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version 1.9, 2011/07/22 07:38:17 version 1.10, 2011/11/21 20:43:16
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   *> \brief \b ZLAQP2
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZLAQP2 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqp2.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqp2.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqp2.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
   *                          WORK )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            LDA, M, N, OFFSET
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            JPVT( * )
   *       DOUBLE PRECISION   VN1( * ), VN2( * )
   *       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZLAQP2 computes a QR factorization with column pivoting of
   *> the block A(OFFSET+1:M,1:N).
   *> The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
   *> \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] OFFSET
   *> \verbatim
   *>          OFFSET is INTEGER
   *>          The number of rows of the matrix A that must be pivoted
   *>          but no factorized. OFFSET >= 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 upper triangle of block A(OFFSET+1:M,1:N) is
   *>          the triangular factor obtained; the elements in block
   *>          A(OFFSET+1:M,1:N) below the diagonal, together with the
   *>          array TAU, represent the orthogonal matrix Q as a product of
   *>          elementary reflectors. Block A(1:OFFSET,1:N) has been
   *>          accordingly pivoted, but no factorized.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A. LDA >= max(1,M).
   *> \endverbatim
   *>
   *> \param[in,out] JPVT
   *> \verbatim
   *>          JPVT is INTEGER array, dimension (N)
   *>          On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
   *>          to the front of A*P (a leading column); if JPVT(i) = 0,
   *>          the i-th column of A is a free column.
   *>          On exit, if JPVT(i) = k, then the i-th column of A*P
   *>          was the k-th column of A.
   *> \endverbatim
   *>
   *> \param[out] TAU
   *> \verbatim
   *>          TAU is COMPLEX*16 array, dimension (min(M,N))
   *>          The scalar factors of the elementary reflectors.
   *> \endverbatim
   *>
   *> \param[in,out] VN1
   *> \verbatim
   *>          VN1 is DOUBLE PRECISION array, dimension (N)
   *>          The vector with the partial column norms.
   *> \endverbatim
   *>
   *> \param[in,out] VN2
   *> \verbatim
   *>          VN2 is DOUBLE PRECISION array, dimension (N)
   *>          The vector with the exact column norms.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is COMPLEX*16 array, dimension (N)
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16OTHERauxiliary
   *
   *> \par Contributors:
   *  ==================
   *>
   *>    G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
   *>    X. Sun, Computer Science Dept., Duke University, USA
   *> \n
   *>  Partial column norm updating strategy modified on April 2011
   *>    Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
   *>    University of Zagreb, Croatia.
   *
   *> \par References:
   *  ================
   *>
   *> LAPACK Working Note 176
   *
   *> \htmlonly
   *> <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a> 
   *> \endhtmlonly 
   *
   *  =====================================================================
       SUBROUTINE ZLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,        SUBROUTINE ZLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
      $                   WORK )       $                   WORK )
 *  *
 *  -- LAPACK auxiliary routine (version 3.3.1) --  *  -- LAPACK auxiliary routine (version 3.4.0) --
 *  -- 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..--
 *  -- April 2011                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            LDA, M, N, OFFSET        INTEGER            LDA, M, N, OFFSET
Line 15 Line 163
       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )        COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZLAQP2 computes a QR factorization with column pivoting of  
 *  the block A(OFFSET+1:M,1:N).  
 *  The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.  
 *  
 *  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.  
 *  
 *  OFFSET  (input) INTEGER  
 *          The number of rows of the matrix A that must be pivoted  
 *          but no factorized. OFFSET >= 0.  
 *  
 *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)  
 *          On entry, the M-by-N matrix A.  
 *          On exit, the upper triangle of block A(OFFSET+1:M,1:N) is  
 *          the triangular factor obtained; the elements in block  
 *          A(OFFSET+1:M,1:N) below the diagonal, together with the  
 *          array TAU, represent the orthogonal matrix Q as a product of  
 *          elementary reflectors. Block A(1:OFFSET,1:N) has been  
 *          accordingly pivoted, but no factorized.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A. LDA >= max(1,M).  
 *  
 *  JPVT    (input/output) INTEGER array, dimension (N)  
 *          On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted  
 *          to the front of A*P (a leading column); if JPVT(i) = 0,  
 *          the i-th column of A is a free column.  
 *          On exit, if JPVT(i) = k, then the i-th column of A*P  
 *          was the k-th column of A.  
 *  
 *  TAU     (output) COMPLEX*16 array, dimension (min(M,N))  
 *          The scalar factors of the elementary reflectors.  
 *  
 *  VN1     (input/output) DOUBLE PRECISION array, dimension (N)  
 *          The vector with the partial column norms.  
 *  
 *  VN2     (input/output) DOUBLE PRECISION array, dimension (N)  
 *          The vector with the exact column norms.  
 *  
 *  WORK    (workspace) COMPLEX*16 array, dimension (N)  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Based on contributions by  
 *    G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain  
 *    X. Sun, Computer Science Dept., Duke University, USA  
 *  
 *  Partial column norm updating strategy modified by  
 *    Z. Drmac and Z. Bujanovic, Dept. of Mathematics,  
 *    University of Zagreb, Croatia.  
 *  -- April 2011                                                      --  
 *  For more details see LAPACK Working Note 176.  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.9  
changed lines
  Added in v.1.10

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