man zlaqsp (Fonctions bibliothèques) - equilibrate a symmetric matrix A using the scaling factors in the vector S
NAME
ZLAQSP - equilibrate 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= 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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.