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775 lines
23 KiB
FortranFixed
775 lines
23 KiB
FortranFixed
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*> \brief \b ZLARFB
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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 ZLARFB + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarfb.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/zlarfb.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/zlarfb.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 ZLARFB( 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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* COMPLEX*16 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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*> ZLARFB applies a complex block reflector H or its transpose H**H to a
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*> complex 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**H from the Left
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*> = 'R': apply H or H**H 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**H (Conjugate 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 COMPLEX*16 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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*> 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 COMPLEX*16 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 COMPLEX*16 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**H*C or C*H or C*H**H.
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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 COMPLEX*16 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 complex16OTHERauxiliary
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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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* =====================================================================
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SUBROUTINE ZLARFB( 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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* -- LAPACK auxiliary routine (version 3.4.0) --
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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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* November 2011
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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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COMPLEX*16 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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COMPLEX*16 ONE
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PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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CHARACTER TRANST
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INTEGER I, J, LASTV, LASTC
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ILAZLR, ILAZLC
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EXTERNAL LSAME, ILAZLR, ILAZLC
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* ..
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* .. External Subroutines ..
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EXTERNAL ZCOPY, ZGEMM, ZLACGV, ZTRMM
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DCONJG
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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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IF( LSAME( TRANS, 'N' ) ) THEN
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TRANST = 'C'
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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( STOREV, 'C' ) ) THEN
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*
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IF( LSAME( DIRECT, 'F' ) ) THEN
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*
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* Let V = ( V1 ) (first K rows)
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* ( V2 )
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* where V1 is unit lower triangular.
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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**H * C where C = ( C1 )
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* ( C2 )
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*
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LASTV = MAX( K, ILAZLR( M, K, V, LDV ) )
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LASTC = ILAZLC( LASTV, N, C, LDC )
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*
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* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK)
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*
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* W := C1**H
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*
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DO 10 J = 1, K
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CALL ZCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
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CALL ZLACGV( LASTC, WORK( 1, J ), 1 )
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10 CONTINUE
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*
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* W := W * V1
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*
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CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
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$ LASTC, K, ONE, V, LDV, WORK, LDWORK )
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IF( LASTV.GT.K ) THEN
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*
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* W := W + C2**H *V2
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*
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CALL ZGEMM( 'Conjugate transpose', 'No transpose',
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$ LASTC, K, LASTV-K, ONE, C( K+1, 1 ), LDC,
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$ V( K+1, 1 ), LDV, ONE, WORK, LDWORK )
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END IF
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*
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* W := W * T**H or W * T
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*
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CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
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$ LASTC, K, ONE, T, LDT, WORK, LDWORK )
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*
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* C := C - V * W**H
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*
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IF( M.GT.K ) THEN
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*
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* C2 := C2 - V2 * W**H
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*
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CALL ZGEMM( 'No transpose', 'Conjugate transpose',
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$ LASTV-K, LASTC, K,
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$ -ONE, V( K+1, 1 ), LDV, WORK, LDWORK,
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$ ONE, C( K+1, 1 ), LDC )
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END IF
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*
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* W := W * V1**H
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*
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CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',
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$ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
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*
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* C1 := C1 - W**H
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*
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DO 30 J = 1, K
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DO 20 I = 1, LASTC
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C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) )
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20 CONTINUE
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30 CONTINUE
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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**H where C = ( C1 C2 )
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*
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LASTV = MAX( K, ILAZLR( N, K, V, LDV ) )
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LASTC = ILAZLR( M, LASTV, C, LDC )
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*
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* W := C * V = (C1*V1 + C2*V2) (stored in WORK)
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*
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* W := C1
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*
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DO 40 J = 1, K
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CALL ZCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
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40 CONTINUE
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*
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* W := W * V1
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*
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CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
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$ LASTC, K, ONE, V, LDV, WORK, LDWORK )
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IF( LASTV.GT.K ) THEN
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*
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* W := W + C2 * V2
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*
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CALL ZGEMM( 'No transpose', 'No transpose',
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$ LASTC, K, LASTV-K,
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$ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV,
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$ ONE, WORK, LDWORK )
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END IF
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*
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* W := W * T or W * T**H
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*
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CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
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$ LASTC, K, ONE, T, LDT, WORK, LDWORK )
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*
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* C := C - W * V**H
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*
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IF( LASTV.GT.K ) THEN
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*
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* C2 := C2 - W * V2**H
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*
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CALL ZGEMM( 'No transpose', 'Conjugate transpose',
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$ LASTC, LASTV-K, K,
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$ -ONE, WORK, LDWORK, V( K+1, 1 ), LDV,
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$ ONE, C( 1, K+1 ), LDC )
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||
|
|
END IF
|
||
|
|
*
|
||
|
|
* W := W * V1**H
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',
|
||
|
|
$ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
|
||
|
|
*
|
||
|
|
* C1 := C1 - W
|
||
|
|
*
|
||
|
|
DO 60 J = 1, K
|
||
|
|
DO 50 I = 1, LASTC
|
||
|
|
C( I, J ) = C( I, J ) - WORK( I, J )
|
||
|
|
50 CONTINUE
|
||
|
|
60 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Let V = ( V1 )
|
||
|
|
* ( V2 ) (last K rows)
|
||
|
|
* where V2 is unit upper triangular.
