redhat man page for spoequ

SPOEQU(l)								 )								 SPOEQU(l)

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

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

	   INTEGER	  INFO, LDA, N

	   REAL 	  AMAX, SCOND

	   REAL 	  A( LDA, * ), S( * )

PURPOSE
       SPOEQU computes row and column scalings intended to equilibrate a symmetric 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 pos-
       sible condition number over all possible diagonal scalings.

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

       A       (input) REAL 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 refer-
	       enced.

       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 version 3.0						   15 June 2000 							 SPOEQU(l)