zlaqhe(3)

NAME

ZLAQHE - equilibrate a Hermitian matrix A using the scal

ing factors in the vector S

SYNOPSIS

SUBROUTINE  ZLAQHE( 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

ZLAQHE equilibrates a Hermitian 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 Hermitian matrix A is stored. = 'U': Upper triangu

lar
= '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 Hermitian matrix A. If UPLO = 'U',

the leading n by n upper triangular part of A contains the upper

triangular part of the matrix A, and the strictly lower triangu

lar part of A is not referenced. If UPLO = 'L', the leading n by

n lower triangular part of A contains the lower triangular 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).

AMAX (input) DOUBLE PRECISION

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.

LAPACK version 3.0 15 June 2000

ZLAQHE(3)