CircularVariance

CircularVariance - Estimate circular variance and standard deviation.

  USAGE

    [v,s] = CircularVariance(angles,dim)

    angles         angles in radians
    dim            optional dimension along which the mean should be computed

  OUTPUT

    v              variance
    s              standard deviation

  SEE

    See also CircularMean, CircularConfidenceIntervals, Concentration,
    ConcentrationTest.

0001 function [v,s] = CircularVariance(angles,dim)
0002 
0003 %CircularVariance - Estimate circular variance and standard deviation.
0004 %
0005 %  USAGE
0006 %
0007 %    [v,s] = CircularVariance(angles,dim)
0008 %
0009 %    angles         angles in radians
0010 %    dim            optional dimension along which the mean should be computed
0011 %
0012 %  OUTPUT
0013 %
0014 %    v              variance
0015 %    s              standard deviation
0016 %
0017 %  SEE
0018 %
0019 %    See also CircularMean, CircularConfidenceIntervals, Concentration,
0020 %    ConcentrationTest.
0021 
0022 % Copyright (C) 2004-2011 by Michaël Zugaro
0023 %
0024 % This program is free software; you can redistribute it and/or modify
0025 % it under the terms of the GNU General Public License as published by
0026 % the Free Software Foundation; either version 3 of the License, or
0027 % (at your option) any later version.
0028 
0029 if nargin < 2,
0030     dim = 1;
0031 end
0032 
0033 isradians(angles);
0034 
0035 angles = exp(i*angles);
0036 r_bar = abs(mean(angles,dim));
0037 v = 1 - r_bar;
0038 s = sqrt(-2*log(r_bar));