NAME

       dgsvj1.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dgsvj1 (JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP,
           WORK, LWORK, INFO)
           DGSVJ1 pre-processor for the routine sgesvj, applies Jacobi rotations targeting only
           particular pivots.

Function/Subroutine Documentation

   subroutine dgsvj1 (character*1JOBV, integerM, integerN, integerN1, double precision,
       dimension( lda, * )A, integerLDA, double precision, dimension( n )D, double precision,
       dimension( n )SVA, integerMV, double precision, dimension( ldv, * )V, integerLDV, double
       precisionEPS, double precisionSFMIN, double precisionTOL, integerNSWEEP, double precision,
       dimension( lwork )WORK, integerLWORK, integerINFO)
       DGSVJ1 pre-processor for the routine sgesvj, applies Jacobi rotations targeting only
       particular pivots.

       Purpose:

            DGSVJ1 is called from SGESVJ as a pre-processor and that is its main
            purpose. It applies Jacobi rotations in the same way as SGESVJ does, but
            it targets only particular pivots and it does not check convergence
            (stopping criterion). Few tunning parameters (marked by [TP]) are
            available for the implementer.

            Further Details
            ~~~~~~~~~~~~~~~
            DGSVJ1 applies few sweeps of Jacobi rotations in the column space of
            the input M-by-N matrix A. The pivot pairs are taken from the (1,2)
            off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The
            block-entries (tiles) of the (1,2) off-diagonal block are marked by the
            [x]'s in the following scheme:

               | *  *  * [x] [x] [x]|
               | *  *  * [x] [x] [x]|    Row-cycling in the nblr-by-nblc [x] blocks.
               | *  *  * [x] [x] [x]|    Row-cyclic pivoting inside each [x] block.
               |[x] [x] [x] *  *  * |
               |[x] [x] [x] *  *  * |
               |[x] [x] [x] *  *  * |

            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
            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.
            The number of sweeps is given in NSWEEP and the orthogonality threshold
            is given in TOL.

       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.

           N1

                     N1 is INTEGER
                     N1 specifies the 2 x 2 block partition, the first N1 columns are
                     rotated 'against' the remaining N-N1 columns of A.

           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 N1, 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 N1, 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:
           September 2012

       Contributors:
           Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)

       Definition at line 236 of file dgsvj1.f.

Author

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