clear;

% example:
%        {  0    if -1<x<0
% f(x) = {
%        {  1    if 0<x<1
%
x=-1:.01:1;

% plot partial sums for N=3, 6, and 20: fN(x,3), fN(x,6), and fN(x,20)
% also plot the exact: f(x)
fexact=f(x);
fN3=fN(x,3);
fN6=fN(x,6);
fN20=fN(x,20);
figure(1);
plot(x,fexact,'k-',x,fN3,x,fN6,x,fN20);
legend('N=\infty','N=3','N=6','N=20','Location','Best');
title('Plotting N=3,6,20');
xlabel('x');
ylabel('f_N');


% now plot the error for each one
figure(2);
plot(x,abs(fexact-fN3),x,abs(fexact-fN6),x,abs(fexact-fN20));
legend('N=3','N=6','N=20','Location','Best');
title('Plotting error for N=3,6,20');
xlabel('x');
ylabel('e_N');

% now print out the max of the absolute value of the error and the squared
% sum of the error
disp('The max errors are:');
disp(['N=' num2str(norm(fexact-fN3,inf))]);
disp(['N-' num2str(norm(fexact-fN6,inf))]);
disp(['N-' num2str(norm(fexact-fN20,inf))]);
disp('The squared sum errors are:');
disp(['N=' num2str(norm(fexact-fN3,2))]);
disp(['N-' num2str(norm(fexact-fN6,2))]);
disp(['N-' num2str(norm(fexact-fN20,2))]);