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    Metadata details:
    filename: PD_PeriodicityWang.m
    path of file: ./repos/hctsa/Operations
    
    the code of the file until where you have to start completion: function out = PD_PeriodicityWang(y)
% PD_PeriodicityWang    Periodicity extraction measure of Wang et al. (2007)
%
% Implements an idea based on the periodicity extraction measure proposed in:
%
% "Structure-based Statistical Features and Multivariate Time Series Clustering"
% X. Wang and A. Wirth and L. Wang
% Seventh IEEE International Conference on Data Mining, 351--360 (2007)
% DOI: 10.1109/ICDM.2007.103
%
% Detrends the time series using a three-knot cubic regression spline
% and then computes autocorrelations up to one third of the length of
% the time series.
% The frequency is the first peak in the autocorrelation function satisfying
% a set of conditions.
%
%---INPUT:
% y, the input time series.
%
% The single threshold of 0.01 was considere
    
function satisfying
% a set of conditions.
%
%---INPUT:
% y, the input time series.
%
% The single threshold of 0.01 was considered in the original paper, this code
% uses a range of thresholds: 0, 0.01, 0.1, 0.2, 1/sqrt{N}, 5/sqrt{N}, and
% 10/sqrt{N}, where N is the length of the time series.

% ------------------------------------------------------------------------------
% Copyright (C) 2020, Ben D. Fulcher <ben.d.fulcher@gmail.com>,
% <http://www.benfulcher.com>
%
% If you use this code for your research, please cite the following two papers:
%
% (1) B.D. Fulcher and N.S. Jones, "hctsa: A Computational Framework for Automated
% Time-Series Phenotyping Using Massive Feature Extraction, Cell Systems 5: 527 (2017).
% DOI: 10.1016/j.cels.2017.10.001
%
% (2) B.D. Fulcher, M.A. Little, N.S. Jones, "Highly comparative time-series
% analysis: the empirical structure of time series and their methods",
% J. Roy. Soc. Interface 10(83) 20130048 (2013).
% DOI: 10.1098/rsif.2013.0048
%
% This function 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/>.
% ------------------------------------------------------------------------------

% ------------------------------------------------------------------------------
%% Preliminaries:
% ------------------------------------------------------------------------------
doPlot = false; % plot outputs to figure

% Check that a Curve-Fitting Toolbox license is available (for the splines):
BF_CheckToolbox('curve_fitting_toolbox')

% Check that the time series is z-scored:
if ~BF_iszscored(y)
    warning('The input time series should be z-scored')
end

% ------------------------------------------------------------------------------
%% Preparation
% ------------------------------------------------------------------------------
N = length(y); % length of the time series
% The thresholds with which to count a peak:
ths = [0,0.01,0.1,0.2,1/sqrt(N),5/sqrt(N),10/sqrt(N)];
numThresholds = length(ths); % the number of thresholds

%-------------------------------------------------------------------------------
%% 1: Detrend