[Octave-cvsupdate] SF.net SVN: octave:[6283] trunk/octave-forge/main/statistics

[<ha...@us...>]

Revision: 6283
          http://octave.svn.sourceforge.net/octave/?rev=6283&view=rev
Author:   hauberg
Date:     2009-09-30 11:16:48 +0000 (Wed, 30 Sep 2009)

Log Message:
-----------
Support Von Mises distributions

Modified Paths:
--------------
    trunk/octave-forge/main/statistics/INDEX

Added Paths:
-----------
    trunk/octave-forge/main/statistics/inst/vmpdf.m
    trunk/octave-forge/main/statistics/inst/vmrnd.m

Modified: trunk/octave-forge/main/statistics/INDEX
===================================================================
--- trunk/octave-forge/main/statistics/INDEX	2009-09-30 08:18:02 UTC (rev 6282)
+++ trunk/octave-forge/main/statistics/INDEX	2009-09-30 11:16:48 UTC (rev 6283)
@@ -12,6 +12,7 @@
  hygestat
  lognstat
  mvnpdf mvnrnd mvncdf
+ vmpdf vmrnd
  mvtcdf
  normstat
  nbinstat

Added: trunk/octave-forge/main/statistics/inst/vmpdf.m
===================================================================
--- trunk/octave-forge/main/statistics/inst/vmpdf.m	                        (rev 0)
+++ trunk/octave-forge/main/statistics/inst/vmpdf.m	2009-09-30 11:16:48 UTC (rev 6283)
@@ -0,0 +1,46 @@
+## Copyright (C) 2009 Soren Hauberg
+##
+## 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} = vmpdf (@var{x}, @var{mu}, @var{k})
+## Evaluates the Von Mises probability density function.
+##
+## 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. By default, @var{mu} is 0 and
+## @var{k} is 1.
+## @seealso{vmrnd}
+## @end deftypefn
+
+function p = vmpdf (x, mu = 0, k = 1)
+  ## Check input
+  if (!isreal (x))
+    error ("vmpdf: first input must be real");
+  endif
+  
+  if (!isreal (mu))
+    error ("vmpdf: second input must be a scalar");
+  endif
+  
+  if (!isreal (k) || k <= 0)
+    error ("vmpdf: third input must be a real positive scalar");
+  endif
+  
+  ## Evaluate PDF
+  Z = 2 * pi * besseli (0, k);
+  p = exp (k * cos (x-mu)) / Z;
+endfunction

Added: trunk/octave-forge/main/statistics/inst/vmrnd.m
===================================================================
--- trunk/octave-forge/main/statistics/inst/vmrnd.m	                        (rev 0)
+++ trunk/octave-forge/main/statistics/inst/vmrnd.m	2009-09-30 11:16:48 UTC (rev 6283)
@@ -0,0 +1,76 @@
+## Copyright (C) 2009 Soren Hauberg
+##
+## 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


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