CLAQSP(1) LAPACK auxiliary routine (version 3.2) CLAQSP(1)NAME
CLAQSP - equilibrates a symmetric matrix A using the scaling factors in
the vector S
SUBROUTINE CLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
CHARACTER EQUED, UPLO
REAL AMAX, SCOND
REAL S( * )
COMPLEX AP( * )
CLAQSP equilibrates a symmetric matrix A using the scaling factors in
the vector S.
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 equili‐
brated matrix: diag(S) * A * diag(S), in the same storage for‐
mat 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
= 'Y': Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).
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 scal‐
ing should be done based on the absolute size of the largest matrix
element. If AMAX > LARGE or AMAX < SMALL, scaling is done.
LAPACK auxiliary routine (versioNovember 2008 CLAQSP(1)