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lapack/SRC/dorcsd.f
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Julie e18d437924 Making LAPACK's code eternal... no more version and date in source files. 
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*> \brief \b DORCSD
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DORCSD + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorcsd.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorcsd.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorcsd.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* RECURSIVE SUBROUTINE DORCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
* SIGNS, M, P, Q, X11, LDX11, X12,
* LDX12, X21, LDX21, X22, LDX22, THETA,
* U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
* LDV2T, WORK, LWORK, IWORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
* INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12,
* $ LDX21, LDX22, LWORK, M, P, Q
* ..
* .. Array Arguments ..
* INTEGER IWORK( * )
* DOUBLE PRECISION THETA( * )
* DOUBLE PRECISION U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ),
* $ V2T( LDV2T, * ), WORK( * ), X11( LDX11, * ),
* $ X12( LDX12, * ), X21( LDX21, * ), X22( LDX22,
* $ * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DORCSD computes the CS decomposition of an M-by-M partitioned
*> orthogonal matrix X:
*>
*> [ I 0 0 | 0 0 0 ]
*> [ 0 C 0 | 0 -S 0 ]
*> [ X11 | X12 ] [ U1 | ] [ 0 0 0 | 0 0 -I ] [ V1 | ]**T
*> X = [-----------] = [---------] [---------------------] [---------] .
*> [ X21 | X22 ] [ | U2 ] [ 0 0 0 | I 0 0 ] [ | V2 ]
*> [ 0 S 0 | 0 C 0 ]
*> [ 0 0 I | 0 0 0 ]
*>
*> X11 is P-by-Q. The orthogonal matrices U1, U2, V1, and V2 are P-by-P,
*> (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are
*> R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in
*> which R = MIN(P,M-P,Q,M-Q).
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] JOBU1
*> \verbatim
*> JOBU1 is CHARACTER
*> = 'Y': U1 is computed;
*> otherwise: U1 is not computed.
*> \endverbatim
*>
*> \param[in] JOBU2
*> \verbatim
*> JOBU2 is CHARACTER
*> = 'Y': U2 is computed;
*> otherwise: U2 is not computed.
*> \endverbatim
*>
*> \param[in] JOBV1T
*> \verbatim
*> JOBV1T is CHARACTER
*> = 'Y': V1T is computed;
*> otherwise: V1T is not computed.
*> \endverbatim
*>
*> \param[in] JOBV2T
*> \verbatim
*> JOBV2T is CHARACTER
*> = 'Y': V2T is computed;
*> otherwise: V2T is not computed.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER
*> = 'T': X, U1, U2, V1T, and V2T are stored in row-major
*> order;
*> otherwise: X, U1, U2, V1T, and V2T are stored in column-
*> major order.
*> \endverbatim
*>
*> \param[in] SIGNS
*> \verbatim
*> SIGNS is CHARACTER
*> = 'O': The lower-left block is made nonpositive (the
*> "other" convention);
*> otherwise: The upper-right block is made nonpositive (the
*> "default" convention).
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows and columns in X.
*> \endverbatim
*>
*> \param[in] P
*> \verbatim
*> P is INTEGER
*> The number of rows in X11 and X12. 0 <= P <= M.
*> \endverbatim
*>
*> \param[in] Q
*> \verbatim
*> Q is INTEGER
*> The number of columns in X11 and X21. 0 <= Q <= M.
*> \endverbatim
*>
*> \param[in,out] X11
*> \verbatim
*> X11 is DOUBLE PRECISION array, dimension (LDX11,Q)
*> On entry, part of the orthogonal matrix whose CSD is desired.
*> \endverbatim
*>
*> \param[in] LDX11
*> \verbatim
*> LDX11 is INTEGER
*> The leading dimension of X11. LDX11 >= MAX(1,P).
*> \endverbatim
*>
*> \param[in,out] X12
*> \verbatim
*> X12 is DOUBLE PRECISION array, dimension (LDX12,M-Q)
*> On entry, part of the orthogonal matrix whose CSD is desired.
*> \endverbatim
*>
*> \param[in] LDX12
*> \verbatim
*> LDX12 is INTEGER
*> The leading dimension of X12. LDX12 >= MAX(1,P).
*> \endverbatim
*>
*> \param[in,out] X21
*> \verbatim
*> X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
*> On entry, part of the orthogonal matrix whose CSD is desired.
*> \endverbatim
*>
*> \param[in] LDX21
*> \verbatim
*> LDX21 is INTEGER
*> The leading dimension of X11. LDX21 >= MAX(1,M-P).
*> \endverbatim
*>
*> \param[in,out] X22
*> \verbatim
*> X22 is DOUBLE PRECISION array, dimension (LDX22,M-Q)
*> On entry, part of the orthogonal matrix whose CSD is desired.
*> \endverbatim
*>
*> \param[in] LDX22
*> \verbatim
*> LDX22 is INTEGER
*> The leading dimension of X11. LDX22 >= MAX(1,M-P).
*> \endverbatim
*>
*> \param[out] THETA
*> \verbatim
*> THETA is DOUBLE PRECISION array, dimension (R), in which R =
*> MIN(P,M-P,Q,M-Q).
*> C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
*> S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).
*> \endverbatim
*>
*> \param[out] U1
*> \verbatim
*> U1 is DOUBLE PRECISION array, dimension (LDU1,P)
*> If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.
*> \endverbatim
*>
*> \param[in] LDU1
*> \verbatim
*> LDU1 is INTEGER
*> The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
*> MAX(1,P).
*> \endverbatim
*>
*> \param[out] U2
*> \verbatim
*> U2 is DOUBLE PRECISION array, dimension (LDU2,M-P)
*> If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
*> matrix U2.
*> \endverbatim
*>
*> \param[in] LDU2
*> \verbatim
*> LDU2 is INTEGER
*> The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
*> MAX(1,M-P).
*> \endverbatim
*>
*> \param[out] V1T
*> \verbatim
*> V1T is DOUBLE PRECISION array, dimension (LDV1T,Q)
*> If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
*> matrix V1**T.
*> \endverbatim
*>
*> \param[in] LDV1T
*> \verbatim
*> LDV1T is INTEGER
*> The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
*> MAX(1,Q).
*> \endverbatim
*>
*> \param[out] V2T
*> \verbatim
*> V2T is DOUBLE PRECISION array, dimension (LDV2T,M-Q)
*> If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal
*> matrix V2**T.
*> \endverbatim
*>
*> \param[in] LDV2T
*> \verbatim
*> LDV2T is INTEGER
*> The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=
*> MAX(1,M-Q).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (MAX(1,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),
*> ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
*> define the matrix in intermediate bidiagonal-block form
*> remaining after nonconvergence. INFO specifies the number
*> of nonzero PHI's.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK.
*>
*> If LWORK = -1, then a workspace query is assumed; the routine
*> only calculates the optimal size of the WORK array, returns
*> this value as the first entry of the work array, and no error
*> message related to LWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (M-MIN(P, M-P, Q, M-Q))
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: DBBCSD did not converge. See the description of WORK
*> above for details.
*> \endverbatim
*
*> \par References:
* ================
*>
*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
*> Algorithms, 50(1):33-65, 2009.
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup doubleOTHERcomputational
*
* =====================================================================
RECURSIVE SUBROUTINE DORCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
$ SIGNS, M, P, Q, X11, LDX11, X12,
$ LDX12, X21, LDX21, X22, LDX22, THETA,
$ U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
$ LDV2T, WORK, LWORK, IWORK, INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12,
$ LDX21, LDX22, LWORK, M, P, Q
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
DOUBLE PRECISION THETA( * )
DOUBLE PRECISION U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ),
$ V2T( LDV2T, * ), WORK( * ), X11( LDX11, * ),
$ X12( LDX12, * ), X21( LDX21, * ), X22( LDX22,
$ * )
* ..
*
* ===================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D0,
$ ZERO = 0.0D0 )
* ..
* .. Local Scalars ..
CHARACTER TRANST, SIGNST
INTEGER CHILDINFO, I, IB11D, IB11E, IB12D, IB12E,
$ IB21D, IB21E, IB22D, IB22E, IBBCSD, IORBDB,
$ IORGLQ, IORGQR, IPHI, ITAUP1, ITAUP2, ITAUQ1,
$ ITAUQ2, J, LBBCSDWORK, LBBCSDWORKMIN,
$ LBBCSDWORKOPT, LORBDBWORK, LORBDBWORKMIN,
$ LORBDBWORKOPT, LORGLQWORK, LORGLQWORKMIN,
$ LORGLQWORKOPT, LORGQRWORK, LORGQRWORKMIN,
$ LORGQRWORKOPT, LWORKMIN, LWORKOPT
LOGICAL COLMAJOR, DEFAULTSIGNS, LQUERY, WANTU1, WANTU2,
$ WANTV1T, WANTV2T
* ..
* .. External Subroutines ..
EXTERNAL DBBCSD, DLACPY, DLAPMR, DLAPMT,
$ DORBDB, DORGLQ, DORGQR, XERBLA
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Intrinsic Functions
INTRINSIC INT, MAX, MIN
* ..
* .. Executable Statements ..
