From 9cf77ce1d80cf17aa79c5da95b578ee2a4490152 Mon Sep 17 00:00:00 2001 From: Desire NUENTSA Date: Mon, 12 Nov 2012 15:20:37 +0100 Subject: Add support for Sparse QR factorization --- lapack/zlarfb.f | 774 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 774 insertions(+) create mode 100644 lapack/zlarfb.f (limited to 'lapack/zlarfb.f') diff --git a/lapack/zlarfb.f b/lapack/zlarfb.f new file mode 100644 index 000000000..30fc4b940 --- /dev/null +++ b/lapack/zlarfb.f @@ -0,0 +1,774 @@ +*> \brief \b ZLARFB +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLARFB + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, +* T, LDT, C, LDC, WORK, LDWORK ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, SIDE, STOREV, TRANS +* INTEGER K, LDC, LDT, LDV, LDWORK, M, N +* .. +* .. Array Arguments .. +* COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ), +* $ WORK( LDWORK, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLARFB applies a complex block reflector H or its transpose H**H to a +*> complex M-by-N matrix C, from either the left or the right. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> = 'L': apply H or H**H from the Left +*> = 'R': apply H or H**H from the Right +*> \endverbatim +*> +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> = 'N': apply H (No transpose) +*> = 'C': apply H**H (Conjugate transpose) +*> \endverbatim +*> +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Indicates how H is formed from a product of elementary +*> reflectors +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Indicates how the vectors which define the elementary +*> reflectors are stored: +*> = 'C': Columnwise +*> = 'R': Rowwise +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix C. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix C. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the matrix T (= the number of elementary +*> reflectors whose product defines the block reflector). +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is COMPLEX*16 array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,M) if STOREV = 'R' and SIDE = 'L' +*> (LDV,N) if STOREV = 'R' and SIDE = 'R' +*> See Further Details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); +*> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); +*> if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] T +*> \verbatim +*> T is COMPLEX*16 array, dimension (LDT,K) +*> The triangular K-by-K matrix T in the representation of the +*> block reflector. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is COMPLEX*16 array, dimension (LDC,N) +*> On entry, the M-by-N matrix C. +*> On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of the array C. LDC >= max(1,M). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (LDWORK,K) +*> \endverbatim +*> +*> \param[in] LDWORK +*> \verbatim +*> LDWORK is INTEGER +*> The leading dimension of the array WORK. +*> If SIDE = 'L', LDWORK >= max(1,N); +*> if SIDE = 'R', LDWORK >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored; the corresponding +*> array elements are modified but restored on exit. The rest of the +*> array is not used. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, + $ T, LDT, C, LDC, WORK, LDWORK ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER DIRECT, SIDE, STOREV, TRANS + INTEGER K, LDC, LDT, LDV, LDWORK, M, N +* .. +* .. Array Arguments .. + COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ), + $ WORK( LDWORK, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ONE + PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + CHARACTER TRANST + INTEGER I, J, LASTV, LASTC +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAZLR, ILAZLC + EXTERNAL LSAME, ILAZLR, ILAZLC +* .. +* .. External Subroutines .. + EXTERNAL ZCOPY, ZGEMM, ZLACGV, ZTRMM +* .. +* .. Intrinsic Functions .. + INTRINSIC DCONJG +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( M.LE.0 .OR. N.LE.0 ) + $ RETURN +* + IF( LSAME( TRANS, 'N' ) ) THEN + TRANST = 'C' + ELSE + TRANST = 'N' + END IF +* + IF( LSAME( STOREV, 'C' ) ) THEN +* + IF( LSAME( DIRECT, 'F' ) ) THEN +* +* Let V = ( V1 ) (first K rows) +* ( V2 ) +* where V1 is unit lower 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 := C1**H +* + DO 10 J = 1, K + CALL ZCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) + CALL ZLACGV( LASTC, WORK( 1, J ), 1 ) + 10 CONTINUE +* +* W := W * V1 +* + CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2**H *V2 +* + CALL ZGEMM( 'Conjugate transpose', 'No transpose', + $ LASTC, K, LASTV-K, ONE, C( K+1, 1 ), LDC, + $ V( K+1, 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 * W**H +* + IF( M.GT.K ) THEN +* +* C2 := C2 - V2 * W**H +* + CALL ZGEMM( 'No transpose', 'Conjugate transpose', + $ LASTV-K, LASTC, K, + $ -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, + $ ONE, C( K+1, 1 ), LDC ) + END IF +* +* W := W * V1**H +* + CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', + $ 'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK ) +* +* C1 := C1 - W**H +* + DO 30 J = 1, K + DO 20 I = 1, LASTC + C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) ) + 20 CONTINUE + 30 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 := C1 +* + DO 40 J = 1, K + CALL ZCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) + 40 CONTINUE +* +* W := W * V1 +* + CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', + $ LASTC, K, ONE, V, LDV, WORK, LDWORK ) + IF( LASTV.GT.K ) THEN +* +* W := W + C2 * V2 +* + CALL ZGEMM( 'No transpose', 'No transpose', + $ LASTC, K, LASTV-K, + $ ONE, C( 1, K+1 ), LDC, V( K+1, 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**H +* + IF( LASTV.GT.K ) THEN +* +* C2 := C2 - W * V2**H +* + CALL ZGEMM( 'No transpose', 'Conjugate transpose', + $ LASTC, LASTV-K, K, + $ -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, + $ ONE, C( 1, K+1 ), LDC ) + 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 -- cgit v1.2.3