--- rpl/lapack/lapack/dorcsd2by1.f 2014/01/27 09:28:24 1.2 +++ rpl/lapack/lapack/dorcsd2by1.f 2016/08/27 15:34:33 1.5 @@ -54,12 +54,11 @@ *> [ 0 S 0 ] *> [ 0 0 I ] *> -*> 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 +*> 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). +*> \endverbatim * * Arguments: * ========== @@ -67,138 +66,137 @@ *> \param[in] JOBU1 *> \verbatim *> JOBU1 is CHARACTER -*> = 'Y': U1 is computed; -*> otherwise: U1 is not computed. +*> = '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. +*> = '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. +*> = 'Y': V1T is computed; +*> otherwise: V1T is not computed. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER -*> The number of rows and columns in X. +*> The number of rows in X. *> \endverbatim *> *> \param[in] P *> \verbatim *> P is INTEGER -*> The number of rows in X11 and X12. 0 <= P <= M. +*> 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. +*> 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. +*> 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). +*> The leading dimension of X11. LDX11 >= 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. +*> 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). +*> The leading dimension of X21. LDX21 >= 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)) ). +*> 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 (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 *> *> \param[in] LDU1 *> \verbatim *> LDU1 is INTEGER -*> The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= -*> MAX(1,P). +*> The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= +*> MAX(1,P). *> \endverbatim *> *> \param[out] U2 *> \verbatim *> U2 is DOUBLE PRECISION array, dimension (M-P) -*> If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal -*> matrix U2. +*> 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). +*> The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= +*> MAX(1,M-P). *> \endverbatim *> *> \param[out] V1T *> \verbatim *> V1T is DOUBLE PRECISION array, dimension (Q) -*> If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal -*> matrix V1**T. +*> 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). +*> The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= +*> MAX(1,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. +*> 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. +*> 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 *> -*> 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. *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q)) @@ -207,12 +205,18 @@ *> \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 +*> = 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: * ======== * @@ -225,13 +229,6 @@ * *> \ingroup doubleOTHERcomputational * -*> \par References: -* ================ -*> -*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. -*> Algorithms, 50(1):33-65, 2009. -*> \endverbatim -*> * ===================================================================== SUBROUTINE DORCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, $ X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, @@ -269,6 +266,9 @@ $ LWORKMIN, LWORKOPT, R LOGICAL LQUERY, WANTU1, WANTU2, WANTV1T * .. +* .. Local Arrays .. + DOUBLE PRECISION DUM1(1), DUM2(1,1) +* .. * .. External Subroutines .. EXTERNAL DBBCSD, DCOPY, DLACPY, DLAPMR, DLAPMT, DORBDB1, $ DORBDB2, DORBDB3, DORBDB4, DORGLQ, DORGQR, @@ -301,11 +301,11 @@ INFO = -8 ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN INFO = -10 - ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN + ELSE IF( WANTU1 .AND. LDU1 .LT. MAX( 1, P ) ) THEN INFO = -13 - ELSE IF( WANTU2 .AND. LDU2 .LT. M - P ) THEN + ELSE IF( WANTU2 .AND. LDU2 .LT. MAX( 1, M - P ) ) THEN INFO = -15 - ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN + ELSE IF( WANTV1T .AND. LDV1T .LT. MAX( 1, Q ) ) THEN INFO = -17 END IF * @@ -347,99 +347,125 @@ 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 DORBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0, - $ 0, 0, WORK, -1, CHILDINFO ) + CALL DORBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, + $ DUM1, DUM1, DUM1, DUM1, WORK, + $ -1, CHILDINFO ) LORBDB = INT( WORK(1) ) - IF( P .GE. M-P ) THEN - CALL DORGQR( P, P, Q, U1, LDU1, 0, WORK(1), -1, - $ CHILDINFO ) - LORGQRMIN = MAX( 1, P ) - LORGQROPT = INT( WORK(1) ) - ELSE - CALL DORGQR( M-P, M-P, Q, U2, LDU2, 0, WORK(1), -1, + IF( WANTU1 .AND. P .GT. 0 ) THEN + CALL DORGQR( P, P, Q, U1, LDU1, DUM1, WORK(1), -1, $ CHILDINFO ) - LORGQRMIN = MAX( 1, M-P ) - LORGQROPT = INT( WORK(1) ) + LORGQRMIN = MAX( LORGQRMIN, P ) + LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) + ENDIF + IF( WANTU2 .AND. M-P .GT. 0 ) THEN + CALL DORGQR( 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 DORGLQ( 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 DORGLQ( MAX(0,Q-1), MAX(0,Q-1), MAX(0,Q-1), V1T, LDV1T, - $ 0, WORK(1), -1, CHILDINFO ) - LORGLQMIN = MAX( 1, Q-1 ) - LORGLQOPT = INT( WORK(1) ) CALL DBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA, - $ 0, U1, LDU1, U2, LDU2, V1T, LDV1T, 0, 1, 0, 0, - $ 0, 0, 0, 0, 0, 0, WORK(1), -1, CHILDINFO ) + $ 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 DORBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0, - $ 0, 0, WORK(1), -1, CHILDINFO ) + CALL DORBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, + $ DUM1, DUM1, DUM1, DUM1, + $ WORK(1), -1, CHILDINFO ) LORBDB = INT( WORK(1) ) - IF( P-1 .GE. M-P ) THEN - CALL DORGQR( P-1, P-1, P-1, U1(2,2), LDU1, 0, WORK(1), + IF( WANTU1 .AND. P .GT. 0 ) THEN + CALL DORGQR( 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 DORGQR( M-P, M-P, Q, U2, LDU2, DUM1, WORK(1), $ -1, CHILDINFO ) - LORGQRMIN = MAX( 1, P-1 ) - LORGQROPT = INT( WORK(1) ) - ELSE - CALL DORGQR( M-P, M-P, Q, U2, LDU2, 0, WORK(1), -1, + LORGQRMIN = MAX( LORGQRMIN, M-P ) + LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) + END IF + IF( WANTV1T .AND. Q .GT. 0 ) THEN + CALL DORGLQ( Q, Q, R, V1T, LDV1T, DUM1, WORK(1), -1, $ CHILDINFO ) - LORGQRMIN = MAX( 1, M-P ) - LORGQROPT = INT( WORK(1) ) + LORGLQMIN = MAX( LORGLQMIN, Q ) + LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) ) END IF - CALL DORGLQ( Q, Q, R, V1T, LDV1T, 0, WORK(1), -1, - $ CHILDINFO ) - LORGLQMIN = MAX( 1, Q ) - LORGLQOPT = INT( WORK(1) ) CALL DBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA, - $ 0, V1T, LDV1T, 0, 1, U1, LDU1, U2, LDU2, 0, 0, - $ 0, 0, 0, 0, 0, 0, WORK(1), -1, CHILDINFO ) + $ 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 DORBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0, - $ 0, 0, WORK(1), -1, CHILDINFO ) + CALL DORBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, + $ DUM1, DUM1, DUM1, DUM1, + $ WORK(1), -1, CHILDINFO ) LORBDB = INT( WORK(1) ) - IF( P .GE. M-P-1 ) THEN - CALL DORGQR( P, P, Q, U1, LDU1, 0, WORK(1), -1, + IF( WANTU1 .AND. P .GT. 0 ) THEN + CALL DORGQR( P, P, Q, U1, LDU1, DUM1, WORK(1), -1, $ CHILDINFO ) - LORGQRMIN = MAX( 1, P ) - LORGQROPT = INT( WORK(1) ) - ELSE - CALL DORGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2, 0, - $ WORK(1), -1, CHILDINFO ) - LORGQRMIN = MAX( 