% 
% Written by:
% -- 
% John L. Weatherwax                2007-07-01
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clc; close all; clear; 

alpha     = +2; % the value of \alpha 

y_lim_min = -2.0; 
y_lim_max = 2.0; 

x       = linspace( -6, +6, 100 ); 

y       = zeros(1,length(x)); 
inds    = find(x>0);
y(inds) = -x(inds); 

% the ramp function: 
% 
plot( x, y, '-' ); axis( [-6, +6, y_lim_min, y_lim_max] ); title('initial ramp function');
saveas( gcf, '../../WriteUp/Graphics/Chapter2/chap_2_prob_9_initial_ramp.eps', 'psc2' );

% the flipped ramp function: 
% 
plot( x, fliplr(y), '-' ); axis( [-6, +6, y_lim_min, y_lim_max] ); title('flipped ramp function');
saveas( gcf, '../../WriteUp/Graphics/Chapter2/chap_2_prob_9_flipped_ramp.eps', 'psc2' );

% the flipped ramp shifted by a to the right:
%
a  = 3/4;
yF = fliplr(y); 
xS = x+a; % shift x by a 
plot( xS, yF, '-' ); axis( [-6, +6, y_lim_min, y_lim_max] ); title(['flipped ramp function shifted right by ',num2str(a)]);
saveas( gcf, '../../WriteUp/Graphics/Chapter2/chap_2_prob_9_flipped_shifted.eps', 'psc2' );

% plot the fixed step function on top of this: 
% 
y       = zeros(1,length(x)); 
inds    = find(x>-alpha & x<+alpha);
y(inds) = 1; 
plot( xS, yF, 'b-' ); hold on; 
plot( x, y, 'r-' ); axis( [-6, +6, y_lim_min, y_lim_max] ); title(['alpha=',num2str(alpha), '; a=',num2str(a)]);
saveas( gcf, '../../WriteUp/Graphics/Chapter2/chap_2_prob_9_flipped_shifted_w_step.eps', 'psc2' );