numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/SRC/sorcsd2by1.f | 27091B | -rw-r--r-- |
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*> \brief \b SORCSD2BY1 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SORCSD2BY1 + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sorcsd2by1.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sorcsd2by1.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorcsd2by1.f"> *> [TXT]</a> *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SORCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, * X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, * LDV1T, WORK, LWORK, IWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBU1, JOBU2, JOBV1T * INTEGER INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21, * $ M, P, Q * .. * .. Array Arguments .. * REAL THETA(*) * REAL U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*), * $ X11(LDX11,*), X21(LDX21,*) * INTEGER IWORK(*) * .. * * *> \par Purpose: * ============= *> *>\verbatim *> *> SORCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with *> orthonormal columns that has been partitioned into a 2-by-1 block *> structure: *> *> [ I1 0 0 ] *> [ 0 C 0 ] *> [ X11 ] [ U1 | ] [ 0 0 0 ] *> X = [-----] = [---------] [----------] V1**T . *> [ X21 ] [ | U2 ] [ 0 0 0 ] *> [ 0 S 0 ] *> [ 0 0 I2] *> *> X11 is P-by-Q. The orthogonal matrices U1, U2, and V1 are P-by-P, *> (M-P)-by-(M-P), and Q-by-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). I1 is a K1-by-K1 identity matrix and I2 is a *> K2-by-K2 identity matrix, where K1 = MAX(Q+P-M,0), K2 = MAX(Q-P,0). *> \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] M *> \verbatim *> M is INTEGER *> The number of rows in X. *> \endverbatim *> *> \param[in] P *> \verbatim *> P is INTEGER *> The number of rows in X11. 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 REAL 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] X21 *> \verbatim *> X21 is REAL 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 X21. LDX21 >= MAX(1,M-P). *> \endverbatim *> *> \param[out] THETA *> \verbatim *> THETA is REAL 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 REAL array, dimension (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 REAL array, dimension (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 REAL array, dimension (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] WORK *> \verbatim *> WORK is REAL 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: SBBCSD 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 uncsd2by1 * * ===================================================================== SUBROUTINE SORCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, $ LDX11, $ X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, $ LDV1T, 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 INTEGER INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21, $ M, P, Q * .. * .. Array Arguments .. REAL THETA(*) REAL U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*), $ X11(LDX11,*), X21(LDX21,*) INTEGER IWORK(*) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E0, ZERO = 0.0E0 ) * .. * .. Local Scalars .. INTEGER CHILDINFO, I, IB11D, IB11E, IB12D, IB12E, $ IB21D, IB21E, IB22D, IB22E, IBBCSD, IORBDB, $ IORGLQ, IORGQR, IPHI, ITAUP1, ITAUP2, ITAUQ1, $ J, LBBCSD, LORBDB, LORGLQ, LORGLQMIN, $ LORGLQOPT, LORGQR, LORGQRMIN, LORGQROPT, $ LWORKMIN, LWORKOPT, R LOGICAL LQUERY, WANTU1, WANTU2, WANTV1T * .. * .. Local Arrays .. REAL DUM1(1), DUM2(1,1) * .. * .. External Subroutines .. EXTERNAL SBBCSD, SCOPY, SLACPY, SLAPMR, SLAPMT, $ SORBDB1, $ SORBDB2, SORBDB3, SORBDB4, SORGLQ, SORGQR, $ XERBLA * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Intrinsic Function .. INTRINSIC INT, MAX, MIN * .. * .. Executable Statements .. * * Test input arguments * INFO = 0 WANTU1 = LSAME( JOBU1, 'Y' ) WANTU2 = LSAME( JOBU2, 'Y' ) WANTV1T = LSAME( JOBV1T, 'Y' ) LQUERY = LWORK .EQ. -1 * IF( M .LT. 0 ) THEN INFO = -4 ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN INFO = -5 ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN INFO = -6 ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN INFO = -8 ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN INFO = -10 ELSE IF( WANTU1 .AND. LDU1 .LT. MAX( 1, P ) ) THEN INFO = -13 ELSE IF( WANTU2 .AND. LDU2 .LT. MAX( 1, M - P ) ) THEN INFO = -15 ELSE IF( WANTV1T .AND. LDV1T .LT. MAX( 1, Q ) ) THEN INFO = -17 END IF * R = MIN( P, M-P, Q, M-Q ) * * Compute workspace * * WORK layout: * |-------------------------------------------------------| * | LWORKOPT (1) | * |-------------------------------------------------------| * | PHI (MAX(1,R-1)) | * |-------------------------------------------------------| * | TAUP1 (MAX(1,P)) | B11D (R) | * | TAUP2 (MAX(1,M-P)) | B11E (R-1) | * | TAUQ1 (MAX(1,Q)) | B12D (R) | * |-----------------------------------------| B12E (R-1) | * | SORBDB WORK | SORGQR WORK | SORGLQ WORK | B21D (R) | * | | | | B21E (R-1) | * | | | | B22D (R) | * | | | | B22E (R-1) | * | | | | SBBCSD WORK | * |-------------------------------------------------------| * IF( INFO .EQ. 0 ) THEN IPHI = 2 IB11D = IPHI + MAX( 1, R-1 ) IB11E = IB11D + MAX( 1, R ) IB12D = IB11E + MAX( 1, R - 1 ) IB12E = IB12D + MAX( 1, R ) IB21D = IB12E + MAX( 1, R - 1 ) IB21E = IB21D + MAX( 1, R ) IB22D = IB21E + MAX( 1, R - 1 ) IB22E = IB22D + MAX( 1, R ) IBBCSD = IB22E + MAX( 1, R - 1 ) ITAUP1 = IPHI + MAX( 1, R-1 ) ITAUP2 = ITAUP1 + MAX( 1, P ) ITAUQ1 = ITAUP2 + MAX( 1, M-P ) IORBDB = ITAUQ1 + MAX( 1, Q ) IORGQR = ITAUQ1 + MAX( 1, Q ) IORGLQ = ITAUQ1 + MAX( 1, Q ) LORGQRMIN = 1 LORGQROPT = 1 LORGLQMIN = 1 LORGLQOPT = 1 IF( R .EQ. Q ) THEN CALL SORBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, $ DUM1, DUM1, DUM1, DUM1, WORK, -1, $ CHILDINFO ) LORBDB = INT( WORK(1) ) IF( WANTU1 .AND. P .GT. 0 ) THEN CALL SORGQR( P, P, Q, U1, LDU1, DUM1, WORK(1), -1, $ CHILDINFO ) LORGQRMIN = MAX( LORGQRMIN, P ) LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) ENDIF IF( WANTU2 .AND. M-P .GT. 0 ) THEN CALL SORGQR( M-P, M-P, Q, U2, LDU2, DUM1, 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 SORGLQ( Q-1, Q-1, Q-1, V1T, LDV1T, $ DUM1, WORK(1), -1, CHILDINFO ) LORGLQMIN = MAX( LORGLQMIN, Q-1 ) LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) ) END IF CALL SBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, $ THETA, $ DUM1, U1, LDU1, U2, LDU2, V1T, LDV1T, DUM2, $ 1, DUM1, DUM1, DUM1, DUM1, DUM1, $ DUM1, DUM1, DUM1, WORK(1), -1, CHILDINFO $ ) LBBCSD = INT( WORK(1) ) ELSE IF( R .EQ. P ) THEN CALL SORBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, $ DUM1, DUM1, DUM1, DUM1, WORK(1), -1, $ CHILDINFO ) LORBDB = INT( WORK(1) ) IF( WANTU1 .AND. P .GT. 0 ) THEN CALL SORGQR( P-1, P-1, P-1, U1(2,2), LDU1, DUM1, $ WORK(1), -1, CHILDINFO ) LORGQRMIN = MAX( LORGQRMIN, P-1 ) LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) END IF IF( WANTU2 .AND. M-P .GT. 0 ) THEN CALL SORGQR( M-P, M-P, Q, U2, LDU2, DUM1, 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 SORGLQ( Q, Q, R, V1T, LDV1T, DUM1, WORK(1), -1, $ CHILDINFO ) LORGLQMIN = MAX( LORGLQMIN, Q ) LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) ) END IF CALL SBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, $ THETA, $ DUM1, V1T, LDV1T, DUM2, 1, U1, LDU1, U2, $ LDU2, DUM1, DUM1, DUM1, DUM1, DUM1, $ DUM1, DUM1, DUM1, WORK(1), -1, CHILDINFO $ ) LBBCSD = INT( WORK(1) ) ELSE IF( R .EQ. M-P ) THEN CALL SORBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, $ DUM1, DUM1, DUM1, DUM1, WORK(1), -1, $ CHILDINFO ) LORBDB = INT( WORK(1) ) IF( WANTU1 .AND. P .GT. 0 ) THEN CALL SORGQR( P, P, Q, U1, LDU1, DUM1, WORK(1), -1, $ CHILDINFO ) LORGQRMIN = MAX( LORGQRMIN, P ) LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) END IF IF( WANTU2 .AND. M-P .GT. 0 ) THEN CALL SORGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2, DUM1, $ WORK(1), -1, CHILDINFO ) LORGQRMIN = MAX( LORGQRMIN, M-P-1 ) LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) END IF IF( WANTV1T .AND. Q .GT. 0 ) THEN CALL SORGLQ( Q, Q, R, V1T, LDV1T, DUM1, WORK(1), -1, $ CHILDINFO ) LORGLQMIN = MAX( LORGLQMIN, Q ) LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) ) END IF CALL SBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P, $ THETA, DUM1, DUM2, 1, V1T, LDV1T, U2, LDU2, $ U1, LDU1, DUM1, DUM1, DUM1, DUM1, $ DUM1, DUM1, DUM1, DUM1, WORK(1), -1, $ CHILDINFO ) LBBCSD = INT( WORK(1) ) ELSE CALL SORBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, $ DUM1, DUM1, DUM1, DUM1, DUM1, $ WORK(1), -1, CHILDINFO ) LORBDB = M + INT( WORK(1) ) IF( WANTU1 .AND. P .GT. 0 ) THEN CALL SORGQR( P, P, M-Q, U1, LDU1, DUM1, WORK(1), -1, $ CHILDINFO ) LORGQRMIN = MAX( LORGQRMIN, P ) LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) END IF IF( WANTU2 .AND. M-P .GT. 0 ) THEN CALL SORGQR( M-P, M-P, M-Q, U2, LDU2, DUM1, 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 SORGLQ( Q, Q, Q, V1T, LDV1T, DUM1, WORK(1), -1, $ CHILDINFO ) LORGLQMIN = MAX( LORGLQMIN, Q ) LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) ) END IF CALL SBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q, $ THETA, DUM1, U2, LDU2, U1, LDU1, DUM2, 1, $ V1T, LDV1T, DUM1, DUM1, DUM1, DUM1, $ DUM1, DUM1, DUM1, DUM1, WORK(1), -1, $ CHILDINFO ) LBBCSD = INT( WORK(1) ) END IF LWORKMIN = MAX( IORBDB+LORBDB-1, $ IORGQR+LORGQRMIN-1, $ IORGLQ+LORGLQMIN-1, $ IBBCSD+LBBCSD-1 ) LWORKOPT = MAX( IORBDB+LORBDB-1, $ IORGQR+LORGQROPT-1, $ IORGLQ+LORGLQOPT-1, $ IBBCSD+LBBCSD-1 ) WORK(1) = REAL( LWORKOPT ) IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN INFO = -19 END IF END IF IF( INFO .NE. 0 ) THEN CALL XERBLA( 'SORCSD2BY1', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF LORGQR = LWORK-IORGQR+1 LORGLQ = LWORK-IORGLQ+1 * * Handle four cases separately: R = Q, R = P, R = M-P, and R = M-Q, * in which R = MIN(P,M-P,Q,M-Q) * IF( R .EQ. Q ) THEN * * Case 1: R = Q * * Simultaneously bidiagonalize X11 and X21 * CALL SORBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, $ WORK(IPHI), WORK(ITAUP1), WORK(ITAUP2), $ WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO ) * * Accumulate Householder reflectors * IF( WANTU1 .AND. P .GT. 0 ) THEN CALL SLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 ) CALL SORGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), $ WORK(IORGQR), $ LORGQR, CHILDINFO ) END IF IF( WANTU2 .AND. M-P .GT. 0 ) THEN CALL SLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 ) CALL SORGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2), $ WORK(IORGQR), LORGQR, CHILDINFO ) END IF IF( WANTV1T .AND. Q .GT. 0 ) THEN V1T(1,1) = ONE DO J = 2, Q V1T(1,J) = ZERO V1T(J,1) = ZERO END DO CALL SLACPY( 'U', Q-1, Q-1, X21(1,2), LDX21, V1T(2,2), $ LDV1T ) CALL SORGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, $ WORK(ITAUQ1), $ WORK(IORGLQ), LORGLQ, CHILDINFO ) END IF * * Simultaneously diagonalize X11 and X21. * CALL SBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA, $ WORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, $ DUM2, 1, WORK(IB11D), WORK(IB11E), WORK(IB12D), $ WORK(IB12E), WORK(IB21D), WORK(IB21E), $ WORK(IB22D), WORK(IB22E), WORK(IBBCSD), LBBCSD, $ CHILDINFO ) * * Permute rows and columns to place zero submatrices in * preferred positions * 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 CALL SLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK ) END IF ELSE IF( R .EQ. P ) THEN * * Case 2: R = P * * Simultaneously bidiagonalize X11 and X21 * CALL SORBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, $ WORK(IPHI), WORK(ITAUP1), WORK(ITAUP2), $ WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO ) * * Accumulate Householder reflectors * IF( WANTU1 .AND. P .GT. 0 ) THEN U1(1,1) = ONE DO J = 2, P U1(1,J) = ZERO U1(J,1) = ZERO END DO CALL SLACPY( 'L', P-1, P-1, X11(2,1), LDX11, U1(2,2), $ LDU1 ) CALL SORGQR( P-1, P-1, P-1, U1(2,2), LDU1, WORK(ITAUP1), $ WORK(IORGQR), LORGQR, CHILDINFO ) END IF IF( WANTU2 .AND. M-P .GT. 0 ) THEN CALL SLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 ) CALL SORGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2), $ WORK(IORGQR), LORGQR, CHILDINFO ) END IF IF( WANTV1T .AND. Q .GT. 0 ) THEN CALL SLACPY( 'U', P, Q, X11, LDX11, V1T, LDV1T ) CALL SORGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1), $ WORK(IORGLQ), LORGLQ, CHILDINFO ) END IF * * Simultaneously diagonalize X11 and X21. * CALL SBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA, $ WORK(IPHI), V1T, LDV1T, DUM1, 1, U1, LDU1, U2, $ LDU2, WORK(IB11D), WORK(IB11E), WORK(IB12D), $ WORK(IB12E), WORK(IB21D), WORK(IB21E), $ WORK(IB22D), WORK(IB22E), WORK(IBBCSD), LBBCSD, $ CHILDINFO ) * * Permute rows and columns to place identity submatrices in * preferred positions * 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 CALL SLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK ) END IF ELSE IF( R .EQ. M-P ) THEN * * Case 3: R = M-P * * Simultaneously bidiagonalize X11 and X21 * CALL SORBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, $ WORK(IPHI), WORK(ITAUP1), WORK(ITAUP2), $ WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO ) * * Accumulate