# cpoequb.f - Man Page

SRC/cpoequb.f

## Synopsis

### Functions/Subroutines

subroutine cpoequb (n, a, lda, s, scond, amax, info)
CPOEQUB

## Function/Subroutine Documentation

### subroutine cpoequb (integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, integer info)

CPOEQUB

Purpose:

``` CPOEQUB computes row and column scalings intended to equilibrate 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 condition number over all possible diagonal
scalings.

This routine differs from CPOEQU by restricting the scaling factors
to a power of the radix.  Barring over- and underflow, scaling by
these factors introduces no additional rounding errors.  However, the
scaled diagonal entries are no longer approximately 1 but lie
Parameters

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 positive definite 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 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
Absolute value of largest matrix element.  If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.```

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.

Definition at line 118 of file cpoequb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK