% Modified from Example 10.6
% 
% epage 415
% 
% 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; 

% Generate some noisy data.
x = linspace(0, 4 * pi,100);
y = sin(x) + 0.75*randn(size(x));

% Create an inline function to evaluate the weights.
mystrg='(2*pi*h^2)^(-1/2)*exp(-0.5*((x - mu)/h).^2)';
wfun = inline(mystrg);

% Set up the space to store the estimated values.
% We will get the estimate at all values of x.
yhatnw = zeros(size(x));
n = length(x);

h_array = [0.1, 0.2, 0.5, 0.75, 1.0, 1.3, 2.0];

fh=figure; plot( x, y, 'ko', 'MarkerFaceColor', 'Black' ); hold on;
ln_colors = 'rbgcmk'; nc = length(ln_colors); 

ph = []; tt = {};

for hi=1:length(h_array),

  % Set the window width.
  h = h_array(hi);
  % find smooth at each value in x
  for i = 1:n
    w = wfun(h,x(i),x);
    yhatnw(i) = sum(w.*y)/sum(w);
  end
  figure(fh); 
  ph(end+1) = plot( x, yhatnw, ['-',ln_colors(mod(hi,nc)+1)]);
  tt{end+1} = ['h = ',num2str(h)]; 
end

axis tight; grid on; 
xlabel( 'independent variable' ); ylabel( 'dependent variable' ); 
title( 'the Nadaraya-Watson Kernel Estimator for various h' ); 
legend( ph, tt, 'location', 'northeast' ); 
saveas( gcf, ['../../WriteUp/Graphics/Chapter10/prob_10_9_kernels_vs_h'], 'epsc' );