Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/tsa-4.2.4/durlev.m b/octave_packages/tsa-4.2.4/durlev.m
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+function [MX,res,arg3] = durlev(AutoCov);
+% function  [AR,RC,PE] = durlev(ACF);
+% function  [MX,PE] = durlev(ACF);
+% estimates AR(p) model parameter by solving the
+% Yule-Walker with the Durbin-Levinson recursion
+% for multiple channels
+%  INPUT:
+% ACF  Autocorrelation function from lag=[0:p]
+%
+%  OUTPUT
+% AR    autoregressive model parameter 
+% RC    reflection coefficients (= -PARCOR coefficients)
+% PE    remaining error variance
+% MX    transformation matrix between ARP and RC (Attention: needs O(p^2) memory)
+%        AR(:,K) = MX(:,K*(K-1)/2+(1:K));
+%        RC(:,K) = 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 AR2RC RC2AR LATTICE
+% 
+% REFERENCES:
+%  Levinson N. (1947) "The Wiener RMS(root-mean-square) error criterion in filter design and prediction." J. Math. Phys., 25, pp.261-278.
+%  Durbin J. (1960) "The fitting of time series models." Rev. Int. Stat. Inst. vol 28., pp 233-244.
+%  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: durlev.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(AutoCov);
+
+res=[AutoCov(:,1), zeros(lr,lc-1)];
+d=zeros(lr,1);
+
+if nargout<3         % needs O(p^2) memory 
+        MX=zeros(lr,lc*(lc-1)/2);   
+        idx=0;
+        idx1=0;
+        % Durbin-Levinson Algorithm
+        for K=1:lc-1,
+                %idx=K*(K-1)/2;  %see below
+                % for L=1:lr, d(L)=arp(L,1:K-1)*transpose(AutoCov(L,K:-1:2));end;  % Matlab 4.x, Octave
+                % d=sum(MX(:,idx+(1:K-1)).*AutoCov(:,K:-1:2),2);              % Matlab 5.x
+                MX(:,idx+K)=(AutoCov(:,K+1)-sum(MX(:,idx1+(1:K-1)).*AutoCov(:,K:-1:2),2))./res(:,K);
+                %rc(:,K)=arp(:,K);
+                %if K>1   %for compatibility with OCTAVE 2.0.13
+                        MX(:,idx+(1:K-1))=MX(:,idx1+(1:K-1))-MX(:,(idx+K)*ones(K-1,1)).*MX(:,idx1+(K-1:-1:1));
+                %end;   
+                % for L=1:lr, d(L)=MX(L,idx+(1:K))*(AutoCov(L,K+1:-1:2).');end; % Matlab 4.x, Octave
+                % d=sum(MX(:,idx+(1:K)).*AutoCov(:,K+1:-1:2),2);              % Matlab 5.x
+                res(:,K+1) = res(:,K).*(1-abs(MX(:,idx+K)).^2);
+                idx1=idx;
+                idx=idx+K;
+        end;
+        %arp=MX(:,K*(K-1)/2+(1:K));
+        %rc =MX(:,(1:K).*(2:K+1)/2);
+        
+else            % needs O(p) memory 
+        
+        arp=zeros(lr,lc-1);
+        rc=zeros(lr,lc-1);
+        
+        % Durbin-Levinson Algorithm
+        for K=1:lc-1,
+                % for L=1:lr, d(L)=arp(L,1:K-1)*transpose(AutoCov(L,K:-1:2));end;  % Matlab 4.x, Octave
+                % d=sum(arp(:,1:K-1).*AutoCov(:,K:-1:2),2);              % Matlab 5.x
+                arp(:,K) = (AutoCov(:,K+1)-sum(arp(:,1:K-1).*AutoCov(:,K:-1:2),2))./res(:,K); % Yule-Walker
+                rc(:,K)  = arp(:,K);
+                %if K>1   %for compatibility with OCTAVE 2.0.13
+                        arp(:,1:K-1)=arp(:,1:K-1)-arp(:,K*ones(K-1,1)).*arp(:,K-1:-1:1);
+                %end;
+                %for L=1:lr, d(L)=arp(L,1:K)*(AutoCov(L,K+1:-1:2).');end; % Matlab 4.x, Octave
+                % d=sum(arp(:,1:K).*AutoCov(:,K+1:-1:2),2);              % Matlab 5.x
+                res(:,K+1) = res(:,K).*(1-abs(arp(:,K)).^2);
+        end;
+        
+        % assign output arguments
+        arg3=res;
+        res=rc;
+        MX=arp;
+end; %if