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# zpoequ

```
NAME
ZPOEQU - compute row and column scalings intended to equili-
brate a Hermitian positive definite matrix A and reduce its
condition number (with respect to the two-norm)

SYNOPSIS
SUBROUTINE ZPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )

INTEGER        INFO, LDA, N

DOUBLE         PRECISION AMAX, SCOND

DOUBLE         PRECISION S( * )

COMPLEX*16     A( LDA, * )

PURPOSE
ZPOEQU computes row and column scalings intended to equili-
brate a Hermitian positive definite 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 con-
dition 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 Hermitian positive definite matrix whose
scaling factors are to be computed.  Only the diago-
nal 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 entry is nonpo-
sitive.
```