# 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 [poly,rvals] = zp2ssg2(rvals)
# [poly,rvals] = zp2ssg2(rvals)
#
#  used internally in zp2ss
# extract 2 values from rvals (if possible) and construct
# a polynomial with those roots.

# A. S. Hodel Aug 1996

# locate imaginary roots (if any)
cidx = find(imag(rvals));

if(!isempty(cidx))
  # select first complex root, omit from cidx
  r1i = cidx(1);      r1 = rvals(r1i);     cidx = complement(r1i,cidx);

  # locate conjugate root (must be in cidx list, just in case there's
  # roundoff)
  err = abs(rvals(cidx) - r1');
  minerr = min(err);
  c2i = find(err == minerr);
  r2i = cidx(c2i);
  r2 = rvals(r2i);
  cidx = complement(r2i,cidx);

  # don't check for divide by zero, since 0 is not complex.
  if(abs(r2 - r1')/abs(r1) > 1e-12)
    error(sprintf("r1=(%f,%f); r2=(%f,%f), not conjugates.", ...
      real(r1),imag(r1),real(r2),imag(r2)));
  endif

  # complex conjugate pair
  poly = [1, -2*real(r1), real(r1)^2+imag(r1)^2];
else
  # select two roots (they're all real)
  r1 = rvals(1);
  r2 = rvals(2);
  poly = [1, -(r1+r2), (r1*r2)];
  r1i = 1;  r2i = 2;
endif

# remove roots used
idx = complement([r1i, r2i],1:length(rvals));
rvals = rvals(idx);

endfunction