Update LAPACK to 3.9.0

lapack-netlib/SRC/dporfsx.f

@@ -135,7 +135,7 @@
 *> \param[in,out] S
 *> \verbatim
 *>          S is DOUBLE PRECISION array, dimension (N)
-*>     The row scale factors for A.  If EQUED = 'Y', A is multiplied on
+*>     The scale factors for A.  If EQUED = 'Y', A is multiplied on
 *>     the left and right by diag(S).  S is an input argument if FACT =
 *>     'F'; otherwise, S is an output argument.  If FACT = 'F' and EQUED
 *>     = 'Y', each element of S must be positive.  If S is output, each
@@ -263,7 +263,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -299,14 +299,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -314,9 +314,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0D+0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the double-precision refinement algorithm,
+*>            = 1.0:  Use the double-precision refinement algorithm,
 *>                    possibly with doubled-single computations if the
 *>                    compilation environment does not support DOUBLE
 *>                    PRECISION.

lapack-netlib/SRC/dposvxx.f

@@ -366,7 +366,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -402,14 +402,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is DOUBLE PRECISION array, dimension NPARAMS
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -417,9 +417,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0D+0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the extra-precise refinement algorithm.
+*>            = 1.0:  Use the extra-precise refinement algorithm.
 *>              (other values are reserved for future use)
 *>
 *>       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual

lapack-netlib/SRC/dsb2st_kernels.f

@@ -1,26 +1,26 @@
 *> \brief \b DSB2ST_KERNELS
 *
 *  @generated from zhb2st_kernels.f, fortran z -> d, Wed Dec  7 08:22:39 2016
-*      
+*
 *  =========== 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 DSB2ST_KERNELS + dependencies 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsb2st_kernels.f"> 
-*> [TGZ]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsb2st_kernels.f"> 
-*> [ZIP]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsb2st_kernels.f"> 
+*> Download DSB2ST_KERNELS + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsb2st_kernels.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsb2st_kernels.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsb2st_kernels.f">
 *> [TXT]</a>
-*> \endhtmlonly 
+*> \endhtmlonly
 *
 *  Definition:
 *  ===========
 *
-*       SUBROUTINE  DSB2ST_KERNELS( UPLO, WANTZ, TTYPE, 
+*       SUBROUTINE  DSB2ST_KERNELS( UPLO, WANTZ, TTYPE,
 *                                   ST, ED, SWEEP, N, NB, IB,
 *                                   A, LDA, V, TAU, LDVT, WORK)
 *
@@ -32,9 +32,9 @@
 *       INTEGER            TTYPE, ST, ED, SWEEP, N, NB, IB, LDA, LDVT
 *       ..
 *       .. Array Arguments ..
-*       DOUBLE PRECISION   A( LDA, * ), V( * ), 
+*       DOUBLE PRECISION   A( LDA, * ), V( * ),
 *                          TAU( * ), WORK( * )
-*  
+*
 *> \par Purpose:
 *  =============
 *>
@@ -124,7 +124,7 @@
 *>          LDVT is INTEGER.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is DOUBLE PRECISION array. Workspace of size nb.
 *> \endverbatim
@@ -147,7 +147,7 @@
 *>  http://doi.acm.org/10.1145/2063384.2063394
 *>
 *>  A. Haidar, J. Kurzak, P. Luszczek, 2013.
-*>  An improved parallel singular value algorithm and its implementation 
+*>  An improved parallel singular value algorithm and its implementation
 *>  for multicore hardware, In Proceedings of 2013 International Conference
 *>  for High Performance Computing, Networking, Storage and Analysis (SC '13).
 *>  Denver, Colorado, USA, 2013.
@@ -155,16 +155,16 @@
 *>  http://doi.acm.org/10.1145/2503210.2503292
 *>
 *>  A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
-*>  A novel hybrid CPU-GPU generalized eigensolver for electronic structure 
+*>  A novel hybrid CPU-GPU generalized eigensolver for electronic structure
 *>  calculations based on fine-grained memory aware tasks.
 *>  International Journal of High Performance Computing Applications.
 *>  Volume 28 Issue 2, Pages 196-209, May 2014.
-*>  http://hpc.sagepub.com/content/28/2/196 
+*>  http://hpc.sagepub.com/content/28/2/196
 *>
 *> \endverbatim
 *>
 *  =====================================================================
-      SUBROUTINE  DSB2ST_KERNELS( UPLO, WANTZ, TTYPE, 
+      SUBROUTINE  DSB2ST_KERNELS( UPLO, WANTZ, TTYPE,
      $                            ST, ED, SWEEP, N, NB, IB,
      $                            A, LDA, V, TAU, LDVT, WORK)
 *
@@ -181,7 +181,7 @@
       INTEGER            TTYPE, ST, ED, SWEEP, N, NB, IB, LDA, LDVT
 *     ..
 *     .. Array Arguments ..
-      DOUBLE PRECISION   A( LDA, * ), V( * ), 
+      DOUBLE PRECISION   A( LDA, * ), V( * ),
      $                   TAU( * ), WORK( * )
 *     ..
 *
@@ -195,8 +195,8 @@
 *     .. Local Scalars ..
       LOGICAL            UPPER
       INTEGER            I, J1, J2, LM, LN, VPOS, TAUPOS,
-     $                   DPOS, OFDPOS, AJETER 
-      DOUBLE PRECISION   CTMP 
+     $                   DPOS, OFDPOS, AJETER
+      DOUBLE PRECISION   CTMP
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           DLARFG, DLARFX, DLARFY
@@ -209,7 +209,7 @@
 *     ..
 *     ..
 *     .. Executable Statements ..
-*      
+*
       AJETER = IB + LDVT
       UPPER = LSAME( UPLO, 'U' )
 
