version 1.5, 2010/12/21 13:53:27
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version 1.6, 2011/07/22 07:38:05
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SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, |
SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, |
+ SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) |
$ SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.3.0) -- |
* -- LAPACK routine (version 3.3.1) -- |
* |
* |
* -- Contributed by Zlatko Drmac of the University of Zagreb and -- |
* -- Contributed by Zlatko Drmac of the University of Zagreb and -- |
* -- Kresimir Veselic of the Fernuniversitaet Hagen -- |
* -- Kresimir Veselic of the Fernuniversitaet Hagen -- |
* November 2010 |
* -- April 2011 -- |
* |
* |
* -- 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..-- |
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* eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0. |
* eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0. |
* |
* |
IMPLICIT NONE |
IMPLICIT NONE |
|
* .. |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP |
INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP |
DOUBLE PRECISION EPS, SFMIN, TOL |
DOUBLE PRECISION EPS, SFMIN, TOL |
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* .. |
* .. |
* .. Array Arguments .. |
* .. Array Arguments .. |
DOUBLE PRECISION A( LDA, * ), SVA( N ), D( N ), V( LDV, * ), |
DOUBLE PRECISION A( LDA, * ), SVA( N ), D( N ), V( LDV, * ), |
+ WORK( LWORK ) |
$ WORK( LWORK ) |
* .. |
* .. |
* |
* |
* Purpose |
* Purpose |
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* .. Local Parameters .. |
* .. Local Parameters .. |
DOUBLE PRECISION ZERO, HALF, ONE, TWO |
DOUBLE PRECISION ZERO, HALF, ONE, TWO |
PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, |
PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, |
+ TWO = 2.0D0 ) |
$ TWO = 2.0D0 ) |
* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, |
DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, |
+ BIGTHETA, CS, MXAAPQ, MXSINJ, ROOTBIG, ROOTEPS, |
$ BIGTHETA, CS, MXAAPQ, MXSINJ, ROOTBIG, ROOTEPS, |
+ ROOTSFMIN, ROOTTOL, SMALL, SN, T, TEMP1, THETA, |
$ ROOTSFMIN, ROOTTOL, SMALL, SN, T, TEMP1, THETA, |
+ THSIGN |
$ THSIGN |
INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1, |
INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1, |
+ ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, NBL, |
$ ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, NBL, |
+ NOTROT, p, PSKIPPED, q, ROWSKIP, SWBAND |
$ NOTROT, p, PSKIPPED, q, ROWSKIP, SWBAND |
LOGICAL APPLV, ROTOK, RSVEC |
LOGICAL APPLV, ROTOK, RSVEC |
* .. |
* .. |
* .. Local Arrays .. |
* .. Local Arrays .. |
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* .. |
* .. |
* .. Executable Statements .. |
* .. Executable Statements .. |
* |
* |
|
* Test the input parameters. |
|
* |
APPLV = LSAME( JOBV, 'A' ) |
APPLV = LSAME( JOBV, 'A' ) |
RSVEC = LSAME( JOBV, 'V' ) |
RSVEC = LSAME( JOBV, 'V' ) |
IF( .NOT.( RSVEC .OR. APPLV .OR. LSAME( JOBV, 'N' ) ) ) THEN |
IF( .NOT.( RSVEC .OR. APPLV .OR. LSAME( JOBV, 'N' ) ) ) THEN |
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ELSE IF( ( RSVEC.OR.APPLV ) .AND. ( MV.LT.0 ) ) THEN |
ELSE IF( ( RSVEC.OR.APPLV ) .AND. ( MV.LT.0 ) ) THEN |
INFO = -8 |
INFO = -8 |
ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR. |
ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR. |
& ( APPLV.AND.( LDV.LT.MV ) ) ) THEN |
$ ( APPLV.AND.( LDV.LT.MV ) ) ) THEN |
INFO = -10 |
INFO = -10 |
ELSE IF( TOL.LE.EPS ) THEN |
ELSE IF( TOL.LE.EPS ) THEN |
INFO = -13 |
INFO = -13 |
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BIGTHETA = ONE / ROOTEPS |
BIGTHETA = ONE / ROOTEPS |
ROOTTOL = DSQRT( TOL ) |
ROOTTOL = DSQRT( TOL ) |
* |
* |
* |
|
* -#- Row-cyclic Jacobi SVD algorithm with column pivoting -#- |
* -#- Row-cyclic Jacobi SVD algorithm with column pivoting -#- |
* |
* |
EMPTSW = ( N*( N-1 ) ) / 2 |
EMPTSW = ( N*( N-1 ) ) / 2 |
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IF( p.NE.q ) THEN |
IF( p.NE.q ) THEN |
CALL DSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) |
CALL DSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) |
IF( RSVEC )CALL DSWAP( MVL, V( 1, p ), 1, |
IF( RSVEC )CALL DSWAP( MVL, V( 1, p ), 1, |
+ V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
TEMP1 = SVA( p ) |
TEMP1 = SVA( p ) |
SVA( p ) = SVA( q ) |
SVA( p ) = SVA( q ) |
SVA( q ) = TEMP1 |
SVA( q ) = TEMP1 |
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* below should read "AAPP = DNRM2( M, A(1,p), 1 ) * D(p)". |
* below should read "AAPP = DNRM2( M, A(1,p), 1 ) * D(p)". |
* |
* |
IF( ( SVA( p ).LT.ROOTBIG ) .AND. |
IF( ( SVA( p ).LT.ROOTBIG ) .AND. |
+ ( SVA( p ).GT.ROOTSFMIN ) ) THEN |
$ ( SVA( p ).GT.ROOTSFMIN ) ) THEN |
SVA( p ) = DNRM2( M, A( 1, p ), 1 )*D( p ) |
SVA( p ) = DNRM2( M, A( 1, p ), 1 )*D( p ) |
ELSE |
ELSE |
TEMP1 = ZERO |
TEMP1 = ZERO |
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ROTOK = ( SMALL*AAPP ).LE.AAQQ |
ROTOK = ( SMALL*AAPP ).LE.AAQQ |
IF( AAPP.LT.( BIG / AAQQ ) ) THEN |
IF( AAPP.LT.( BIG / AAQQ ) ) THEN |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
+ q ), 1 )*D( p )*D( q ) / AAQQ ) |
$ q ), 1 )*D( p )*D( q ) / AAQQ ) |
+ / AAPP |
$ / AAPP |
ELSE |
ELSE |
CALL DCOPY( M, A( 1, p ), 1, WORK, 1 ) |
CALL DCOPY( M, A( 1, p ), 1, WORK, 1 ) |
CALL DLASCL( 'G', 0, 0, AAPP, D( p ), |
CALL DLASCL( 'G', 0, 0, AAPP, D( p ), |
+ M, 1, WORK, LDA, IERR ) |
$ M, 1, WORK, LDA, IERR ) |
AAPQ = DDOT( M, WORK, 1, A( 1, q ), |
AAPQ = DDOT( M, WORK, 1, A( 1, q ), |
+ 1 )*D( q ) / AAQQ |
$ 1 )*D( q ) / AAQQ |
END IF |
END IF |
ELSE |
ELSE |
ROTOK = AAPP.LE.( AAQQ / SMALL ) |
ROTOK = AAPP.LE.( AAQQ / SMALL ) |
IF( AAPP.GT.( SMALL / AAQQ ) ) THEN |
IF( AAPP.GT.( SMALL / AAQQ ) ) THEN |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
+ q ), 1 )*D( p )*D( q ) / AAQQ ) |
$ q ), 1 )*D( p )*D( q ) / AAQQ ) |
+ / AAPP |
$ / AAPP |
ELSE |
ELSE |
