version 1.2, 2010/04/21 13:45:22
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version 1.17, 2018/05/29 07:18:03
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*> \brief \b DORGRQ |
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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 DORGRQ + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgrq.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/dorgrq.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/dorgrq.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 DORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INFO, K, LDA, LWORK, M, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION 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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*> DORGRQ generates an M-by-N real matrix Q with orthonormal rows, |
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*> which is defined as the last M rows of a product of K elementary |
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*> reflectors of order N |
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*> |
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*> Q = H(1) H(2) . . . H(k) |
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*> |
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*> as returned by DGERQF. |
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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 Q. 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 Q. N >= M. |
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*> \endverbatim |
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*> |
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*> \param[in] K |
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*> \verbatim |
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*> K is INTEGER |
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*> The number of elementary reflectors whose product defines the |
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*> matrix Q. M >= K >= 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 DOUBLE PRECISION array, dimension (LDA,N) |
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*> On entry, the (m-k+i)-th row must contain the vector which |
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*> defines the elementary reflector H(i), for i = 1,2,...,k, as |
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*> returned by DGERQF in the last k rows of its array argument |
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*> A. |
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*> On exit, the M-by-N matrix Q. |
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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 first dimension of the array A. LDA >= max(1,M). |
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*> \endverbatim |
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*> |
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*> \param[in] TAU |
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*> \verbatim |
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*> TAU is DOUBLE PRECISION array, dimension (K) |
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*> TAU(i) must contain the scalar factor of the elementary |
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*> reflector H(i), as returned by DGERQF. |
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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 DOUBLE PRECISION 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 >= max(1,M). |
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*> For optimum performance LWORK >= M*NB, where NB is the |
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*> 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] 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 has 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 December 2016 |
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* |
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*> \ingroup doubleOTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) |
SUBROUTINE DORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- 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..-- |
* November 2006 |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, K, LDA, LWORK, M, N |
INTEGER INFO, K, LDA, LWORK, M, N |
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DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) |
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DORGRQ generates an M-by-N real matrix Q with orthonormal rows, |
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* which is defined as the last M rows of a product of K elementary |
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* reflectors of order N |
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* |
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* Q = H(1) H(2) . . . H(k) |
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* |
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* as returned by DGERQF. |
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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 Q. M >= 0. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix Q. N >= M. |
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* |
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* K (input) INTEGER |
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* The number of elementary reflectors whose product defines the |
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* matrix Q. M >= K >= 0. |
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* |
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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
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* On entry, the (m-k+i)-th row must contain the vector which |
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* defines the elementary reflector H(i), for i = 1,2,...,k, as |
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* returned by DGERQF in the last k rows of its array argument |
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* A. |
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* On exit, the M-by-N matrix Q. |
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* |
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* LDA (input) INTEGER |
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* The first dimension of the array A. LDA >= max(1,M). |
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* |
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* TAU (input) DOUBLE PRECISION array, dimension (K) |
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* TAU(i) must contain the scalar factor of the elementary |
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* reflector H(i), as returned by DGERQF. |
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* |
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* WORK (workspace/output) DOUBLE PRECISION 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 >= max(1,M). |
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* For optimum performance LWORK >= M*NB, where NB is the |
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* 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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* INFO (output) INTEGER |
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* = 0: successful exit |
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* < 0: if INFO = -i, the i-th argument has an illegal value |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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CALL DLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB, |
CALL DLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB, |
$ A( II, 1 ), LDA, TAU( I ), WORK, LDWORK ) |
$ A( II, 1 ), LDA, TAU( I ), WORK, LDWORK ) |
* |
* |
* Apply H' to A(1:m-k+i-1,1:n-k+i+ib-1) from the right |
* Apply H**T to A(1:m-k+i-1,1:n-k+i+ib-1) from the right |
* |
* |
CALL DLARFB( 'Right', 'Transpose', 'Backward', 'Rowwise', |
CALL DLARFB( 'Right', 'Transpose', 'Backward', 'Rowwise', |
$ II-1, N-K+I+IB-1, IB, A( II, 1 ), LDA, WORK, |
$ II-1, N-K+I+IB-1, IB, A( II, 1 ), LDA, WORK, |
$ LDWORK, A, LDA, WORK( IB+1 ), LDWORK ) |
$ LDWORK, A, LDA, WORK( IB+1 ), LDWORK ) |
END IF |
END IF |
* |
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* Apply H' to columns 1:n-k+i+ib-1 of current block |
* Apply H**T to columns 1:n-k+i+ib-1 of current block |
* |
* |
CALL DORGR2( IB, N-K+I+IB-1, IB, A( II, 1 ), LDA, TAU( I ), |
CALL DORGR2( IB, N-K+I+IB-1, IB, A( II, 1 ), LDA, TAU( I ), |
$ WORK, IINFO ) |
$ WORK, IINFO ) |