# zsyequb.f man page

zsyequb.f —

## Synopsis

### Functions/Subroutines

subroutinezsyequb(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)ZSYEQUB

## Function/Subroutine Documentation

### subroutine zsyequb (characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, complex*16, dimension( * )WORK, integerINFO)

**ZSYEQUB**

**Purpose:**

```
ZSYEQUB computes row and column scalings intended to equilibrate a
symmetric matrix A and reduce its condition number
(with respect to the two-norm). S contains the scale factors,
S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This
choice of S puts the condition number of B within a factor N of the
smallest possible condition number over all possible diagonal
scalings.
```

**Parameters:**

*UPLO*

```
UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= 'U': Upper triangular, form is A = U*D*U**T;
= 'L': Lower triangular, form is A = L*D*L**T.
```

*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 symmetric matrix whose scaling
factors are to be computed. Only the diagonal elements of A
are referenced.
```

*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
Absolute value of largest 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 (3*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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

**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://ruready.utah.edu/archive/papers/…

Definition at line 137 of file zsyequb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zsyequb(3) is an alias of zsyequb.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK