version 1.9, 2012/07/31 11:06:35
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version 1.22, 2023/08/07 08:38:51
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*> \brief \b DGSVJ1 |
*> \brief \b DGSVJ1 pre-processor for the routine dgesvj, applies Jacobi rotations targeting only particular pivots. |
* |
* |
* =========== 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 DGSVJ1 + dependencies |
*> Download DGSVJ1 + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgsvj1.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgsvj1.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgsvj1.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgsvj1.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgsvj1.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgsvj1.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, |
* SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, |
* EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) |
* EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* DOUBLE PRECISION EPS, SFMIN, TOL |
* DOUBLE PRECISION EPS, SFMIN, TOL |
* INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP |
* INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP |
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* DOUBLE PRECISION A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), |
* DOUBLE PRECISION A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), |
* $ WORK( LWORK ) |
* $ WORK( LWORK ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
*> |
*> |
*> \verbatim |
*> \verbatim |
*> |
*> |
*> DGSVJ1 is called from SGESVJ as a pre-processor and that is its main |
*> DGSVJ1 is called from DGESVJ as a pre-processor and that is its main |
*> purpose. It applies Jacobi rotations in the same way as SGESVJ does, but |
*> purpose. It applies Jacobi rotations in the same way as DGESVJ does, but |
*> it targets only particular pivots and it does not check convergence |
*> 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. |
*> available for the implementer. |
*> |
*> |
*> Further Details |
*> Further Details |
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*> In terms of the columns of A, the first N1 columns are rotated 'against' |
*> 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 |
*> 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 |
*> 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 |
*> The number of sweeps is given in NSWEEP and the orthogonality threshold |
*> is given in TOL. |
*> is given in TOL. |
*> \endverbatim |
*> \endverbatim |
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*> \param[in] MV |
*> \param[in] MV |
*> \verbatim |
*> \verbatim |
*> MV is INTEGER |
*> 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. |
*> sequence of Jacobi rotations. |
*> If JOBV = 'N', then MV is not referenced. |
*> If JOBV = 'N', then MV is not referenced. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in,out] V |
*> \param[in,out] V |
*> \verbatim |
*> \verbatim |
*> V is DOUBLE PRECISION array, dimension (LDV,N) |
*> 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. |
*> 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. |
*> sequence of Jacobi rotations. |
*> If JOBV = 'N', then V is not referenced. |
*> If JOBV = 'N', then V is not referenced. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] LDV |
*> \param[in] LDV |
*> \verbatim |
*> \verbatim |
*> LDV is INTEGER |
*> LDV is INTEGER |
*> The leading dimension of the array V, LDV >= 1. |
*> The leading dimension of the array V, LDV >= 1. |
*> If JOBV = 'V', LDV .GE. N. |
*> If JOBV = 'V', LDV >= N. |
*> If JOBV = 'A', LDV .GE. MV. |
*> If JOBV = 'A', LDV >= MV. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[in] EPS |
*> \param[in] EPS |
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*> TOL is DOUBLE PRECISION |
*> TOL is DOUBLE PRECISION |
*> TOL is the threshold for Jacobi rotations. For a pair |
*> TOL is the threshold for Jacobi rotations. For a pair |
*> A(:,p), A(:,q) of pivot columns, the Jacobi rotation is |
*> 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 |
*> \endverbatim |
*> |
*> |
*> \param[in] NSWEEP |
*> \param[in] NSWEEP |
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*> \param[in] LWORK |
*> \param[in] LWORK |
*> \verbatim |
*> \verbatim |
*> LWORK is INTEGER |
*> LWORK is INTEGER |
*> LWORK is the dimension of WORK. LWORK .GE. M. |
*> LWORK is the dimension of WORK. LWORK >= M. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
*> \param[out] INFO |
*> \param[out] INFO |
*> \verbatim |
*> \verbatim |
*> INFO is INTEGER |
*> INFO is INTEGER |
*> = 0 : successful exit. |
*> = 0: successful exit. |
*> < 0 : if INFO = -i, then the i-th argument had an illegal value |
*> < 0: if INFO = -i, then the i-th argument had an illegal value |
*> \endverbatim |
*> \endverbatim |
* |
* |
* 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 November 2011 |
|
* |
* |
*> \ingroup doubleOTHERcomputational |
*> \ingroup doubleOTHERcomputational |
* |
* |
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SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, |
SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, |
$ EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) |