CALL DCOPY( M, A( 1, q ), 1, WORK, 1 ) |
CALL DCOPY( M, A( 1, q ), 1, WORK, 1 ) |
CALL DLASCL( 'G', 0, 0, AAQQ, D( q ), |
CALL DLASCL( 'G', 0, 0, AAQQ, D( q ), |
+ M, 1, WORK, LDA, IERR ) |
$ M, 1, WORK, LDA, IERR ) |
AAPQ = DDOT( M, WORK, 1, A( 1, p ), |
AAPQ = DDOT( M, WORK, 1, A( 1, p ), |
+ 1 )*D( p ) / AAPP |
$ 1 )*D( p ) / AAPP |
END IF |
END IF |
END IF |
END IF |
* |
* |
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* |
* |
AQOAP = AAQQ / AAPP |
AQOAP = AAQQ / AAPP |
APOAQ = AAPP / AAQQ |
APOAQ = AAPP / AAQQ |
THETA = -HALF*DABS( AQOAP-APOAQ ) / |
THETA = -HALF*DABS( AQOAP-APOAQ )/AAPQ |
+ AAPQ |
|
* |
* |
IF( DABS( THETA ).GT.BIGTHETA ) THEN |
IF( DABS( THETA ).GT.BIGTHETA ) THEN |
* |
* |
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FASTR( 3 ) = T*D( p ) / D( q ) |
FASTR( 3 ) = T*D( p ) / D( q ) |
FASTR( 4 ) = -T*D( q ) / D( p ) |
FASTR( 4 ) = -T*D( q ) / D( p ) |
CALL DROTM( M, A( 1, p ), 1, |
CALL DROTM( M, A( 1, p ), 1, |
+ A( 1, q ), 1, FASTR ) |
$ A( 1, q ), 1, FASTR ) |
IF( RSVEC )CALL DROTM( MVL, |
IF( RSVEC )CALL DROTM( MVL, |
+ 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( DMAX1( ZERO, |
+ ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
+ ONE-T*AQOAP*AAPQ ) ) |
$ ONE-T*AQOAP*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, DABS( T ) ) |
MXSINJ = DMAX1( MXSINJ, DABS( T ) ) |
* |
* |
ELSE |
ELSE |
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* |
* |
THSIGN = -DSIGN( ONE, AAPQ ) |
THSIGN = -DSIGN( ONE, AAPQ ) |
T = ONE / ( THETA+THSIGN* |
T = ONE / ( THETA+THSIGN* |
+ 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 = DMAX1( MXSINJ, DABS( SN ) ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
+ ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
+ ONE-T*AQOAP*AAPQ ) ) |
$ ONE-T*AQOAP*AAPQ ) ) |
* |
* |
APOAQ = D( p ) / D( q ) |
APOAQ = D( p ) / D( q ) |
AQOAP = D( q ) / D( p ) |
AQOAP = D( q ) / D( p ) |
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D( p ) = D( p )*CS |
D( p ) = D( p )*CS |
D( q ) = D( q )*CS |
D( q ) = D( q )*CS |
CALL DROTM( M, A( 1, p ), 1, |
CALL DROTM( M, A( 1, p ), 1, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ FASTR ) |
$ FASTR ) |
IF( RSVEC )CALL DROTM( MVL, |
IF( RSVEC )CALL DROTM( MVL, |
+ V( 1, p ), 1, V( 1, q ), |
$ V( 1, p ), 1, V( 1, q ), |
+ 1, FASTR ) |
$ 1, FASTR ) |
ELSE |
ELSE |
CALL DAXPY( M, -T*AQOAP, |
CALL DAXPY( M, -T*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
CALL DAXPY( M, CS*SN*APOAQ, |
CALL DAXPY( M, CS*SN*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
D( p ) = D( p )*CS |
D( p ) = D( p )*CS |
D( q ) = D( q ) / CS |
D( q ) = D( q ) / CS |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, -T*AQOAP, |
CALL DAXPY( MVL, -T*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ CS*SN*APOAQ, |
$ CS*SN*APOAQ, |
+ V( 1, p ), 1, |
$ V( 1, p ), 1, |
+ V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
END IF |
END IF |
END IF |
END IF |
ELSE |
ELSE |
IF( D( q ).GE.ONE ) THEN |
