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DSYEQUB(1) LAPACK routine (version 3.2) DSYEQUB(1)

NAME

DSYEQUB - computes row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number (with respect to the two-norm)

SYNOPSIS

UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )

IMPLICIT NONE INTEGER INFO, LDA, N DOUBLE PRECISION AMAX, SCOND CHARACTER UPLO DOUBLE PRECISION A( LDA, * ), S( * ), WORK( * )

PURPOSE

DSYEQUB computes row and column scalings intended to equilibrate a symmetric 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

The order of the matrix A. N >= 0.
The N-by-N symmetric matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.
The leading dimension of the array A. LDA >= max(1,N).
If INFO = 0, S contains the scale factors for A.
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.
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.
November 2008 LAPACK routine (version 3.2)