version 1.3, 2016/08/27 15:34:48
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version 1.5, 2017/06/17 11:06:46
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*> \brief \b ZGSVJ0 pre-processor for the routine zgesvj. |
*> \brief <b> ZGSVJ0 pre-processor for the routine zgesvj. </b> |
* |
* |
* =========== DOCUMENTATION =========== |
* =========== DOCUMENTATION =========== |
* |
* |
* Online html documentation available at |
* Online html documentation available at |
* http://www.netlib.org/lapack/explore-html/ |
* http://www.netlib.org/lapack/explore-html/ |
* |
* |
*> \htmlonly |
*> \htmlonly |
*> Download ZGSVJ0 + dependencies |
*> Download ZGSVJ0 + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgsvj0.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgsvj0.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgsvj0.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgsvj0.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgsvj0.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgsvj0.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* SUBROUTINE ZGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, |
* SUBROUTINE ZGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, |
* SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) |
* SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) |
* |
* |
* .. 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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* COMPLEX*16 A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK ) |
* COMPLEX*16 A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK ) |
* DOUBLE PRECISION SVA( N ) |
* DOUBLE PRECISION SVA( N ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
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*> the matrix A*diag(D). |
*> the matrix A*diag(D). |
*> On exit, SVA contains the Euclidean norms of the columns of |
*> On exit, SVA contains the Euclidean norms of the columns of |
*> the matrix A_onexit*diag(D_onexit). |
*> the matrix A_onexit*diag(D_onexit). |
|
*> \endverbatim |
*> |
*> |
*> \param[in] MV |
*> \param[in] MV |
*> \verbatim |
*> \verbatim |
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* Authors: |
* Authors: |
* ======== |
* ======== |
* |
* |
*> \author Univ. of Tennessee |
*> \author Univ. of Tennessee |
*> \author Univ. of California Berkeley |
*> \author Univ. of California Berkeley |
*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
* |
*> \date June 2016 |
*> \date June 2016 |
* |
* |
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*> ZGSVJ0 is used just to enable ZGESVJ to call a simplified version of |
*> ZGSVJ0 is used just to enable ZGESVJ to call a simplified version of |
*> itself to work on a submatrix of the original matrix. |
*> itself to work on a submatrix of the original matrix. |
*> |
*> |
*> Contributors: |
*> Contributor: |
* ============= |
* ============= |
