# zheequb.f - Man Page

SRC/zheequb.f

## Synopsis

### Functions/Subroutines

subroutine zheequb (uplo, n, a, lda, s, scond, amax, work, info)
ZHEEQUB

## Function/Subroutine Documentation

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

ZHEEQUB

Purpose:

``` ZHEEQUB computes row and column scalings intended to equilibrate a
Hermitian matrix A (with respect to the Euclidean norm) and reduce
its condition number. The scale factors S are computed by the BIN
algorithm (see references) so that the scaled matrix B with elements
B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of
the smallest possible condition number over all possible diagonal
scalings.```
Parameters

UPLO

```          UPLO is CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.```

N

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

A

```          A is COMPLEX*16 array, dimension (LDA,N)
The N-by-N Hermitian matrix whose scaling factors are to be
computed.```

LDA

```          LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).```

S

```          S is DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.```

SCOND

```          SCOND is DOUBLE PRECISION
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i). If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.```

AMAX

```          AMAX is DOUBLE PRECISION
Largest absolute value of any matrix element. If AMAX is
very close to overflow or very close to underflow, the
matrix should be scaled.```

WORK

`          WORK is COMPLEX*16 array, dimension (2*N)`

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the i-th diagonal element is nonpositive.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

References:

Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

Definition at line 131 of file zheequb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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