*
* Test input arguments
*
INFO = 0
WANTU1 = LSAME( JOBU1, 'Y' )
WANTU2 = LSAME( JOBU2, 'Y' )
WANTV1T = LSAME( JOBV1T, 'Y' )
WANTV2T = LSAME( JOBV2T, 'Y' )
COLMAJOR = .NOT. LSAME( TRANS, 'T' )
DEFAULTSIGNS = .NOT. LSAME( SIGNS, 'O' )
LQUERY = LWORK .EQ. -1
IF( M .LT. 0 ) THEN
INFO = -7
ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
INFO = -8
ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN
INFO = -9
ELSE IF ( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN
INFO = -11
ELSE IF (.NOT. COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN
INFO = -11
ELSE IF (COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN
INFO = -13
ELSE IF (.NOT. COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN
INFO = -13
ELSE IF (COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN
INFO = -15
ELSE IF (.NOT. COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN
INFO = -15
ELSE IF (COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN
INFO = -17
ELSE IF (.NOT. COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN
INFO = -17
ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN
INFO = -20
ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN
INFO = -22
ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN
INFO = -24
ELSE IF( WANTV2T .AND. LDV2T .LT. M-Q ) THEN
INFO = -26
END IF
*
* Work with transpose if convenient
*
IF( INFO .EQ. 0 .AND. MIN( P, M-P ) .LT. MIN( Q, M-Q ) ) THEN
IF( COLMAJOR ) THEN
TRANST = 'T'
ELSE
TRANST = 'N'
END IF
IF( DEFAULTSIGNS ) THEN
SIGNST = 'O'
ELSE
SIGNST = 'D'
END IF
CALL DORCSD( JOBV1T, JOBV2T, JOBU1, JOBU2, TRANST, SIGNST, M,
$ Q, P, X11, LDX11, X21, LDX21, X12, LDX12, X22,
$ LDX22, THETA, V1T, LDV1T, V2T, LDV2T, U1, LDU1,
$ U2, LDU2, WORK, LWORK, IWORK, INFO )
RETURN
END IF
*
* Work with permutation [ 0 I; I 0 ] * X * [ 0 I; I 0 ] if
* convenient
*
IF( INFO .EQ. 0 .AND. M-Q .LT. Q ) THEN
IF( DEFAULTSIGNS ) THEN
SIGNST = 'O'
ELSE
SIGNST = 'D'
END IF
CALL DORCSD( JOBU2, JOBU1, JOBV2T, JOBV1T, TRANS, SIGNST, M,
$ M-P, M-Q, X22, LDX22, X21, LDX21, X12, LDX12, X11,
$ LDX11, THETA, U2, LDU2, U1, LDU1, V2T, LDV2T, V1T,
$ LDV1T, WORK, LWORK, IWORK, INFO )
RETURN
END IF
*
* Compute workspace
*
IF( INFO .EQ. 0 ) THEN
*
IPHI = 2
ITAUP1 = IPHI + MAX( 1, Q - 1 )
ITAUP2 = ITAUP1 + MAX( 1, P )
ITAUQ1 = ITAUP2 + MAX( 1, M - P )
ITAUQ2 = ITAUQ1 + MAX( 1, Q )
IORGQR = ITAUQ2 + MAX( 1, M - Q )
CALL DORGQR( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1,
$ CHILDINFO )
LORGQRWORKOPT = INT( WORK(1) )
LORGQRWORKMIN = MAX( 1, M - Q )
IORGLQ = ITAUQ2 + MAX( 1, M - Q )
CALL DORGLQ( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1,
$ CHILDINFO )
LORGLQWORKOPT = INT( WORK(1) )
LORGLQWORKMIN = MAX( 1, M - Q )
IORBDB = ITAUQ2 + MAX( 1, M - Q )
CALL DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
$ X21, LDX21, X22, LDX22, THETA, V1T, U1, U2, V1T,
$ V2T, WORK, -1, CHILDINFO )
LORBDBWORKOPT = INT( WORK(1) )
LORBDBWORKMIN = LORBDBWORKOPT
IB11D = ITAUQ2 + MAX( 1, M - Q )
IB11E = IB11D + MAX( 1, Q )
IB12D = IB11E + MAX( 1, Q - 1 )
IB12E = IB12D + MAX( 1, Q )
IB21D = IB12E + MAX( 1, Q - 1 )
IB21E = IB21D + MAX( 1, Q )
IB22D = IB21E + MAX( 1, Q - 1 )
IB22E = IB22D + MAX( 1, Q )
IBBCSD = IB22E + MAX( 1, Q - 1 )
CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
$ THETA, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
$ LDV2T, U1, U1, U1, U1, U1, U1, U1, U1, WORK, -1,
$ CHILDINFO )
LBBCSDWORKOPT = INT( WORK(1) )
LBBCSDWORKMIN = LBBCSDWORKOPT
LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT,
$ IORBDB + LORBDBWORKOPT, IBBCSD + LBBCSDWORKOPT ) - 1
LWORKMIN = MAX( IORGQR + LORGQRWORKMIN, IORGLQ + LORGLQWORKMIN,
$ IORBDB + LORBDBWORKOPT, IBBCSD + LBBCSDWORKMIN ) - 1
WORK(1) = MAX(LWORKOPT,LWORKMIN)
*
