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version 1.1.1.1, 2010/01/26 15:22:45 version 1.18, 2023/08/07 08:39:44
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   *> \brief \b ZUNGRQ
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download ZUNGRQ + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zungrq.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zungrq.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zungrq.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZUNGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, K, LDA, LWORK, M, N
   *       ..
   *       .. Array Arguments ..
   *       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZUNGRQ generates an M-by-N complex matrix Q with orthonormal rows,
   *> which is defined as the last M rows of a product of K elementary
   *> reflectors of order N
   *>
   *>       Q  =  H(1)**H H(2)**H . . . H(k)**H
   *>
   *> as returned by ZGERQF.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of rows of the matrix Q. M >= 0.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The number of columns of the matrix Q. N >= M.
   *> \endverbatim
   *>
   *> \param[in] K
   *> \verbatim
   *>          K is INTEGER
   *>          The number of elementary reflectors whose product defines the
   *>          matrix Q. M >= K >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] A
   *> \verbatim
   *>          A is COMPLEX*16 array, dimension (LDA,N)
   *>          On entry, the (m-k+i)-th row must contain the vector which
   *>          defines the elementary reflector H(i), for i = 1,2,...,k, as
   *>          returned by ZGERQF in the last k rows of its array argument
   *>          A.
   *>          On exit, the M-by-N matrix Q.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The first dimension of the array A. LDA >= max(1,M).
   *> \endverbatim
   *>
   *> \param[in] TAU
   *> \verbatim
   *>          TAU is COMPLEX*16 array, dimension (K)
   *>          TAU(i) must contain the scalar factor of the elementary
   *>          reflector H(i), as returned by ZGERQF.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
   *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   *> \endverbatim
   *>
   *> \param[in] LWORK
   *> \verbatim
   *>          LWORK is INTEGER
   *>          The dimension of the array WORK. LWORK >= max(1,M).
   *>          For optimum performance LWORK >= M*NB, where NB is the
   *>          optimal blocksize.
   *>
   *>          If LWORK = -1, then a workspace query is assumed; the routine
   *>          only calculates the optimal size of the WORK array, returns
   *>          this value as the first entry of the WORK array, and no error
   *>          message related to LWORK is issued by XERBLA.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument has an illegal value
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \ingroup complex16OTHERcomputational
   *
   *  =====================================================================
       SUBROUTINE ZUNGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )        SUBROUTINE ZUNGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK computational routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, K, LDA, LWORK, M, N        INTEGER            INFO, K, LDA, LWORK, M, N
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       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )        COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZUNGRQ generates an M-by-N complex matrix Q with orthonormal rows,  
 *  which is defined as the last M rows of a product of K elementary  
 *  reflectors of order N  
 *  
 *        Q  =  H(1)' H(2)' . . . H(k)'  
 *  
 *  as returned by ZGERQF.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  M       (input) INTEGER  
 *          The number of rows of the matrix Q. M >= 0.  
 *  
 *  N       (input) INTEGER  
 *          The number of columns of the matrix Q. N >= M.  
 *  
 *  K       (input) INTEGER  
 *          The number of elementary reflectors whose product defines the  
 *          matrix Q. M >= K >= 0.  
 *  
 *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)  
 *          On entry, the (m-k+i)-th row must contain the vector which  
 *          defines the elementary reflector H(i), for i = 1,2,...,k, as  
 *          returned by ZGERQF in the last k rows of its array argument  
 *          A.  
 *          On exit, the M-by-N matrix Q.  
 *  
 *  LDA     (input) INTEGER  
 *          The first dimension of the array A. LDA >= max(1,M).  
 *  
 *  TAU     (input) COMPLEX*16 array, dimension (K)  
 *          TAU(i) must contain the scalar factor of the elementary  
 *          reflector H(i), as returned by ZGERQF.  
 *  
 *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))  
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.  
 *  
 *  LWORK   (input) INTEGER  
 *          The dimension of the array WORK. LWORK >= max(1,M).  
 *          For optimum performance LWORK >= M*NB, where NB is the  
 *          optimal blocksize.  
 *  
 *          If LWORK = -1, then a workspace query is assumed; the routine  
 *          only calculates the optimal size of the WORK array, returns  
 *          this value as the first entry of the WORK array, and no error  
 *          message related to LWORK is issued by XERBLA.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument has an illegal value  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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                CALL ZLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB,                 CALL ZLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB,
      $                      A( II, 1 ), LDA, TAU( I ), WORK, LDWORK )       $                      A( II, 1 ), LDA, TAU( I ), WORK, LDWORK )
 *  *
 *              Apply H' to A(1:m-k+i-1,1:n-k+i+ib-1) from the right  *              Apply H**H to A(1:m-k+i-1,1:n-k+i+ib-1) from the right
 *  *
                CALL ZLARFB( 'Right', 'Conjugate transpose', 'Backward',                 CALL ZLARFB( 'Right', 'Conjugate transpose', 'Backward',
      $                      'Rowwise', II-1, N-K+I+IB-1, IB, A( II, 1 ),       $                      'Rowwise', II-1, N-K+I+IB-1, IB, A( II, 1 ),
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      $                      LDWORK )       $                      LDWORK )
             END IF              END IF
 *  *
 *           Apply H' to columns 1:n-k+i+ib-1 of current block  *           Apply H**H to columns 1:n-k+i+ib-1 of current block
 *  *
             CALL ZUNGR2( IB, N-K+I+IB-1, IB, A( II, 1 ), LDA, TAU( I ),              CALL ZUNGR2( IB, N-K+I+IB-1, IB, A( II, 1 ), LDA, TAU( I ),
      $                   WORK, IINFO )       $                   WORK, IINFO )
Removed from v.1.1.1.1  
changed lines
  Added in v.1.18

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