--- /dev/null
+ 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
+