version 1.7, 2012/08/22 09:48:21
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version 1.16, 2023/08/07 08:39:01
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* |
* |
* =========== 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 DORCSD + dependencies |
*> Download DORCSD + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorcsd.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorcsd.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorcsd.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorcsd.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorcsd.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorcsd.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
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* LDX12, X21, LDX21, X22, LDX22, THETA, |
* LDX12, X21, LDX21, X22, LDX22, THETA, |
* U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, |
* U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, |
* LDV2T, WORK, LWORK, IWORK, INFO ) |
* LDV2T, WORK, LWORK, IWORK, INFO ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS |
* CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS |
* INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12, |
* INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12, |
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* $ X12( LDX12, * ), X21( LDX21, * ), X22( LDX22, |
* $ X12( LDX12, * ), X21( LDX21, * ), X22( LDX22, |
* $ * ) |
* $ * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
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*> |
*> |
*> \param[out] U1 |
*> \param[out] U1 |
*> \verbatim |
*> \verbatim |
*> U1 is DOUBLE PRECISION array, dimension (P) |
*> U1 is DOUBLE PRECISION array, dimension (LDU1,P) |
*> If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1. |
*> If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
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*> |
*> |
*> \param[out] U2 |
*> \param[out] U2 |
*> \verbatim |
*> \verbatim |
*> U2 is DOUBLE PRECISION array, dimension (M-P) |
*> U2 is DOUBLE PRECISION array, dimension (LDU2,M-P) |
*> If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal |
*> If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal |
*> matrix U2. |
*> matrix U2. |
*> \endverbatim |
*> \endverbatim |
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*> |
*> |
*> \param[out] V1T |
*> \param[out] V1T |
*> \verbatim |
*> \verbatim |
*> V1T is DOUBLE PRECISION array, dimension (Q) |
*> V1T is DOUBLE PRECISION array, dimension (LDV1T,Q) |
*> If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal |
*> If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal |
*> matrix V1**T. |
*> matrix V1**T. |
*> \endverbatim |
*> \endverbatim |
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*> |
*> |
*> \param[out] V2T |
*> \param[out] V2T |
*> \verbatim |
*> \verbatim |
*> V2T is DOUBLE PRECISION array, dimension (M-Q) |
*> V2T is DOUBLE PRECISION array, dimension (LDV2T,M-Q) |
*> If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal |
*> If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal |
*> matrix V2**T. |
*> matrix V2**T. |
*> \endverbatim |
*> \endverbatim |
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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 doubleOTHERcomputational |
*> \ingroup doubleOTHERcomputational |
* |
* |
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$ U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, |
$ U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, |
$ LDV2T, WORK, LWORK, IWORK, INFO ) |
$ LDV2T, WORK, LWORK, IWORK, INFO ) |
* |
* |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- LAPACK computational 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 JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS |
CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS |
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$ WANTV1T, WANTV2T |
$ WANTV1T, WANTV2T |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL DBBCSD, DLACPY, DLAPMR, DLAPMT, DLASCL, DLASET, |
EXTERNAL DBBCSD, DLACPY, DLAPMR, DLAPMT, |
$ DORBDB, DORGLQ, DORGQR, XERBLA |
$ DORBDB, DORGLQ, DORGQR, XERBLA |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
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INFO = -8 |
INFO = -8 |
ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN |
ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN |
INFO = -9 |
INFO = -9 |
ELSE IF( ( COLMAJOR .AND. LDX11 .LT. MAX(1,P) ) .OR. |
ELSE IF ( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN |
$ ( .NOT.COLMAJOR .AND. LDX11 .LT. MAX(1,Q) ) ) THEN |
INFO = -11 |
INFO = -11 |
ELSE IF (.NOT. COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN |
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INFO = -11 |
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ELSE IF (COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN |
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INFO = -13 |
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ELSE IF (.NOT. COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN |
