/usr/share/octave/packages/3.2/tsa-4.1.0/durlev.m is in octave-tsa 4.1.0+svn20110501-1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 | 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
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