clear
%%
% We get a cardinal function if we use data that is one at a node and zero
% at the others. 
N = 7;  
n = (N-1)/2;
t = 2*(-n:n)'/N;
y = zeros(N,1);  
y(n+1) = 1;
plot(t, y, '.')
hold on

p = triginterp(t, y);

figure(1)
fplot(p, [-1 1])
xlabel('x')
ylabel('p(x)')
title('Trig cardinal function')
grid on

%%
% Here is a 2-periodic function and one of its interpolants.
figure(2)
f = @(x) exp(sin(pi*x)-2*cos(pi*x));
fplot(f,[-1 1])
hold on
y = f(t);  
plot(t, y, '.')
fplot(triginterp(t,y),[-1 1])
xlabel('x')
ylabel('p(x)')
title('Trig interpolation')
grid on

%%
% The convergence of the interpolant is exponential (spectral). We let $N$
% go needlessly large here in order to demonstrate that unlike polynomials,
% trigonometric interpolation is stable on equally spaced nodes.
N = (3:3:90)';
err = 0*N;
x = linspace(-1,1,1601)';  % for measuring error
for k = 1:length(N)
    n = (N(k)-1)/2;   
    t = 2*(-n:n)'/N(k);
    p = triginterp(t,f(t));
    err(k) = norm(f(x)-p(x),inf);
end

figure(3)
semilogy(N, err, '.-')
title('Error in trig interpolation')
xlabel('N')
ylabel('max error')
grid on