# v_vonmisespdf

## PURPOSE

V_VONMISESPDF Von Mises probability distribution P=(x,m,k)

## SYNOPSIS

function p=v_vonmisespdf(x,m,k)

## DESCRIPTION

    V_VONMISESPDF Von Mises probability distribution P=(x,m,k)

      Inputs:  X         matrix of input values (in radians)
               M         mean angle of distribution (in radians)
               K         concentration parameter

     Outputs:  P         matrix of probability density values (same size as X)
                         (with no output argument, the function will plot a graph)

     The von Mises distribution describes the pdf of an angle over the range [0,2pi).
     For large K, the distribution approximates a Gaussian with mean M and
     variance 1/K. For small K, the distribution is uniform.

## CROSS-REFERENCE INFORMATION

This function calls:

- v_axisenlarge V_AXISENLARGE - enlarge the axes of a figure (f,h)
- v_vonmisespdf V_VONMISESPDF Von Mises probability distribution P=(x,m,k)

This function is called by:

- v_vonmisespdf V_VONMISESPDF Von Mises probability distribution P=(x,m,k)

## SOURCE CODE

    0001 function p=v_vonmisespdf(x,m,k)
    0002 %V_VONMISESPDF Von Mises probability distribution P=(x,m,k)
    0003 %
    0004 %  Inputs:  X         matrix of input values (in radians)
    0005 %           M         mean angle of distribution (in radians)
    0006 %           K         concentration parameter
    0007 %
    0008 % Outputs:  P         matrix of probability density values (same size as X)
    0009 %                     (with no output argument, the function will plot a graph)
    0010 %
    0011 % The von Mises distribution describes the pdf of an angle over the range [0,2pi).
    0012 % For large K, the distribution approximates a Gaussian with mean M and
    0013 % variance 1/K. For small K, the distribution is uniform.
    0014
    0015 %      Copyright (C) Mike Brookes 1997-2011
    0016 %      Version: $Id: v_vonmisespdf.m 10865 2018-09-21 17:22:45Z dmb $
    0017 %
    0018 %   VOICEBOX is a MATLAB toolbox for speech processing.
    0019 %   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
    0020 %
    0021 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    0022 %   This program is free software; you can redistribute it and/or modify
    0023 %   it under the terms of the GNU Lesser General Public License as published by
    0024 %   the Free Software Foundation; either version 3 of the License, or
    0025 %   (at your option) any later version.
    0026 %
    0027 %   This program is distributed in the hope that it will be useful,
    0028 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
    0029 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    0030 %   GNU Lesser General Public License for more details.
    0031 %
    0032 %   You can obtain a copy of the GNU Lesser General Public License from
    0033 %   https://www.gnu.org/licenses/ .
    0034 %
    0035 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    0036 if nargout>0
    0037     p=exp(k*cos(x-m))/(2*pi*besseli(0,k));
    0038 else
    0039     if nargin<1 || isempty(x)
    0040         x=linspace(-pi,pi,181);
    0041     end
    0042     if nargin<2 || isempty(m)
    0043         m=0;
    0044     end
    0045     if nargin<3 || isempty(k)
    0046         k=[0 pow2(-1:3)];
    0047     end
    0048     nm=length(m);
    0049     nk=length(k);
    0050     np=max(nm,nk);
    0051     pp=zeros(length(x),np);
    0052     pl=cell(np,1);
    0053     for i=1:np
    0054         mi=m(1+rem(i-1,nm));
    0055         ki=k(1+rem(i-1,nk));
    0056         pp(:,i)=v_vonmisespdf(x(:),mi,ki);
    0057         pl{i}=sprintf('\\mu=%.1f, \\kappa=%.1f',mi,ki);
    0058     end
    0059     plot(x,pp);
    0060     v_axisenlarge([-1 -1.05]);
    0061     legend(pl,'location','northeast');
    0062 end
    0063