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version 1.4, 2010/12/21 13:53:44 version 1.16, 2018/05/29 07:18:15
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   *> \brief \b ZGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download ZGEQR2P + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeqr2p.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeqr2p.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeqr2p.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, LDA, M, N
   *       ..
   *       .. Array Arguments ..
   *       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZGEQR2P computes a QR factorization of a complex m by n matrix A:
   *> A = Q * R. The diagonal entries of R are real and nonnegative.
   *> \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 diagonal entries of R
   *>          are real and nonnegative; the elements below the diagonal,
   *>          with the array TAU, represent the unitary matrix Q as a
   *>          product of 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 (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.
   *
   *> \date December 2016
   *
   *> \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).
   *>
   *> See Lapack Working Note 203 for details
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE ZGEQR2P( M, N, A, LDA, TAU, WORK, INFO )        SUBROUTINE ZGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
 *  *
 *  -- LAPACK routine (version 3.2.2) --  *  -- LAPACK computational routine (version 3.7.0) --
 *  -- 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..--
 *     June 2010  *     December 2016
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N        INTEGER            INFO, LDA, M, N
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       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )        COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZGEQR2P 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 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) COMPLEX*16 array, dimension (N)  
 *  
 *  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).  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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      $                TAU( I ) )       $                TAU( I ) )
          IF( I.LT.N ) THEN           IF( I.LT.N ) THEN
 *  *
 *           Apply H(i)' to A(i:m,i+1:n) from the left  *           Apply H(i)**H to A(i:m,i+1:n) from the left
 *  *
             ALPHA = A( I, I )              ALPHA = A( I, I )
             A( I, I ) = ONE              A( I, I ) = ONE
Removed from v.1.4  
changed lines
  Added in v.1.16

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