SGSVJ0(1LAPACK routine (version 3.2)SGSVJ0(1)NAME
SGSVJ0 - is called from SGESVJ as a pre-processor and that is its main
purpose
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 drmac@math.hr. 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 per‐
formed.
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
LAPACK routine (version 3.2) November 2008 SGSVJ0(1)
