
 *
       RETURN
 *
diff --git a/TESTING/EIG/serrst.f b/TESTING/EIG/serrst.f
index 471fa3599..642a0648c 100644
--- a/TESTING/EIG/serrst.f
+++ b/TESTING/EIG/serrst.f
@@ -86,6 +86,7 @@ SUBROUTINE SERRST( PATH, NUNIT )
      $                   E( NMAX ), Q( NMAX, NMAX ), R( NMAX ),
      $                   TAU( NMAX ), W( LW ), X( NMAX ),
      $                   Z( NMAX, NMAX )
+      REAL               RINF, RZERO
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAMEN
@@ -439,6 +440,49 @@ SUBROUTINE SERRST( PATH, NUNIT )
          CALL CHKXER( 'SSTEIN', INFOT, NOUT, LERR, OK )
          NT = NT + 4
 *
+*        A matrix that holds an infinity must come back from the
+*        drivers that scale it, instead of reaching XERBLA with a
+*        scale factor of zero.
+*
+         RZERO = 0.0E0
+         RINF = 1.0E0 / RZERO
+         DO 50 J = 1, NMAX
+            D( J ) = REAL( J )
+            E( J ) = 1.0E0 / REAL( J+1 )
+            DO 40 I = 1, NMAX
+               A( I, J ) = RZERO
+   40       CONTINUE
+            A( J, J ) = D( J )
+   50    CONTINUE
+         D( 1 ) = RINF
+         A( 1, 1 ) = RINF
+         E( NMAX ) = RZERO
+         A( 1, 2 ) = E( 1 )
+         A( 2, 3 ) = E( 2 )
+         SRNAMT = 'SSTEVX'
+         INFOT = 0
+         LERR = .FALSE.
+         CALL SSTEVX( 'V', 'V', NMAX, D, E, RZERO, 1.0E0, 1, NMAX,
+     $                RZERO, M, X, Z, NMAX, W, IW, I3, INFO )
+         IF( LERR ) THEN
+            WRITE( NOUT, FMT = 9997 )'SSTEVX'
+            OK = .FALSE.
+         END IF
+         D( 1 ) = RINF
+         E( 1 ) = 1.0E0 / REAL( 2 )
+         E( 2 ) = 1.0E0 / REAL( 3 )
+         E( NMAX ) = RZERO
+         SRNAMT = 'SSYEVX'
+         INFOT = 0
+         LERR = .FALSE.
+         CALL SSYEVX( 'V', 'V', 'U', NMAX, A, NMAX, RZERO, 1.0E0, 1,
+     $                NMAX, RZERO, M, X, Z, NMAX, W, LW, IW, I3, INFO )
+         IF( LERR ) THEN
+            WRITE( NOUT, FMT = 9997 )'SSYEVX'
+            OK = .FALSE.
+         END IF
+         NT = NT + 2
+*
 *        SSTEQR
 *
          SRNAMT = 'SSTEQR'
@@ -1425,6 +1469,8 @@ SUBROUTINE SERRST( PATH, NUNIT )
      $      ' (', I3, ' tests done)' )
  9998 FORMAT( ' *** ', A3, ' routines failed the tests of the error ',
      $      'exits ***' )
+ 9997 FORMAT( ' *** ', A6, ' called XERBLA for a matrix with an ',
+     $      'infinity ***' )
 *
       RETURN
 *