Update LAPACK to 3.9.0

lapack-netlib/SRC/zhb2st_kernels.f

@@ -1,26 +1,26 @@
 *> \brief \b ZHB2ST_KERNELS
 *
 *  @precisions fortran z -> s d c
-*      
+*
 *  =========== 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 ZHB2ST_KERNELS + dependencies 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhb2st_kernels.f"> 
-*> [TGZ]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhb2st_kernels.f"> 
-*> [ZIP]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhb2st_kernels.f"> 
+*> Download ZHB2ST_KERNELS + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhb2st_kernels.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhb2st_kernels.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhb2st_kernels.f">
 *> [TXT]</a>
-*> \endhtmlonly 
+*> \endhtmlonly
 *
 *  Definition:
 *  ===========
 *
-*       SUBROUTINE  ZHB2ST_KERNELS( UPLO, WANTZ, TTYPE, 
+*       SUBROUTINE  ZHB2ST_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 ..
-*       COMPLEX*16         A( LDA, * ), V( * ), 
+*       COMPLEX*16         A( LDA, * ), V( * ),
 *                          TAU( * ), WORK( * )
-*  
+*
 *> \par Purpose:
 *  =============
 *>
@@ -124,7 +124,7 @@
 *>          LDVT is INTEGER.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is COMPLEX*16 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  ZHB2ST_KERNELS( UPLO, WANTZ, TTYPE, 
+      SUBROUTINE  ZHB2ST_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 ..
-      COMPLEX*16         A( LDA, * ), V( * ), 
+      COMPLEX*16         A( LDA, * ), V( * ),
      $                   TAU( * ), WORK( * )
 *     ..
 *
@@ -195,8 +195,8 @@
 *     .. Local Scalars ..
       LOGICAL            UPPER
       INTEGER            I, J1, J2, LM, LN, VPOS, TAUPOS,
-     $                   DPOS, OFDPOS, AJETER 
-      COMPLEX*16         CTMP 
+     $                   DPOS, OFDPOS, AJETER
+      COMPLEX*16         CTMP
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           ZLARFG, ZLARFX, ZLARFY
@@ -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 )         = DCONJG( A( OFDPOS-I, ST+I ) )
-                  A( OFDPOS-I, ST+I ) = ZERO  
+                  A( OFDPOS-I, ST+I ) = ZERO
    10         CONTINUE
               CTMP = DCONJG( A( OFDPOS, ST ) )
-              CALL ZLARFG( LM, CTMP, V( VPOS+1 ), 1, 
+              CALL ZLARFG( 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 )          =
      $                                    DCONJG( A( DPOS-NB-I, J1+I ) )
                       A( DPOS-NB-I, J1+I ) = ZERO
    30             CONTINUE
                   CTMP = DCONJG( A( DPOS-NB, J1 ) )
                   CALL ZLARFG( LM, CTMP, V( VPOS+1 ), 1, TAU( TAUPOS ) )
                   A( DPOS-NB, J1 ) = CTMP
-*                 
+*
                   CALL ZLARFX( '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 ZLARFG( LM, A( OFDPOS, ST-1 ), V( VPOS+1 ), 1, 
+              CALL ZLARFG( 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 ZLARFX( 'Right', LM, LN, V( VPOS ), 
+                  CALL ZLARFX( '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 ZLARFG( LM, A( DPOS+NB, ST ), V( VPOS+1 ), 1, 
+                  CALL ZLARFG( LM, A( DPOS+NB, ST ), V( VPOS+1 ), 1,
      $                                        TAU( TAUPOS ) )
 *
-                  CALL ZLARFX( 'Left', LM, LN-1, V( VPOS ), 
+                  CALL ZLARFX( 'Left', LM, LN-1, V( VPOS ),
      $                         DCONJG( TAU( TAUPOS ) ),
      $                         A( DPOS+NB-1, ST+1 ), LDA-1, WORK)
-             
+
               ENDIF
           ENDIF
       ENDIF
@@ -374,4 +374,4 @@
 *
 *     END OF ZHB2ST_KERNELS
 *
-      END      
+      END

lapack-netlib/SRC/zhecon_3.f

@@ -19,7 +19,7 @@
 *  ===========
 *
 *       SUBROUTINE ZHECON_3( UPLO, N, A, LDA, E, IPIV, ANORM, RCOND,
-*                            WORK, IWORK, INFO )
+*                            WORK, INFO )
 *
 *       .. Scalar Arguments ..
 *       CHARACTER          UPLO
@@ -27,7 +27,7 @@
 *       DOUBLE PRECISION   ANORM, RCOND
 *       ..
 *       .. Array Arguments ..
-*       INTEGER            IPIV( * ), IWORK( * )
+*       INTEGER            IPIV( * )
 *       COMPLEX*16         A( LDA, * ), E ( * ), WORK( * )
 *       ..
 *
@@ -129,11 +129,6 @@
 *>          WORK is COMPLEX*16 array, dimension (2*N)
 *> \endverbatim
 *>
-*> \param[out] IWORK
-*> \verbatim
-*>          IWORK is INTEGER array, dimension (N)
-*> \endverbatim
-*>
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER

lapack-netlib/SRC/zheevr.f

@@ -210,7 +210,7 @@
 *>          eigenvalues are computed to high relative accuracy when
 *>          possible in future releases.  The current code does not
 *>          make any guarantees about high relative accuracy, but
-*>          furutre releases will. See J. Barlow and J. Demmel,
+*>          future releases will. See J. Barlow and J. Demmel,
 *>          "Computing Accurate Eigensystems of Scaled Diagonally
 *>          Dominant Matrices", LAPACK Working Note #7, for a discussion
 *>          of which matrices define their eigenvalues to high relative

lapack-netlib/SRC/zheevr_2stage.f

@@ -217,7 +217,7 @@
 *>          eigenvalues are computed to high relative accuracy when
 *>          possible in future releases.  The current code does not
 *>          make any guarantees about high relative accuracy, but
-*>          furutre releases will. See J. Barlow and J. Demmel,
+*>          future releases will. See J. Barlow and J. Demmel,
 *>          "Computing Accurate Eigensystems of Scaled Diagonally
 *>          Dominant Matrices", LAPACK Working Note #7, for a discussion
 *>          of which matrices define their eigenvalues to high relative

lapack-netlib/SRC/zhegs2.f

@@ -97,6 +97,7 @@
 *>          B is COMPLEX*16 array, dimension (LDB,N)
 *>          The triangular factor from the Cholesky factorization of B,
 *>          as returned by ZPOTRF.
+*>          B is modified by the routine but restored on exit.
 *> \endverbatim
 *>
 *> \param[in] LDB

lapack-netlib/SRC/zhegst.f

@@ -97,6 +97,7 @@
 *>          B is COMPLEX*16 array, dimension (LDB,N)
 *>          The triangular factor from the Cholesky factorization of B,
 *>          as returned by ZPOTRF.
+*>          B is modified by the routine but restored on exit.
 *> \endverbatim
 *>
 *> \param[in] LDB

lapack-netlib/SRC/zherfsx.f

@@ -102,7 +102,7 @@
 *> \param[in] A
 *> \verbatim
 *>          A is COMPLEX*16 array, dimension (LDA,N)
-*>     The symmetric matrix A.  If UPLO = 'U', the leading N-by-N
+*>     The Hermitian matrix A.  If UPLO = 'U', the leading N-by-N
 *>     upper triangular part of A contains the upper triangular
 *>     part of the matrix A, and the strictly lower triangular
 *>     part of A is not referenced.  If UPLO = 'L', the leading
@@ -270,7 +270,7 @@
 *>     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
@@ -306,14 +306,14 @@
 *> \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.
@@ -321,9 +321,9 @@
 *>       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/zhesv_aa.f

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

lapack-netlib/SRC/zhesv_aa_2stage.f

@@ -44,7 +44,7 @@
 *> matrices.
 *>
 *> Aasen's 2-stage algorithm is used to factor A as
-*>    A = U * T * U**H,  if UPLO = 'U', or
+*>    A = U**H * T * U,  if UPLO = 'U', or
 *>    A = L * T * L**H,  if UPLO = 'L',
 *> where U (or L) is a product of permutation and unit upper (lower)
 *> triangular matrices, and T is Hermitian and band. The matrix T is
@@ -211,9 +211,7 @@
 *
 *     .. Local Scalars ..
       LOGICAL            UPPER, TQUERY, WQUERY
-      INTEGER            I, J, K, I1, I2, TD
-      INTEGER            LDTB, LWKOPT, NB, KB, NT, IINFO
-      COMPLEX            PIV
+      INTEGER            LWKOPT
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -263,7 +261,7 @@
          RETURN
       END IF
 *
-*     Compute the factorization A = U*T*U**H or A = L*T*L**H.
+*     Compute the factorization A = U**H*T*U or A = L*T*L**H.
 *
       CALL ZHETRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2,
      $                       WORK, LWORK, INFO )

lapack-netlib/SRC/zhesvxx.f

@@ -46,7 +46,7 @@
 *>
 *>    ZHESVXX uses the diagonal pivoting factorization to compute the
 *>    solution to a complex*16 system of linear equations A * X = B, where
-*>    A is an N-by-N symmetric matrix and X and B are N-by-NRHS
+*>    A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
 *>    matrices.
 *>
 *>    If requested, both normwise and maximum componentwise error bounds
@@ -88,7 +88,7 @@
 *>       A = L * D * L**T,  if UPLO = 'L',
 *>
 *>    where U (or L) is a product of permutation and unit upper (lower)
-*>    triangular matrices, and D is symmetric and block diagonal with
+*>    triangular matrices, and D is Hermitian and block diagonal with
 *>    1-by-1 and 2-by-2 diagonal blocks.
 *>
 *>    3. If some D(i,i)=0, so that D is exactly singular, then the
@@ -161,7 +161,7 @@
 *> \param[in,out] A
 *> \verbatim
 *>          A is COMPLEX*16 array, dimension (LDA,N)
-*>     The symmetric matrix A.  If UPLO = 'U', the leading N-by-N
+*>     The Hermitian matrix A.  If UPLO = 'U', the leading N-by-N
 *>     upper triangular part of A contains the upper triangular
 *>     part of the matrix A, and the strictly lower triangular
 *>     part of A is not referenced.  If UPLO = 'L', the leading
@@ -378,7 +378,7 @@
 *>     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
@@ -414,14 +414,14 @@
 *> \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.
@@ -429,9 +429,9 @@
 *>       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/zhetf2_rk.f

@@ -322,7 +322,7 @@
 *
 *        Factorize A as U*D*U**H 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 ) = CZERO
@@ -676,7 +676,7 @@
 *
 *        Factorize A as L*D*L**H 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 ) = CZERO
 *

lapack-netlib/SRC/zhetrd_2stage.f

@@ -123,23 +123,22 @@
 *>
 *> \param[out] HOUS2
 *> \verbatim
-*>          HOUS2 is COMPLEX*16 array, dimension LHOUS2, that
-*>          store the Householder representation of the stage2
+*>          HOUS2 is COMPLEX*16 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/zhetrd_hb2st.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 zhetrd_he2hb routine
 *>                  was not called before this routine to reproduce AB. 
@@ -512,8 +512,7 @@ C                 END IF
 *
 *                         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/zhetrd_he2hb.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 ZLASET( "A", LDT, KD, ZERO, ZERO, WORK( TPOS ), LDT )
 *

lapack-netlib/SRC/zhetrf_aa.f

@@ -37,7 +37,7 @@
 *> ZHETRF_AA computes the factorization of a complex hermitian matrix A
 *> using the Aasen's algorithm.  The form of the factorization is
 *>
-*>    A = U*T*U**H  or  A = L*T*L**H
+*>    A = U**H*T*U  or  A = L*T*L**H
 *>
 *> where U (or L) is a product of permutation and unit upper (lower)
 *> triangular matrices, and T is a hermitian tridiagonal matrix.
@@ -223,7 +223,7 @@
       IF( UPPER ) THEN
 *
 *        .....................................................
-*        Factorize A as L*D*L**H using the upper triangle of A
+*        Factorize A as U**H*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
@@ -376,7 +376,7 @@
      $                      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/zhetrf_aa_2stage.f

@@ -38,7 +38,7 @@
 *> ZHETRF_AA_2STAGE computes the factorization of a double hermitian 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**H*T*U  or  A = L*T*L**H
 *>
 *> where U (or L) is a product of permutation and unit upper (lower)
 *> triangular matrices, and T is a hermitian band matrix with the
@@ -66,7 +66,7 @@
 *>
 *> \param[in,out] A
 *> \verbatim
-*>          A is COMPLEX array, dimension (LDA,N)
+*>          A is COMPLEX*16 array, dimension (LDA,N)
 *>          On entry, the hermitian matrix A.  If UPLO = 'U', the leading
 *>          N-by-N upper triangular part of A contains the upper
 *>          triangular part of the matrix A, and the strictly lower
@@ -87,7 +87,7 @@
 *>
 *> \param[out] TB
 *> \verbatim
-*>          TB is COMPLEX array, dimension (LTB)
+*>          TB is COMPLEX*16 array, dimension (LTB)
 *>          On exit, details of the LU factorization of the band matrix.
 *> \endverbatim
 *>
@@ -121,7 +121,7 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is COMPLEX workspace of size LWORK
+*>          WORK is COMPLEX*16 workspace of size LWORK
 *> \endverbatim
 *>
 *> \param[in] LWORK
@@ -276,7 +276,7 @@
       IF( UPPER ) THEN
 *
 *        .....................................................
-*        Factorize A as L*D*L**T using the upper triangle of A
+*        Factorize A as U**H*D*U using the upper triangle of A
 *        .....................................................
 *
          DO J = 0, NT-1
@@ -452,14 +452,17 @@ c               END IF
 *                    > Apply pivots to previous columns of L
                      CALL ZSWAP( 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 ZSWAP( 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) ) THEN
+                        CALL ZSWAP( I2-I1-1, A( I1, I1+1 ), LDA,
+     $                                       A( I1+1, I2 ), 1 )
+                        CALL ZLACGV( I2-I1-1, A( I1+1, I2 ), 1 )
+                     END IF
                      CALL ZLACGV( I2-I1, A( I1, I1+1 ), LDA )
-                     CALL ZLACGV( I2-I1-1, A( I1+1, I2 ), 1 )
 *                    > Swap A(I2+1:M, I1) with A(I2+1:M, I2)
-                     CALL ZSWAP( N-I2, A( I1, I2+1 ), LDA,
-     $                                 A( I2, I2+1 ), LDA ) 
+                     IF( I2.LT.N )
+     $                  CALL ZSWAP( 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 )
@@ -476,7 +479,7 @@ c               END IF
       ELSE
 *
 *        .....................................................
-*        Factorize A as L*D*L**T using the lower triangle of A
+*        Factorize A as L*D*L**H using the lower triangle of A
 *        .....................................................
 *
          DO J = 0, NT-1
@@ -629,14 +632,17 @@ c               END IF
 *                    > Apply pivots to previous columns of L
                      CALL ZSWAP( 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 ZSWAP( I2-I1-1, A( I1+1, I1 ), 1,
-     $                                    A( I2, I1+1 ), LDA )
+*                    > Swap A(I1+1:M, I1) with A(I2, I1+1:M)
+                     IF( I2.GT.(I1+1) ) THEN
+                        CALL ZSWAP( I2-I1-1, A( I1+1, I1 ), 1,
+     $                                       A( I2, I1+1 ), LDA )
+                        CALL ZLACGV( I2-I1-1, A( I2, I1+1 ), LDA )
+                     END IF
                      CALL ZLACGV( I2-I1, A( I1+1, I1 ), 1 )
-                     CALL ZLACGV( I2-I1-1, A( I2, I1+1 ), LDA )
 *                    > Swap A(I2+1:M, I1) with A(I2+1:M, I2)
-                     CALL ZSWAP( N-I2, A( I2+1, I1 ), 1,
-     $                                 A( I2+1, I2 ), 1 ) 
+                     IF( I2.LT.N )
+     $                  CALL ZSWAP( 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/zhetri2.f

@@ -62,7 +62,7 @@
 *> \param[in,out] A
 *> \verbatim
 *>          A is COMPLEX*16 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 ZHETRF.
 *>
 *>          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 ZHETRF.
 *> \endverbatim
 *>

lapack-netlib/SRC/zhetrs_aa.f

@@ -38,8 +38,8 @@
 *> \verbatim
 *>
 *> ZHETRS_AA solves a system of linear equations A*X = B with a complex
-*> hermitian matrix A using the factorization A = U*T*U**H or
-*> A = L*T*L**T computed by ZHETRF_AA.
+*> hermitian matrix A using the factorization A = U**H*T*U or
+*> A = L*T*L**H computed by ZHETRF_AA.
 *> \endverbatim
 *
 *  Arguments:
@@ -50,7 +50,7 @@
 *>          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**H;
+*>          = 'U':  Upper triangular, form is A = U**H*T*U;
 *>          = 'L':  Lower triangular, form is A = L*T*L**H.
 *> \endverbatim
 *>
@@ -98,14 +98,16 @@
 *>          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 COMPLEX*16 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
@@ -199,61 +201,80 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*T*U**T.
+*        Solve A*X = B, where A = U**H*T*U.
 *
-*        Pivot, P**T * B
+*        1) Forward substitution with U**H
 *
-         DO K = 1, N
-            KP = IPIV( K )
-            IF( KP.NE.K )
-     $          CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
-         END DO
+         IF( N.GT.1 ) THEN
 *
-*        Compute (U \P**T * B) -> B    [ (U \P**T * B) ]
+*           Pivot, P**T * B -> B
 *
-         CALL ZTRSM('L', 'U', 'C', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
-     $               B( 2, 1 ), LDB)
+            DO K = 1, N
+               KP = IPIV( K )
+               IF( KP.NE.K )
+     $            CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+            END DO
 *
-*        Compute T \ B -> B   [ T \ (U \P**T * B) ]
+*           Compute U**H \ B -> B    [ (U**H \P**T * B) ]
 *
-         CALL ZLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
+            CALL ZTRSM( 'L', 'U', 'C', 'U', N-1, NRHS, ONE, A( 1, 2 ),
+     $                  LDA, B( 2, 1 ), LDB )
+         END IF
+*
+*        2) Solve with triangular matrix T
+*
+*        Compute T \ B -> B   [ T \ (U**H \P**T * B) ]
+*
+         CALL ZLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1 )
          IF( N.GT.1 ) THEN
              CALL ZLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 2*N ), 1)
-             CALL ZLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 1 ), 1)
+             CALL ZLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 1 ), 1 )
              CALL ZLACGV( N-1, WORK( 1 ), 1 )
          END IF
-         CALL ZGTSV(N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB,
-     $              INFO)
+         CALL ZGTSV( N, NRHS, WORK(1), WORK(N), WORK(2*N), B, LDB,
+     $               INFO )
+*
+*        3) Backward substitution with U
+*
+         IF( N.GT.1 ) THEN
 *
-*        Compute (U**T \ B) -> B   [ U**T \ (T \ (U \P**T * B) ) ]
+*           Compute U \ B -> B   [ U \ (T \ (U**H \P**T * B) ) ]
 *
-         CALL ZTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ), LDA,
-     $               B(2, 1), LDB)
+            CALL ZTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ),
+     $                  LDA, B(2, 1), LDB)
 *
-*        Pivot, P * B  [ P * (U**T \ (T \ (U \P**T * B) )) ]
+*           Pivot, P * B  [ P * (U**H \ (T \ (U \P**T * B) )) ]
 *
-         DO K = N, 1, -1
-            KP = IPIV( K )
-            IF( KP.NE.K )
-     $         CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
-         END DO
+            DO K = N, 1, -1
+               KP = IPIV( K )
+               IF( KP.NE.K )
+     $            CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+            END DO
+         END IF
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*T*L**T.
+*        Solve A*X = B, where A = L*T*L**H.
+*
+*        1) Forward substitution with L
 *
-*        Pivot, P**T * B
+         IF( N.GT.1 ) THEN
+*
+*           Pivot, P**T * B -> B
 *
-         DO K = 1, N
-            KP = IPIV( K )
-            IF( KP.NE.K )
-     $         CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
-         END DO
+            DO K = 1, N
+               KP = IPIV( K )
+               IF( KP.NE.K )
+     $            CALL ZSWAP( 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 ZTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
-     $               B(2, 1), LDB)
+            CALL ZTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ),
+     $                  LDA, B(2, 1), LDB)
+         END IF
+*
+*        2) Solve with triangular matrix T
 *
 *        Compute T \ B -> B   [ T \ (L \P**T * B) ]
 *
@@ -266,18 +287,23 @@
          CALL ZGTSV(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**H
+*
+         IF( N.GT.1 ) THEN
 *
-         CALL ZTRSM( 'L', 'L', 'C', 'U', N-1, NRHS, ONE, A( 2, 1 ), LDA,
-     $              B( 2, 1 ), LDB)
+*           Compute L**H \ B -> B   [ L**H \ (T \ (L \P**T * B) ) ]
 *
-*        Pivot, P * B  [ P * (L**T \ (T \ (L \P**T * B) )) ]
+            CALL ZTRSM( 'L', 'L', 'C', '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 ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
-         END DO
+*           Pivot, P * B  [ P * (L**H \ (T \ (L \P**T * B) )) ]
+*
+            DO K = N, 1, -1
+               KP = IPIV( K )
+               IF( KP.NE.K )
+     $            CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+            END DO
+         END IF
 *
       END IF
 *

lapack-netlib/SRC/zhetrs_aa_2stage.f

@@ -38,8 +38,8 @@
 *> \verbatim
 *>
 *> ZHETRS_AA_2STAGE solves a system of linear equations A*X = B with a 
-*> hermitian matrix A using the factorization A = U*T*U**T or
-*> A = L*T*L**T computed by ZHETRF_AA_2STAGE.
+*> hermitian matrix A using the factorization A = U**H*T*U or
+*> A = L*T*L**H computed by ZHETRF_AA_2STAGE.
 *> \endverbatim
 *
 *  Arguments:
@@ -50,8 +50,8 @@
 *>          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;
-*>          = 'L':  Lower triangular, form is A = L*T*L**T.
+*>          = 'U':  Upper triangular, form is A = U**H*T*U;
+*>          = 'L':  Lower triangular, form is A = L*T*L**H.
 *> \endverbatim
 *>
 *> \param[in] N
@@ -210,33 +210,33 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*T*U**T.
+*        Solve A*X = B, where A = U**H*T*U.
 *
          IF( N.GT.NB ) THEN
 *
-*           Pivot, P**T * B
+*           Pivot, P**T * B -> B
 *
             CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
 *
-*           Compute (U**T \P**T * B) -> B    [ (U**T \P**T * B) ]
+*           Compute (U**H \ B) -> B    [ (U**H \P**T * B) ]
 *
             CALL ZTRSM( 'L', 'U', 'C', 'U', N-NB, NRHS, ONE, A(1, NB+1),
      $                 LDA, B(NB+1, 1), LDB)
 *
          END IF
 *
-*        Compute T \ B -> B   [ T \ (U**T \P**T * B) ]
+*        Compute T \ B -> B   [ T \ (U**H \P**T * B) ]
 *
          CALL ZGBTRS( 'N', N, NB, NB, NRHS, TB, LDTB, IPIV2, B, LDB,
      $               INFO)
          IF( N.GT.NB ) THEN
 *
-*           Compute (U \ B) -> B   [ U \ (T \ (U**T \P**T * B) ) ]
+*           Compute (U \ B) -> B   [ U \ (T \ (U**H \P**T * B) ) ]
 *
             CALL ZTRSM( '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**H \P**T * B) )) ]
 *
             CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
 *
@@ -244,15 +244,15 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*T*L**T.
+*        Solve A*X = B, where A = L*T*L**H.
 *
          IF( N.GT.NB ) THEN
 *
-*           Pivot, P**T * B
+*           Pivot, P**T * B -> B
 *
             CALL ZLASWP( 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 ZTRSM( 'L', 'L', 'N', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
      $                 LDA, B(NB+1, 1), LDB)
@@ -265,12 +265,12 @@
      $               INFO)
          IF( N.GT.NB ) THEN
 *
-*           Compute (L**T \ B) -> B   [ L**T \ (T \ (L \P**T * B) ) ]
+*           Compute (L**H \ B) -> B   [ L**H \ (T \ (L \P**T * B) ) ]
 *
             CALL ZTRSM( 'L', 'L', 'C', '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**H \ (T \ (L \P**T * B) )) ]
 *
             CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
 *

lapack-netlib/SRC/zhseqr.f

@@ -69,7 +69,7 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>           The order of the matrix H.  N .GE. 0.
+*>           The order of the matrix H.  N >= 0.
 *> \endverbatim
 *>
 *> \param[in] ILO
@@ -86,7 +86,7 @@
 *>           set by a previous call to ZGEBAL, and then passed to ZGEHRD
 *>           when the matrix output by ZGEBAL is reduced to Hessenberg
 *>           form. Otherwise ILO and IHI should be set to 1 and N
-*>           respectively.  If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N.
+*>           respectively.  If N > 0, then 1 <= ILO <= IHI <= N.
 *>           If N = 0, then ILO = 1 and IHI = 0.
 *> \endverbatim
 *>
@@ -98,17 +98,17 @@
 *>           triangular matrix T from the Schur decomposition (the
 *>           Schur form). If INFO = 0 and JOB = 'E', the contents of
 *>           H are unspecified on exit.  (The output value of H when
-*>           INFO.GT.0 is given under the description of INFO below.)
+*>           INFO > 0 is given under the description of INFO below.)
 *>
 *>           Unlike earlier versions of ZHSEQR, this subroutine may
-*>           explicitly H(i,j) = 0 for i.GT.j and j = 1, 2, ... ILO-1
+*>           explicitly H(i,j) = 0 for i > j and j = 1, 2, ... ILO-1
 *>           or j = IHI+1, IHI+2, ... N.
 *> \endverbatim
 *>
 *> \param[in] LDH
 *> \verbatim
 *>          LDH is INTEGER
-*>           The leading dimension of the array H. LDH .GE. max(1,N).
+*>           The leading dimension of the array H. LDH >= max(1,N).
 *> \endverbatim
 *>
 *> \param[out] W
@@ -131,7 +131,7 @@
 *>           if INFO = 0, Z contains Q*Z.
 *>           Normally Q is the unitary matrix generated by ZUNGHR
 *>           after the call to ZGEHRD which formed the Hessenberg matrix
-*>           H. (The output value of Z when INFO.GT.0 is given under
+*>           H. (The output value of Z when INFO > 0 is given under
 *>           the description of INFO below.)
 *> \endverbatim
 *>
@@ -139,7 +139,7 @@
 *> \verbatim
 *>          LDZ is INTEGER
 *>           The leading dimension of the array Z.  if COMPZ = 'I' or
-*>           COMPZ = 'V', then LDZ.GE.MAX(1,N).  Otherwize, LDZ.GE.1.
+*>           COMPZ = 'V', then LDZ >= MAX(1,N).  Otherwise, LDZ >= 1.
 *> \endverbatim
 *>
 *> \param[out] WORK
@@ -152,7 +152,7 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>           The dimension of the array WORK.  LWORK .GE. max(1,N)
+*>           The dimension of the array WORK.  LWORK >= max(1,N)
 *>           is sufficient and delivers very good and sometimes
 *>           optimal performance.  However, LWORK as large as 11*N
 *>           may be required for optimal performance.  A workspace
@@ -170,21 +170,21 @@
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>             =  0:  successful exit
-*>           .LT. 0:  if INFO = -i, the i-th argument had an illegal
+*>             = 0:  successful exit
+*>             < 0:  if INFO = -i, the i-th argument had an illegal
 *>                    value
-*>           .GT. 0:  if INFO = i, ZHSEQR failed to compute all of
-*>                the eigenvalues.  Elements 1:ilo-1 and i+1:n of WR
-*>                and WI contain those eigenvalues which have been
+*>             > 0:  if INFO = i, ZHSEQR failed to compute all of
+*>                the eigenvalues.  Elements 1:ilo-1 and i+1:n of W
+*>                contain those eigenvalues which have been
 *>                successfully computed.  (Failures are rare.)
 *>
-*>                If INFO .GT. 0 and JOB = 'E', then on exit, the
+*>                If INFO > 0 and JOB = 'E', then on exit, the
 *>                remaining unconverged eigenvalues are the eigen-
 *>                values of the upper Hessenberg matrix rows and
 *>                columns ILO through INFO of the final, output
 *>                value of H.
 *>
-*>                If INFO .GT. 0 and JOB   = 'S', then on exit
+*>                If INFO > 0 and JOB   = 'S', then on exit
 *>
 *>           (*)  (initial value of H)*U  = U*(final value of H)
 *>
@@ -192,19 +192,19 @@
 *>                value of  H is upper Hessenberg and triangular in
 *>                rows and columns INFO+1 through IHI.
 *>
-*>                If INFO .GT. 0 and COMPZ = 'V', then on exit
+*>                If INFO > 0 and COMPZ = 'V', then on exit
 *>
 *>                  (final value of Z)  =  (initial value of Z)*U
 *>
 *>                where U is the unitary matrix in (*) (regard-
 *>                less of the value of JOB.)
 *>
-*>                If INFO .GT. 0 and COMPZ = 'I', then on exit
+*>                If INFO > 0 and COMPZ = 'I', then on exit
 *>                      (final value of Z)  = U
 *>                where U is the unitary matrix in (*) (regard-
 *>                less of the value of JOB.)
 *>
-*>                If INFO .GT. 0 and COMPZ = 'N', then Z is not
+*>                If INFO > 0 and COMPZ = 'N', then Z is not
 *>                accessed.
 *> \endverbatim
 *
@@ -244,8 +244,8 @@
 *>                      This depends on ILO, IHI and NS.  NS is the
 *>                      number of simultaneous shifts returned
 *>                      by ILAENV(ISPEC=15).  (See ISPEC=15 below.)
-*>                      The default for (IHI-ILO+1).LE.500 is NS.
-*>                      The default for (IHI-ILO+1).GT.500 is 3*NS/2.
+*>                      The default for (IHI-ILO+1) <= 500 is NS.
+*>                      The default for (IHI-ILO+1) >  500 is 3*NS/2.
 *>
 *>            ISPEC=14: Nibble crossover point. (See IPARMQ for
 *>                      details.)  Default: 14% of deflation window
@@ -323,8 +323,8 @@
       PARAMETER          ( NTINY = 11 )
 *
 *     ==== NL allocates some local workspace to help small matrices
-*     .    through a rare ZLAHQR failure.  NL .GT. NTINY = 11 is
-*     .    required and NL .LE. NMIN = ILAENV(ISPEC=12,...) is recom-
+*     .    through a rare ZLAHQR failure.  NL > NTINY = 11 is
+*     .    required and NL <= NMIN = ILAENV(ISPEC=12,...) is recom-
 *     .    mended.  (The default value of NMIN is 75.)  Using NL = 49
 *     .    allows up to six simultaneous shifts and a 16-by-16
 *     .    deflation window.  ====

lapack-netlib/SRC/zla_gbrcond_c.f

@@ -133,13 +133,13 @@
 *>     i > 0:  The ith argument is invalid.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is COMPLEX*16 array, dimension (2*N).
 *>     Workspace.
 *> \endverbatim
 *>
-*> \param[in] RWORK
+*> \param[out] RWORK
 *> \verbatim
 *>          RWORK is DOUBLE PRECISION array, dimension (N).
 *>     Workspace.

lapack-netlib/SRC/zla_gbrcond_x.f

@@ -126,13 +126,13 @@
 *>     i > 0:  The ith argument is invalid.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is COMPLEX*16 array, dimension (2*N).
 *>     Workspace.
 *> \endverbatim
 *>
-*> \param[in] RWORK
+*> \param[out] RWORK
 *> \verbatim
 *>          RWORK is DOUBLE PRECISION array, dimension (N).
 *>     Workspace.

lapack-netlib/SRC/zla_gbrfsx_extended.f

@@ -65,19 +65,19 @@
 *> \verbatim
 *>          PREC_TYPE is INTEGER
 *>     Specifies the intermediate precision to be used in refinement.
-*>     The value is defined by ILAPREC(P) where P is a CHARACTER and
-*>     P    = 'S':  Single
+*>     The value is defined by ILAPREC(P) where P is a CHARACTER and P
+*>          = 'S':  Single
 *>          = 'D':  Double
 *>          = 'I':  Indigenous
-*>          = 'X', 'E':  Extra
+*>          = 'X' or 'E':  Extra
 *> \endverbatim
 *>
 *> \param[in] TRANS_TYPE
 *> \verbatim
 *>          TRANS_TYPE is INTEGER
 *>     Specifies the transposition operation on A.
-*>     The value is defined by ILATRANS(T) where T is a CHARACTER and
-*>     T    = 'N':  No transpose
+*>     The value is defined by ILATRANS(T) where T is a CHARACTER and T
+*>          = 'N':  No transpose
 *>          = 'T':  Transpose
 *>          = 'C':  Conjugate transpose
 *> \endverbatim
@@ -269,7 +269,7 @@
 *>     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

lapack-netlib/SRC/zla_gercond_c.f

@@ -22,7 +22,7 @@
 *                                                LDAF, IPIV, C, CAPPLY,
 *                                                INFO, WORK, RWORK )
 *
-*       .. Scalar Aguments ..
+*       .. Scalar Arguments ..
 *       CHARACTER          TRANS
 *       LOGICAL            CAPPLY
 *       INTEGER            N, LDA, LDAF, INFO
@@ -114,13 +114,13 @@
 *>     i > 0:  The ith argument is invalid.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is COMPLEX*16 array, dimension (2*N).
 *>     Workspace.
 *> \endverbatim
 *>
-*> \param[in] RWORK
+*> \param[out] RWORK
 *> \verbatim
 *>          RWORK is DOUBLE PRECISION array, dimension (N).
 *>     Workspace.
@@ -148,7 +148,7 @@
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
-*     .. Scalar Aguments ..
+*     .. Scalar Arguments ..
       CHARACTER          TRANS
       LOGICAL            CAPPLY
       INTEGER            N, LDA, LDAF, INFO

lapack-netlib/SRC/zla_gercond_x.f

@@ -107,13 +107,13 @@
 *>     i > 0:  The ith argument is invalid.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is COMPLEX*16 array, dimension (2*N).
 *>     Workspace.
 *> \endverbatim
 *>
-*> \param[in] RWORK
+*> \param[out] RWORK
 *> \verbatim
 *>          RWORK is DOUBLE PRECISION array, dimension (N).
 *>     Workspace.

lapack-netlib/SRC/zla_gerfsx_extended.f

@@ -64,19 +64,19 @@
 *> \verbatim
 *>          PREC_TYPE is INTEGER
 *>     Specifies the intermediate precision to be used in refinement.
-*>     The value is defined by ILAPREC(P) where P is a CHARACTER and
-*>     P    = 'S':  Single
+*>     The value is defined by ILAPREC(P) where P is a CHARACTER and P
+*>          = 'S':  Single
 *>          = 'D':  Double
 *>          = 'I':  Indigenous
-*>          = 'X', 'E':  Extra
+*>          = 'X' or 'E':  Extra
 *> \endverbatim
 *>
 *> \param[in] TRANS_TYPE
 *> \verbatim
 *>          TRANS_TYPE is INTEGER
 *>     Specifies the transposition operation on A.
-*>     The value is defined by ILATRANS(T) where T is a CHARACTER and
-*>     T    = 'N':  No transpose
+*>     The value is defined by ILATRANS(T) where T is a CHARACTER and T
+*>          = 'N':  No transpose
 *>          = 'T':  Transpose
 *>          = 'C':  Conjugate transpose
 *> \endverbatim
@@ -256,7 +256,7 @@
 *>     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
-*>     ERRS_C is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERRS_C is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERRS_C(i,:) corresponds to the ith

lapack-netlib/SRC/zla_hercond_c.f

@@ -111,13 +111,13 @@
 *>     i > 0:  The ith argument is invalid.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is COMPLEX*16 array, dimension (2*N).
 *>     Workspace.
 *> \endverbatim
 *>
-*> \param[in] RWORK
+*> \param[out] RWORK
 *> \verbatim
 *>          RWORK is DOUBLE PRECISION array, dimension (N).
 *>     Workspace.

lapack-netlib/SRC/zla_hercond_x.f

@@ -104,13 +104,13 @@
 *>     i > 0:  The ith argument is invalid.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is COMPLEX*16 array, dimension (2*N).
 *>     Workspace.
 *> \endverbatim
 *>
-*> \param[in] RWORK
+*> \param[out] RWORK
 *> \verbatim
 *>          RWORK is DOUBLE PRECISION array, dimension (N).
 *>     Workspace.

lapack-netlib/SRC/zla_herfsx_extended.f

@@ -66,11 +66,11 @@
 *> \verbatim
 *>          PREC_TYPE is INTEGER
 *>     Specifies the intermediate precision to be used in refinement.
-*>     The value is defined by ILAPREC(P) where P is a CHARACTER and
-*>     P    = 'S':  Single
+*>     The value is defined by ILAPREC(P) where P is a CHARACTER and P
+*>          = 'S':  Single
 *>          = 'D':  Double
 *>          = 'I':  Indigenous
-*>          = 'X', 'E':  Extra
+*>          = 'X' or 'E':  Extra
 *> \endverbatim
 *>
 *> \param[in] UPLO
@@ -254,7 +254,7 @@
 *>     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

lapack-netlib/SRC/zla_herpvgrw.f

@@ -102,7 +102,7 @@
 *>     as determined by ZHETRF.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (2*N)
 *> \endverbatim

lapack-netlib/SRC/zla_porcond_c.f

@@ -103,13 +103,13 @@
 *>     i > 0:  The ith argument is invalid.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is COMPLEX*16 array, dimension (2*N).
 *>     Workspace.
 *> \endverbatim
 *>
-*> \param[in] RWORK
+*> \param[out] RWORK
 *> \verbatim
 *>          RWORK is DOUBLE PRECISION array, dimension (N).
 *>     Workspace.

lapack-netlib/SRC/zla_porcond_x.f

@@ -96,13 +96,13 @@
 *>     i > 0:  The ith argument is invalid.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is COMPLEX*16 array, dimension (2*N).
 *>     Workspace.
 *> \endverbatim
 *>
-*> \param[in] RWORK
+*> \param[out] RWORK
 *> \verbatim
 *>          RWORK is DOUBLE PRECISION array, dimension (N).
 *>     Workspace.

lapack-netlib/SRC/zla_porfsx_extended.f

@@ -65,11 +65,11 @@
 *> \verbatim
 *>          PREC_TYPE is INTEGER
 *>     Specifies the intermediate precision to be used in refinement.
-*>     The value is defined by ILAPREC(P) where P is a CHARACTER and
-*>     P    = 'S':  Single
+*>     The value is defined by ILAPREC(P) where P is a CHARACTER and P
+*>          = 'S':  Single
 *>          = 'D':  Double
 *>          = 'I':  Indigenous
-*>          = 'X', 'E':  Extra
+*>          = 'X' or 'E':  Extra
 *> \endverbatim
 *>
 *> \param[in] UPLO
@@ -246,7 +246,7 @@
 *>     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

lapack-netlib/SRC/zla_porpvgrw.f

@@ -86,7 +86,7 @@
 *>     The leading dimension of the array AF.  LDAF >= max(1,N).
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (2*N)
 *> \endverbatim

lapack-netlib/SRC/zla_syrcond_c.f

@@ -111,13 +111,13 @@
 *>     i > 0:  The ith argument is invalid.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is COMPLEX*16 array, dimension (2*N).
 *>     Workspace.
 *> \endverbatim
 *>
-*> \param[in] RWORK
+*> \param[out] RWORK
 *> \verbatim
 *>          RWORK is DOUBLE PRECISION array, dimension (N).
 *>     Workspace.

lapack-netlib/SRC/zla_syrcond_x.f

@@ -104,13 +104,13 @@
 *>     i > 0:  The ith argument is invalid.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is COMPLEX*16 array, dimension (2*N).
 *>     Workspace.
 *> \endverbatim
 *>
-*> \param[in] RWORK
+*> \param[out] RWORK
 *> \verbatim
 *>          RWORK is DOUBLE PRECISION array, dimension (N).
 *>     Workspace.

lapack-netlib/SRC/zla_syrfsx_extended.f

@@ -66,11 +66,11 @@
 *> \verbatim
 *>          PREC_TYPE is INTEGER
 *>     Specifies the intermediate precision to be used in refinement.
-*>     The value is defined by ILAPREC(P) where P is a CHARACTER and
-*>     P    = 'S':  Single
+*>     The value is defined by ILAPREC(P) where P is a CHARACTER and P
+*>          = 'S':  Single
 *>          = 'D':  Double
 *>          = 'I':  Indigenous
-*>          = 'X', 'E':  Extra
+*>          = 'X' or 'E':  Extra
 *> \endverbatim
 *>
 *> \param[in] UPLO
@@ -254,7 +254,7 @@
 *>     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

lapack-netlib/SRC/zla_syrpvgrw.f

@@ -102,7 +102,7 @@
 *>     as determined by ZSYTRF.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (2*N)
 *> \endverbatim

lapack-netlib/SRC/zla_wwaddw.f

@@ -36,7 +36,7 @@
 *>    ZLA_WWADDW adds a vector W into a doubled-single vector (X, Y).
 *>
 *>    This works for all extant IBM's hex and binary floating point
-*>    arithmetics, but not for decimal.
+*>    arithmetic, but not for decimal.
 *> \endverbatim
 *
 *  Arguments:

lapack-netlib/SRC/zlahef_aa.f

@@ -288,8 +288,9 @@
 *
 *              Swap A(I1, I2+1:N) with A(I2, I2+1:N)
 *
-               CALL ZSWAP( M-I2, A( J1+I1-1, I2+1 ), LDA,
-     $                           A( J1+I2-1, I2+1 ), LDA )
+               IF( I2.LT.M )
+     $            CALL ZSWAP( M-I2, A( J1+I1-1, I2+1 ), LDA,
+     $                              A( J1+I2-1, I2+1 ), LDA )
 *
 *              Swap A(I1, I1) with A(I2,I2)
 *
@@ -329,13 +330,15 @@
 *           Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1),
 *            where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1)
 *
-            IF( A( K, J+1 ).NE.ZERO ) THEN
-               ALPHA = ONE / A( K, J+1 )
-               CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( K, J+2 ), LDA )
-               CALL ZSCAL( M-J-1, ALPHA, A( K, J+2 ), LDA )
-            ELSE
-               CALL ZLASET( 'Full', 1, M-J-1, ZERO, ZERO,
-     $                      A( K, J+2 ), LDA)
+            IF( J.LT.(M-1) ) THEN
+               IF( A( K, J+1 ).NE.ZERO ) THEN
+                  ALPHA = ONE / A( K, J+1 )
+                  CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( K, J+2 ), LDA )
+                  CALL ZSCAL( M-J-1, ALPHA, A( K, J+2 ), LDA )
+               ELSE
+                  CALL ZLASET( 'Full', 1, M-J-1, ZERO, ZERO,
+     $                         A( K, J+2 ), LDA)
+               END IF
             END IF
          END IF
          J = J + 1
@@ -440,8 +443,9 @@
 *
 *              Swap A(I2+1:N, I1) with A(I2+1:N, I2)
 *
-               CALL ZSWAP( M-I2, A( I2+1, J1+I1-1 ), 1,
-     $                           A( I2+1, J1+I2-1 ), 1 )
+               IF( I2.LT.M )
+     $            CALL ZSWAP( M-I2, A( I2+1, J1+I1-1 ), 1,
+     $                              A( I2+1, J1+I2-1 ), 1 )
 *
 *              Swap A(I1, I1) with A(I2, I2)
 *
@@ -481,13 +485,15 @@
 *           Compute L(J+2, J+1) = WORK( 3:N ) / T(J, J+1),
 *            where A(J, J+1) = T(J, J+1) and A(J+2:N, J) = L(J+2:N, J+1)
 *
-            IF( A( J+1, K ).NE.ZERO ) THEN
-               ALPHA = ONE / A( J+1, K )
-               CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( J+2, K ), 1 )
-               CALL ZSCAL( M-J-1, ALPHA, A( J+2, K ), 1 )
-            ELSE
-               CALL ZLASET( 'Full', M-J-1, 1, ZERO, ZERO,
-     $                      A( J+2, K ), LDA )
+            IF( J.LT.(M-1) ) THEN
+               IF( A( J+1, K ).NE.ZERO ) THEN
+                  ALPHA = ONE / A( J+1, K )
+                  CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( J+2, K ), 1 )
+                  CALL ZSCAL( M-J-1, ALPHA, A( J+2, K ), 1 )
+               ELSE
+                  CALL ZLASET( 'Full', M-J-1, 1, ZERO, ZERO,
+     $                         A( J+2, K ), LDA )
+               END IF
             END IF
          END IF
          J = J + 1

lapack-netlib/SRC/zlahef_rk.f

@@ -331,7 +331,7 @@
 *        Factorize the trailing columns of A using the upper triangle
 *        of A and working backwards, and compute the matrix W = U12*D
 *        for use in updating A11 (note that conjg(W) is actually stored)
-*        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 ) = CZERO
@@ -789,7 +789,7 @@
 *        of A and working forwards, and compute the matrix W = L21*D
 *        for use in updating A22 (note that conjg(W) is actually stored)
 *
-*        Initilize the unused last entry of the subdiagonal array E.
+*        Initialize the unused last entry of the subdiagonal array E.
 *
          E( N ) = CZERO
 *

lapack-netlib/SRC/zlahqr.f

@@ -138,26 +138,26 @@
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>           =   0: successful exit
-*>          .GT. 0: if INFO = i, ZLAHQR failed to compute all the
+*>           = 0:   successful exit
+*>           > 0:   if INFO = i, ZLAHQR failed to compute all the
 *>                  eigenvalues ILO to IHI in a total of 30 iterations
 *>                  per eigenvalue; elements i+1:ihi of W contain
 *>                  those eigenvalues which have been successfully
 *>                  computed.
 *>
-*>                  If INFO .GT. 0 and WANTT is .FALSE., then on exit,
+*>                  If INFO > 0 and WANTT is .FALSE., then on exit,
 *>                  the remaining unconverged eigenvalues are the
 *>                  eigenvalues of the upper Hessenberg matrix
-*>                  rows and columns ILO thorugh INFO of the final,
+*>                  rows and columns ILO through INFO of the final,
 *>                  output value of H.
 *>
-*>                  If INFO .GT. 0 and WANTT is .TRUE., then on exit
+*>                  If INFO > 0 and WANTT is .TRUE., then on exit
 *>          (*)       (initial value of H)*U  = U*(final value of H)
-*>                  where U is an orthognal matrix.    The final
+*>                  where U is an orthogonal matrix.    The final
 *>                  value of H is upper Hessenberg and triangular in
 *>                  rows and columns INFO+1 through IHI.
 *>
-*>                  If INFO .GT. 0 and WANTZ is .TRUE., then on exit
+*>                  If INFO > 0 and WANTZ is .TRUE., then on exit
 *>                      (final value of Z)  = (initial value of Z)*U
 *>                  where U is the orthogonal matrix in (*)
 *>                  (regardless of the value of WANTT.)

