function retval = is_controllable (a,b,tol)

# usage: is_controllable (a,b{,tol})
#
# returns 1 the pair(a,b) is controllable, then return value is the 
# dimension of x.  0therwise, returns a value of 0
#
# See also: size, rows, columns, length, is_matrix, is_scalar, is_vector

# This should really use the method below, but I'm being lazy for now:
#
# Controllability is determined by applying Arnoldi iteration with complete
# re-orthogonalization to obtain an orthogonal basis of the Krylov subspace
#                   n-1
# span([b,a*b,...,a^   b]).  tol is a roundoff paramter, 
# set to 2*eps if omitted

  if ((nargin == 2) || (nargin == 3))
    n = is_square(a);
    [nr, nc] = size (b);
    if((n == 0) || (n != nr) || (nc == 0))
      retval = 0;
    else

      m = b;
      tmp = b;
      for ii=1:(n-1)
        tmp = a*tmp;
        m = [m,tmp];
      endfor

      # if n is of any significant size, m will be low rank, so be careful!
      if(nargin == 3)
        if(is_scalar(tol))
          retval = (rank(m,tol) == n);
        else
          error('is_controllable: tol must be a scalar')
        endif
      else
        retval = (rank(m) == n);
      endif
    endif
  else
    error ("usage: is_controllable (a,b)");
  endif

endfunction