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version 1.6, 2011/07/22 07:38:05 version 1.7, 2011/11/21 20:42:52
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       SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,  *> \brief \b DGSVJ0
      $                   SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )  *
   *  =========== DOCUMENTATION ===========
 *  *
 *  -- LAPACK routine (version 3.3.1)                                  --  * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
 *  *
 *  -- Contributed by Zlatko Drmac of the University of Zagreb and     --  *> \htmlonly
 *  -- Kresimir Veselic of the Fernuniversitaet Hagen                  --  *> Download DGSVJ0 + dependencies 
 *  -- April 2011                                                      --  *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgsvj0.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgsvj0.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgsvj0.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
   *                          SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP
   *       DOUBLE PRECISION   EPS, SFMIN, TOL
   *       CHARACTER*1        JOBV
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   A( LDA, * ), SVA( N ), D( N ), V( LDV, * ),
   *      $                   WORK( LWORK )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DGSVJ0 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
   *> it does not check convergence (stopping criterion). Few tuning
   *> parameters (marked by [TP]) are available for the implementer.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] JOBV
   *> \verbatim
   *>          JOBV is CHARACTER*1
   *>          Specifies whether the output from this procedure is used
   *>          to compute the matrix V:
   *>          = 'V': the product of the Jacobi rotations is accumulated
   *>                 by postmulyiplying the N-by-N array V.
   *>                (See the description of V.)
   *>          = 'A': the product of the Jacobi rotations is accumulated
   *>                 by postmulyiplying the MV-by-N array V.
   *>                (See the descriptions of MV and V.)
   *>          = 'N': the Jacobi rotations are not accumulated.
   *> \endverbatim
   *>
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of rows of the input matrix A.  M >= 0.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The number of columns of the input matrix A.
   *>          M >= N >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] A
   *> \verbatim
   *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   *>          On entry, M-by-N matrix A, such that A*diag(D) represents
   *>          the input matrix.
   *>          On exit,
   *>          A_onexit * D_onexit represents the input matrix A*diag(D)
   *>          post-multiplied by a sequence of Jacobi rotations, where the
   *>          rotation threshold and the total number of sweeps are given in
   *>          TOL and NSWEEP, respectively.
   *>          (See the descriptions of D, TOL and NSWEEP.)
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A.  LDA >= max(1,M).
   *> \endverbatim
   *>
   *> \param[in,out] D
   *> \verbatim
   *>          D is DOUBLE PRECISION array, dimension (N)
   *>          The array D accumulates the scaling factors from the fast scaled
   *>          Jacobi rotations.
   *>          On entry, A*diag(D) represents the input matrix.
   *>          On exit, A_onexit*diag(D_onexit) represents the input matrix
   *>          post-multiplied by a sequence of Jacobi rotations, where the
   *>          rotation threshold and the total number of sweeps are given in
   *>          TOL and NSWEEP, respectively.
   *>          (See the descriptions of A, TOL and NSWEEP.)
   *> \endverbatim
   *>
   *> \param[in,out] SVA
   *> \verbatim
   *>          SVA is DOUBLE PRECISION array, dimension (N)
   *>          On entry, SVA contains the Euclidean norms of the columns of
   *>          the matrix A*diag(D).
   *>          On exit, SVA contains the Euclidean norms of the columns of
   *>          the matrix onexit*diag(D_onexit).
   *> \endverbatim
   *>
   *> \param[in] MV
   *> \verbatim
   *>          MV is INTEGER
   *>          If JOBV .EQ. 'A', then MV rows of V are post-multipled by a
   *>                           sequence of Jacobi rotations.
   *>          If JOBV = 'N',   then MV is not referenced.
   *> \endverbatim
   *>
   *> \param[in,out] V
   *> \verbatim
   *>          V is DOUBLE PRECISION array, dimension (LDV,N)
   *>          If JOBV .EQ. '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
   *>                           sequence of Jacobi rotations.
   *>          If JOBV = 'N',   then V is not referenced.
   *> \endverbatim
   *>
   *> \param[in] LDV
   *> \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.
   *> \endverbatim
   *>
   *> \param[in] EPS
   *> \verbatim
   *>          EPS is DOUBLE PRECISION
   *>          EPS = DLAMCH('Epsilon')
   *> \endverbatim
   *>
   *> \param[in] SFMIN
   *> \verbatim
   *>          SFMIN is DOUBLE PRECISION
   *>          SFMIN = DLAMCH('Safe Minimum')
   *> \endverbatim
   *>
   *> \param[in] TOL
   *> \verbatim
   *>          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 DABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.
   *> \endverbatim
   *>
   *> \param[in] NSWEEP
   *> \verbatim
   *>          NSWEEP is INTEGER
   *>          NSWEEP is the number of sweeps of Jacobi rotations to be
   *>          performed.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (LWORK)
   *> \endverbatim
   *>
   *> \param[in] LWORK
   *> \verbatim
   *>          LWORK is INTEGER
   *>          LWORK is the dimension of WORK. LWORK .GE. 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
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleOTHERcomputational
   *
   *> \par Further Details:
   *  =====================
   *>
   *> DGSVJ0 is used just to enable DGESVJ to call a simplified version of
   *> itself to work on a submatrix of the original matrix.
   *>
   *> \par Contributors:
   *  ==================
   *>
   *> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
   *>
   *> \par Bugs, Examples and Comments:
   *  =================================
   *>
   *> Please report all bugs and send interesting test examples and comments to
   *> drmac@math.hr. Thank you.
 *  *
   *  =====================================================================
         SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
        $                   SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
   *
   *  -- LAPACK computational routine (version 3.4.0) --
 *  -- 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..--
   *     November 2011
 *  *
 * This routine is also part of SIGMA (version 1.23, October 23. 2008.)  
 * SIGMA is a library of algorithms for highly accurate algorithms for  
 * computation of SVD, PSVD, QSVD, (H,K)-SVD, and for solution of the  
 * eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0.  
 *  
       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
Line 27 Line 233
      $                   WORK( LWORK )       $                   WORK( LWORK )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DGSVJ0 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  
 *  it does not check convergence (stopping criterion). Few tuning  
 *  parameters (marked by [TP]) are available for the implementer.  
 *  
 *  Further Details  
 *  ~~~~~~~~~~~~~~~  
 *  DGSVJ0 is used just to enable SGESVJ to call a simplified version of  
 *  itself to work on a submatrix of the original matrix.  
 *  
 *  Contributors  
 *  ~~~~~~~~~~~~  
 *  Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)  
 *  
 *  Bugs, Examples and Comments  
 *  ~~~~~~~~~~~~~~~~~~~~~~~~~~~  
 *  Please report all bugs and send interesting test examples and comments to  
 *  drmac@math.hr. Thank you.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  JOBV    (input) CHARACTER*1  
 *          Specifies whether the output from this procedure is used  
 *          to compute the matrix V:  
 *          = 'V': the product of the Jacobi rotations is accumulated  
 *                 by postmulyiplying the N-by-N array V.  
 *                (See the description of V.)  
 *          = 'A': the product of the Jacobi rotations is accumulated  
 *                 by postmulyiplying the MV-by-N array V.  
 *                (See the descriptions of MV and V.)  
 *          = 'N': the Jacobi rotations are not accumulated.  
 *  
 *  M       (input) INTEGER  
 *          The number of rows of the input matrix A.  M >= 0.  
 *  
 *  N       (input) INTEGER  
 *          The number of columns of the input matrix A.  
 *          M >= N >= 0.  
 *  
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)  
 *          On entry, M-by-N matrix A, such that A*diag(D) represents  
 *          the input matrix.  
 *          On exit,  
 *          A_onexit * D_onexit represents the input matrix A*diag(D)  
 *          post-multiplied by a sequence of Jacobi rotations, where the  
 *          rotation threshold and the total number of sweeps are given in  
 *          TOL and NSWEEP, respectively.  
 *          (See the descriptions of D, TOL and NSWEEP.)  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A.  LDA >= max(1,M).  
 *  
 *  D       (input/workspace/output) DOUBLE PRECISION array, dimension (N)  
 *          The array D accumulates the scaling factors from the fast scaled  
 *          Jacobi rotations.  
 *          On entry, A*diag(D) represents the input matrix.  
 *          On exit, A_onexit*diag(D_onexit) represents the input matrix  
 *          post-multiplied by a sequence of Jacobi rotations, where the  
 *          rotation threshold and the total number of sweeps are given in  
 *          TOL and NSWEEP, respectively.  
 *          (See the descriptions of A, TOL and NSWEEP.)  
 *  
 *  SVA     (input/workspace/output) DOUBLE PRECISION array, dimension (N)  
 *          On entry, SVA contains the Euclidean norms of the columns of  
 *          the matrix A*diag(D).  
 *          On exit, SVA contains the Euclidean norms of the columns of  
 *          the matrix onexit*diag(D_onexit).  
 *  
 *  MV      (input) INTEGER  
 *          If JOBV .EQ. 'A', then MV rows of V are post-multipled by a  
 *                           sequence of Jacobi rotations.  
 *          If JOBV = 'N',   then MV is not referenced.  
 *  
 *  V       (input/output) DOUBLE PRECISION array, dimension (LDV,N)  
 *          If JOBV .EQ. '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  
 *                           sequence of Jacobi rotations.  
 *          If JOBV = 'N',   then V is not referenced.  
 *  
 *  LDV     (input) INTEGER  
 *          The leading dimension of the array V,  LDV >= 1.  
 *          If JOBV = 'V', LDV .GE. N.  
 *          If JOBV = 'A', LDV .GE. MV.  
 *  
 *  EPS     (input) DOUBLE PRECISION  
 *          EPS = DLAMCH('Epsilon')  
 *  
 *  SFMIN   (input) DOUBLE PRECISION  
 *          SFMIN = DLAMCH('Safe Minimum')  
 *  
 *  TOL     (input) 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 DABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.  
 *  
 *  NSWEEP  (input) INTEGER  
 *          NSWEEP is the number of sweeps of Jacobi rotations to be  
 *          performed.  
 *  
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK)  
 *  
 *  LWORK   (input) INTEGER  
 *          LWORK is the dimension of WORK. LWORK .GE. M.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0 : successful exit.  
 *          < 0 : if INFO = -i, then the i-th argument had an illegal value  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Parameters ..  *     .. Local Parameters ..
Removed from v.1.6  
changed lines
  Added in v.1.7

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