version 1.1, 2014/01/27 09:24:37
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version 1.5, 2016/08/27 15:35:12
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*> [ 0 S 0 ] |
*> [ 0 S 0 ] |
*> [ 0 0 I ] |
*> [ 0 0 I ] |
*> |
*> |
*> X11 is P-by-Q. The unitary matrices U1, U2, V1, and V2 are P-by-P, |
*> X11 is P-by-Q. The unitary matrices U1, U2, and V1 are P-by-P, |
*> (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are |
*> (M-P)-by-(M-P), and Q-by-Q, respectively. C and S are R-by-R |
*> R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in |
*> nonnegative diagonal matrices satisfying C^2 + S^2 = I, in which |
*> which R = MIN(P,M-P,Q,M-Q). |
*> R = MIN(P,M-P,Q,M-Q). |
*> |
*> \endverbatim |
*>\endverbatim |
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* |
* |
* Arguments: |
* Arguments: |
* ========== |
* ========== |
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*> \param[in] JOBU1 |
*> \param[in] JOBU1 |
*> \verbatim |
*> \verbatim |
*> JOBU1 is CHARACTER |
*> JOBU1 is CHARACTER |
*> = 'Y': U1 is computed; |
*> = 'Y': U1 is computed; |
*> otherwise: U1 is not computed. |
*> otherwise: U1 is not computed. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] JOBU2 |
*> \param[in] JOBU2 |
*> \verbatim |
*> \verbatim |
*> JOBU2 is CHARACTER |
*> JOBU2 is CHARACTER |
*> = 'Y': U2 is computed; |
*> = 'Y': U2 is computed; |
*> otherwise: U2 is not computed. |
*> otherwise: U2 is not computed. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] JOBV1T |
*> \param[in] JOBV1T |
*> \verbatim |
*> \verbatim |
*> JOBV1T is CHARACTER |
*> JOBV1T is CHARACTER |
*> = 'Y': V1T is computed; |
*> = 'Y': V1T is computed; |
*> otherwise: V1T is not computed. |
*> otherwise: V1T is not computed. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] M |
*> \param[in] M |
*> \verbatim |
*> \verbatim |
*> M is INTEGER |
*> M is INTEGER |
*> The number of rows and columns in X. |
*> The number of rows in X. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] P |
*> \param[in] P |
*> \verbatim |
*> \verbatim |
*> P is INTEGER |
*> P is INTEGER |
*> The number of rows in X11 and X12. 0 <= P <= M. |
*> The number of rows in X11. 0 <= P <= M. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] Q |
*> \param[in] Q |
*> \verbatim |
*> \verbatim |
*> Q is INTEGER |
*> Q is INTEGER |
*> The number of columns in X11 and X21. 0 <= Q <= M. |
*> The number of columns in X11 and X21. 0 <= Q <= M. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in,out] X11 |
*> \param[in,out] X11 |
*> \verbatim |
*> \verbatim |
*> X11 is COMPLEX*16 array, dimension (LDX11,Q) |
*> X11 is COMPLEX*16 array, dimension (LDX11,Q) |
*> On entry, part of the unitary matrix whose CSD is |
*> On entry, part of the unitary matrix whose CSD is desired. |
*> desired. |
|
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] LDX11 |
*> \param[in] LDX11 |
*> \verbatim |
*> \verbatim |
*> LDX11 is INTEGER |
*> LDX11 is INTEGER |
*> The leading dimension of X11. LDX11 >= MAX(1,P). |
*> The leading dimension of X11. LDX11 >= MAX(1,P). |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in,out] X21 |
*> \param[in,out] X21 |
*> \verbatim |
*> \verbatim |
*> X21 is COMPLEX*16 array, dimension (LDX21,Q) |
*> X21 is COMPLEX*16 array, dimension (LDX21,Q) |
*> On entry, part of the unitary matrix whose CSD is |
*> On entry, part of the unitary matrix whose CSD is desired. |
*> desired. |
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*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] LDX21 |
*> \param[in] LDX21 |
