This GIT respository contains all files needed for an adequate analysis of the gait (6MWT) accelerometer data.
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function [L_Estimate,ExtraArgsOut] = CalcMaxLyapWolfFixedEvolv(ThisTimeSeries,FS,ExtraArgsIn)
%% Description
% This function calculates the maximum Lyapunov exponent from a time
% series, based on the method described by Wolf et al. in
% Wolf, A., et al., Determining Lyapunov exponents from a time series.
% Physica D: 8 Nonlinear Phenomena, 1985. 16(3): p. 285-317.
%
% Input:
% ThisTimeSeries: a vector or matrix with the time series
% FS: sample frequency of the ThisTimeSeries
% ExtraArgsIn: a struct containing optional input arguments
% J (embedding delay)
% m (embedding dimension)
% Output:
% L_Estimate: The Lyapunov estimate
% ExtraArgsOut: a struct containing the additional output arguments
% J (embedding delay)
% m (embedding dimension)
%% Copyright
% COPYRIGHT (c) 2012 Sietse Rispens, VU University Amsterdam
%
% 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/>.
%% Author
% Sietse Rispens
%% History
% April 2012, initial version of CalcMaxLyapWolf
% 23 October 2012, use fixed evolve time instead of adaptable
if nargin > 2
if isfield(ExtraArgsIn,'J')
J=ExtraArgsIn.J;
end
if isfield(ExtraArgsIn,'m')
m=ExtraArgsIn.m;
end
end
%% Initialize output args
L_Estimate=nan;ExtraArgsOut.J=nan;ExtraArgsOut.m=nan;
%% Some checks
% predefined J and m should not be NaN or Inf
if (exist('J','var') && ~isempty(J) && ~isfinite(J)) || (exist('m','var') && ~isempty(m) && ~isfinite(m))
warning('Predefined J and m cannot be NaN or Inf');
return;
end
% multidimensional time series need predefined J and m
if size(ThisTimeSeries,2) > 1 && (~exist('J','var') || ~exist('m','var') || isempty(J) || isempty(m))
warning('Multidimensional time series needs predefined J and m, can''t determine Lyapunov');
return;
end
%Check that there are no NaN or Inf values in the TimeSeries
if any(~isfinite(ThisTimeSeries(:)))
warning('Time series contains NaN or Inf, can''t determine Lyapunov');
return;
end
%Check that there is variation in the TimeSeries
if ~(nanstd(ThisTimeSeries) > 0)
warning('Time series is constant, can''t determine Lyapunov');
return;
end
%% Determine J
if ~exist('J','var') || isempty(J)
% Calculate mutual information and take first local minimum Tau as J
bV = min(40,floor(sqrt(size(ThisTimeSeries,1))));
tauVmax = 70;
[mutMPro,cummutMPro,minmuttauVPro] = MutualInformationHisPro(ThisTimeSeries,(0:tauVmax),bV,1); % (xV,tauV,bV,flag)
if isnan(minmuttauVPro)
display(mutMPro);
warning('minmuttauVPro is NaN. Consider increasing tauVmax.');
return;
end
J=minmuttauVPro;
end
ExtraArgsOut.J=J;
%% Determine m
if ~exist('m','var') || isempty(m)
escape = 10;
max_m = 20;
max_fnnM = 0.02;
mV = 0;
fnnM = 1;
for mV = 2:max_m % for m=1, FalseNearestNeighbors is slow and lets matlab close if N>500000
fnnM = FalseNearestNeighborsSR(ThisTimeSeries,J,mV,escape,FS); % (xV,tauV,mV,escape,theiler)
if fnnM <= max_fnnM || isnan(fnnM)
break
end
end
if fnnM <= max_fnnM
m = mV;
else
warning('Too many false nearest neighbours');
return;
end
end
ExtraArgsOut.m=m;
%% Create state space based upon J and m
N_ss = size(ThisTimeSeries,1)-(m-1)*J;
StateSpace=nan(N_ss,m*size(ThisTimeSeries,2));
for dim=1:size(ThisTimeSeries,2),
for delay=1:m,
StateSpace(:,(dim-1)*m+delay)=ThisTimeSeries((1:N_ss)'+(delay-1)*J,dim);
end
end
%% Parameters for Lyapunov estimation
CriticalLen=J*m;
max_dist = sqrt(sum(std(StateSpace).^2))/10;
max_dist_mult = 5;
min_dist = max_dist/2;
max_theta = 0.3;
evolv = J;
%% Calculate Lambda
[L_Estimate]=div_wolf_fixed_evolv(StateSpace, FS, min_dist, max_dist, max_dist_mult, max_theta, CriticalLen, evolv);