--- rpl/lapack/lapack/dgsvj0.f 2012/12/14 12:30:21 1.11
+++ rpl/lapack/lapack/dgsvj0.f 2023/08/07 08:38:51 1.21
@@ -1,26 +1,26 @@
-*> \brief \b DGSVJ0 pre-processor for the routine sgesvj.
+*> \brief \b DGSVJ0 pre-processor for the routine dgesvj.
*
* =========== 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 DGSVJ0 + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download DGSVJ0 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
* SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
-*
+*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP
* DOUBLE PRECISION EPS, SFMIN, TOL
@@ -30,7 +30,7 @@
* DOUBLE PRECISION A( LDA, * ), SVA( N ), D( N ), V( LDV, * ),
* $ WORK( LWORK )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -117,7 +117,7 @@
*> \param[in] MV
*> \verbatim
*> MV is INTEGER
-*> If JOBV .EQ. 'A', then MV rows of V are post-multipled by a
+*> If JOBV = 'A', then MV rows of V are post-multipled by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then MV is not referenced.
*> \endverbatim
@@ -125,9 +125,9 @@
*> \param[in,out] V
*> \verbatim
*> V is DOUBLE PRECISION array, dimension (LDV,N)
-*> If JOBV .EQ. 'V' then N rows of V are post-multipled by a
+*> If JOBV = 'V' then N rows of V are post-multipled by a
*> sequence of Jacobi rotations.
-*> If JOBV .EQ. 'A' then MV rows of V are post-multipled by a
+*> If JOBV = 'A' then MV rows of V are post-multipled by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then V is not referenced.
*> \endverbatim
@@ -136,8 +136,8 @@
*> \verbatim
*> LDV is INTEGER
*> The leading dimension of the array V, LDV >= 1.
-*> If JOBV = 'V', LDV .GE. N.
-*> If JOBV = 'A', LDV .GE. MV.
+*> If JOBV = 'V', LDV >= N.
+*> If JOBV = 'A', LDV >= MV.
*> \endverbatim
*>
*> \param[in] EPS
@@ -157,7 +157,7 @@
*> TOL is DOUBLE PRECISION
*> TOL is the threshold for Jacobi rotations. For a pair
*> A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
-*> applied only if DABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.
+*> applied only if DABS(COS(angle(A(:,p),A(:,q)))) > TOL.
*> \endverbatim
*>
*> \param[in] NSWEEP
@@ -175,25 +175,23 @@
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
-*> LWORK is the dimension of WORK. LWORK .GE. M.
+*> LWORK is the dimension of WORK. LWORK >= M.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
-*> = 0 : successful exit.
-*> < 0 : if INFO = -i, then the i-th argument had an illegal value
+*> = 0: successful exit.
+*> < 0: if INFO = -i, then the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
-*> \author Univ. of Tennessee
-*> \author Univ. of California Berkeley
-*> \author Univ. of Colorado Denver
-*> \author NAG Ltd.
-*
-*> \date September 2012
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
*> \ingroup doubleOTHERcomputational
*
@@ -218,10 +216,9 @@
SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
$ SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
*
-* -- LAPACK computational routine (version 3.4.2) --
+* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* September 2012
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP
@@ -253,7 +250,7 @@
DOUBLE PRECISION FASTR( 5 )
* ..
* .. Intrinsic Functions ..
- INTRINSIC DABS, DMAX1, DBLE, MIN0, DSIGN, DSQRT
+ INTRINSIC DABS, MAX, DBLE, MIN, DSIGN, DSQRT
* ..
* .. External Functions ..
DOUBLE PRECISION DDOT, DNRM2
@@ -262,7 +259,8 @@
EXTERNAL IDAMAX, LSAME, DDOT, DNRM2
* ..
* .. External Subroutines ..
- EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP
+ EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP,
+ $ XERBLA
* ..
* .. Executable Statements ..
*
@@ -280,7 +278,7 @@
INFO = -5
ELSE IF( ( RSVEC.OR.APPLV ) .AND. ( MV.LT.0 ) ) THEN
INFO = -8
- ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR.
+ ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR.
$ ( APPLV.AND.( LDV.LT.MV ) ) ) THEN
INFO = -10
ELSE IF( TOL.LE.EPS ) THEN
@@ -329,7 +327,7 @@
* Jacobi SVD algorithm SGESVJ. For sweeps i=1:SWBAND the procedure
* ......
- 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
@@ -341,7 +339,7 @@
BLSKIP = ( KBL**2 ) + 1
*[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
@@ -363,11 +361,11 @@
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
q = IDAMAX( N-p+1, SVA( p ), 1 ) + p - 1
@@ -391,7 +389,7 @@
* Some BLAS implementations compute DNRM2(M,A(1,p),1)
* as DSQRT(DDOT(M,A(1,p),1,A(1,p),1)), which may result in
* overflow for ||A(:,p)||_2 > DSQRT(overflow_threshold), and
-* undeflow for ||A(:,p)||_2 < DSQRT(underflow_threshold).
+* underflow for ||A(:,p)||_2 < DSQRT(underflow_threshold).
* Hence, DNRM2 cannot be trusted, not even in the case when
* the true norm is far from the under(over)flow boundaries.
* If properly implemented DNRM2 is available, the IF-THEN-ELSE
@@ -416,7 +414,7 @@
*
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 )
@@ -451,7 +449,7 @@
END IF
END IF
*
- MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) )
+ MXAAPQ = MAX( MXAAPQ, DABS( AAPQ ) )
*
* TO rotate or NOT to rotate, THAT is the question ...
*
@@ -483,11 +481,11 @@
$ 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
*
@@ -499,10 +497,10 @@
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 = D( p ) / D( q )
@@ -613,9 +611,9 @@
$ 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
*
@@ -679,7 +677,7 @@
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
@@ -700,7 +698,7 @@
* 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 )
*
@@ -708,7 +706,7 @@
*
PSKIPPED = 0
*
- DO 2200 q = jgl, MIN0( jgl+KBL-1, N )
+ DO 2200 q = jgl, MIN( jgl+KBL-1, N )
*
AAQQ = SVA( q )
*
@@ -755,7 +753,7 @@
END IF
END IF
*
- MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) )
+ MXAAPQ = MAX( MXAAPQ, DABS( AAPQ ) )
*
* TO rotate or NOT to rotate, THAT is the question ...
*
@@ -782,11 +780,11 @@
$ 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
@@ -797,10 +795,10 @@
$ 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 = D( p ) / D( q )
@@ -915,9 +913,9 @@
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,
$ 1 )
@@ -932,9 +930,9 @@
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
@@ -1002,7 +1000,7 @@
*
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
@@ -1012,7 +1010,7 @@
* 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
*
@@ -1044,7 +1042,7 @@
1993 CONTINUE
* end i=1:NSWEEP loop
-* #:) Reaching this point means that the procedure has comleted the given
+* #:) Reaching this point means that the procedure has completed the given
* number of iterations.
INFO = NSWEEP - 1
GO TO 1995