version 1.1.1.1, 2010/01/26 15:22:45
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version 1.16, 2017/06/17 10:53:59
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*> \brief \b DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm). |
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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 DORMR3 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormr3.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/dormr3.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/dormr3.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 DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, |
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* WORK, 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, 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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*> DORMR3 overwrites the general real m by n matrix C with |
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*> |
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*> Q * C if SIDE = 'L' and TRANS = 'N', or |
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*> |
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*> Q**T* C if SIDE = 'L' and TRANS = 'C', or |
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*> |
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*> C * Q if SIDE = 'R' and TRANS = 'N', or |
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*> |
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*> C * Q**T if SIDE = 'R' and TRANS = 'C', |
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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': apply Q (No transpose) |
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*> = 'T': apply Q**T (Transpose) |
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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**T*C or C*Q**T 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 |
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*> (N) if SIDE = 'L', |
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*> (M) if SIDE = 'R' |
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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 December 2016 |
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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 DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, |
SUBROUTINE DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, |
$ WORK, INFO ) |
$ WORK, 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 .. |
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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* DORMR3 overwrites the general real m by n matrix C with |
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* |
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* Q * C if SIDE = 'L' and TRANS = 'N', or |
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* |
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* Q'* C if SIDE = 'L' and TRANS = 'T', or |
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* |
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* C * Q if SIDE = 'R' and TRANS = 'N', or |
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* |
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* C * Q' if SIDE = 'R' and TRANS = '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' from the Left |
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* = 'R': apply Q or Q' from the Right |
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* |
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* TRANS (input) CHARACTER*1 |
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* = 'N': apply Q (No transpose) |
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* = 'T': apply Q' (Transpose) |
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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'*C or C*Q' 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) DOUBLE PRECISION array, dimension |
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* (N) if SIDE = 'L', |
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* (M) if SIDE = 'R' |
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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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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |
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DO 10 I = I1, I2, I3 |
DO 10 I = I1, I2, I3 |
IF( LEFT ) THEN |
IF( LEFT ) THEN |
* |
* |
* H(i) or H(i)' is applied to C(i:m,1:n) |
* H(i) or H(i)**T is applied to C(i:m,1:n) |
* |
* |
MI = M - I + 1 |
MI = M - I + 1 |
IC = I |
IC = I |
ELSE |
ELSE |
* |
* |
* H(i) or H(i)' is applied to C(1:m,i:n) |
* H(i) or H(i)**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(i) or H(i)' |
* Apply H(i) or H(i)**T |
* |
* |
CALL DLARZ( SIDE, MI, NI, L, A( I, JA ), LDA, TAU( I ), |
CALL DLARZ( SIDE, MI, NI, L, A( I, JA ), LDA, TAU( I ), |
$ C( IC, JC ), LDC, WORK ) |
$ C( IC, JC ), LDC, WORK ) |