--- rpl/lapack/lapack/dgesvj.f 2011/11/21 20:42:52 1.7
+++ rpl/lapack/lapack/dgesvj.f 2017/06/17 10:53:49 1.16
@@ -2,25 +2,25 @@
*
* =========== 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 DGESVJ + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download DGESVJ + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V,
* LDV, WORK, LWORK, INFO )
-*
+*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDV, LWORK, M, MV, N
* CHARACTER*1 JOBA, JOBU, JOBV
@@ -29,7 +29,7 @@
* DOUBLE PRECISION A( LDA, * ), SVA( N ), V( LDV, * ),
* $ WORK( LWORK )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -45,6 +45,8 @@
*> 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
*> 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
*
* Arguments:
@@ -101,7 +103,7 @@
*> \param[in] M
*> \verbatim
*> M is INTEGER
-*> The number of rows of the input matrix A. 1/DLAMCH('E') > M >= 0.
+*> The number of rows of the input matrix A. 1/DLAMCH('E') > M >= 0.
*> \endverbatim
*>
*> \param[in] N
@@ -206,7 +208,7 @@
*>
*> \param[in,out] WORK
*> \verbatim
-*> WORK is DOUBLE PRECISION array, dimension max(4,M+N).
+*> WORK is DOUBLE PRECISION array, dimension MAX(6,M+N).
*> On entry :
*> If JOBU .EQ. 'C' :
*> WORK(1) = CTOL, where CTOL defines the threshold for convergence.
@@ -253,12 +255,12 @@
* 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 November 2011
+*> \date December 2016
*
*> \ingroup doubleGEcomputational
*
@@ -335,10 +337,10 @@
SUBROUTINE DGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V,
$ LDV, WORK, LWORK, INFO )
*
-* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2011
+* December 2016
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDV, LWORK, M, MV, N
@@ -352,9 +354,8 @@
* =====================================================================
*
* .. Local Parameters ..
- DOUBLE PRECISION ZERO, HALF, ONE, TWO
- PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0,
- $ TWO = 2.0D0 )
+ DOUBLE PRECISION ZERO, HALF, ONE
+ PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0)
INTEGER NSWEEP
PARAMETER ( NSWEEP = 30 )
* ..
@@ -375,7 +376,7 @@
DOUBLE PRECISION FASTR( 5 )
* ..
* .. Intrinsic Functions ..
- INTRINSIC DABS, DMAX1, DMIN1, DBLE, MIN0, DSIGN, DSQRT
+ INTRINSIC DABS, MAX, MIN, DBLE, DSIGN, DSQRT
* ..
* .. External Functions ..
* ..
@@ -429,7 +430,7 @@
INFO = -11
ELSE IF( UCTOL .AND. ( WORK( 1 ).LE.ONE ) ) THEN
INFO = -12
- ELSE IF( LWORK.LT.MAX0( M+N, 6 ) ) THEN
+ ELSE IF( LWORK.LT.MAX( M+N, 6 ) ) THEN
INFO = -13
ELSE
INFO = 0
@@ -595,8 +596,8 @@
AAPP = ZERO
AAQQ = BIG
DO 4781 p = 1, N
- IF( SVA( p ).NE.ZERO )AAQQ = DMIN1( AAQQ, SVA( p ) )
- AAPP = DMAX1( AAPP, SVA( p ) )
+ IF( SVA( p ).NE.ZERO )AAQQ = MIN( AAQQ, SVA( p ) )
+ AAPP = MAX( AAPP, SVA( p ) )
4781 CONTINUE
*
* #:) Quick return for zero matrix
@@ -637,19 +638,19 @@
TEMP1 = DSQRT( BIG / DBLE( N ) )
IF( ( AAPP.LE.SN ) .OR. ( AAQQ.GE.TEMP1 ) .OR.
