SGSVJ0 (3) - Linux Manuals

sgsvj0.f -

SYNOPSIS

Functions/Subroutines

subroutine sgsvj0 (JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO)
SGSVJ0 pre-processor for the routine sgesvj.

Function/Subroutine Documentation

subroutine sgsvj0 (character*1JOBV, integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( n )D, real, dimension( n )SVA, integerMV, real, dimension( ldv, * )V, integerLDV, realEPS, realSFMIN, realTOL, integerNSWEEP, real, dimension( lwork )WORK, integerLWORK, integerINFO)

SGSVJ0 pre-processor for the routine sgesvj.

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.

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 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

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

D

D is 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

SVA is 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

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 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

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 REAL
EPS = SLAMCH('Epsilon')

SFMIN

SFMIN is REAL
SFMIN = SLAMCH('Safe Minimum')

TOL

TOL is 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

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

WORK

WORK is REAL 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

NAG Ltd.

Date:

September 2012

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)