version 1.8, 2011/07/22 07:38:08
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version 1.12, 2012/08/22 09:48:21
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*> \brief \b DORGBR |
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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 DORGBR + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgbr.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/dorgbr.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/dorgbr.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 DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER VECT |
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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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*> DORGBR generates one of the real orthogonal matrices Q or P**T |
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*> determined by DGEBRD when reducing a real matrix A to bidiagonal |
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*> form: A = Q * B * P**T. Q and P**T are defined as products of |
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*> elementary reflectors H(i) or G(i) respectively. |
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*> |
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*> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q |
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*> is of order M: |
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*> if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n |
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*> columns of Q, where m >= n >= k; |
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*> if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an |
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*> M-by-M matrix. |
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*> |
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*> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T |
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*> is of order N: |
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*> if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m |
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*> rows of P**T, where n >= m >= k; |
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*> if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as |
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*> an N-by-N matrix. |
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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] VECT |
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*> \verbatim |
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*> VECT is CHARACTER*1 |
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*> Specifies whether the matrix Q or the matrix P**T is |
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*> required, as defined in the transformation applied by DGEBRD: |
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*> = 'Q': generate Q; |
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*> = 'P': generate P**T. |
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*> \endverbatim |
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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 or P**T to be returned. |
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*> 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 or P**T to be returned. |
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*> N >= 0. |
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*> If VECT = 'Q', M >= N >= min(M,K); |
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*> if VECT = 'P', N >= M >= min(N,K). |
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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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*> If VECT = 'Q', the number of columns in the original M-by-K |
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*> matrix reduced by DGEBRD. |
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*> If VECT = 'P', the number of rows in the original K-by-N |
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*> matrix reduced by DGEBRD. |
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*> 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 vectors which define the elementary reflectors, |
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*> as returned by DGEBRD. |
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*> On exit, the M-by-N matrix Q or P**T. |
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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] TAU |
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*> \verbatim |
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*> TAU is DOUBLE PRECISION array, dimension |
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*> (min(M,K)) if VECT = 'Q' |
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*> (min(N,K)) if VECT = 'P' |
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*> TAU(i) must contain the scalar factor of the elementary |
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*> reflector H(i) or G(i), which determines Q or P**T, as |
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*> returned by DGEBRD in its array argument TAUQ or TAUP. |
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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,min(M,N)). |
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*> For optimum performance LWORK >= min(M,N)*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] 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 April 2012 |
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* |
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*> \ingroup doubleGBcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) |
SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.4.1) -- |
* -- 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 |
* April 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER VECT |
CHARACTER VECT |
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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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* DORGBR generates one of the real orthogonal matrices Q or P**T |
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* determined by DGEBRD when reducing a real matrix A to bidiagonal |
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* form: A = Q * B * P**T. Q and P**T are defined as products of |
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* elementary reflectors H(i) or G(i) respectively. |
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* |
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* If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q |
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* is of order M: |
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* if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n |
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* columns of Q, where m >= n >= k; |
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* if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an |
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* M-by-M matrix. |
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* |
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* If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T |
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* is of order N: |
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* if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m |
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* rows of P**T, where n >= m >= k; |
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* if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as |
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* an N-by-N matrix. |
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* |
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* Arguments |
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* ========= |
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* |
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* VECT (input) CHARACTER*1 |
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* Specifies whether the matrix Q or the matrix P**T is |
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* required, as defined in the transformation applied by DGEBRD: |
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* = 'Q': generate Q; |
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* = 'P': generate P**T. |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix Q or P**T to be returned. |
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* 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 or P**T to be returned. |
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* N >= 0. |
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* If VECT = 'Q', M >= N >= min(M,K); |
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* if VECT = 'P', N >= M >= min(N,K). |
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* |
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* K (input) INTEGER |
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* If VECT = 'Q', the number of columns in the original M-by-K |
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* matrix reduced by DGEBRD. |
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* If VECT = 'P', the number of rows in the original K-by-N |
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* matrix reduced by DGEBRD. |
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* 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 vectors which define the elementary reflectors, |
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* as returned by DGEBRD. |
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* On exit, the M-by-N matrix Q or P**T. |
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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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* TAU (input) DOUBLE PRECISION array, dimension |
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* (min(M,K)) if VECT = 'Q' |
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* (min(N,K)) if VECT = 'P' |
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* TAU(i) must contain the scalar factor of the elementary |
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* reflector H(i) or G(i), which determines Q or P**T, as |
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* returned by DGEBRD in its array argument TAUQ or TAUP. |
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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,min(M,N)). |
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* For optimum performance LWORK >= min(M,N)*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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* 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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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
LOGICAL LQUERY, WANTQ |
LOGICAL LQUERY, WANTQ |
INTEGER I, IINFO, J, LWKOPT, MN, NB |
INTEGER I, IINFO, J, LWKOPT, MN |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
LOGICAL LSAME |
LOGICAL LSAME |
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END IF |
END IF |
* |
* |
IF( INFO.EQ.0 ) THEN |
IF( INFO.EQ.0 ) THEN |
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WORK( 1 ) = 1 |
IF( WANTQ ) THEN |
IF( WANTQ ) THEN |
NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 ) |
IF( M.GE.K ) THEN |
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CALL DORGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO ) |
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ELSE |
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IF( M.GT.1 ) THEN |
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CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK, |
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$ -1, IINFO ) |
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END IF |
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END IF |
ELSE |
ELSE |
NB = ILAENV( 1, 'DORGLQ', ' ', M, N, K, -1 ) |
IF( K.LT.N ) THEN |
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CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO ) |
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ELSE |
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IF( N.GT.1 ) THEN |
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CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, |
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$ -1, IINFO ) |
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END IF |
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END IF |
END IF |
END IF |
LWKOPT = MAX( 1, MN )*NB |
LWKOPT = WORK( 1 ) |
WORK( 1 ) = LWKOPT |
LWKOPT = MAX (LWKOPT, MN) |
END IF |
END IF |
* |
* |
IF( INFO.NE.0 ) THEN |
IF( INFO.NE.0 ) THEN |
CALL XERBLA( 'DORGBR', -INFO ) |
CALL XERBLA( 'DORGBR', -INFO ) |
RETURN |
RETURN |
ELSE IF( LQUERY ) THEN |
ELSE IF( LQUERY ) THEN |
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WORK( 1 ) = LWKOPT |
RETURN |
RETURN |
END IF |
END IF |
* |
* |