Mercurial > forge
view extra/tsa/inst/lattice.m @ 12580:b6eace8bc216 octave-forge
[tsa] update contact email address
author | schloegl |
---|---|
date | Thu, 02 Apr 2015 10:00:34 +0000 |
parents | 65a4be217166 |
children |
line wrap: on
line source
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. % $Id$ % Copyright (C) 1996-2002,2008,2010 by Alois Schloegl <alois.schloegl@gmail.com> % 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