version 1.11, 2012/12/14 12:30:20
|
version 1.14, 2015/11/26 11:44:15
|
Line 45
|
Line 45
|
*> matrix, and V is an N-by-N orthogonal matrix. The diagonal elements |
*> matrix, and V is an N-by-N orthogonal matrix. The diagonal elements |
*> of SIGMA are the singular values of A. The columns of U and V are the |
*> of SIGMA are the singular values of A. The columns of U and V are the |
*> left and the right singular vectors of A, respectively. |
*> left and the right singular vectors of A, respectively. |
|
*> DGESVJ can sometimes compute tiny singular values and their singular vectors much |
|
*> more accurately than other SVD routines, see below under Further Details. |
*> \endverbatim |
*> \endverbatim |
* |
* |
* Arguments: |
* Arguments: |
Line 258
|
Line 260
|
*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
* |
*> \date September 2012 |
*> \date November 2015 |
* |
* |
*> \ingroup doubleGEcomputational |
*> \ingroup doubleGEcomputational |
* |
* |
Line 335
|
Line 337
|
SUBROUTINE DGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V, |
SUBROUTINE DGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V, |
$ LDV, WORK, LWORK, INFO ) |
$ LDV, WORK, LWORK, INFO ) |
* |
* |
* -- LAPACK computational routine (version 3.4.2) -- |
* -- LAPACK computational routine (version 3.6.0) -- |
* -- 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..-- |
* September 2012 |
* November 2015 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, LDA, LDV, LWORK, M, MV, N |
INTEGER INFO, LDA, LDV, LWORK, M, MV, N |
Line 374
|
Line 376
|
DOUBLE PRECISION FASTR( 5 ) |
DOUBLE PRECISION FASTR( 5 ) |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC DABS, DMAX1, DMIN1, DBLE, MIN0, DSIGN, DSQRT |
INTRINSIC DABS, MAX, MIN, DBLE, DSIGN, DSQRT |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
* .. |
* .. |
Line 428
|
Line 430
|
INFO = -11 |
INFO = -11 |
ELSE IF( UCTOL .AND. ( WORK( 1 ).LE.ONE ) ) THEN |
ELSE IF( UCTOL .AND. ( WORK( 1 ).LE.ONE ) ) THEN |
INFO = -12 |
INFO = -12 |
ELSE IF( LWORK.LT.MAX0( M+N, 6 ) ) THEN |
ELSE IF( LWORK.LT.MAX( M+N, 6 ) ) THEN |
INFO = -13 |
INFO = -13 |
ELSE |
ELSE |
INFO = 0 |
INFO = 0 |
Line 594
|
Line 596
|
AAPP = ZERO |
AAPP = ZERO |
AAQQ = BIG |
AAQQ = BIG |
DO 4781 p = 1, N |
DO 4781 p = 1, N |
IF( SVA( p ).NE.ZERO )AAQQ = DMIN1( AAQQ, SVA( p ) ) |
IF( SVA( p ).NE.ZERO )AAQQ = MIN( AAQQ, SVA( p ) ) |
AAPP = DMAX1( AAPP, SVA( p ) ) |
AAPP = MAX( AAPP, SVA( p ) ) |
4781 CONTINUE |
4781 CONTINUE |
* |
* |
* #:) Quick return for zero matrix |
* #:) Quick return for zero matrix |
Line 636
|
Line 638
|
TEMP1 = DSQRT( BIG / DBLE( N ) ) |
TEMP1 = DSQRT( BIG / DBLE( N ) ) |
IF( ( AAPP.LE.SN ) .OR. ( AAQQ.GE.TEMP1 ) .OR. |
IF( ( AAPP.LE.SN ) .OR. ( AAQQ.GE.TEMP1 ) .OR. |
$ ( ( SN.LE.AAQQ ) .AND. ( AAPP.LE.TEMP1 ) ) ) THEN |
$ ( ( SN.LE.AAQQ ) .AND. ( AAPP.LE.TEMP1 ) ) ) THEN |
TEMP1 = DMIN1( BIG, TEMP1 / AAPP ) |
