version 1.6, 2010/08/13 21:03:54
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version 1.13, 2014/01/27 09:28:25
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*> \brief \b DORMRZ |
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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 DORMRZ + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormrz.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/dormrz.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/dormrz.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 DORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, |
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* WORK, LWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER SIDE, TRANS |
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* INTEGER INFO, K, L, LDA, LDC, LWORK, M, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), 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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*> DORMRZ overwrites the general real M-by-N matrix C with |
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*> |
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*> SIDE = 'L' SIDE = 'R' |
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*> TRANS = 'N': Q * C C * Q |
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*> TRANS = 'T': Q**T * C C * Q**T |
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*> |
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*> where Q is a real orthogonal matrix defined as the product of k |
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*> elementary reflectors |
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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 DTZRZF. Q is of order M if SIDE = 'L' and of order N |
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*> if SIDE = 'R'. |
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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] SIDE |
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*> \verbatim |
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*> SIDE is CHARACTER*1 |
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*> = 'L': apply Q or Q**T from the Left; |
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*> = 'R': apply Q or Q**T from the Right. |
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*> \endverbatim |
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*> |
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*> \param[in] TRANS |
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*> \verbatim |
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*> TRANS is CHARACTER*1 |
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*> = 'N': No transpose, apply Q; |
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*> = 'T': Transpose, apply Q**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 C. 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 C. N >= 0. |
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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 |
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*> the matrix Q. |
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*> If SIDE = 'L', M >= K >= 0; |
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*> if SIDE = 'R', N >= K >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] L |
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*> \verbatim |
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*> L is INTEGER |
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*> The number of columns of the matrix A containing |
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*> the meaningful part of the Householder reflectors. |
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*> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] A |
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*> \verbatim |
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*> A is DOUBLE PRECISION array, dimension |
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*> (LDA,M) if SIDE = 'L', |
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*> (LDA,N) if SIDE = 'R' |
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*> The i-th row must contain the vector which defines the |
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*> elementary reflector H(i), for i = 1,2,...,k, as returned by |
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*> DTZRZF in the last k rows of its array argument A. |
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*> A is modified by the routine but restored on exit. |
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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,K). |
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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 DTZRZF. |
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*> \endverbatim |
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*> |
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*> \param[in,out] C |
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*> \verbatim |
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*> C is DOUBLE PRECISION array, dimension (LDC,N) |
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*> On entry, the M-by-N matrix C. |
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*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. |
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*> \endverbatim |
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*> |
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*> \param[in] LDC |
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*> \verbatim |
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*> LDC is INTEGER |
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*> The leading dimension of the array C. LDC >= max(1,M). |
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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. |
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*> If SIDE = 'L', LWORK >= max(1,N); |
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*> if SIDE = 'R', LWORK >= max(1,M). |
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*> For optimum performance LWORK >= N*NB if SIDE = 'L', and |
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*> LWORK >= M*NB if SIDE = 'R', where NB is the optimal |
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*> 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 November 2011 |
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* |
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*> \ingroup doubleOTHERcomputational |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
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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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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE DORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, |
SUBROUTINE DORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, |
$ WORK, LWORK, INFO ) |
$ WORK, LWORK, 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..-- |
* January 2007 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER SIDE, TRANS |
CHARACTER SIDE, TRANS |
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DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) |
DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DORMRZ overwrites the general real M-by-N matrix C with |
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* |
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* SIDE = 'L' SIDE = 'R' |
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* TRANS = 'N': Q * C C * Q |
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* TRANS = 'T': Q**T * C C * Q**T |
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* |
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* where Q is a real orthogonal matrix defined as the product of k |
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* elementary reflectors |
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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 DTZRZF. Q is of order M if SIDE = 'L' and of order N |
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* if SIDE = 'R'. |
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* |
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* Arguments |
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* ========= |
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* |
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* SIDE (input) CHARACTER*1 |
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* = 'L': apply Q or Q**T from the Left; |
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* = 'R': apply Q or Q**T from the Right. |
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* |
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* TRANS (input) CHARACTER*1 |
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* = 'N': No transpose, apply Q; |
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* = 'T': Transpose, apply Q**T. |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix C. M >= 0. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix C. N >= 0. |
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* |
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* K (input) INTEGER |
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* The number of elementary reflectors whose product defines |
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* the matrix Q. |
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* If SIDE = 'L', M >= K >= 0; |
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* if SIDE = 'R', N >= K >= 0. |
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* |
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* L (input) INTEGER |
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* The number of columns of the matrix A containing |
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* the meaningful part of the Householder reflectors. |
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* If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. |
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* |
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* A (input) DOUBLE PRECISION array, dimension |
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* (LDA,M) if SIDE = 'L', |
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* (LDA,N) if SIDE = 'R' |
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* The i-th row must contain the vector which defines the |
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* elementary reflector H(i), for i = 1,2,...,k, as returned by |
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* DTZRZF in the last k rows of its array argument A. |
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* A is modified by the routine but restored on exit. |
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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,K). |
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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 DTZRZF. |
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* |
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* C (input/output) DOUBLE PRECISION array, dimension (LDC,N) |
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* On entry, the M-by-N matrix C. |
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* On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. |
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* |
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* LDC (input) INTEGER |
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* The leading dimension of the array C. LDC >= max(1,M). |
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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. |
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* If SIDE = 'L', LWORK >= max(1,N); |
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* if SIDE = 'R', LWORK >= max(1,M). |
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* For optimum performance LWORK >= N*NB if SIDE = 'L', and |
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* LWORK >= M*NB if SIDE = 'R', where NB is the optimal |
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* 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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* Further Details |
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* =============== |
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* |
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* Based on contributions by |
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* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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* |
* |
IF( LEFT ) THEN |
IF( LEFT ) THEN |
* |
* |
* H or H' is applied to C(i:m,1:n) |
* H or H**T is applied to C(i:m,1:n) |
* |
* |
MI = M - I + 1 |
MI = M - I + 1 |
IC = I |
IC = I |
ELSE |
ELSE |
* |
* |
* H or H' is applied to C(1:m,i:n) |
* H or H**T is applied to C(1:m,i:n) |
* |
* |
NI = N - I + 1 |
NI = N - I + 1 |
JC = I |
JC = I |
END IF |
END IF |
* |
* |
* Apply H or H' |
* Apply H or H**T |
* |
* |
CALL DLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI, |
CALL DLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI, |
$ IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ), |
$ IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ), |