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INFO = -13 |
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ELSE IF (COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN |
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INFO = -15 |
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ELSE IF (.NOT. COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN |
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INFO = -15 |
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ELSE IF (COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN |
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INFO = -17 |
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ELSE IF (.NOT. COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN |
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INFO = -17 |
ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN |
ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN |
INFO = -20 |
INFO = -20 |
ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN |
ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN |
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ITAUQ1 = ITAUP2 + MAX( 1, M - P ) |
ITAUQ1 = ITAUP2 + MAX( 1, M - P ) |
ITAUQ2 = ITAUQ1 + MAX( 1, Q ) |
ITAUQ2 = ITAUQ1 + MAX( 1, Q ) |
IORGQR = ITAUQ2 + MAX( 1, M - Q ) |
IORGQR = ITAUQ2 + MAX( 1, M - Q ) |
CALL DORGQR( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1, |
CALL DORGQR( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1, |
$ CHILDINFO ) |
$ CHILDINFO ) |
LORGQRWORKOPT = INT( WORK(1) ) |
LORGQRWORKOPT = INT( WORK(1) ) |
LORGQRWORKMIN = MAX( 1, M - Q ) |
LORGQRWORKMIN = MAX( 1, M - Q ) |
IORGLQ = ITAUQ2 + MAX( 1, M - Q ) |
IORGLQ = ITAUQ2 + MAX( 1, M - Q ) |
CALL DORGLQ( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1, |
CALL DORGLQ( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1, |
$ CHILDINFO ) |
$ CHILDINFO ) |
LORGLQWORKOPT = INT( WORK(1) ) |
LORGLQWORKOPT = INT( WORK(1) ) |
LORGLQWORKMIN = MAX( 1, M - Q ) |
LORGLQWORKMIN = MAX( 1, M - Q ) |
IORBDB = ITAUQ2 + MAX( 1, M - Q ) |
IORBDB = ITAUQ2 + MAX( 1, M - Q ) |
CALL DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, |
CALL DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, |
$ X21, LDX21, X22, LDX22, 0, 0, 0, 0, 0, 0, WORK, |
$ X21, LDX21, X22, LDX22, THETA, V1T, U1, U2, V1T, |
$ -1, CHILDINFO ) |
$ V2T, WORK, -1, CHILDINFO ) |
LORBDBWORKOPT = INT( WORK(1) ) |
LORBDBWORKOPT = INT( WORK(1) ) |
LORBDBWORKMIN = LORBDBWORKOPT |
LORBDBWORKMIN = LORBDBWORKOPT |
IB11D = ITAUQ2 + MAX( 1, M - Q ) |
IB11D = ITAUQ2 + MAX( 1, M - Q ) |
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IB22D = IB21E + MAX( 1, Q - 1 ) |
IB22D = IB21E + MAX( 1, Q - 1 ) |
IB22E = IB22D + MAX( 1, Q ) |
IB22E = IB22D + MAX( 1, Q ) |
IBBCSD = IB22E + MAX( 1, Q - 1 ) |
IBBCSD = IB22E + MAX( 1, Q - 1 ) |
CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, 0, |
CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, |
$ 0, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, 0, |
$ THETA, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, |
$ 0, 0, 0, 0, 0, 0, 0, WORK, -1, CHILDINFO ) |
$ LDV2T, U1, U1, U1, U1, U1, U1, U1, U1, WORK, -1, |
|
$ CHILDINFO ) |
LBBCSDWORKOPT = INT( WORK(1) ) |
LBBCSDWORKOPT = INT( WORK(1) ) |
LBBCSDWORKMIN = LBBCSDWORKOPT |
LBBCSDWORKMIN = LBBCSDWORKOPT |
LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT, |
LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT, |
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END IF |
END IF |
IF( WANTV2T .AND. M-Q .GT. 0 ) THEN |
IF( WANTV2T .AND. M-Q .GT. 0 ) THEN |
CALL DLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T ) |
CALL DLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T ) |
CALL DLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22, |
IF (M-P .GT. Q) Then |
$ V2T(P+1,P+1), LDV2T ) |
CALL DLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22, |
CALL DORGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2), |
$ V2T(P+1,P+1), LDV2T ) |
$ WORK(IORGLQ), LORGLQWORK, INFO ) |
END IF |
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IF (M .GT. Q) THEN |
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CALL DORGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2), |
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$ WORK(IORGLQ), LORGLQWORK, INFO ) |
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END IF |
END IF |
END IF |
ELSE |
ELSE |
IF( WANTU1 .AND. P .GT. 0 ) THEN |
IF( WANTU1 .AND. P .GT. 0 ) THEN |
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* Permute rows and columns to place identity submatrices in top- |
* Permute rows and columns to place identity submatrices in top- |
* left corner of (1,1)-block and/or bottom-right corner of (1,2)- |
* left corner of (1,1)-block and/or bottom-right corner of (1,2)- |
* block and/or bottom-right corner of (2,1)-block and/or top-left |
* block and/or bottom-right corner of (2,1)-block and/or top-left |
* corner of (2,2)-block |
* corner of (2,2)-block |
* |
* |
IF( Q .GT. 0 .AND. WANTU2 ) THEN |
IF( Q .GT. 0 .AND. WANTU2 ) THEN |
DO I = 1, Q |
DO I = 1, Q |