*> |
*> |
*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) |
*> Zlatko Drmac (Zagreb, Croatia) |
*> |
*> |
*> Bugs, Examples and Comments: |
*> \par Bugs, Examples and Comments: |
* ============================ |
* ============================ |
*> |
*> |
*> Please report all bugs and send interesting test examples and comments to |
*> Please report all bugs and send interesting test examples and comments to |
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SUBROUTINE ZGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, |
SUBROUTINE ZGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, |
$ SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) |
$ SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) |
* |
* |
* -- LAPACK computational routine (version 3.6.1) -- |
* -- LAPACK computational routine (version 3.7.0) -- |
* -- 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..-- |
* June 2016 |
* June 2016 |
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* .. |
* .. |
* .. Array Arguments .. |
* .. Array Arguments .. |
COMPLEX*16 A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK ) |
COMPLEX*16 A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK ) |
DOUBLE PRECISION SVA( N ) |
DOUBLE PRECISION SVA( N ) |
* .. |
* .. |
* |
* |
* ===================================================================== |
* ===================================================================== |
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* .. |
* .. |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC ABS, DMAX1, DCONJG, DBLE, MIN0, DSIGN, DSQRT |
INTRINSIC ABS, MAX, CONJG, DBLE, MIN, SIGN, SQRT |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
DOUBLE PRECISION DZNRM2 |
DOUBLE PRECISION DZNRM2 |
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INFO = -5 |
INFO = -5 |
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 |
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END IF |
END IF |
RSVEC = RSVEC .OR. APPLV |
RSVEC = RSVEC .OR. APPLV |
|
|
ROOTEPS = DSQRT( EPS ) |
ROOTEPS = SQRT( EPS ) |
ROOTSFMIN = DSQRT( SFMIN ) |
ROOTSFMIN = SQRT( SFMIN ) |
SMALL = SFMIN / EPS |
SMALL = SFMIN / EPS |
BIG = ONE / SFMIN |
BIG = ONE / SFMIN |
ROOTBIG = ONE / ROOTSFMIN |
ROOTBIG = ONE / ROOTSFMIN |
BIGTHETA = ONE / ROOTEPS |
BIGTHETA = ONE / ROOTEPS |
ROOTTOL = DSQRT( TOL ) |
ROOTTOL = SQRT( TOL ) |
* |
* |
* .. Row-cyclic Jacobi SVD algorithm with column pivoting .. |
* .. Row-cyclic Jacobi SVD algorithm with column pivoting .. |
* |
* |
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* The boundaries are determined dynamically, based on the number of |
* The boundaries are determined dynamically, based on the number of |
* pivots above a threshold. |
* 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 |
*[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 |
* tiling of the p-q loops of pivot pairs. In general, an optimal |
