/usr/share/octave/packages/tsa-4.2.7/lattice.m is in octave-tsa 4.2.7-1build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 | 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 11693 2013-03-04 06:40:14Z 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
|