claqsp(3P)

NAME

claqsp - equilibrate a symmetric matrix A using the scaling factors in the vector S

SYNOPSIS

SUBROUTINE CLAQSP(
UPLO, N, AP, S, SCOND, AMAX, EQUED )

void claqsp(char uplo, long int n, complex ∗cap, float ∗s,
float scond, float amax, char ∗equed)

CHARACTER EQUED, UPLO

INTEGER N

REAL AMAX, SCOND

REAL S( ∗ )

COMPLEX AP( ∗ )

PURPOSE

CLAQSP 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 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) 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= ’Y’: Equilibration was done, i.e., A has been replaced by diag(S) ∗ A ∗ diag(S).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.