* value of KBL depends on the matrix dimensions and on the |
* value of KBL depends on the matrix dimensions and on the |
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BLSKIP = KBL**2 |
BLSKIP = KBL**2 |
*[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. |
*[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. |
*[TP] ROWSKIP is a tuning parameter. |
* |
* |
LKAHEAD = 1 |
LKAHEAD = 1 |
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* |
* |
igl = ( ibr-1 )*KBL + 1 |
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 |
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 |
* .. de Rijk's pivoting |
* |
* |
q = IDAMAX( N-p+1, SVA( p ), 1 ) + p - 1 |
q = IDAMAX( N-p+1, SVA( p ), 1 ) + p - 1 |
IF( p.NE.q ) THEN |
IF( p.NE.q ) THEN |
CALL ZSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) |
CALL ZSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) |
IF( RSVEC )CALL ZSWAP( MVL, V( 1, p ), 1, |
IF( RSVEC )CALL ZSWAP( 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 ) |
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* If properly implemented DZNRM2 is available, the IF-THEN-ELSE-END IF |
* If properly implemented DZNRM2 is available, the IF-THEN-ELSE-END IF |
* below should be replaced with "AAPP = DZNRM2( M, A(1,p), 1 )". |
* below should be replaced with "AAPP = DZNRM2( M, A(1,p), 1 )". |
* |
* |
IF( ( SVA( p ).LT.ROOTBIG ) .AND. |
IF( ( SVA( p ).LT.ROOTBIG ) .AND. |
$ ( SVA( p ).GT.ROOTSFMIN ) ) THEN |
$ ( SVA( p ).GT.ROOTSFMIN ) ) THEN |
SVA( p ) = DZNRM2( M, A( 1, p ), 1 ) |
SVA( p ) = DZNRM2( M, A( 1, p ), 1 ) |
ELSE |
ELSE |
TEMP1 = ZERO |
TEMP1 = ZERO |
AAPP = ONE |
AAPP = ONE |
CALL ZLASSQ( M, A( 1, p ), 1, TEMP1, AAPP ) |
CALL ZLASSQ( M, A( 1, p ), 1, TEMP1, AAPP ) |
SVA( p ) = TEMP1*DSQRT( AAPP ) |
SVA( p ) = TEMP1*SQRT( AAPP ) |
END IF |
END IF |
AAPP = SVA( p ) |
AAPP = SVA( p ) |
ELSE |
ELSE |
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* |
* |
PSKIPPED = 0 |
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 ) |
AAQQ = SVA( q ) |
* |
* |
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IF( AAQQ.GE.ONE ) THEN |
IF( AAQQ.GE.ONE ) THEN |
ROTOK = ( SMALL*AAPP ).LE.AAQQ |
ROTOK = ( SMALL*AAPP ).LE.AAQQ |
IF( AAPP.LT.( BIG / AAQQ ) ) THEN |
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 |
$ A( 1, q ), 1 ) / AAQQ ) / AAPP |
ELSE |
ELSE |
CALL ZCOPY( M, A( 1, p ), 1, |
CALL ZCOPY( M, A( 1, p ), 1, |
$ WORK, 1 ) |
$ WORK, 1 ) |
CALL ZLASCL( 'G', 0, 0, AAPP, ONE, |
CALL ZLASCL( 'G', 0, 0, AAPP, ONE, |
$ M, 1, WORK, LDA, IERR ) |
$ M, 1, WORK, LDA, IERR ) |
AAPQ = ZDOTC( M, WORK, 1, |
AAPQ = ZDOTC( M, WORK, 1, |
$ A( 1, q ), 1 ) / AAQQ |
$ A( 1, q ), 1 ) / AAQQ |
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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 = ( ZDOTC( M, A( 1, p ), 1, |
AAPQ = ( ZDOTC( M, A( 1, p ), 1, |
$ A( 1, q ), 1 ) / AAQQ ) / AAPP |
