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## man page of LAPACK-3

### LAPACK-3: equilibrates a Hermitian matrix A using the scaling factors in the vector S

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## NAME

LAPACK-3 - equilibrates a Hermitian matrix A using the scaling factors in the vector S## SYNOPSIS

SUBROUTINE ZLAQHP( UPLO, N, AP, S, SCOND, AMAX, EQUED ) CHARACTER EQUED, UPLO INTEGER N DOUBLE PRECISION AMAX, SCOND DOUBLE PRECISION S( * ) COMPLEX*16 AP( * )## PURPOSE

ZLAQHP equilibrates a Hermitian 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 Hermitian 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 Hermitian 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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).## PARAMETERS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. LAPACK auxiliary routine (versionMarch 2011 LAPACK-3(3)

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