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zp2ssg2.m
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1999-03-05
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# Copyright (C) 1996,1998 A. Scottedward Hodel
#
# 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, 675 Mass Ave, Cambridge, MA 02139, 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