spoequ(3)

NAME

SPOEQU - compute row and column scalings intended to equi

librate a symmetric positive definite matrix A and reduce its

condition number (with respect to the two-norm)

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 equi

librate 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.

ARGUMENTS

N (input) INTEGER

The order of the matrix A. N >= 0.

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 ele

ments 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 i-th argument had an ille

gal value
> 0: if INFO = i, the i-th diagonal element is

nonpositive.

LAPACK version 3.0 15 June 2000

SPOEQU(3)