$ 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, -- |
* -- 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..-- |
* November 2011 |
|
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
DOUBLE PRECISION EPS, SFMIN, TOL |
DOUBLE PRECISION EPS, SFMIN, TOL |
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DOUBLE PRECISION FASTR( 5 ) |
DOUBLE PRECISION FASTR( 5 ) |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC DABS, DMAX1, DBLE, MIN0, DSIGN, DSQRT |
INTRINSIC DABS, MAX, DBLE, MIN, DSIGN, DSQRT |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
DOUBLE PRECISION DDOT, DNRM2 |
DOUBLE PRECISION DDOT, DNRM2 |
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EXTERNAL IDAMAX, LSAME, DDOT, DNRM2 |
EXTERNAL IDAMAX, LSAME, DDOT, DNRM2 |
* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP |
EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP, |
|
$ XERBLA |
* .. |
* .. |
* .. Executable Statements .. |
* .. Executable Statements .. |
* |
* |
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INFO = -6 |
INFO = -6 |
ELSE IF( ( RSVEC.OR.APPLV ) .AND. ( MV.LT.0 ) ) THEN |
ELSE IF( ( RSVEC.OR.APPLV ) .AND. ( MV.LT.0 ) ) THEN |
INFO = -9 |
INFO = -9 |
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 = -11 |
INFO = -11 |
ELSE IF( TOL.LE.EPS ) THEN |
ELSE IF( TOL.LE.EPS ) THEN |
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* |
* |
* .. Row-cyclic pivot strategy with de Rijk's pivoting .. |
* .. Row-cyclic pivot strategy with de Rijk's pivoting .. |
* |
* |
KBL = MIN0( 8, N ) |
KBL = MIN( 8, N ) |
NBLR = N1 / KBL |
NBLR = N1 / KBL |
IF( ( NBLR*KBL ).NE.N1 )NBLR = NBLR + 1 |
IF( ( NBLR*KBL ).NE.N1 )NBLR = NBLR + 1 |
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BLSKIP = ( KBL**2 ) + 1 |
BLSKIP = ( KBL**2 ) + 1 |
*[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. |
*[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. |
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ROWSKIP = MIN0( 5, KBL ) |
ROWSKIP = MIN( 5, KBL ) |
*[TP] ROWSKIP is a tuning parameter. |
*[TP] ROWSKIP is a tuning parameter. |
SWBAND = 0 |
SWBAND = 0 |
*[TP] SWBAND is a tuning parameter. It is meaningful and effective |
*[TP] SWBAND is a tuning parameter. It is meaningful and effective |
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* doing the block at ( ibr, jbc ) |
* doing the block at ( ibr, jbc ) |
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IJBLSK = 0 |
IJBLSK = 0 |
DO 2100 p = igl, MIN0( igl+KBL-1, N1 ) |
DO 2100 p = igl, MIN( igl+KBL-1, N1 ) |
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AAPP = SVA( p ) |
AAPP = SVA( p ) |
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PSKIPPED = 0 |
PSKIPPED = 0 |
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DO 2200 q = jgl, MIN0( jgl+KBL-1, N ) |
DO 2200 q = jgl, MIN( jgl+KBL-1, N ) |
* |
* |
AAQQ = SVA( q ) |
AAQQ = SVA( q ) |
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END IF |
END IF |
END IF |
END IF |
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MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) ) |
MXAAPQ = MAX( MXAAPQ, DABS( AAPQ ) ) |
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* TO rotate or NOT to rotate, THAT is the question ... |
* TO rotate or NOT to rotate, THAT is the question ... |
* |
* |
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$ 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( MAX( ZERO, |
$ ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*DSQRT( MAX( ZERO, |
$ ONE-T*AQOAP*AAPQ ) ) |
$ ONE-T*AQOAP*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, DABS( T ) ) |
MXSINJ = MAX( MXSINJ, DABS( T ) ) |
ELSE |
ELSE |
* |
* |
* .. choose correct signum for THETA and rotate |
* .. choose correct signum for THETA and rotate |
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$ 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 = MAX( MXSINJ, DABS( SN ) ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( MAX( ZERO, |
$ ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*DSQRT( MAX( ZERO, |
$ ONE-T*AQOAP*AAPQ ) ) |
$ ONE-T*AQOAP*AAPQ ) ) |
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APOAQ = D( p ) / D( q ) |
APOAQ = D( p ) / D( q ) |
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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( MAX( ZERO, |
$ ONE-AAPQ*AAPQ ) ) |
$ ONE-AAPQ*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = MAX( MXSINJ, SFMIN ) |
ELSE |
ELSE |
CALL DCOPY( M, A( 1, q ), 1, WORK, |
CALL DCOPY( M, A( 1, q ), 1, WORK, |
$ 1 ) |
$ 1 ) |
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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( MAX( ZERO, |
$ ONE-AAPQ*AAPQ ) ) |
$ ONE-AAPQ*AAPQ ) ) |
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 |
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* |
* |
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 |
*** IF ( NOTROT .GE. EMPTSW ) GO TO 2011 |
*** IF ( NOTROT .GE. EMPTSW ) GO TO 2011 |
END IF |
END IF |
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* 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 ) = DABS( SVA( p ) ) |
SVA( p ) = DABS( SVA( p ) ) |
2012 CONTINUE |
2012 CONTINUE |
*** IF ( NOTROT .GE. EMPTSW ) GO TO 1994 |
*** IF ( NOTROT .GE. EMPTSW ) GO TO 1994 |