version 1.1.1.1, 2010/01/26 15:22:45
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version 1.21, 2023/08/07 08:39:31
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*> \brief \b ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular 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 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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*> If SIDE = 'L', M >= K >= 0; |
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*> if SIDE = 'R', N >= K >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] 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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*> \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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* ===================================================================== |
SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, |
SUBROUTINE ZLARFB( 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 3.2) -- |
* -- LAPACK auxiliary 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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* ZLARFB applies a complex block reflector H or its transpose H' to a |
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* complex 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' 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' (Conjugate 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) 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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* 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) 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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* |
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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) 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'*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) COMPLEX*16 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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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
CHARACTER TRANST |
CHARACTER TRANST |
INTEGER I, J, LASTV, LASTC |
INTEGER I, J |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
LOGICAL LSAME |
LOGICAL LSAME |
INTEGER ILAZLR, ILAZLC |
EXTERNAL LSAME |
EXTERNAL LSAME, ILAZLR, ILAZLC |
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* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL ZCOPY, ZGEMM, ZLACGV, ZTRMM |
EXTERNAL ZCOPY, ZGEMM, ZLACGV, ZTRMM |
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* |
* |
IF( LSAME( SIDE, 'L' ) ) THEN |
IF( LSAME( SIDE, 'L' ) ) THEN |
* |
* |
* Form H * C or H' * C where C = ( C1 ) |
* Form H * C or H**H * C where C = ( C1 ) |
* ( C2 ) |
* ( C2 ) |
* |
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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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* |
* |
* W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) |
* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) |
* |
* |
* W := C1' |
* W := C1**H |
* |
* |
DO 10 J = 1, K |
DO 10 J = 1, K |
CALL ZCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) |
CALL ZCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) |
CALL ZLACGV( LASTC, WORK( 1, J ), 1 ) |
CALL ZLACGV( N, WORK( 1, J ), 1 ) |
10 CONTINUE |
10 CONTINUE |
* |
* |
* W := W * V1 |
* W := W * V1 |
* |
* |
CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', |
CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N, |
$ LASTC, K, ONE, V, LDV, WORK, LDWORK ) |
$ K, ONE, V, LDV, WORK, LDWORK ) |
IF( LASTV.GT.K ) THEN |
IF( M.GT.K ) THEN |
* |
* |
* W := W + C2'*V2 |
* W := W + C2**H * V2 |
* |
* |
CALL ZGEMM( 'Conjugate transpose', 'No transpose', |
CALL ZGEMM( 'Conjugate transpose', 'No transpose', N, |
$ LASTC, K, LASTV-K, ONE, C( K+1, 1 ), LDC, |
$ K, M-K, ONE, C( K+1, 1 ), LDC, |
$ V( K+1, 1 ), LDV, ONE, WORK, LDWORK ) |
