Updated comments in (s,d,c,z)sytf2.f and (c,z)hetf2.f

6 files changed, 159 insertions, 81 deletions

diff --git a/SRC/chetf2.f b/SRC/chetf2.f
index 101bc1ee..27295bc7 100644
--- a/SRC/chetf2.f
+++ b/SRC/chetf2.f
@@ -90,13 +90,22 @@
 *> \verbatim
 *>          IPIV is INTEGER array, dimension (N)
 *>          Details of the interchanges and the block structure of D.
-*>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
-*>          interchanged and D(k,k) is a 1-by-1 diagonal block.
-*>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
-*>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
-*>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
-*>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
-*>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'U':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k-1) < 0, then rows and columns
+*>             k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
+*>             is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k+1) < 0, then rows and columns
+*>             k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
+*>             is a 2-by-2 diagonal block.
 *> \endverbatim
 *>
 *> \param[out] INFO
@@ -268,7 +277,8 @@
          ABSAKK = ABS( REAL( A( K, K ) ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.GT.1 ) THEN
             IMAX = ICAMAX( K-1, A( 1, K ), 1 )
@@ -279,7 +289,8 @@
 *
          IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or contains a NaN: set INFO and continue
+*           Column K is or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -450,7 +461,8 @@
          ABSAKK = ABS( REAL( A( K, K ) ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.LT.N ) THEN
             IMAX = K + ICAMAX( N-K, A( K+1, K ), 1 )
@@ -461,7 +473,8 @@
 *
          IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or contains a NaN: set INFO and continue
+*           Column K is zero or underflow, contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
diff --git a/SRC/csytf2.f b/SRC/csytf2.f
index c1889f12..b779497d 100644
--- a/SRC/csytf2.f
+++ b/SRC/csytf2.f
@@ -90,13 +90,22 @@
 *> \verbatim
 *>          IPIV is INTEGER array, dimension (N)
 *>          Details of the interchanges and the block structure of D.
-*>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
-*>          interchanged and D(k,k) is a 1-by-1 diagonal block.
-*>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
-*>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
-*>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
-*>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
-*>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'U':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k-1) < 0, then rows and columns
+*>             k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
+*>             is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k+1) < 0, then rows and columns
+*>             k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
+*>             is a 2-by-2 diagonal block.
 *> \endverbatim
 *>
 *> \param[out] INFO
@@ -273,7 +282,8 @@
          ABSAKK = CABS1( A( K, K ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.GT.1 ) THEN
             IMAX = ICAMAX( K-1, A( 1, K ), 1 )
@@ -284,7 +294,8 @@
 *
          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO .OR. SISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or NaN: set INFO and continue
+*           Column K is zero or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -441,7 +452,8 @@
          ABSAKK = CABS1( A( K, K ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.LT.N ) THEN
             IMAX = K + ICAMAX( N-K, A( K+1, K ), 1 )
@@ -452,7 +464,8 @@
 *
          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO .OR. SISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or NaN: set INFO and continue
+*           Column K is zero or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
diff --git a/SRC/dsytf2.f b/SRC/dsytf2.f
index 23d8889d..3a90da85 100644
--- a/SRC/dsytf2.f
+++ b/SRC/dsytf2.f
@@ -90,13 +90,22 @@
 *> \verbatim
 *>          IPIV is INTEGER array, dimension (N)
 *>          Details of the interchanges and the block structure of D.
-*>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
-*>          interchanged and D(k,k) is a 1-by-1 diagonal block.
-*>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
-*>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
-*>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
-*>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
-*>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'U':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k-1) < 0, then rows and columns
+*>             k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
+*>             is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k+1) < 0, then rows and columns
+*>             k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
+*>             is a 2-by-2 diagonal block.
 *> \endverbatim
 *>
 *> \param[out] INFO
@@ -268,7 +277,8 @@
          ABSAKK = ABS( A( K, K ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.GT.1 ) THEN
             IMAX = IDAMAX( K-1, A( 1, K ), 1 )
@@ -279,7 +289,8 @@
 *
          IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or contains a NaN: set INFO and continue
+*           Column K is zero or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -436,7 +447,8 @@
          ABSAKK = ABS( A( K, K ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.LT.N ) THEN
             IMAX = K + IDAMAX( N-K, A( K+1, K ), 1 )
@@ -447,7 +459,8 @@
 *
          IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or contains a NaN: set INFO and continue
+*           Column K is zero or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
diff --git a/SRC/ssytf2.f b/SRC/ssytf2.f
index 68e4dee6..689007ea 100644
--- a/SRC/ssytf2.f
+++ b/SRC/ssytf2.f
@@ -90,13 +90,22 @@
 *> \verbatim
 *>          IPIV is INTEGER array, dimension (N)
 *>          Details of the interchanges and the block structure of D.
-*>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
-*>          interchanged and D(k,k) is a 1-by-1 diagonal block.
-*>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
-*>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
-*>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
-*>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
-*>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'U':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k-1) < 0, then rows and columns
+*>             k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
+*>             is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k+1) < 0, then rows and columns
+*>             k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
+*>             is a 2-by-2 diagonal block.
