Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / tsa-4.2.4 / ar2rc.m

diff --git a/octave_packages/tsa-4.2.4/ar2rc.m b/octave_packages/tsa-4.2.4/ar2rc.m
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+function [MX,res,arg3] = ar2rc(ar);
+% converts autoregressive parameters into reflection coefficients 
+% with the Durbin-Levinson recursion for multiple channels
+% function  [AR,RC,PE] = ar2rc(AR);
+% function  [MX,PE] = ar2rc(AR);
+%
+%  INPUT:
+% AR    autoregressive model parameter 
+%
+%  OUTPUT
+% AR    autoregressive model parameter 
+% RC    reflection coefficients (= -PARCOR coefficients)
+% PE    remaining error variance (relative to PE(1)=1)
+% MX    transformation matrix between ARP and RC (Attention: needs O(p^2) memory)
+%        AR = MX(:,K*(K-1)/2+(1:K));
+%        RC = MX(:,(1:K).*(2:K+1)/2);
+%
+% All input and output parameters are organized in rows, one row 
+% corresponds to the parameters of one channel
+%
+% see also ACOVF ACORF DURLEV RC2AR 
+% 
+% REFERENCES:
+%  P.J. Brockwell and R. A. Davis "Time Series: Theory and Methods", 2nd ed. Springer, 1991.
+%  S. Haykin "Adaptive Filter Theory" 3rd ed. Prentice Hall, 1996.
+%  M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981. 
+%  W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
+
+%       $Id: ar2rc.m 5090 2008-06-05 08:12:04Z schloegl $
+%       Copyright (C) 1998-2002,2008 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/>.
+
+% Inititialization
+[lr,lc]=size(ar);
+res=[ones(lr,1) zeros(lr,lc)];
+
+if nargout<3         % needs O(p^2) memory 
+        MX=zeros(lr,lc*(lc+1)/2);   
+       MX(:,lc*(lc-1)/2+(1:lc))=ar;
+       
+        % Durbin-Levinson Algorithm
+        idx=lc*(lc-1)/2;
+        for K=lc:-1:2; 
+                %idx=K*(K-1)/2;  %see below
+                MX(:,(K-2)*(K-1)/2+(1:K-1)) = (MX(:,idx+(1:K-1)) + MX(:,(idx+K)*ones(K-1,1)).*MX(:,idx+(K-1:-1:1)))./((ones(lr,1)-abs(MX(:,idx+K)).^2)*ones(1,K-1));
+               idx=idx-K+1;
+        end;
+       for K=1:lc
+               idx=K*(K-1)/2;  %see below
+                res(:,K+1) = res(:,K).*(1-abs(MX(:,idx+K)).^2);
+        end;
+           
+        %arp=MX(:,K*(K-1)/2+(1:K));
+        %rc =MX(:,(1:K).*(2:K+1)/2);
+
+else            % needs O(p) memory 
+        
+        %ar=zeros(lr,lc);
+        rc=zeros(lr,lc);
+       rc(:,lc)=ar(:,lc);
+       MX=ar; % assign output
+       
+       % Durbin-Levinson Algorithm
+        for K=lc-1:-1:1,
+                ar(:,1:K)=(ar(:,1:K)+ar(:,(K+1)*ones(K,1)).*ar(:,K:-1:1))./((ones(lr,1)-abs(ar(:,K+1)).^2)*ones(1,K));
+                rc(:,K)=ar(:,K);
+       end;
+       
+       for K=1:lc,
+                res(:,K+1) = res(:,K) .* (1-abs(ar(:,K)).^2);
+        end;
+        
+        % assign output arguments
+        arg3=res;
+        res=rc;
+        %MX=ar;
+end; %if