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LAPACK version 3.0
spoequ(3)

PURPOSE
  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)

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

      INTEGER	     INFO, LDA, N

      REAL	     AMAX, SCOND

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

DESCRIPTION
  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 possible 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
	  referenced.

  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.