%
% Example epage: 28
% Problem epage: 41 
% 
% Written by:
% -- 
% John L. Weatherwax                2008-02-20
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clear all; 
close all; drawnow; 
clc; 

addpath('../../Code/eda_toolbox');
addpath('../../Code/eda_data');

n = 100; p = 2; 
X = randn(n,p); 

orig_dists = pdist(X); 
figure; 
odh=plot( sort(orig_dists), 'o' ); hold on; 

Xz = zscore(X);                   % <- this implements equation 1.1 
z_dists = pdist(Xz); 
dt1h=plot( sort(z_dists), 'rx' ); 

Xn1 = X./repmat( std(X), [n,1] ); % <- this implements equation 1.2 ... since mean(X)=0 it is the same ... 
n1_dists = pdist(Xn1); 
dt2h=plot( sort(n1_dists), 'kd' ); 
xlabel( '(i,j) index' ); ylabel( 'distance' ); 
legend( [odh,dt1h,dt2h], {'original data','Eq 1.1','Eq 1.2'}, 'location', 'northwest' ); 
title( 'the original distance and the normalized distance' ); 

saveas( gcf, '../../WriteUp/Graphics/Chapter1/prob_1_8_distances', 'eps' );