--- rpl/lapack/lapack/ztzrqf.f	2010/08/07 13:18:09	1.5
+++ rpl/lapack/lapack/ztzrqf.f	2023/08/07 08:39:42	1.19
@@ -1,9 +1,144 @@
+*> \brief \b ZTZRQF
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZTZRQF + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztzrqf.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztzrqf.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztzrqf.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE ZTZRQF( M, N, A, LDA, TAU, INFO )
+*
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, LDA, M, N
+*       ..
+*       .. Array Arguments ..
+*       COMPLEX*16         A( LDA, * ), TAU( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> This routine is deprecated and has been replaced by routine ZTZRZF.
+*>
+*> ZTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
+*> to upper triangular form by means of unitary transformations.
+*>
+*> The upper trapezoidal matrix A is factored as
+*>
+*>    A = ( R  0 ) * Z,
+*>
+*> where Z is an N-by-N unitary matrix and R is an M-by-M upper
+*> triangular matrix.
+*> \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 >= M.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*>          A is COMPLEX*16 array, dimension (LDA,N)
+*>          On entry, the leading M-by-N upper trapezoidal part of the
+*>          array A must contain the matrix to be factorized.
+*>          On exit, the leading M-by-M upper triangular part of A
+*>          contains the upper triangular matrix R, and elements M+1 to
+*>          N of the first M rows of A, with the array TAU, represent the
+*>          unitary matrix Z as a product of M elementary reflectors.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*>          TAU is COMPLEX*16 array, dimension (M)
+*>          The scalar factors of the elementary reflectors.
+*> \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 complex16OTHERcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  The  factorization is obtained by Householder's method.  The kth
+*>  transformation matrix, Z( k ), whose conjugate transpose is used to
+*>  introduce zeros into the (m - k + 1)th row of A, is given in the form
+*>
+*>     Z( k ) = ( I     0   ),
+*>              ( 0  T( k ) )
+*>
+*>  where
+*>
+*>     T( k ) = I - tau*u( k )*u( k )**H,   u( k ) = (   1    ),
+*>                                                   (   0    )
+*>                                                   ( z( k ) )
+*>
+*>  tau is a scalar and z( k ) is an ( n - m ) element vector.
+*>  tau and z( k ) are chosen to annihilate the elements of the kth row
+*>  of X.
+*>
+*>  The scalar tau is returned in the kth element of TAU and the vector
+*>  u( k ) in the kth row of A, such that the elements of z( k ) are
+*>  in  a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
+*>  the upper triangular part of A.
+*>
+*>  Z is given by
+*>
+*>     Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
+*> \endverbatim
+*>
+*  =====================================================================
       SUBROUTINE ZTZRQF( M, N, A, LDA, TAU, INFO )
 *
-*  -- LAPACK routine (version 3.2.2) --
+*  -- LAPACK computational routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     June 2010
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N
@@ -12,77 +147,6 @@
       COMPLEX*16         A( LDA, * ), TAU( * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  This routine is deprecated and has been replaced by routine ZTZRZF.
-*
-*  ZTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
-*  to upper triangular form by means of unitary transformations.
-*
-*  The upper trapezoidal matrix A is factored as
-*
-*     A = ( R  0 ) * Z,
-*
-*  where Z is an N-by-N unitary matrix and R is an M-by-M upper
-*  triangular matrix.
-*
-*  Arguments
-*  =========
-*
-*  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 >= M.
-*
-*  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
-*          On entry, the leading M-by-N upper trapezoidal part of the
-*          array A must contain the matrix to be factorized.
-*          On exit, the leading M-by-M upper triangular part of A
-*          contains the upper triangular matrix R, and elements M+1 to
-*          N of the first M rows of A, with the array TAU, represent the
-*          unitary matrix Z as a product of M elementary reflectors.
-*
-*  LDA     (input) INTEGER
-*          The leading dimension of the array A.  LDA >= max(1,M).
-*
-*  TAU     (output) COMPLEX*16 array, dimension (M)
-*          The scalar factors of the elementary reflectors.
-*
-*  INFO    (output) INTEGER
-*          = 0: successful exit
-*          < 0: if INFO = -i, the i-th argument had an illegal value
-*
-*  Further Details
-*  ===============
-*
-*  The  factorization is obtained by Householder's method.  The kth
-*  transformation matrix, Z( k ), whose conjugate transpose is used to
-*  introduce zeros into the (m - k + 1)th row of A, is given in the form
-*
-*     Z( k ) = ( I     0   ),
-*              ( 0  T( k ) )
-*
-*  where
-*
-*     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
-*                                                 (   0    )
-*                                                 ( z( k ) )
-*
-*  tau is a scalar and z( k ) is an ( n - m ) element vector.
-*  tau and z( k ) are chosen to annihilate the elements of the kth row
-*  of X.
-*
-*  The scalar tau is returned in the kth element of TAU and the vector
-*  u( k ) in the kth row of A, such that the elements of z( k ) are
-*  in  a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
-*  the upper triangular part of A.
-*
-*  Z is given by
-*
-*     Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*
 * =====================================================================
 *
 *     .. Parameters ..
@@ -142,7 +206,7 @@
 *
             IF( TAU( K ).NE.CZERO .AND. K.GT.1 ) THEN
 *
-*              We now perform the operation  A := A*P( k )'.
+*              We now perform the operation  A := A*P( k )**H.
 *
 *              Use the first ( k - 1 ) elements of TAU to store  a( k ),
 *              where  a( k ) consists of the first ( k - 1 ) elements of
@@ -157,7 +221,7 @@
      $                     LDA, A( K, M1 ), LDA, CONE, TAU, 1 )
 *
 *              Now form  a( k ) := a( k ) - conjg(tau)*w
-*              and       B      := B      - conjg(tau)*w*z( k )'.
+*              and       B      := B      - conjg(tau)*w*z( k )**H.
 *
                CALL ZAXPY( K-1, -DCONJG( TAU( K ) ), TAU, 1, A( 1, K ),
      $                     1 )