%
% Written by:
% -- 
% John L. Weatherwax                2005-08-14
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clear functions; 
clear; 
close all; 
clc; 

randn('seed',0); rand('seed',0);

% Integrate each system with measurements to the point t_final
%
t_final = 0.2;

% Part (a): 
%
[t_a,y_a] = ode45( @sect_5_1_ode_fn_part_a, [0, t_final], [0;0;0] );

% Part (b): 
%
[t_b,y_b] = ode45( @sect_5_1_ode_fn_part_b, [0, t_final], [0;0;0] );

% Part (c): 
%
[t_c,y_c] = ode45( @sect_5_1_ode_fn_part_c, [0, t_final], [0;0;0] );

% Integrate the modified systems dropping the measurement variance reduction term in each case
%
[t_a_p,y_a_p] = ode45( @sect_5_1_ode_fn, [t_final,2*t_final], y_a(end,:));
[t_b_p,y_b_p] = ode45( @sect_5_1_ode_fn, [t_final,2*t_final], y_b(end,:));
[t_c_p,y_c_p] = ode45( @sect_5_1_ode_fn, [t_final,2*t_final], y_c(end,:));


figure; 
subplot( 1,3, 1 ); plot( t_a, y_a(:,1), 'r' ); hold on; 
plot( t_a_p, y_a_p(:,1), '-.r' ); 
plot( t_b, y_b(:,1), 'g' ); 
plot( t_b_p, y_b_p(:,1), '-.g' ); 
plot( t_c, y_c(:,1), 'b' ); 
plot( t_c_p, y_c_p(:,1), '-.b' ); 
axis tight; title('p11');

subplot( 1,3, 2 ); ha= plot( t_a, y_a(:,2), 'r' ); hold on; 
hap= plot( t_a_p, y_a_p(:,2), '-.r' ); 
hb= plot( t_b, y_b(:,2), 'g' ); 
hbp= plot( t_b_p, y_b_p(:,2), '-.g' ); 
hc= plot( t_c, y_c(:,2), 'b' ); 
hcp= plot( t_c_p, y_c_p(:,2), '-.b' ); 
axis tight; title('p12');

subplot( 1,3, 3 ); ha= plot( t_a, y_a(:,3), 'r' ); hold on; 
hap= plot( t_a_p, y_a_p(:,3), '-.r' ); 
hb= plot( t_b, y_b(:,3), 'g' ); 
hpb= plot( t_b_p, y_b_p(:,3), '-.g' ); 
hc= plot( t_c, y_c(:,3), 'b' ); 
hcp= plot( t_c_p, y_c_p(:,3), '-.b' ); legend( [ha,hap,hb,hbp,hc,hcp], {'Part (a)','(a)-pred','Part (b)','(b)-pred','Part (c)','(c)-pred'}, 'location', 'southeast' );
axis tight; title('p22');


fn = [ '../../WriteUp/Graphics/Chapter4/sect_5_prob_2_plots.eps' ];
%saveas( gcf, fn, 'epsc' );