NAME

       dgsvj0.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dgsvj0 (JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP, WORK,
           LWORK, INFO)
           DGSVJ0 pre-processor for the routine dgesvj.

Function/Subroutine Documentation

   subroutine dgsvj0 (character*1 JOBV, integer M, integer N, double precision, dimension( lda, *
       ) A, integer LDA, double precision, dimension( n ) D, double precision, dimension( n )
       SVA, integer MV, double precision, dimension( ldv, * ) V, integer LDV, double precision
       EPS, double precision SFMIN, double precision TOL, integer NSWEEP, double precision,
       dimension( lwork ) WORK, integer LWORK, integer INFO)
       DGSVJ0 pre-processor for the routine dgesvj.

       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.

       Parameters:
           JOBV

                     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.

           M

                     M is INTEGER
                     The number of rows of the input matrix A.  M >= 0.

           N

                     N is INTEGER
                     The number of columns of the input matrix A.
                     M >= N >= 0.

           A

                     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.)

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           D

                     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.)

           SVA

                     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).

           MV

                     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.

           V

                     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.

           LDV

                     LDV is INTEGER
                     The leading dimension of the array V,  LDV >= 1.
                     If JOBV = 'V', LDV .GE. N.
                     If JOBV = 'A', LDV .GE. MV.

           EPS

                     EPS is DOUBLE PRECISION
                     EPS = DLAMCH('Epsilon')

           SFMIN

                     SFMIN is DOUBLE PRECISION
                     SFMIN = DLAMCH('Safe Minimum')

           TOL

                     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.

           NSWEEP

                     NSWEEP is INTEGER
                     NSWEEP is the number of sweeps of Jacobi rotations to be
                     performed.

           WORK

                     WORK is DOUBLE PRECISION array, dimension (LWORK)

           LWORK

                     LWORK is INTEGER
                     LWORK is the dimension of WORK. LWORK .GE. M.

           INFO

                     INFO is INTEGER
                     = 0 : successful exit.
                     < 0 : if INFO = -i, then the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2015

       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.

       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.

Author

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