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DPOEQU(l)			       )			     DPOEQU(l)

NAME
       DPOEQU - compute row and column scalings intended to equilibrate a sym‐
       metric positive definite 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 sym‐
       metric 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 condi‐
       tion 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 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) 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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