|
||
|
|
*
|
||
|
|
IF( LSAME( SIDE, 'L' ) ) THEN
|
||
|
|
*
|
||
|
|
* Form H * C or H**H * C where C = ( C1 )
|
||
|
|
* ( C2 )
|
||
|
|
*
|
||
|
|
LASTV = MAX( K, ILAZLR( M, K, V, LDV ) )
|
||
|
|
LASTC = ILAZLC( LASTV, N, C, LDC )
|
||
|
|
*
|
||
|
|
* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK)
|
||
|
|
*
|
||
|
|
* W := C2**H
|
||
|
|
*
|
||
|
|
DO 70 J = 1, K
|
||
|
|
CALL ZCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
|
||
|
|
$ WORK( 1, J ), 1 )
|
||
|
|
CALL ZLACGV( LASTC, WORK( 1, J ), 1 )
|
||
|
|
70 CONTINUE
|
||
|
|
*
|
||
|
|
* W := W * V2
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
|
||
|
|
$ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
|
||
|
|
$ WORK, LDWORK )
|
||
|
|
IF( LASTV.GT.K ) THEN
|
||
|
|
*
|
||
|
|
* W := W + C1**H*V1
|
||
|
|
*
|
||
|
|
CALL ZGEMM( 'Conjugate transpose', 'No transpose',
|
||
|
|
$ LASTC, K, LASTV-K,
|
||
|
|
$ ONE, C, LDC, V, LDV,
|
||
|
|
$ ONE, WORK, LDWORK )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* W := W * T**H or W * T
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
|
||
|
|
$ LASTC, K, ONE, T, LDT, WORK, LDWORK )
|
||
|
|
*
|
||
|
|
* C := C - V * W**H
|
||
|
|
*
|
||
|
|
IF( LASTV.GT.K ) THEN
|
||
|
|
*
|
||
|
|
* C1 := C1 - V1 * W**H
|
||
|
|
*
|
||
|
|
CALL ZGEMM( 'No transpose', 'Conjugate transpose',
|
||
|
|
$ LASTV-K, LASTC, K,
|
||
|
|
$ -ONE, V, LDV, WORK, LDWORK,
|
||
|
|
$ ONE, C, LDC )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* W := W * V2**H
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
|
||
|
|
$ 'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
|
||
|
|
$ WORK, LDWORK )
|
||
|
|
*
|
||
|
|
* C2 := C2 - W**H
|
||
|
|
*
|
||
|
|
DO 90 J = 1, K
|
||
|
|
DO 80 I = 1, LASTC
|
||
|
|
C( LASTV-K+J, I ) = C( LASTV-K+J, I ) -
|
||
|
|
$ DCONJG( WORK( I, J ) )
|
||
|
|
80 CONTINUE
|
||
|
|
90 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( LSAME( SIDE, 'R' ) ) THEN
|
||
|
|
*
|
||
|
|
* Form C * H or C * H**H where C = ( C1 C2 )
|
||
|
|
*
|
||
|
|
LASTV = MAX( K, ILAZLR( N, K, V, LDV ) )
|
||
|
|
LASTC = ILAZLR( M, LASTV, C, LDC )
|
||
|
|
*
|
||
|
|
* W := C * V = (C1*V1 + C2*V2) (stored in WORK)
|
||
|
|
*
|
||
|
|
* W := C2
|
||
|
|
*
|
||
|
|
DO 100 J = 1, K
|
||
|
|
CALL ZCOPY( LASTC, C( 1, LASTV-K+J ), 1,
|
||
|
|
$ WORK( 1, J ), 1 )
|
||
|
|
100 CONTINUE
|
||
|
|
*
|
||
|
|
* W := W * V2
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
|
||
|
|
$ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
|
||
|
|
$ WORK, LDWORK )
|
||
|
|
IF( LASTV.GT.K ) THEN
|
||
|
|
*
|
||
|
|
* W := W + C1 * V1
|
||
|
|
*
|
||
|
|
CALL ZGEMM( 'No transpose', 'No transpose',
|
||
|
|
$ LASTC, K, LASTV-K,
|
||
|
|
$ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* W := W * T or W * T**H
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
|
||
|
|
$ LASTC, K, ONE, T, LDT, WORK, LDWORK )
|
||
|
|
*
|
||
|
|
* C := C - W * V**H
|
||
|
|
*
|
||
|
|
IF( LASTV.GT.K ) THEN
|
||
|
|
*
|
||
|
|
* C1 := C1 - W * V1**H
|
||
|
|
*
|
||
|
|
CALL ZGEMM( 'No transpose', 'Conjugate transpose',
|
||
|
|
$ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,
|
||
|
|
$ ONE, C, LDC )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* W := W * V2**H
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
|
||
|
|
$ 'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
|
||
|
|
$ WORK, LDWORK )
|
||
|
|
*
|
||
|
|
* C2 := C2 - W
|
||
|
|
*
|
||
|
|
DO 120 J = 1, K
|
||
|
|
DO 110 I = 1, LASTC
|
||
|
|
C( I, LASTV-K+J ) = C( I, LASTV-K+J )
|
||
|
|
$ - WORK( I, J )
|
||
|
|
110 CONTINUE
|
||
|
|
120 CONTINUE
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE IF( LSAME( STOREV, 'R' ) ) THEN
|
||
|
|
*
|
||
|
|
IF( LSAME( DIRECT, 'F' ) ) THEN
|
||
|
|
*
|
||
|
|
* Let V = ( V1 V2 ) (V1: first K columns)
|
||
|
|
* where V1 is unit upper triangular.
|
||
|
|
*
|
||
|
|
IF( LSAME( SIDE, 'L' ) ) THEN
|
||
|
|
*
|
||
|
|
* Form H * C or H**H * C where C = ( C1 )
|
||
|
|
* ( C2 )
|
||
|
|
*
|
||
|
|
LASTV = MAX( K, ILAZLC( K, M, V, LDV ) )
|
||
|
|
LASTC = ILAZLC( LASTV, N, C, LDC )
|
||
|
|
*
|
||
|
|
* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
|
||
|
|
*
|
||
|
|
* W := C1**H
|
||
|
|
*
|
||
|
|
DO 130 J = 1, K
|
||
|
|
CALL ZCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
|
||
|
|
CALL ZLACGV( LASTC, WORK( 1, J ), 1 )
|
||
|
|
130 CONTINUE
|
||
|
|
*
|
||
|
|
* W := W * V1**H
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
|
||
|
|
$ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
|
||
|
|
IF( LASTV.GT.K ) THEN
|
||
|
|
*
|
||
|
|
* W := W + C2**H*V2**H
|
||
|
|
*
|
||
|
|
CALL ZGEMM( 'Conjugate transpose',
|
||
|
|
$ 'Conjugate transpose', LASTC, K, LASTV-K,
|
||
|
|
$ ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV,
|
||
|
|
$ ONE, WORK, LDWORK )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* W := W * T**H or W * T
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
|
||
|
|
$ LASTC, K, ONE, T, LDT, WORK, LDWORK )
|
||
|
|
*
|
||
|
|
* C := C - V**H * W**H
|
||
|
|
*
|
