version 1.4, 2010/08/06 15:32:44
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version 1.13, 2012/12/14 12:30:32
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*> \brief \b ZLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. |
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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 ZLAQPS + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqps.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/zlaqps.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/zlaqps.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 ZLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, |
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* VN2, AUXV, F, LDF ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER KB, LDA, LDF, M, N, NB, 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, * ), AUXV( * ), F( LDF, * ), TAU( * ) |
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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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*> ZLAQPS computes a step of QR factorization with column pivoting |
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*> of a complex M-by-N matrix A by using Blas-3. It tries to factorize |
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*> NB columns from A starting from the row OFFSET+1, and updates all |
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*> of the matrix with Blas-3 xGEMM. |
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*> |
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*> In some cases, due to catastrophic cancellations, it cannot |
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*> factorize NB columns. Hence, the actual number of factorized |
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*> columns is returned in KB. |
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*> |
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*> 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 A that have been factorized in |
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*> previous steps. |
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*> \endverbatim |
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*> |
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*> \param[in] NB |
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*> \verbatim |
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*> NB is INTEGER |
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*> The number of columns to factorize. |
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*> \endverbatim |
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*> |
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*> \param[out] KB |
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*> \verbatim |
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*> KB is INTEGER |
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*> The number of columns actually factorized. |
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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, block A(OFFSET+1:M,1:KB) is the triangular |
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*> factor obtained and block A(1:OFFSET,1:N) has been |
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*> accordingly pivoted, but no factorized. |
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*> The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has |
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*> been updated. |
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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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*> JPVT(I) = K <==> Column K of the full matrix A has been |
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*> permuted into position I in AP. |
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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 (KB) |
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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[in,out] AUXV |
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*> \verbatim |
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*> AUXV is COMPLEX*16 array, dimension (NB) |
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*> Auxiliar vector. |
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*> \endverbatim |
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*> |
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*> \param[in,out] F |
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*> \verbatim |
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*> F is COMPLEX*16 array, dimension (LDF,NB) |
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*> Matrix F**H = L * Y**H * A. |
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*> \endverbatim |
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*> |
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*> \param[in] LDF |
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*> \verbatim |
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*> LDF is INTEGER |
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*> The leading dimension of the array F. LDF >= max(1,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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*> \date September 2012 |
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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 ZLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, |
SUBROUTINE ZLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, |
$ VN2, AUXV, F, LDF ) |
$ VN2, AUXV, F, LDF ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.4.2) -- |
* -- 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 |
* September 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER KB, LDA, LDF, M, N, NB, OFFSET |
INTEGER KB, LDA, LDF, M, N, NB, OFFSET |
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COMPLEX*16 A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ) |
COMPLEX*16 A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZLAQPS computes a step of QR factorization with column pivoting |
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* of a complex M-by-N matrix A by using Blas-3. It tries to factorize |
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* NB columns from A starting from the row OFFSET+1, and updates all |
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* of the matrix with Blas-3 xGEMM. |
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* |
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* In some cases, due to catastrophic cancellations, it cannot |
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* factorize NB columns. Hence, the actual number of factorized |
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* columns is returned in KB. |
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* |
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* 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 A that have been factorized in |
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* previous steps. |
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* |
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* NB (input) INTEGER |
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* The number of columns to factorize. |
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* |
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* KB (output) INTEGER |
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* The number of columns actually factorized. |
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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, block A(OFFSET+1:M,1:KB) is the triangular |
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* factor obtained and block A(1:OFFSET,1:N) has been |
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* accordingly pivoted, but no factorized. |
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* The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has |
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* been updated. |
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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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* JPVT(I) = K <==> Column K of the full matrix A has been |
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* permuted into position I in AP. |
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* |
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* TAU (output) COMPLEX*16 array, dimension (KB) |
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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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* AUXV (input/output) COMPLEX*16 array, dimension (NB) |
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* Auxiliar vector. |
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* |
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* F (input/output) COMPLEX*16 array, dimension (LDF,NB) |
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* Matrix F' = L*Y'*A. |
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* |
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* LDF (input) INTEGER |
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* The leading dimension of the array F. LDF >= max(1,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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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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COMPLEX*16 AKK |
COMPLEX*16 AKK |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL ZGEMM, ZGEMV, ZLARFP, ZSWAP |
EXTERNAL ZGEMM, ZGEMV, ZLARFG, ZSWAP |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC ABS, DBLE, DCONJG, MAX, MIN, NINT, SQRT |
INTRINSIC ABS, DBLE, DCONJG, MAX, MIN, NINT, SQRT |
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END IF |
END IF |
* |
* |
* Apply previous Householder reflectors to column K: |
* Apply previous Householder reflectors to column K: |
* A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'. |
* A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)**H. |
* |
* |
IF( K.GT.1 ) THEN |
IF( K.GT.1 ) THEN |
DO 20 J = 1, K - 1 |
DO 20 J = 1, K - 1 |
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* Generate elementary reflector H(k). |
* Generate elementary reflector H(k). |
* |
* |
IF( RK.LT.M ) THEN |
IF( RK.LT.M ) THEN |
CALL ZLARFP( M-RK+1, A( RK, K ), A( RK+1, K ), 1, TAU( K ) ) |
CALL ZLARFG( M-RK+1, A( RK, K ), A( RK+1, K ), 1, TAU( K ) ) |
ELSE |
ELSE |
CALL ZLARFP( 1, A( RK, K ), A( RK, K ), 1, TAU( K ) ) |
CALL ZLARFG( 1, A( RK, K ), A( RK, K ), 1, TAU( K ) ) |
END IF |
END IF |
* |
* |
AKK = A( RK, K ) |
AKK = A( RK, K ) |
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* |
* |
* Compute Kth column of F: |
* Compute Kth column of F: |
* |
* |
* Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K). |
* Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)**H*A(RK:M,K). |
* |
* |
IF( K.LT.N ) THEN |
IF( K.LT.N ) THEN |
CALL ZGEMV( 'Conjugate transpose', M-RK+1, N-K, TAU( K ), |
CALL ZGEMV( 'Conjugate transpose', M-RK+1, N-K, TAU( K ), |
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40 CONTINUE |
40 CONTINUE |
* |
* |
* Incremental updating of F: |
* Incremental updating of F: |
* F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)' |
* F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)**H |
* *A(RK:M,K). |
* *A(RK:M,K). |
* |
* |
IF( K.GT.1 ) THEN |
IF( K.GT.1 ) THEN |
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END IF |
END IF |
* |
* |
* Update the current row of A: |
* Update the current row of A: |
* A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'. |
* A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)**H. |
* |
* |
IF( K.LT.N ) THEN |
IF( K.LT.N ) THEN |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', 1, N-K, |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', 1, N-K, |
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* |
* |
* Apply the block reflector to the rest of the matrix: |
* Apply the block reflector to the rest of the matrix: |
* A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - |
* A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - |
* A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)'. |
* A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)**H. |
* |
* |
IF( KB.LT.MIN( N, M-OFFSET ) ) THEN |
IF( KB.LT.MIN( N, M-OFFSET ) ) THEN |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', M-RK, N-KB, |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', M-RK, N-KB, |