--- rpl/lapack/lapack/zgbbrd.f	2010/08/13 21:04:01	1.6
+++ rpl/lapack/lapack/zgbbrd.f	2023/08/07 08:39:15	1.18
@@ -1,10 +1,199 @@
+*> \brief \b ZGBBRD
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZGBBRD + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgbbrd.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgbbrd.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgbbrd.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE ZGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,
+*                          LDQ, PT, LDPT, C, LDC, WORK, RWORK, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          VECT
+*       INTEGER            INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   D( * ), E( * ), RWORK( * )
+*       COMPLEX*16         AB( LDAB, * ), C( LDC, * ), PT( LDPT, * ),
+*      $                   Q( LDQ, * ), WORK( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> ZGBBRD reduces a complex general m-by-n band matrix A to real upper
+*> bidiagonal form B by a unitary transformation: Q**H * A * P = B.
+*>
+*> The routine computes B, and optionally forms Q or P**H, or computes
+*> Q**H*C for a given matrix C.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] VECT
+*> \verbatim
+*>          VECT is CHARACTER*1
+*>          Specifies whether or not the matrices Q and P**H are to be
+*>          formed.
+*>          = 'N': do not form Q or P**H;
+*>          = 'Q': form Q only;
+*>          = 'P': form P**H only;
+*>          = 'B': form both.
+*> \endverbatim
+*>
+*> \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] NCC
+*> \verbatim
+*>          NCC is INTEGER
+*>          The number of columns of the matrix C.  NCC >= 0.
+*> \endverbatim
+*>
+*> \param[in] KL
+*> \verbatim
+*>          KL is INTEGER
+*>          The number of subdiagonals of the matrix A. KL >= 0.
+*> \endverbatim
+*>
+*> \param[in] KU
+*> \verbatim
+*>          KU is INTEGER
+*>          The number of superdiagonals of the matrix A. KU >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] AB
+*> \verbatim
+*>          AB is COMPLEX*16 array, dimension (LDAB,N)
+*>          On entry, the m-by-n band matrix A, stored in rows 1 to
+*>          KL+KU+1. The j-th column of A is stored in the j-th column of
+*>          the array AB as follows:
+*>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
+*>          On exit, A is overwritten by values generated during the
+*>          reduction.
+*> \endverbatim
+*>
+*> \param[in] LDAB
+*> \verbatim
+*>          LDAB is INTEGER
+*>          The leading dimension of the array A. LDAB >= KL+KU+1.
+*> \endverbatim
+*>
+*> \param[out] D
+*> \verbatim
+*>          D is DOUBLE PRECISION array, dimension (min(M,N))
+*>          The diagonal elements of the bidiagonal matrix B.
+*> \endverbatim
+*>
+*> \param[out] E
+*> \verbatim
+*>          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
+*>          The superdiagonal elements of the bidiagonal matrix B.
+*> \endverbatim
+*>
+*> \param[out] Q
+*> \verbatim
+*>          Q is COMPLEX*16 array, dimension (LDQ,M)
+*>          If VECT = 'Q' or 'B', the m-by-m unitary matrix Q.
+*>          If VECT = 'N' or 'P', the array Q is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDQ
+*> \verbatim
+*>          LDQ is INTEGER
+*>          The leading dimension of the array Q.
+*>          LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.
+*> \endverbatim
+*>
+*> \param[out] PT
+*> \verbatim
+*>          PT is COMPLEX*16 array, dimension (LDPT,N)
+*>          If VECT = 'P' or 'B', the n-by-n unitary matrix P'.
+*>          If VECT = 'N' or 'Q', the array PT is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDPT
+*> \verbatim
+*>          LDPT is INTEGER
+*>          The leading dimension of the array PT.
+*>          LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.
+*> \endverbatim
+*>
+*> \param[in,out] C
+*> \verbatim
+*>          C is COMPLEX*16 array, dimension (LDC,NCC)
+*>          On entry, an m-by-ncc matrix C.
+*>          On exit, C is overwritten by Q**H*C.
+*>          C is not referenced if NCC = 0.
+*> \endverbatim
+*>
+*> \param[in] LDC
+*> \verbatim
+*>          LDC is INTEGER
+*>          The leading dimension of the array C.
+*>          LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX*16 array, dimension (max(M,N))
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*>          RWORK is DOUBLE PRECISION array, dimension (max(M,N))
+*> \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.
