# cheequb.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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cheequb.f

## SYNOPSIS

### Functions/Subroutines

subroutine cheequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
CHEEQUB

## Function/Subroutine Documentation

### subroutine cheequb (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) S, real SCOND, real AMAX, complex, dimension( * ) WORK, integer INFO)

CHEEQUB

Purpose:

``` CHEEQUB 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 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 REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.
```

SCOND

```          SCOND is REAL
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 REAL
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 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.

Date:

April 2012

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 134 of file cheequb.f.

## Author

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