$ V( K+1, 1 ), LDV, ONE, WORK, LDWORK ) |
END IF |
END IF |
* |
* |
* W := W * T' or W * T |
* W := W * T**H or W * T |
* |
* |
CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit', |
CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K, |
$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) |
$ ONE, T, LDT, WORK, LDWORK ) |
* |
* |
* C := C - V * W' |
* C := C - V * W**H |
* |
* |
IF( M.GT.K ) THEN |
IF( M.GT.K ) THEN |
* |
* |
* C2 := C2 - V2 * W' |
* C2 := C2 - V2 * W**H |
* |
* |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', |
$ LASTV-K, LASTC, K, |
$ M-K, N, K, -ONE, V( K+1, 1 ), LDV, WORK, |
$ -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, |
$ LDWORK, ONE, C( K+1, 1 ), LDC ) |
$ ONE, C( K+1, 1 ), LDC ) |
|
END IF |
END IF |
* |
* |
* W := W * V1' |
* W := W * V1**H |
* |
* |
CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', |
CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', |
$ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK ) |
$ 'Unit', N, K, ONE, V, LDV, WORK, LDWORK ) |
* |
* |
* C1 := C1 - W' |
* C1 := C1 - W**H |
* |
* |
DO 30 J = 1, K |
DO 30 J = 1, K |
DO 20 I = 1, LASTC |
DO 20 I = 1, N |
C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) ) |
C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) ) |
20 CONTINUE |
20 CONTINUE |
30 CONTINUE |
30 CONTINUE |
* |
* |
ELSE IF( LSAME( SIDE, 'R' ) ) THEN |
ELSE IF( LSAME( SIDE, 'R' ) ) THEN |
* |
* |
* Form C * H or C * H' where C = ( C1 C2 ) |
* Form C * H or C * H**H where C = ( C1 C2 ) |
* |
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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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* |
* |
* W := C * V = (C1*V1 + C2*V2) (stored in WORK) |
* W := C * V = (C1*V1 + C2*V2) (stored in WORK) |
* |
* |
* W := C1 |
* W := C1 |
* |
* |
DO 40 J = 1, K |
DO 40 J = 1, K |
CALL ZCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) |
CALL ZCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) |
40 CONTINUE |
40 CONTINUE |
* |
* |
* W := W * V1 |
* W := W * V1 |
* |
* |
CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', |
CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M, |
$ LASTC, K, ONE, V, LDV, WORK, LDWORK ) |
$ K, ONE, V, LDV, WORK, LDWORK ) |
IF( LASTV.GT.K ) THEN |
IF( N.GT.K ) THEN |
* |
* |
* W := W + C2 * V2 |
* W := W + C2 * V2 |
* |
* |
CALL ZGEMM( 'No transpose', 'No transpose', |
CALL ZGEMM( 'No transpose', 'No transpose', M, K, N-K, |
$ LASTC, K, LASTV-K, |
$ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV, |
$ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV, |
$ ONE, WORK, LDWORK ) |
$ ONE, WORK, LDWORK ) |
|
END IF |
END IF |
* |
* |
* W := W * T or W * T' |
* W := W * T or W * T**H |
* |
* |
CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit', |
CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K, |
$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) |
$ ONE, T, LDT, WORK, LDWORK ) |
* |
* |
* C := C - W * V' |
* C := C - W * V**H |
* |
* |
IF( LASTV.GT.K ) THEN |
IF( N.GT.K ) THEN |
* |
* |
* C2 := C2 - W * V2' |
* C2 := C2 - W * V2**H |
* |
* |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, |
$ LASTC, LASTV-K, K, |
$ N-K, K, -ONE, WORK, LDWORK, V( K+1, 1 ), |
$ -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, |
$ LDV, ONE, C( 1, K+1 ), LDC ) |
$ ONE, C( 1, K+1 ), LDC ) |
|
END IF |
END IF |
* |
* |
* W := W * V1' |
* W := W * V1**H |
* |
* |
CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', |
CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', |
$ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK ) |
$ 'Unit', M, K, ONE, V, LDV, WORK, LDWORK ) |
* |
* |
* C1 := C1 - W |
* C1 := C1 - W |
* |
* |
DO 60 J = 1, K |
DO 60 J = 1, K |
DO 50 I = 1, LASTC |
DO 50 I = 1, M |
C( I, J ) = C( I, J ) - WORK( I, J ) |
C( I, J ) = C( I, J ) - WORK( I, J ) |
50 CONTINUE |
50 CONTINUE |
60 CONTINUE |
60 CONTINUE |
