Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - is called from SGESVJ as a pre-processor and that is its main purpose

SYNOPSIS

       SUBROUTINE DGSVJ1( JOBV,  M,  N,  N1, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP,
                          WORK, LWORK, INFO )

           IMPLICIT       NONE

           DOUBLE         PRECISION EPS, SFMIN, TOL

           INTEGER        INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP

           CHARACTER*1    JOBV

           DOUBLE         PRECISION A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), WORK( LWORK )

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

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.

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

        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 N1, 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 N1, 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

 LAPACK routine (version 3.3.1)             April 2011                            DGSVJ1(3lapack)