ucp.m

MATLAB的时间序列分析相关函数,涵盖对时间序列分析所需要所有重要函数

function b=ucp(c)
% UCP(C) tests if the polynomial C is a Unit-Circle-Polynomial.
%	It tests if all roots lie inside the unit circle like
%       B=ucp(C) does the same as
%	B=all(abs(roots(C))<1) but much faster.
%	The Algorithm is based on the Jury-Scheme.
%	C are the elements of the Polynomial
%	C(1)*X^N + ... + C(N)*X + C(N+1).
% 
% REFERENCES:
%  O. Foellinger "Lineare Abtastsysteme", Oldenburg Verlag, Muenchen, 1986.
%  F. Gausch "Systemtechnik", Textbook, University of Technology Graz, 1993. 


% 	$Id: ucp.m 5090 2008-06-05 08:12:04Z schloegl $
% 	Copyright (C) 1996-1999,2008 by Alois Schloegl <[e-mail]>
%
%    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);

% JURY-Scheme
b=ones(lr,1);
lambda=zeros(lr,1);
while (lc > 1), 
     	lambda = c(:,lc)./c(:,1);
%       disp([lc,size(lambda), sum(b),toc]);
	% ratio must be less then 1
	b = b & (abs(lambda) < 1);
	% and reduced polynomial must be a UCP, too.
	c(:,1:lc-1) = c(:,1:lc-1) - lambda(:,ones(1,lc-1)).*c(:,lc:-1:2);
	lc = lc-1;
end;