X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fstatistics-1.1.3%2Fmvncdf.m;fp=octave_packages%2Fstatistics-1.1.3%2Fmvncdf.m;h=864badccb88ab422de5302c5488baba640aae796;hp=0000000000000000000000000000000000000000;hb=f5f7a74bd8a4900f0b797da6783be80e11a68d86;hpb=1705066eceaaea976f010f669ce8e972f3734b05

diff --git a/octave_packages/statistics-1.1.3/mvncdf.m b/octave_packages/statistics-1.1.3/mvncdf.m
new file mode 100644
index 0000000..864badc
--- /dev/null
+++ b/octave_packages/statistics-1.1.3/mvncdf.m
@@ -0,0 +1,173 @@
+## Copyright (C) 2008 Arno Onken <asnelt@asnelt.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{p} =} mvncdf (@var{x}, @var{mu}, @var{sigma})
+## @deftypefnx {Function File} {} mvncdf (@var{a}, @var{x}, @var{mu}, @var{sigma})
+## @deftypefnx {Function File} {[@var{p}, @var{err}] =} mvncdf (@dots{})
+## Compute the cumulative distribution function of the multivariate
+## normal distribution.
+##
+## @subheading Arguments
+##
+## @itemize @bullet
+## @item
+## @var{x} is the upper limit for integration where each row corresponds
+## to an observation.
+##
+## @item
+## @var{mu} is the mean.
+##
+## @item
+## @var{sigma} is the correlation matrix.
+##
+## @item
+## @var{a} is the lower limit for integration where each row corresponds
+## to an observation. @var{a} must have the same size as @var{x}.
+## @end itemize
+##
+## @subheading Return values
+##
+## @itemize @bullet
+## @item
+## @var{p} is the cumulative distribution at each row of @var{x} and
+## @var{a}.
+##
+## @item
+## @var{err} is the estimated error.
+## @end itemize
+##
+## @subheading Examples
+##
+## @example
+## @group
+## x = [1 2];
+## mu = [0.5 1.5];
+## sigma = [1.0 0.5; 0.5 1.0];
+## p = mvncdf (x, mu, sigma)
+## @end group
+##
+## @group
+## a = [-inf 0];
+## p = mvncdf (a, x, mu, sigma)
+## @end group
+## @end example
+##
+## @subheading References
+##
+## @enumerate
+## @item
+## Alan Genz and Frank Bretz. Numerical Computation of Multivariate
+## t-Probabilities with Application to Power Calculation of Multiple
+## Constrasts. @cite{Journal of Statistical Computation and Simulation},
+## 63, pages 361-378, 1999.
+## @end enumerate
+## @end deftypefn
+
+## Author: Arno Onken <asnelt@asnelt.org>
+## Description: CDF of the multivariate normal distribution
+
+function [p, err] = mvncdf (varargin)
+
+  # Monte-Carlo confidence factor for the standard error: 99 %
+  gamma = 2.5;
+  # Tolerance
+  err_eps = 1e-3;
+
+  if (length (varargin) == 1)
+    x = varargin{1};
+    mu = [];
+    sigma = eye (size (x, 2));
+    a = -Inf .* ones (size (x));
+  elseif (length (varargin) == 3)
+    x = varargin{1};
+    mu = varargin{2};
+    sigma = varargin{3};
+    a = -Inf .* ones (size (x));
+  elseif (length (varargin) == 4)
+    a = varargin{1};
+    x = varargin{2};
+    mu = varargin{3};
+    sigma = varargin{4};
+  else
+    print_usage ();
+  endif
+
+  # Dimension
+  q = size (sigma, 1);
+  cases = size (x, 1);
+
+  # Default value for mu
+  if (isempty (mu))
+    mu = zeros (1, q);
+  endif
+
+  # Check parameters
+  if (size (x, 2) != q)
+    error ("mvncdf: x must have the same number of columns as sigma");
+  endif
+
+  if (any (size (x) != size (a)))
+    error ("mvncdf: a must have the same size as x");
+  endif
+
+  if (isscalar (mu))
+    mu = ones (1, q) .* mu;
+  elseif (! isvector (mu) || size (mu, 2) != q)
+    error ("mvncdf: mu must be a scalar or a vector with the same number of columns as x");
+  endif
+
+  x = x - repmat (mu, cases, 1);
+
+  if (q < 1 || size (sigma, 2) != q || any (any (sigma != sigma')) || min (eig (sigma)) <= 0)
+    error ("mvncdf: sigma must be nonempty symmetric positive definite");
+  endif
+
+  c = chol (sigma)';
+
+  # Number of integral transformations
+  n = 1;
+
+  p = zeros (cases, 1);
+  varsum = zeros (cases, 1);
+
+  err = ones (cases, 1) .* err_eps;
+  # Apply crude Monte-Carlo estimation
+  while any (err >= err_eps)
+    # Sample from q-1 dimensional unit hypercube
+    w = rand (cases, q - 1);
+
+    # Transformation of the multivariate normal integral
+    dvev = normcdf ([a(:, 1) / c(1, 1), x(:, 1) / c(1, 1)]);
+    dv = dvev(:, 1);
+    ev = dvev(:, 2);
+    fv = ev - dv;
+    y = zeros (cases, q - 1);
+    for i = 1:(q - 1)
+      y(:, i) = norminv (dv + w(:, i) .* (ev - dv));
+      dvev = normcdf ([(a(:, i + 1) - c(i + 1, 1:i) .* y(:, 1:i)) ./ c(i + 1, i + 1), (x(:, i + 1) - c(i + 1, 1:i) .* y(:, 1:i)) ./ c(i + 1, i + 1)]);
+      dv = dvev(:, 1);
+      ev = dvev(:, 2);
+      fv = (ev - dv) .* fv;
+    endfor
+
+    n++;
+    # Estimate standard error
+    varsum += (n - 1) .* ((fv - p) .^ 2) ./ n;
+    err = gamma .* sqrt (varsum ./ (n .* (n - 1)));
+    p += (fv - p) ./ n;
+  endwhile
+
+endfunction