version 1.9, 2011/11/21 20:43:17
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version 1.21, 2023/08/07 08:39:31
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*> \brief \b ZLARFB |
*> \brief \b ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix. |
* |
* |
* =========== DOCUMENTATION =========== |
* =========== DOCUMENTATION =========== |
* |
* |
* Online html documentation available at |
* Online html documentation available at |
* http://www.netlib.org/lapack/explore-html/ |
* http://www.netlib.org/lapack/explore-html/ |
* |
* |
*> \htmlonly |
*> \htmlonly |
*> Download ZLARFB + dependencies |
*> Download ZLARFB + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarfb.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarfb.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarfb.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarfb.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarfb.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarfb.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* 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 ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* CHARACTER DIRECT, SIDE, STOREV, TRANS |
* CHARACTER DIRECT, SIDE, STOREV, TRANS |
* INTEGER K, LDC, LDT, LDV, LDWORK, M, N |
* INTEGER K, LDC, LDT, LDV, LDWORK, M, N |
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* COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ), |
* COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ), |
* $ WORK( LDWORK, * ) |
* $ WORK( LDWORK, * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
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*> K is INTEGER |
*> K is INTEGER |
*> The order of the matrix T (= the number of elementary |
*> The order of the matrix T (= the number of elementary |
*> reflectors whose product defines the block reflector). |
*> reflectors whose product defines the block reflector). |
|
*> If SIDE = 'L', M >= K >= 0; |
|
*> if SIDE = 'R', N >= K >= 0. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] V |
*> \param[in] V |
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* Authors: |
* Authors: |
* ======== |
* ======== |
* |
* |
*> \author Univ. of Tennessee |
*> \author Univ. of Tennessee |
*> \author Univ. of California Berkeley |
*> \author Univ. of California Berkeley |
*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
|
*> \date November 2011 |
|
* |
* |
*> \ingroup complex16OTHERauxiliary |
*> \ingroup complex16OTHERauxiliary |
* |
* |
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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 ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.4.0) -- |
* -- 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 2011 |
|
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER DIRECT, SIDE, STOREV, TRANS |
CHARACTER DIRECT, SIDE, STOREV, TRANS |
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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 |
|
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL ZCOPY, ZGEMM, ZLACGV, ZTRMM |
EXTERNAL ZCOPY, ZGEMM, ZLACGV, ZTRMM |
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* Form H * C or H**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 ) |
|
* |
|
* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) |
* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) |
* |
* |
* W := C1**H |
* 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**H *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**H 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**H |
* C := C - V * W**H |
* |
* |
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* C2 := C2 - V2 * W**H |
* 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**H |
* 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**H |
* 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 |
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* |
* |
* Form C * H or C * H**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 := 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**H |
* 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**H |
* C := C - W * V**H |
* |
* |
IF( LASTV.GT.K ) THEN |
IF( N.GT.K ) THEN |
* |
* |
* C2 := C2 - W * V2**H |
* 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**H |
* 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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* Form H * C or H**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 ) |
|
* |
|
* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) |
* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) |
* |
* |
* W := C2**H |
* 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**H * V1 |
* W := W + C1**H*V1 |
* |
* |
CALL ZGEMM( 'Conjugate transpose', 'No transpose', N, |
CALL ZGEMM( 'Conjugate transpose', 'No transpose', |
$ K, M-K, ONE, C, LDC, V, LDV, ONE, WORK, |
$ LASTC, K, LASTV-K, |
$ LDWORK ) |
$ ONE, C, LDC, V, LDV, |
|
$ ONE, WORK, LDWORK ) |
|
END IF |
END IF |
* |
* |
* W := W * T**H 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**H |
* C := C - V * W**H |
* |
* |
IF( LASTV.GT.K ) THEN |
IF( M.GT.K ) THEN |
* |
* |
* C1 := C1 - V1 * W**H |
* 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**H |
* 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**H |
* 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 |
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* |
* |
* Form C * H or C * H**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**H |
* 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**H |
* C := C - W * V**H |
* |
* |
IF( LASTV.GT.K ) THEN |
IF( N.GT.K ) THEN |
* |
* |
* C1 := C1 - W * V1**H |
* 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**H |
* 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 |
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* Form H * C or H**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**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) |
* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) |
* |
* |
* W := C1**H |
* 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**H |
* 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**H*V2**H |
* 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**H 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**H * W**H |
* C := C - V**H * W**H |
* |
* |
IF( LASTV.GT.K ) THEN |
IF( M.GT.K ) THEN |
* |
* |
* C2 := C2 - V2**H * W**H |
* 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**H |
* 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 |
Line 577
|
Line 549
|
* |
* |
* Form C * H or C * H**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**H = (C1*V1**H + C2*V2**H) (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**H |
* 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**H |
* 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**H |
* 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 643
|
Line 611
|
* Form H * C or H**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**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) |
* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) |
* |
* |
* W := C2**H |
* 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**H |
* 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**H * V1**H |
* 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**H 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**H * W**H |
* C := C - V**H * W**H |
* |
* |
IF( LASTV.GT.K ) THEN |
IF( M.GT.K ) THEN |
* |
* |
* C1 := C1 - V1**H * W**H |
* 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**H |
* 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 |
Line 705
|
Line 668
|
* |
* |
* Form C * H or C * H**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**H = (C1*V1**H + C2*V2**H) (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**H |
* 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**H |
* 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**H |
* 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 |
* |
* |