||
|
|
IF( LASTV.GT.K ) THEN
|
||
|
|
*
|
||
|
|
* C2 := C2 - V2**H * W**H
|
||
|
|
*
|
||
|
|
CALL ZGEMM( 'Conjugate transpose',
|
||
|
|
$ 'Conjugate transpose', LASTV-K, LASTC, K,
|
||
|
|
$ -ONE, V( 1, K+1 ), LDV, WORK, LDWORK,
|
||
|
|
$ ONE, C( K+1, 1 ), LDC )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* W := W * V1
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
|
||
|
|
$ LASTC, K, ONE, V, LDV, WORK, LDWORK )
|
||
|
|
*
|
||
|
|
* C1 := C1 - W**H
|
||
|
|
*
|
||
|
|
DO 150 J = 1, K
|
||
|
|
DO 140 I = 1, LASTC
|
||
|
|
C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) )
|
||
|
|
140 CONTINUE
|
||
|
|
150 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( LSAME( SIDE, 'R' ) ) THEN
|
||
|
|
*
|
||
|
|
* Form C * H or C * H**H where C = ( C1 C2 )
|
||
|
|
*
|
||
|
|
LASTV = MAX( K, ILAZLC( K, N, V, LDV ) )
|
||
|
|
LASTC = ILAZLR( M, LASTV, C, LDC )
|
||
|
|
*
|
||
|
|
* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK)
|
||
|
|
*
|
||
|
|
* W := C1
|
||
|
|
*
|
||
|
|
DO 160 J = 1, K
|
||
|
|
CALL ZCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
|
||
|
|
160 CONTINUE
|
||
|
|
*
|
||
|
|
* W := W * V1**H
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
|
||
|
|
$ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
|
||
|
|
IF( LASTV.GT.K ) THEN
|
||
|
|
*
|
||
|
|
* W := W + C2 * V2**H
|
||
|
|
*
|
||
|
|
CALL ZGEMM( 'No transpose', 'Conjugate transpose',
|
||
|
|
$ LASTC, K, LASTV-K, ONE, C( 1, K+1 ), LDC,
|
||
|
|
$ V( 1, K+1 ), LDV, ONE, WORK, LDWORK )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* W := W * T or W * T**H
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
|
||
|
|
$ LASTC, K, ONE, T, LDT, WORK, LDWORK )
|
||
|
|
*
|
||
|
|
* C := C - W * V
|
||
|
|
*
|
||
|
|
IF( LASTV.GT.K ) THEN
|
||
|
|
*
|
||
|
|
* C2 := C2 - W * V2
|
||
|
|
*
|
||
|
|
CALL ZGEMM( 'No transpose', 'No transpose',
|
||
|
|
$ LASTC, LASTV-K, K,
|
||
|
|
$ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV,
|
||
|
|
$ ONE, C( 1, K+1 ), LDC )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* W := W * V1
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
|
||
|
|
$ LASTC, K, ONE, V, LDV, WORK, LDWORK )
|
||
|
|
*
|
||
|
|
* C1 := C1 - W
|
||
|
|
*
|
||
|
|
DO 180 J = 1, K
|
||
|
|
DO 170 I = 1, LASTC
|
||
|
|
C( I, J ) = C( I, J ) - WORK( I, J )
|
||
|
|
170 CONTINUE
|
||
|
|
180 CONTINUE
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Let V = ( V1 V2 ) (V2: last K columns)
|
||
|
|
* where V2 is unit lower triangular.
