Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3  -  computes row and column scalings intended to equilibrate a symmetric matrix A
and reduce its condition number (with respect to the two-norm)

```

#### SYNOPSIS

```       SUBROUTINE ZHEEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )

IMPLICIT        NONE

INTEGER         INFO, LDA, N

DOUBLE          PRECISION AMAX, SCOND

CHARACTER       UPLO

COMPLEX*16      A( LDA, * ), WORK( * )

DOUBLE          PRECISION S( * )

```

#### 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.

```

#### ARGUMENTS

```        N       (input) INTEGER
The order of the matrix A.  N >= 0.

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

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

SCOND   (output) 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    (output) 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.
INFO    (output) 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.

LAPACK routine (version 3.2.2)          April 2011                           ZHEEQUB(3lapack)
```