lapack-netlib/SRC/zlamswlq.f

@@ -1,3 +1,4 @@
+*> \brief \b ZLAMSWLQ
 *
 *  Definition:
 *  ===========

lapack-netlib/SRC/zlamtsqr.f

@@ -1,3 +1,4 @@
+*> \brief \b ZLAMTSQR
 *
 *  Definition:
 *  ===========

lapack-netlib/SRC/zlangb.f

@@ -130,6 +130,7 @@
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
+      IMPLICIT NONE
 *     .. Scalar Arguments ..
       CHARACTER          NORM
       INTEGER            KL, KU, LDAB, N
@@ -147,14 +148,17 @@
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, J, K, L
-      DOUBLE PRECISION   SCALE, SUM, VALUE, TEMP
+      DOUBLE PRECISION   SUM, VALUE, TEMP
+*     ..
+*     .. Local Arrays ..
+      DOUBLE PRECISION   SSQ( 2 ), COLSSQ( 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, DISNAN
       EXTERNAL           LSAME, DISNAN
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           ZLASSQ
+      EXTERNAL           ZLASSQ, DCOMBSSQ
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, MAX, MIN, SQRT
@@ -207,15 +211,22 @@
       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
 *
 *        Find normF(A).
+*        SSQ(1) is scale
+*        SSQ(2) is sum-of-squares
+*        For better accuracy, sum each column separately.
 *
-         SCALE = ZERO
-         SUM = ONE
+         SSQ( 1 ) = ZERO
+         SSQ( 2 ) = ONE
          DO 90 J = 1, N
             L = MAX( 1, J-KU )
             K = KU + 1 - J + L
-            CALL ZLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
+            COLSSQ( 1 ) = ZERO
+            COLSSQ( 2 ) = ONE
+            CALL ZLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1,
+     $                   COLSSQ( 1 ), COLSSQ( 2 ) )
+            CALL DCOMBSSQ( SSQ, COLSSQ )
    90    CONTINUE
-         VALUE = SCALE*SQRT( SUM )
+         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
       END IF
 *
       ZLANGB = VALUE

lapack-netlib/SRC/zlange.f

@@ -120,6 +120,7 @@
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
+      IMPLICIT NONE
 *     .. Scalar Arguments ..
       CHARACTER          NORM
       INTEGER            LDA, M, N
@@ -137,14 +138,17 @@
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, J
-      DOUBLE PRECISION   SCALE, SUM, VALUE, TEMP
+      DOUBLE PRECISION   SUM, VALUE, TEMP
+*     ..
+*     .. Local Arrays ..
+      DOUBLE PRECISION   SSQ( 2 ), COLSSQ( 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, DISNAN
       EXTERNAL           LSAME, DISNAN
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           ZLASSQ
+      EXTERNAL           ZLASSQ, DCOMBSSQ
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, MIN, SQRT
@@ -196,13 +200,19 @@
       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
 *
 *        Find normF(A).
+*        SSQ(1) is scale
+*        SSQ(2) is sum-of-squares
+*        For better accuracy, sum each column separately.
 *
-         SCALE = ZERO
-         SUM = ONE
+         SSQ( 1 ) = ZERO
+         SSQ( 2 ) = ONE
          DO 90 J = 1, N
-            CALL ZLASSQ( M, A( 1, J ), 1, SCALE, SUM )
+            COLSSQ( 1 ) = ZERO
+            COLSSQ( 2 ) = ONE
+            CALL ZLASSQ( M, A( 1, J ), 1, COLSSQ( 1 ), COLSSQ( 2 ) )
+            CALL DCOMBSSQ( SSQ, COLSSQ )
    90    CONTINUE
-         VALUE = SCALE*SQRT( SUM )
+         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
       END IF
 *
       ZLANGE = VALUE

lapack-netlib/SRC/zlanhb.f

@@ -137,6 +137,7 @@
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
+      IMPLICIT NONE
 *     .. Scalar Arguments ..
       CHARACTER          NORM, UPLO
       INTEGER            K, LDAB, N
@@ -154,14 +155,17 @@
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, J, L
-      DOUBLE PRECISION   ABSA, SCALE, SUM, VALUE
+      DOUBLE PRECISION   ABSA, SUM, VALUE
+*     ..
+*     .. Local Arrays ..
+      DOUBLE PRECISION   SSQ( 2 ), COLSSQ( 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, DISNAN
       EXTERNAL           LSAME, DISNAN
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           ZLASSQ
+      EXTERNAL           ZLASSQ, DCOMBSSQ
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, DBLE, MAX, MIN, SQRT
@@ -233,39 +237,57 @@
       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
 *
 *        Find normF(A).
+*        SSQ(1) is scale
+*        SSQ(2) is sum-of-squares
+*        For better accuracy, sum each column separately.
+*
+         SSQ( 1 ) = ZERO
+         SSQ( 2 ) = ONE
+*
+*        Sum off-diagonals
 *
-         SCALE = ZERO
-         SUM = ONE
          IF( K.GT.0 ) THEN
             IF( LSAME( UPLO, 'U' ) ) THEN
                DO 110 J = 2, N
+                  COLSSQ( 1 ) = ZERO
+                  COLSSQ( 2 ) = ONE
                   CALL ZLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ),
-     $                         1, SCALE, SUM )
+     $                         1, COLSSQ( 1 ), COLSSQ( 2 ) )
+                  CALL DCOMBSSQ( SSQ, COLSSQ )
   110          CONTINUE
                L = K + 1
             ELSE
                DO 120 J = 1, N - 1
-                  CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
-     $                         SUM )
+                  COLSSQ( 1 ) = ZERO
+                  COLSSQ( 2 ) = ONE
+                  CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1,
+     $                         COLSSQ( 1 ), COLSSQ( 2 ) )
+                  CALL DCOMBSSQ( SSQ, COLSSQ )
   120          CONTINUE
                L = 1
             END IF
-            SUM = 2*SUM
+            SSQ( 2 ) = 2*SSQ( 2 )
          ELSE
             L = 1
          END IF
+*
+*        Sum diagonal
+*
+         COLSSQ( 1 ) = ZERO
+         COLSSQ( 2 ) = ONE
          DO 130 J = 1, N
             IF( DBLE( AB( L, J ) ).NE.ZERO ) THEN
                ABSA = ABS( DBLE( AB( L, J ) ) )
-               IF( SCALE.LT.ABSA ) THEN
-                  SUM = ONE + SUM*( SCALE / ABSA )**2
-                  SCALE = ABSA
+               IF( COLSSQ( 1 ).LT.ABSA ) THEN
+                  COLSSQ( 2 ) = ONE + COLSSQ(2)*( COLSSQ(1) / ABSA )**2
+                  COLSSQ( 1 ) = ABSA
                ELSE
-                  SUM = SUM + ( ABSA / SCALE )**2
+                  COLSSQ( 2 ) = COLSSQ( 2 ) + ( ABSA / COLSSQ( 1 ) )**2
                END IF
             END IF
   130    CONTINUE
-         VALUE = SCALE*SQRT( SUM )
+         CALL DCOMBSSQ( SSQ, COLSSQ )
+         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
       END IF
 *
       ZLANHB = VALUE

lapack-netlib/SRC/zlanhe.f

@@ -129,6 +129,7 @@
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
+      IMPLICIT NONE
 *     .. Scalar Arguments ..
       CHARACTER          NORM, UPLO
       INTEGER            LDA, N
@@ -146,14 +147,17 @@
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, J
-      DOUBLE PRECISION   ABSA, SCALE, SUM, VALUE
+      DOUBLE PRECISION   ABSA, SUM, VALUE
+*     ..
+*     .. Local Arrays ..
+      DOUBLE PRECISION   SSQ( 2 ), COLSSQ( 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, DISNAN
       EXTERNAL           LSAME, DISNAN
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           ZLASSQ
+      EXTERNAL           ZLASSQ, DCOMBSSQ
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, DBLE, SQRT
@@ -223,31 +227,48 @@
       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
 *
 *        Find normF(A).
+*        SSQ(1) is scale
+*        SSQ(2) is sum-of-squares
+*        For better accuracy, sum each column separately.
+*
+         SSQ( 1 ) = ZERO
+         SSQ( 2 ) = ONE
+*
+*        Sum off-diagonals
 *
-         SCALE = ZERO
-         SUM = ONE
          IF( LSAME( UPLO, 'U' ) ) THEN
             DO 110 J = 2, N
-               CALL ZLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
+               COLSSQ( 1 ) = ZERO
+               COLSSQ( 2 ) = ONE
+               CALL ZLASSQ( J-1, A( 1, J ), 1,
+     $                      COLSSQ( 1 ), COLSSQ( 2 ) )
+               CALL DCOMBSSQ( SSQ, COLSSQ )
   110       CONTINUE
          ELSE
             DO 120 J = 1, N - 1
-               CALL ZLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
+               COLSSQ( 1 ) = ZERO
+               COLSSQ( 2 ) = ONE
+               CALL ZLASSQ( N-J, A( J+1, J ), 1,
+     $                      COLSSQ( 1 ), COLSSQ( 2 ) )
+               CALL DCOMBSSQ( SSQ, COLSSQ )
   120       CONTINUE
          END IF
-         SUM = 2*SUM
+         SSQ( 2 ) = 2*SSQ( 2 )
+*
+*        Sum diagonal
+*
          DO 130 I = 1, N
             IF( DBLE( A( I, I ) ).NE.ZERO ) THEN
                ABSA = ABS( DBLE( A( I, I ) ) )
-               IF( SCALE.LT.ABSA ) THEN
-                  SUM = ONE + SUM*( SCALE / ABSA )**2
-                  SCALE = ABSA
+               IF( SSQ( 1 ).LT.ABSA ) THEN
+                  SSQ( 2 ) = ONE + SSQ( 2 )*( SSQ( 1 ) / ABSA )**2
+                  SSQ( 1 ) = ABSA
                ELSE
-                  SUM = SUM + ( ABSA / SCALE )**2
+                  SSQ( 2 ) = SSQ( 2 ) + ( ABSA / SSQ( 1 ) )**2
                END IF
             END IF
   130    CONTINUE
-         VALUE = SCALE*SQRT( SUM )
+         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
       END IF
 *
       ZLANHE = VALUE

lapack-netlib/SRC/zlanhp.f

@@ -122,6 +122,7 @@
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
+      IMPLICIT NONE
 *     .. Scalar Arguments ..
       CHARACTER          NORM, UPLO
       INTEGER            N
@@ -139,14 +140,17 @@
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, J, K
-      DOUBLE PRECISION   ABSA, SCALE, SUM, VALUE
+      DOUBLE PRECISION   ABSA, SUM, VALUE
+*     ..
+*     .. Local Arrays ..
+      DOUBLE PRECISION   SSQ( 2 ), COLSSQ( 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, DISNAN
       EXTERNAL           LSAME, DISNAN
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           ZLASSQ
+      EXTERNAL           ZLASSQ, DCOMBSSQ
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, DBLE, SQRT
@@ -225,31 +229,48 @@
       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
 *
 *        Find normF(A).
+*        SSQ(1) is scale
+*        SSQ(2) is sum-of-squares
+*        For better accuracy, sum each column separately.
+*
+         SSQ( 1 ) = ZERO
+         SSQ( 2 ) = ONE
+*
+*        Sum off-diagonals
 *
-         SCALE = ZERO
-         SUM = ONE
          K = 2
          IF( LSAME( UPLO, 'U' ) ) THEN
             DO 110 J = 2, N
-               CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
+               COLSSQ( 1 ) = ZERO
+               COLSSQ( 2 ) = ONE
+               CALL ZLASSQ( J-1, AP( K ), 1, COLSSQ( 1 ), COLSSQ( 2 ) )
+               CALL DCOMBSSQ( SSQ, COLSSQ )
                K = K + J
   110       CONTINUE
          ELSE
             DO 120 J = 1, N - 1
-               CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
+               COLSSQ( 1 ) = ZERO
+               COLSSQ( 2 ) = ONE
+               CALL ZLASSQ( N-J, AP( K ), 1, COLSSQ( 1 ), COLSSQ( 2 ) )
+               CALL DCOMBSSQ( SSQ, COLSSQ )
                K = K + N - J + 1
   120       CONTINUE
          END IF
-         SUM = 2*SUM
+         SSQ( 2 ) = 2*SSQ( 2 )
+*
+*        Sum diagonal
+*
          K = 1
+         COLSSQ( 1 ) = ZERO
+         COLSSQ( 2 ) = ONE
          DO 130 I = 1, N
             IF( DBLE( AP( K ) ).NE.ZERO ) THEN
                ABSA = ABS( DBLE( AP( K ) ) )
-               IF( SCALE.LT.ABSA ) THEN
-                  SUM = ONE + SUM*( SCALE / ABSA )**2
-                  SCALE = ABSA
+               IF( COLSSQ( 1 ).LT.ABSA ) THEN
+                  COLSSQ( 2 ) = ONE + COLSSQ(2)*( COLSSQ(1) / ABSA )**2
+                  COLSSQ( 1 ) = ABSA
                ELSE
-                  SUM = SUM + ( ABSA / SCALE )**2
+                  COLSSQ( 2 ) = COLSSQ( 2 ) + ( ABSA / COLSSQ( 1 ) )**2
                END IF
             END IF
             IF( LSAME( UPLO, 'U' ) ) THEN
@@ -258,7 +279,8 @@
                K = K + N - I + 1
             END IF
   130    CONTINUE
-         VALUE = SCALE*SQRT( SUM )
+         CALL DCOMBSSQ( SSQ, COLSSQ )
+         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
       END IF
 *
       ZLANHP = VALUE

lapack-netlib/SRC/zlanhs.f

@@ -114,6 +114,7 @@
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
+      IMPLICIT NONE
 *     .. Scalar Arguments ..
       CHARACTER          NORM
       INTEGER            LDA, N
@@ -131,14 +132,17 @@
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, J
-      DOUBLE PRECISION   SCALE, SUM, VALUE
+      DOUBLE PRECISION   SUM, VALUE
+*     ..
+*     .. Local Arrays ..
+      DOUBLE PRECISION   SSQ( 2 ), COLSSQ( 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, DISNAN
       EXTERNAL           LSAME, DISNAN
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           ZLASSQ
+      EXTERNAL           ZLASSQ, DCOMBSSQ
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, MIN, SQRT
@@ -190,13 +194,20 @@
       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
 *
 *        Find normF(A).
+*        SSQ(1) is scale
+*        SSQ(2) is sum-of-squares
+*        For better accuracy, sum each column separately.
 *
-         SCALE = ZERO
-         SUM = ONE
+         SSQ( 1 ) = ZERO
+         SSQ( 2 ) = ONE
          DO 90 J = 1, N
-            CALL ZLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM )
+            COLSSQ( 1 ) = ZERO
+            COLSSQ( 2 ) = ONE
+            CALL ZLASSQ( MIN( N, J+1 ), A( 1, J ), 1,
+     $                   COLSSQ( 1 ), COLSSQ( 2 ) )
+            CALL DCOMBSSQ( SSQ, COLSSQ )
    90    CONTINUE
-         VALUE = SCALE*SQRT( SUM )
+         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
       END IF
 *
       ZLANHS = VALUE

lapack-netlib/SRC/zlansb.f

@@ -135,6 +135,7 @@
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
+      IMPLICIT NONE
 *     .. Scalar Arguments ..
       CHARACTER          NORM, UPLO
       INTEGER            K, LDAB, N
@@ -152,14 +153,17 @@
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, J, L
-      DOUBLE PRECISION   ABSA, SCALE, SUM, VALUE
+      DOUBLE PRECISION   ABSA, SUM, VALUE
+*     ..
+*     .. Local Arrays ..
+      DOUBLE PRECISION   SSQ( 2 ), COLSSQ( 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, DISNAN
       EXTERNAL           LSAME, DISNAN
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           ZLASSQ
+      EXTERNAL           ZLASSQ, DCOMBSSQ
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, MAX, MIN, SQRT
@@ -227,29 +231,47 @@
       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
 *
 *        Find normF(A).
+*        SSQ(1) is scale
+*        SSQ(2) is sum-of-squares
+*        For better accuracy, sum each column separately.
+*
+         SSQ( 1 ) = ZERO
+         SSQ( 2 ) = ONE
+*
+*        Sum off-diagonals
 *
-         SCALE = ZERO
-         SUM = ONE
          IF( K.GT.0 ) THEN
             IF( LSAME( UPLO, 'U' ) ) THEN
                DO 110 J = 2, N
+                  COLSSQ( 1 ) = ZERO
+                  COLSSQ( 2 ) = ONE
                   CALL ZLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ),
-     $                         1, SCALE, SUM )
+     $                         1, COLSSQ( 1 ), COLSSQ( 2 ) )
+                  CALL DCOMBSSQ( SSQ, COLSSQ )
   110          CONTINUE
                L = K + 1
             ELSE
                DO 120 J = 1, N - 1
-                  CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
-     $                         SUM )
+                  COLSSQ( 1 ) = ZERO
+                  COLSSQ( 2 ) = ONE
+                  CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1,
+     $                         COLSSQ( 1 ), COLSSQ( 2 ) )
+                  CALL DCOMBSSQ( SSQ, COLSSQ )
   120          CONTINUE
                L = 1
             END IF
-            SUM = 2*SUM
+            SSQ( 2 ) = 2*SSQ( 2 )
          ELSE
             L = 1
          END IF
-         CALL ZLASSQ( N, AB( L, 1 ), LDAB, SCALE, SUM )
-         VALUE = SCALE*SQRT( SUM )
+*
+*        Sum diagonal
+*
+         COLSSQ( 1 ) = ZERO
+         COLSSQ( 2 ) = ONE
+         CALL ZLASSQ( N, AB( L, 1 ), LDAB, COLSSQ( 1 ), COLSSQ( 2 ) )
+         CALL DCOMBSSQ( SSQ, COLSSQ )
+         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
       END IF
 *
       ZLANSB = VALUE

