version 1.1, 2010/01/26 15:22:45
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version 1.19, 2023/08/07 08:38:58
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*> \brief \b DLARZB applies a block reflector or its transpose to a general matrix. |
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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 DLARZB + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarzb.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/dlarzb.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/dlarzb.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 DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, |
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* LDV, T, LDT, C, LDC, WORK, LDWORK ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER DIRECT, SIDE, STOREV, TRANS |
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* INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), |
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* $ WORK( LDWORK, * ) |
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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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*> DLARZB applies a real block reflector H or its transpose H**T to |
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*> a real distributed M-by-N C from the left or the right. |
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*> |
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*> Currently, only STOREV = 'R' and DIRECT = 'B' are supported. |
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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 H or H**T from the Left |
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*> = 'R': apply H or H**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 H (No transpose) |
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*> = 'C': apply H**T (Transpose) |
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*> \endverbatim |
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*> |
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*> \param[in] DIRECT |
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*> \verbatim |
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*> DIRECT is CHARACTER*1 |
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*> Indicates how H is formed from a product of elementary |
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*> reflectors |
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*> = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet) |
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*> = 'B': H = H(k) . . . H(2) H(1) (Backward) |
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*> \endverbatim |
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*> |
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*> \param[in] STOREV |
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*> \verbatim |
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*> STOREV is CHARACTER*1 |
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*> Indicates how the vectors which define the elementary |
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*> reflectors are stored: |
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*> = 'C': Columnwise (not supported yet) |
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*> = 'R': Rowwise |
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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. |
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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. |
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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 order of the matrix T (= the number of elementary |
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*> reflectors whose product defines the block reflector). |
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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 V containing the |
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*> 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] V |
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*> \verbatim |
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*> V is DOUBLE PRECISION array, dimension (LDV,NV). |
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*> If STOREV = 'C', NV = K; if STOREV = 'R', NV = L. |
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*> \endverbatim |
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*> |
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*> \param[in] LDV |
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*> \verbatim |
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*> LDV is INTEGER |
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*> The leading dimension of the array V. |
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*> If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K. |
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*> \endverbatim |
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*> |
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*> \param[in] T |
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*> \verbatim |
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*> T is DOUBLE PRECISION array, dimension (LDT,K) |
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*> The triangular K-by-K matrix T in the representation of the |
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*> block reflector. |
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*> \endverbatim |
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*> |
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*> \param[in] LDT |
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*> \verbatim |
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*> LDT is INTEGER |
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*> The leading dimension of the array T. LDT >= K. |
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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 H*C or H**T*C or C*H or C*H**T. |
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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 (LDWORK,K) |
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*> \endverbatim |
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*> |
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*> \param[in] LDWORK |
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*> \verbatim |
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*> LDWORK is INTEGER |
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*> The leading dimension of the array WORK. |
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*> If SIDE = 'L', LDWORK >= max(1,N); |
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*> if SIDE = 'R', LDWORK >= max(1,M). |
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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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*> \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 DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, |
SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, |
$ LDV, T, LDT, C, LDC, WORK, LDWORK ) |
$ LDV, T, LDT, C, LDC, WORK, LDWORK ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine -- |
* -- 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 |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER DIRECT, SIDE, STOREV, TRANS |
CHARACTER DIRECT, SIDE, STOREV, TRANS |
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$ WORK( LDWORK, * ) |
