--- rpl/lapack/lapack/zgsvj1.f 2016/08/27 15:34:48 1.3
+++ rpl/lapack/lapack/zgsvj1.f 2023/08/07 08:39:22 1.9
@@ -2,35 +2,35 @@
*
* =========== 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 ZGSVJ1 + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download ZGSVJ1 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZGSVJ1( 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
* CHARACTER*1 JOBV
* ..
* .. Array Arguments ..
-* COMPLEX*16 A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK )
-* DOUBLE PRECISION SVA( N )
+* COMPLEX*16 A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK )
+* DOUBLE PRECISION SVA( N )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -40,7 +40,7 @@
*> ZGSVJ1 is called from ZGESVJ as a pre-processor and that is its main
*> purpose. It applies Jacobi rotations in the same way as ZGESVJ 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
@@ -147,7 +147,7 @@
*> \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
@@ -155,9 +155,9 @@
*> \param[in,out] V
*> \verbatim
*> V is COMPLEX*16 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
@@ -166,8 +166,8 @@
*> \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
@@ -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 ABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.
+*> applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL.
*> \endverbatim
*>
*> \param[in] NSWEEP
@@ -205,43 +205,40 @@
*> \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 June 2016
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
*> \ingroup complex16OTHERcomputational
*
-*> \par Contributors:
+*> \par Contributor:
* ==================
*>
-*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
+*> Zlatko Drmac (Zagreb, Croatia)
*
* =====================================================================
SUBROUTINE ZGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
$ EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
*
-* -- LAPACK computational routine (version 3.6.1) --
+* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* June 2016
*
- IMPLICIT NONE
+ IMPLICIT NONE
* .. Scalar Arguments ..
DOUBLE PRECISION EPS, SFMIN, TOL
INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
@@ -249,7 +246,7 @@
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK )
- DOUBLE PRECISION SVA( N )
+ DOUBLE PRECISION SVA( N )
* ..
*
* =====================================================================
@@ -261,7 +258,7 @@
* .. Local Scalars ..
COMPLEX*16 AAPQ, OMPQ
DOUBLE PRECISION AAPP, AAPP0, AAPQ1, AAQQ, APOAQ, AQOAP, BIG,
- $ BIGTHETA, CS, LARGE, MXAAPQ, MXSINJ, ROOTBIG,
+ $ BIGTHETA, CS, MXAAPQ, MXSINJ, ROOTBIG,
$ ROOTEPS, ROOTSFMIN, ROOTTOL, SMALL, SN, T,
$ TEMP1, THETA, THSIGN
INTEGER BLSKIP, EMPTSW, i, ibr, igl, IERR, IJBLSK,
@@ -271,7 +268,7 @@
* ..
* ..
* .. Intrinsic Functions ..
- INTRINSIC ABS, DCONJG, DMAX1, DBLE, MIN0, DSIGN, DSQRT
+ INTRINSIC ABS, CONJG, MAX, DBLE, MIN, SIGN, SQRT
* ..
* .. External Functions ..
DOUBLE PRECISION DZNRM2
@@ -281,8 +278,8 @@
EXTERNAL IDAMAX, LSAME, ZDOTC, DZNRM2
* ..
* .. External Subroutines ..
-* .. from BLAS
- EXTERNAL ZCOPY, ZROT, ZSWAP
+* .. from BLAS
+ EXTERNAL ZCOPY, ZROT, ZSWAP, ZAXPY
* .. from LAPACK
EXTERNAL ZLASCL, ZLASSQ, XERBLA
* ..
@@ -304,7 +301,7 @@
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
@@ -330,14 +327,14 @@
END IF
RSVEC = RSVEC .OR. APPLV
- ROOTEPS = DSQRT( EPS )
- ROOTSFMIN = DSQRT( SFMIN )
+ ROOTEPS = SQRT( EPS )
+ ROOTSFMIN = SQRT( SFMIN )
SMALL = SFMIN / EPS
BIG = ONE / SFMIN
ROOTBIG = ONE / ROOTSFMIN
- LARGE = BIG / DSQRT( DBLE( M*N ) )
+* LARGE = BIG / SQRT( DBLE( M*N ) )
BIGTHETA = ONE / ROOTEPS
- ROOTTOL = DSQRT( TOL )
+ ROOTTOL = SQRT( TOL )
*
* .. Initialize the right singular vector matrix ..
