%
% Examples 9.15 and 9.17
% 
% epage 432
% 
% 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');

randn('seed',0); 

x = linspace( 0, +1, 100 ); 

% our spatially dependent variance: 
var = ones(size(x));     % <- a constant variance of ONE

% generate noise with this variance: 
noise_eps = zeros(1,length(x)); 
for ii=1:length(x),
  noise_eps(ii) = normrnd(0,sqrt(var(ii)));
end

% our dependent function "y": 
y_truth = 4*x.^3 + 6*x.^2 - 1;
y       = y_truth + noise_eps; 

% plot the original data: 
fd=figure; 
ht = plot( x, y_truth, '-og' ); hold on; grid on; 
ho = plot( x, y, 'xr' ); 

fr=figure; hold on; 

line_styles={'-',':','--'}; 
line_colors='cmk'; 
data_plt_h = []; 
res_plt_h = []; 

for ii=1:3,

  % assume we *know* the dimension of the polynomial to fit: 
  [pcoef,s] = polyfit(x,y,ii); 
  
  % evaluate this polynomial model:
  yp = polyval(pcoef,x); 
  
  % plot this polynomial model:
  figure(fd); 
  tph=plot( x, yp, ['-',line_colors(ii)] ); 
  data_plt_h(end+1) = tph; 
  
  % plot the residuals v.s. the fitted value yp: 
  res = y-yp; 
  figure(fr); 
  tph=plot( x, res, [line_styles{ii},line_colors(ii)] ); 
  xlabel( 'predictor x' ); ylabel( 'residual' ); 
  title( ['residual dependence plot for a polynomial model of degree', num2str(ii)] ); 
  axis( [0 1 -2.5 2.5] );
  res_plt_h(end+1) = tph; 
end

figure(fd); 
legend(data_plt_h, {'poly deg 1','poly deg 2','poly deg 3'}, 'location', 'north' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter10/prob_10_2_truth_n_data', 'epsc' ); 

figure(fr); 
legend(res_plt_h,  {'poly deg 1','poly deg 2','poly deg 3'}, 'location', 'north' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter10/prob_10_2_res_plts', 'epsc' ); 

clear functions;