*> \verbatim |
*> \verbatim |
*> LDX21 is INTEGER |
*> LDX21 is INTEGER |
*> The leading dimension of X21. LDX21 >= MAX(1,M-P). |
*> The leading dimension of X21. LDX21 >= MAX(1,M-P). |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[out] THETA |
*> \param[out] THETA |
*> \verbatim |
*> \verbatim |
*> THETA is COMPLEX*16 array, dimension (R), in which R = |
*> THETA is DOUBLE PRECISION array, dimension (R), in which R = |
*> MIN(P,M-P,Q,M-Q). |
*> MIN(P,M-P,Q,M-Q). |
*> C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and |
*> C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and |
*> S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ). |
*> S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ). |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[out] U1 |
*> \param[out] U1 |
*> \verbatim |
*> \verbatim |
*> U1 is COMPLEX*16 array, dimension (P) |
*> U1 is COMPLEX*16 array, dimension (P) |
*> If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1. |
*> If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] LDU1 |
*> \param[in] LDU1 |
*> \verbatim |
*> \verbatim |
*> LDU1 is INTEGER |
*> LDU1 is INTEGER |
*> The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= |
*> The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= |
*> MAX(1,P). |
*> MAX(1,P). |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[out] U2 |
*> \param[out] U2 |
*> \verbatim |
*> \verbatim |
*> U2 is COMPLEX*16 array, dimension (M-P) |
*> U2 is COMPLEX*16 array, dimension (M-P) |
*> If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary |
*> If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary |
*> matrix U2. |
*> matrix U2. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] LDU2 |
*> \param[in] LDU2 |
*> \verbatim |
*> \verbatim |
*> LDU2 is INTEGER |
*> LDU2 is INTEGER |
*> The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= |
*> The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= |
*> MAX(1,M-P). |
*> MAX(1,M-P). |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[out] V1T |
*> \param[out] V1T |
*> \verbatim |
*> \verbatim |
*> V1T is COMPLEX*16 array, dimension (Q) |
*> V1T is COMPLEX*16 array, dimension (Q) |
*> If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary |
*> If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary |
*> matrix V1**T. |
*> matrix V1**T. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] LDV1T |
*> \param[in] LDV1T |
*> \verbatim |
*> \verbatim |
*> LDV1T is INTEGER |
*> LDV1T is INTEGER |
*> The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= |
*> The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= |
*> MAX(1,Q). |
*> MAX(1,Q). |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[out] WORK |
*> \param[out] WORK |
*> \verbatim |
*> \verbatim |
*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) |
*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) |
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
*> If INFO > 0 on exit, WORK(2:R) contains the values PHI(1), |
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*> ..., PHI(R-1) that, together with THETA(1), ..., THETA(R), |
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*> define the matrix in intermediate bidiagonal-block form |
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*> remaining after nonconvergence. INFO specifies the number |
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*> of nonzero PHI's. |
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*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] LWORK |
*> \param[in] LWORK |
*> \verbatim |
*> \verbatim |
*> LWORK is INTEGER |
*> LWORK is INTEGER |
*> The dimension of the array WORK. |
*> The dimension of the array WORK. |
*> \endverbatim |
*> |
*> \verbatim |
*> If LWORK = -1, then a workspace query is assumed; the routine |
*> If LWORK = -1, then a workspace query is assumed; the routine |
*> only calculates the optimal size of the WORK array, returns |
*> only calculates the optimal size of the WORK array, returns |
*> this value as the first entry of the work array, and no error |
*> this value as the first entry of the work array, and no error |
*> message related to LWORK is issued by XERBLA. |
*> message related to LWORK is issued by XERBLA. |
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*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[out] RWORK |
*> \param[out] RWORK |
*> \verbatim |
*> \verbatim |
*> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) |
*> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) |
*> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. |
*> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. |
*> If INFO > 0 on exit, RWORK(2:R) contains the values PHI(1), |
*> If INFO > 0 on exit, RWORK(2:R) contains the values PHI(1), |
*> ..., PHI(R-1) that, together with THETA(1), ..., THETA(R), |
*> ..., PHI(R-1) that, together with THETA(1), ..., THETA(R), |
*> define the matrix in intermediate bidiagonal-block form |
*> define the matrix in intermediate bidiagonal-block form |
*> remaining after nonconvergence. INFO specifies the number |
*> remaining after nonconvergence. INFO specifies the number |
*> of nonzero PHI's. |
*> of nonzero PHI's. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] LRWORK |
*> \param[in] LRWORK |
*> \verbatim |
*> \verbatim |
*> LRWORK is INTEGER |
*> LRWORK is INTEGER |
*> The dimension of the array RWORK. |
*> The dimension of the array RWORK. |
*> |
*> |
*> If LRWORK = -1, then a workspace query is assumed; the routine |
*> If LRWORK = -1, then a workspace query is assumed; the routine |
*> only calculates the optimal size of the RWORK array, returns |
*> only calculates the optimal size of the RWORK array, returns |
*> this value as the first entry of the work array, and no error |
*> this value as the first entry of the work array, and no error |
*> message related to LRWORK is issued by XERBLA. |
*> message related to LRWORK is issued by XERBLA. |
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*> \endverbatim |
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* |
*> \param[out] IWORK |
*> \param[out] IWORK |
*> \verbatim |
*> \verbatim |
*> IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q)) |
*> IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q)) |
*> \endverbatim |
*> \endverbatim |
*> \endverbatim |
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*> |
*> |
*> \param[out] INFO |
*> \param[out] INFO |
*> \verbatim |
*> \verbatim |
*> INFO is INTEGER |
*> INFO is INTEGER |
*> = 0: successful exit. |
*> = 0: successful exit. |
*> < 0: if INFO = -i, the i-th argument had an illegal value. |
*> < 0: if INFO = -i, the i-th argument had an illegal value. |
*> > 0: ZBBCSD did not converge. See the description of WORK |
*> > 0: ZBBCSD did not converge. See the description of WORK |
*> above for details. |
*> above for details. |
*> \endverbatim |
*> \endverbatim |
* |
* |
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$ LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, |
$ LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, |
$ INFO ) |
$ INFO ) |
* |
* |