Householder reflectors * IF( WANTU1 .AND. P .GT. 0 ) THEN CALL SLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 ) CALL SORGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), $ WORK(IORGQR), $ LORGQR, CHILDINFO ) END IF IF( WANTU2 .AND. M-P .GT. 0 ) THEN U2(1,1) = ONE DO J = 2, M-P U2(1,J) = ZERO U2(J,1) = ZERO END DO CALL SLACPY( 'L', M-P-1, M-P-1, X21(2,1), LDX21, U2(2,2), $ LDU2 ) CALL SORGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2, $ WORK(ITAUP2), WORK(IORGQR), LORGQR, CHILDINFO ) END IF IF( WANTV1T .AND. Q .GT. 0 ) THEN CALL SLACPY( 'U', M-P, Q, X21, LDX21, V1T, LDV1T ) CALL SORGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1), $ WORK(IORGLQ), LORGLQ, CHILDINFO ) END IF * * Simultaneously diagonalize X11 and X21. * CALL SBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P, $ THETA, WORK(IPHI), DUM1, 1, V1T, LDV1T, U2, $ LDU2, U1, LDU1, WORK(IB11D), WORK(IB11E), $ WORK(IB12D), WORK(IB12E), WORK(IB21D), $ WORK(IB21E), WORK(IB22D), WORK(IB22E), $ WORK(IBBCSD), LBBCSD, CHILDINFO ) * * Permute rows and columns to place identity submatrices in * preferred positions * IF( Q .GT. R ) THEN DO I = 1, R IWORK(I) = Q - R + I END DO DO I = R + 1, Q IWORK(I) = I - R END DO IF( WANTU1 ) THEN CALL SLAPMT( .FALSE., P, Q, U1, LDU1, IWORK ) END IF IF( WANTV1T ) THEN CALL SLAPMR( .FALSE., Q, Q, V1T, LDV1T, IWORK ) END IF END IF ELSE * * Case 4: R = M-Q * * Simultaneously bidiagonalize X11 and X21 * CALL SORBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, $ WORK(IPHI), WORK(ITAUP1), WORK(ITAUP2), $ WORK(ITAUQ1), WORK(IORBDB), WORK(IORBDB+M), $ LORBDB-M, CHILDINFO ) * * Accumulate Householder reflectors * IF( WANTU2 .AND. M-P .GT. 0 ) THEN CALL SCOPY( M-P, WORK(IORBDB+P), 1, U2, 1 ) END IF IF( WANTU1 .AND. P .GT. 0 ) THEN CALL SCOPY( P, WORK(IORBDB), 1, U1, 1 ) DO J = 2, P U1(1,J) = ZERO END DO CALL SLACPY( 'L', P-1, M-Q-1, X11(2,1), LDX11, U1(2,2), $ LDU1 ) CALL SORGQR( P, P, M-Q, U1, LDU1, WORK(ITAUP1), $ WORK(IORGQR), LORGQR, CHILDINFO ) END IF IF( WANTU2 .AND. M-P .GT. 0 ) THEN DO J = 2, M-P U2(1,J) = ZERO END DO CALL SLACPY( 'L', M-P-1, M-Q-1, X21(2,1), LDX21, U2(2,2), $ LDU2 ) CALL SORGQR( M-P, M-P, M-Q, U2, LDU2, WORK(ITAUP2), $ WORK(IORGQR), LORGQR, CHILDINFO ) END IF IF( WANTV1T .AND. Q .GT. 0 ) THEN CALL SLACPY( 'U', M-Q, Q, X21, LDX21, V1T, LDV1T ) CALL SLACPY( 'U', P-(M-Q), Q-(M-Q), X11(M-Q+1,M-Q+1), $ LDX11, $ V1T(M-Q+1,M-Q+1), LDV1T ) CALL SLACPY( 'U', -P+Q, Q-P, X21(M-Q+1,P+1), LDX21, $ V1T(P+1,P+1), LDV1T ) CALL SORGLQ( Q, Q, Q, V1T, LDV1T, WORK(ITAUQ1), $ WORK(IORGLQ), LORGLQ, CHILDINFO ) END IF * * Simultaneously diagonalize X11 and X21. * CALL SBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q, $ THETA, WORK(IPHI), U2, LDU2, U1, LDU1, DUM1, 1, $ V1T, LDV1T, WORK(IB11D), WORK(IB11E), WORK(IB12D), $ WORK(IB12E), WORK(IB21D), WORK(IB21E), $ WORK(IB22D), WORK(IB22E), WORK(IBBCSD), LBBCSD, $ CHILDINFO ) * * Permute rows and columns to place identity submatrices in * preferred positions * IF( P .GT. R ) THEN DO I = 1, R IWORK(I) = P - R + I END DO DO I = R + 1, P IWORK(I) = I - R END DO IF( WANTU1 ) THEN CALL SLAPMT( .FALSE., P, P, U1, LDU1, IWORK ) END IF IF( WANTV1T ) THEN CALL SLAPMR( .FALSE., P, Q, V1T, LDV1T, IWORK ) END IF END IF END IF * RETURN * * End of SORCSD2BY1 * END