--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main/statistics/inst/iwishpdf.m	Mon Dec 30 19:18:19 2013 +0000
@@ -0,0 +1,67 @@
+## Copyright (C) 2013 Nir Krakauer <nkrakauer@ccny.cuny.edu>
+##
+## 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.
+##
+## Octave 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 Octave; see the file COPYING.  If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn  {Function File} {} @var{y} = iwishpdf (@var{W}, @var{Tau}, @var{df}, @var{log_y}=false)
+## Compute the probability density function of the Wishart distribution
+##
+## Inputs: A @var{p} x @var{p} matrix @var{W} where to find the PDF and the @var{p} x @var{p} positive definite scale matrix @var{Tau} and scalar degrees of freedom parameter @var{df} characterizing the inverse Wishart distribution. (For the density to be finite, need @var{df} > (@var{p} - 1).)
+## If the flag @var{log_y} is set, return the log probability density -- this helps avoid underflow when the numerical value of the density is very small
+##
+## Output: @var{y} is the probability density of Wishart(@var{Sigma}, @var{df}) at @var{W}.
+## 
+## @seealso{iwishrnd, wishpdf}
+## @end deftypefn
+
+## Author: Nir Krakauer <nkrakauer@ccny.cuny.edu>
+## Description: Compute the probability density function of the inverse Wishart distribution
+
+function [y] = iwishpdf(W, Tau, df, log_y=false)
+
+if (nargin < 3)
+  print_usage ();
+endif
+
+p = size(Tau, 1);
+
+if (df <= (p - 1))
+  error('df too small, no finite densities exist')
+endif 
+
+#calculate the logarithm of G_d(df/2), the multivariate gamma function
+g = (p * (p-1) / 4) * log(pi);
+for i = 1:p
+  g = g + log(gamma((df + (1 - i))/2)); #using lngamma_gsl(.) from the gsl package instead of log(gamma(.)) might help avoid underflow/overflow 
+endfor
+
+C = chol(W);
+
+#use formulas for determinant of positive definite matrix for better efficiency and numerical accuracy
+logdet_W = 2*sum(log(diag(C)));
+logdet_Tau = 2*sum(log(diag(chol(Tau))));
+
+y = -(df*p)/2 * log(2) + (df/2)*logdet_Tau - g - ((df + p + 1)/2)*logdet_W - trace(Tau*chol2inv(C))/2;
+
+if ~log_y
+  y = exp(y);
+endif
+
+
+endfunction
+
+##test results cross-checked against diwish function in R MCMCpack library 
+%!assert(iwishpdf(4, 3, 3.1), 0.04226595, 1E-7);
+%!assert(iwishpdf([2 -0.3;-0.3 4], [1 0.3;0.3 1], 4), 1.60166e-05, 1E-10);
+%!assert(iwishpdf([6 2 5; 2 10 -5; 5 -5 25], [9 5 5; 5 10 -8; 5 -8 22], 5.1), 4.946831e-12, 1E-17);
+
+%% Test input validation
+%!error iwishpdf ()
+%!error iwishpdf (1, 2)
+%!error iwishpdf (1, 2, 0)
+
+%!error wishpdf (1, 2)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main/statistics/inst/wishpdf.m	Mon Dec 30 19:18:19 2013 +0000
@@ -0,0 +1,67 @@
+## Copyright (C) 2013 Nir Krakauer <nkrakauer@ccny.cuny.edu>
+##
+## 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.
+##
+## Octave 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 Octave; see the file COPYING.  If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn  {Function File} {} @var{y} = wishpdf (@var{W}, @var{Sigma}, @var{df}, @var{log_y}=false)
+## Compute the probability density function of the Wishart distribution
+##
+## Inputs: A @var{p} x @var{p} matrix @var{W} where to find the PDF. The @var{p} x @var{p} positive definite matrix @var{Sigma} and scalar degrees of freedom parameter @var{df} characterizing the Wishart distribution. (For the density to be finite, need @var{df} > (@var{p} - 1).)
+## If the flag @var{log_y} is set, return the log probability density -- this helps avoid underflow when the numerical value of the density is very small
+##
+## Output: @var{y} is the probability density of Wishart(@var{Sigma}, @var{df}) at @var{W}.
+## 
+## @seealso{wishrnd, iwishpdf}
+## @end deftypefn
+
+## Author: Nir Krakauer <nkrakauer@ccny.cuny.edu>
+## Description: Compute the probability density function of the Wishart distribution
+
+function [y] = wishpdf(W, Sigma, df, log_y=false)
+
+if (nargin < 3)
+  print_usage ();
+endif
+
+p = size(Sigma, 1);
+
+if (df <= (p - 1))
+  error('df too small, no finite densities exist')
+endif 
+
+#calculate the logarithm of G_d(df/2), the multivariate gamma function
+g = (p * (p-1) / 4) * log(pi);
+for i = 1:p
+  g = g + log(gamma((df + (1 - i))/2)); #using lngamma_gsl(.) from the gsl package instead of log(gamma(.)) might help avoid underflow/overflow 
+endfor
+
+C = chol(Sigma);
+
+#use formulas for determinant of positive definite matrix for better efficiency and numerical accuracy
+logdet_W = 2*sum(log(diag(chol(W))));
+logdet_Sigma = 2*sum(log(diag(C)));
+
+y = -(df*p)/2 * log(2) - (df/2)*logdet_Sigma - g + ((df - p - 1)/2)*logdet_W - trace(chol2inv(C)*W)/2;
+
+if ~log_y
+  y = exp(y);
+endif
+
+
+endfunction
+
+##test results cross-checked against dwish function in R MCMCpack library 
+%!assert(wishpdf(4, 3, 3.1), 0.07702496, 1E-7);
+%!assert(wishpdf([2 -0.3;-0.3 4], [1 0.3;0.3 1], 4), 0.004529741, 1E-7);
+%!assert(wishpdf([6 2 5; 2 10 -5; 5 -5 25], [9 5 5; 5 10 -8; 5 -8 22], 5.1), 4.474865e-10, 1E-15);
+
+%% Test input validation
+%!error wishpdf ()
+%!error wishpdf (1, 2)
+%!error wishpdf (1, 2, 0)
+
+%!error wishpdf (1, 2)