* -- LAPACK computational routine (version 3.5.0) -- |
* -- LAPACK computational routine (version 3.6.1) -- |
* -- 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..-- |
* July 2012 |
* July 2012 |
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$ LWORKMIN, LWORKOPT, R |
$ LWORKMIN, LWORKOPT, R |
LOGICAL LQUERY, WANTU1, WANTU2, WANTV1T |
LOGICAL LQUERY, WANTU1, WANTU2, WANTV1T |
* .. |
* .. |
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* .. Local Arrays .. |
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DOUBLE PRECISION DUM( 1 ) |
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COMPLEX*16 CDUM( 1, 1 ) |
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* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL ZBBCSD, ZCOPY, ZLACPY, ZLAPMR, ZLAPMT, ZUNBDB1, |
EXTERNAL ZBBCSD, ZCOPY, ZLACPY, ZLAPMR, ZLAPMT, ZUNBDB1, |
$ ZUNBDB2, ZUNBDB3, ZUNBDB4, ZUNGLQ, ZUNGQR, |
$ ZUNBDB2, ZUNBDB3, ZUNBDB4, ZUNGLQ, ZUNGQR, |
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INFO = -8 |
INFO = -8 |
ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN |
ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN |
INFO = -10 |
INFO = -10 |
ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN |
ELSE IF( WANTU1 .AND. LDU1 .LT. MAX( 1, P ) ) THEN |
INFO = -13 |
INFO = -13 |
ELSE IF( WANTU2 .AND. LDU2 .LT. M - P ) THEN |
ELSE IF( WANTU2 .AND. LDU2 .LT. MAX( 1, M - P ) ) THEN |
INFO = -15 |
INFO = -15 |
ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN |
ELSE IF( WANTV1T .AND. LDV1T .LT. MAX( 1, Q ) ) THEN |
INFO = -17 |
INFO = -17 |
END IF |
END IF |
* |
* |
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IORBDB = ITAUQ1 + MAX( 1, Q ) |
IORBDB = ITAUQ1 + MAX( 1, Q ) |
IORGQR = ITAUQ1 + MAX( 1, Q ) |
IORGQR = ITAUQ1 + MAX( 1, Q ) |
IORGLQ = ITAUQ1 + MAX( 1, Q ) |
IORGLQ = ITAUQ1 + MAX( 1, Q ) |
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LORGQRMIN = 1 |
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LORGQROPT = 1 |
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LORGLQMIN = 1 |
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LORGLQOPT = 1 |
IF( R .EQ. Q ) THEN |
IF( R .EQ. Q ) THEN |
CALL ZUNBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0, |
CALL ZUNBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, DUM, |
$ 0, 0, WORK, -1, CHILDINFO ) |
$ CDUM, CDUM, CDUM, WORK, -1, CHILDINFO ) |
LORBDB = INT( WORK(1) ) |
LORBDB = INT( WORK(1) ) |
IF( P .GE. M-P ) THEN |
IF( WANTU1 .AND. P .GT. 0 ) THEN |
CALL ZUNGQR( P, P, Q, U1, LDU1, 0, WORK(1), -1, |
CALL ZUNGQR( P, P, Q, U1, LDU1, CDUM, WORK(1), -1, |
$ CHILDINFO ) |
$ CHILDINFO ) |
LORGQRMIN = MAX( 1, P ) |
LORGQRMIN = MAX( LORGQRMIN, P ) |
LORGQROPT = INT( WORK(1) ) |
LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) |
ELSE |
ENDIF |
CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, 0, WORK(1), -1, |
IF( WANTU2 .AND. M-P .GT. 0 ) THEN |
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CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, CDUM, WORK(1), -1, |
$ CHILDINFO ) |
$ CHILDINFO ) |
LORGQRMIN = MAX( 1, M-P ) |
LORGQRMIN = MAX( LORGQRMIN, M-P ) |
LORGQROPT = INT( WORK(1) ) |
LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) |
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END IF |
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IF( WANTV1T .AND. Q .GT. 0 ) THEN |
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CALL ZUNGLQ( Q-1, Q-1, Q-1, V1T, LDV1T, |
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$ CDUM, WORK(1), -1, CHILDINFO ) |
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LORGLQMIN = MAX( LORGLQMIN, Q-1 ) |
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LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) ) |
END IF |
END IF |
CALL ZUNGLQ( MAX(0,Q-1), MAX(0,Q-1), MAX(0,Q-1), V1T, LDV1T, |
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$ 0, WORK(1), -1, CHILDINFO ) |
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LORGLQMIN = MAX( 1, Q-1 ) |
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LORGLQOPT = INT( WORK(1) ) |
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CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA, |
CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA, |
$ 0, U1, LDU1, U2, LDU2, V1T, LDV1T, 0, 1, 0, 0, |
$ DUM, U1, LDU1, U2, LDU2, V1T, LDV1T, CDUM, 1, |
$ 0, 0, 0, 0, 0, 0, RWORK(1), -1, CHILDINFO ) |
$ DUM, DUM, DUM, DUM, DUM, DUM, DUM, DUM, |
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$ RWORK(1), -1, CHILDINFO ) |
LBBCSD = INT( RWORK(1) ) |
LBBCSD = INT( RWORK(1) ) |
ELSE IF( R .EQ. P ) THEN |
ELSE IF( R .EQ. P ) THEN |
CALL ZUNBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0, |
CALL ZUNBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, DUM, |
$ 0, 0, WORK(1), -1, CHILDINFO ) |
$ CDUM, CDUM, CDUM, WORK(1), -1, CHILDINFO ) |
LORBDB = INT( WORK(1) ) |
LORBDB = INT( WORK(1) ) |
IF( P-1 .GE. M-P ) THEN |
IF( WANTU1 .AND. P .GT. 0 ) THEN |
CALL ZUNGQR( P-1, P-1, P-1, U1(2,2), LDU1, 0, WORK(1), |
CALL ZUNGQR( P-1, P-1, P-1, U1(2,2), LDU1, CDUM, WORK(1), |
$ -1, CHILDINFO ) |
$ -1, CHILDINFO ) |
LORGQRMIN = MAX( 1, P-1 ) |
LORGQRMIN = MAX( LORGQRMIN, P-1 ) |
LORGQROPT = INT( WORK(1) ) |
LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) |
ELSE |
END IF |
CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, 0, WORK(1), -1, |
IF( WANTU2 .AND. M-P .GT. 0 ) THEN |
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CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, CDUM, WORK(1), -1, |
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$ CHILDINFO ) |
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LORGQRMIN = MAX( LORGQRMIN, M-P ) |
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LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) |
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END IF |
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IF( WANTV1T .AND. Q .GT. 0 ) THEN |
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CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, CDUM, WORK(1), -1, |
$ CHILDINFO ) |
$ CHILDINFO ) |
LORGQRMIN = MAX( 1, M-P ) |
LORGLQMIN = MAX( LORGLQMIN, Q ) |
LORGQROPT = INT( WORK(1) ) |
LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) ) |
END IF |
END IF |
CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, 0, WORK(1), -1, |
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$ CHILDINFO ) |
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LORGLQMIN = MAX( 1, Q ) |
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LORGLQOPT = INT( WORK(1) ) |
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CALL ZBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA, |
CALL ZBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA, |
$ 0, V1T, LDV1T, 0, 1, U1, LDU1, U2, LDU2, 0, 0, |
$ DUM, V1T, LDV1T, CDUM, 1, U1, LDU1, U2, LDU2, |
$ 0, 0, 0, 0, 0, 0, RWORK(1), -1, CHILDINFO ) |
$ DUM, DUM, DUM, DUM, DUM, DUM, DUM, DUM, |
|
$ RWORK(1), -1, CHILDINFO ) |
LBBCSD = INT( RWORK(1) ) |
LBBCSD = INT( RWORK(1) ) |
ELSE IF( R .EQ. M-P ) THEN |
ELSE IF( R .EQ. M-P ) THEN |
CALL ZUNBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0, |
