# 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= 'Y':  Equilibration was done, i.e., A has been replaced by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

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