--- rpl/lapack/lapack/dorcsd2by1.f 2015/11/26 11:44:19 1.3 +++ rpl/lapack/lapack/dorcsd2by1.f 2017/06/17 10:53:58 1.6 @@ -2,8 +2,8 @@ * * =========== DOCUMENTATION =========== * -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORCSD2BY1 + dependencies @@ -21,7 +21,7 @@ * SUBROUTINE DORCSD2BY1( 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, @@ -33,31 +33,30 @@ * $ X11(LDX11,*), X21(LDX21,*) * INTEGER IWORK(*) * .. -* -* +* +* *> \par Purpose: *> ============= *> *>\verbatim -*> Purpose: -*> ======== *> *> DORCSD2BY1 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: *> -*> [ I 0 0 ] +*> [ I1 0 0 ] *> [ 0 C 0 ] *> [ X11 ] [ U1 | ] [ 0 0 0 ] *> X = [-----] = [---------] [----------] V1**T . *> [ X21 ] [ | U2 ] [ 0 0 0 ] *> [ 0 S 0 ] -*> [ 0 0 I ] -*> +*> [ 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). +*> 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: @@ -220,10 +219,10 @@ * Authors: * ======== * -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * *> \date July 2012 * @@ -250,7 +249,7 @@ $ X11(LDX11,*), X21(LDX21,*) INTEGER IWORK(*) * .. -* +* * ===================================================================== * * .. Parameters .. @@ -266,6 +265,9 @@ $ 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, @@ -298,11 +300,11 @@ 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 * @@ -344,99 +346,125 @@ 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, @@ -497,16 +525,16 @@ CALL DORGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1), $ WORK(IORGLQ), LORGLQ, CHILDINFO ) END IF -* +* * 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 * @@ -551,16 +579,16 @@ CALL DORGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1), $ WORK(IORGLQ), LORGLQ, CHILDINFO ) END IF -* +* * 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 ) -* +* * Permute rows and columns to place identity submatrices in * preferred positions * @@ -606,16 +634,16 @@ CALL DORGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1), $ WORK(IORGLQ), LORGLQ, CHILDINFO ) END IF -* +* * 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 * @@ -675,16 +703,16 @@ CALL DORGLQ( Q, Q, Q, V1T, LDV1T, WORK(ITAUQ1), $ WORK(IORGLQ), LORGLQ, CHILDINFO ) END IF -* +* * 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 *