@@ -240,10 +240,10 @@
               V( VPOS ) = ONE
               DO 10 I = 1, LM-1
                   V( VPOS+I )         = ( A( OFDPOS-I, ST+I ) )
-                  A( OFDPOS-I, ST+I ) = ZERO  
+                  A( OFDPOS-I, ST+I ) = ZERO
    10         CONTINUE
               CTMP = ( A( OFDPOS, ST ) )
-              CALL DLARFG( LM, CTMP, V( VPOS+1 ), 1, 
+              CALL DLARFG( LM, CTMP, V( VPOS+1 ), 1,
      $                                       TAU( TAUPOS ) )
               A( OFDPOS, ST ) = CTMP
 *
@@ -281,14 +281,14 @@
 *
                   V( VPOS ) = ONE
                   DO 30 I = 1, LM-1
-                      V( VPOS+I )          = 
+                      V( VPOS+I )          =
      $                                    ( A( DPOS-NB-I, J1+I ) )
                       A( DPOS-NB-I, J1+I ) = ZERO
    30             CONTINUE
                   CTMP = ( A( DPOS-NB, J1 ) )
                   CALL DLARFG( LM, CTMP, V( VPOS+1 ), 1, TAU( TAUPOS ) )
                   A( DPOS-NB, J1 ) = CTMP
-*                 
+*
                   CALL DLARFX( 'Right', LN-1, LM, V( VPOS ),
      $                         TAU( TAUPOS ),
      $                         A( DPOS-NB+1, J1 ), LDA-1, WORK)
@@ -296,9 +296,9 @@
           ENDIF
 *
 *     Lower case
-*  
+*
       ELSE
-*      
+*
           IF( WANTZ ) THEN
               VPOS   = MOD( SWEEP-1, 2 ) * N + ST
               TAUPOS = MOD( SWEEP-1, 2 ) * N + ST
@@ -313,9 +313,9 @@
               V( VPOS ) = ONE
               DO 20 I = 1, LM-1
                   V( VPOS+I )         = A( OFDPOS+I, ST-1 )
-                  A( OFDPOS+I, ST-1 ) = ZERO  
+                  A( OFDPOS+I, ST-1 ) = ZERO
    20         CONTINUE
-              CALL DLARFG( LM, A( OFDPOS, ST-1 ), V( VPOS+1 ), 1, 
+              CALL DLARFG( LM, A( OFDPOS, ST-1 ), V( VPOS+1 ), 1,
      $                                       TAU( TAUPOS ) )
 *
               LM = ED - ST + 1
@@ -342,7 +342,7 @@
               LM = J2-J1+1
 *
               IF( LM.GT.0) THEN
-                  CALL DLARFX( 'Right', LM, LN, V( VPOS ), 
+                  CALL DLARFX( 'Right', LM, LN, V( VPOS ),
      $                         TAU( TAUPOS ), A( DPOS+NB, ST ),
      $                         LDA-1, WORK)
 *
@@ -359,13 +359,13 @@
                       V( VPOS+I )        = A( DPOS+NB+I, ST )
                       A( DPOS+NB+I, ST ) = ZERO
    40             CONTINUE
-                  CALL DLARFG( LM, A( DPOS+NB, ST ), V( VPOS+1 ), 1, 
+                  CALL DLARFG( LM, A( DPOS+NB, ST ), V( VPOS+1 ), 1,
      $                                        TAU( TAUPOS ) )
 *
-                  CALL DLARFX( 'Left', LM, LN-1, V( VPOS ), 
+                  CALL DLARFX( 'Left', LM, LN-1, V( VPOS ),
      $                         ( TAU( TAUPOS ) ),
      $                         A( DPOS+NB-1, ST+1 ), LDA-1, WORK)
-             
+
               ENDIF
           ENDIF
       ENDIF
@@ -374,4 +374,4 @@
 *
 *     END OF DSB2ST_KERNELS
 *
-      END      
+      END

lapack-netlib/SRC/dsbgvx.f

@@ -261,11 +261,11 @@
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>          = 0 : successful exit
-*>          < 0 : if INFO = -i, the i-th argument had an illegal value
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
 *>          <= N: if INFO = i, then i eigenvectors failed to converge.
 *>                  Their indices are stored in IFAIL.
-*>          > N : DPBSTF returned an error code; i.e.,
+*>          > N:  DPBSTF returned an error code; i.e.,
 *>                if INFO = N + i, for 1 <= i <= N, then the leading
 *>                minor of order i of B is not positive definite.
 *>                The factorization of B could not be completed and

lapack-netlib/SRC/dsgesv.f

@@ -92,9 +92,9 @@
 *>          dimension (LDA,N)
 *>          On entry, the N-by-N coefficient matrix A.
 *>          On exit, if iterative refinement has been successfully used
-*>          (INFO.EQ.0 and ITER.GE.0, see description below), then A is
+*>          (INFO = 0 and ITER >= 0, see description below), then A is
 *>          unchanged, if double precision factorization has been used
-*>          (INFO.EQ.0 and ITER.LT.0, see description below), then the
+*>          (INFO = 0 and ITER < 0, see description below), then the
 *>          array A contains the factors L and U from the factorization
 *>          A = P*L*U; the unit diagonal elements of L are not stored.
 *> \endverbatim
@@ -111,8 +111,8 @@
 *>          The pivot indices that define the permutation matrix P;
 *>          row i of the matrix was interchanged with row IPIV(i).
 *>          Corresponds either to the single precision factorization
-*>          (if INFO.EQ.0 and ITER.GE.0) or the double precision
-*>          factorization (if INFO.EQ.0 and ITER.LT.0).
+*>          (if INFO = 0 and ITER >= 0) or the double precision
+*>          factorization (if INFO = 0 and ITER < 0).
 *> \endverbatim
 *>
 *> \param[in] B
@@ -406,7 +406,7 @@
    30 CONTINUE
 *
 *     If we are at this place of the code, this is because we have
-*     performed ITER=ITERMAX iterations and never satisified the
+*     performed ITER=ITERMAX iterations and never satisfied the
 *     stopping criterion, set up the ITER flag accordingly and follow up
 *     on double precision routine.
 *

