% 
% Written by:
% -- 
% John L. Weatherwax                2005-08-04
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
% Epage 106
% 
%-----

close all; clc; clear; 

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

% Generate the required data:
%
mu1 = [ 1, 1 ].';
mu2 = [ 0, 0 ].';
sigmasSquared = 0.2; 
d = size(mu1,1); 

nFeats = 100;

X1 = mvnrnd( mu1, sigmasSquared*eye(d), nFeats ); 
X2 = mvnrnd( mu2, sigmasSquared*eye(d), nFeats ); 

h1 = plot( X1(:,1), X1(:,2), '.b' ); hold on; 
h2 = plot( X2(:,1), X2(:,2), '.r' ); hold on; 
legend( [h1,h2], {'class 1', 'class 2'} ); 

data = [X1;X2];
inds_1 = 1:nFeats;
inds_2 = (nFeats+1):(2*nFeats);

N = size(data,1);

% the target values for the LMS algorithm: 
Y_targets = +1*ones(2*nFeats,1);
Y_targets(inds_2) = -1; 

%
% Code begins:
%---

% Append +1 to all data: 
X = [ data, ones(size(data,1),1) ]; 
l_extended = size(data,2);

XTX = X' * X;
XTY = X' * Y_targets;

w_hat = XTX \ XTY;

% draw the decision boundary w^T x = 0 
%
x1_grid = linspace( min(data(:,1)), max(data(:,1)), 50 );
x2_db   = ( -w_hat(3) - w_hat(1) * x1_grid ) / w_hat(2);
plot( x1_grid, x2_db, '-g' );
title('sum of square error computed decision line');

fn = ['chap_3_prob_9_class_regions.eps'];
saveas(gcf,['../../WriteUp/Graphics/Chapter3/',fn],'epsc');