subroutine cheequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
CHEEQUB
CHEEQUB
Purpose:
CHEEQUB computes row and column scalings intended to equilibrate a Hermitian matrix A (with respect to the Euclidean norm) and reduce its condition number. The scale factors S are computed by the BIN algorithm (see references) so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of the smallest possible condition number over all possible diagonal scalings.
Parameters:
UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
N
N is INTEGER The order of the matrix A. N >= 0.
A
A is COMPLEX array, dimension (LDA,N) The N-by-N Hermitian matrix whose scaling factors are to be computed.
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 Largest absolute value of any matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
WORK
WORK is COMPLEX array, dimension (2*N)
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:
References:
Definition at line 134 of file cheequb.f.
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