% 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);
% Set the window width.
h = 1;
% get diff array (the case i=1 is a bit singular) ... 
df = [h, diff(x)]; 

% find smooth at each value in x
for i = 1:n
  w = wfun(h,x(i),x);              % <- the kernel centered at the point x(i) ... evaluate at ALL x's
  yhatpc(i) = sum(df.*w.*y)/h;
end

plot( x, y, 'ok' ); hold on; 
plot( x, yhatpc, '-rx' ); axis tight; 
xlabel( 'independent variable' ); ylabel( 'dependent variable' ); 
title( 'the Priesley-Chao Kernel Estimator' ); 
saveas( gcf, ['../../WriteUp/Graphics/Chapter10/prob_10_8_pc_kernel'], 'epsc' );