$ A( 1, q ), 1 ) / AAPP ) / AAQQ |
ELSE |
ELSE |
CALL ZCOPY( M, A( 1, q ), 1, |
CALL ZCOPY( M, A( 1, q ), 1, |
$ WORK, 1 ) |
$ WORK, 1 ) |
CALL ZLASCL( 'G', 0, 0, AAQQ, |
CALL ZLASCL( 'G', 0, 0, AAQQ, |
$ ONE, M, 1, |
$ ONE, M, 1, |
$ WORK, LDA, IERR ) |
$ WORK, LDA, IERR ) |
AAPQ = ZDOTC( M, A( 1, p ), 1, |
AAPQ = ZDOTC( M, A( 1, p ), 1, |
$ WORK, 1 ) / AAPP |
$ WORK, 1 ) / AAPP |
END IF |
END IF |
END IF |
END IF |
* |
* |
OMPQ = AAPQ / ABS(AAPQ) |
* AAPQ = AAPQ * CONJG( CWORK(p) ) * CWORK(q) |
* AAPQ = AAPQ * DCONJG( CWORK(p) ) * CWORK(q) |
AAPQ1 = -ABS(AAPQ) |
AAPQ1 = -ABS(AAPQ) |
MXAAPQ = MAX( MXAAPQ, -AAPQ1 ) |
MXAAPQ = DMAX1( MXAAPQ, -AAPQ1 ) |
|
* |
* |
* TO rotate or NOT to rotate, THAT is the question ... |
* TO rotate or NOT to rotate, THAT is the question ... |
* |
* |
IF( ABS( AAPQ1 ).GT.TOL ) THEN |
IF( ABS( AAPQ1 ).GT.TOL ) THEN |
|
OMPQ = AAPQ / ABS(AAPQ) |
* |
* |
* .. rotate |
* .. rotate |
*[RTD] ROTATED = ROTATED + ONE |
*[RTD] ROTATED = ROTATED + ONE |
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THETA = -HALF*ABS( AQOAP-APOAQ )/AAPQ1 |
THETA = -HALF*ABS( AQOAP-APOAQ )/AAPQ1 |
* |
* |
IF( ABS( THETA ).GT.BIGTHETA ) THEN |
IF( ABS( THETA ).GT.BIGTHETA ) THEN |
* |
* |
T = HALF / THETA |
T = HALF / THETA |
CS = ONE |
CS = ONE |
|
|
CALL ZROT( M, A(1,p), 1, A(1,q), 1, |
CALL ZROT( M, A(1,p), 1, A(1,q), 1, |
$ CS, DCONJG(OMPQ)*T ) |
$ CS, CONJG(OMPQ)*T ) |
IF ( RSVEC ) THEN |
IF ( RSVEC ) THEN |
CALL ZROT( MVL, V(1,p), 1, |
CALL ZROT( MVL, V(1,p), 1, |
$ V(1,q), 1, CS, DCONJG(OMPQ)*T ) |
$ V(1,q), 1, CS, CONJG(OMPQ)*T ) |
END IF |
END IF |
|
|
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*SQRT( MAX( ZERO, |
$ ONE+T*APOAQ*AAPQ1 ) ) |
$ ONE+T*APOAQ*AAPQ1 ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*SQRT( MAX( ZERO, |
$ ONE-T*AQOAP*AAPQ1 ) ) |
$ ONE-T*AQOAP*AAPQ1 ) ) |
MXSINJ = DMAX1( MXSINJ, ABS( T ) ) |
MXSINJ = MAX( MXSINJ, ABS( T ) ) |
* |
* |
ELSE |
ELSE |
* |
* |
* .. choose correct signum for THETA and rotate |
* .. choose correct signum for THETA and rotate |
* |
* |
THSIGN = -DSIGN( ONE, AAPQ1 ) |
THSIGN = -SIGN( ONE, AAPQ1 ) |
T = ONE / ( THETA+THSIGN* |
T = ONE / ( THETA+THSIGN* |
$ DSQRT( ONE+THETA*THETA ) ) |
$ SQRT( ONE+THETA*THETA ) ) |
CS = DSQRT( ONE / ( ONE+T*T ) ) |
CS = SQRT( ONE / ( ONE+T*T ) ) |
SN = T*CS |
SN = T*CS |
* |
* |
MXSINJ = DMAX1( MXSINJ, ABS( SN ) ) |
MXSINJ = MAX( MXSINJ, ABS( SN ) ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*SQRT( MAX( ZERO, |
$ ONE+T*APOAQ*AAPQ1 ) ) |
$ ONE+T*APOAQ*AAPQ1 ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*SQRT( MAX( ZERO, |
$ ONE-T*AQOAP*AAPQ1 ) ) |
$ ONE-T*AQOAP*AAPQ1 ) ) |
* |
* |
CALL ZROT( M, A(1,p), 1, A(1,q), 1, |
CALL ZROT( M, A(1,p), 1, A(1,q), 1, |
$ CS, DCONJG(OMPQ)*SN ) |
$ CS, CONJG(OMPQ)*SN ) |
IF ( RSVEC ) THEN |
IF ( RSVEC ) THEN |
CALL ZROT( MVL, V(1,p), 1, |
CALL ZROT( MVL, V(1,p), 1, |
$ V(1,q), 1, CS, DCONJG(OMPQ)*SN ) |
