DLAQSP(1) LAPACK auxiliary routine (version 3.2) DLAQSP(1)NAME
DLAQSP - equilibrates a symmetric matrix A using the scaling factors in
the vector S
SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
CHARACTER EQUED, UPLO
DOUBLE PRECISION AMAX, SCOND
DOUBLE PRECISION AP( * ), S( * )
DLAQSP 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) DOUBLE PRECISION 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) 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
= 'Y': Equilibration was done, i.e., A has been replaced by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 DLAQSP(1)