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DPOEQU(l)					)					DPOEQU(l)

NAME
       DPOEQU - compute row and column scalings intended to equilibrate a symmetric positive def-
       inite matrix A and reduce its condition number (with respect to the two-norm)

SYNOPSIS
       SUBROUTINE DPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )

	   INTEGER	  INFO, LDA, N

	   DOUBLE	  PRECISION AMAX, SCOND

	   DOUBLE	  PRECISION A( LDA, * ), S( * )

PURPOSE
       DPOEQU computes row and column scalings intended to equilibrate a symmetric 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
       diagonal scalings.

ARGUMENTS
       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       A       (input) DOUBLE PRECISION array, dimension (LDA,N)
	       The N-by-N symmetric 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) DOUBLE PRECISION array, dimension (N)
	       If INFO = 0, S contains the scale factors for A.

       SCOND   (output) DOUBLE PRECISION
	       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) DOUBLE PRECISION
	       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 				DPOEQU(l)
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