SYNOPSIS

SUBROUTINE SGSVJ0(

JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,

    

+ SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )

    

IMPLICIT NONE

    

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

    

REAL EPS, SFMIN, TOL

    

CHARACTER*1 JOBV

    

REAL A( LDA, * ), SVA( N ), D( N ), V( LDV, * ),

    

+ WORK( LWORK )

PURPOSE

SGSVJ0 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 does not check convergence (stopping criterion). Few tuning parameters (marked by [TP]) are available for the implementer. Further Details
SGSVJ0 is used just to enable SGESVJ 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 [email protected]. Thank you.

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.

A (input/output) REAL 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 (input) INTEGER

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

D (input/workspace/output) REAL 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 (input/workspace/output) REAL 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) REAL 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) INTEGER

EPS = SLAMCH('Epsilon')

SFMIN (input) INTEGER

SFMIN = SLAMCH('Safe Minimum')

TOL (input) REAL

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 (input) INTEGER

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

WORK (workspace) REAL 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