factor for the controllability Grammian in (1)
          or (3). See METHOD.

  SCALEO  (output) DOUBLE PRECISION
          Scaling factor for the observability Grammian in (2)
          or (4). See METHOD.

  S       (output) DOUBLE PRECISION array, dimension (LDS,N)
          The leading N-by-N upper triangular part of this array
          contains the Cholesky factor S of the frequency-weighted
          cotrollability Grammian P = S*S'. See METHOD.

  LDS     INTEGER
          The leading dimension of a