# zlaqhe.f - Man Page

SRC/zlaqhe.f

## Synopsis

### Functions/Subroutines

subroutine **zlaqhe** (uplo, n, a, lda, s, scond, amax, equed)**ZLAQHE** scales a Hermitian matrix.

## Function/Subroutine Documentation

### subroutine zlaqhe (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

**ZLAQHE** scales a Hermitian matrix.

**Purpose:**

ZLAQHE equilibrates a Hermitian matrix A using the scaling factors in the vector S.

**Parameters***UPLO*UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular

*N*N is INTEGER The order of the matrix A. N >= 0.

*A*A is COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian 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*LDA is INTEGER The leading dimension of the array A. LDA >= max(N,1).

*S*S is DOUBLE PRECISION array, dimension (N) The scale factors for A.

*SCOND*SCOND is DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i).

*AMAX*AMAX is DOUBLE PRECISION Absolute value of largest matrix entry.

*EQUED*EQUED is 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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).

**Internal 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.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **133** of file **zlaqhe.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlaqhe(3) is an alias of zlaqhe.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK