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cpoequ

 NAME
      CPOEQU - compute row and column scalings intended to equili-
      brate a Hermitian positive definite matrix A and reduce its
      condition number (with respect to the two-norm)

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

          INTEGER        INFO, LDA, N

          REAL           AMAX, SCOND

          REAL           S( * )

          COMPLEX        A( LDA, * )

 PURPOSE
      CPOEQU computes row and column scalings intended to equili-
      brate a Hermitian 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) COMPLEX array, dimension (LDA,N)
              The N-by-N Hermitian 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) 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 entry is nonpo-
              sitive.