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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 con- tains 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 tri- angular 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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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 scal- ing should be done based on the absolute size of the largest matrix element. If AMAX > LARGE or AMAX < SMALL, scaling is done.