--- rpl/lapack/lapack/dgsvj1.f 2012/07/31 11:06:35 1.9
+++ rpl/lapack/lapack/dgsvj1.f 2023/08/07 08:38:51 1.22
@@ -1,26 +1,26 @@
-*> \brief \b DGSVJ1
+*> \brief \b DGSVJ1 pre-processor for the routine dgesvj, applies Jacobi rotations targeting only particular pivots.
*
* =========== 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 DGSVJ1 + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download DGSVJ1 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
* EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
-*
+*
* .. Scalar Arguments ..
* DOUBLE PRECISION EPS, SFMIN, TOL
* INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
@@ -30,17 +30,17 @@
* DOUBLE PRECISION A( LDA, * ), D( N ), SVA( N ), V( LDV, * ),
* $ WORK( LWORK )
* ..
-*
+*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
-*> DGSVJ1 is called from SGESVJ as a pre-processor and that is its main
-*> purpose. It applies Jacobi rotations in the same way as SGESVJ does, but
+*> DGSVJ1 is called from DGESVJ as a pre-processor and that is its main
+*> purpose. It applies Jacobi rotations in the same way as DGESVJ does, but
*> it targets only particular pivots and it does not check convergence
-*> (stopping criterion). Few tunning parameters (marked by [TP]) are
+*> (stopping criterion). Few tuning parameters (marked by [TP]) are
*> available for the implementer.
*>
*> Further Details
@@ -61,7 +61,7 @@
*> In terms of the columns of A, the first N1 columns are rotated 'against'
*> the remaining N-N1 columns, trying to increase the angle between the
*> corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is
-*> tiled using quadratic tiles of side KBL. Here, KBL is a tunning parmeter.
+*> tiled using quadratic tiles of side KBL. Here, KBL is a tuning parameter.
*> The number of sweeps is given in NSWEEP and the orthogonality threshold
*> is given in TOL.
*> \endverbatim
@@ -147,27 +147,27 @@
*> \param[in] MV
*> \verbatim
*> MV is INTEGER
-*> If JOBV .EQ. 'A', then MV rows of V are post-multipled by a
-*> sequence of Jacobi rotations.
-*> If JOBV = 'N', then MV is not referenced.
+*> 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
*>
*> \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
-*> sequence of Jacobi rotations.
-*> If JOBV .EQ. 'A' then MV rows of V are post-multipled by a
-*> sequence of Jacobi rotations.
-*> If JOBV = 'N', then V is not referenced.
+*> If JOBV = 'V', then N rows of V are post-multipled by a
+*> sequence of Jacobi rotations.
+*> 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
*>
*> \param[in] LDV
*> \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
@@ -187,7 +187,7 @@
*> 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
@@ -205,25 +205,23 @@
*> \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 November 2011
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
*> \ingroup doubleOTHERcomputational
*
@@ -236,10 +234,9 @@
SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
$ EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
*
-* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2011
*
* .. Scalar Arguments ..
DOUBLE PRECISION EPS, SFMIN, TOL
@@ -271,7 +268,7 @@
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
@@ -280,7 +277,8 @@
EXTERNAL IDAMAX, LSAME, DDOT, DNRM2
* ..
* .. External Subroutines ..
- EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP
+ EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP,
+ $ XERBLA
* ..
* .. Executable Statements ..
*
@@ -300,7 +298,7 @@
INFO = -6
ELSE IF( ( RSVEC.OR.APPLV ) .AND. ( MV.LT.0 ) ) THEN
INFO = -9
- ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR.
+ ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR.
$ ( APPLV.AND.( LDV.LT.MV ) ) ) THEN
INFO = -11
ELSE IF( TOL.LE.EPS ) THEN
@@ -345,7 +343,7 @@
*
* .. Row-cyclic pivot strategy with de Rijk's pivoting ..
*
- KBL = MIN0( 8, N )
+ KBL = MIN( 8, N )
NBLR = N1 / KBL
IF( ( NBLR*KBL ).NE.N1 )NBLR = NBLR + 1
@@ -356,7 +354,7 @@
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.
SWBAND = 0
*[TP] SWBAND is a tuning parameter. It is meaningful and effective
@@ -399,7 +397,7 @@
* doing the block at ( ibr, jbc )
IJBLSK = 0
- DO 2100 p = igl, MIN0( igl+KBL-1, N1 )
+ DO 2100 p = igl, MIN( igl+KBL-1, N1 )
AAPP = SVA( p )
@@ -407,7 +405,7 @@
PSKIPPED = 0
- DO 2200 q = jgl, MIN0( jgl+KBL-1, N )
+ DO 2200 q = jgl, MIN( jgl+KBL-1, N )
*
AAQQ = SVA( q )
@@ -454,7 +452,7 @@
END IF
END IF
- MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) )
+ MXAAPQ = MAX( MXAAPQ, DABS( AAPQ ) )
* TO rotate or NOT to rotate, THAT is the question ...
*
@@ -481,11 +479,11 @@
$ 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
@@ -496,10 +494,10 @@
$ 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 )
@@ -614,9 +612,9 @@
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 )
@@ -631,9 +629,9 @@
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
@@ -704,7 +702,7 @@
*
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
*** IF ( NOTROT .GE. EMPTSW ) GO TO 2011
END IF
@@ -715,7 +713,7 @@
* 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
*** IF ( NOTROT .GE. EMPTSW ) GO TO 1994