lapack-netlib/SRC/zlansp.f

@@ -120,6 +120,7 @@
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
+      IMPLICIT NONE
 *     .. Scalar Arguments ..
       CHARACTER          NORM, UPLO
       INTEGER            N
@@ -137,14 +138,17 @@
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, J, K
-      DOUBLE PRECISION   ABSA, SCALE, SUM, VALUE
+      DOUBLE PRECISION   ABSA, SUM, VALUE
+*     ..
+*     .. Local Arrays ..
+      DOUBLE PRECISION   SSQ( 2 ), COLSSQ( 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, DISNAN
       EXTERNAL           LSAME, DISNAN
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           ZLASSQ
+      EXTERNAL           ZLASSQ, DCOMBSSQ
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, DBLE, DIMAG, SQRT
@@ -219,40 +223,57 @@
       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
 *
 *        Find normF(A).
+*        SSQ(1) is scale
+*        SSQ(2) is sum-of-squares
+*        For better accuracy, sum each column separately.
+*
+         SSQ( 1 ) = ZERO
+         SSQ( 2 ) = ONE
+*
+*        Sum off-diagonals
 *
-         SCALE = ZERO
-         SUM = ONE
          K = 2
          IF( LSAME( UPLO, 'U' ) ) THEN
             DO 110 J = 2, N
-               CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
+               COLSSQ( 1 ) = ZERO
+               COLSSQ( 2 ) = ONE
+               CALL ZLASSQ( J-1, AP( K ), 1, COLSSQ( 1 ), COLSSQ( 2 ) )
+               CALL DCOMBSSQ( SSQ, COLSSQ )
                K = K + J
   110       CONTINUE
          ELSE
             DO 120 J = 1, N - 1
-               CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
+               COLSSQ( 1 ) = ZERO
+               COLSSQ( 2 ) = ONE
+               CALL ZLASSQ( N-J, AP( K ), 1, COLSSQ( 1 ), COLSSQ( 2 ) )
+               CALL DCOMBSSQ( SSQ, COLSSQ )
                K = K + N - J + 1
   120       CONTINUE
          END IF
-         SUM = 2*SUM
+         SSQ( 2 ) = 2*SSQ( 2 )
+*
+*        Sum diagonal
+*
          K = 1
+         COLSSQ( 1 ) = ZERO
+         COLSSQ( 2 ) = ONE
          DO 130 I = 1, N
             IF( DBLE( AP( K ) ).NE.ZERO ) THEN
                ABSA = ABS( DBLE( AP( K ) ) )
-               IF( SCALE.LT.ABSA ) THEN
-                  SUM = ONE + SUM*( SCALE / ABSA )**2
-                  SCALE = ABSA
+               IF( COLSSQ( 1 ).LT.ABSA ) THEN
+                  COLSSQ( 2 ) = ONE + COLSSQ(2)*( COLSSQ(1) / ABSA )**2
+                  COLSSQ( 1 ) = ABSA
                ELSE
-                  SUM = SUM + ( ABSA / SCALE )**2
+                  COLSSQ( 2 ) = COLSSQ( 2 ) + ( ABSA / COLSSQ( 1 ) )**2
                END IF
             END IF
             IF( DIMAG( AP( K ) ).NE.ZERO ) THEN
                ABSA = ABS( DIMAG( AP( K ) ) )
-               IF( SCALE.LT.ABSA ) THEN
-                  SUM = ONE + SUM*( SCALE / ABSA )**2
-                  SCALE = ABSA
+               IF( COLSSQ( 1 ).LT.ABSA ) THEN
+                  COLSSQ( 2 ) = ONE + COLSSQ(2)*( COLSSQ(1) / ABSA )**2
+                  COLSSQ( 1 ) = ABSA
                ELSE
-                  SUM = SUM + ( ABSA / SCALE )**2
+                  COLSSQ( 2 ) = COLSSQ( 2 ) + ( ABSA / COLSSQ( 1 ) )**2
                END IF
             END IF
             IF( LSAME( UPLO, 'U' ) ) THEN
@@ -261,7 +282,8 @@
                K = K + N - I + 1
             END IF
   130    CONTINUE
-         VALUE = SCALE*SQRT( SUM )
+         CALL DCOMBSSQ( SSQ, COLSSQ )
+         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
       END IF
 *
       ZLANSP = VALUE

lapack-netlib/SRC/zlansy.f

@@ -128,6 +128,7 @@
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
+      IMPLICIT NONE
 *     .. Scalar Arguments ..
       CHARACTER          NORM, UPLO
       INTEGER            LDA, N
@@ -145,14 +146,17 @@
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, J
-      DOUBLE PRECISION   ABSA, SCALE, SUM, VALUE
+      DOUBLE PRECISION   ABSA, SUM, VALUE
+*     ..
+*     .. Local Arrays ..
+      DOUBLE PRECISION   SSQ( 2 ), COLSSQ( 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, DISNAN
       EXTERNAL           LSAME, DISNAN
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           ZLASSQ
+      EXTERNAL           ZLASSQ, DCOMBSSQ
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, SQRT
@@ -218,21 +222,39 @@
       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
 *
 *        Find normF(A).
+*        SSQ(1) is scale
+*        SSQ(2) is sum-of-squares
+*        For better accuracy, sum each column separately.
+*
+         SSQ( 1 ) = ZERO
+         SSQ( 2 ) = ONE
+*
+*        Sum off-diagonals
 *
-         SCALE = ZERO
-         SUM = ONE
          IF( LSAME( UPLO, 'U' ) ) THEN
             DO 110 J = 2, N
-               CALL ZLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
+               COLSSQ( 1 ) = ZERO
+               COLSSQ( 2 ) = ONE
+               CALL ZLASSQ( J-1, A( 1, J ), 1, COLSSQ(1), COLSSQ(2) )
+               CALL DCOMBSSQ( SSQ, COLSSQ )
   110       CONTINUE
          ELSE
             DO 120 J = 1, N - 1
-               CALL ZLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
+               COLSSQ( 1 ) = ZERO
+               COLSSQ( 2 ) = ONE
+               CALL ZLASSQ( N-J, A( J+1, J ), 1, COLSSQ(1), COLSSQ(2) )
+               CALL DCOMBSSQ( SSQ, COLSSQ )
   120       CONTINUE
          END IF
-         SUM = 2*SUM
-         CALL ZLASSQ( N, A, LDA+1, SCALE, SUM )
-         VALUE = SCALE*SQRT( SUM )
+         SSQ( 2 ) = 2*SSQ( 2 )
+*
+*        Sum diagonal
+*
+         COLSSQ( 1 ) = ZERO
+         COLSSQ( 2 ) = ONE
+         CALL ZLASSQ( N, A, LDA+1, COLSSQ( 1 ), COLSSQ( 2 ) )
+         CALL DCOMBSSQ( SSQ, COLSSQ )
+         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
       END IF
 *
       ZLANSY = VALUE

lapack-netlib/SRC/zlantb.f

@@ -146,6 +146,7 @@
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
+      IMPLICIT NONE
 *     .. Scalar Arguments ..
       CHARACTER          DIAG, NORM, UPLO
       INTEGER            K, LDAB, N
@@ -164,14 +165,17 @@
 *     .. Local Scalars ..
       LOGICAL            UDIAG
       INTEGER            I, J, L
-      DOUBLE PRECISION   SCALE, SUM, VALUE
+      DOUBLE PRECISION   SUM, VALUE
+*     ..
+*     .. Local Arrays ..
+      DOUBLE PRECISION   SSQ( 2 ), COLSSQ( 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, DISNAN
       EXTERNAL           LSAME, DISNAN
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           ZLASSQ
+      EXTERNAL           ZLASSQ, DCOMBSSQ
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, MAX, MIN, SQRT
@@ -313,46 +317,61 @@
       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
 *
 *        Find normF(A).
+*        SSQ(1) is scale
+*        SSQ(2) is sum-of-squares
+*        For better accuracy, sum each column separately.
 *
          IF( LSAME( UPLO, 'U' ) ) THEN
             IF( LSAME( DIAG, 'U' ) ) THEN
-               SCALE = ONE
-               SUM = N
+               SSQ( 1 ) = ONE
+               SSQ( 2 ) = N
                IF( K.GT.0 ) THEN
                   DO 280 J = 2, N
+                     COLSSQ( 1 ) = ZERO
+                     COLSSQ( 2 ) = ONE
                      CALL ZLASSQ( MIN( J-1, K ),
-     $                            AB( MAX( K+2-J, 1 ), J ), 1, SCALE,
-     $                            SUM )
+     $                            AB( MAX( K+2-J, 1 ), J ), 1,
+     $                            COLSSQ( 1 ), COLSSQ( 2 ) )
+                     CALL DCOMBSSQ( SSQ, COLSSQ )
   280             CONTINUE
                END IF
             ELSE
-               SCALE = ZERO
-               SUM = ONE
+               SSQ( 1 ) = ZERO
+               SSQ( 2 ) = ONE
                DO 290 J = 1, N
+                  COLSSQ( 1 ) = ZERO
+                  COLSSQ( 2 ) = ONE
                   CALL ZLASSQ( MIN( J, K+1 ), AB( MAX( K+2-J, 1 ), J ),
-     $                         1, SCALE, SUM )
+     $                         1, COLSSQ( 1 ), COLSSQ( 2 ) )
+                  CALL DCOMBSSQ( SSQ, COLSSQ )
   290          CONTINUE
             END IF
          ELSE
             IF( LSAME( DIAG, 'U' ) ) THEN
-               SCALE = ONE
-               SUM = N
+               SSQ( 1 ) = ONE
+               SSQ( 2 ) = N
                IF( K.GT.0 ) THEN
                   DO 300 J = 1, N - 1
-                     CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
-     $                            SUM )
+                     COLSSQ( 1 ) = ZERO
+                     COLSSQ( 2 ) = ONE
+                     CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1,
+     $                            COLSSQ( 1 ), COLSSQ( 2 ) )
+                     CALL DCOMBSSQ( SSQ, COLSSQ )
   300             CONTINUE
                END IF
             ELSE
-               SCALE = ZERO
-               SUM = ONE
+               SSQ( 1 ) = ZERO
+               SSQ( 2 ) = ONE
                DO 310 J = 1, N
-                  CALL ZLASSQ( MIN( N-J+1, K+1 ), AB( 1, J ), 1, SCALE,
-     $                         SUM )
+                  COLSSQ( 1 ) = ZERO
+                  COLSSQ( 2 ) = ONE
+                  CALL ZLASSQ( MIN( N-J+1, K+1 ), AB( 1, J ), 1,
+     $                         COLSSQ( 1 ), COLSSQ( 2 ) )
+                  CALL DCOMBSSQ( SSQ, COLSSQ )
   310          CONTINUE
             END IF
          END IF
-         VALUE = SCALE*SQRT( SUM )
+         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
       END IF
 *
       ZLANTB = VALUE

lapack-netlib/SRC/zlantp.f

@@ -130,6 +130,7 @@
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
+      IMPLICIT NONE
 *     .. Scalar Arguments ..
       CHARACTER          DIAG, NORM, UPLO
       INTEGER            N
@@ -148,14 +149,17 @@
 *     .. Local Scalars ..
       LOGICAL            UDIAG
       INTEGER            I, J, K
-      DOUBLE PRECISION   SCALE, SUM, VALUE
+      DOUBLE PRECISION   SUM, VALUE
+*     ..
+*     .. Local Arrays ..
+      DOUBLE PRECISION   SSQ( 2 ), COLSSQ( 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, DISNAN
       EXTERNAL           LSAME, DISNAN
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           ZLASSQ
+      EXTERNAL           ZLASSQ, DCOMBSSQ
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, SQRT
@@ -308,45 +312,64 @@
       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
 *
 *        Find normF(A).
+*        SSQ(1) is scale
+*        SSQ(2) is sum-of-squares
+*        For better accuracy, sum each column separately.
 *
          IF( LSAME( UPLO, 'U' ) ) THEN
             IF( LSAME( DIAG, 'U' ) ) THEN
-               SCALE = ONE
-               SUM = N
+               SSQ( 1 ) = ONE
+               SSQ( 2 ) = N
                K = 2
                DO 280 J = 2, N
-                  CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
+                  COLSSQ( 1 ) = ZERO
+                  COLSSQ( 2 ) = ONE
+                  CALL ZLASSQ( J-1, AP( K ), 1,
+     $                         COLSSQ( 1 ), COLSSQ( 2 ) )
+                  CALL DCOMBSSQ( SSQ, COLSSQ )
                   K = K + J
   280          CONTINUE
             ELSE
-               SCALE = ZERO
-               SUM = ONE
+               SSQ( 1 ) = ZERO
+               SSQ( 2 ) = ONE
                K = 1
                DO 290 J = 1, N
-                  CALL ZLASSQ( J, AP( K ), 1, SCALE, SUM )
+                  COLSSQ( 1 ) = ZERO
+                  COLSSQ( 2 ) = ONE
+                  CALL ZLASSQ( J, AP( K ), 1,
+     $                         COLSSQ( 1 ), COLSSQ( 2 ) )
+                  CALL DCOMBSSQ( SSQ, COLSSQ )
                   K = K + J
   290          CONTINUE
             END IF
          ELSE
             IF( LSAME( DIAG, 'U' ) ) THEN
-               SCALE = ONE
-               SUM = N
+               SSQ( 1 ) = ONE
+               SSQ( 2 ) = N
                K = 2
                DO 300 J = 1, N - 1
-                  CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
+                  COLSSQ( 1 ) = ZERO
+                  COLSSQ( 2 ) = ONE
+                  CALL ZLASSQ( N-J, AP( K ), 1,
+     $                         COLSSQ( 1 ), COLSSQ( 2 ) )
+                  CALL DCOMBSSQ( SSQ, COLSSQ )
                   K = K + N - J + 1
   300          CONTINUE
             ELSE
-               SCALE = ZERO
-               SUM = ONE
+               SSQ( 1 ) = ZERO
+               SSQ( 2 ) = ONE
                K = 1
                DO 310 J = 1, N
-                  CALL ZLASSQ( N-J+1, AP( K ), 1, SCALE, SUM )
+                  COLSSQ( 1 ) = ZERO
+                  COLSSQ( 2 ) = ONE
+                  CALL ZLASSQ( N-J+1, AP( K ), 1,
+     $                         COLSSQ( 1 ), COLSSQ( 2 ) )
+                  CALL DCOMBSSQ( SSQ, COLSSQ )
                   K = K + N - J + 1
   310          CONTINUE
             END IF
          END IF
-         VALUE = SCALE*SQRT( SUM )
+         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
       END IF
 *
       ZLANTP = VALUE