lapack-netlib/SRC/dsposv.f

@@ -106,9 +106,9 @@
 *>          triangular part of the matrix A, and the strictly upper
 *>          triangular part of A is not referenced.
 *>          On exit, if iterative refinement has been successfully used
-*>          (INFO.EQ.0 and ITER.GE.0, see description below), then A is
+*>          (INFO = 0 and ITER >= 0, see description below), then A is
 *>          unchanged, if double precision factorization has been used
-*>          (INFO.EQ.0 and ITER.LT.0, see description below), then the
+*>          (INFO = 0 and ITER < 0, see description below), then the
 *>          array A contains the factor U or L from the Cholesky
 *>          factorization A = U**T*U or A = L*L**T.
 *> \endverbatim
@@ -413,7 +413,7 @@
    30 CONTINUE
 *
 *     If we are at this place of the code, this is because we have
-*     performed ITER=ITERMAX iterations and never satisified the
+*     performed ITER=ITERMAX iterations and never satisfied the
 *     stopping criterion, set up the ITER flag accordingly and follow
 *     up on double precision routine.
 *

lapack-netlib/SRC/dstemr.f

@@ -233,13 +233,13 @@
 *> \param[in,out] TRYRAC
 *> \verbatim
 *>          TRYRAC is LOGICAL
-*>          If TRYRAC.EQ..TRUE., indicates that the code should check whether
+*>          If TRYRAC = .TRUE., indicates that the code should check whether
 *>          the tridiagonal matrix defines its eigenvalues to high relative
 *>          accuracy.  If so, the code uses relative-accuracy preserving
 *>          algorithms that might be (a bit) slower depending on the matrix.
 *>          If the matrix does not define its eigenvalues to high relative
 *>          accuracy, the code can uses possibly faster algorithms.
-*>          If TRYRAC.EQ..FALSE., the code is not required to guarantee
+*>          If TRYRAC = .FALSE., the code is not required to guarantee
 *>          relatively accurate eigenvalues and can use the fastest possible
 *>          techniques.
 *>          On exit, a .TRUE. TRYRAC will be set to .FALSE. if the matrix

lapack-netlib/SRC/dsyconvf.f

@@ -291,7 +291,7 @@
 *
 *           Convert PERMUTATIONS and IPIV
 *
-*           Apply permutaions to submatrices of upper part of A
+*           Apply permutations to submatrices of upper part of A
 *           in factorization order where i decreases from N to 1
 *
             I = N
@@ -344,7 +344,7 @@
 *
 *           Revert PERMUTATIONS and IPIV
 *
-*           Apply permutaions to submatrices of upper part of A
+*           Apply permutations to submatrices of upper part of A
 *           in reverse factorization order where i increases from 1 to N
 *
             I = 1
@@ -435,7 +435,7 @@
 *
 *           Convert PERMUTATIONS and IPIV
 *
-*           Apply permutaions to submatrices of lower part of A
+*           Apply permutations to submatrices of lower part of A
 *           in factorization order where k increases from 1 to N
 *
             I = 1
@@ -488,7 +488,7 @@
 *
 *           Revert PERMUTATIONS and IPIV
 *
-*           Apply permutaions to submatrices of lower part of A
+*           Apply permutations to submatrices of lower part of A
 *           in reverse factorization order where i decreases from N to 1
 *
             I = N

lapack-netlib/SRC/dsyconvf_rook.f

@@ -282,7 +282,7 @@
 *
 *           Convert PERMUTATIONS
 *
-*           Apply permutaions to submatrices of upper part of A
+*           Apply permutations to submatrices of upper part of A
 *           in factorization order where i decreases from N to 1
 *
             I = N
@@ -333,7 +333,7 @@
 *
 *           Revert PERMUTATIONS
 *
-*           Apply permutaions to submatrices of upper part of A
+*           Apply permutations to submatrices of upper part of A
 *           in reverse factorization order where i increases from 1 to N
 *
             I = 1
@@ -423,7 +423,7 @@
 *
 *           Convert PERMUTATIONS
 *
-*           Apply permutaions to submatrices of lower part of A
+*           Apply permutations to submatrices of lower part of A
 *           in factorization order where i increases from 1 to N
 *
             I = 1
@@ -474,7 +474,7 @@
 *
 *           Revert PERMUTATIONS
 *
-*           Apply permutaions to submatrices of lower part of A
+*           Apply permutations to submatrices of lower part of A
 *           in reverse factorization order where i decreases from N to 1
 *
             I = N

lapack-netlib/SRC/dsyev_2stage.f

@@ -317,7 +317,7 @@
       IF( .NOT.WANTZ ) THEN
          CALL DSTERF( N, W, WORK( INDE ), INFO )
       ELSE
-*        Not available in this release, and agrument checking should not
+*        Not available in this release, and argument checking should not
 *        let it getting here
          RETURN
          CALL DORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ),

lapack-netlib/SRC/dsyevd_2stage.f

@@ -385,7 +385,7 @@
       IF( .NOT.WANTZ ) THEN
          CALL DSTERF( N, W, WORK( INDE ), INFO )
       ELSE
-*        Not available in this release, and agrument checking should not
+*        Not available in this release, and argument checking should not
 *        let it getting here
          RETURN
          CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N,

lapack-netlib/SRC/dsyrfsx.f

@@ -271,7 +271,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -307,14 +307,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -322,9 +322,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0D+0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the double-precision refinement algorithm,
+*>            = 1.0:  Use the double-precision refinement algorithm,
 *>                    possibly with doubled-single computations if the
 *>                    compilation environment does not support DOUBLE
 *>                    PRECISION.

lapack-netlib/SRC/dsysv_aa.f

@@ -42,7 +42,7 @@
 *> matrices.
 *>
 *> Aasen's algorithm is used to factor A as
-*>    A = U * T * U**T,  if UPLO = 'U', or
+*>    A = U**T * T * U,  if UPLO = 'U', or
 *>    A = L * T * L**T,  if UPLO = 'L',
 *> where U (or L) is a product of permutation and unit upper (lower)
 *> triangular matrices, and T is symmetric tridiagonal. The factored
@@ -86,7 +86,7 @@
 *>
 *>          On exit, if INFO = 0, the tridiagonal matrix T and the
 *>          multipliers used to obtain the factor U or L from the
-*>          factorization A = U*T*U**T or A = L*T*L**T as computed by
+*>          factorization A = U**T*T*U or A = L*T*L**T as computed by
 *>          DSYTRF.
 *> \endverbatim
 *>
@@ -230,7 +230,7 @@
          RETURN
       END IF
 *
-*     Compute the factorization A = U*T*U**T or A = L*T*L**T.
+*     Compute the factorization A = U**T*T*U or A = L*T*L**T.
 *
       CALL DSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
       IF( INFO.EQ.0 ) THEN

lapack-netlib/SRC/dsysv_aa_2stage.f

@@ -45,7 +45,7 @@
 *> matrices.
 *>
 *> Aasen's 2-stage algorithm is used to factor A as
-*>    A = U * T * U**T,  if UPLO = 'U', or
+*>    A = U**T * T * U,  if UPLO = 'U', or
 *>    A = L * T * L**T,  if UPLO = 'L',
 *> where U (or L) is a product of permutation and unit upper (lower)
 *> triangular matrices, and T is symmetric and band. The matrix T is
@@ -259,7 +259,7 @@
       END IF
 *
 *
-*     Compute the factorization A = U*T*U**T or A = L*T*L**T.
+*     Compute the factorization A = U**T*T*U or A = L*T*L**T.
 *
       CALL DSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2,
      $                       WORK, LWORK, INFO )

lapack-netlib/SRC/dsysvxx.f

@@ -377,7 +377,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -413,14 +413,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -428,9 +428,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0D+0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the extra-precise refinement algorithm.
+*>            = 1.0:  Use the extra-precise refinement algorithm.
 *>              (other values are reserved for future use)
 *>
 *>       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual

lapack-netlib/SRC/dsytf2_rk.f

@@ -312,7 +312,7 @@
 *
 *        Factorize A as U*D*U**T using the upper triangle of A
 *
-*        Initilize the first entry of array E, where superdiagonal
+*        Initialize the first entry of array E, where superdiagonal
 *        elements of D are stored
 *
          E( 1 ) = ZERO
@@ -623,7 +623,7 @@
 *
 *        Factorize A as L*D*L**T using the lower triangle of A
 *
-*        Initilize the unused last entry of the subdiagonal array E.
+*        Initialize the unused last entry of the subdiagonal array E.
 *
          E( N ) = ZERO
 *

lapack-netlib/SRC/dsytrd_2stage.f

@@ -123,23 +123,22 @@
 *>
 *> \param[out] HOUS2
 *> \verbatim
-*>          HOUS2 is DOUBLE PRECISION array, dimension LHOUS2, that
-*>          store the Householder representation of the stage2
+*>          HOUS2 is DOUBLE PRECISION array, dimension (LHOUS2)
+*>          Stores the Householder representation of the stage2
 *>          band to tridiagonal.
 *> \endverbatim
 *>
 *> \param[in] LHOUS2
 *> \verbatim
 *>          LHOUS2 is INTEGER
-*>          The dimension of the array HOUS2. LHOUS2 = MAX(1, dimension)
-*>          If LWORK = -1, or LHOUS2=-1,
+*>          The dimension of the array HOUS2.
+*>          If LWORK = -1, or LHOUS2 = -1,
 *>          then a query is assumed; the routine
 *>          only calculates the optimal size of the HOUS2 array, returns
 *>          this value as the first entry of the HOUS2 array, and no error
 *>          message related to LHOUS2 is issued by XERBLA.
-*>          LHOUS2 = MAX(1, dimension) where
-*>          dimension = 4*N if VECT='N'
-*>          not available now if VECT='H'
+*>          If VECT='N', LHOUS2 = max(1, 4*n);
+*>          if VECT='V', option not yet available.
 *> \endverbatim
 *>
 *> \param[out] WORK

