NAME¶

CLAQHE - equilibrates a Hermitian matrix A using the scaling factors in the vector S

SYNOPSIS¶

SUBROUTINE CLAQHE(

UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )

CHARACTER EQUED, UPLO INTEGER LDA, N REAL AMAX, SCOND REAL S( * ) COMPLEX A( LDA, * )

PURPOSE¶

CLAQHE 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 triangular
= 'L': Lower triangular

N (input) INTEGER

The order of the matrix A. N >= 0.

A (input/output) COMPLEX 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 triangular 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) REAL array, dimension (N)

The scale factors for A.

SCOND (input) REAL

Ratio of the smallest S(i) to the largest S(i).

AMAX (input) REAL

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= 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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.