IF( D( q ).GE.ONE ) THEN |
CALL DAXPY( M, T*APOAQ, |
CALL DAXPY( M, T*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
CALL DAXPY( M, -CS*SN*AQOAP, |
CALL DAXPY( M, -CS*SN*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
D( p ) = D( p ) / CS |
D( p ) = D( p ) / CS |
D( q ) = D( q )*CS |
D( q ) = D( q )*CS |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, T*APOAQ, |
CALL DAXPY( MVL, T*APOAQ, |
+ V( 1, p ), 1, |
$ V( 1, p ), 1, |
+ V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
END IF |
END IF |
ELSE |
ELSE |
IF( D( p ).GE.D( q ) ) THEN |
IF( D( p ).GE.D( q ) ) THEN |
CALL DAXPY( M, -T*AQOAP, |
CALL DAXPY( M, -T*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
CALL DAXPY( M, CS*SN*APOAQ, |
CALL DAXPY( M, CS*SN*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
D( p ) = D( p )*CS |
D( p ) = D( p )*CS |
D( q ) = D( q ) / CS |
D( q ) = D( q ) / CS |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ -T*AQOAP, |
$ -T*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ CS*SN*APOAQ, |
$ CS*SN*APOAQ, |
+ V( 1, p ), 1, |
$ V( 1, p ), 1, |
+ V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
END IF |
END IF |
ELSE |
ELSE |
CALL DAXPY( M, T*APOAQ, |
CALL DAXPY( M, T*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
CALL DAXPY( M, |
CALL DAXPY( M, |
+ -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
D( p ) = D( p ) / CS |
D( p ) = D( p ) / CS |
D( q ) = D( q )*CS |
D( q ) = D( q )*CS |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ T*APOAQ, V( 1, p ), |
$ T*APOAQ, V( 1, p ), |
+ 1, V( 1, q ), 1 ) |
$ 1, V( 1, q ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
END IF |
END IF |
END IF |
END IF |
END IF |
END IF |
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* .. have to use modified Gram-Schmidt like transformation |
* .. have to use modified Gram-Schmidt like transformation |
CALL DCOPY( M, A( 1, p ), 1, WORK, 1 ) |
CALL DCOPY( M, A( 1, p ), 1, WORK, 1 ) |
CALL DLASCL( 'G', 0, 0, AAPP, ONE, M, |
CALL DLASCL( 'G', 0, 0, AAPP, ONE, M, |
+ 1, WORK, LDA, IERR ) |
$ 1, WORK, LDA, IERR ) |
CALL DLASCL( 'G', 0, 0, AAQQ, ONE, M, |
CALL DLASCL( 'G', 0, 0, AAQQ, ONE, M, |
+ 1, A( 1, q ), LDA, IERR ) |
$ 1, A( 1, q ), LDA, IERR ) |
TEMP1 = -AAPQ*D( p ) / D( q ) |
TEMP1 = -AAPQ*D( p ) / D( q ) |
CALL DAXPY( M, TEMP1, WORK, 1, |
CALL DAXPY( M, TEMP1, WORK, 1, |
+ 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( DMAX1( ZERO, |
+ ONE-AAPQ*AAPQ ) ) |
$ ONE-AAPQ*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
END IF |
END IF |
* END IF ROTOK THEN ... ELSE |
* END IF ROTOK THEN ... ELSE |
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* In the case of cancellation in updating SVA(q), SVA(p) |
* In the case of cancellation in updating SVA(q), SVA(p) |
* recompute SVA(q), SVA(p). |
* recompute SVA(q), SVA(p). |
IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) |
IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) |
+ THEN |
$ THEN |
IF( ( AAQQ.LT.ROOTBIG ) .AND. |
IF( ( AAQQ.LT.ROOTBIG ) .AND. |
+ ( AAQQ.GT.ROOTSFMIN ) ) THEN |
$ ( AAQQ.GT.ROOTSFMIN ) ) THEN |
SVA( q ) = DNRM2( M, A( 1, q ), 1 )* |
SVA( q ) = DNRM2( M, A( 1, q ), 1 )* |
+ D( q ) |
$ D( q ) |
ELSE |
ELSE |
T = ZERO |
T = ZERO |
AAQQ = ONE |
AAQQ = ONE |
CALL DLASSQ( M, A( 1, q ), 1, T, |
CALL DLASSQ( M, A( 1, q ), 1, T, |
+ AAQQ ) |
$ AAQQ ) |
SVA( q ) = T*DSQRT( AAQQ )*D( q ) |
SVA( q ) = T*DSQRT( AAQQ )*D( q ) |
END IF |
END IF |
END IF |
END IF |
IF( ( AAPP / AAPP0 ).LE.ROOTEPS ) THEN |
IF( ( AAPP / AAPP0 ).LE.ROOTEPS ) THEN |
IF( ( AAPP.LT.ROOTBIG ) .AND. |
IF( ( AAPP.LT.ROOTBIG ) .AND. |
+ ( AAPP.GT.ROOTSFMIN ) ) THEN |
$ ( AAPP.GT.ROOTSFMIN ) ) THEN |
AAPP = DNRM2( M, A( 1, p ), 1 )* |
AAPP = DNRM2( M, A( 1, p ), 1 )* |
+ D( p ) |
$ D( p ) |
ELSE |
ELSE |
T = ZERO |
T = ZERO |
AAPP = ONE |
AAPP = ONE |
CALL DLASSQ( M, A( 1, p ), 1, T, |
CALL DLASSQ( M, A( 1, p ), 1, T, |
+ AAPP ) |
$ AAPP ) |
AAPP = T*DSQRT( AAPP )*D( p ) |
AAPP = T*DSQRT( AAPP )*D( p ) |
END IF |
END IF |
SVA( p ) = AAPP |
SVA( p ) = AAPP |
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Line 570
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END IF |
END IF |
* |
* |
IF( ( i.LE.SWBAND ) .AND. |
IF( ( i.LE.SWBAND ) .AND. |
+ ( PSKIPPED.GT.ROWSKIP ) ) THEN |
$ ( PSKIPPED.GT.ROWSKIP ) ) THEN |
IF( ir1.EQ.0 )AAPP = -AAPP |
IF( ir1.EQ.0 )AAPP = -AAPP |
NOTROT = 0 |
NOTROT = 0 |
GO TO 2103 |
GO TO 2103 |
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Line 587
|
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 + MIN0( igl+KBL-1, N ) - p |
END IF |
END IF |
* |
* |
2001 CONTINUE |
2001 CONTINUE |
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|
Line 635
|
END IF |
END IF |
IF( AAPP.LT.( BIG / AAQQ ) ) THEN |
IF( AAPP.LT.( BIG / AAQQ ) ) THEN |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
+ q ), 1 )*D( p )*D( q ) / AAQQ ) |
$ q ), 1 )*D( p )*D( q ) / AAQQ ) |
+ / AAPP |
$ / AAPP |
ELSE |
ELSE |
CALL DCOPY( M, A( 1, p ), 1, WORK, 1 ) |
CALL DCOPY( M, A( 1, p ), 1, WORK, 1 ) |
CALL DLASCL( 'G', 0, 0, AAPP, D( p ), |
CALL DLASCL( 'G', 0, 0, AAPP, D( p ), |
+ M, 1, WORK, LDA, IERR ) |
$ M, 1, WORK, LDA, IERR ) |
AAPQ = DDOT( M, WORK, 1, A( 1, q ), |
AAPQ = DDOT( M, WORK, 1, A( 1, q ), |
+ 1 )*D( q ) / AAQQ |
$ 1 )*D( q ) / AAQQ |
END IF |
END IF |
ELSE |
ELSE |
IF( AAPP.GE.AAQQ ) THEN |
IF( AAPP.GE.AAQQ ) THEN |
Line 651
|
Line 652
|
END IF |
END IF |
IF( AAPP.GT.( SMALL / AAQQ ) ) THEN |
IF( AAPP.GT.( SMALL / AAQQ ) ) THEN |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
+ q ), 1 )*D( p )*D( q ) / AAQQ ) |
$ q ), 1 )*D( p )*D( q ) / AAQQ ) |
+ / AAPP |
$ / AAPP |
ELSE |
ELSE |
CALL DCOPY( M, A( 1, q ), 1, WORK, 1 ) |
CALL DCOPY( M, A( 1, q ), 1, WORK, 1 ) |
CALL DLASCL( 'G', 0, 0, AAQQ, D( q ), |
CALL DLASCL( 'G', 0, 0, AAQQ, D( q ), |
+ M, 1, WORK, LDA, IERR ) |
$ M, 1, WORK, LDA, IERR ) |
AAPQ = DDOT( M, WORK, 1, A( 1, p ), |
AAPQ = DDOT( M, WORK, 1, A( 1, p ), |
+ 1 )*D( p ) / AAPP |
$ 1 )*D( p ) / AAPP |
END IF |