$ ( ( SN.LE.AAQQ ) .AND. ( AAPP.LE.TEMP1 ) ) ) THEN
- TEMP1 = DMIN1( BIG, TEMP1 / AAPP )
+ TEMP1 = MIN( BIG, TEMP1 / AAPP )
* AAQQ = AAQQ*TEMP1
* AAPP = AAPP*TEMP1
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
* AAPP = AAPP*TEMP1
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
* AAPP = AAPP*TEMP1
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
* AAPP = AAPP*TEMP1
ELSE
@@ -690,7 +691,7 @@
* The boundaries are determined dynamically, based on the number of
* 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
* tiling of the p-q loops of pivot pairs. In general, an optimal
* value of KBL depends on the matrix dimensions and on the
@@ -702,7 +703,7 @@
BLSKIP = KBL**2
*[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.
*
LKAHEAD = 1
@@ -713,7 +714,7 @@
* invokes cubic convergence. Big part of this cycle is done inside
* 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
* tuning parameters.
N4 = N / 4
@@ -811,11 +812,11 @@
*
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
*
- DO 2001 p = igl, MIN0( igl+KBL-1, N-1 )
+ DO 2001 p = igl, MIN( igl+KBL-1, N-1 )
*
* .. de Rijk's pivoting
*
@@ -864,7 +865,7 @@
*
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 )
*
@@ -903,7 +904,7 @@
END IF
END IF
*
- MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) )
+ MXAAPQ = MAX( MXAAPQ, DABS( AAPQ ) )
*
* TO rotate or NOT to rotate, THAT is the question ...
*
@@ -936,11 +937,11 @@
$ V( 1, p ), 1,
$ V( 1, q ), 1,
$ FASTR )
- SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
+ SVA( q ) = AAQQ*DSQRT( MAX( ZERO,
$ ONE+T*APOAQ*AAPQ ) )
- AAPP = AAPP*DSQRT( DMAX1( ZERO,
+ AAPP = AAPP*DSQRT( MAX( ZERO,
$ ONE-T*AQOAP*AAPQ ) )
- MXSINJ = DMAX1( MXSINJ, DABS( T ) )
+ MXSINJ = MAX( MXSINJ, DABS( T ) )
*
ELSE
*
@@ -952,10 +953,10 @@
CS = DSQRT( ONE / ( ONE+T*T ) )
SN = T*CS
*
- MXSINJ = DMAX1( MXSINJ, DABS( SN ) )
- SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
+ MXSINJ = MAX( MXSINJ, DABS( SN ) )
+ SVA( q ) = AAQQ*DSQRT( MAX( ZERO,
$ ONE+T*APOAQ*AAPQ ) )
- AAPP = AAPP*DSQRT( DMAX1( ZERO,
+ AAPP = AAPP*DSQRT( MAX( ZERO,
$ ONE-T*AQOAP*AAPQ ) )
*
APOAQ = WORK( p ) / WORK( q )
@@ -1069,9 +1070,9 @@
$ A( 1, q ), 1 )
CALL DLASCL( 'G', 0, 0, ONE, AAQQ, M,
$ 1, A( 1, q ), LDA, IERR )
- SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
+ SVA( q ) = AAQQ*DSQRT( MAX( ZERO,
$ ONE-AAPQ*AAPQ ) )
- MXSINJ = DMAX1( MXSINJ, SFMIN )
+ MXSINJ = MAX( MXSINJ, SFMIN )
END IF
* END IF ROTOK THEN ... ELSE
*
@@ -1137,7 +1138,7 @@
ELSE
SVA( p ) = AAPP
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
*
2001 CONTINUE
@@ -1157,14 +1158,14 @@
* doing the block at ( ibr, jbc )
*
IJBLSK = 0
- DO 2100 p = igl, MIN0( igl+KBL-1, N )
+ DO 2100 p = igl, MIN( igl+KBL-1, N )
*
AAPP = SVA( p )
IF( AAPP.GT.ZERO ) THEN
*
PSKIPPED = 0
*
- DO 2200 q = jgl, MIN0( jgl+KBL-1, N )
+ DO 2200 q = jgl, MIN( jgl+KBL-1, N )
*
AAQQ = SVA( q )
IF( AAQQ.GT.ZERO ) THEN
@@ -1214,7 +1215,7 @@
END IF
END IF
*
- MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) )
+ MXAAPQ = MAX( MXAAPQ, DABS( AAPQ ) )
*
* TO rotate or NOT to rotate, THAT is the question ...