$ V(1,q), 1, CS, CONJG(OMPQ)*SN ) |
END IF |
END IF |
END IF |
END IF |
D(p) = -D(q) * OMPQ |
D(p) = -D(q) * OMPQ |
* |
* |
ELSE |
ELSE |
* .. have to use modified Gram-Schmidt like transformation |
* .. have to use modified Gram-Schmidt like transformation |
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$ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
CALL ZLASCL( 'G', 0, 0, ONE, AAQQ, M, |
CALL ZLASCL( '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*SQRT( MAX( ZERO, |
$ ONE-AAPQ1*AAPQ1 ) ) |
$ ONE-AAPQ1*AAPQ1 ) ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = MAX( MXSINJ, SFMIN ) |
END IF |
END IF |
* END IF ROTOK THEN ... ELSE |
* END IF ROTOK THEN ... ELSE |
* |
* |
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AAQQ = ONE |
AAQQ = ONE |
CALL ZLASSQ( M, A( 1, q ), 1, T, |
CALL ZLASSQ( M, A( 1, q ), 1, T, |
$ AAQQ ) |
$ AAQQ ) |
SVA( q ) = T*DSQRT( AAQQ ) |
SVA( q ) = T*SQRT( AAQQ ) |
END IF |
END IF |
END IF |
END IF |
IF( ( AAPP / AAPP0 ).LE.ROOTEPS ) THEN |
IF( ( AAPP / AAPP0 ).LE.ROOTEPS ) THEN |
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AAPP = ONE |
AAPP = ONE |
CALL ZLASSQ( M, A( 1, p ), 1, T, |
CALL ZLASSQ( M, A( 1, p ), 1, T, |
$ AAPP ) |
$ AAPP ) |
AAPP = T*DSQRT( AAPP ) |
AAPP = T*SQRT( AAPP ) |
END IF |
END IF |
SVA( p ) = AAPP |
SVA( p ) = AAPP |
END IF |
END IF |
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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 + MIN( igl+KBL-1, N ) - p |
END IF |
END IF |
* |
* |
2001 CONTINUE |
2001 CONTINUE |
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* doing the block at ( ibr, jbc ) |
* doing the block at ( ibr, jbc ) |
* |
* |
IJBLSK = 0 |
IJBLSK = 0 |
DO 2100 p = igl, MIN0( igl+KBL-1, N ) |
DO 2100 p = igl, MIN( igl+KBL-1, N ) |
* |
* |
AAPP = SVA( p ) |
AAPP = SVA( p ) |
IF( AAPP.GT.ZERO ) THEN |
IF( AAPP.GT.ZERO ) THEN |
* |
* |
PSKIPPED = 0 |
PSKIPPED = 0 |
* |
* |
DO 2200 q = jgl, MIN0( jgl+KBL-1, N ) |
DO 2200 q = jgl, MIN( jgl+KBL-1, N ) |
* |
* |
AAQQ = SVA( q ) |
AAQQ = SVA( q ) |
IF( AAQQ.GT.ZERO ) THEN |
IF( AAQQ.GT.ZERO ) THEN |
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ROTOK = ( SMALL*AAQQ ).LE.AAPP |
ROTOK = ( SMALL*AAQQ ).LE.AAPP |
END IF |
END IF |
IF( AAPP.LT.( BIG / AAQQ ) ) THEN |
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 |
$ A( 1, q ), 1 ) / AAQQ ) / AAPP |
ELSE |
ELSE |
CALL ZCOPY( M, A( 1, p ), 1, |
CALL ZCOPY( M, A( 1, p ), 1, |
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ROTOK = AAQQ.LE.( AAPP / SMALL ) |
ROTOK = AAQQ.LE.( AAPP / SMALL ) |
END IF |
END IF |
IF( AAPP.GT.( SMALL / AAQQ ) ) THEN |
IF( AAPP.GT.( SMALL / AAQQ ) ) THEN |
AAPQ = ( ZDOTC( M, A( 1, p ), 1, |
AAPQ = ( ZDOTC( M, A( 1, p ), 1, |
$ A( 1, q ), 1 ) / AAQQ ) / AAPP |
$ A( 1, q ), 1 ) / MAX(AAQQ,AAPP) ) |
|
$ / MIN(AAQQ,AAPP) |
ELSE |
ELSE |
CALL ZCOPY( M, A( 1, q ), 1, |
CALL ZCOPY( M, A( 1, q ), 1, |
