% 
% 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);

% the required data:
%
var_scale = 0.01; 
nPts = 100; 
X1 = mvnrnd( [0,1], var_scale*eye(2), nPts ); % blue points 
X2 = mvnrnd( [-1,-1], var_scale*eye(2), nPts ); % red points 
X3 = mvnrnd( [+1,-1], var_scale*eye(2), nPts ); % green points 

h1 = plot( X1(:,1), X1(:,2), '.b' ); hold on; 
h2 = plot( X2(:,1), X2(:,2), '.r' ); 
h3 = plot( X3(:,1), X3(:,2), '.g' ); 
legend( [h1,h2,h3], {'class 1', 'class 2','class 3'} ); axis( 4*[-1,+1,-1,+1] ); 

% draw the three decision lines w^T x = 0 
%
title('');

% separate out blue class correctly
%
x1_grid = linspace( -4, +4, 50 );
w_i = [ -.1, 1, -0.25 ]; 
x2_db   = ( -w_i(3) - w_i(1) * x1_grid ) / w_i(2);
plot( x1_grid, x2_db, '-b' );
text( -3.5, 0.25, 'g_1(x)=0' ); 
text( 3.7, .8, '+' ); text( 3.7, 0.5, '-' ); 

% separate out red class correctly
%
w_i = [ 1, 1, 1 ]; 
x2_db   = ( -w_i(3) - w_i(1) * x1_grid ) / w_i(2);
plot( x1_grid, x2_db, '-r' );
text( -3.5, 2.75, 'g_2(x)=0' ); 
text( 2.4, -3.6, '+' ); text( 2.8, -3.6, '-' ); 

% separate out green class correctly
%
w_i = [ -20.0, 1., 10 ]; 
x2_db   = ( -w_i(3) - w_i(1) * x1_grid ) / w_i(2);
plot( x1_grid, x2_db, '-g' );
text( -0.5, -3.75, 'g_3(x)=0' ); 
text( 0.75, 3.6, '+' ); text( 0.45, 3.6, '-' ); 

text( -3.5, 1.5, '(+,+,-)' );
text( -1.5, 3, '(+,-,-)' );
text( 2.5, 2, '(+,-,+)' );
text( -3.5, -3, '(-,+,-)' );
text( -.35, -.3, '(-,-,-)' );
text( 3, -2, '(-,-,+)' );
text( 1, -3.5, '(-,+,+)' );

fn = ['chap_3_prob_15_class_regions.eps'];
saveas(gcf,['../../WriteUp/Graphics/Chapter3/',fn],'epsc');