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version 1.1, 2010/01/26 15:22:46 version 1.19, 2023/08/07 08:39:19
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   *> \brief \b ZGEQRF
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download ZGEQRF + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeqrf.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeqrf.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeqrf.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, LDA, LWORK, M, N
   *       ..
   *       .. Array Arguments ..
   *       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZGEQRF computes a QR factorization of a complex M-by-N matrix A:
   *>
   *>    A = Q * ( R ),
   *>            ( 0 )
   *>
   *> where:
   *>
   *>    Q is a M-by-M orthogonal matrix;
   *>    R is an upper-triangular N-by-N matrix;
   *>    0 is a (M-N)-by-N zero matrix, if M > N.
   *>
   *> \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 A.
   *>          On exit, the elements on and above the diagonal of the array
   *>          contain the min(M,N)-by-N upper trapezoidal matrix R (R is
   *>          upper triangular if m >= n); the elements below the diagonal,
   *>          with the array TAU, represent the unitary matrix Q as a
   *>          product of min(m,n) elementary reflectors (see Further
   *>          Details).
   *> \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 (min(M,N))
   *>          The scalar factors of the elementary reflectors (see Further
   *>          Details).
   *> \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 >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise.
   *>          For optimum performance LWORK >= N*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 had an illegal value
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \ingroup complex16GEcomputational
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  The matrix Q is represented as a product of elementary reflectors
   *>
   *>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
   *>
   *>  Each H(i) has the form
   *>
   *>     H(i) = I - tau * v * v**H
   *>
   *>  where tau is a complex scalar, and v is a complex vector with
   *>  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
   *>  and tau in TAU(i).
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE ZGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )        SUBROUTINE ZGEQRF( M, N, 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, LDA, LWORK, M, N        INTEGER            INFO, LDA, LWORK, M, N
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       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )        COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZGEQRF computes a QR factorization of a complex M-by-N matrix A:  
 *  A = Q * R.  
 *  
 *  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 >= 0.  
 *  
 *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)  
 *          On entry, the M-by-N matrix A.  
 *          On exit, the elements on and above the diagonal of the array  
 *          contain the min(M,N)-by-N upper trapezoidal matrix R (R is  
 *          upper triangular if m >= n); the elements below the diagonal,  
 *          with the array TAU, represent the unitary matrix Q as a  
 *          product of min(m,n) elementary reflectors (see Further  
 *          Details).  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A.  LDA >= max(1,M).  
 *  
 *  TAU     (output) COMPLEX*16 array, dimension (min(M,N))  
 *          The scalar factors of the elementary reflectors (see Further  
 *          Details).  
 *  
 *  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,N).  
 *          For optimum performance LWORK >= N*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 had an illegal value  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  The matrix Q is represented as a product of elementary reflectors  
 *  
 *     Q = H(1) H(2) . . . H(k), where k = min(m,n).  
 *  
 *  Each H(i) has the form  
 *  
 *     H(i) = I - tau * v * v'  
 *  
 *  where tau is a complex scalar, and v is a complex vector with  
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),  
 *  and tau in TAU(i).  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
Line 96 Line 176
 *  *
 *     Test the input arguments  *     Test the input arguments
 *  *
         K = MIN( M, N )
       INFO = 0        INFO = 0
       NB = ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 )        NB = ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 )
       LWKOPT = N*NB  
       WORK( 1 ) = LWKOPT  
       LQUERY = ( LWORK.EQ.-1 )        LQUERY = ( LWORK.EQ.-1 )
       IF( M.LT.0 ) THEN        IF( M.LT.0 ) THEN
          INFO = -1           INFO = -1
Line 107 Line 186
          INFO = -2           INFO = -2
       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN        ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
          INFO = -4           INFO = -4
       ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN        ELSE IF( .NOT.LQUERY ) THEN
          INFO = -7           IF( LWORK.LE.0 .OR. ( M.GT.0 .AND. LWORK.LT.MAX( 1, N ) ) )
        $      INFO = -7
       END IF        END IF
       IF( INFO.NE.0 ) THEN        IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'ZGEQRF', -INFO )           CALL XERBLA( 'ZGEQRF', -INFO )
          RETURN           RETURN
       ELSE IF( LQUERY ) THEN        ELSE IF( LQUERY ) THEN
            IF( K.EQ.0 ) THEN
               LWKOPT = 1
            ELSE
               LWKOPT = N*NB
            END IF
            WORK( 1 ) = LWKOPT
          RETURN           RETURN
       END IF        END IF
 *  *
 *     Quick return if possible  *     Quick return if possible
 *  *
       K = MIN( M, N )  
       IF( K.EQ.0 ) THEN        IF( K.EQ.0 ) THEN
          WORK( 1 ) = 1           WORK( 1 ) = 1
          RETURN           RETURN
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                CALL ZLARFT( 'Forward', 'Columnwise', M-I+1, IB,                 CALL ZLARFT( 'Forward', 'Columnwise', M-I+1, IB,
      $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )       $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )
 *  *
 *              Apply H' to A(i:m,i+ib:n) from the left  *              Apply H**H to A(i:m,i+ib:n) from the left
 *  *
                CALL ZLARFB( 'Left', 'Conjugate transpose', 'Forward',                 CALL ZLARFB( 'Left', 'Conjugate transpose', 'Forward',
      $                      'Columnwise', M-I+1, N-I-IB+1, IB,       $                      'Columnwise', M-I+1, N-I-IB+1, IB,
Removed from v.1.1  
changed lines
  Added in v.1.19

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