DPOEQU(l) ) DPOEQU(l)
DPOEQU - compute row and column scalings intended to equilibrate a symmetric positive def-
inite matrix A and reduce its condition number (with respect to the two-norm)
SUBROUTINE DPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
INTEGER INFO, LDA, N
DOUBLE PRECISION AMAX, SCOND
DOUBLE PRECISION A( LDA, * ), S( * )
DPOEQU computes row and column scalings intended to equilibrate a symmetric positive defi-
nite 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
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
The N-by-N 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) DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.
SCOND (output) 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
AMAX (output) 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 (output) 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.
LAPACK version 3.0 15 June 2000 DPOEQU(l)