CSYEQUB(1) LAPACK routine (version 3.2) CSYEQUB(1)NAME
CSYEQUB - computes row and column scalings intended to equilibrate a
symmetric matrix A and reduce its condition number (with respect to the
two-norm)
SYNOPSIS
SUBROUTINE CSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )
IMPLICIT NONE
INTEGER INFO, LDA, N
REAL AMAX, SCOND
CHARACTER UPLO
COMPLEX A( LDA, * ), WORK( * )
REAL S( * )
PURPOSE
CSYEQUB computes row and column scalings intended to equilibrate a sym‐
metric 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) COMPLEX array, dimension (LDA,N)
The N-by-N symmetric matrix whose scaling factors are to be
computed. 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 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 illegal value
> 0: if INFO = i, the i-th diagonal element is nonpositive.
LAPACK routine (version 3.2) November 2008 CSYEQUB(1)
