| *> \brief \b ZLARFB |
| * |
| * =========== DOCUMENTATION =========== |
| * |
| * Online html documentation available at |
| * http://www.netlib.org/lapack/explore-html/ |
| * |
| *> \htmlonly |
| *> Download ZLARFB + dependencies |
| *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarfb.f"> |
| *> [TGZ]</a> |
| *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarfb.f"> |
| *> [ZIP]</a> |
| *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarfb.f"> |
| *> [TXT]</a> |
| *> \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 |
