NAME¶

ZLAQSP - equilibrates a symmetric matrix A using the scaling 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 symmetric 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. = '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= 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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.