nmix.m

this a SVM toolbox,it is very useful for someone who just learn SVM.In order to be undestood easily,

function [XMix,IMix]=nmix(MI,SIGMA,PP,N)
% function [XMix,IMix]=nmix(MI,SIGMA,PP,N)
% NMIX generates mixture of the normal distributed random values
%  which have mean value MI, covariance SIGMA and a priori
%  probability PP. Number of samples in the mixture is N.
%
% Input:
%  MI [DxK] contains K mean vectors which are D-dimensional, 
%     i.e. MI=[mi_1,mi_2,..mi_K].
%  SIGMA [Dx(kxD)] contains K covariance D-by-D matrices,
%     i.e. SIGMA=[sigma_1, sigma_2, ...,sigma_K].
%  PP [1xK] contains K real positive numbers their sum is equal to 1.
%  N [1x1] an integer that determines number of points in the mixture.
%   
% Output:
%  XMix [DxK] created mixture consisting of K vectors.
%  IMix [1xK] K integers which determine label (component of given 
%     given mixture) corresponding to given vector.
%

% Statistical Pattern Recognition Toolbox, Vojtech Franc, Vaclav Hlavac
% (c) Czech Technical University Prague, http://cmp.felk.cvut.cz
% Written Vojtech Franc (diploma thesis) 02.01.2000
% Modifications
% 24. 6.00 V. Hlavac, comments polished.
% 17-march-2001, V. Franc, repared

% get DIMension and # of classes
DIM=size(MI,1);
K=size(MI,2);

% computes transf. matrixes for each sigma
AT=[];
for i=1:K,
   [A,p]=chol(inv(SIGMA(:,(i-1)*DIM+1:i*DIM)));
   AT=[AT,inv(A)];
end

% roulette
pcurr=0;
for i=1:K
   PPD(i)=pcurr+PP(i);
   pcurr=PPD(i);
end

% generate mixture
IMix=[];
XMix=[];
for i=1:N,

   % rand. class
   rclass=rand(1);
   class=1;
   while PPD(class) < rclass & class < K,
      class=class+1;
   end
   IMix=[IMix,class];     % store class

   % random point falling to the current class p(x|c)=N(MI(class),SIGMA(class))
   point=AT(:,(class-1)*DIM+1:DIM*class)*randn(DIM,1)+MI(:,class);
   XMix=[XMix,point];     % store point
end