.TH SPOEQU 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
SPOEQU - row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)
.SH SYNOPSIS
.TP 19
SUBROUTINE SPOEQU(
N, A, LDA, S, SCOND, AMAX, INFO )
.TP 19
.ti +4
INTEGER
INFO, LDA, N
.TP 19
.ti +4
REAL
AMAX, SCOND
.TP 19
.ti +4
REAL
A( LDA, * ), S( * )
.SH PURPOSE
SPOEQU 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.
.br
.SH ARGUMENTS
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0.
.TP 8
A (input) REAL 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.
.TP 8
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
.TP 8
S (output) REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.
.TP 8
SCOND (output) 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.
.TP 8
AMAX (output) REAL
Absolute value of largest matrix element. If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value
.br
> 0: if INFO = i, the i-th diagonal element is nonpositive.