END IF |
END IF |
END IF |
* |
* |
Line 676
|
Line 677
|
* |
* |
AQOAP = AAQQ / AAPP |
AQOAP = AAQQ / AAPP |
APOAQ = AAPP / AAQQ |
APOAQ = AAPP / AAQQ |
THETA = -HALF*DABS( AQOAP-APOAQ ) / |
THETA = -HALF*DABS( AQOAP-APOAQ )/AAPQ |
+ AAPQ |
|
IF( AAQQ.GT.AAPP0 )THETA = -THETA |
IF( AAQQ.GT.AAPP0 )THETA = -THETA |
* |
* |
IF( DABS( THETA ).GT.BIGTHETA ) THEN |
IF( DABS( THETA ).GT.BIGTHETA ) THEN |
Line 685
|
Line 685
|
FASTR( 3 ) = T*D( p ) / D( q ) |
FASTR( 3 ) = T*D( p ) / D( q ) |
FASTR( 4 ) = -T*D( q ) / D( p ) |
FASTR( 4 ) = -T*D( q ) / D( p ) |
CALL DROTM( M, A( 1, p ), 1, |
CALL DROTM( M, A( 1, p ), 1, |
+ A( 1, q ), 1, FASTR ) |
$ A( 1, q ), 1, FASTR ) |
IF( RSVEC )CALL DROTM( MVL, |
IF( RSVEC )CALL DROTM( MVL, |
+ 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( DMAX1( ZERO, |
+ ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
+ ONE-T*AQOAP*AAPQ ) ) |
$ ONE-T*AQOAP*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, DABS( T ) ) |
MXSINJ = DMAX1( MXSINJ, DABS( T ) ) |
ELSE |
ELSE |
* |
* |
Line 702
|
Line 702
|
THSIGN = -DSIGN( ONE, AAPQ ) |
THSIGN = -DSIGN( ONE, AAPQ ) |
IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN |
IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN |
T = ONE / ( THETA+THSIGN* |
T = ONE / ( THETA+THSIGN* |
+ 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 = DMAX1( MXSINJ, DABS( SN ) ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
+ ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
+ ONE-T*AQOAP*AAPQ ) ) |
$ ONE-T*AQOAP*AAPQ ) ) |
* |
* |
APOAQ = D( p ) / D( q ) |
APOAQ = D( p ) / D( q ) |
AQOAP = D( q ) / D( p ) |
AQOAP = D( q ) / D( p ) |
Line 721
|
Line 721
|
D( p ) = D( p )*CS |
D( p ) = D( p )*CS |
D( q ) = D( q )*CS |
D( q ) = D( q )*CS |
CALL DROTM( M, A( 1, p ), 1, |
CALL DROTM( M, A( 1, p ), 1, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ FASTR ) |
$ FASTR ) |
IF( RSVEC )CALL DROTM( MVL, |
IF( RSVEC )CALL DROTM( MVL, |
+ V( 1, p ), 1, V( 1, q ), |
$ V( 1, p ), 1, V( 1, q ), |
+ 1, FASTR ) |
$ 1, FASTR ) |
ELSE |
ELSE |
CALL DAXPY( M, -T*AQOAP, |
CALL DAXPY( M, -T*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
CALL DAXPY( M, CS*SN*APOAQ, |
CALL DAXPY( M, CS*SN*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, -T*AQOAP, |
CALL DAXPY( MVL, -T*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ CS*SN*APOAQ, |
$ CS*SN*APOAQ, |
+ V( 1, p ), 1, |
$ V( 1, p ), 1, |
+ V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
END IF |
END IF |
D( p ) = D( p )*CS |
D( p ) = D( p )*CS |
D( q ) = D( q ) / CS |
D( q ) = D( q ) / CS |
Line 748
|
Line 748
|
ELSE |
ELSE |
IF( D( q ).GE.ONE ) THEN |
IF( D( q ).GE.ONE ) THEN |
CALL DAXPY( M, T*APOAQ, |
CALL DAXPY( M, T*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
CALL DAXPY( M, -CS*SN*AQOAP, |
CALL DAXPY( M, -CS*SN*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, T*APOAQ, |
CALL DAXPY( MVL, T*APOAQ, |
+ V( 1, p ), 1, |
$ V( 1, p ), 1, |
+ V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