TEMP1 = MIN( BIG, TEMP1 / AAPP ) |
* AAQQ = AAQQ*TEMP1 |
* AAQQ = AAQQ*TEMP1 |
* AAPP = AAPP*TEMP1 |
* AAPP = AAPP*TEMP1 |
ELSE IF( ( AAQQ.LE.SN ) .AND. ( AAPP.LE.TEMP1 ) ) THEN |
ELSE IF( ( AAQQ.LE.SN ) .AND. ( AAPP.LE.TEMP1 ) ) THEN |
TEMP1 = DMIN1( SN / AAQQ, BIG / ( AAPP*DSQRT( DBLE( N ) ) ) ) |
TEMP1 = MIN( SN / AAQQ, BIG / ( AAPP*DSQRT( DBLE( N ) ) ) ) |
* AAQQ = AAQQ*TEMP1 |
* AAQQ = AAQQ*TEMP1 |
* AAPP = AAPP*TEMP1 |
* AAPP = AAPP*TEMP1 |
ELSE IF( ( AAQQ.GE.SN ) .AND. ( AAPP.GE.TEMP1 ) ) THEN |
ELSE IF( ( AAQQ.GE.SN ) .AND. ( AAPP.GE.TEMP1 ) ) THEN |
TEMP1 = DMAX1( SN / AAQQ, TEMP1 / AAPP ) |
TEMP1 = MAX( SN / AAQQ, TEMP1 / AAPP ) |
* AAQQ = AAQQ*TEMP1 |
* AAQQ = AAQQ*TEMP1 |
* AAPP = AAPP*TEMP1 |
* AAPP = AAPP*TEMP1 |
ELSE IF( ( AAQQ.LE.SN ) .AND. ( AAPP.GE.TEMP1 ) ) THEN |
ELSE IF( ( AAQQ.LE.SN ) .AND. ( AAPP.GE.TEMP1 ) ) THEN |
TEMP1 = DMIN1( SN / AAQQ, BIG / ( DSQRT( DBLE( N ) )*AAPP ) ) |
TEMP1 = MIN( SN / AAQQ, BIG / ( DSQRT( DBLE( N ) )*AAPP ) ) |
* AAQQ = AAQQ*TEMP1 |
* AAQQ = AAQQ*TEMP1 |
* AAPP = AAPP*TEMP1 |
* AAPP = AAPP*TEMP1 |
ELSE |
ELSE |
Line 689
|
Line 691
|
* The boundaries are determined dynamically, based on the number of |
* The boundaries are determined dynamically, based on the number of |
* pivots above a threshold. |
* pivots above a threshold. |
* |
* |
KBL = MIN0( 8, N ) |
KBL = MIN( 8, N ) |
*[TP] KBL is a tuning parameter that defines the tile size in the |
*[TP] KBL is a tuning parameter that defines the tile size in the |
* tiling of the p-q loops of pivot pairs. In general, an optimal |
* tiling of the p-q loops of pivot pairs. In general, an optimal |
* value of KBL depends on the matrix dimensions and on the |
* value of KBL depends on the matrix dimensions and on the |
Line 701
|
Line 703
|
BLSKIP = KBL**2 |
BLSKIP = KBL**2 |
*[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. |
*[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. |
* |
* |
ROWSKIP = MIN0( 5, KBL ) |
ROWSKIP = MIN( 5, KBL ) |
*[TP] ROWSKIP is a tuning parameter. |
*[TP] ROWSKIP is a tuning parameter. |
* |
* |
LKAHEAD = 1 |
LKAHEAD = 1 |
Line 712
|
Line 714
|
* invokes cubic convergence. Big part of this cycle is done inside |
* invokes cubic convergence. Big part of this cycle is done inside |
* canonical subspaces of dimensions less than M. |
* canonical subspaces of dimensions less than M. |
* |
* |
IF( ( LOWER .OR. UPPER ) .AND. ( N.GT.MAX0( 64, 4*KBL ) ) ) THEN |
IF( ( LOWER .OR. UPPER ) .AND. ( N.GT.MAX( 64, 4*KBL ) ) ) THEN |
*[TP] The number of partition levels and the actual partition are |
*[TP] The number of partition levels and the actual partition are |
* tuning parameters. |
* tuning parameters. |
N4 = N / 4 |
N4 = N / 4 |
Line 810
|
Line 812
|
* |
* |
igl = ( ibr-1 )*KBL + 1 |
igl = ( ibr-1 )*KBL + 1 |
* |
* |
DO 1002 ir1 = 0, MIN0( LKAHEAD, NBL-ibr ) |
DO 1002 ir1 = 0, MIN( LKAHEAD, NBL-ibr ) |
* |
* |
igl = igl + ir1*KBL |
