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LAPACK version 3.0
sppequ(3)

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

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

      CHARACTER	     UPLO

      INTEGER	     INFO, N

      REAL	     AMAX, SCOND

      REAL	     AP( * ), S( * )

DESCRIPTION
  SPPEQU computes row and column scalings intended to equilibrate a symmetric
  positive definite 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 linear 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.