lapack-netlib/SRC/zlantr.f

@@ -147,6 +147,7 @@
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
+      IMPLICIT NONE
 *     .. Scalar Arguments ..
       CHARACTER          DIAG, NORM, UPLO
       INTEGER            LDA, M, N
@@ -165,14 +166,17 @@
 *     .. Local Scalars ..
       LOGICAL            UDIAG
       INTEGER            I, J
-      DOUBLE PRECISION   SCALE, SUM, VALUE
+      DOUBLE PRECISION   SUM, VALUE
+*     ..
+*     .. Local Arrays ..
+      DOUBLE PRECISION   SSQ( 2 ), COLSSQ( 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, DISNAN
       EXTERNAL           LSAME, DISNAN
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           ZLASSQ
+      EXTERNAL           ZLASSQ, DCOMBSSQ
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, MIN, SQRT
@@ -283,7 +287,7 @@
             END IF
          ELSE
             IF( LSAME( DIAG, 'U' ) ) THEN
-               DO 210 I = 1, N
+               DO 210 I = 1, MIN( M, N )
                   WORK( I ) = ONE
   210          CONTINUE
                DO 220 I = N + 1, M
@@ -313,38 +317,56 @@
       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
 *
 *        Find normF(A).
+*        SSQ(1) is scale
+*        SSQ(2) is sum-of-squares
+*        For better accuracy, sum each column separately.
 *
          IF( LSAME( UPLO, 'U' ) ) THEN
             IF( LSAME( DIAG, 'U' ) ) THEN
-               SCALE = ONE
-               SUM = MIN( M, N )
+               SSQ( 1 ) = ONE
+               SSQ( 2 ) = MIN( M, N )
                DO 290 J = 2, N
-                  CALL ZLASSQ( MIN( M, J-1 ), A( 1, J ), 1, SCALE, SUM )
+                  COLSSQ( 1 ) = ZERO
+                  COLSSQ( 2 ) = ONE
+                  CALL ZLASSQ( MIN( M, J-1 ), A( 1, J ), 1,
+     $                         COLSSQ( 1 ), COLSSQ( 2 ) )
+                  CALL DCOMBSSQ( SSQ, COLSSQ )
   290          CONTINUE
             ELSE
-               SCALE = ZERO
-               SUM = ONE
+               SSQ( 1 ) = ZERO
+               SSQ( 2 ) = ONE
                DO 300 J = 1, N
-                  CALL ZLASSQ( MIN( M, J ), A( 1, J ), 1, SCALE, SUM )
+                  COLSSQ( 1 ) = ZERO
+                  COLSSQ( 2 ) = ONE
+                  CALL ZLASSQ( MIN( M, J ), A( 1, J ), 1,
+     $                         COLSSQ( 1 ), COLSSQ( 2 ) )
+                  CALL DCOMBSSQ( SSQ, COLSSQ )
   300          CONTINUE
             END IF
          ELSE
             IF( LSAME( DIAG, 'U' ) ) THEN
-               SCALE = ONE
-               SUM = MIN( M, N )
+               SSQ( 1 ) = ONE
+               SSQ( 2 ) = MIN( M, N )
                DO 310 J = 1, N
-                  CALL ZLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, SCALE,
-     $                         SUM )
+                  COLSSQ( 1 ) = ZERO
+                  COLSSQ( 2 ) = ONE
+                  CALL ZLASSQ( M-J, A( MIN( M, J+1 ), J ), 1,
+     $                         COLSSQ( 1 ), COLSSQ( 2 ) )
+                  CALL DCOMBSSQ( SSQ, COLSSQ )
   310          CONTINUE
             ELSE
-               SCALE = ZERO
-               SUM = ONE
+               SSQ( 1 ) = ZERO
+               SSQ( 2 ) = ONE
                DO 320 J = 1, N
-                  CALL ZLASSQ( M-J+1, A( J, J ), 1, SCALE, SUM )
+                  COLSSQ( 1 ) = ZERO
+                  COLSSQ( 2 ) = ONE
+                  CALL ZLASSQ( M-J+1, A( J, J ), 1,
+     $                         COLSSQ( 1 ), COLSSQ( 2 ) )
+                  CALL DCOMBSSQ( SSQ, COLSSQ )
   320          CONTINUE
             END IF
          END IF
-         VALUE = SCALE*SQRT( SUM )
+         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
       END IF
 *
       ZLANTR = VALUE

lapack-netlib/SRC/zlaqps.f

@@ -127,7 +127,7 @@
 *> \param[in,out] AUXV
 *> \verbatim
 *>          AUXV is COMPLEX*16 array, dimension (NB)
-*>          Auxiliar vector.
+*>          Auxiliary vector.
 *> \endverbatim
 *>
 *> \param[in,out] F

lapack-netlib/SRC/zlaqr0.f

@@ -66,7 +66,7 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>           The order of the matrix H.  N .GE. 0.
+*>           The order of the matrix H.  N >= 0.
 *> \endverbatim
 *>
 *> \param[in] ILO
@@ -79,12 +79,12 @@
 *>          IHI is INTEGER
 *>
 *>           It is assumed that H is already upper triangular in rows
-*>           and columns 1:ILO-1 and IHI+1:N and, if ILO.GT.1,
+*>           and columns 1:ILO-1 and IHI+1:N and, if ILO > 1,
 *>           H(ILO,ILO-1) is zero. ILO and IHI are normally set by a
 *>           previous call to ZGEBAL, and then passed to ZGEHRD when the
 *>           matrix output by ZGEBAL is reduced to Hessenberg form.
 *>           Otherwise, ILO and IHI should be set to 1 and N,
-*>           respectively.  If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N.
+*>           respectively.  If N > 0, then 1 <= ILO <= IHI <= N.
 *>           If N = 0, then ILO = 1 and IHI = 0.
 *> \endverbatim
 *>
@@ -96,17 +96,17 @@
 *>           contains the upper triangular matrix T from the Schur
 *>           decomposition (the Schur form). If INFO = 0 and WANT is
 *>           .FALSE., then the contents of H are unspecified on exit.
-*>           (The output value of H when INFO.GT.0 is given under the
+*>           (The output value of H when INFO > 0 is given under the
 *>           description of INFO below.)
 *>
-*>           This subroutine may explicitly set H(i,j) = 0 for i.GT.j and
+*>           This subroutine may explicitly set H(i,j) = 0 for i > j and
 *>           j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N.
 *> \endverbatim
 *>
 *> \param[in] LDH
 *> \verbatim
 *>          LDH is INTEGER
-*>           The leading dimension of the array H. LDH .GE. max(1,N).
+*>           The leading dimension of the array H. LDH >= max(1,N).
 *> \endverbatim
 *>
 *> \param[out] W
@@ -128,7 +128,7 @@
 *>          IHIZ is INTEGER
 *>           Specify the rows of Z to which transformations must be
 *>           applied if WANTZ is .TRUE..
-*>           1 .LE. ILOZ .LE. ILO; IHI .LE. IHIZ .LE. N.
+*>           1 <= ILOZ <= ILO; IHI <= IHIZ <= N.
 *> \endverbatim
 *>
 *> \param[in,out] Z
@@ -138,7 +138,7 @@
 *>           If WANTZ is .TRUE., then Z(ILO:IHI,ILOZ:IHIZ) is
 *>           replaced by Z(ILO:IHI,ILOZ:IHIZ)*U where U is the
 *>           orthogonal Schur factor of H(ILO:IHI,ILO:IHI).
-*>           (The output value of Z when INFO.GT.0 is given under
+*>           (The output value of Z when INFO > 0 is given under
 *>           the description of INFO below.)
 *> \endverbatim
 *>
@@ -146,7 +146,7 @@
 *> \verbatim
 *>          LDZ is INTEGER
 *>           The leading dimension of the array Z.  if WANTZ is .TRUE.
-*>           then LDZ.GE.MAX(1,IHIZ).  Otherwize, LDZ.GE.1.
+*>           then LDZ >= MAX(1,IHIZ).  Otherwise, LDZ >= 1.
 *> \endverbatim
 *>
 *> \param[out] WORK
@@ -159,7 +159,7 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>           The dimension of the array WORK.  LWORK .GE. max(1,N)
+*>           The dimension of the array WORK.  LWORK >= max(1,N)
 *>           is sufficient, but LWORK typically as large as 6*N may
 *>           be required for optimal performance.  A workspace query
 *>           to determine the optimal workspace size is recommended.
@@ -175,19 +175,19 @@
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>             =  0:  successful exit
-*>           .GT. 0:  if INFO = i, ZLAQR0 failed to compute all of
+*>             = 0:  successful exit
+*>             > 0:  if INFO = i, ZLAQR0 failed to compute all of
 *>                the eigenvalues.  Elements 1:ilo-1 and i+1:n of WR
 *>                and WI contain those eigenvalues which have been
 *>                successfully computed.  (Failures are rare.)
 *>
-*>                If INFO .GT. 0 and WANT is .FALSE., then on exit,
+*>                If INFO > 0 and WANT is .FALSE., then on exit,
 *>                the remaining unconverged eigenvalues are the eigen-
 *>                values of the upper Hessenberg matrix rows and
 *>                columns ILO through INFO of the final, output
 *>                value of H.
 *>
-*>                If INFO .GT. 0 and WANTT is .TRUE., then on exit
+*>                If INFO > 0 and WANTT is .TRUE., then on exit
 *>
 *>           (*)  (initial value of H)*U  = U*(final value of H)
 *>
@@ -195,7 +195,7 @@
 *>                value of  H is upper Hessenberg and triangular in
 *>                rows and columns INFO+1 through IHI.
 *>
-*>                If INFO .GT. 0 and WANTZ is .TRUE., then on exit
+*>                If INFO > 0 and WANTZ is .TRUE., then on exit
 *>
 *>                  (final value of Z(ILO:IHI,ILOZ:IHIZ)
 *>                   =  (initial value of Z(ILO:IHI,ILOZ:IHIZ)*U
@@ -203,7 +203,7 @@
 *>                where U is the unitary matrix in (*) (regard-
 *>                less of the value of WANTT.)
 *>
-*>                If INFO .GT. 0 and WANTZ is .FALSE., then Z is not
+*>                If INFO > 0 and WANTZ is .FALSE., then Z is not
 *>                accessed.
 *> \endverbatim
 *
@@ -641,7 +641,7 @@
                   END IF
                END IF
 *
-*              ==== Use up to NS of the the smallest magnatiude
+*              ==== Use up to NS of the the smallest magnitude
 *              .    shifts.  If there aren't NS shifts available,
 *              .    then use them all, possibly dropping one to
 *              .    make the number of shifts even. ====

lapack-netlib/SRC/zlaqr1.f

@@ -64,7 +64,7 @@
 *> \verbatim
 *>          LDH is INTEGER
 *>              The leading dimension of H as declared in
-*>              the calling procedure.  LDH.GE.N
+*>              the calling procedure.  LDH >= N
 *> \endverbatim
 *>
 *> \param[in] S1

lapack-netlib/SRC/zlaqr2.f

@@ -103,7 +103,7 @@
 *> \param[in] NW
 *> \verbatim
 *>          NW is INTEGER
-*>          Deflation window size.  1 .LE. NW .LE. (KBOT-KTOP+1).
+*>          Deflation window size.  1 <= NW <= (KBOT-KTOP+1).
 *> \endverbatim
 *>
 *> \param[in,out] H
@@ -121,7 +121,7 @@
 *> \verbatim
 *>          LDH is INTEGER
 *>          Leading dimension of H just as declared in the calling
-*>          subroutine.  N .LE. LDH
+*>          subroutine.  N <= LDH
 *> \endverbatim
 *>
 *> \param[in] ILOZ
@@ -133,7 +133,7 @@
 *> \verbatim
 *>          IHIZ is INTEGER
 *>          Specify the rows of Z to which transformations must be
-*>          applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N.
+*>          applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N.
 *> \endverbatim
 *>
 *> \param[in,out] Z
@@ -149,7 +149,7 @@
 *> \verbatim
 *>          LDZ is INTEGER
 *>          The leading dimension of Z just as declared in the
-*>          calling subroutine.  1 .LE. LDZ.
+*>          calling subroutine.  1 <= LDZ.
 *> \endverbatim
 *>
 *> \param[out] NS
@@ -186,13 +186,13 @@
 *> \verbatim
 *>          LDV is INTEGER
 *>          The leading dimension of V just as declared in the
-*>          calling subroutine.  NW .LE. LDV
+*>          calling subroutine.  NW <= LDV
 *> \endverbatim
 *>
 *> \param[in] NH
 *> \verbatim
 *>          NH is INTEGER
-*>          The number of columns of T.  NH.GE.NW.
+*>          The number of columns of T.  NH >= NW.
 *> \endverbatim
 *>
 *> \param[out] T
@@ -204,14 +204,14 @@
 *> \verbatim
 *>          LDT is INTEGER
 *>          The leading dimension of T just as declared in the
-*>          calling subroutine.  NW .LE. LDT
+*>          calling subroutine.  NW <= LDT
 *> \endverbatim
 *>
 *> \param[in] NV
 *> \verbatim
 *>          NV is INTEGER
 *>          The number of rows of work array WV available for
-*>          workspace.  NV.GE.NW.
+*>          workspace.  NV >= NW.
 *> \endverbatim
 *>
 *> \param[out] WV
@@ -223,7 +223,7 @@
 *> \verbatim
 *>          LDWV is INTEGER
 *>          The leading dimension of W just as declared in the
-*>          calling subroutine.  NW .LE. LDV
+*>          calling subroutine.  NW <= LDV
 *> \endverbatim
 *>
 *> \param[out] WORK

lapack-netlib/SRC/zlaqr3.f

@@ -100,7 +100,7 @@
 *> \param[in] NW
 *> \verbatim
 *>          NW is INTEGER
-*>          Deflation window size.  1 .LE. NW .LE. (KBOT-KTOP+1).
+*>          Deflation window size.  1 <= NW <= (KBOT-KTOP+1).
 *> \endverbatim
 *>
 *> \param[in,out] H
@@ -118,7 +118,7 @@
 *> \verbatim
 *>          LDH is INTEGER
 *>          Leading dimension of H just as declared in the calling
-*>          subroutine.  N .LE. LDH
+*>          subroutine.  N <= LDH
 *> \endverbatim
 *>
 *> \param[in] ILOZ
@@ -130,7 +130,7 @@
 *> \verbatim
 *>          IHIZ is INTEGER
 *>          Specify the rows of Z to which transformations must be
-*>          applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N.
+*>          applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N.
 *> \endverbatim
 *>
 *> \param[in,out] Z
@@ -146,7 +146,7 @@
 *> \verbatim
 *>          LDZ is INTEGER
 *>          The leading dimension of Z just as declared in the
-*>          calling subroutine.  1 .LE. LDZ.
+*>          calling subroutine.  1 <= LDZ.
 *> \endverbatim
 *>
 *> \param[out] NS
@@ -183,13 +183,13 @@
 *> \verbatim
 *>          LDV is INTEGER
 *>          The leading dimension of V just as declared in the
-*>          calling subroutine.  NW .LE. LDV
+*>          calling subroutine.  NW <= LDV
 *> \endverbatim
 *>
 *> \param[in] NH
 *> \verbatim
 *>          NH is INTEGER
-*>          The number of columns of T.  NH.GE.NW.
+*>          The number of columns of T.  NH >= NW.
 *> \endverbatim
 *>
 *> \param[out] T
@@ -201,14 +201,14 @@
 *> \verbatim
 *>          LDT is INTEGER
 *>          The leading dimension of T just as declared in the
-*>          calling subroutine.  NW .LE. LDT
+*>          calling subroutine.  NW <= LDT
 *> \endverbatim
 *>
 *> \param[in] NV
 *> \verbatim
 *>          NV is INTEGER
 *>          The number of rows of work array WV available for
-*>          workspace.  NV.GE.NW.
+*>          workspace.  NV >= NW.
 *> \endverbatim
 *>
 *> \param[out] WV
@@ -220,7 +220,7 @@
 *> \verbatim
 *>          LDWV is INTEGER
 *>          The leading dimension of W just as declared in the
-*>          calling subroutine.  NW .LE. LDV
+*>          calling subroutine.  NW <= LDV
 *> \endverbatim
 *>
 *> \param[out] WORK

