Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / statistics-1.1.3 / vmrnd.m

diff --git a/octave_packages/statistics-1.1.3/vmrnd.m b/octave_packages/statistics-1.1.3/vmrnd.m
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+## Copyright (C) 2009 Soren Hauberg <soren@hauberg.org>
+##
+## 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/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} @var{theta} = vmrnd (@var{mu}, @var{k})
+## @deftypefnx{Function File} @var{theta} = vmrnd (@var{mu}, @var{k}, @var{sz})
+## Draw random angles from a Von Mises distribution with mean @var{mu} and
+## concentration @var{k}.
+##
+## The Von Mises distribution has probability density function
+## @example
+## f (@var{x}) = exp (@var{k} * cos (@var{x} - @var{mu})) / @var{Z} ,
+## @end example
+## where @var{Z} is a normalisation constant.
+##
+## The output, @var{theta}, is a matrix of size @var{sz} containing random angles
+## drawn from the given Von Mises distribution. By default, @var{mu} is 0
+## and @var{k} is 1.
+## @seealso{vmpdf}
+## @end deftypefn
+
+function theta = vmrnd (mu = 0, k = 1, sz = 1)
+  ## Check input
+  if (!isreal (mu))
+    error ("vmrnd: first input must be a scalar");
+  endif
+  
+  if (!isreal (k) || k <= 0)
+    error ("vmrnd: second input must be a real positive scalar");
+  endif
+  
+  if (isscalar (sz))
+    sz = [sz, sz];
+  elseif (!isvector (sz))
+    error ("vmrnd: third input must be a scalar or a vector");
+  endif
+  
+  ## Simulate!
+  if (k < 1e-6)
+    ## k is small: sample uniformly on circle
+    theta = 2 * pi * rand (sz) - pi;
+  
+  else
+    a = 1 + sqrt (1 + 4 * k.^2);
+    b = (a - sqrt (2 * a)) / (2 * k);
+    r = (1 + b^2) / (2 * b);
+
+    N = prod (sz);
+    notdone = true (N, 1);
+    while (any (notdone))
+      u (:, notdone) = rand (3, N);
+      
+      z (notdone) = cos (pi * u (1, notdone));
+      f (notdone) = (1 + r * z (notdone)) ./ (r + z (notdone));
+      c (notdone) = k * (r - f (notdone));
+      
+      notdone = (u (2, :) >= c .* (2 - c)) & (log (c) - log (u (2, :)) + 1 - c < 0);
+      N = sum (notdone);
+    endwhile
+    
+    theta = mu + sign (u (3, :) - 0.5) .* acos (f);
+    theta = reshape (theta, sz);
+  endif
+endfunction