*
@@ -1242,11 +1243,11 @@
$ V( 1, p ), 1,
$ V( 1, q ), 1,
$ FASTR )
- SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
+ SVA( q ) = AAQQ*DSQRT( MAX( ZERO,
$ ONE+T*APOAQ*AAPQ ) )
- AAPP = AAPP*DSQRT( DMAX1( ZERO,
+ AAPP = AAPP*DSQRT( MAX( ZERO,
$ ONE-T*AQOAP*AAPQ ) )
- MXSINJ = DMAX1( MXSINJ, DABS( T ) )
+ MXSINJ = MAX( MXSINJ, DABS( T ) )
ELSE
*
* .. choose correct signum for THETA and rotate
@@ -1257,10 +1258,10 @@
$ DSQRT( ONE+THETA*THETA ) )
CS = DSQRT( ONE / ( ONE+T*T ) )
SN = T*CS
- MXSINJ = DMAX1( MXSINJ, DABS( SN ) )
- SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
+ MXSINJ = MAX( MXSINJ, DABS( SN ) )
+ SVA( q ) = AAQQ*DSQRT( MAX( ZERO,
$ ONE+T*APOAQ*AAPQ ) )
- AAPP = AAPP*DSQRT( DMAX1( ZERO,
+ AAPP = AAPP*DSQRT( MAX( ZERO,
$ ONE-T*AQOAP*AAPQ ) )
*
APOAQ = WORK( p ) / WORK( q )
@@ -1377,9 +1378,9 @@
CALL DLASCL( 'G', 0, 0, ONE, AAQQ,
$ M, 1, A( 1, q ), LDA,
$ IERR )
- SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
+ SVA( q ) = AAQQ*DSQRT( MAX( ZERO,
$ ONE-AAPQ*AAPQ ) )
- MXSINJ = DMAX1( MXSINJ, SFMIN )
+ MXSINJ = MAX( MXSINJ, SFMIN )
ELSE
CALL DCOPY( M, A( 1, q ), 1,
$ WORK( N+1 ), 1 )
@@ -1395,9 +1396,9 @@
CALL DLASCL( 'G', 0, 0, ONE, AAPP,
$ M, 1, A( 1, p ), LDA,
$ IERR )
- SVA( p ) = AAPP*DSQRT( DMAX1( ZERO,
+ SVA( p ) = AAPP*DSQRT( MAX( ZERO,
$ ONE-AAPQ*AAPQ ) )
- MXSINJ = DMAX1( MXSINJ, SFMIN )
+ MXSINJ = MAX( MXSINJ, SFMIN )
END IF
END IF
* END IF ROTOK THEN ... ELSE
@@ -1467,7 +1468,7 @@
ELSE
*
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
*
END IF
@@ -1478,7 +1479,7 @@
* end of the jbc-loop
2011 CONTINUE
*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 ) )
2012 CONTINUE
***
@@ -1574,11 +1575,11 @@
END IF
*
* Undo scaling, if necessary (and possible).
- IF( ( ( SKL.GT.ONE ) .AND. ( SVA( 1 ).LT.( BIG /
- $ SKL) ) ) .OR. ( ( SKL.LT.ONE ) .AND. ( SVA( N2 ).GT.
+ IF( ( ( SKL.GT.ONE ) .AND. ( SVA( 1 ).LT.( BIG / SKL) ) )
+ $ .OR. ( ( SKL.LT.ONE ) .AND. ( SVA( MAX( N2, 1 ) ) .GT.
$ ( SFMIN / SKL) ) ) ) THEN
DO 2400 p = 1, N
- SVA( p ) = SKL*SVA( p )
+ SVA( P ) = SKL*SVA( P )
2400 CONTINUE
SKL= ONE
END IF