1, M-P-1 ) - LORGQROPT = INT( WORK(1) ) + LORGQRMIN = MAX( LORGQRMIN, P ) + LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) + END IF + IF( WANTU2 .AND. M-P .GT. 0 ) THEN + CALL DORGQR( 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 DORGLQ( Q, Q, R, V1T, LDV1T, DUM1, WORK(1), -1, + $ CHILDINFO ) + LORGLQMIN = MAX( LORGLQMIN, Q ) + LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) ) END IF - CALL DORGLQ( Q, Q, R, V1T, LDV1T, 0, WORK(1), -1, - $ CHILDINFO ) - LORGLQMIN = MAX( 1, Q ) - LORGLQOPT = INT( WORK(1) ) CALL DBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P, - $ THETA, 0, 0, 1, V1T, LDV1T, U2, LDU2, U1, LDU1, - $ 0, 0, 0, 0, 0, 0, 0, 0, WORK(1), -1, - $ CHILDINFO ) + $ 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 DORBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0, - $ 0, 0, 0, WORK(1), -1, CHILDINFO ) + CALL DORBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, + $ DUM1, DUM1, DUM1, DUM1, + $ DUM1, WORK(1), -1, CHILDINFO ) LORBDB = M + INT( WORK(1) ) - IF( P .GE. M-P ) THEN - CALL DORGQR( P, P, M-Q, U1, LDU1, 0, WORK(1), -1, + IF( WANTU1 .AND. P .GT. 0 ) THEN + CALL DORGQR( P, P, M-Q, U1, LDU1, DUM1, WORK(1), -1, $ CHILDINFO ) - LORGQRMIN = MAX( 1, P ) - LORGQROPT = INT( WORK(1) ) - ELSE - CALL DORGQR( M-P, M-P, M-Q, U2, LDU2, 0, WORK(1), -1, + LORGQRMIN = MAX( LORGQRMIN, P ) + LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) ) + END IF + IF( WANTU2 .AND. M-P .GT. 0 ) THEN + CALL DORGQR( 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 DORGLQ( Q, Q, Q, V1T, LDV1T, DUM1, WORK(1), -1, $ CHILDINFO ) - LORGQRMIN = MAX( 1, M-P ) - LORGQROPT = INT( WORK(1) ) + LORGLQMIN = MAX( LORGLQMIN, Q ) + LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) ) END IF - CALL DORGLQ( Q, Q, Q, V1T, LDV1T, 0, WORK(1), -1, - $ CHILDINFO ) - LORGLQMIN = MAX( 1, Q ) - LORGLQOPT = INT( WORK(1) ) CALL DBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q, - $ THETA, 0, U2, LDU2, U1, LDU1, 0, 1, V1T, LDV1T, - $ 0, 0, 0, 0, 0, 0, 0, 0, WORK(1), -1, - $ CHILDINFO ) + $ 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, @@ -504,11 +530,11 @@ * Simultaneously diagonalize X11 and X21. * CALL DBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA, - $ WORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, 0, 1, - $ WORK(IB11D), WORK(IB11E), WORK(IB12D), - $ WORK(IB12E), WORK(IB21D), WORK(IB21E), - $ WORK(IB22D), WORK(IB22E), WORK(IBBCSD), LBBCSD, - $ CHILDINFO ) + $ 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 @@ -558,8 +584,8 @@ * Simultaneously diagonalize X11 and X21. * CALL DBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA, - $ WORK(IPHI), V1T, LDV1T, 0, 1, U1, LDU1, U2, LDU2, - $ WORK(IB11D), WORK(IB11E), WORK(IB12D), + $ WORK(IPHI), V1T, LDV1T, DUM2, 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 ) @@ -613,11 +639,11 @@ * Simultaneously diagonalize X11 and X21. * CALL DBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P, - $ THETA, WORK(IPHI), 0, 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 ) + $ THETA, WORK(IPHI), DUM2, 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 @@ -682,11 +708,11 @@ * Simultaneously diagonalize X11 and X21. * CALL DBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q, - $ THETA, WORK(IPHI), U2, LDU2, U1, LDU1, 0, 1, V1T, - $ LDV1T, WORK(IB11D), WORK(IB11E), WORK(IB12D), - $ WORK(IB12E), WORK(IB21D), WORK(IB21E), - $ WORK(IB22D), WORK(IB22E), WORK(IBBCSD), LBBCSD, - $ CHILDINFO ) + $ THETA, WORK(IPHI), U2, LDU2, U1, LDU1, DUM2, + $ 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