% 
% Written by:
% -- 
% John L. Weatherwax                2007-07-01
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; clear all; %clc; 

randn('seed',0); rand('seed',0);

addpath('../../../Nabney/Code/NETLAB/');

X = [ 2, 0 ; sqrt(2), sqrt(2) ; 0, 2 ; -sqrt(2), sqrt(2) ; -2, 0 ; -sqrt(2), -sqrt(2) ; 0, -2 ; sqrt(2), -sqrt(2) ]; 
x1 = X(:,1) + 2; 
x2 =  X(:,2); 

plot( X(:,1), X(:,2), 'go', 'markersize', 8, 'markerfacecolor', 'g' ); hold on; 
plot( x1, x2, 'ro', 'markersize', 8, 'markerfacecolor', 'r' ); 

fn = '../../WriteUp/Graphics/Chapter14/chap_14_prob_5_plot';
%saveas( gcf, fn, 'epsc' );

% the entire data set: 
X_all  = [ X; [ x1, x2 ] ]; n = size(X_all,1);
labels = ones(n,1); 

% initialize the mixture of Gaussians to fit to this data (centers initialized to random values)
nin = size(X_all,2); % state dimension 
ncentres = 2; % two Gaussians
nclasses = 1; % only one class 
mixc = gmm(nin, ncentres, 'full'); 

% initialize the centers of each cluster using the k-means algo:
options = foptions;
options(14) = 5;
mixc = gmminit(mixc,X_all,options);

% Now learn the parameters (mean and covariance) of the data:
options(1) = 1;  % Print error values
options(5) = 1;  % Prevent collapse of variances
options(14) = 15; % Number of iterations
mixc = gmmem(mixc, X_all, options);

% display the results:
mixc
mixc.centres(1,:)
mixc.covars(:,:,1)

mixc.centres(2,:)
mixc.covars(:,:,2)