*
@@ -348,7 +345,7 @@
*
* .. 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
@@ -359,7 +356,7 @@
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
@@ -402,21 +399,21 @@
igl = ( ibr-1 )*KBL + 1
*
* DO 2010 jbc = ibr + 1, NBL
- DO 2010 jbc = 1, NBLC
+ DO 2010 jbc = 1, NBLC
*
jgl = ( jbc-1 )*KBL + N1 + 1
*
* 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 )
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
@@ -433,7 +430,7 @@
ROTOK = ( SMALL*AAQQ ).LE.AAPP
END IF
IF( AAPP.LT.( BIG / AAQQ ) ) THEN
- AAPQ = ( ZDOTC( M, A( 1, p ), 1,
+ AAPQ = ( ZDOTC( M, A( 1, p ), 1,
$ A( 1, q ), 1 ) / AAQQ ) / AAPP
ELSE
CALL ZCOPY( M, A( 1, p ), 1,
@@ -451,8 +448,9 @@
ROTOK = AAQQ.LE.( AAPP / SMALL )
END IF
IF( AAPP.GT.( SMALL / AAQQ ) ) THEN
- AAPQ = ( ZDOTC( M, A( 1, p ), 1,
- $ A( 1, q ), 1 ) / AAQQ ) / AAPP
+ AAPQ = ( ZDOTC( M, A( 1, p ), 1,
+ $ A( 1, q ), 1 ) / MAX(AAQQ,AAPP) )
+ $ / MIN(AAQQ,AAPP)
ELSE
CALL ZCOPY( M, A( 1, q ), 1,
$ WORK, 1 )
@@ -464,14 +462,14 @@
END IF
END IF
*
- OMPQ = AAPQ / ABS(AAPQ)
-* AAPQ = AAPQ * DCONJG(CWORK(p))*CWORK(q)
+* AAPQ = AAPQ * CONJG(CWORK(p))*CWORK(q)
AAPQ1 = -ABS(AAPQ)
- MXAAPQ = DMAX1( MXAAPQ, -AAPQ1 )
+ MXAAPQ = MAX( MXAAPQ, -AAPQ1 )
*
* TO rotate or NOT to rotate, THAT is the question ...
*
IF( ABS( AAPQ1 ).GT.TOL ) THEN
+ OMPQ = AAPQ / ABS(AAPQ)
NOTROT = 0
*[RTD] ROTATED = ROTATED + 1
PSKIPPED = 0
@@ -486,39 +484,39 @@
*
IF( ABS( THETA ).GT.BIGTHETA ) THEN
T = HALF / THETA
- CS = ONE
+ CS = ONE
CALL ZROT( M, A(1,p), 1, A(1,q), 1,
- $ CS, DCONJG(OMPQ)*T )
+ $ CS, CONJG(OMPQ)*T )
IF( RSVEC ) THEN
- CALL ZROT( MVL, V(1,p), 1,
- $ V(1,q), 1, CS, DCONJG(OMPQ)*T )
+ CALL ZROT( MVL, V(1,p), 1,
+ $ V(1,q), 1, CS, CONJG(OMPQ)*T )
END IF
- SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
+ SVA( q ) = AAQQ*SQRT( MAX( ZERO,
$ ONE+T*APOAQ*AAPQ1 ) )
- AAPP = AAPP*DSQRT( DMAX1( ZERO,
+ AAPP = AAPP*SQRT( MAX( ZERO,
$ ONE-T*AQOAP*AAPQ1 ) )
- MXSINJ = DMAX1( MXSINJ, ABS( T ) )
+ MXSINJ = MAX( MXSINJ, ABS( T ) )
ELSE
*
* .. choose correct signum for THETA and rotate
*
- THSIGN = -DSIGN( ONE, AAPQ1 )
+ THSIGN = -SIGN( ONE, AAPQ1 )
IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN
T = ONE / ( THETA+THSIGN*
- $ DSQRT( ONE+THETA*THETA ) )
- CS = DSQRT( ONE / ( ONE+T*T ) )
+ $ SQRT( ONE+THETA*THETA ) )
+ CS = SQRT( ONE / ( ONE+T*T ) )
SN = T*CS
- MXSINJ = DMAX1( MXSINJ, ABS( SN ) )
- SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
+ MXSINJ = MAX( MXSINJ, ABS( SN ) )
+ SVA( q ) = AAQQ*SQRT( MAX( ZERO,
$ ONE+T*APOAQ*AAPQ1 ) )
- AAPP = AAPP*DSQRT( DMAX1( ZERO,
+ AAPP = AAPP*SQRT( MAX( ZERO,
$ ONE-T*AQOAP*AAPQ1 ) )
*
CALL ZROT( M, A(1,p), 1, A(1,q), 1,
- $ CS, DCONJG(OMPQ)*SN )
+ $ CS, CONJG(OMPQ)*SN )
IF( RSVEC ) THEN
- CALL ZROT( MVL, V(1,p), 1,
- $ V(1,q), 1, CS, DCONJG(OMPQ)*SN )
+ CALL ZROT( MVL, V(1,p), 1,
+ $ V(1,q), 1, CS, CONJG(OMPQ)*SN )
END IF
END IF
D(p) = -D(q) * OMPQ
@@ -539,9 +537,9 @@
CALL ZLASCL( 'G', 0, 0, ONE, AAQQ,
$ M, 1, A( 1, q ), LDA,
$ IERR )
- SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
+ SVA( q ) = AAQQ*SQRT( MAX( ZERO,
$ ONE-AAPQ1*AAPQ1 ) )
- MXSINJ = DMAX1( MXSINJ, SFMIN )
+ MXSINJ = MAX( MXSINJ, SFMIN )
ELSE
CALL ZCOPY( M, A( 1, q ), 1,
$ WORK, 1 )
@@ -551,14 +549,14 @@
CALL ZLASCL( 'G', 0, 0, AAPP, ONE,
$ M, 1, A( 1, p ), LDA,
$ IERR )
- CALL ZAXPY( M, -DCONJG(AAPQ),
+ CALL ZAXPY( M, -CONJG(AAPQ),
$ WORK, 1, A( 1, p ), 1 )
CALL ZLASCL( 'G', 0, 0, ONE, AAPP,
$ M, 1, A( 1, p ), LDA,
$ IERR )
- SVA( p ) = AAPP*DSQRT( DMAX1( ZERO,
+ SVA( p ) = AAPP*SQRT( MAX( ZERO,
$ ONE-AAPQ1*AAPQ1 ) )
- MXSINJ = DMAX1( MXSINJ, SFMIN )
+ MXSINJ = MAX( MXSINJ, SFMIN )
END IF
END IF
* END IF ROTOK THEN ... ELSE
@@ -575,7 +573,7 @@
AAQQ = ONE
CALL ZLASSQ( M, A( 1, q ), 1, T,
$ AAQQ )
- SVA( q ) = T*DSQRT( AAQQ )
+ SVA( q ) = T*SQRT( AAQQ )
END IF
END IF
IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN
@@ -587,7 +585,7 @@
AAPP = ONE
CALL ZLASSQ( M, A( 1, p ), 1, T,
$ AAPP )
- AAPP = T*DSQRT( AAPP )
+ AAPP = T*SQRT( AAPP )
END IF
SVA( p ) = AAPP
END IF
@@ -626,7 +624,7 @@
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
@@ -637,7 +635,7 @@
* 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 ) = ABS( SVA( p ) )
2012 CONTINUE
***
@@ -652,7 +650,7 @@
T = ZERO
AAPP = ONE
CALL ZLASSQ( M, A( 1, N ), 1, T, AAPP )
- SVA( N ) = T*DSQRT( AAPP )
+ SVA( N ) = T*SQRT( AAPP )
END IF
*
* Additional steering devices
@@ -660,7 +658,7 @@
IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR.
$ ( ISWROT.LE.N ) ) )SWBAND = i
*
- IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.DSQRT( DBLE( N ) )*
+ IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.SQRT( DBLE( N ) )*
$ TOL ) .AND. ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN
GO TO 1994
END IF