$ WORK, 1 ) |
$ WORK, 1 ) |
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Line 695
|
END IF |
END IF |
END IF |
END IF |
* |
* |
OMPQ = AAPQ / ABS(AAPQ) |
* AAPQ = AAPQ * CONJG(CWORK(p))*CWORK(q) |
* AAPQ = AAPQ * DCONJG(CWORK(p))*CWORK(q) |
|
AAPQ1 = -ABS(AAPQ) |
AAPQ1 = -ABS(AAPQ) |
MXAAPQ = DMAX1( MXAAPQ, -AAPQ1 ) |
MXAAPQ = MAX( MXAAPQ, -AAPQ1 ) |
* |
* |
* TO rotate or NOT to rotate, THAT is the question ... |
* TO rotate or NOT to rotate, THAT is the question ... |
* |
* |
IF( ABS( AAPQ1 ).GT.TOL ) THEN |
IF( ABS( AAPQ1 ).GT.TOL ) THEN |
|
OMPQ = AAPQ / ABS(AAPQ) |
NOTROT = 0 |
NOTROT = 0 |
*[RTD] ROTATED = ROTATED + 1 |
*[RTD] ROTATED = ROTATED + 1 |
PSKIPPED = 0 |
PSKIPPED = 0 |
Line 715
|
Line 717
|
* |
* |
IF( ABS( THETA ).GT.BIGTHETA ) THEN |
IF( ABS( THETA ).GT.BIGTHETA ) THEN |
T = HALF / THETA |
T = HALF / THETA |
CS = ONE |
CS = ONE |
CALL ZROT( M, A(1,p), 1, A(1,q), 1, |
CALL ZROT( M, A(1,p), 1, A(1,q), 1, |
$ CS, DCONJG(OMPQ)*T ) |
$ CS, CONJG(OMPQ)*T ) |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL ZROT( MVL, V(1,p), 1, |
CALL ZROT( MVL, V(1,p), 1, |
$ V(1,q), 1, CS, DCONJG(OMPQ)*T ) |
$ V(1,q), 1, CS, CONJG(OMPQ)*T ) |
END IF |
END IF |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*SQRT( MAX( ZERO, |
$ ONE+T*APOAQ*AAPQ1 ) ) |
$ ONE+T*APOAQ*AAPQ1 ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*SQRT( MAX( ZERO, |
$ ONE-T*AQOAP*AAPQ1 ) ) |
$ ONE-T*AQOAP*AAPQ1 ) ) |
MXSINJ = DMAX1( MXSINJ, ABS( T ) ) |
MXSINJ = MAX( MXSINJ, ABS( T ) ) |
ELSE |
ELSE |
* |
* |
* .. choose correct signum for THETA and rotate |
* .. choose correct signum for THETA and rotate |
* |
* |
THSIGN = -DSIGN( ONE, AAPQ1 ) |
THSIGN = -SIGN( ONE, AAPQ1 ) |
IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN |
IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN |
T = ONE / ( THETA+THSIGN* |
T = ONE / ( THETA+THSIGN* |
$ DSQRT( ONE+THETA*THETA ) ) |
$ SQRT( ONE+THETA*THETA ) ) |
CS = DSQRT( ONE / ( ONE+T*T ) ) |
CS = SQRT( ONE / ( ONE+T*T ) ) |
SN = T*CS |
SN = T*CS |
MXSINJ = DMAX1( MXSINJ, ABS( SN ) ) |
MXSINJ = MAX( MXSINJ, ABS( SN ) ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*SQRT( MAX( ZERO, |
$ ONE+T*APOAQ*AAPQ1 ) ) |
$ ONE+T*APOAQ*AAPQ1 ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*SQRT( MAX( ZERO, |
$ ONE-T*AQOAP*AAPQ1 ) ) |
$ ONE-T*AQOAP*AAPQ1 ) ) |
* |
* |
CALL ZROT( M, A(1,p), 1, A(1,q), 1, |
CALL ZROT( M, A(1,p), 1, A(1,q), 1, |
$ CS, DCONJG(OMPQ)*SN ) |
$ CS, CONJG(OMPQ)*SN ) |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL ZROT( MVL, V(1,p), 1, |
CALL ZROT( MVL, V(1,p), 1, |
$ V(1,q), 1, CS, DCONJG(OMPQ)*SN ) |
$ V(1,q), 1, CS, CONJG(OMPQ)*SN ) |
END IF |
END IF |
END IF |
END IF |
D(p) = -D(q) * OMPQ |
D(p) = -D(q) * OMPQ |
Line 768
|
Line 770
|
CALL ZLASCL( 'G', 0, 0, ONE, AAQQ, |
CALL ZLASCL( '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*SQRT( MAX( ZERO, |
$ ONE-AAPQ1*AAPQ1 ) ) |
