dgsvj1.f(3)

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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