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SPPEQU(l)					)					SPPEQU(l)

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

SYNOPSIS
       SUBROUTINE SPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, N

	   REAL 	  AMAX, SCOND

	   REAL 	  AP( * ), S( * )

PURPOSE
       SPPEQU computes row and column scalings intended to equilibrate a symmetric positive defi-
       nite matrix A in packed storage 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
       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

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

       AP      (input) REAL array, dimension (N*(N+1)/2)
	       The upper or lower triangle of the symmetric matrix A, packed columnwise in a lin-
	       ear  array.   The j-th column of A is stored in the array AP as follows: if UPLO =
	       'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2)
	       = A(i,j) for j<=i<=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 version 3.0			   15 June 2000 				SPPEQU(l)
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