lapack-netlib/SRC/dsytrd_sb2st.F

@@ -50,9 +50,9 @@
 *  Arguments:
 *  ==========
 *
-*> \param[in] STAGE
+*> \param[in] STAGE1
 *> \verbatim
-*>          STAGE is CHARACTER*1
+*>          STAGE1 is CHARACTER*1
 *>          = 'N':  "No": to mention that the stage 1 of the reduction  
 *>                  from dense to band using the dsytrd_sy2sb routine
 *>                  was not called before this routine to reproduce AB. 
@@ -481,7 +481,7 @@
 *
 *                         Call the kernel
 *                             
-#if defined(_OPENMP) &&  _OPENMP >= 201307
+#if defined(_OPENMP)
                           IF( TTYPE.NE.1 ) THEN      
 !$OMP TASK DEPEND(in:WORK(MYID+SHIFT-1))
 !$OMP$     DEPEND(in:WORK(MYID-1))

lapack-netlib/SRC/dsytrd_sy2sb.f

@@ -363,7 +363,7 @@
 *
 *
 *     Set the workspace of the triangular matrix T to zero once such a
-*     way everytime T is generated the upper/lower portion will be always zero  
+*     way every time T is generated the upper/lower portion will be always zero
 *   
       CALL DLASET( "A", LDT, KD, ZERO, ZERO, WORK( TPOS ), LDT )
 *

lapack-netlib/SRC/dsytrf.f

@@ -39,7 +39,7 @@
 *> the Bunch-Kaufman diagonal pivoting method.  The form of the
 *> factorization is
 *>
-*>    A = U*D*U**T  or  A = L*D*L**T
+*>    A = U**T*D*U  or  A = L*D*L**T
 *>
 *> where U (or L) is a product of permutation and unit upper (lower)
 *> triangular matrices, and D is symmetric and block diagonal with
@@ -144,7 +144,7 @@
 *>
 *> \verbatim
 *>
-*>  If UPLO = 'U', then A = U*D*U**T, where
+*>  If UPLO = 'U', then A = U**T*D*U, where
 *>     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *>  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *>  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -262,7 +262,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U**T using the upper triangle of A
+*        Factorize A as U**T*D*U using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        KB, where KB is the number of columns factorized by DLASYF;

lapack-netlib/SRC/dsytrf_aa.f

@@ -37,7 +37,7 @@
 *> DSYTRF_AA computes the factorization of a real symmetric matrix A
 *> using the Aasen's algorithm.  The form of the factorization is
 *>
-*>    A = U*T*U**T  or  A = L*T*L**T
+*>    A = U**T*T*U  or  A = L*T*L**T
 *>
 *> where U (or L) is a product of permutation and unit upper (lower)
 *> triangular matrices, and T is a symmetric tridiagonal matrix.
@@ -223,7 +223,7 @@
       IF( UPPER ) THEN
 *
 *        .....................................................
-*        Factorize A as L*D*L**T using the upper triangle of A
+*        Factorize A as U**T*D*U using the upper triangle of A
 *        .....................................................
 *
 *        Copy first row A(1, 1:N) into H(1:n) (stored in WORK(1:N))
@@ -256,7 +256,7 @@
      $                      A( MAX(1, J), J+1 ), LDA,
      $                      IPIV( J+1 ), WORK, N, WORK( N*NB+1 ) )
 *
-*        Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*        Adjust IPIV and apply it back (J-th step picks (J+1)-th pivot)
 *
          DO J2 = J+2, MIN(N, J+JB+1)
             IPIV( J2 ) = IPIV( J2 ) + J
@@ -375,7 +375,7 @@
      $                      A( J+1, MAX(1, J) ), LDA,
      $                      IPIV( J+1 ), WORK, N, WORK( N*NB+1 ) )
 *
-*        Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*        Adjust IPIV and apply it back (J-th step picks (J+1)-th pivot)
 *
          DO J2 = J+2, MIN(N, J+JB+1)
             IPIV( J2 ) = IPIV( J2 ) + J

