# dpoequb.f man page

dpoequb.f

## Synopsis

### Functions/Subroutines

subroutine dpoequb (N, A, LDA, S, SCOND, AMAX, INFO)
DPOEQUB

## Function/Subroutine Documentation

### subroutine dpoequb (integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) S, double precision SCOND, double precision AMAX, integer INFO)

DPOEQUB

Purpose:

``` DPOEQUB computes row and column scalings intended to equilibrate a
symmetric 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 DPOEQU 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 DOUBLE PRECISION array, dimension (LDA,N)
The N-by-N symmetric 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 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.```

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:

December 2016

Definition at line 120 of file dpoequb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK