NAME
slaqge - equilibrate a general M by N matrix A using the row
and scaling factors in the vectors R and C
SYNOPSIS
SUBROUTINE SLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
EQUED )
CHARACTER EQUED
INTEGER LDA, M, N
REAL AMAX, COLCND, ROWCND
REAL A( LDA, * ), C( * ), R( * )
#include <sunperf.h>
void slaqge(int m, int n, float *sa, int lda, float *r,
float *sc, float rowcnd, float colcnd, float amax,
char *equed) ;
PURPOSE
SLAQGE equilibrates a general M by N matrix A using the row
and scaling factors in the vectors R and C.
ARGUMENTS
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the M by N matrix A. On exit, the
equilibrated matrix. See EQUED for the form of
the equilibrated matrix.
LDA (input) INTEGER
The leading dimension of the array A. LDA >=
max(M,1).
R (input) REAL array, dimension (M)
The row scale factors for A.
C (input) REAL array, dimension (N)
The column scale factors for A.
ROWCND (input) REAL
Ratio of the smallest R(i) to the largest R(i).
COLCND (input) REAL
Ratio of the smallest C(i) to the largest C(i).
AMAX (input) REAL
Absolute value of largest matrix entry.
EQUED (output) CHARACTER*1
Specifies the form of equilibration that was done.
= 'N': No equilibration
= 'R': Row equilibration, i.e., A has been
premultiplied by diag(R). = 'C': Column equili-
bration, i.e., A has been postmultiplied by
diag(C). = 'B': Both row and column equilibra-
tion, i.e., A has been replaced by diag(R) * A *
diag(C).
PARAMETERS
THRESH is a threshold value used to decide if row or column
scaling should be done based on the ratio of the row or
column scaling factors. If ROWCND < THRESH, row scaling is
done, and if COLCND < THRESH, column scaling is done.
LARGE and SMALL are threshold values used to decide if row
scaling should be done based on the absolute size of the
largest matrix element. If AMAX > LARGE or AMAX < SMALL,
row scaling is done.
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