# Copyright (C) 1996,1998 Auburn University.  All Rights Reserved
#
# 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. 
# 
# Octave is distributed in the hope that it will be useful, but 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 USA. 
 
function [a,b,c,d] = tf2ss(num,den)
  # Conversion from tranfer function to state-space.
  # The state space system
  #      .
  #      x = Ax + Bu
  #      y = Cx + Du
  #
  # is obtained from a transfer function
  #
  #                num(s)
  #          G(s)=-------
  #                den(s)
  #
  # via the function call [a,b,c,d] = tf2ss(num,den).
  # The vector 'den' must contain only one row, whereas the vector 'num'
  # may contain as many rows as there are outputs of the system 'y'.
  # The state space system matrices obtained from this function will be
  # in controllable canonical form as described in "Modern Control Theory",
  # [Brogan, 1991].


  # Written by R. Bruce Tenison (June 22, 1994) btenison@eng.auburn.edu
  # mod A S Hodel July, Aug  1995

  if(nargin != 2)        error("tf2ss: wrong number of input arguments")
  elseif(isempty(num))   error("tf2ss: empty numerator");
  elseif(isempty(den))   error("tf2ss: empy denominator");
  elseif(!is_vector(num)) 
    error(sprintf("num(%dx%d) must be a vector",rows(num),columns(num)));
  elseif(!is_vector(den)) 
    error(sprintf("den(%dx%d) must be a vector",rows(den),columns(den)));
  endif

  # strip leading zeros from num, den
  nz = find(num != 0);
  if(isempty(nz)) num = 0;
  else num = num(nz(1):length(num));         endif
  nz = find(den != 0);
  if(isempty(nz)) error("denominator is 0.");
  else den = den(nz(1):length(den));         endif

  # force num, den to be row vectors
  num = vec(num)';        den = vec(den)';
  nn = length(num);       nd = length(den);
  if(nn > nd) error(sprintf("deg(num)=%d > deg(den)= %d",nn,nd)); endif

   # Check sizes
   if (nd == 1)      a = []; b = []; c = []; d = num(:,1) / den(1); 
   else
    # Pad num so that length(num) = length(den)
    if (nd-nn > 0) num = [zeros(1,nd-nn), num]; endif

    # Normalize the numerator and denominator vector w.r.t. the leading 
    # coefficient
    d1 = den(1);    num = num / d1;    den = den(2:nd)/d1;
    sw = nd-1:-1:1;

    # Form the A matrix
    if(nd > 2)      a = [zeros(nd-2,1),eye(nd-2,nd-2);-den(sw)];
    else            a = -den(sw);                                endif

    # Form the B matrix
    b = zeros(nd-1,1);           b(nd-1,1) = 1;

    # Form the C matrix
    c = num(:,2:nd)-num(:,1)*den;        c = c(:,sw);

    # Form the D matrix
    d = num(:,1);
  endif

endfunction