lapack-netlib/SRC/dsytrf_aa_2stage.f

@@ -38,7 +38,7 @@
 *> DSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A
 *> using the Aasen's algorithm.  The form of the factorization is
 *>
-*>    A = U*T*U**T  or  A = L*T*L**T
+*>    A = U**T*T*U  or  A = L*T*L**T
 *>
 *> where U (or L) is a product of permutation and unit upper (lower)
 *> triangular matrices, and T is a symmetric band matrix with the
@@ -103,6 +103,22 @@
 *>          no error message related to LTB is issued by XERBLA.
 *> \endverbatim
 *>
+*> \param[out] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          On exit, it contains the details of the interchanges, i.e.,
+*>          the row and column k of A were interchanged with the
+*>          row and column IPIV(k).
+*> \endverbatim
+*>
+*> \param[out] IPIV2
+*> \verbatim
+*>          IPIV2 is INTEGER array, dimension (N)
+*>          On exit, it contains the details of the interchanges, i.e.,
+*>          the row and column k of T were interchanged with the
+*>          row and column IPIV2(k).
+*> \endverbatim
+*>
 *> \param[out] WORK
 *> \verbatim
 *>          WORK is DOUBLE PRECISION workspace of size LWORK
@@ -120,22 +136,6 @@
 *>          no error message related to LWORK is issued by XERBLA.
 *> \endverbatim
 *>
-*> \param[out] IPIV
-*> \verbatim
-*>          IPIV is INTEGER array, dimension (N)
-*>          On exit, it contains the details of the interchanges, i.e.,
-*>          the row and column k of A were interchanged with the
-*>          row and column IPIV(k).
-*> \endverbatim
-*>
-*> \param[out] IPIV2
-*> \verbatim
-*>          IPIV2 is INTEGER array, dimension (N)
-*>          On exit, it contains the details of the interchanges, i.e.,
-*>          the row and column k of T were interchanged with the
-*>          row and column IPIV2(k).
-*> \endverbatim
-*>
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
@@ -275,7 +275,7 @@
       IF( UPPER ) THEN
 *
 *        .....................................................
-*        Factorize A as L*D*L**T using the upper triangle of A
+*        Factorize A as U**T*D*U using the upper triangle of A
 *        .....................................................
 *
          DO J = 0, NT-1
@@ -442,12 +442,14 @@ c               END IF
 *                    > Apply pivots to previous columns of L
                      CALL DSWAP( K-1, A( (J+1)*NB+1, I1 ), 1, 
      $                                A( (J+1)*NB+1, I2 ), 1 )
-*                    > Swap A(I1+1:M, I1) with A(I2, I1+1:M)               
-                     CALL DSWAP( I2-I1-1, A( I1, I1+1 ), LDA,
-     $                                    A( I1+1, I2 ), 1 )
+*                    > Swap A(I1+1:M, I1) with A(I2, I1+1:M)
+                     IF( I2.GT.(I1+1) )
+     $                  CALL DSWAP( I2-I1-1, A( I1, I1+1 ), LDA,
+     $                                       A( I1+1, I2 ), 1 )
 *                    > Swap A(I2+1:M, I1) with A(I2+1:M, I2)
-                     CALL DSWAP( N-I2, A( I1, I2+1 ), LDA,
-     $                                 A( I2, I2+1 ), LDA ) 
+                     IF( I2.LT.N )
+     $                  CALL DSWAP( N-I2, A( I1, I2+1 ), LDA,
+     $                                    A( I2, I2+1 ), LDA ) 
 *                    > Swap A(I1, I1) with A(I2, I2)
                      PIV = A( I1, I1 )
                      A( I1, I1 ) = A( I2, I2 )
@@ -616,11 +618,13 @@ c               END IF
                      CALL DSWAP( K-1, A( I1, (J+1)*NB+1 ), LDA, 
      $                                A( I2, (J+1)*NB+1 ), LDA )
 *                    > Swap A(I1+1:M, I1) with A(I2, I1+1:M)               
-                     CALL DSWAP( I2-I1-1, A( I1+1, I1 ), 1,
-     $                                    A( I2, I1+1 ), LDA )
+                     IF( I2.GT.(I1+1) )
+     $                  CALL DSWAP( I2-I1-1, A( I1+1, I1 ), 1,
+     $                                       A( I2, I1+1 ), LDA )
 *                    > Swap A(I2+1:M, I1) with A(I2+1:M, I2)
-                     CALL DSWAP( N-I2, A( I2+1, I1 ), 1,
-     $                                 A( I2+1, I2 ), 1 ) 
+                     IF( I2.LT.N )
+     $                  CALL DSWAP( N-I2, A( I2+1, I1 ), 1,
+     $                                    A( I2+1, I2 ), 1 ) 
 *                    > Swap A(I1, I1) with A(I2, I2)
                      PIV = A( I1, I1 )
                      A( I1, I1 ) = A( I2, I2 )

lapack-netlib/SRC/dsytri2.f

@@ -62,7 +62,7 @@
 *> \param[in,out] A
 *> \verbatim
 *>          A is DOUBLE PRECISION array, dimension (LDA,N)
-*>          On entry, the NB diagonal matrix D and the multipliers
+*>          On entry, the block diagonal matrix D and the multipliers
 *>          used to obtain the factor U or L as computed by DSYTRF.
 *>
 *>          On exit, if INFO = 0, the (symmetric) inverse of the original
@@ -82,7 +82,7 @@
 *> \param[in] IPIV
 *> \verbatim
 *>          IPIV is INTEGER array, dimension (N)
-*>          Details of the interchanges and the NB structure of D
+*>          Details of the interchanges and the block structure of D
 *>          as determined by DSYTRF.
 *> \endverbatim
 *>

