SLAQSY - equilibrate a symmetric matrix A using the scal
ing factors in the vector S
SYNOPSIS
SUBROUTINE SLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED
)
CHARACTER EQUED, UPLO
INTEGER LDA, N
REAL AMAX, SCOND
REAL A( LDA, * ), S( * )
PURPOSE
SLAQSY equilibrates a symmetric matrix A using the scaling
factors in the vector S.
ARGUMENTS
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular
part of the symmetric matrix A is stored. = 'U':
Upper triangular
= 'L': Lower triangular
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U',
the leading n by n upper triangular part of A con
tains the upper triangular part of the matrix A,
and the strictly lower triangular part of A is not
referenced. If UPLO = 'L', the leading n by n
lower triangular part of A contains the lower tri
angular part of the matrix A, and the strictly
upper triangular part of A is not referenced.
On exit, if EQUED = 'Y', the equilibrated matrix:
diag(S) * A * diag(S).
LDA (input) INTEGER
The leading dimension of the array A. LDA >=
max(N,1).
S (input) REAL array, dimension (N)
The scale factors for A.
SCOND (input) REAL
Ratio of the smallest S(i) to the largest S(i).
Absolute value of largest matrix entry.
EQUED (output) CHARACTER*1
Specifies whether or not equilibration was done.
= 'N': No equilibration.
= 'Y': Equilibration was done, i.e., A has been
replaced by diag(S) * A * diag(S).
PARAMETERS
THRESH is a threshold value used to decide if scaling
should be done based on the ratio of the scaling factors.
If SCOND < THRESH, scaling is done.
LARGE and SMALL are threshold values used to decide if
scaling should be done based on the absolute size of the
largest matrix element. If AMAX > LARGE or AMAX < SMALL,
scaling is done.
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