
SPOEQU(l) ) SPOEQU(l)
NAME
SPOEQU  compute row and column scalings intended to equilibrate a symmetric positive def
inite matrix A and reduce its condition number (with respect to the twonorm)
SYNOPSIS
SUBROUTINE SPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
INTEGER INFO, LDA, N
REAL AMAX, SCOND
REAL A( LDA, * ), S( * )
PURPOSE
SPOEQU computes row and column scalings intended to equilibrate a symmetric positive defi
nite matrix A and reduce its condition number (with respect to the twonorm). 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) REAL array, dimension (LDA,N)
The NbyN symmetric positive definite matrix whose scaling factors are to be com
puted. Only the diagonal elements of A are referenced.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
S (output) REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.
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.
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.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: if INFO = i, the ith diagonal element is nonpositive.
LAPACK version 3.0 15 June 2000 SPOEQU(l) 
