%%
% We measure the convergence rate for piecewise linear interpolation of
% exp(sin(7*x)).
f = @(x) exp(sin(7*x));
x = linspace(0, 1, 10001)';  % sample the difference at many points
n = 2.^(3:10)';
err = 0*n;

for i = 1:length(n)
    nn = n(i);
    t = linspace(0, 1, nn+1)';   % interpolation nodes
    p = plinterp(t, f(t));
    err(i) = max(abs(f(x) - p(x)));
end

%%
% Since we expect convergence that is O(h^2)=O(1/n^2), we use a log-log
% graph of error and expect a straight line of slope $-2$.
loglog(n, err, '.-')
hold on 
loglog(n, 0.1*(n/n(1)).^(-2), '--' )
xlabel('n') 
ylabel('||f-p||_\infty')
title('Convergence of PL interpolation')
legend('error', '2nd order')
axis tight
grid on