igl = igl + ir1*KBL |
* |
* |
DO 2001 p = igl, MIN0( igl+KBL-1, N-1 ) |
DO 2001 p = igl, MIN( igl+KBL-1, N-1 ) |
* |
* |
* .. de Rijk's pivoting |
* .. de Rijk's pivoting |
* |
* |
Line 863
|
Line 865
|
* |
* |
PSKIPPED = 0 |
PSKIPPED = 0 |
* |
* |
DO 2002 q = p + 1, MIN0( igl+KBL-1, N ) |
DO 2002 q = p + 1, MIN( igl+KBL-1, N ) |
* |
* |
AAQQ = SVA( q ) |
AAQQ = SVA( q ) |
* |
* |
Line 902
|
Line 904
|
END IF |
END IF |
END IF |
END IF |
* |
* |
MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) ) |
MXAAPQ = MAX( MXAAPQ, DABS( AAPQ ) ) |
* |
* |
* TO rotate or NOT to rotate, THAT is the question ... |
* TO rotate or NOT to rotate, THAT is the question ... |
* |
* |
Line 935
|
Line 937
|
$ V( 1, p ), 1, |
$ V( 1, p ), 1, |
$ V( 1, q ), 1, |
$ V( 1, q ), 1, |
$ FASTR ) |
$ FASTR ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( MAX( ZERO, |
$ ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*DSQRT( MAX( ZERO, |
$ ONE-T*AQOAP*AAPQ ) ) |
$ ONE-T*AQOAP*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, DABS( T ) ) |
MXSINJ = MAX( MXSINJ, DABS( T ) ) |
* |
* |
ELSE |
ELSE |
* |
* |
Line 951
|
Line 953
|
CS = DSQRT( ONE / ( ONE+T*T ) ) |
CS = DSQRT( ONE / ( ONE+T*T ) ) |
SN = T*CS |
SN = T*CS |
* |
* |
MXSINJ = DMAX1( MXSINJ, DABS( SN ) ) |
MXSINJ = MAX( MXSINJ, DABS( SN ) ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( MAX( ZERO, |
$ ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*DSQRT( MAX( ZERO, |
$ ONE-T*AQOAP*AAPQ ) ) |
$ ONE-T*AQOAP*AAPQ ) ) |
* |
* |
APOAQ = WORK( p ) / WORK( q ) |
APOAQ = WORK( p ) / WORK( q ) |
Line 1068
|
Line 1070
|
$ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
CALL DLASCL( 'G', 0, 0, ONE, AAQQ, M, |
CALL DLASCL( 'G', 0, 0, ONE, AAQQ, M, |
$ 1, A( 1, q ), LDA, IERR ) |
$ 1, A( 1, q ), LDA, IERR ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( MAX( ZERO, |
$ ONE-AAPQ*AAPQ ) ) |
$ ONE-AAPQ*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = MAX( MXSINJ, SFMIN ) |
END IF |
END IF |
* END IF ROTOK THEN ... ELSE |
* END IF ROTOK THEN ... ELSE |
* |
* |
Line 1136
|
Line 1138
|
ELSE |
ELSE |
SVA( p ) = AAPP |
SVA( p ) = AAPP |
IF( ( ir1.EQ.0 ) .AND. ( AAPP.EQ.ZERO ) ) |
IF( ( ir1.EQ.0 ) .AND. ( AAPP.EQ.ZERO ) ) |
$ NOTROT = NOTROT + MIN0( igl+KBL-1, N ) - p |
$ NOTROT = NOTROT + MIN( igl+KBL-1, N ) - p |
END IF |
END IF |
* |
* |
2001 CONTINUE |
2001 CONTINUE |
Line 1156
|
Line 1158
|
* doing the block at ( ibr, jbc ) |
* doing the block at ( ibr, jbc ) |
* |
* |
IJBLSK = 0 |
IJBLSK = 0 |
DO 2100 p = igl, MIN0( igl+KBL-1, N ) |
DO 2100 p = igl, MIN( igl+KBL-1, N ) |
* |
* |
AAPP = SVA( p ) |
AAPP = SVA( p ) |
IF( AAPP.GT.ZERO ) THEN |
IF( AAPP.GT.ZERO ) THEN |
* |
* |
PSKIPPED = 0 |
PSKIPPED = 0 |
* |
* |
DO 2200 q = jgl, MIN0( jgl+KBL-1, N ) |
DO 2200 q = jgl, MIN( jgl+KBL-1, N ) |
* |
* |
AAQQ = SVA( q ) |
AAQQ = SVA( q ) |
IF( AAQQ.GT.ZERO ) THEN |
IF( AAQQ.GT.ZERO ) THEN |