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* |
* |
IF( LSAME( SIDE, 'L' ) ) THEN |
IF( LSAME( SIDE, 'L' ) ) THEN |
* |
* |
* Form H * C or H' * C where C = ( C1 ) |
* Form H * C or H**H * C where C = ( C1 ) |
* ( C2 ) |
* ( C2 ) |
* |
|
LASTV = MAX( K, ILAZLR( M, K, V, LDV ) ) |
|
LASTC = ILAZLC( LASTV, N, C, LDC ) |
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* |
* |
* W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) |
* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) |
* |
* |
* W := C2' |
* W := C2**H |
* |
* |
DO 70 J = 1, K |
DO 70 J = 1, K |
CALL ZCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, |
CALL ZCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 ) |
$ WORK( 1, J ), 1 ) |
CALL ZLACGV( N, WORK( 1, J ), 1 ) |
CALL ZLACGV( LASTC, WORK( 1, J ), 1 ) |
|
70 CONTINUE |
70 CONTINUE |
* |
* |
* W := W * V2 |
* W := W * V2 |
* |
* |
CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', |
CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N, |
$ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, |
$ K, ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK ) |
$ WORK, LDWORK ) |
IF( M.GT.K ) THEN |
IF( LASTV.GT.K ) THEN |
|
* |
* |
* W := W + C1'*V1 |
* W := W + C1**H * V1 |
* |
* |
CALL ZGEMM( 'Conjugate transpose', 'No transpose', |
CALL ZGEMM( 'Conjugate transpose', 'No transpose', N, |
$ LASTC, K, LASTV-K, |
$ K, M-K, ONE, C, LDC, V, LDV, ONE, WORK, |
$ ONE, C, LDC, V, LDV, |
$ LDWORK ) |
$ ONE, WORK, LDWORK ) |
|
END IF |
END IF |
* |
* |
* W := W * T' or W * T |
* W := W * T**H or W * T |
* |
* |
CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', |
CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, |
$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) |
$ ONE, T, LDT, WORK, LDWORK ) |
* |
* |
* C := C - V * W' |
* C := C - V * W**H |
* |
* |
IF( LASTV.GT.K ) THEN |
IF( M.GT.K ) THEN |
* |
* |
* C1 := C1 - V1 * W' |
* C1 := C1 - V1 * W**H |
* |
* |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', |
$ LASTV-K, LASTC, K, |
$ M-K, N, K, -ONE, V, LDV, WORK, LDWORK, |
$ -ONE, V, LDV, WORK, LDWORK, |
$ ONE, C, LDC ) |
$ ONE, C, LDC ) |
|
END IF |
END IF |
* |
* |
* W := W * V2' |
* W := W * V2**H |
* |
* |
CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', |
CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', |
$ 'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, |
$ 'Unit', N, K, ONE, V( M-K+1, 1 ), LDV, WORK, |
$ WORK, LDWORK ) |
$ LDWORK ) |
* |
* |
* C2 := C2 - W' |
* C2 := C2 - W**H |
* |
* |
DO 90 J = 1, K |
DO 90 J = 1, K |
DO 80 I = 1, LASTC |
DO 80 I = 1, N |
C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - |
C( M-K+J, I ) = C( M-K+J, I ) - |
$ DCONJG( WORK( I, J ) ) |
$ DCONJG( WORK( I, J ) ) |
80 CONTINUE |
80 CONTINUE |
90 CONTINUE |
90 CONTINUE |
* |
* |
ELSE IF( LSAME( SIDE, 'R' ) ) THEN |
ELSE IF( LSAME( SIDE, 'R' ) ) THEN |
* |
* |
* Form C * H or C * H' where C = ( C1 C2 ) |
* 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 := C * V = (C1*V1 + C2*V2) (stored in WORK) |
* |
* |
* W := C2 |
* W := C2 |
* |
* |
DO 100 J = 1, K |
DO 100 J = 1, K |
CALL ZCOPY( LASTC, C( 1, LASTV-K+J ), 1, |
CALL ZCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) |
$ WORK( 1, J ), 1 ) |
|
100 CONTINUE |
100 CONTINUE |
* |
* |
* W := W * V2 |
* W := W * V2 |
* |
* |
CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', |
CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M, |
$ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, |
$ K, ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK ) |
$ WORK, LDWORK ) |
IF( N.GT.K ) THEN |
IF( LASTV.GT.K ) THEN |
|
* |
* |
* W := W + C1 * V1 |
* W := W + C1 * V1 |
* |
* |
CALL ZGEMM( 'No transpose', 'No transpose', |
CALL ZGEMM( 'No transpose', 'No transpose', M, K, N-K, |
$ LASTC, K, LASTV-K, |
$ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) |
$ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) |
|
END IF |
END IF |
* |
* |
* W := W * T or W * T' |
* W := W * T or W * T**H |
* |
* |
CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit', |
CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, |
$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) |
$ ONE, T, LDT, WORK, LDWORK ) |
* |
* |
* C := C - W * V' |
* C := C - W * V**H |
* |
* |
IF( LASTV.GT.K ) THEN |
IF( N.GT.K ) THEN |
* |
* |
* C1 := C1 - W * V1' |
* C1 := C1 - W * V1**H |
* |
* |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, |
$ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, |
$ N-K, K, -ONE, WORK, LDWORK, V, LDV, ONE, |
$ ONE, C, LDC ) |
$ C, LDC ) |
END IF |
END IF |
* |
* |
* W := W * V2' |
* W := W * V2**H |
* |
* |
CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', |
CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', |
$ 'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, |
$ 'Unit', M, K, ONE, V( N-K+1, 1 ), LDV, WORK, |
$ WORK, LDWORK ) |
$ LDWORK ) |
* |
* |
* C2 := C2 - W |
* C2 := C2 - W |
* |
* |
DO 120 J = 1, K |
DO 120 J = 1, K |
DO 110 I = 1, LASTC |
DO 110 I = 1, M |
C( I, LASTV-K+J ) = C( I, LASTV-K+J ) |
C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J ) |
$ - WORK( I, J ) |
|
110 CONTINUE |
110 CONTINUE |
120 CONTINUE |
120 CONTINUE |
END IF |
END IF |
Line 393
|
Line 489
|
* |
* |
IF( LSAME( SIDE, 'L' ) ) THEN |
IF( LSAME( SIDE, 'L' ) ) THEN |
* |
* |
* Form H * C or H' * C where C = ( C1 ) |
* Form H * C or H**H * C where C = ( C1 ) |
* ( C2 ) |
* ( C2 ) |
* |
|
LASTV = MAX( K, ILAZLC( K, M, V, LDV ) ) |
|
LASTC = ILAZLC( LASTV, N, C, LDC ) |
|
* |
* |
* W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) |
* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) |
* |
* |
* W := C1' |
* W := C1**H |
* |
* |
DO 130 J = 1, K |
DO 130 J = 1, K |
CALL ZCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) |
CALL ZCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) |
CALL ZLACGV( LASTC, WORK( 1, J ), 1 ) |
CALL ZLACGV( N, WORK( 1, J ), 1 ) |
130 CONTINUE |
130 CONTINUE |
* |
* |
* W := W * V1' |
* W := W * V1**H |
* |
* |
CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', |
CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', |
$ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK ) |
$ 'Unit', N, K, ONE, V, LDV, WORK, LDWORK ) |
IF( LASTV.GT.K ) THEN |
IF( M.GT.K ) THEN |
* |
* |
* W := W + C2'*V2' |
* W := W + C2**H * V2**H |
* |
* |
CALL ZGEMM( 'Conjugate transpose', |
CALL ZGEMM( 'Conjugate transpose', |
$ 'Conjugate transpose', LASTC, K, LASTV-K, |
$ 'Conjugate transpose', N, K, M-K, ONE, |
$ ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, |
$ C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, ONE, |
$ ONE, WORK, LDWORK ) |
$ WORK, LDWORK ) |
END IF |
END IF |
* |
* |
* W := W * T' or W * T |
* W := W * T**H or W * T |
* |
* |
CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit', |
CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K, |
$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) |
$ ONE, T, LDT, WORK, LDWORK ) |
* |
* |
* C := C - V' * W' |
* C := C - V**H * W**H |
* |
* |
IF( LASTV.GT.K ) THEN |
IF( M.GT.K ) THEN |
* |
* |
* C2 := C2 - V2' * W' |
* C2 := C2 - V2**H * W**H |
* |
* |
CALL ZGEMM( 'Conjugate transpose', |
CALL ZGEMM( 'Conjugate transpose', |
$ 'Conjugate transpose', LASTV-K, LASTC, K, |
$ 'Conjugate transpose', M-K, N, K, -ONE, |
$ -ONE, V( 1, K+1 ), LDV, WORK, LDWORK, |
$ V( 1, K+1 ), LDV, WORK, LDWORK, ONE, |
$ ONE, C( K+1, 1 ), LDC ) |
$ C( K+1, 1 ), LDC ) |
END IF |
END IF |
* |
* |
* W := W * V1 |
* W := W * V1 |
* |
* |
CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', |
CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N, |
$ LASTC, K, ONE, V, LDV, WORK, LDWORK ) |
$ K, ONE, V, LDV, WORK, LDWORK ) |
* |
* |
* C1 := C1 - W' |
* C1 := C1 - W**H |
* |
* |
DO 150 J = 1, K |
DO 150 J = 1, K |
DO 140 I = 1, LASTC |
DO 140 I = 1, N |
C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) ) |