|
||
|
|
*
|
||
|
|
IF( LSAME( SIDE, 'L' ) ) THEN
|
||
|
|
*
|
||
|
|
* Form H * C or H**H * C where C = ( C1 )
|
||
|
|
* ( C2 )
|
||
|
|
*
|
||
|
|
LASTV = MAX( K, ILAZLC( K, M, V, LDV ) )
|
||
|
|
LASTC = ILAZLC( LASTV, N, C, LDC )
|
||
|
|
*
|
||
|
|
* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
|
||
|
|
*
|
||
|
|
* W := C2**H
|
||
|
|
*
|
||
|
|
DO 190 J = 1, K
|
||
|
|
CALL ZCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
|
||
|
|
$ WORK( 1, J ), 1 )
|
||
|
|
CALL ZLACGV( LASTC, WORK( 1, J ), 1 )
|
||
|
|
190 CONTINUE
|
||
|
|
*
|
||
|
|
* W := W * V2**H
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',
|
||
|
|
$ 'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
|
||
|
|
$ WORK, LDWORK )
|
||
|
|
IF( LASTV.GT.K ) THEN
|
||
|
|
*
|
||
|
|
* W := W + C1**H * V1**H
|
||
|
|
*
|
||
|
|
CALL ZGEMM( 'Conjugate transpose',
|
||
|
|
$ 'Conjugate transpose', LASTC, K, LASTV-K,
|
||
|
|
$ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* W := W * T**H or W * T
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
|
||
|
|
$ LASTC, K, ONE, T, LDT, WORK, LDWORK )
|
||
|
|
*
|
||
|
|
* C := C - V**H * W**H
|
||
|
|
*
|
||
|
|
IF( LASTV.GT.K ) THEN
|
||
|
|
*
|
||
|
|
* C1 := C1 - V1**H * W**H
|
||
|
|
*
|
||
|
|
CALL ZGEMM( 'Conjugate transpose',
|
||
|
|
$ 'Conjugate transpose', LASTV-K, LASTC, K,
|
||
|
|
$ -ONE, V, LDV, WORK, LDWORK, ONE, C, LDC )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* W := W * V2
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
|
||
|
|
$ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
|
||
|
|
$ WORK, LDWORK )
|
||
|
|
*
|
||
|
|
* C2 := C2 - W**H
|
||
|
|
*
|
||
|
|
DO 210 J = 1, K
|
||
|
|
DO 200 I = 1, LASTC
|
||
|
|
C( LASTV-K+J, I ) = C( LASTV-K+J, I ) -
|
||
|
|
$ DCONJG( WORK( I, J ) )
|
||
|
|
200 CONTINUE
|
||
|
|
210 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE IF( LSAME( SIDE, 'R' ) ) THEN
|
||
|
|
*
|
||
|
|
* Form C * H or C * H**H where C = ( C1 C2 )
|
||
|
|
*
|
||
|
|
LASTV = MAX( K, ILAZLC( K, N, V, LDV ) )
|
||
|
|
LASTC = ILAZLR( M, LASTV, C, LDC )
|
||
|
|
*
|
||
|
|
* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK)
|
||
|
|
*
|
||
|
|
* W := C2
|
||
|
|
*
|
||
|
|
DO 220 J = 1, K
|
||
|
|
CALL ZCOPY( LASTC, C( 1, LASTV-K+J ), 1,
|
||
|
|
$ WORK( 1, J ), 1 )
|
||
|
|
220 CONTINUE
|
||
|
|
*
|
||
|
|
* W := W * V2**H
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',
|
||
|
|
$ 'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
|
||
|
|
$ WORK, LDWORK )
|
||
|
|
IF( LASTV.GT.K ) THEN
|
||
|
|
*
|
||
|
|
* W := W + C1 * V1**H
|
||
|
|
*
|
||
|
|
CALL ZGEMM( 'No transpose', 'Conjugate transpose',
|
||
|
|
$ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, ONE,
|
||
|
|
$ WORK, LDWORK )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* W := W * T or W * T**H
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
|
||
|
|
$ LASTC, K, ONE, T, LDT, WORK, LDWORK )
|
||
|
|
*
|
||
|
|
* C := C - W * V
|
||
|
|
*
|
||
|
|
IF( LASTV.GT.K ) THEN
|
||
|
|
*
|
||
|
|
* C1 := C1 - W * V1
|
||
|
|
*
|
||
|
|
CALL ZGEMM( 'No transpose', 'No transpose',
|
||
|
|
$ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,
|
||
|
|
$ ONE, C, LDC )
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* W := W * V2
|
||
|
|
*
|
||
|
|
CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit',
|
||
|
|
$ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
|
||
|
|
$ WORK, LDWORK )
|
||
|
|
*
|
||
|
|
* C1 := C1 - W
|
||
|
|
*
|
||
|
|
DO 240 J = 1, K
|
||
|
|
DO 230 I = 1, LASTC
|
||
|
|
C( I, LASTV-K+J ) = C( I, LASTV-K+J )
|
||
|
|
$ - WORK( I, J )
|
||
|
|
230 CONTINUE
|
||
|
|
240 CONTINUE
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of ZLARFB
|
||
|
|
*
|
||
|
|
END
|