man zlaqsy (Fonctions bibliothèques) - equilibrate a symmetric matrix A using the scaling factors in the vector S
NAME
ZLAQSY - equilibrate a symmetric matrix A using the scaling factors in the vector S
SYNOPSIS
- SUBROUTINE ZLAQSY(
- UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
- CHARACTER EQUED, UPLO
- INTEGER LDA, N
- DOUBLE PRECISION AMAX, SCOND
- DOUBLE PRECISION S( * )
- COMPLEX*16 A( LDA, * )
PURPOSE
ZLAQSY 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.
- A (input/output) COMPLEX*16 array, dimension (LDA,N)
- On entry, the symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S).
- LDA (input) INTEGER
- The leading dimension of the array A. LDA >= max(N,1).
- 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= 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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.