CPOEQU(l) ) CPOEQU(l)
CPOEQU - compute row and column scalings intended to equilibrate a Hermitian positive def-
inite matrix A and reduce its condition number (with respect to the two-norm)
SUBROUTINE CPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
INTEGER INFO, LDA, N
REAL AMAX, SCOND
REAL S( * )
COMPLEX A( LDA, * )
CPOEQU computes row and column scalings intended to equilibrate a Hermitian 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) COMPLEX array, dimension (LDA,N)
The N-by-N Hermitian 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
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 illegal value
> 0: if INFO = i, the i-th diagonal element is nonpositive.
LAPACK version 3.0 15 June 2000 CPOEQU(l)