NAME¶

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

SYNOPSIS¶

SUBROUTINE CLAQHP(

UPLO, N, AP, S, SCOND, AMAX, EQUED )

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

PURPOSE¶

CLAQHP 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.

AP (input/output) COMPLEX array, dimension (N*(N+1)/2)

On entry, the upper or lower triangle of the Hermitian 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) 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= 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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.