C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) ) |
140 CONTINUE |
140 CONTINUE |
150 CONTINUE |
150 CONTINUE |
* |
* |
ELSE IF( LSAME( SIDE, 'R' ) ) THEN |
ELSE IF( LSAME( SIDE, 'R' ) ) THEN |
* |
* |
* Form C * H or C * H' where C = ( C1 C2 ) |
* 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' = (C1*V1' + C2*V2') (stored in WORK) |
* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) |
* |
* |
* W := C1 |
* W := C1 |
* |
* |
DO 160 J = 1, K |
DO 160 J = 1, K |
CALL ZCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) |
CALL ZCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) |
160 CONTINUE |
160 CONTINUE |
* |
* |
* W := W * V1' |
* W := W * V1**H |
* |
* |
CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', |
CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', |
$ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK ) |
$ 'Unit', M, K, ONE, V, LDV, WORK, LDWORK ) |
IF( LASTV.GT.K ) THEN |
IF( N.GT.K ) THEN |
* |
* |
* W := W + C2 * V2' |
* W := W + C2 * V2**H |
* |
* |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, |
$ LASTC, K, LASTV-K, ONE, C( 1, K+1 ), LDC, |
$ K, N-K, ONE, C( 1, K+1 ), LDC, |
$ V( 1, K+1 ), LDV, ONE, WORK, LDWORK ) |
$ V( 1, K+1 ), LDV, ONE, WORK, LDWORK ) |
END IF |
END IF |
* |
* |
* W := W * T or W * T' |
* W := W * T or W * T**H |
* |
* |
CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit', |
CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K, |
$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) |
$ ONE, T, LDT, WORK, LDWORK ) |
* |
* |
* C := C - W * V |
* C := C - W * V |
* |
* |
IF( LASTV.GT.K ) THEN |
IF( N.GT.K ) THEN |
* |
* |
* C2 := C2 - W * V2 |
* C2 := C2 - W * V2 |
* |
* |
CALL ZGEMM( 'No transpose', 'No transpose', |
CALL ZGEMM( 'No transpose', 'No transpose', M, N-K, K, |
$ LASTC, LASTV-K, K, |
$ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, ONE, |
$ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, |
$ C( 1, K+1 ), LDC ) |
$ ONE, C( 1, K+1 ), LDC ) |
|
END IF |
END IF |
* |
* |
* W := W * V1 |
* W := W * V1 |
* |
* |
CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', |
CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M, |
$ LASTC, K, ONE, V, LDV, WORK, LDWORK ) |
$ K, ONE, V, LDV, WORK, LDWORK ) |
* |
* |
* C1 := C1 - W |
* C1 := C1 - W |
* |
* |
DO 180 J = 1, K |
DO 180 J = 1, K |
DO 170 I = 1, LASTC |
DO 170 I = 1, M |
C( I, J ) = C( I, J ) - WORK( I, J ) |
C( I, J ) = C( I, J ) - WORK( I, J ) |
170 CONTINUE |
170 CONTINUE |
180 CONTINUE |
180 CONTINUE |
Line 519
|
Line 608
|
* |
* |
IF( LSAME( SIDE, 'L' ) ) THEN |
IF( LSAME( SIDE, 'L' ) ) THEN |
* |
* |
* Form H * C or H' * C where C = ( C1 ) |
* Form H * C or H**H * C where C = ( C1 ) |
* ( C2 ) |
* ( C2 ) |
* |
|
LASTV = MAX( K, ILAZLC( K, M, V, LDV ) ) |
|
LASTC = ILAZLC( LASTV, N, C, LDC ) |
|
* |
* |
* W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) |
* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) |
* |
* |
* W := C2' |
* W := C2**H |
* |
* |
DO 190 J = 1, K |
DO 190 J = 1, K |
CALL ZCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, |
CALL ZCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 ) |
$ WORK( 1, J ), 1 ) |
CALL ZLACGV( N, WORK( 1, J ), 1 ) |
CALL ZLACGV( LASTC, WORK( 1, J ), 1 ) |
|
190 CONTINUE |
190 CONTINUE |
* |
* |
* W := W * V2' |
* W := W * V2**H |
* |
* |
CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', |
CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', |
$ 'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, |
$ 'Unit', N, K, ONE, V( 1, M-K+1 ), LDV, WORK, |
$ WORK, LDWORK ) |
$ LDWORK ) |
IF( LASTV.GT.K ) THEN |
IF( M.GT.K ) THEN |
* |
* |
* W := W + C1'*V1' |
* W := W + C1**H * V1**H |
* |
* |
CALL ZGEMM( 'Conjugate transpose', |
CALL ZGEMM( 'Conjugate transpose', |
$ 'Conjugate transpose', LASTC, K, LASTV-K, |
$ 'Conjugate transpose', N, K, M-K, ONE, C, |
$ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) |