Line 1213
|
Line 1215
|
END IF |
END IF |
END IF |
END IF |
* |
* |
MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) ) |
MXAAPQ = MAX( MXAAPQ, DABS( AAPQ ) ) |
* |
* |
* TO rotate or NOT to rotate, THAT is the question ... |
* TO rotate or NOT to rotate, THAT is the question ... |
* |
* |
Line 1241
|
Line 1243
|
$ V( 1, p ), 1, |
$ V( 1, p ), 1, |
$ V( 1, q ), 1, |
$ V( 1, q ), 1, |
$ FASTR ) |
$ FASTR ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( MAX( ZERO, |
$ ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*DSQRT( MAX( ZERO, |
$ ONE-T*AQOAP*AAPQ ) ) |
$ ONE-T*AQOAP*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, DABS( T ) ) |
MXSINJ = MAX( MXSINJ, DABS( T ) ) |
ELSE |
ELSE |
* |
* |
* .. choose correct signum for THETA and rotate |
* .. choose correct signum for THETA and rotate |
Line 1256
|
Line 1258
|
$ DSQRT( ONE+THETA*THETA ) ) |
$ DSQRT( ONE+THETA*THETA ) ) |
CS = DSQRT( ONE / ( ONE+T*T ) ) |
CS = DSQRT( ONE / ( ONE+T*T ) ) |
SN = T*CS |
SN = T*CS |
MXSINJ = DMAX1( MXSINJ, DABS( SN ) ) |
MXSINJ = MAX( MXSINJ, DABS( SN ) ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( MAX( ZERO, |
$ ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*DSQRT( MAX( ZERO, |
$ ONE-T*AQOAP*AAPQ ) ) |
$ ONE-T*AQOAP*AAPQ ) ) |
* |
* |
APOAQ = WORK( p ) / WORK( q ) |
APOAQ = WORK( p ) / WORK( q ) |
Line 1376
|
Line 1378
|
CALL DLASCL( 'G', 0, 0, ONE, AAQQ, |
CALL DLASCL( 'G', 0, 0, ONE, AAQQ, |
$ M, 1, A( 1, q ), LDA, |
$ M, 1, A( 1, q ), LDA, |
$ IERR ) |
$ IERR ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( MAX( ZERO, |
$ ONE-AAPQ*AAPQ ) ) |
$ ONE-AAPQ*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = MAX( MXSINJ, SFMIN ) |
ELSE |
ELSE |
CALL DCOPY( M, A( 1, q ), 1, |
CALL DCOPY( M, A( 1, q ), 1, |
$ WORK( N+1 ), 1 ) |
$ WORK( N+1 ), 1 ) |
Line 1394
|
Line 1396
|
CALL DLASCL( 'G', 0, 0, ONE, AAPP, |
CALL DLASCL( 'G', 0, 0, ONE, AAPP, |
$ M, 1, A( 1, p ), LDA, |
$ M, 1, A( 1, p ), LDA, |
$ IERR ) |
$ IERR ) |
SVA( p ) = AAPP*DSQRT( DMAX1( ZERO, |
SVA( p ) = AAPP*DSQRT( MAX( ZERO, |
$ ONE-AAPQ*AAPQ ) ) |
$ ONE-AAPQ*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = MAX( MXSINJ, SFMIN ) |
END IF |
END IF |
END IF |
END IF |
* END IF ROTOK THEN ... ELSE |
* END IF ROTOK THEN ... ELSE |
Line 1466
|
Line 1468
|
ELSE |
ELSE |
* |
* |
IF( AAPP.EQ.ZERO )NOTROT = NOTROT + |
IF( AAPP.EQ.ZERO )NOTROT = NOTROT + |
$ MIN0( jgl+KBL-1, N ) - jgl + 1 |
$ MIN( jgl+KBL-1, N ) - jgl + 1 |
IF( AAPP.LT.ZERO )NOTROT = 0 |
IF( AAPP.LT.ZERO )NOTROT = 0 |
* |
* |
END IF |
END IF |
Line 1477
|
Line 1479
|
* end of the jbc-loop |
* end of the jbc-loop |
2011 CONTINUE |
2011 CONTINUE |
*2011 bailed out of the jbc-loop |
*2011 bailed out of the jbc-loop |
DO 2012 p = igl, MIN0( igl+KBL-1, N ) |
DO 2012 p = igl, MIN( igl+KBL-1, N ) |
SVA( p ) = DABS( SVA( p ) ) |
SVA( p ) = DABS( SVA( p ) ) |
2012 CONTINUE |
2012 CONTINUE |
*** |
*** |