subroutine cpoequb (N, A, LDA, S, SCOND, AMAX, INFO)
CPOEQUB
CPOEQUB
Purpose:
CPOEQUB computes row and column scalings intended to equilibrate a Hermitian 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. This routine differs from CPOEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled diagonal entries are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).
Parameters:
N is INTEGER
The order of the matrix A. N >= 0.
A
A is COMPLEX array, dimension (LDA,N)
The N-by-N Hermitian positive definite matrix whose scaling
factors are to be computed. Only the diagonal elements of A
are referenced.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
S
S is REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.
SCOND
SCOND is 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
AMAX is 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
INFO is 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.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Definition at line 121 of file cpoequb.f.
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