Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/tsa-4.2.4/lattice.m b/octave_packages/tsa-4.2.4/lattice.m
new file mode 100644 (file)
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+++ b/octave_packages/tsa-4.2.4/lattice.m
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+ function [MX,PE,arg3] = lattice(Y,lc,Mode);
+% Estimates AR(p) model parameter with lattice algorithm (Burg 1968) 
+% for multiple channels. 
+% If you have the NaN-tools, LATTICE.M can handle missing values (NaN), 
+%
+% [...] = lattice(y [,Pmax [,Mode]]);
+%
+% [AR,RC,PE] = lattice(...);
+% [MX,PE] = lattice(...);
+%
+%  INPUT:
+% y    signal (one per row), can contain missing values (encoded as NaN)
+% Pmax max. model order (default size(y,2)-1))
+% Mode  'BURG' (default) Burg algorithm
+%      'GEOL' geometric lattice
+%
+%  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)); = MX(:,sum(1:K-1)+(1:K)); 
+%        RC(:,K) = MX(:,cumsum(1: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 DURLEV SUMSKIPNAN 
+% 
+% REFERENCE(S):
+%  J.P. Burg, "Maximum Entropy Spectral Analysis" Proc. 37th Meeting of the Society of Exp. Geophysiscists, Oklahoma City, OK 1967
+%  J.P. Burg, "Maximum Entropy Spectral Analysis" PhD-thesis, Dept. of Geophysics, Stanford University, Stanford, CA. 1975.
+%  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: lattice.m 7687 2010-09-08 18:39:23Z schloegl $ 
+%      Copyright (C) 1996-2002,2008,2010 by Alois Schloegl <a.schloegl@ieee.org>
+%       This is part of the TSA-toolbox. See also 
+%       http://biosig-consulting.com/matlab/tsa/
+%
+%    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/>.
+
+
+if nargin<3, Mode='BURG'; 
+else Mode=upper(Mode(1:4));end;
+BURG=~strcmp(Mode,'GEOL');
+
+% Inititialization
+[lr,N]=size(Y);
+if nargin<2, lc=N-1; end;
+F=Y;
+B=Y;
+[DEN,nn] = sumskipnan((Y.*Y),2);
+PE = [DEN./nn,zeros(lr,lc)];
+
+if nargout<3         % needs O(p^2) memory 
+        MX = zeros(lr,lc*(lc+1)/2);   
+        idx= 0;
+        
+        % Durbin-Levinson Algorithm
+        for K=1:lc,
+                [TMP,nn] = sumskipnan(F(:,K+1:N).*B(:,1:N-K),2);
+                MX(:,idx+K) = TMP./DEN; %Burg
+                if K>1,   %for compatibility with OCTAVE 2.0.13
+                        MX(:,idx+(1:K-1))=MX(:,(K-2)*(K-1)/2+(1:K-1))-MX(:,(idx+K)*ones(K-1,1)).*MX(:,(K-2)*(K-1)/2+(K-1:-1:1));
+                end;   
+                
+                tmp = F(:,K+1:N) - MX(:,(idx+K)*ones(1,N-K)).*B(:,1:N-K);
+                B(:,1:N-K) = B(:,1:N-K) - MX(:,(idx+K)*ones(1,N-K)).*F(:,K+1:N);
+                F(:,K+1:N) = tmp;
+                
+                [PE(:,K+1),nn] = sumskipnan([F(:,K+1:N).^2,B(:,1:N-K).^2],2);        
+                if ~BURG,
+                        [f,nf] = sumskipnan(F(:,K+1:N).^2,2);
+                        [b,nb] = sumskipnan(B(:,1:N-K).^2,2); 
+                        DEN = sqrt(b.*f); 
+                else
+                        DEN = PE(:,K+1);
+                end;
+                idx=idx+K;
+               PE(:,K+1) = PE(:,K+1)./nn;      % estimate of covariance
+        end;
+else            % needs O(p) memory 
+        arp=zeros(lr,lc-1);
+        rc=zeros(lr,lc-1);
+        % Durbin-Levinson Algorithm
+        for K=1:lc,
+                [TMP,nn] = sumskipnan(F(:,K+1:N).*B(:,1:N-K),2);
+                arp(:,K) = TMP./DEN; %Burg
+                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;
+                
+                tmp = F(:,K+1:N) - rc(:,K*ones(1,N-K)).*B(:,1:N-K);
+                B(:,1:N-K) = B(:,1:N-K) - rc(:,K*ones(1,N-K)).*F(:,K+1:N);
+                F(:,K+1:N) = tmp;
+                
+                [PE(:,K+1),nn] = sumskipnan([F(:,K+1:N).^2,B(:,1:N-K).^2],2);        
+                if ~BURG,
+                        [f,nf] = sumskipnan(F(:,K+1:N).^2,2);
+                        [b,nb] = sumskipnan(B(:,1:N-K).^2,2); 
+                        DEN = sqrt(b.*f); 
+                else
+                        DEN = PE(:,K+1);
+                end;
+               PE(:,K+1) = PE(:,K+1)./nn;      % estimate of covariance
+        end;
+% assign output arguments
+       arg3=PE;
+        PE=rc;
+        MX=arp;
+end; %if
+