function out = DN_cv(x,k)
% DN_cv     Coefficient of variation
%
% Coefficient of variation of order k is sigma^k / mu^k (for sigma, standard
% deviation and mu, mean) of a data vector, x
%
%---INPUTS:
%
% x, the input data vector
% k, the order of coefficient of variation (k = 1 is default)

% ------------------------------------------------------------------------------
% 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/>.
% ------------------------------------------------------------------------------

%-------------------------------------------------------------------------------
% Check inputs
%-------------------------------------------------------------------------------
if nargin < 2 || isempty(k)
    k = 1; % Do standard CV by default
end

if (rem(k,1) ~= 0) || (k < 0)
    warning('k should probably be a positive integer');
    % Carry on with just this warning, though
end

% Compute the coefficient of variation (of order k) of the data

out = (std(x))^k / (mean(x))^k;

end