CALL ZUNBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, DUM, |
$ 0, 0, WORK(1), -1, CHILDINFO ) |
$ CDUM, CDUM, CDUM, WORK(1), -1, CHILDINFO ) |
LORBDB = INT( WORK(1) ) |
LORBDB = INT( WORK(1) ) |
IF( P .GE. M-P-1 ) THEN |
IF( WANTU1 .AND. P .GT. 0 ) THEN |
CALL ZUNGQR( P, P, Q, U1, LDU1, 0, WORK(1), -1, |
CALL ZUNGQR( P, P, Q, U1, LDU1, CDUM, WORK(1), -1, |
$ CHILDINFO ) |
$ CHILDINFO ) |
LORGQRMIN = MAX( 1, P ) |
LORGQRMIN = MAX( LORGQRMIN, P ) |
LORGQROPT = INT( WORK(1) ) |
LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) |
ELSE |
END IF |
CALL ZUNGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2, 0, |
IF( WANTU2 .AND. M-P .GT. 0 ) THEN |
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CALL ZUNGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2, CDUM, |
$ WORK(1), -1, CHILDINFO ) |
$ WORK(1), -1, CHILDINFO ) |
LORGQRMIN = MAX( 1, M-P-1 ) |
LORGQRMIN = MAX( LORGQRMIN, M-P-1 ) |
LORGQROPT = INT( WORK(1) ) |
LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) |
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END IF |
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IF( WANTV1T .AND. Q .GT. 0 ) THEN |
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CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, CDUM, WORK(1), -1, |
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$ CHILDINFO ) |
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LORGLQMIN = MAX( LORGLQMIN, Q ) |
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LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) ) |
END IF |
END IF |
CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, 0, WORK(1), -1, |
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$ CHILDINFO ) |
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LORGLQMIN = MAX( 1, Q ) |
|
LORGLQOPT = INT( WORK(1) ) |
|
CALL ZBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P, |
CALL ZBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P, |
$ THETA, 0, 0, 1, V1T, LDV1T, U2, LDU2, U1, LDU1, |
$ THETA, DUM, CDUM, 1, V1T, LDV1T, U2, LDU2, U1, |
$ 0, 0, 0, 0, 0, 0, 0, 0, RWORK(1), -1, |
$ LDU1, DUM, DUM, DUM, DUM, DUM, DUM, DUM, DUM, |
$ CHILDINFO ) |
$ RWORK(1), -1, CHILDINFO ) |
LBBCSD = INT( RWORK(1) ) |
LBBCSD = INT( RWORK(1) ) |
ELSE |
ELSE |
CALL ZUNBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0, |
CALL ZUNBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, DUM, |
$ 0, 0, 0, WORK(1), -1, CHILDINFO ) |
$ CDUM, CDUM, CDUM, CDUM, WORK(1), -1, CHILDINFO |
|
$ ) |
LORBDB = M + INT( WORK(1) ) |
LORBDB = M + INT( WORK(1) ) |
IF( P .GE. M-P ) THEN |
IF( WANTU1 .AND. P .GT. 0 ) THEN |
CALL ZUNGQR( P, P, M-Q, U1, LDU1, 0, WORK(1), -1, |
CALL ZUNGQR( P, P, M-Q, U1, LDU1, CDUM, WORK(1), -1, |
$ CHILDINFO ) |
$ CHILDINFO ) |
LORGQRMIN = MAX( 1, P ) |
LORGQRMIN = MAX( LORGQRMIN, P ) |
LORGQROPT = INT( WORK(1) ) |
LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) |
ELSE |
END IF |
CALL ZUNGQR( M-P, M-P, M-Q, U2, LDU2, 0, WORK(1), -1, |
IF( WANTU2 .AND. M-P .GT. 0 ) THEN |
|
CALL ZUNGQR( M-P, M-P, M-Q, U2, LDU2, CDUM, WORK(1), -1, |
|
$ CHILDINFO ) |
|
LORGQRMIN = MAX( LORGQRMIN, M-P ) |
|
LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) |
|
END IF |
|
IF( WANTV1T .AND. Q .GT. 0 ) THEN |
|
CALL ZUNGLQ( Q, Q, Q, V1T, LDV1T, CDUM, WORK(1), -1, |
$ CHILDINFO ) |
$ CHILDINFO ) |
LORGQRMIN = MAX( 1, M-P ) |
LORGLQMIN = MAX( LORGLQMIN, Q ) |
LORGQROPT = INT( WORK(1) ) |
LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) ) |
END IF |
END IF |
CALL ZUNGLQ( Q, Q, Q, V1T, LDV1T, 0, WORK(1), -1, |
|
$ CHILDINFO ) |
|
LORGLQMIN = MAX( 1, Q ) |
|
LORGLQOPT = INT( WORK(1) ) |
|
CALL ZBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q, |
CALL ZBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q, |
$ THETA, 0, U2, LDU2, U1, LDU1, 0, 1, V1T, LDV1T, |
$ THETA, DUM, U2, LDU2, U1, LDU1, CDUM, 1, V1T, |
$ 0, 0, 0, 0, 0, 0, 0, 0, RWORK(1), -1, |
$ LDV1T, DUM, DUM, DUM, DUM, DUM, DUM, DUM, DUM, |
$ CHILDINFO ) |
$ RWORK(1), -1, CHILDINFO ) |
LBBCSD = INT( RWORK(1) ) |
LBBCSD = INT( RWORK(1) ) |
END IF |
END IF |
LRWORKMIN = IBBCSD+LBBCSD-1 |
LRWORKMIN = IBBCSD+LBBCSD-1 |
Line 545
|
Line 560
|
* Simultaneously diagonalize X11 and X21. |
* Simultaneously diagonalize X11 and X21. |
* |
* |
CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA, |
CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA, |
$ RWORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, 0, 1, |
$ RWORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, CDUM, |
$ RWORK(IB11D), RWORK(IB11E), RWORK(IB12D), |
$ 1, RWORK(IB11D), RWORK(IB11E), RWORK(IB12D), |
$ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E), |
$ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E), |
$ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD, |
$ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD, |
$ CHILDINFO ) |
$ CHILDINFO ) |
Line 599
|
Line 614
|
* Simultaneously diagonalize X11 and X21. |
* Simultaneously diagonalize X11 and X21. |
* |
* |
CALL ZBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA, |
CALL ZBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA, |
$ RWORK(IPHI), V1T, LDV1T, 0, 1, U1, LDU1, U2, LDU2, |
$ RWORK(IPHI), V1T, LDV1T, CDUM, 1, U1, LDU1, U2, |
$ RWORK(IB11D), RWORK(IB11E), RWORK(IB12D), |
$ LDU2, RWORK(IB11D), RWORK(IB11E), RWORK(IB12D), |
$ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E), |
$ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E), |
$ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD, |
$ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD, |
$ CHILDINFO ) |
$ CHILDINFO ) |
Line 654
|
Line 669
|
* Simultaneously diagonalize X11 and X21. |
* Simultaneously diagonalize X11 and X21. |
* |
* |
CALL ZBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P, |
CALL ZBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P, |
$ THETA, RWORK(IPHI), 0, 1, V1T, LDV1T, U2, LDU2, |
$ THETA, RWORK(IPHI), CDUM, 1, V1T, LDV1T, U2, LDU2, |
$ U1, LDU1, RWORK(IB11D), RWORK(IB11E), |
$ U1, LDU1, RWORK(IB11D), RWORK(IB11E), |
$ RWORK(IB12D), RWORK(IB12E), RWORK(IB21D), |
$ RWORK(IB12D), RWORK(IB12E), RWORK(IB21D), |
$ RWORK(IB21E), RWORK(IB22D), RWORK(IB22E), |
$ RWORK(IB21E), RWORK(IB22D), RWORK(IB22E), |
Line 723
|
Line 738
|
* Simultaneously diagonalize X11 and X21. |
* Simultaneously diagonalize X11 and X21. |
* |
* |
CALL ZBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q, |
CALL ZBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q, |
$ THETA, RWORK(IPHI), U2, LDU2, U1, LDU1, 0, 1, V1T, |
$ THETA, RWORK(IPHI), U2, LDU2, U1, LDU1, CDUM, 1, |
$ LDV1T, RWORK(IB11D), RWORK(IB11E), RWORK(IB12D), |
$ V1T, LDV1T, RWORK(IB11D), RWORK(IB11E), |
$ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E), |
$ RWORK(IB12D), RWORK(IB12E), RWORK(IB21D), |
$ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD, |
$ RWORK(IB21E), RWORK(IB22D), RWORK(IB22E), |
$ CHILDINFO ) |
$ RWORK(IBBCSD), LBBCSD, CHILDINFO ) |
* |
* |
* Permute rows and columns to place identity submatrices in |
* Permute rows and columns to place identity submatrices in |
* preferred positions |
* preferred positions |