--- rpl/lapack/lapack/zlatzm.f	2010/12/21 13:53:52	1.7
+++ rpl/lapack/lapack/zlatzm.f	2023/08/07 08:39:33	1.18
@@ -1,9 +1,158 @@
+*> \brief \b ZLATZM
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZLATZM + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlatzm.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlatzm.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlatzm.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE ZLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          SIDE
+*       INTEGER            INCV, LDC, M, N
+*       COMPLEX*16         TAU
+*       ..
+*       .. Array Arguments ..
+*       COMPLEX*16         C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> This routine is deprecated and has been replaced by routine ZUNMRZ.
+*>
+*> ZLATZM applies a Householder matrix generated by ZTZRQF to a matrix.
+*>
+*> Let P = I - tau*u*u**H,   u = ( 1 ),
+*>                               ( v )
+*> where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
+*> SIDE = 'R'.
+*>
+*> If SIDE equals 'L', let
+*>        C = [ C1 ] 1
+*>            [ C2 ] m-1
+*>              n
+*> Then C is overwritten by P*C.
+*>
+*> If SIDE equals 'R', let
+*>        C = [ C1, C2 ] m
+*>               1  n-1
+*> Then C is overwritten by C*P.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] SIDE
+*> \verbatim
+*>          SIDE is CHARACTER*1
+*>          = 'L': form P * C
+*>          = 'R': form C * P
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*>          M is INTEGER
+*>          The number of rows of the matrix C.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The number of columns of the matrix C.
+*> \endverbatim
+*>
+*> \param[in] V
+*> \verbatim
+*>          V is COMPLEX*16 array, dimension
+*>                  (1 + (M-1)*abs(INCV)) if SIDE = 'L'
+*>                  (1 + (N-1)*abs(INCV)) if SIDE = 'R'
+*>          The vector v in the representation of P. V is not used
+*>          if TAU = 0.
+*> \endverbatim
+*>
+*> \param[in] INCV
+*> \verbatim
+*>          INCV is INTEGER
+*>          The increment between elements of v. INCV <> 0
+*> \endverbatim
+*>
+*> \param[in] TAU
+*> \verbatim
+*>          TAU is COMPLEX*16
+*>          The value tau in the representation of P.
+*> \endverbatim
+*>
+*> \param[in,out] C1
+*> \verbatim
+*>          C1 is COMPLEX*16 array, dimension
+*>                         (LDC,N) if SIDE = 'L'
+*>                         (M,1)   if SIDE = 'R'
+*>          On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1
+*>          if SIDE = 'R'.
+*>
+*>          On exit, the first row of P*C if SIDE = 'L', or the first
+*>          column of C*P if SIDE = 'R'.
+*> \endverbatim
+*>
+*> \param[in,out] C2
+*> \verbatim
+*>          C2 is COMPLEX*16 array, dimension
+*>                         (LDC, N)   if SIDE = 'L'
+*>                         (LDC, N-1) if SIDE = 'R'
+*>          On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the
+*>          m x (n - 1) matrix C2 if SIDE = 'R'.
+*>
+*>          On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P
+*>          if SIDE = 'R'.
+*> \endverbatim
+*>
+*> \param[in] LDC
+*> \verbatim
+*>          LDC is INTEGER
+*>          The leading dimension of the arrays C1 and C2.
+*>          LDC >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX*16 array, dimension
+*>                      (N) if SIDE = 'L'
+*>                      (M) if SIDE = 'R'
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup complex16OTHERcomputational
+*
+*  =====================================================================
       SUBROUTINE ZLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
 *
-*  -- LAPACK routine (version 3.2) --
+*  -- LAPACK computational routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2006
 *
 *     .. Scalar Arguments ..
       CHARACTER          SIDE
@@ -14,80 +163,6 @@
       COMPLEX*16         C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  This routine is deprecated and has been replaced by routine ZUNMRZ.
-*
-*  ZLATZM applies a Householder matrix generated by ZTZRQF to a matrix.
-*
-*  Let P = I - tau*u*u',   u = ( 1 ),
-*                              ( v )
-*  where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
-*  SIDE = 'R'.
-*
-*  If SIDE equals 'L', let
-*         C = [ C1 ] 1
-*             [ C2 ] m-1
-*               n
-*  Then C is overwritten by P*C.
-*
-*  If SIDE equals 'R', let
-*         C = [ C1, C2 ] m
-*                1  n-1
-*  Then C is overwritten by C*P.
-*
-*  Arguments
-*  =========
-*
-*  SIDE    (input) CHARACTER*1
-*          = 'L': form P * C
-*          = 'R': form C * P
-*
-*  M       (input) INTEGER
-*          The number of rows of the matrix C.
-*
-*  N       (input) INTEGER
-*          The number of columns of the matrix C.
-*
-*  V       (input) COMPLEX*16 array, dimension
-*                  (1 + (M-1)*abs(INCV)) if SIDE = 'L'
-*                  (1 + (N-1)*abs(INCV)) if SIDE = 'R'
-*          The vector v in the representation of P. V is not used
-*          if TAU = 0.
-*
-*  INCV    (input) INTEGER
-*          The increment between elements of v. INCV <> 0
-*
-*  TAU     (input) COMPLEX*16
-*          The value tau in the representation of P.
-*
-*  C1      (input/output) COMPLEX*16 array, dimension
-*                         (LDC,N) if SIDE = 'L'
-*                         (M,1)   if SIDE = 'R'
-*          On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1
-*          if SIDE = 'R'.
-*
-*          On exit, the first row of P*C if SIDE = 'L', or the first
-*          column of C*P if SIDE = 'R'.
-*
-*  C2      (input/output) COMPLEX*16 array, dimension
-*                         (LDC, N)   if SIDE = 'L'
-*                         (LDC, N-1) if SIDE = 'R'
-*          On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the
-*          m x (n - 1) matrix C2 if SIDE = 'R'.
-*
-*          On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P
-*          if SIDE = 'R'.
-*
-*  LDC     (input) INTEGER
-*          The leading dimension of the arrays C1 and C2.
-*          LDC >= max(1,M).
-*
-*  WORK    (workspace) COMPLEX*16 array, dimension
-*                      (N) if SIDE = 'L'
-*                      (M) if SIDE = 'R'
-*
 *  =====================================================================
 *
 *     .. Parameters ..
@@ -112,14 +187,14 @@
 *
       IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*        w :=  conjg( C1 + v' * C2 )
+*        w :=  ( C1 + v**H * C2 )**H
 *
          CALL ZCOPY( N, C1, LDC, WORK, 1 )
          CALL ZLACGV( N, WORK, 1 )
          CALL ZGEMV( 'Conjugate transpose', M-1, N, ONE, C2, LDC, V,
      $               INCV, ONE, WORK, 1 )
 *
-*        [ C1 ] := [ C1 ] - tau* [ 1 ] * w'
+*        [ C1 ] := [ C1 ] - tau* [ 1 ] * w**H
 *        [ C2 ]    [ C2 ]        [ v ]
 *
          CALL ZLACGV( N, WORK, 1 )
@@ -134,7 +209,7 @@
          CALL ZGEMV( 'No transpose', M, N-1, ONE, C2, LDC, V, INCV, ONE,
      $               WORK, 1 )
 *
-*        [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v']
+*        [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**H]
 *
          CALL ZAXPY( M, -TAU, WORK, 1, C1, 1 )
          CALL ZGERC( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC )