ZLAQSP - equilibrate a symmetric matrix A using the scal
ing factors in the vector S
SYNOPSIS
SUBROUTINE ZLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
CHARACTER EQUED, UPLO
INTEGER N
DOUBLE PRECISION AMAX, SCOND
DOUBLE PRECISION S( * )
COMPLEX*16 AP( * )
PURPOSE
ZLAQSP 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.
AP (input/output) COMPLEX*16 array, dimension
(N*(N+1)/2)
On entry, the upper or lower triangle of the sym
metric matrix A, packed columnwise in a linear
array. The j-th column of A is stored in the
array AP as follows: if UPLO = 'U', AP(i +
(j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L',
AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
On exit, the equilibrated matrix: diag(S) * A *
diag(S), in the same storage format as A.
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).
AMAX (input) DOUBLE PRECISION
Absolute value of largest matrix entry.
EQUED (output) CHARACTER*1
Specifies whether or not equilibration was done.
= 'Y': Equilibration was done, i.e., A has been
replaced by diag(S) * A * diag(S).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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