 *> \endverbatim
 *>
 *> \param[out] INFO
@@ -269,7 +278,8 @@
          ABSAKK = ABS( A( K, K ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.GT.1 ) THEN
             IMAX = ISAMAX( K-1, A( 1, K ), 1 )
@@ -280,7 +290,8 @@
 *
          IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or contains a NaN: set INFO and continue
+*           Column K is zero or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -437,7 +448,8 @@
          ABSAKK = ABS( A( K, K ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.LT.N ) THEN
             IMAX = K + ISAMAX( N-K, A( K+1, K ), 1 )
@@ -448,7 +460,8 @@
 *
          IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or contains a NaN: set INFO and continue
+*           Column K is zero or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
diff --git a/SRC/zhetf2.f b/SRC/zhetf2.f
index 85968c20..2fb40902 100644
--- a/SRC/zhetf2.f
+++ b/SRC/zhetf2.f
@@ -2,24 +2,24 @@
 *
 *  =========== DOCUMENTATION ===========
 *
-* Online html documentation available at 
-*            http://www.netlib.org/lapack/explore-html/ 
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
 *
 *> \htmlonly
-*> Download ZHETF2 + dependencies 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetf2.f"> 
-*> [TGZ]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetf2.f"> 
-*> [ZIP]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetf2.f"> 
+*> Download ZHETF2 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetf2.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetf2.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetf2.f">
 *> [TXT]</a>
-*> \endhtmlonly 
+*> \endhtmlonly
 *
 *  Definition:
 *  ===========
 *
 *       SUBROUTINE ZHETF2( UPLO, N, A, LDA, IPIV, INFO )
-* 
+*
 *       .. Scalar Arguments ..
 *       CHARACTER          UPLO
 *       INTEGER            INFO, LDA, N
@@ -28,7 +28,7 @@
 *       INTEGER            IPIV( * )
 *       COMPLEX*16         A( LDA, * )
 *       ..
-*  
+*
 *
 *> \par Purpose:
 *  =============
@@ -90,13 +90,22 @@
 *> \verbatim
 *>          IPIV is INTEGER array, dimension (N)
 *>          Details of the interchanges and the block structure of D.
-*>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
-*>          interchanged and D(k,k) is a 1-by-1 diagonal block.
-*>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
-*>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
-*>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
-*>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
-*>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'U':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k-1) < 0, then rows and columns
+*>             k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
+*>             is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k+1) < 0, then rows and columns
+*>             k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
+*>             is a 2-by-2 diagonal block.
 *> \endverbatim
 *>
 *> \param[out] INFO
@@ -113,10 +122,10 @@
 *  Authors:
 *  ========
 *
-*> \author Univ. of Tennessee 
-*> \author Univ. of California Berkeley 
-*> \author Univ. of Colorado Denver 
-*> \author NAG Ltd. 
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
 *
 *> \date September 2012
 *
@@ -273,7 +282,8 @@
          ABSAKK = ABS( DBLE( A( K, K ) ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.GT.1 ) THEN
             IMAX = IZAMAX( K-1, A( 1, K ), 1 )
@@ -284,7 +294,8 @@
 *
          IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or contains a NaN: set INFO and continue
+*           Column K is zero or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -456,7 +467,8 @@
          ABSAKK = ABS( DBLE( A( K, K ) ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.LT.N ) THEN
             IMAX = K + IZAMAX( N-K, A( K+1, K ), 1 )
@@ -467,7 +479,8 @@
 *
          IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or contains a NaN: set INFO and continue
+*           Column K is zero or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
diff --git a/SRC/zsytf2.f b/SRC/zsytf2.f
index cf604ecf..23564091 100644
--- a/SRC/zsytf2.f
+++ b/SRC/zsytf2.f
@@ -90,13 +90,22 @@
 *> \verbatim
 *>          IPIV is INTEGER array, dimension (N)
 *>          Details of the interchanges and the block structure of D.
-*>          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
-*>          interchanged and D(k,k) is a 1-by-1 diagonal block.
-*>          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
-*>          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
-*>          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
-*>          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
-*>          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'U':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k-1) < 0, then rows and columns
+*>             k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
+*>             is a 2-by-2 diagonal block.
+*>
+*>          If UPLO = 'L':
+*>             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*>             interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*>             If IPIV(k) = IPIV(k+1) < 0, then rows and columns
+*>             k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
+*>             is a 2-by-2 diagonal block.
 *> \endverbatim
 *>
 *> \param[out] INFO
@@ -273,7 +282,8 @@
          ABSAKK = CABS1( A( K, K ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.GT.1 ) THEN
             IMAX = IZAMAX( K-1, A( 1, K ), 1 )
@@ -284,7 +294,8 @@
 *
          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO .OR. DISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or NaN: set INFO and continue
+*           Column K is zero or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -441,7 +452,8 @@
          ABSAKK = CABS1( A( K, K ) )
 *
 *        IMAX is the row-index of the largest off-diagonal element in
-*        column K, and COLMAX is its absolute value
+*        column K, and COLMAX is its absolute value.
+*        Determine both COLMAX and IMAX.
 *
          IF( K.LT.N ) THEN
             IMAX = K + IZAMAX( N-K, A( K+1, K ), 1 )
@@ -452,7 +464,8 @@
 *
          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO .OR. DISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or NaN: set INFO and continue
+*           Column K is zero or underflow, or contains a NaN:
+*           set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K