CLAQSP(1) LAPACK auxiliary routine (version 3.2) CLAQSP(1)[top]NAMECLAQSP - equilibrates a symmetric matrix A using the scaling factors in the vector SSYNOPSISSUBROUTINE CLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED ) CHARACTER EQUED, UPLO INTEGER N REAL AMAX, SCOND REAL S( * ) COMPLEX AP( * )PURPOSECLAQSP equilibrates a symmetric matrix A using the scaling factors in the vector S.ARGUMENTSUPLO (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 equilibration. = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).PARAMETERSTHRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors.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)

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