zgsvj0.f - Man Page

subroutine zgsvj0 (JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO)
ZGSVJ0 pre-processor for the routine zgesvj.

ZGSVJ0 pre-processor for the routine zgesvj.  

Purpose:

 ZGSVJ0 is called from ZGESVJ as a pre-processor and that is its main
 purpose. It applies Jacobi rotations in the same way as ZGESVJ 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 COMPLEX*16 array, dimension (LDA,N)
          On entry, M-by-N matrix A, such that A*diag(D) represents
          the input matrix.
          On exit,
          A_onexit * diag(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 COMPLEX*16 array, dimension (N)
          The array D accumulates the scaling factors from the complex 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 A_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 COMPLEX*16 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 ABS(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 COMPLEX*16 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:

June 2016

Further Details:

ZGSVJ0 is used just to enable ZGESVJ to call a simplified version of itself to work on a submatrix of the original matrix.

Contributor: Zlatko Drmac (Zagreb, Croatia)

Bugs, Examples and Comments:

Definition at line 220 of file zgsvj0.f.