lapack-netlib/SRC/zlaqr4.f

@@ -73,7 +73,7 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>           The order of the matrix H.  N .GE. 0.
+*>           The order of the matrix H.  N >= 0.
 *> \endverbatim
 *>
 *> \param[in] ILO
@@ -85,12 +85,12 @@
 *> \verbatim
 *>          IHI is INTEGER
 *>           It is assumed that H is already upper triangular in rows
-*>           and columns 1:ILO-1 and IHI+1:N and, if ILO.GT.1,
+*>           and columns 1:ILO-1 and IHI+1:N and, if ILO > 1,
 *>           H(ILO,ILO-1) is zero. ILO and IHI are normally set by a
 *>           previous call to ZGEBAL, and then passed to ZGEHRD when the
 *>           matrix output by ZGEBAL is reduced to Hessenberg form.
 *>           Otherwise, ILO and IHI should be set to 1 and N,
-*>           respectively.  If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N.
+*>           respectively.  If N > 0, then 1 <= ILO <= IHI <= N.
 *>           If N = 0, then ILO = 1 and IHI = 0.
 *> \endverbatim
 *>
@@ -102,17 +102,17 @@
 *>           contains the upper triangular matrix T from the Schur
 *>           decomposition (the Schur form). If INFO = 0 and WANT is
 *>           .FALSE., then the contents of H are unspecified on exit.
-*>           (The output value of H when INFO.GT.0 is given under the
+*>           (The output value of H when INFO > 0 is given under the
 *>           description of INFO below.)
 *>
-*>           This subroutine may explicitly set H(i,j) = 0 for i.GT.j and
+*>           This subroutine may explicitly set H(i,j) = 0 for i > j and
 *>           j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N.
 *> \endverbatim
 *>
 *> \param[in] LDH
 *> \verbatim
 *>          LDH is INTEGER
-*>           The leading dimension of the array H. LDH .GE. max(1,N).
+*>           The leading dimension of the array H. LDH >= max(1,N).
 *> \endverbatim
 *>
 *> \param[out] W
@@ -134,7 +134,7 @@
 *>          IHIZ is INTEGER
 *>           Specify the rows of Z to which transformations must be
 *>           applied if WANTZ is .TRUE..
-*>           1 .LE. ILOZ .LE. ILO; IHI .LE. IHIZ .LE. N.
+*>           1 <= ILOZ <= ILO; IHI <= IHIZ <= N.
 *> \endverbatim
 *>
 *> \param[in,out] Z
@@ -144,7 +144,7 @@
 *>           If WANTZ is .TRUE., then Z(ILO:IHI,ILOZ:IHIZ) is
 *>           replaced by Z(ILO:IHI,ILOZ:IHIZ)*U where U is the
 *>           orthogonal Schur factor of H(ILO:IHI,ILO:IHI).
-*>           (The output value of Z when INFO.GT.0 is given under
+*>           (The output value of Z when INFO > 0 is given under
 *>           the description of INFO below.)
 *> \endverbatim
 *>
@@ -152,7 +152,7 @@
 *> \verbatim
 *>          LDZ is INTEGER
 *>           The leading dimension of the array Z.  if WANTZ is .TRUE.
-*>           then LDZ.GE.MAX(1,IHIZ).  Otherwize, LDZ.GE.1.
+*>           then LDZ >= MAX(1,IHIZ).  Otherwise, LDZ >= 1.
 *> \endverbatim
 *>
 *> \param[out] WORK
@@ -165,7 +165,7 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>           The dimension of the array WORK.  LWORK .GE. max(1,N)
+*>           The dimension of the array WORK.  LWORK >= max(1,N)
 *>           is sufficient, but LWORK typically as large as 6*N may
 *>           be required for optimal performance.  A workspace query
 *>           to determine the optimal workspace size is recommended.
@@ -182,18 +182,18 @@
 *> \verbatim
 *>          INFO is INTEGER
 *>             =  0:  successful exit
-*>           .GT. 0:  if INFO = i, ZLAQR4 failed to compute all of
+*>             > 0:  if INFO = i, ZLAQR4 failed to compute all of
 *>                the eigenvalues.  Elements 1:ilo-1 and i+1:n of WR
 *>                and WI contain those eigenvalues which have been
 *>                successfully computed.  (Failures are rare.)
 *>
-*>                If INFO .GT. 0 and WANT is .FALSE., then on exit,
+*>                If INFO > 0 and WANT is .FALSE., then on exit,
 *>                the remaining unconverged eigenvalues are the eigen-
 *>                values of the upper Hessenberg matrix rows and
 *>                columns ILO through INFO of the final, output
 *>                value of H.
 *>
-*>                If INFO .GT. 0 and WANTT is .TRUE., then on exit
+*>                If INFO > 0 and WANTT is .TRUE., then on exit
 *>
 *>           (*)  (initial value of H)*U  = U*(final value of H)
 *>
@@ -201,7 +201,7 @@
 *>                value of  H is upper Hessenberg and triangular in
 *>                rows and columns INFO+1 through IHI.
 *>
-*>                If INFO .GT. 0 and WANTZ is .TRUE., then on exit
+*>                If INFO > 0 and WANTZ is .TRUE., then on exit
 *>
 *>                  (final value of Z(ILO:IHI,ILOZ:IHIZ)
 *>                   =  (initial value of Z(ILO:IHI,ILOZ:IHIZ)*U
@@ -209,7 +209,7 @@
 *>                where U is the unitary matrix in (*) (regard-
 *>                less of the value of WANTT.)
 *>
-*>                If INFO .GT. 0 and WANTZ is .FALSE., then Z is not
+*>                If INFO > 0 and WANTZ is .FALSE., then Z is not
 *>                accessed.
 *> \endverbatim
 *
@@ -641,7 +641,7 @@
                   END IF
                END IF
 *
-*              ==== Use up to NS of the the smallest magnatiude
+*              ==== Use up to NS of the the smallest magnitude
 *              .    shifts.  If there aren't NS shifts available,
 *              .    then use them all, possibly dropping one to
 *              .    make the number of shifts even. ====

lapack-netlib/SRC/zlaqr5.f

@@ -125,7 +125,7 @@
 *> \verbatim
 *>          LDH is INTEGER
 *>             LDH is the leading dimension of H just as declared in the
-*>             calling procedure.  LDH.GE.MAX(1,N).
+*>             calling procedure.  LDH >= MAX(1,N).
 *> \endverbatim
 *>
 *> \param[in] ILOZ
@@ -137,7 +137,7 @@
 *> \verbatim
 *>          IHIZ is INTEGER
 *>             Specify the rows of Z to which transformations must be
-*>             applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N
+*>             applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N
 *> \endverbatim
 *>
 *> \param[in,out] Z
@@ -153,7 +153,7 @@
 *> \verbatim
 *>          LDZ is INTEGER
 *>             LDA is the leading dimension of Z just as declared in
-*>             the calling procedure. LDZ.GE.N.
+*>             the calling procedure. LDZ >= N.
 *> \endverbatim
 *>
 *> \param[out] V
@@ -165,7 +165,7 @@
 *> \verbatim
 *>          LDV is INTEGER
 *>             LDV is the leading dimension of V as declared in the
-*>             calling procedure.  LDV.GE.3.
+*>             calling procedure.  LDV >= 3.
 *> \endverbatim
 *>
 *> \param[out] U
@@ -177,33 +177,14 @@
 *> \verbatim
 *>          LDU is INTEGER
 *>             LDU is the leading dimension of U just as declared in the
-*>             in the calling subroutine.  LDU.GE.3*NSHFTS-3.
-*> \endverbatim
-*>
-*> \param[in] NH
-*> \verbatim
-*>          NH is INTEGER
-*>             NH is the number of columns in array WH available for
-*>             workspace. NH.GE.1.
-*> \endverbatim
-*>
-*> \param[out] WH
-*> \verbatim
-*>          WH is COMPLEX*16 array, dimension (LDWH,NH)
-*> \endverbatim
-*>
-*> \param[in] LDWH
-*> \verbatim
-*>          LDWH is INTEGER
-*>             Leading dimension of WH just as declared in the
-*>             calling procedure.  LDWH.GE.3*NSHFTS-3.
+*>             in the calling subroutine.  LDU >= 3*NSHFTS-3.
 *> \endverbatim
 *>
 *> \param[in] NV
 *> \verbatim
 *>          NV is INTEGER
 *>             NV is the number of rows in WV agailable for workspace.
-*>             NV.GE.1.
+*>             NV >= 1.
 *> \endverbatim
 *>
 *> \param[out] WV
@@ -215,9 +196,28 @@
 *> \verbatim
 *>          LDWV is INTEGER
 *>             LDWV is the leading dimension of WV as declared in the
-*>             in the calling subroutine.  LDWV.GE.NV.
+*>             in the calling subroutine.  LDWV >= NV.
 *> \endverbatim
 *
+*> \param[in] NH
+*> \verbatim
+*>          NH is INTEGER
+*>             NH is the number of columns in array WH available for
+*>             workspace. NH >= 1.
+*> \endverbatim
+*>
+*> \param[out] WH
+*> \verbatim
+*>          WH is COMPLEX*16 array, dimension (LDWH,NH)
+*> \endverbatim
+*>
+*> \param[in] LDWH
+*> \verbatim
+*>          LDWH is INTEGER
+*>             Leading dimension of WH just as declared in the
+*>             calling procedure.  LDWH >= 3*NSHFTS-3.
+*> \endverbatim
+*>
 *  Authors:
 *  ========
 *

lapack-netlib/SRC/zlarfb.f

@@ -92,6 +92,8 @@
 *>          K is INTEGER
 *>          The order of the matrix T (= the number of elementary
 *>          reflectors whose product defines the block reflector).
+*>          If SIDE = 'L', M >= K >= 0;
+*>          if SIDE = 'R', N >= K >= 0.
 *> \endverbatim
 *>
 *> \param[in] V

lapack-netlib/SRC/zlarfx.f

@@ -94,7 +94,7 @@
 *> \param[in] LDC
 *> \verbatim
 *>          LDC is INTEGER
-*>          The leading dimension of the array C. LDA >= max(1,M).
+*>          The leading dimension of the array C. LDC >= max(1,M).
 *> \endverbatim
 *>
 *> \param[out] WORK

lapack-netlib/SRC/zlarfy.f

@@ -103,7 +103,7 @@
 *
 *> \date December 2016
 *
-*> \ingroup complex16_eig
+*> \ingroup complex16OTHERauxiliary
 *
 *  =====================================================================
       SUBROUTINE ZLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )

lapack-netlib/SRC/zlarrv.f

@@ -143,7 +143,7 @@
 *>          RTOL2 is DOUBLE PRECISION
 *>           Parameters for bisection.
 *>           An interval [LEFT,RIGHT] has converged if
-*>           RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )
+*>           RIGHT-LEFT < MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )
 *> \endverbatim
 *>
 *> \param[in,out] W

lapack-netlib/SRC/zlassq.f

@@ -41,7 +41,7 @@
 *> where x( i ) = abs( X( 1 + ( i - 1 )*INCX ) ). The value of sumsq is
 *> assumed to be at least unity and the value of ssq will then satisfy
 *>
-*>    1.0 .le. ssq .le. ( sumsq + 2*n ).
+*>    1.0 <= ssq <= ( sumsq + 2*n ).
 *>
 *> scale is assumed to be non-negative and scl returns the value
 *>
@@ -65,7 +65,7 @@
 *>
 *> \param[in] X
 *> \verbatim
-*>          X is COMPLEX*16 array, dimension (N)
+*>          X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
 *>          The vector x as described above.
 *>             x( i )  = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
 *> \endverbatim

lapack-netlib/SRC/zlaswlq.f

@@ -1,3 +1,4 @@
+*> \brief \b ZLASWLQ
 *
 *  Definition:
 *  ===========
@@ -18,9 +19,20 @@
 *>
 *> \verbatim
 *>
-*>          ZLASWLQ computes a blocked Short-Wide LQ factorization of a
-*>          M-by-N matrix A, where N >= M:
-*>          A = L * Q
+*> ZLASWLQ computes a blocked Tall-Skinny LQ factorization of
+*> a complexx M-by-N matrix A for M <= N:
+*>
+*>    A = ( L 0 ) *  Q,
+*>
+*> where:
+*>
+*>    Q is a n-by-N orthogonal matrix, stored on exit in an implicit
+*>    form in the elements above the digonal of the array A and in
+*>    the elemenst of the array T;
+*>    L is an lower-triangular M-by-M matrix stored on exit in
+*>    the elements on and below the diagonal of the array A.
+*>    0 is a M-by-(N-M) zero matrix, if M < N, and is not stored.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -150,7 +162,7 @@
       SUBROUTINE ZLASWLQ( M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK,
      $                  INFO)
 *
-*  -- LAPACK computational routine (version 3.7.1) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. --
 *     June 2017

lapack-netlib/SRC/zlasyf_aa.f

@@ -284,8 +284,9 @@
 *
 *              Swap A(I1, I2+1:M) with A(I2, I2+1:M)
 *
-               CALL ZSWAP( M-I2, A( J1+I1-1, I2+1 ), LDA,
-     $                           A( J1+I2-1, I2+1 ), LDA )
+               IF( I2.LT.M )
+     $            CALL ZSWAP( M-I2, A( J1+I1-1, I2+1 ), LDA,
+     $                              A( J1+I2-1, I2+1 ), LDA )
 *
 *              Swap A(I1, I1) with A(I2,I2)
 *
@@ -325,13 +326,15 @@
 *           Compute L(J+2, J+1) = WORK( 3:M ) / T(J, J+1),
 *            where A(J, J+1) = T(J, J+1) and A(J+2:M, J) = L(J+2:M, J+1)
 *
-            IF( A( K, J+1 ).NE.ZERO ) THEN
-               ALPHA = ONE / A( K, J+1 )
-               CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( K, J+2 ), LDA )
-               CALL ZSCAL( M-J-1, ALPHA, A( K, J+2 ), LDA )
-            ELSE
-               CALL ZLASET( 'Full', 1, M-J-1, ZERO, ZERO,
-     $                      A( K, J+2 ), LDA)
+            IF( J.LT.(M-1) ) THEN
+               IF( A( K, J+1 ).NE.ZERO ) THEN
+                  ALPHA = ONE / A( K, J+1 )
+                  CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( K, J+2 ), LDA )
+                  CALL ZSCAL( M-J-1, ALPHA, A( K, J+2 ), LDA )
+               ELSE
+                  CALL ZLASET( 'Full', 1, M-J-1, ZERO, ZERO,
+     $                         A( K, J+2 ), LDA)
+               END IF
             END IF
          END IF
          J = J + 1
@@ -432,8 +435,9 @@
 *
 *              Swap A(I2+1:M, I1) with A(I2+1:M, I2)
 *
-               CALL ZSWAP( M-I2, A( I2+1, J1+I1-1 ), 1,
-     $                           A( I2+1, J1+I2-1 ), 1 )
+               IF( I2.LT.M )
+     $            CALL ZSWAP( M-I2, A( I2+1, J1+I1-1 ), 1,
+     $                              A( I2+1, J1+I2-1 ), 1 )
 *
 *              Swap A(I1, I1) with A(I2, I2)
 *
@@ -473,13 +477,15 @@
 *           Compute L(J+2, J+1) = WORK( 3:M ) / T(J, J+1),
 *            where A(J, J+1) = T(J, J+1) and A(J+2:M, J) = L(J+2:M, J+1)
 *
-            IF( A( J+1, K ).NE.ZERO ) THEN
-               ALPHA = ONE / A( J+1, K )
-               CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( J+2, K ), 1 )
-               CALL ZSCAL( M-J-1, ALPHA, A( J+2, K ), 1 )
-            ELSE
-               CALL ZLASET( 'Full', M-J-1, 1, ZERO, ZERO,
-     $                      A( J+2, K ), LDA )
+            IF( J.LT.(M-1) ) THEN
+               IF( A( J+1, K ).NE.ZERO ) THEN
+                  ALPHA = ONE / A( J+1, K )
+                  CALL ZCOPY( M-J-1, WORK( 3 ), 1, A( J+2, K ), 1 )
+                  CALL ZSCAL( M-J-1, ALPHA, A( J+2, K ), 1 )
+               ELSE
+                  CALL ZLASET( 'Full', M-J-1, 1, ZERO, ZERO,
+     $                         A( J+2, K ), LDA )
+               END IF
             END IF
          END IF
          J = J + 1

lapack-netlib/SRC/zlasyf_rk.f

@@ -330,7 +330,7 @@
 *        of A and working backwards, and compute the matrix W = U12*D
 *        for use in updating A11
 *
-*        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 ) = CZERO
@@ -658,7 +658,7 @@
 *        of A and working forwards, and compute the matrix W = L21*D
 *        for use in updating A22
 *
-*        Initilize the unused last entry of the subdiagonal array E.
+*        Initialize the unused last entry of the subdiagonal array E.
 *
          E( N ) = CZERO
 *

lapack-netlib/SRC/zlatdf.f

@@ -261,7 +261,7 @@
 *
 *        Solve for U- part, lockahead for RHS(N) = +-1. This is not done
 *        In BSOLVE and will hopefully give us a better estimate because
-*        any ill-conditioning of the original matrix is transfered to U
+*        any ill-conditioning of the original matrix is transferred to U
 *        and not to L. U(N, N) is an approximation to sigma_min(LU).
 *
          CALL ZCOPY( N-1, RHS, 1, WORK, 1 )

lapack-netlib/SRC/zlatsqr.f

@@ -1,3 +1,4 @@
+*> \brief \b ZLATSQR
 *
 *  Definition:
 *  ===========
@@ -18,9 +19,23 @@
 *>
 *> \verbatim
 *>
-*> SLATSQR computes a blocked Tall-Skinny QR factorization of
-*> an M-by-N matrix A, where M >= N:
-*> A = Q * R .
+*> ZLATSQR computes a blocked Tall-Skinny QR factorization of
+*> a complex M-by-N matrix A for M >= N:
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a M-by-M orthogonal matrix, stored on exit in an implicit
+*>    form in the elements below the digonal of the array A and in
+*>    the elemenst of the array T;
+*>
+*>    R is an upper-triangular N-by-N matrix, stored on exit in
+*>    the elements on and above the diagonal of the array A.
+*>
+*>    0 is a (M-N)-by-N zero matrix, and is not stored.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -149,10 +164,10 @@
       SUBROUTINE ZLATSQR( M, N, MB, NB, A, LDA, T, LDT, WORK,
      $                    LWORK, INFO)
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. --
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER           INFO, LDA, M, N, MB, NB, LDT, LWORK

lapack-netlib/SRC/zlaunhr_col_getrfnp.f

@@ -0,0 +1,248 @@
+*> \brief \b ZLAUNHR_COL_GETRFNP
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZLAUNHR_COL_GETRFNP + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaunhr_col_getrfnp.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaunhr_col_getrfnp.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaunhr_col_getrfnp.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE ZLAUNHR_COL_GETRFNP( M, N, A, LDA, D, INFO )
+*
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, LDA, M, N
+*       ..
+*       .. Array Arguments ..
+*       COMPLEX*16         A( LDA, * ), D( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> ZLAUNHR_COL_GETRFNP computes the modified LU factorization without
+*> pivoting of a complex general M-by-N matrix A. The factorization has
+*> the form:
+*>
+*>     A - S = L * U,
+*>
+*> where:
+*>    S is a m-by-n diagonal sign matrix with the diagonal D, so that
+*>    D(i) = S(i,i), 1 <= i <= min(M,N). The diagonal D is constructed
+*>    as D(i)=-SIGN(A(i,i)), where A(i,i) is the value after performing
+*>    i-1 steps of Gaussian elimination. This means that the diagonal
+*>    element at each step of "modified" Gaussian elimination is
+*>    at least one in absolute value (so that division-by-zero not
+*>    not possible during the division by the diagonal element);
+*>
+*>    L is a M-by-N lower triangular matrix with unit diagonal elements
+*>    (lower trapezoidal if M > N);
+*>
+*>    and U is a M-by-N upper triangular matrix
+*>    (upper trapezoidal if M < N).
+*>
+*> This routine is an auxiliary routine used in the Householder
+*> reconstruction routine ZUNHR_COL. In ZUNHR_COL, this routine is
+*> applied to an M-by-N matrix A with orthonormal columns, where each
+*> element is bounded by one in absolute value. With the choice of
+*> the matrix S above, one can show that the diagonal element at each
+*> step of Gaussian elimination is the largest (in absolute value) in
+*> the column on or below the diagonal, so that no pivoting is required
+*> for numerical stability [1].
+*>
+*> For more details on the Householder reconstruction algorithm,
+*> including the modified LU factorization, see [1].
+*>
+*> This is the blocked right-looking version of the algorithm,
+*> calling Level 3 BLAS to update the submatrix. To factorize a block,
+*> this routine calls the recursive routine ZLAUNHR_COL_GETRFNP2.
+*>
+*> [1] "Reconstructing Householder vectors from tall-skinny QR",
+*>     G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H.D. Nguyen,
+*>     E. Solomonik, J. Parallel Distrib. Comput.,
+*>     vol. 85, pp. 3-31, 2015.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>          The number of rows of the matrix A.  M >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The number of columns of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX*16 array, dimension (LDA,N)
+*>          On entry, the M-by-N matrix to be factored.
+*>          On exit, the factors L and U from the factorization
+*>          A-S=L*U; the unit diagonal elements of L are not stored.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] D
+*> \verbatim
+*>          D is COMPLEX*16 array, dimension min(M,N)
+*>          The diagonal elements of the diagonal M-by-N sign matrix S,
+*>          D(i) = S(i,i), where 1 <= i <= min(M,N). The elements can be
+*>          only ( +1.0, 0.0 ) or (-1.0, 0.0 ).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*>
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2019
+*
+*> \ingroup complex16GEcomputational
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*> November 2019, Igor Kozachenko,
+*>                Computer Science Division,
+*>                University of California, Berkeley
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      SUBROUTINE ZLAUNHR_COL_GETRFNP( M, N, A, LDA, D, INFO )
+      IMPLICIT NONE
+*
+*  -- LAPACK computational routine (version 3.9.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2019
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, LDA, M, N
+*     ..
+*     .. Array Arguments ..
+      COMPLEX*16         A( LDA, * ), D( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      COMPLEX*16         CONE
+      PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
+*     ..
+*     .. Local Scalars ..
+      INTEGER            IINFO, J, JB, NB
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           ZGEMM, ZLAUNHR_COL_GETRFNP2, ZTRSM, XERBLA
+*     ..
+*     .. External Functions ..
+      INTEGER            ILAENV
+      EXTERNAL           ILAENV
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          MAX, MIN
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters.
+*
+      INFO = 0
+      IF( M.LT.0 ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
+         INFO = -4
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'ZLAUNHR_COL_GETRFNP', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( MIN( M, N ).EQ.0 )
+     $   RETURN
+*
+*     Determine the block size for this environment.
+*
+
+      NB = ILAENV( 1, 'ZLAUNHR_COL_GETRFNP', ' ', M, N, -1, -1 )
+
+      IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
+*
+*        Use unblocked code.
+*
+         CALL ZLAUNHR_COL_GETRFNP2( M, N, A, LDA, D, INFO )
+      ELSE
+*
+*        Use blocked code.
+*
+         DO J = 1, MIN( M, N ), NB
+            JB = MIN( MIN( M, N )-J+1, NB )
+*
+*           Factor diagonal and subdiagonal blocks.
+*
+            CALL ZLAUNHR_COL_GETRFNP2( M-J+1, JB, A( J, J ), LDA,
+     $                                 D( J ), IINFO )
+*
+            IF( J+JB.LE.N ) THEN
+*
+*              Compute block row of U.
+*
+               CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB,
+     $                     N-J-JB+1, CONE, A( J, J ), LDA, A( J, J+JB ),
+     $                     LDA )
+               IF( J+JB.LE.M ) THEN
+*
+*                 Update trailing submatrix.
+*
+                  CALL ZGEMM( 'No transpose', 'No transpose', M-J-JB+1,
+     $                        N-J-JB+1, JB, -CONE, A( J+JB, J ), LDA,
+     $                        A( J, J+JB ), LDA, CONE, A( J+JB, J+JB ),
+     $                        LDA )
+               END IF
+            END IF
+         END DO
+      END IF
+      RETURN
+*
+*     End of ZLAUNHR_COL_GETRFNP
+*
+      END

lapack-netlib/SRC/zlaunhr_col_getrfnp2.f

@@ -0,0 +1,314 @@
+*> \brief \b ZLAUNHR_COL_GETRFNP2
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZLAUNHR_COL_GETRFNP2 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaunhr_col_getrfnp2.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaunhr_col_getrfnp2.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaunhr_col_getrfnp2.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       RECURSIVE SUBROUTINE ZLAUNHR_COL_GETRFNP2( M, N, A, LDA, D, INFO )
+*
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, LDA, M, N
+*       ..
+*       .. Array Arguments ..
+*       COMPLEX*16         A( LDA, * ), D( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> ZLAUNHR_COL_GETRFNP2 computes the modified LU factorization without
+*> pivoting of a complex general M-by-N matrix A. The factorization has
+*> the form:
+*>
+*>     A - S = L * U,
+*>
+*> where:
+*>    S is a m-by-n diagonal sign matrix with the diagonal D, so that
+*>    D(i) = S(i,i), 1 <= i <= min(M,N). The diagonal D is constructed
+*>    as D(i)=-SIGN(A(i,i)), where A(i,i) is the value after performing
+*>    i-1 steps of Gaussian elimination. This means that the diagonal
+*>    element at each step of "modified" Gaussian elimination is at
+*>    least one in absolute value (so that division-by-zero not
+*>    possible during the division by the diagonal element);
+*>
+*>    L is a M-by-N lower triangular matrix with unit diagonal elements
+*>    (lower trapezoidal if M > N);
+*>
+*>    and U is a M-by-N upper triangular matrix
+*>    (upper trapezoidal if M < N).
+*>
+*> This routine is an auxiliary routine used in the Householder
+*> reconstruction routine ZUNHR_COL. In ZUNHR_COL, this routine is
+*> applied to an M-by-N matrix A with orthonormal columns, where each
+*> element is bounded by one in absolute value. With the choice of
+*> the matrix S above, one can show that the diagonal element at each
+*> step of Gaussian elimination is the largest (in absolute value) in
+*> the column on or below the diagonal, so that no pivoting is required
+*> for numerical stability [1].
+*>
+*> For more details on the Householder reconstruction algorithm,
+*> including the modified LU factorization, see [1].
+*>
+*> This is the recursive version of the LU factorization algorithm.
+*> Denote A - S by B. The algorithm divides the matrix B into four
+*> submatrices:
+*>
+*>        [  B11 | B12  ]  where B11 is n1 by n1,
+*>    B = [ -----|----- ]        B21 is (m-n1) by n1,
+*>        [  B21 | B22  ]        B12 is n1 by n2,
+*>                               B22 is (m-n1) by n2,
+*>                               with n1 = min(m,n)/2, n2 = n-n1.
+*>
+*>
+*> The subroutine calls itself to factor B11, solves for B21,
+*> solves for B12, updates B22, then calls itself to factor B22.
+*>
+*> For more details on the recursive LU algorithm, see [2].
+*>
+*> ZLAUNHR_COL_GETRFNP2 is called to factorize a block by the blocked
+*> routine ZLAUNHR_COL_GETRFNP, which uses blocked code calling
+*. Level 3 BLAS to update the submatrix. However, ZLAUNHR_COL_GETRFNP2
+*> is self-sufficient and can be used without ZLAUNHR_COL_GETRFNP.
+*>
+*> [1] "Reconstructing Householder vectors from tall-skinny QR",
+*>     G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H.D. Nguyen,
+*>     E. Solomonik, J. Parallel Distrib. Comput.,
+*>     vol. 85, pp. 3-31, 2015.
+*>
+*> [2] "Recursion leads to automatic variable blocking for dense linear
+*>     algebra algorithms", F. Gustavson, IBM J. of Res. and Dev.,
+*>     vol. 41, no. 6, pp. 737-755, 1997.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>          The number of rows of the matrix A.  M >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The number of columns of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX*16 array, dimension (LDA,N)
+*>          On entry, the M-by-N matrix to be factored.
+*>          On exit, the factors L and U from the factorization
+*>          A-S=L*U; the unit diagonal elements of L are not stored.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] D
+*> \verbatim
+*>          D is COMPLEX*16 array, dimension min(M,N)
+*>          The diagonal elements of the diagonal M-by-N sign matrix S,
+*>          D(i) = S(i,i), where 1 <= i <= min(M,N). The elements can be
+*>          only ( +1.0, 0.0 ) or (-1.0, 0.0 ).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*>
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2019
+*
+*> \ingroup complex16GEcomputational
+*
+*> \par Contributors:
+*  ==================
+*>
+*> \verbatim
+*>
+*> November 2019, Igor Kozachenko,
+*>                Computer Science Division,
+*>                University of California, Berkeley
+*>
+*> \endverbatim
+*
+*  =====================================================================
+      RECURSIVE SUBROUTINE ZLAUNHR_COL_GETRFNP2( M, N, A, LDA, D, INFO )
+      IMPLICIT NONE
+*
+*  -- LAPACK computational routine (version 3.9.0) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2019
+*
+*     .. Scalar Arguments ..
+      INTEGER            INFO, LDA, M, N
+*     ..
+*     .. Array Arguments ..
+      COMPLEX*16         A( LDA, * ), D( * )
+*     ..
+*
+*  =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ONE
+      PARAMETER          ( ONE = 1.0D+0 )
+      COMPLEX*16         CONE
+      PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
+*     ..
+*     .. Local Scalars ..
+      DOUBLE PRECISION   SFMIN
+      INTEGER            I, IINFO, N1, N2
+      COMPLEX*16         Z
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION   DLAMCH
+      EXTERNAL           DLAMCH
+*     ..
+*     .. External Subroutines ..
+      EXTERNAL           ZGEMM, ZSCAL, ZTRSM, XERBLA
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC          ABS, DBLE, DCMPLX, DIMAG, DSIGN, MAX, MIN
+*     ..
+*     .. Statement Functions ..
+      DOUBLE PRECISION   CABS1
+*     ..
+*     .. Statement Function definitions ..
+      CABS1( Z ) = ABS( DBLE( Z ) ) + ABS( DIMAG( Z ) )
+*     ..
+*     .. Executable Statements ..
+*
+*     Test the input parameters
+*
+      INFO = 0
+      IF( M.LT.0 ) THEN
+         INFO = -1
+      ELSE IF( N.LT.0 ) THEN
+         INFO = -2
+      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
+         INFO = -4
+      END IF
+      IF( INFO.NE.0 ) THEN
+         CALL XERBLA( 'ZLAUNHR_COL_GETRFNP2', -INFO )
+         RETURN
+      END IF
+*
+*     Quick return if possible
+*
+      IF( MIN( M, N ).EQ.0 )
+     $   RETURN
+
+      IF ( M.EQ.1 ) THEN
+*
+*        One row case, (also recursion termination case),
+*        use unblocked code
+*
+*        Transfer the sign
+*
+         D( 1 ) = DCMPLX( -DSIGN( ONE, DBLE( A( 1, 1 ) ) ) )
+*
+*        Construct the row of U
+*
+         A( 1, 1 ) = A( 1, 1 ) - D( 1 )
+*
+      ELSE IF( N.EQ.1 ) THEN
+*
+*        One column case, (also recursion termination case),
+*        use unblocked code
+*
+*        Transfer the sign
+*
+         D( 1 ) = DCMPLX( -DSIGN( ONE, DBLE( A( 1, 1 ) ) ) )
+*
+*        Construct the row of U
+*
+         A( 1, 1 ) = A( 1, 1 ) - D( 1 )
+*
+*        Scale the elements 2:M of the column
+*
+*        Determine machine safe minimum
+*
+         SFMIN = DLAMCH('S')
+*
+*        Construct the subdiagonal elements of L
+*
+         IF( CABS1( A( 1, 1 ) ) .GE. SFMIN ) THEN
+            CALL ZSCAL( M-1, CONE / A( 1, 1 ), A( 2, 1 ), 1 )
+         ELSE
+            DO I = 2, M
+               A( I, 1 ) = A( I, 1 ) / A( 1, 1 )
+            END DO
+         END IF
+*
+      ELSE
+*
+*        Divide the matrix B into four submatrices
+*
+         N1 = MIN( M, N ) / 2
+         N2 = N-N1
+
+*
+*        Factor B11, recursive call
+*
+         CALL ZLAUNHR_COL_GETRFNP2( N1, N1, A, LDA, D, IINFO )
+*
+*        Solve for B21
+*
+         CALL ZTRSM( 'R', 'U', 'N', 'N', M-N1, N1, CONE, A, LDA,
+     $               A( N1+1, 1 ), LDA )
+*
+*        Solve for B12
+*
+         CALL ZTRSM( 'L', 'L', 'N', 'U', N1, N2, CONE, A, LDA,
+     $               A( 1, N1+1 ), LDA )
+*
+*        Update B22, i.e. compute the Schur complement
+*        B22 := B22 - B21*B12
+*
+         CALL ZGEMM( 'N', 'N', M-N1, N2, N1, -CONE, A( N1+1, 1 ), LDA,
+     $               A( 1, N1+1 ), LDA, CONE, A( N1+1, N1+1 ), LDA )
+*
+*        Factor B22, recursive call
+*
+         CALL ZLAUNHR_COL_GETRFNP2( M-N1, N2, A( N1+1, N1+1 ), LDA,
+     $                              D( N1+1 ), IINFO )
+*
+      END IF
+      RETURN
+*
+*     End of ZLAUNHR_COL_GETRFNP2
+*
+      END