$ ONE-AAPQ1*AAPQ1 ) ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = MAX( MXSINJ, SFMIN ) |
ELSE |
ELSE |
CALL ZCOPY( M, A( 1, q ), 1, |
CALL ZCOPY( M, A( 1, q ), 1, |
$ WORK, 1 ) |
$ WORK, 1 ) |
Line 780
|
Line 782
|
CALL ZLASCL( 'G', 0, 0, AAPP, ONE, |
CALL ZLASCL( 'G', 0, 0, AAPP, ONE, |
$ M, 1, A( 1, p ), LDA, |
$ M, 1, A( 1, p ), LDA, |
$ IERR ) |
$ IERR ) |
CALL ZAXPY( M, -DCONJG(AAPQ), |
CALL ZAXPY( M, -CONJG(AAPQ), |
$ WORK, 1, A( 1, p ), 1 ) |
$ WORK, 1, A( 1, p ), 1 ) |
CALL ZLASCL( 'G', 0, 0, ONE, AAPP, |
CALL ZLASCL( '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*SQRT( MAX( ZERO, |
$ ONE-AAPQ1*AAPQ1 ) ) |
$ ONE-AAPQ1*AAPQ1 ) ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = MAX( MXSINJ, SFMIN ) |
END IF |
END IF |
END IF |
END IF |
* END IF ROTOK THEN ... ELSE |
* END IF ROTOK THEN ... ELSE |
Line 804
|
Line 806
|
AAQQ = ONE |
AAQQ = ONE |
CALL ZLASSQ( M, A( 1, q ), 1, T, |
CALL ZLASSQ( M, A( 1, q ), 1, T, |
$ AAQQ ) |
$ AAQQ ) |
SVA( q ) = T*DSQRT( AAQQ ) |
SVA( q ) = T*SQRT( AAQQ ) |
END IF |
END IF |
END IF |
END IF |
IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN |
IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN |
Line 816
|
Line 818
|
AAPP = ONE |
AAPP = ONE |
CALL ZLASSQ( M, A( 1, p ), 1, T, |
CALL ZLASSQ( M, A( 1, p ), 1, T, |
$ AAPP ) |
$ AAPP ) |
AAPP = T*DSQRT( AAPP ) |
AAPP = T*SQRT( AAPP ) |
END IF |
END IF |
SVA( p ) = AAPP |
SVA( p ) = AAPP |
END IF |
END IF |
Line 855
|
Line 857
|
ELSE |
ELSE |
* |
* |
IF( AAPP.EQ.ZERO )NOTROT = NOTROT + |
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( AAPP.LT.ZERO )NOTROT = 0 |
* |
* |
END IF |
END IF |
Line 866
|
Line 868
|
* end of the jbc-loop |
* end of the jbc-loop |
2011 CONTINUE |
2011 CONTINUE |
*2011 bailed out of the jbc-loop |
*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 ) ) |
SVA( p ) = ABS( SVA( p ) ) |
2012 CONTINUE |
2012 CONTINUE |
*** |
*** |
Line 881
|
Line 883
|
T = ZERO |
T = ZERO |
AAPP = ONE |
AAPP = ONE |
CALL ZLASSQ( M, A( 1, N ), 1, T, AAPP ) |
CALL ZLASSQ( M, A( 1, N ), 1, T, AAPP ) |
SVA( N ) = T*DSQRT( AAPP ) |
SVA( N ) = T*SQRT( AAPP ) |
END IF |
END IF |
* |
* |
* Additional steering devices |
* Additional steering devices |
Line 889
|
Line 891
|
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.DSQRT( DBLE( N ) )* |
IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.SQRT( DBLE( N ) )* |
$ TOL ) .AND. ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN |
$ TOL ) .AND. ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN |
GO TO 1994 |
GO TO 1994 |
END IF |
END IF |
Line 909
|
Line 911
|
* |
* |
INFO = 0 |
INFO = 0 |
* #:) INFO = 0 confirms successful iterations. |
* #:) INFO = 0 confirms successful iterations. |
1995 CONTINUE |
1995 CONTINUE |
* |
* |
* Sort the vector SVA() of column norms. |
* Sort the vector SVA() of column norms. |
DO 5991 p = 1, N - 1 |
DO 5991 p = 1, N - 1 |