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dpoequ

 NAME
      DPOEQU - compute row and column scalings intended to equili-
      brate a symmetric 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 equili-
      brate 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 con-
      dition 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 diago-
              nal 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 under-
              flow, 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 entry is nonpo-
              sitive.