$ LDC, V, LDV, ONE, WORK, LDWORK ) |
END IF |
END IF |
* |
* |
* W := W * T' or W * T |
* W := W * T**H or W * T |
* |
* |
CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', |
CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, |
$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) |
$ ONE, T, LDT, WORK, LDWORK ) |
* |
* |
* C := C - V' * W' |
* C := C - V**H * W**H |
* |
* |
IF( LASTV.GT.K ) THEN |
IF( M.GT.K ) THEN |
* |
* |
* C1 := C1 - V1' * W' |
* C1 := C1 - V1**H * W**H |
* |
* |
CALL ZGEMM( 'Conjugate transpose', |
CALL ZGEMM( 'Conjugate transpose', |
$ 'Conjugate transpose', LASTV-K, LASTC, K, |
$ 'Conjugate transpose', M-K, N, K, -ONE, V, |
$ -ONE, V, LDV, WORK, LDWORK, ONE, C, LDC ) |
$ LDV, WORK, LDWORK, ONE, C, LDC ) |
END IF |
END IF |
* |
* |
* W := W * V2 |
* W := W * V2 |
* |
* |
CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', |
CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N, |
$ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, |
$ K, ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK ) |
$ WORK, LDWORK ) |
|
* |
* |
* C2 := C2 - W' |
* C2 := C2 - W**H |
* |
* |
DO 210 J = 1, K |
DO 210 J = 1, K |
DO 200 I = 1, LASTC |
DO 200 I = 1, N |
C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - |
C( M-K+J, I ) = C( M-K+J, I ) - |
$ DCONJG( WORK( I, J ) ) |
$ DCONJG( WORK( I, J ) ) |
200 CONTINUE |
200 CONTINUE |
210 CONTINUE |
210 CONTINUE |
* |
* |
ELSE IF( LSAME( SIDE, 'R' ) ) THEN |
ELSE IF( LSAME( SIDE, 'R' ) ) THEN |
* |
* |
* Form C * H or C * H' where C = ( C1 C2 ) |
* 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' = (C1*V1' + C2*V2') (stored in WORK) |
* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) |
* |
* |
* W := C2 |
* W := C2 |
* |
* |
DO 220 J = 1, K |
DO 220 J = 1, K |
CALL ZCOPY( LASTC, C( 1, LASTV-K+J ), 1, |
CALL ZCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) |
$ WORK( 1, J ), 1 ) |
|
220 CONTINUE |
220 CONTINUE |
* |
* |
* W := W * V2' |
* W := W * V2**H |
* |
* |
CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', |
CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', |
$ 'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, |
$ 'Unit', M, K, ONE, V( 1, N-K+1 ), LDV, WORK, |
$ WORK, LDWORK ) |
$ LDWORK ) |
IF( LASTV.GT.K ) THEN |
IF( N.GT.K ) THEN |
* |
* |
* W := W + C1 * V1' |
* W := W + C1 * V1**H |
* |
* |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', |
CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, |
$ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, ONE, |
$ K, N-K, ONE, C, LDC, V, LDV, ONE, WORK, |
$ WORK, LDWORK ) |
$ LDWORK ) |
END IF |
END IF |
* |
* |
* W := W * T or W * T' |
* W := W * T or W * T**H |
* |
* |
CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit', |
CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, |
$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) |
$ ONE, T, LDT, WORK, LDWORK ) |
* |
* |
* C := C - W * V |
* C := C - W * V |
* |
* |
IF( LASTV.GT.K ) THEN |
IF( N.GT.K ) THEN |
* |
* |
* C1 := C1 - W * V1 |
* C1 := C1 - W * V1 |
* |
* |
CALL ZGEMM( 'No transpose', 'No transpose', |
CALL ZGEMM( 'No transpose', 'No transpose', M, N-K, K, |
$ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, |
$ -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC ) |
$ ONE, C, LDC ) |
|
END IF |
END IF |
* |
* |
* W := W * V2 |
* W := W * V2 |
* |
* |
CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', |
CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M, |
$ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, |
$ K, ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK ) |
$ WORK, LDWORK ) |
|
* |
* |
* C1 := C1 - W |
* C1 := C1 - W |
* |
* |
DO 240 J = 1, K |
DO 240 J = 1, K |
DO 230 I = 1, LASTC |
DO 230 I = 1, M |
C( I, LASTV-K+J ) = C( I, LASTV-K+J ) |
C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J ) |
$ - WORK( I, J ) |
|
230 CONTINUE |
230 CONTINUE |
240 CONTINUE |
240 CONTINUE |
* |
* |