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321 lines
8.8 KiB
321 lines
8.8 KiB
2 years ago
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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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* =====================================================================
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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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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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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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*
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* .. Parameters ..
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DOUBLE PRECISION ONE
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PARAMETER ( ONE = 1.0D+0 )
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* ..
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* .. Local Scalars ..
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CHARACTER TRANST
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INTEGER I, INFO, J
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL DCOPY, DGEMM, DTRMM, XERBLA
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* ..
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* .. Executable Statements ..
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*
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* Quick return if possible
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*
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IF( M.LE.0 .OR. N.LE.0 )
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$ RETURN
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*
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* Check for currently supported options
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*
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INFO = 0
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IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
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INFO = -3
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ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
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INFO = -4
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DLARZB', -INFO )
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RETURN
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END IF
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*
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IF( LSAME( TRANS, 'N' ) ) THEN
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TRANST = 'T'
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ELSE
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TRANST = 'N'
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END IF
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*
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IF( LSAME( SIDE, 'L' ) ) THEN
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*
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* Form H * C or H**T * C
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*
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* W( 1:n, 1:k ) = C( 1:k, 1:n )**T
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*
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DO 10 J = 1, K
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CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
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10 CONTINUE
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*
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* W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
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* C( m-l+1:m, 1:n )**T * V( 1:k, 1:l )**T
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*
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IF( L.GT.0 )
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$ CALL DGEMM( 'Transpose', 'Transpose', N, K, L, ONE,
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$ C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK, LDWORK )
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*
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* W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T
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*
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CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
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$ LDT, WORK, LDWORK )
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*
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* C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**T
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*
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DO 30 J = 1, N
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DO 20 I = 1, K
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C( I, J ) = C( I, J ) - WORK( J, I )
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20 CONTINUE
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30 CONTINUE
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*
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* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
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* V( 1:k, 1:l )**T * W( 1:n, 1:k )**T
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*
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IF( L.GT.0 )
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$ CALL DGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
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$ WORK, LDWORK, ONE, C( M-L+1, 1 ), LDC )
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*
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ELSE IF( LSAME( SIDE, 'R' ) ) THEN
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*
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* Form C * H or C * H**T
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*
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* W( 1:m, 1:k ) = C( 1:m, 1:k )
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*
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DO 40 J = 1, K
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CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
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40 CONTINUE
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*
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* W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
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* C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**T
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*
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IF( L.GT.0 )
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$ CALL DGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
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$ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
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*
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* W( 1:m, 1:k ) = W( 1:m, 1:k ) * T or W( 1:m, 1:k ) * T**T
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*
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CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
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$ LDT, WORK, LDWORK )
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*
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* C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
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*
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DO 60 J = 1, K
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DO 50 I = 1, M
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C( I, J ) = C( I, J ) - WORK( I, J )
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50 CONTINUE
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60 CONTINUE
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*
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* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
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* W( 1:m, 1:k ) * V( 1:k, 1:l )
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*
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IF( L.GT.0 )
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$ CALL DGEMM( 'No transpose', 'No transpose', M, L, K, -ONE,
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$ WORK, LDWORK, V, LDV, ONE, C( 1, N-L+1 ), LDC )
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*
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END IF
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*
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RETURN
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*
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* End of DLARZB
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*
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END
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