lapack-netlib/SRC/dsytrs_aa.f

@@ -37,7 +37,7 @@
 *> \verbatim
 *>
 *> DSYTRS_AA solves a system of linear equations A*X = B with a real
-*> symmetric matrix A using the factorization A = U*T*U**T or
+*> symmetric matrix A using the factorization A = U**T*T*U or
 *> A = L*T*L**T computed by DSYTRF_AA.
 *> \endverbatim
 *
@@ -49,7 +49,7 @@
 *>          UPLO is CHARACTER*1
 *>          Specifies whether the details of the factorization are stored
 *>          as an upper or lower triangular matrix.
-*>          = 'U':  Upper triangular, form is A = U*T*U**T;
+*>          = 'U':  Upper triangular, form is A = U**T*T*U;
 *>          = 'L':  Lower triangular, form is A = L*T*L**T.
 *> \endverbatim
 *>
@@ -97,14 +97,16 @@
 *>          The leading dimension of the array B.  LDB >= max(1,N).
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
-*>          WORK is DOUBLE array, dimension (MAX(1,LWORK))
+*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
 *> \endverbatim
 *>
 *> \param[in] LWORK
 *> \verbatim
-*>          LWORK is INTEGER, LWORK >= MAX(1,3*N-2).
+*>          LWORK is INTEGER
+*>          The dimension of the array WORK. LWORK >= max(1,3*N-2).
+*> \endverbatim
 *>
 *> \param[out] INFO
 *> \verbatim
@@ -198,22 +200,29 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*T*U**T.
+*        Solve A*X = B, where A = U**T*T*U.
+*
+*        1) Forward substitution with U**T
+*
+         IF( N.GT.1 ) THEN
+*
+*           Pivot, P**T * B -> B
 *
-*        Pivot, P**T * B
+            DO K = 1, N
+               KP = IPIV( K )
+               IF( KP.NE.K )
+     $             CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+            END DO
 *
-         DO K = 1, N
-            KP = IPIV( K )
-            IF( KP.NE.K )
-     $          CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
-         END DO
+*           Compute U**T \ B -> B    [ (U**T \P**T * B) ]
 *
-*        Compute (U \P**T * B) -> B    [ (U \P**T * B) ]
+            CALL DTRSM('L', 'U', 'T', 'U', N-1, NRHS, ONE, A( 1, 2 ),
+     $                  LDA, B( 2, 1 ), LDB)
+         END IF
 *
-         CALL DTRSM('L', 'U', 'T', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
-     $               B( 2, 1 ), LDB)
+*        2) Solve with triangular matrix T
 *
-*        Compute T \ B -> B   [ T \ (U \P**T * B) ]
+*        Compute T \ B -> B   [ T \ (U**T \P**T * B) ]
 *
          CALL DLACPY( 'F', 1, N, A( 1, 1 ), LDA+1, WORK( N ), 1)
          IF( N.GT.1 ) THEN
@@ -223,35 +232,47 @@
          CALL DGTSV( N, NRHS, WORK( 1 ), WORK( N ), WORK( 2*N ), B, LDB,
      $               INFO )
 *
-*        Compute (U**T \ B) -> B   [ U**T \ (T \ (U \P**T * B) ) ]
+*        3) Backward substitution with U
+*
+         IF( N.GT.1 ) THEN
 *
-         CALL DTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
-     $               B( 2, 1 ), LDB)
+*           Compute U \ B -> B   [ U \ (T \ (U**T \P**T * B) ) ]
 *
-*        Pivot, P * B  [ P * (U**T \ (T \ (U \P**T * B) )) ]
+            CALL DTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ),
+     $                  LDA, B( 2, 1 ), LDB)
 *
-         DO K = N, 1, -1
-            KP = IPIV( K )
-            IF( KP.NE.K )
-     $         CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
-         END DO
+*           Pivot, P * B -> B  [ P * (U \ (T \ (U**T \P**T * B) )) ]
+*
+            DO K = N, 1, -1
+               KP = IPIV( K )
+               IF( KP.NE.K )
+     $            CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+            END DO
+         END IF
 *
       ELSE
 *
 *        Solve A*X = B, where A = L*T*L**T.
 *
-*        Pivot, P**T * B
+*        1) Forward substitution with L
 *
-         DO K = 1, N
-            KP = IPIV( K )
-            IF( KP.NE.K )
-     $         CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
-         END DO
+         IF( N.GT.1 ) THEN
+*
+*           Pivot, P**T * B -> B
+*
+            DO K = 1, N
+               KP = IPIV( K )
+               IF( KP.NE.K )
+     $            CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+            END DO
 *
-*        Compute (L \P**T * B) -> B    [ (L \P**T * B) ]
+*           Compute L \ B -> B    [ (L \P**T * B) ]
+*
+            CALL DTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ),
+     $                  LDA, B( 2, 1 ), LDB)
+         END IF
 *
-         CALL DTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
-     $               B( 2, 1 ), LDB)
+*        2) Solve with triangular matrix T
 *
 *        Compute T \ B -> B   [ T \ (L \P**T * B) ]
 *
@@ -263,18 +284,23 @@
          CALL DGTSV( N, NRHS, WORK( 1 ), WORK(N), WORK( 2*N ), B, LDB,
      $               INFO)
 *
-*        Compute (L**T \ B) -> B   [ L**T \ (T \ (L \P**T * B) ) ]
+*        3) Backward substitution with L**T
 *
-         CALL DTRSM( 'L', 'L', 'T', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
-     $              B( 2, 1 ), LDB)
+         IF( N.GT.1 ) THEN
+*
+*           Compute (L**T \ B) -> B   [ L**T \ (T \ (L \P**T * B) ) ]
 *
-*        Pivot, P * B  [ P * (L**T \ (T \ (L \P**T * B) )) ]
+            CALL DTRSM( 'L', 'L', 'T', 'U', N-1, NRHS, ONE, A( 2, 1 ),
+     $                  LDA, B( 2, 1 ), LDB)
 *
-         DO K = N, 1, -1
-            KP = IPIV( K )
-            IF( KP.NE.K )
-     $         CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
-         END DO
+*           Pivot, P * B -> B  [ P * (L**T \ (T \ (L \P**T * B) )) ]
+*
+            DO K = N, 1, -1
+               KP = IPIV( K )
+               IF( KP.NE.K )
+     $            CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+            END DO
+         END IF
 *
       END IF
 *

lapack-netlib/SRC/dsytrs_aa_2stage.f

@@ -36,7 +36,7 @@
 *> \verbatim
 *>
 *> DSYTRS_AA_2STAGE solves a system of linear equations A*X = B with a real
-*> symmetric matrix A using the factorization A = U*T*U**T or
+*> symmetric matrix A using the factorization A = U**T*T*U or
 *> A = L*T*L**T computed by DSYTRF_AA_2STAGE.
 *> \endverbatim
 *
@@ -48,7 +48,7 @@
 *>          UPLO is CHARACTER*1
 *>          Specifies whether the details of the factorization are stored
 *>          as an upper or lower triangular matrix.
-*>          = 'U':  Upper triangular, form is A = U*T*U**T;
+*>          = 'U':  Upper triangular, form is A = U**T*T*U;
 *>          = 'L':  Lower triangular, form is A = L*T*L**T.
 *> \endverbatim
 *>
@@ -208,15 +208,15 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*T*U**T.
+*        Solve A*X = B, where A = U**T*T*U.
 *
          IF( N.GT.NB ) THEN
 *
-*           Pivot, P**T * B
+*           Pivot, P**T * B -> B
 *
             CALL DLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
 *
-*           Compute (U**T \P**T * B) -> B    [ (U**T \P**T * B) ]
+*           Compute (U**T \ B) -> B    [ (U**T \P**T * B) ]
 *
             CALL DTRSM( 'L', 'U', 'T', 'U', N-NB, NRHS, ONE, A(1, NB+1),
      $                 LDA, B(NB+1, 1), LDB)
@@ -234,7 +234,7 @@
             CALL DTRSM( 'L', 'U', 'N', 'U', N-NB, NRHS, ONE, A(1, NB+1),
      $                  LDA, B(NB+1, 1), LDB)
 *
-*           Pivot, P * B  [ P * (U \ (T \ (U**T \P**T * B) )) ]
+*           Pivot, P * B -> B  [ P * (U \ (T \ (U**T \P**T * B) )) ]
 *
             CALL DLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
 *
@@ -246,11 +246,11 @@
 *
          IF( N.GT.NB ) THEN
 *
-*           Pivot, P**T * B
+*           Pivot, P**T * B -> B
 *
             CALL DLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
 *
-*           Compute (L \P**T * B) -> B    [ (L \P**T * B) ]
+*           Compute (L \ B) -> B    [ (L \P**T * B) ]
 *
             CALL DTRSM( 'L', 'L', 'N', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
      $                 LDA, B(NB+1, 1), LDB)
@@ -268,7 +268,7 @@
             CALL DTRSM( 'L', 'L', 'T', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
      $                  LDA, B(NB+1, 1), LDB)
 *
-*           Pivot, P * B  [ P * (L**T \ (T \ (L \P**T * B) )) ]
+*           Pivot, P * B -> B  [ P * (L**T \ (T \ (L \P**T * B) )) ]
 *
             CALL DLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
 *

lapack-netlib/SRC/dtgsy2.f

@@ -71,7 +71,7 @@
 *>             R  * B**T + L  * E**T  = scale * -F
 *>
 *> This case is used to compute an estimate of Dif[(A, D), (B, E)] =
-*> sigma_min(Z) using reverse communicaton with DLACON.
+*> sigma_min(Z) using reverse communication with DLACON.
 *>
 *> DTGSY2 also (IJOB >= 1) contributes to the computation in DTGSYL
 *> of an upper bound on the separation between to matrix pairs. Then
@@ -85,7 +85,7 @@
 *> \param[in] TRANS
 *> \verbatim
 *>          TRANS is CHARACTER*1
-*>          = 'N', solve the generalized Sylvester equation (1).
+*>          = 'N': solve the generalized Sylvester equation (1).
 *>          = 'T': solve the 'transposed' system (3).
 *> \endverbatim
 *>

lapack-netlib/SRC/dtgsyl.f

@@ -88,20 +88,20 @@
 *> \param[in] TRANS
 *> \verbatim
 *>          TRANS is CHARACTER*1
-*>          = 'N', solve the generalized Sylvester equation (1).
-*>          = 'T', solve the 'transposed' system (3).
+*>          = 'N': solve the generalized Sylvester equation (1).
+*>          = 'T': solve the 'transposed' system (3).
 *> \endverbatim
 *>
 *> \param[in] IJOB
 *> \verbatim
 *>          IJOB is INTEGER
 *>          Specifies what kind of functionality to be performed.
-*>           =0: solve (1) only.
-*>           =1: The functionality of 0 and 3.
-*>           =2: The functionality of 0 and 4.
-*>           =3: Only an estimate of Dif[(A,D), (B,E)] is computed.
+*>          = 0: solve (1) only.
+*>          = 1: The functionality of 0 and 3.
+*>          = 2: The functionality of 0 and 4.
+*>          = 3: Only an estimate of Dif[(A,D), (B,E)] is computed.
 *>               (look ahead strategy IJOB  = 1 is used).
-*>           =4: Only an estimate of Dif[(A,D), (B,E)] is computed.
+*>          = 4: Only an estimate of Dif[(A,D), (B,E)] is computed.
 *>               ( DGECON on sub-systems is used ).
 *>          Not referenced if TRANS = 'T'.
 *> \endverbatim

lapack-netlib/SRC/dtpmlqt.f

@@ -94,7 +94,7 @@
 *>
 *> \param[in] V
 *> \verbatim
-*>          V is DOUBLE PRECISION array, dimension (LDA,K)
+*>          V is DOUBLE PRECISION array, dimension (LDV,K)
 *>          The i-th row must contain the vector which defines the
 *>          elementary reflector H(i), for i = 1,2,...,k, as returned by
 *>          DTPLQT in B.  See Further Details.

lapack-netlib/SRC/dtpmqrt.f

@@ -94,7 +94,7 @@
 *>
 *> \param[in] V
 *> \verbatim
-*>          V is DOUBLE PRECISION array, dimension (LDA,K)
+*>          V is DOUBLE PRECISION array, dimension (LDV,K)
 *>          The i-th column must contain the vector which defines the
 *>          elementary reflector H(i), for i = 1,2,...,k, as returned by
 *>          CTPQRT in B.  See Further Details.

lapack-netlib/SRC/dtprfb.f

@@ -152,8 +152,8 @@
 *> \verbatim
 *>          LDA is INTEGER
 *>          The leading dimension of the array A.
-*>          If SIDE = 'L', LDC >= max(1,K);
-*>          If SIDE = 'R', LDC >= max(1,M).
+*>          If SIDE = 'L', LDA >= max(1,K);
+*>          If SIDE = 'R', LDA >= max(1,M).
 *> \endverbatim
 *>
 *> \param[in,out] B