%
% 
% epage 433
% 
% 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 helmets; 

[stime,inds] = sort(time); 
saccel = accel(inds);
x=stime; y=saccel; 

fd1=figure; rd=plot( time, accel, '.k' ); hold on; grid on; 
xlabel( 'time' ); ylabel( 'accel' ); 

x_sample = linspace( min(time), max(time), 300 ); 

% the data is relativly "sparse" so we'll use a large value of alpha:
alpha = 0.3; 

deg=1;
%y_loess = csloessr(x,y,x_sample,alpha,deg);
[y_loess,ylo,xlo,yup,xup] = csloessenv(x,y,x,alpha,deg,0);   % <- regular (non-robust) loess
%[y_loess,ylo,xlo,yup,xup] = csloessenv(x,y,x,alpha,deg,1);   % <- robust loess
figure(fd1); 
plot(x,y_loess,'-x',xlo,ylo,'-g',xup,yup,'-g'); 

% add in this loess correction to the main model: 
figure(fd1); 
title( 'the helmets data with a loess model of degree 1' ); 
saveas( gcf, ['../../WriteUp/Graphics/Chapter10/prob_10_14_loess_deg_1'], 'epsc' ); 

fd2=figure; rd=plot( time, accel, '.k' ); hold on; grid on; 
xlabel( 'time' ); ylabel( 'accel' );

% the data is relativly "sparse" so we'll use a large value of alpha:
%alpha = 0.5;
alpha = 0.4;

deg=2;
[y_loess,ylo,xlo,yup,xup] = csloessenv(x,y,x,alpha,deg,0);   % <- regular (non-robust) loess
%[y_loess,ylo,xlo,yup,xup] = csloessenv(x,y,x,alpha,deg,1);   % <- robust loess
figure(fd2); 
plot(x,y_loess,'-x',xlo,ylo,'-g',xup,yup,'-g'); 

figure(fd2); 
title( 'the helmets data with a loess model of degree 2' ); 
saveas( gcf, ['../../WriteUp/Graphics/Chapter10/prob_10_14_loess_deg_2'], 'epsc' ); 

clear functions;