sampleNormal

 sample from n-dim standard normal distribution

 Syntax: [pointMatrix, probabilityVector] = sampleNormal(nDim, nSample)
   OR     .. = sampleNormal(.., mean, cov)

 THIS IS NO USER FUNCTION

• discretizeDistribution discretize a continuous distribution
• obtainDistributionDiscrete obtain a discrete probability distribution

0001 function [pointMatrix probabilityVector] = sampleNormal(...
0002     nDim, nSample, mean, cov)
0003 % sample from n-dim standard normal distribution
0004 %
0005 % Syntax: [pointMatrix, probabilityVector] = sampleNormal(nDim, nSample)
0006 %   OR     .. = sampleNormal(.., mean, cov)
0007 %
0008 % THIS IS NO USER FUNCTION
0009 
0010 % The elk-library: convex geometry applied to crystallization modeling.
0011 %   Copyright (C) 2013 Alexander Reinhold
0012 %
0013 % This program is free software: you can redistribute it and/or modify it
0014 %   under the terms of the GNU General Public License as published by the
0015 %   Free Software Foundation, either version 3 of the License, or (at your
0016 %   option) any later version.
0017 %
0018 % This program is distributed in the hope that it will be useful, but
0019 %   WITHOUT ANY WARRANTY; without even the implied warranty of
0020 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0021 %   General Public License for more details.
0022 %
0023 % You should have received a copy of the GNU General Public License along
0024 %   with this program.  If not, see <http://www.gnu.org/licenses/>.
0025 
0026 % The standard normal distribution has the parameters:
0027 %   mean = zeros
0028 %   cov = eye
0029 % A coordinate transformation of these x:
0030 %     y = a + B*x
0031 % results in a normal distribution of y with parameters:
0032 %     mean = a
0033 %     cov = B*B'
0034 % Hence, given the parameters, the transformation parameters are:
0035 %     a = mean
0036 %     B = chol(cov)
0037 
0038 % points
0039 pointMatrix = randn(nDim, nSample);
0040 
0041 % some conveniance
0042 if ~exist('mean', 'var') || isempty(mean)
0043     mean = zeros(nDim, 1);
0044 end
0045 if ~exist('cov', 'var') || isempty(cov)
0046     cov = eye(nDim);
0047 end
0048 
0049 % get the transformation matrix
0050 try
0051     B = chol(cov);
0052 catch me
0053     error('elk:distribution:wrongInput', ['The covariance matrix must ' ...
0054         'be symmetric and positive definite ''chol'' has thrown the ' ...
0055         'following message: ' me.message]);
0056 end
0057 
0058 pointMatrix = bsxfun(@plus, B*pointMatrix, mean);
0059 probabilityVector = mvnpdf(pointMatrix', mean', cov)';