This GIT respository contains all files needed for an adequate analysis of the gait (6MWT) accelerometer data.
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function [Lambda]=div_wolf_fixed_evolv(states, fs, min_dist, max_dist, max_dist_mult, max_theta, period, evolv) %% Description % Calculate maximum lyapunov exponent from state space according to Wolf's method: % Wolf, A., et al., Determining Lyapunov exponents from a time series. % Physica D: 8 Nonlinear Phenomena, 1985. 16(3): p. 285-317. % % Input: % states: states in state space % fs: sample frequency % min_dist: neighbours should be more than this distandce away to be % selected (assumed noise amplitude ) % max_dist: maximum distance to which the divergence may grow before % replacing the neighbour % max_theta: maximum angle between vectors from feducial point to old and % new neighbours, this is the absolute maximum, first search % nearer % period: indicates period of time-wise near samples to exclude in % nearest neighbour search % evolv: time step after which the neighbour is replaced % % Output: % Lambda: the estimated Lyapunov exponent % ExtraArgs: optional struct containing additional info for debugging or % analysis of the method % %% 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 % 23 October 2012, initial version based on div_wolf [N,D]=size(states); N_opt = N-evolv; states_opt = states(1:N_opt,:); One2N_opt=(1:N_opt)'; is=1; % search closest point to states(1,:), but further than min_dist away DeltaFidPoint = zeros(N_opt,D); for dim = 1:D, DeltaFidPoint(:,dim) = states_opt(:,dim)-states(is,dim); end DeltaFidPointSqr = DeltaFidPoint.^2; DistSqr = sum(DeltaFidPointSqr,2); Distances = sqrt(DistSqr); CosTh = zeros(N_opt,1); in = find(DistSqr==min(DistSqr(DistSqr>=min_dist^2 & abs(One2N_opt-is)>period)) & abs(One2N_opt-is)>period,1,'first'); if isempty(in) warning('Cannot calculate Wolf''s Lyapunov exponent, no states further than min_dist from starting point'); Lambda = nan; return; end DistStart = Distances(in); LnDistReplacementsSum = 0; for is=(1+evolv):evolv:N, in = in+evolv; % fill distance and cos matrices with new values DeltaOld = (states(in,:)-states(is,:))'; DistOld = sqrt(sum(DeltaOld.^2)); for dim = 1:D, DeltaFidPoint(:,dim) = states_opt(:,dim)-states(is,dim); end DeltaFidPointSqr(:,:) = DeltaFidPoint.^2; DistSqr(:,:) = sum(DeltaFidPointSqr,2); Distances(:,:) = sqrt(DistSqr); CosTh(:,:) = abs(DeltaFidPoint*DeltaOld)./DistOld./Distances; Index = []; search_theta = max_theta; while isempty(Index) && search_theta < pi dist_mult = 1; while isempty(Index) && dist_mult <= max_dist_mult search_dist = dist_mult*max_dist; Candidates = find(Distances <= search_dist & CosTh >= cos(search_theta) ... & Distances>= min_dist & abs(One2N_opt-is)>period); if ~isempty(Candidates) % find the best of candidates if numel(Candidates) > 1 Candidates = Candidates(CosTh(Candidates)==max(CosTh(Candidates))); if numel(Candidates) > 1 Candidates = Candidates(Distances(Candidates)==min(Distances(Candidates))); if numel(Candidates) > 1 Candidates = Candidates(abs(One2N_opt(Candidates)-is)==max(abs(