END IF |
END IF |
D( p ) = D( p ) / CS |
D( p ) = D( p ) / CS |
D( q ) = D( q )*CS |
D( q ) = D( q )*CS |
ELSE |
ELSE |
IF( D( p ).GE.D( q ) ) THEN |
IF( D( p ).GE.D( q ) ) THEN |
CALL DAXPY( M, -T*AQOAP, |
CALL DAXPY( M, -T*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
CALL DAXPY( M, CS*SN*APOAQ, |
CALL DAXPY( M, CS*SN*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
D( p ) = D( p )*CS |
D( p ) = D( p )*CS |
D( q ) = D( q ) / CS |
D( q ) = D( q ) / CS |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ -T*AQOAP, |
$ -T*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ CS*SN*APOAQ, |
$ CS*SN*APOAQ, |
+ V( 1, p ), 1, |
$ V( 1, p ), 1, |
+ V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
END IF |
END IF |
ELSE |
ELSE |
CALL DAXPY( M, T*APOAQ, |
CALL DAXPY( M, T*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
CALL DAXPY( M, |
CALL DAXPY( M, |
+ -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
D( p ) = D( p ) / CS |
D( p ) = D( p ) / CS |
D( q ) = D( q )*CS |
D( q ) = D( q )*CS |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ T*APOAQ, V( 1, p ), |
$ T*APOAQ, V( 1, p ), |
+ 1, V( 1, q ), 1 ) |
$ 1, V( 1, q ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
END IF |
END IF |
END IF |
END IF |
END IF |
END IF |
Line 811
|
Line 811
|
ELSE |
ELSE |
IF( AAPP.GT.AAQQ ) THEN |
IF( AAPP.GT.AAQQ ) THEN |
CALL DCOPY( M, A( 1, p ), 1, WORK, |
CALL DCOPY( M, A( 1, p ), 1, WORK, |
+ 1 ) |
$ 1 ) |
CALL DLASCL( 'G', 0, 0, AAPP, ONE, |
CALL DLASCL( 'G', 0, 0, AAPP, ONE, |
+ M, 1, WORK, LDA, IERR ) |
$ M, 1, WORK, LDA, IERR ) |
CALL DLASCL( 'G', 0, 0, AAQQ, ONE, |
CALL DLASCL( 'G', 0, 0, AAQQ, ONE, |
+ M, 1, A( 1, q ), LDA, |
$ M, 1, A( 1, q ), LDA, |
+ IERR ) |
$ IERR ) |
TEMP1 = -AAPQ*D( p ) / D( q ) |
TEMP1 = -AAPQ*D( p ) / D( q ) |
CALL DAXPY( M, TEMP1, WORK, 1, |
CALL DAXPY( M, TEMP1, WORK, 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
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( DMAX1( ZERO, |
+ ONE-AAPQ*AAPQ ) ) |
$ ONE-AAPQ*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
ELSE |
ELSE |
CALL DCOPY( M, A( 1, q ), 1, WORK, |
CALL DCOPY( M, A( 1, q ), 1, WORK, |
+ 1 ) |
$ 1 ) |
CALL DLASCL( 'G', 0, 0, AAQQ, ONE, |
CALL DLASCL( 'G', 0, 0, AAQQ, ONE, |
+ M, 1, WORK, LDA, IERR ) |
$ M, 1, WORK, LDA, IERR ) |
CALL DLASCL( 'G', 0, 0, AAPP, ONE, |
CALL DLASCL( 'G', 0, 0, AAPP, ONE, |
+ M, 1, A( 1, p ), LDA, |
$ M, 1, A( 1, p ), LDA, |
+ IERR ) |
$ IERR ) |
TEMP1 = -AAPQ*D( q ) / D( p ) |
TEMP1 = -AAPQ*D( q ) / D( p ) |
CALL DAXPY( M, TEMP1, WORK, 1, |
CALL DAXPY( M, TEMP1, WORK, 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
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( DMAX1( ZERO, |
+ ONE-AAPQ*AAPQ ) ) |
$ ONE-AAPQ*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
END IF |
END IF |
END IF |
END IF |
Line 850
|
Line 850
|
* In the case of cancellation in updating SVA(q) |
* In the case of cancellation in updating SVA(q) |
* .. recompute SVA(q) |