$ WORK( LDWORK, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DLARZB applies a real block reflector H or its transpose H**T to |
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* a real distributed M-by-N C from the left or the right. |
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* |
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* Currently, only STOREV = 'R' and DIRECT = 'B' are supported. |
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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 H or H' from the Left |
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* = 'R': apply H or H' from the Right |
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* |
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* TRANS (input) CHARACTER*1 |
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* = 'N': apply H (No transpose) |
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* = 'C': apply H' (Transpose) |
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* |
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* DIRECT (input) CHARACTER*1 |
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* Indicates how H is formed from a product of elementary |
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* reflectors |
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* = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet) |
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* = 'B': H = H(k) . . . H(2) H(1) (Backward) |
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* |
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* STOREV (input) CHARACTER*1 |
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* Indicates how the vectors which define the elementary |
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* reflectors are stored: |
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* = 'C': Columnwise (not supported yet) |
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* = 'R': Rowwise |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix C. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix C. |
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* |
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* K (input) INTEGER |
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* The order of the matrix T (= the number of elementary |
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* reflectors whose product defines the block reflector). |
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* |
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* L (input) INTEGER |
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* The number of columns of the matrix V containing the |
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* 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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* V (input) DOUBLE PRECISION array, dimension (LDV,NV). |
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* If STOREV = 'C', NV = K; if STOREV = 'R', NV = L. |
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* |
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* LDV (input) INTEGER |
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* The leading dimension of the array V. |
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* If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K. |
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* |
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* T (input) DOUBLE PRECISION array, dimension (LDT,K) |
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* The triangular K-by-K matrix T in the representation of the |
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* block reflector. |
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* |
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* LDT (input) INTEGER |
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* The leading dimension of the array T. LDT >= K. |
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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 H*C or H'*C or C*H or C*H'. |
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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 (LDWORK,K) |
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* |
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* LDWORK (input) INTEGER |
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* The leading dimension of the array WORK. |
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* If SIDE = 'L', LDWORK >= max(1,N); |
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* if SIDE = 'R', LDWORK >= max(1,M). |
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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( LSAME( SIDE, 'L' ) ) THEN |
IF( LSAME( SIDE, 'L' ) ) THEN |
* |
* |
* Form H * C or H' * C |
* Form H * C or H**T * C |
* |
* |
* W( 1:n, 1:k ) = C( 1:k, 1:n )' |
* W( 1:n, 1:k ) = C( 1:k, 1:n )**T |
* |
* |
DO 10 J = 1, K |
DO 10 J = 1, K |
CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) |
CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) |
10 CONTINUE |
10 CONTINUE |
* |
* |
* W( 1:n, 1:k ) = W( 1:n, 1:k ) + ... |
* W( 1:n, 1:k ) = W( 1:n, 1:k ) + ... |
* C( m-l+1:m, 1:n )' * V( 1:k, 1:l )' |
* C( m-l+1:m, 1:n )**T * V( 1:k, 1:l )**T |
* |
* |
IF( L.GT.0 ) |
IF( L.GT.0 ) |
$ CALL DGEMM( 'Transpose', 'Transpose', N, K, L, ONE, |
$ CALL DGEMM( 'Transpose', 'Transpose', N, K, L, ONE, |
$ C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK, LDWORK ) |
$ C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK, LDWORK ) |
* |
* |
* W( 1:n, 1:k ) = W( 1:n, 1:k ) * T' or W( 1:m, 1:k ) * T |
* W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T |
* |
* |
CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T, |
CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T, |
$ LDT, WORK, LDWORK ) |
$ LDT, WORK, LDWORK ) |
* |
* |
* C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )' |
* C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**T |
* |
* |
DO 30 J = 1, N |
DO 30 J = 1, N |
DO 20 I = 1, K |
DO 20 I = 1, K |
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30 CONTINUE |
30 CONTINUE |
* |
* |
* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ... |
* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ... |
* V( 1:k, 1:l )' * W( 1:n, 1:k )' |
* V( 1:k, 1:l )**T * W( 1:n, 1:k )**T |
* |
* |
IF( L.GT.0 ) |
IF( L.GT.0 ) |
$ CALL DGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV, |
$ CALL DGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV, |
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* |
* |
ELSE IF( LSAME( SIDE, 'R' ) ) THEN |
ELSE IF( LSAME( SIDE, 'R' ) ) THEN |
* |
* |
* Form C * H or C * H' |
* Form C * H or C * H**T |
* |
* |
* W( 1:m, 1:k ) = C( 1:m, 1:k ) |
* W( 1:m, 1:k ) = C( 1:m, 1:k ) |
* |
* |
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40 CONTINUE |
40 CONTINUE |
* |
* |
* W( 1:m, 1:k ) = W( 1:m, 1:k ) + ... |
* W( 1:m, 1:k ) = W( 1:m, 1:k ) + ... |
* C( 1:m, n-l+1:n ) * V( 1:k, 1:l )' |
* C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**T |
* |
* |
IF( L.GT.0 ) |
IF( L.GT.0 ) |
$ CALL DGEMM( 'No transpose', 'Transpose', M, K, L, ONE, |
$ CALL DGEMM( 'No transpose', 'Transpose', M, K, L, ONE, |
$ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK ) |
$ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK ) |
* |
* |
* W( 1:m, 1:k ) = W( 1:m, 1:k ) * T or W( 1:m, 1:k ) * T' |
* W( 1:m, 1:k ) = W( 1:m, 1:k ) * T or W( 1:m, 1:k ) * T**T |
* |
* |
CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T, |
CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T, |
$ LDT, WORK, LDWORK ) |
$ LDT, WORK, LDWORK ) |