### Copyright (C) 1996 John W. Eaton
###
### This file is part of Octave.
###
### Octave is free software; you can redistribute it and/or modify it
### under the terms of the GNU General Public License as published by
### the Free Software Foundation; either version 2, or (at your option)
### any later version.
###
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### WITHOUT ANY WARRANTY; without even the implied warranty of
### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
### General Public License for more details.
###
### You should have received a copy of the GNU General Public License
### along with Octave; see the file COPYING.  If not, write to the Free
### Software Foundation, 59 Temple Place - Suite 330, Boston, MA
### 02111-1307, USA.

## Usage: is_controllable (a, b {,tol})
##
## Returns 1 if the pair (a, b) is controllable, or 0 if not.
##
## 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.
##
## (FIX ME... The Krylov subspace approach is not done yet!)
##                      n-1
##   span ([b,a*b,...,a^   b]).
##
## tol is a roundoff paramter, set to 2*eps if omitted.

## Author: A. S. Hodel <scotte@eng.auburn.edu>
## Created: August 1993
## Adapted-By: jwe

function retval = is_controllable (a, b, tol)

  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
    usage ("is_controllable (a, b)");
  endif

endfunction