* .. recompute SVA(q) |
IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) |
IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) |
+ THEN |
$ THEN |
IF( ( AAQQ.LT.ROOTBIG ) .AND. |
IF( ( AAQQ.LT.ROOTBIG ) .AND. |
+ ( AAQQ.GT.ROOTSFMIN ) ) THEN |
$ ( AAQQ.GT.ROOTSFMIN ) ) THEN |
SVA( q ) = DNRM2( M, A( 1, q ), 1 )* |
SVA( q ) = DNRM2( M, A( 1, q ), 1 )* |
+ D( q ) |
$ D( q ) |
ELSE |
ELSE |
T = ZERO |
T = ZERO |
AAQQ = ONE |
AAQQ = ONE |
CALL DLASSQ( M, A( 1, q ), 1, T, |
CALL DLASSQ( M, A( 1, q ), 1, T, |
+ AAQQ ) |
$ AAQQ ) |
SVA( q ) = T*DSQRT( AAQQ )*D( q ) |
SVA( q ) = T*DSQRT( AAQQ )*D( q ) |
END IF |
END IF |
END IF |
END IF |
IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN |
IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN |
IF( ( AAPP.LT.ROOTBIG ) .AND. |
IF( ( AAPP.LT.ROOTBIG ) .AND. |
+ ( AAPP.GT.ROOTSFMIN ) ) THEN |
$ ( AAPP.GT.ROOTSFMIN ) ) THEN |
AAPP = DNRM2( M, A( 1, p ), 1 )* |
AAPP = DNRM2( M, A( 1, p ), 1 )* |
+ D( p ) |
$ D( p ) |
ELSE |
ELSE |
T = ZERO |
T = ZERO |
AAPP = ONE |
AAPP = ONE |
CALL DLASSQ( M, A( 1, p ), 1, T, |
CALL DLASSQ( M, A( 1, p ), 1, T, |
+ AAPP ) |
$ AAPP ) |
AAPP = T*DSQRT( AAPP )*D( p ) |
AAPP = T*DSQRT( AAPP )*D( p ) |
END IF |
END IF |
SVA( p ) = AAPP |
SVA( p ) = AAPP |
Line 890
|
Line 890
|
END IF |
END IF |
* |
* |
IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) ) |
IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) ) |
+ THEN |
$ THEN |
SVA( p ) = AAPP |
SVA( p ) = AAPP |
NOTROT = 0 |
NOTROT = 0 |
GO TO 2011 |
GO TO 2011 |
END IF |
END IF |
IF( ( i.LE.SWBAND ) .AND. |
IF( ( i.LE.SWBAND ) .AND. |
+ ( PSKIPPED.GT.ROWSKIP ) ) THEN |
$ ( PSKIPPED.GT.ROWSKIP ) ) THEN |
AAPP = -AAPP |
AAPP = -AAPP |
NOTROT = 0 |
NOTROT = 0 |
GO TO 2203 |
GO TO 2203 |
Line 910
|
Line 910
|
* |
* |
ELSE |
ELSE |
IF( AAPP.EQ.ZERO )NOTROT = NOTROT + |
IF( AAPP.EQ.ZERO )NOTROT = NOTROT + |
+ MIN0( jgl+KBL-1, N ) - jgl + 1 |
$ MIN0( jgl+KBL-1, N ) - jgl + 1 |
IF( AAPP.LT.ZERO )NOTROT = 0 |
IF( AAPP.LT.ZERO )NOTROT = 0 |
END IF |
END IF |
|
|
Line 929
|
Line 929
|
* |
* |
* .. update SVA(N) |
* .. update SVA(N) |
IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) ) |
IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) ) |
+ THEN |
$ THEN |
SVA( N ) = DNRM2( M, A( 1, N ), 1 )*D( N ) |
SVA( N ) = DNRM2( M, A( 1, N ), 1 )*D( N ) |
ELSE |
ELSE |
T = ZERO |
T = ZERO |
Line 941
|
Line 941
|
* Additional steering devices |
* Additional steering devices |
* |
* |
IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. |
IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. |
+ ( ISWROT.LE.N ) ) )SWBAND = i |
$ ( ISWROT.LE.N ) ) )SWBAND = i |
* |
* |
IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.DBLE( N )*TOL ) .AND. |
IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.DBLE( N )*TOL ) .AND. |
+ ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN |
$ ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN |
GO TO 1994 |
GO TO 1994 |
END IF |
END IF |
* |
* |