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version 1.16, 2016/08/27 15:34:24 version 1.22, 2023/08/07 08:38:51
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 *  *
 *  =========== 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:
 *  =============  *  =============
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 *> DGSVJ1 is called from DGESVJ 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 DGESVJ 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 June 2016  
 *  *
 *> \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 3.6.1) --  *  -- 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..--
 *     June 2016  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       DOUBLE PRECISION   EPS, SFMIN, TOL        DOUBLE PRECISION   EPS, SFMIN, TOL
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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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                                     MXSINJ = MAX( MXSINJ, DABS( SN ) )                                      MXSINJ = MAX( MXSINJ, DABS( SN ) )
                                     SVA( q ) = AAQQ*DSQRT( MAX( ZERO,                                      SVA( q ) = AAQQ*DSQRT( MAX( ZERO,
      $                                         ONE+T*APOAQ*AAPQ ) )       $                                         ONE+T*APOAQ*AAPQ ) )
                                     AAPP = AAPP*DSQRT( MAX( ZERO,                                       AAPP = AAPP*DSQRT( MAX( ZERO,
      $                                    ONE-T*AQOAP*AAPQ ) )       $                                    ONE-T*AQOAP*AAPQ ) )
   
                                     APOAQ = D( p ) / D( q )                                      APOAQ = D( p ) / D( q )
Removed from v.1.16  
changed lines
  Added in v.1.22

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