version 1.1, 2010/01/26 15:22:46
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version 1.20, 2023/08/07 08:39:30
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*> \brief \b ZLAQP2 computes a QR factorization with column pivoting of the matrix block. |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download ZLAQP2 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqp2.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqp2.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqp2.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE ZLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, |
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* WORK ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER LDA, M, N, OFFSET |
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* .. |
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* .. Array Arguments .. |
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* INTEGER JPVT( * ) |
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* DOUBLE PRECISION VN1( * ), VN2( * ) |
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* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> ZLAQP2 computes a QR factorization with column pivoting of |
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*> the block A(OFFSET+1:M,1:N). |
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*> The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] M |
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*> \verbatim |
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*> M is INTEGER |
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*> The number of rows of the matrix A. M >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The number of columns of the matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] OFFSET |
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*> \verbatim |
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*> OFFSET is INTEGER |
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*> The number of rows of the matrix A that must be pivoted |
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*> but no factorized. OFFSET >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] A |
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*> \verbatim |
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*> A is COMPLEX*16 array, dimension (LDA,N) |
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*> On entry, the M-by-N matrix A. |
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*> On exit, the upper triangle of block A(OFFSET+1:M,1:N) is |
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*> the triangular factor obtained; the elements in block |
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*> A(OFFSET+1:M,1:N) below the diagonal, together with the |
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*> array TAU, represent the orthogonal matrix Q as a product of |
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*> elementary reflectors. Block A(1:OFFSET,1:N) has been |
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*> accordingly pivoted, but no factorized. |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> The leading dimension of the array A. LDA >= max(1,M). |
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*> \endverbatim |
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*> |
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*> \param[in,out] JPVT |
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*> \verbatim |
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*> JPVT is INTEGER array, dimension (N) |
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*> On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted |
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*> to the front of A*P (a leading column); if JPVT(i) = 0, |
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*> the i-th column of A is a free column. |
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*> On exit, if JPVT(i) = k, then the i-th column of A*P |
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*> was the k-th column of A. |
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*> \endverbatim |
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*> |
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*> \param[out] TAU |
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*> \verbatim |
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*> TAU is COMPLEX*16 array, dimension (min(M,N)) |
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*> The scalar factors of the elementary reflectors. |
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*> \endverbatim |
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*> |
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*> \param[in,out] VN1 |
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*> \verbatim |
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*> VN1 is DOUBLE PRECISION array, dimension (N) |
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*> The vector with the partial column norms. |
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*> \endverbatim |
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*> |
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*> \param[in,out] VN2 |
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*> \verbatim |
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*> VN2 is DOUBLE PRECISION array, dimension (N) |
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*> The vector with the exact column norms. |
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*> \endverbatim |
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*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is COMPLEX*16 array, dimension (N) |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \ingroup complex16OTHERauxiliary |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain |
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*> X. Sun, Computer Science Dept., Duke University, USA |
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*> \n |
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*> Partial column norm updating strategy modified on April 2011 |
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*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics, |
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*> University of Zagreb, Croatia. |
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* |
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*> \par References: |
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* ================ |
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*> |
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*> LAPACK Working Note 176 |
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* |
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*> \htmlonly |
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*> <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a> |
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*> \endhtmlonly |
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* |
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* ===================================================================== |
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 3.2) -- |
* -- LAPACK auxiliary 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 |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER LDA, M, N, OFFSET |
INTEGER LDA, M, N, OFFSET |
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COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) |
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZLAQP2 computes a QR factorization with column pivoting of |
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* the block A(OFFSET+1:M,1:N). |
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* The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. |
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* |
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* Arguments |
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* ========= |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix A. M >= 0. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix A. N >= 0. |
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* |
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* OFFSET (input) INTEGER |
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* The number of rows of the matrix A that must be pivoted |
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* but no factorized. OFFSET >= 0. |
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* |
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* A (input/output) COMPLEX*16 array, dimension (LDA,N) |
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* On entry, the M-by-N matrix A. |
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* On exit, the upper triangle of block A(OFFSET+1:M,1:N) is |
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* the triangular factor obtained; the elements in block |
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* A(OFFSET+1:M,1:N) below the diagonal, together with the |
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* array TAU, represent the orthogonal matrix Q as a product of |
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* elementary reflectors. Block A(1:OFFSET,1:N) has been |
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* accordingly pivoted, but no factorized. |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(1,M). |
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* |
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* JPVT (input/output) INTEGER array, dimension (N) |
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* On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted |
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* to the front of A*P (a leading column); if JPVT(i) = 0, |
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* the i-th column of A is a free column. |
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* On exit, if JPVT(i) = k, then the i-th column of A*P |
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* was the k-th column of A. |
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* |
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* TAU (output) COMPLEX*16 array, dimension (min(M,N)) |
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* The scalar factors of the elementary reflectors. |
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* |
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* VN1 (input/output) DOUBLE PRECISION array, dimension (N) |
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* The vector with the partial column norms. |
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* |
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* VN2 (input/output) DOUBLE PRECISION array, dimension (N) |
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* The vector with the exact column norms. |
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* |
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* WORK (workspace) COMPLEX*16 array, dimension (N) |
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* |
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* Further Details |
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* =============== |
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* |
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* Based on contributions by |
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* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain |
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* X. Sun, Computer Science Dept., Duke University, USA |
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* |
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* Partial column norm updating strategy modified by |
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* Z. Drmac and Z. Bujanovic, Dept. of Mathematics, |
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* University of Zagreb, Croatia. |
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* June 2006. |
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* For more details see LAPACK Working Note 176. |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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COMPLEX*16 AII |
COMPLEX*16 AII |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL ZLARF, ZLARFP, ZSWAP |
EXTERNAL ZLARF, ZLARFG, ZSWAP |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC ABS, DCONJG, MAX, MIN, SQRT |
INTRINSIC ABS, DCONJG, MAX, MIN, SQRT |
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* Generate elementary reflector H(i). |
* Generate elementary reflector H(i). |
* |
* |
IF( OFFPI.LT.M ) THEN |
IF( OFFPI.LT.M ) THEN |
CALL ZLARFP( M-OFFPI+1, A( OFFPI, I ), A( OFFPI+1, I ), 1, |
CALL ZLARFG( M-OFFPI+1, A( OFFPI, I ), A( OFFPI+1, I ), 1, |
$ TAU( I ) ) |
$ TAU( I ) ) |
ELSE |
ELSE |
CALL ZLARFP( 1, A( M, I ), A( M, I ), 1, TAU( I ) ) |
CALL ZLARFG( 1, A( M, I ), A( M, I ), 1, TAU( I ) ) |
END IF |
END IF |
* |
* |
IF( I.LT.N ) THEN |
IF( I.LT.N ) THEN |
* |
* |
* Apply H(i)' to A(offset+i:m,i+1:n) from the left. |
* Apply H(i)**H to A(offset+i:m,i+1:n) from the left. |
* |
* |
AII = A( OFFPI, I ) |
AII = A( OFFPI, I ) |
A( OFFPI, I ) = CONE |
A( OFFPI, I ) = CONE |