cpoequ(3F)

NAME
     CPOEQU - compute row and column scalings intended to equilibrate 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 equilibrate 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
     condition 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 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.