+*
+*> \ingroup complex16GBcomputational
+*
+*  =====================================================================
       SUBROUTINE ZGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,
      $                   LDQ, PT, LDPT, C, LDC, WORK, RWORK, INFO )
 *
-*  -- 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          VECT
@@ -16,91 +205,6 @@
      $                   Q( LDQ, * ), WORK( * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  ZGBBRD reduces a complex general m-by-n band matrix A to real upper
-*  bidiagonal form B by a unitary transformation: Q' * A * P = B.
-*
-*  The routine computes B, and optionally forms Q or P', or computes
-*  Q'*C for a given matrix C.
-*
-*  Arguments
-*  =========
-*
-*  VECT    (input) CHARACTER*1
-*          Specifies whether or not the matrices Q and P' are to be
-*          formed.
-*          = 'N': do not form Q or P';
-*          = 'Q': form Q only;
-*          = 'P': form P' only;
-*          = 'B': form both.
-*
-*  M       (input) INTEGER
-*          The number of rows of the matrix A.  M >= 0.
-*
-*  N       (input) INTEGER
-*          The number of columns of the matrix A.  N >= 0.
-*
-*  NCC     (input) INTEGER
-*          The number of columns of the matrix C.  NCC >= 0.
-*
-*  KL      (input) INTEGER
-*          The number of subdiagonals of the matrix A. KL >= 0.
-*
-*  KU      (input) INTEGER
-*          The number of superdiagonals of the matrix A. KU >= 0.
-*
-*  AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
-*          On entry, the m-by-n band matrix A, stored in rows 1 to
-*          KL+KU+1. The j-th column of A is stored in the j-th column of
-*          the array AB as follows:
-*          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
-*          On exit, A is overwritten by values generated during the
-*          reduction.
-*
-*  LDAB    (input) INTEGER
-*          The leading dimension of the array A. LDAB >= KL+KU+1.
-*
-*  D       (output) DOUBLE PRECISION array, dimension (min(M,N))
-*          The diagonal elements of the bidiagonal matrix B.
-*
-*  E       (output) DOUBLE PRECISION array, dimension (min(M,N)-1)
-*          The superdiagonal elements of the bidiagonal matrix B.
-*
-*  Q       (output) COMPLEX*16 array, dimension (LDQ,M)
-*          If VECT = 'Q' or 'B', the m-by-m unitary matrix Q.
-*          If VECT = 'N' or 'P', the array Q is not referenced.
-*
-*  LDQ     (input) INTEGER
-*          The leading dimension of the array Q.
-*          LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.
-*
-*  PT      (output) COMPLEX*16 array, dimension (LDPT,N)
-*          If VECT = 'P' or 'B', the n-by-n unitary matrix P'.
-*          If VECT = 'N' or 'Q', the array PT is not referenced.
-*
-*  LDPT    (input) INTEGER
-*          The leading dimension of the array PT.
-*          LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.
-*
-*  C       (input/output) COMPLEX*16 array, dimension (LDC,NCC)
-*          On entry, an m-by-ncc matrix C.
-*          On exit, C is overwritten by Q'*C.
-*          C is not referenced if NCC = 0.
-*
-*  LDC     (input) INTEGER
-*          The leading dimension of the array C.
-*          LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.
-*
-*  WORK    (workspace) COMPLEX*16 array, dimension (max(M,N))
-*
-*  RWORK   (workspace) DOUBLE PRECISION array, dimension (max(M,N))
-*
-*  INFO    (output) INTEGER
-*          = 0:  successful exit.
-*          < 0:  if INFO = -i, the i-th argument had an illegal value.
-*
 *  =====================================================================
 *
 *     .. Parameters ..
@@ -165,7 +269,7 @@
          RETURN
       END IF
 *
-*     Initialize Q and P' to the unit matrix, if needed
+*     Initialize Q and P**H to the unit matrix, if needed
 *
       IF( WANTQ )
      $   CALL ZLASET( 'Full', M, M, CZERO, CONE, Q, LDQ )
@@ -338,7 +442,7 @@
 *
                IF( WANTPT ) THEN
 *
-*                 accumulate product of plane rotations in P'
+*                 accumulate product of plane rotations in P**H
 *
                   DO 60 J = J1, J2, KB1
                      CALL ZROT( N, PT( J+KUN-1, 1 ), LDPT,