IF( LWORK .LT. LWORKMIN .AND. .NOT. LQUERY ) THEN
INFO = -22
ELSE
LORGQRWORK = LWORK - IORGQR + 1
LORGLQWORK = LWORK - IORGLQ + 1
LORBDBWORK = LWORK - IORBDB + 1
LBBCSDWORK = LWORK - IBBCSD + 1
END IF
END IF
*
* Abort if any illegal arguments
*
IF( INFO .NE. 0 ) THEN
CALL XERBLA( 'DORCSD', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Transform to bidiagonal block form
*
CALL DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21,
$ LDX21, X22, LDX22, THETA, WORK(IPHI), WORK(ITAUP1),
$ WORK(ITAUP2), WORK(ITAUQ1), WORK(ITAUQ2),
$ WORK(IORBDB), LORBDBWORK, CHILDINFO )
*
* Accumulate Householder reflectors
*
IF( COLMAJOR ) THEN
IF( WANTU1 .AND. P .GT. 0 ) THEN
CALL DLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
CALL DORGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
$ LORGQRWORK, INFO)
END IF
IF( WANTU2 .AND. M-P .GT. 0 ) THEN
CALL DLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
CALL DORGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
$ WORK(IORGQR), LORGQRWORK, INFO )
END IF
IF( WANTV1T .AND. Q .GT. 0 ) THEN
CALL DLACPY( 'U', Q-1, Q-1, X11(1,2), LDX11, V1T(2,2),
$ LDV1T )
V1T(1, 1) = ONE
DO J = 2, Q
V1T(1,J) = ZERO
V1T(J,1) = ZERO
END DO
CALL DORGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
$ WORK(IORGLQ), LORGLQWORK, INFO )
END IF
IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
CALL DLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T )
IF (M-P .GT. Q) Then
CALL DLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22,
$ V2T(P+1,P+1), LDV2T )
END IF
IF (M .GT. Q) THEN
CALL DORGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
$ WORK(IORGLQ), LORGLQWORK, INFO )
END IF
END IF
ELSE
IF( WANTU1 .AND. P .GT. 0 ) THEN
CALL DLACPY( 'U', Q, P, X11, LDX11, U1, LDU1 )
CALL DORGLQ( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGLQ),
$ LORGLQWORK, INFO)
END IF
IF( WANTU2 .AND. M-P .GT. 0 ) THEN
CALL DLACPY( 'U', Q, M-P, X21, LDX21, U2, LDU2 )
CALL DORGLQ( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
$ WORK(IORGLQ), LORGLQWORK, INFO )
END IF
IF( WANTV1T .AND. Q .GT. 0 ) THEN
CALL DLACPY( 'L', Q-1, Q-1, X11(2,1), LDX11, V1T(2,2),
$ LDV1T )
V1T(1, 1) = ONE
DO J = 2, Q
V1T(1,J) = ZERO
V1T(J,1) = ZERO
END DO
CALL DORGQR( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
$ WORK(IORGQR), LORGQRWORK, INFO )
END IF
IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
CALL DLACPY( 'L', M-Q, P, X12, LDX12, V2T, LDV2T )
CALL DLACPY( 'L', M-P-Q, M-P-Q, X22(P+1,Q+1), LDX22,
$ V2T(P+1,P+1), LDV2T )
CALL DORGQR( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
$ WORK(IORGQR), LORGQRWORK, INFO )
END IF
END IF
*
* Compute the CSD of the matrix in bidiagonal-block form
*
CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA,
$ WORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
$ LDV2T, WORK(IB11D), WORK(IB11E), WORK(IB12D),
$ WORK(IB12E), WORK(IB21D), WORK(IB21E), WORK(IB22D),
$ WORK(IB22E), WORK(IBBCSD), LBBCSDWORK, INFO )
*
* Permute rows and columns to place identity submatrices in top-
* 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
* corner of (2,2)-block
*
IF( Q .GT. 0 .AND. WANTU2 ) THEN
DO I = 1, Q
IWORK(I) = M - P - Q + I
END DO
DO I = Q + 1, M - P
IWORK(I) = I - Q
END DO
IF( COLMAJOR ) THEN
CALL DLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
ELSE
CALL DLAPMR( .FALSE., M-P, M-P, U2, LDU2, IWORK )
END IF
END IF
IF( M .GT. 0 .AND. WANTV2T ) THEN
DO I = 1, P
IWORK(I) = M - P - Q + I
END DO
DO I = P + 1, M - Q
IWORK(I) = I - P
END DO
IF( .NOT. COLMAJOR ) THEN
CALL DLAPMT( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK )
ELSE
CALL DLAPMR( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK )
END IF
END IF
*
RETURN
*
* End DORCSD
*
END
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