%
% 
% Written by:
% -- 
% John L. Weatherwax                2009-04-21
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; drawnow; 
rehash; 
clc; 

clear; addpath( '../../Code/eda_data' ); addpath( '../../Code/eda_toolbox' ); addpath( '../Chapter1' ); 

rho = 0.99; n = 20; 
z1 = randn(1,n);
z2 = rho * z1 + sqrt( 1 - rho^2 ) * randn(1,n); 

% test that we are generating correlated random variables correctly the (1,2) element should equal rho above: 
CC = corrcoef( z1, z2 );
fprintf('sample correlation coefficient rho(z1,z2) = %10.6f\n', CC(1,2) );  

figure; parallelcoords( [ z1(:), z2(:) ] ); title( 'parallel coordinate plot rho=+1.0' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter10/prob_10_11_rho_p1', 'epsc' ); 


rho = -0.99; n = 20; 
z1 = randn(1,n);
z2 = rho * z1 + sqrt( 1 - rho^2 ) * randn(1,n); 

% test that we are generating correlated random variables correctly the (1,2) element should equal rho above: 
CC = corrcoef( z1, z2 );
fprintf('sample correlation coefficient rho(z1,z2) = %10.6f\n', CC(1,2) );  

figure; parallelcoords( [ z1(:), z2(:) ] ); title( 'parallel coordinate plot rho=-1.0' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter10/prob_10_11_rho_m1', 'epsc' );