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version 1.9, 2011/11/21 20:43:09
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*> \brief \b ZGEQP3 |
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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 ZGEQP3 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeqp3.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/zgeqp3.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/zgeqp3.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 ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, |
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* INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INFO, LDA, LWORK, M, N |
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* .. |
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* .. Array Arguments .. |
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* INTEGER JPVT( * ) |
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* DOUBLE PRECISION RWORK( * ) |
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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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*> ZGEQP3 computes a QR factorization with column pivoting of a |
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*> matrix A: A*P = Q*R using Level 3 BLAS. |
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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,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 the array contains the |
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*> min(M,N)-by-N upper trapezoidal matrix R; the elements below |
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*> the diagonal, together with the array TAU, represent the |
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*> unitary matrix Q as a product of min(M,N) elementary |
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*> reflectors. |
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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(J).ne.0, the J-th column of A is permuted |
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*> to the front of A*P (a leading column); if JPVT(J)=0, |
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*> the J-th column of A is a free column. |
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*> On exit, if JPVT(J)=K, then the J-th column of A*P was the |
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*> 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[out] WORK |
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*> \verbatim |
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*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) |
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*> On exit, if INFO=0, WORK(1) returns the optimal LWORK. |
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*> \endverbatim |
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*> |
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*> \param[in] LWORK |
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*> \verbatim |
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*> LWORK is INTEGER |
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*> The dimension of the array WORK. LWORK >= N+1. |
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*> For optimal performance LWORK >= ( N+1 )*NB, where NB |
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*> is the optimal blocksize. |
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*> |
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*> If LWORK = -1, then a workspace query is assumed; the routine |
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*> only calculates the optimal size of the WORK array, returns |
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*> this value as the first entry of the WORK array, and no error |
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*> message related to LWORK is issued by XERBLA. |
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*> \endverbatim |
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*> |
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*> \param[out] RWORK |
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*> \verbatim |
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*> RWORK is DOUBLE PRECISION array, dimension (2*N) |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit. |
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*> < 0: if INFO = -i, the i-th argument had an illegal value. |
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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 November 2011 |
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* |
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*> \ingroup complex16GEcomputational |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> The matrix Q is represented as a product of elementary reflectors |
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*> |
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*> Q = H(1) H(2) . . . H(k), where k = min(m,n). |
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*> |
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*> Each H(i) has the form |
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*> |
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*> H(i) = I - tau * v * v**H |
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*> |
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*> where tau is a real/complex scalar, and v is a real/complex vector |
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*> with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in |
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*> A(i+1:m,i), and tau in TAU(i). |
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*> \endverbatim |
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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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*> |
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* ===================================================================== |
SUBROUTINE ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, |
SUBROUTINE ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, |
$ INFO ) |
$ INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational 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..-- |
* November 2006 |
* November 2011 |
* |
* |
* .. 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 |
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* ======= |
|
* |
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* ZGEQP3 computes a QR factorization with column pivoting of a |
|
* matrix A: A*P = Q*R using Level 3 BLAS. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
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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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* 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 the array contains the |
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* min(M,N)-by-N upper trapezoidal matrix R; the elements below |
|
* the diagonal, together with the array TAU, represent the |
|
* unitary matrix Q as a product of min(M,N) elementary |
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* reflectors. |
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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(J).ne.0, the J-th column of A is permuted |
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* to the front of A*P (a leading column); if JPVT(J)=0, |
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* the J-th column of A is a free column. |
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* On exit, if JPVT(J)=K, then the J-th column of A*P was the |
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* 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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* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) |
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* On exit, if INFO=0, WORK(1) returns the optimal LWORK. |
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* |
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* LWORK (input) INTEGER |
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* The dimension of the array WORK. LWORK >= N+1. |
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* For optimal performance LWORK >= ( N+1 )*NB, where NB |
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* is the optimal blocksize. |
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* |
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* If LWORK = -1, then a workspace query is assumed; the routine |
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* only calculates the optimal size of the WORK array, returns |
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* this value as the first entry of the WORK array, and no error |
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* message related to LWORK is issued by XERBLA. |
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* |
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* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit. |
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* < 0: if INFO = -i, the i-th argument had an illegal value. |
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* |
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* Further Details |
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* =============== |
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* |
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* The matrix Q is represented as a product of elementary reflectors |
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* |
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* Q = H(1) H(2) . . . H(k), where k = min(m,n). |
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* |
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* Each H(i) has the form |
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* |
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* H(i) = I - tau * v * v' |
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* |
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* where tau is a real/complex scalar, and v is a real/complex vector |
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* with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in |
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* A(i+1:m,i), and tau in TAU(i). |
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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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* .. Executable Statements .. |
* .. Executable Statements .. |
* |
* |
* Test input arguments |
* Test input arguments |
* ==================== |
* ==================== |
* |
* |
INFO = 0 |
INFO = 0 |
LQUERY = ( LWORK.EQ.-1 ) |
LQUERY = ( LWORK.EQ.-1 ) |
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NFXD = NFXD - 1 |
NFXD = NFXD - 1 |
* |
* |
* Factorize fixed columns |
* Factorize fixed columns |
* ======================= |
* ======================= |
* |
* |
* Compute the QR factorization of fixed columns and update |
* Compute the QR factorization of fixed columns and update |
* remaining columns. |
* remaining columns. |
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END IF |
END IF |
* |
* |
* Factorize free columns |
* Factorize free columns |
* ====================== |
* ====================== |
* |
* |
IF( NFXD.LT.MINMN ) THEN |
IF( NFXD.LT.MINMN ) THEN |
* |
* |