ZLAQSY - equilibrate a symmetric matrix A using the scal
ing factors in the vector S
SYNOPSIS
SUBROUTINE ZLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED
)
CHARACTER EQUED, UPLO
INTEGER LDA, N
DOUBLE PRECISION AMAX, SCOND
DOUBLE PRECISION S( * )
COMPLEX*16 A( LDA, * )
PURPOSE
ZLAQSY 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) COMPLEX*16 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) DOUBLE PRECISION array, dimension (N)
The scale factors for A.
SCOND (input) DOUBLE PRECISION
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= 'Y': Equilibration was done, i.e., A has been
replaced by diag(S) * A * diag(S).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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