version 1.8, 2011/07/22 07:38:07
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version 1.9, 2011/11/21 20:42:57
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*> \brief \b DLARFB |
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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 DLARFB + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfb.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/dlarfb.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/dlarfb.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 DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, |
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* 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, 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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*> DLARFB applies a real block reflector H or its transpose H**T to a |
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*> real m by n matrix C, from either the left or the right. |
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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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*> = 'T': 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) |
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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 |
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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] V |
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*> \verbatim |
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*> V is DOUBLE PRECISION array, dimension |
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*> (LDV,K) if STOREV = 'C' |
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*> (LDV,M) if STOREV = 'R' and SIDE = 'L' |
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*> (LDV,N) if STOREV = 'R' and SIDE = 'R' |
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*> The matrix V. See Further Details. |
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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' and SIDE = 'L', LDV >= max(1,M); |
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*> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); |
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*> 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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*> \date November 2011 |
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* |
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*> \ingroup doubleOTHERauxiliary |
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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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*> |
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*> The shape of the matrix V and the storage of the vectors which define |
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*> the H(i) is best illustrated by the following example with n = 5 and |
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*> k = 3. The elements equal to 1 are not stored; the corresponding |
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*> array elements are modified but restored on exit. The rest of the |
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*> array is not used. |
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*> |
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*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': |
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*> |
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*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) |
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*> ( v1 1 ) ( 1 v2 v2 v2 ) |
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*> ( v1 v2 1 ) ( 1 v3 v3 ) |
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*> ( v1 v2 v3 ) |
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*> ( v1 v2 v3 ) |
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*> |
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*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': |
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*> |
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*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) |
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*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) |
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*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) |
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*> ( 1 v3 ) |
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*> ( 1 ) |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, |
SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, |
$ T, LDT, C, LDC, WORK, LDWORK ) |
$ T, LDT, C, LDC, WORK, LDWORK ) |
IMPLICIT NONE |
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* |
* |
* -- LAPACK auxiliary routine (version 3.3.1) -- |
* -- LAPACK auxiliary 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..-- |
* -- April 2011 -- |
* November 2011 |
* |
* |
* .. 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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* DLARFB applies a real block reflector H or its transpose H**T to a |
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* real m by n matrix C, from either the left or the right. |
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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**T from the Left |
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* = 'R': apply H or H**T 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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* = 'T': apply H**T (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) |
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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 |
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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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* V (input) DOUBLE PRECISION array, dimension |
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* (LDV,K) if STOREV = 'C' |
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* (LDV,M) if STOREV = 'R' and SIDE = 'L' |
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* (LDV,N) if STOREV = 'R' and SIDE = 'R' |
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* The matrix V. See Further Details. |
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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' and SIDE = 'L', LDV >= max(1,M); |
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* if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); |
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* 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**T*C or C*H or C*H**T. |
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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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* The shape of the matrix V and the storage of the vectors which define |
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* the H(i) is best illustrated by the following example with n = 5 and |
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* k = 3. The elements equal to 1 are not stored; the corresponding |
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* array elements are modified but restored on exit. The rest of the |
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* array is not used. |
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* |
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* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': |
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* |
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* V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) |
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* ( v1 1 ) ( 1 v2 v2 v2 ) |
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* ( v1 v2 1 ) ( 1 v3 v3 ) |
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* ( v1 v2 v3 ) |
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* ( v1 v2 v3 ) |
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* |
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* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': |
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* |
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* V = ( v1 v2 v3 ) V = ( v1 v1 1 ) |
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* ( v1 v2 v3 ) ( v2 v2 v2 1 ) |
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* ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) |
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* ( 1 v3 ) |
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* ( 1 ) |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |