octave-tsa 4.2.7-1build1 / usr / share / octave / packages / tsa-4.2.7 / hup.m

function b=hup(C)
%HUP(C)	tests if the polynomial C is a Hurwitz-Polynomial.
%	It tests if all roots lie in the left half of the complex
%	plane 
%       B=hup(C) is the same as 
%       B=all(real(roots(c))<0) but much faster.
%	The Algorithm is based on the Routh-Scheme.
%	C are the elements of the Polynomial
%	C(1)*X^N + ... + C(N)*X + C(N+1).
%
%       HUP2 works also for multiple polynomials, 
%       each row a poly - Yet not tested
%
% REFERENCES:
%  F. Gausch "Systemtechnik", Textbook, University of Technology Graz, 1993. 
%  Ch. Langraf and G. Schneider "Elemente der Regeltechnik", Springer Verlag, 1970.

%	$Id: hup.m 11693 2013-03-04 06:40:14Z schloegl $
%	Copyright (c) 1995-1998,2008 by Alois Schloegl <a.schloegl@ieee.org>
%
%    This program 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 3 of the License, or
%    (at your option) any later version.
%
%    This program 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 this program.  If not, see <http://www.gnu.org/licenses/>.

[lr,lc] = size(c);

% Strip leading zeros and throw away.
	% not considered yet
%d=(c(:,1)==0);

% Trailing zeros mean there are roots at zero
b=(c(:,lc)~=0);
lambda=b;

n=zeros(lc);
if lc>3
	n(4:2:lc,2:2:lc-2)=1;
end;
while lc>1               
	lambda(b)=c(b,1)./c(b,2);
	b = b & (lambda>=0) & (lambda<Inf);
	c=c(:,2:lc)-lambda(:,ones(1,lc-1)).*(c*n(1:lc,1:lc-1));
	lc=lc-1;
end;