%
% Problem Epage 200 
% Example 5.23 Epage 173
% 
% 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; 
clc; 

addpath('../../Code/CSTool');
load iris;   % <- three matrics setosa/versicolor/virginica of size [n,p]

% define the plotting domain: 
theta = (-pi+eps):0.1:(pi-eps);
n = 50; % <- the number of samples of each type of flower 
p = 4;  % <- the number of features 
yvirginica  = zeros(n,p);
yversicolor = zeros(n,p); 

% compute the dot product of our trig function with each sample's component: 
%
ang  = zeros(length(theta),p); % <- space to hold angle x feature
fstr = '[1/sqrt(2) sin(i) cos(i) sin(2*i)]';
k=1; 
% evaluate sin/cos at each angle:
for i=theta,
  ang(k,:) = eval(fstr);
  k=k+1; 
end
% now take the dot product producing a function for each observation: 
for i=1:n,
  for j=1:length(theta),
    % find dot product:
    yvirginica(i,j)  = virginica(i,:)*ang(j,:)';
    yversicolor(i,j) = versicolor(i,:)*ang(j,:)';
  end
end
% do all plots: 
plot(theta,yvirginica(1,:),'r',theta,yversicolor(1,:),'b-.'); hold on; 
legend('Iris virginica','Iris versicolor'); 
for i=2:n,
  plot(theta,yvirginica(i,:),'r',theta,yversicolor(i,:),'b-.'); 
end
title( 'Andrews Plot' ); 
xlabel('t'); ylabel('Andrews Curve'); 
grid on; 
saveas( gcf, 'andrews_virg_vers', 'epsc' );