% 
% problem epage: 
% example epage: 
%
% Written by:
% -- 
% John L. Weatherwax                2005-08-14
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

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

close all; drawnow; 
clc; 
clear; 


load yeast;
[n,p] = size(data); 
datac = data - repmat(sum(data)/n,n,1); 
%com = cov(datac);      % Find the covariance matrix:
com = corrcoef(datac); % Find the correlation matrix:

[eigvec,eigval] = eig(com); 
eigval = diag(eigval); 
% Order in decending order: 
eigval = flipud(eigval); 
eigvec = eigvec(:,p:-1:1); 

% Do a scree plot of this data: 
fh=figure; plot(1:length(eigval),eigval,'ko-'); hold on; grid on; 

% Compute the same for random variables:
data2 = randn(n,p); 
com = cov(data2); 
[eigvec,eigval] = eig(com); 
eigval = diag(eigval); 
% Order in decending order: 
eigval = flipud(eigval); 
eigvec = eigvec(:,p:-1:1); 

% Add to the original scree plot:
figure(fh);
plot(1:length(eigval),eigval,'r.-'); hold on; 
title( 'Yeast-Random scree plot' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter2/prob_2_2_scree', 'eps' );