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 5090 2008-06-05 08:12:04Z schloegl $
%	Copyright (C) 1996-2002,2008 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/>.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