/usr/share/octave/packages/tsa-4.3.3/acovf.m is in octave-tsa 4.3.3-1.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 | function [ACF,NN] = acovf(Z,KMAX,Mode,Mode2);
% ACOVF estimates autocovariance function (not normalized)
% NaN's are interpreted as missing values.
%
% [ACF,NN] = acovf(Z,MAXLAG,Mode);
%
% Input:
% Z Signal (one channel per row);
% MAXLAG maximum lag
% Mode 'biased' : normalizes with N [default]
% 'unbiased': normalizes with N-lag
% 'coeff' : normalizes such that lag 0 is 1
% others : no normalization
%
% Output:
% ACF autocovariance function
% NN number of valid elements
%
% REFERENCES:
% A.V. Oppenheim and R.W. Schafer, Digital Signal Processing, Prentice-Hall, 1975.
% S. Haykin "Adaptive Filter Theory" 3ed. Prentice Hall, 1996.
% M.B. Priestley "Spectral Analysis and Time Series" Academic Press, 1981.
% W.S. Wei "Time Series Analysis" Addison Wesley, 1990.
% J.S. Bendat and A.G.Persol "Random Data: Analysis and Measurement procedures", Wiley, 1986.
% $Id: acovf.m 12766 2015-04-02 10:00:34Z schloegl $
% Copyright (C) 1998-2003,2008,2010 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='biased'; end;
[lr,lc] = size(Z);
MISSES = sum(isnan(Z)')';
if any(MISSES); % missing values
M = real(~isnan(Z));
Z(isnan(Z))=0;
end;
if (nargin == 1)
KMAX = lc-1;
elseif (KMAX >= lc-1)
KMAX = lc-1;
end;
ACF = zeros(lr,KMAX+1);
if nargin>3, % for testing, use arg4 for comparing the methods,
elseif (KMAX*KMAX > lc*log2(lc)) % & isempty(MISSES);
Mode2 = 1;
elseif (10*KMAX > lc);
Mode2 = 3;
else
Mode2 = 4;
end;
%%%%% ESTIMATION of non-normalized ACF %%%%%
% the following algorithms gve equivalent results, however, the computational effort is different,
% depending on lr,lc and KMAX, a different algorithm is most efficient.
if Mode2==1; % KMAX*KMAX > lc*log(lc); % O(n.logn)+O(K²)
tmp = fft(Z',2^nextpow2(size(Z,2))*2);
tmp = ifft(tmp.*conj(tmp));
ACF = tmp(1:KMAX+1,:)';
if ~any(any(imag(Z))), ACF=real(ACF); end; % should not be neccessary, unfortunately it is.
elseif Mode2==3; % (10*KMAX > lc) % O(n*K) % use fast Built-in filter function
for L = 1:lr,
acf = filter(Z(L,lc:-1:1),1,Z(L,:));
ACF(L,:)= acf(lc:-1:lc-KMAX);
end;
else Mode2==4; % O(n*K)
for L = 1:lr,
for K = 0:KMAX,
ACF(L,K+1) = Z(L,1:lc-K) * Z(L,1+K:lc)';
end;
end;
end;
%%%%% GET number of elements used for estimating ACF - is needed for normalizing ACF %%%%%
if any(MISSES),
% the following algorithms gve equivalent results, however, the computational effort is different,
% depending on lr,lc and KMAX, a different algorithm is most efficient.
if Mode2==1; % KMAX*KMAX > lc*log(lc); % O(n.logn)+O(K²)
tmp = fft(M',2^nextpow2(size(M,2))*2);
tmp = ifft(tmp.*conj(tmp));
NN = tmp(1:KMAX+1,:)';
if ~any(any(imag(M))), NN=real(NN); end; % should not be neccessary, unfortunately it is.
elseif Mode2==3; % (10*KMAX > lc) % O(n*K) % use fast Built-in filter function
for L = 1:lr,
acf = filter(M(L,lc:-1:1),1,M(L,:));
NN(L,:)= acf(lc:-1:lc-KMAX);
end;
else Mode2==4; % O(n*K)
for L = 1:lr,
for K = 0:KMAX,
NN(L,K+1) = M(L,1:lc-K) * M(L,1+K:lc)';
end;
end;
end;
else
NN = (ones(lr,1)*(lc:-1:lc-KMAX));
end;
if strcmp(Mode,'biased')
if ~any(MISSES),
ACF=ACF/lc;
else
%ACF=ACF./((lc-MISSES)*ones(1,KMAX+1));
ACF=ACF./max(NN + ones(lr,1)*(0:KMAX),0);
end;
elseif strcmp(Mode,'unbiased')
ACF=ACF./NN;
%if ~any(MISSES),
% ACF=ACF./(ones(lr,1)*(lc:-1:lc-KMAX));
%else
% ACF=ACF./((lc-MISSES)*ones(1,KMAX+1) - ones(lr,1)*(0:KMAX));
%end;
elseif strcmp(Mode,'coeff')
%ACF = ACF ./ ACF(:,ones(1,KMAX+1)) .* ((lc-MISSES)*ones(1,KMAX+1));
ACF = ACF./NN;
ACF = ACF./(ACF(:,1)*ones(1,size(ACF,2)));
else
end;
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