% This script tests functor.m for correctness

functor = @(x) myfft(x);

fprintf('Test 1: Gaussian ...');
sample = exp(-linspace(-4,4,256).^2);
assert(all(abs(functor(sample) - fft(sample))<1e-10));
fprintf('\tpassed\n');

fprintf('Test 1.1: Gaussian with a different Matlab dimension ...');
sample = exp(-linspace(-4,4,256).^2)';
assert(all(abs(functor(sample) - fft(sample))<1e-10));
fprintf('\tpassed\n');

fprintf('Test 1.2: Gaussian complex ...');
sample = 1i*exp(-linspace(-4,4,256).^2);
assert(all(abs(functor(sample) - fft(sample))<1e-10));
fprintf('\tpassed\n');

fprintf('Test 2: sawtooth ...');
sample = linspace(-1,1,256);
assert(all(abs(functor(sample) - fft(sample))<1e-10));
fprintf('\tpassed\n');

fprintf('Test 3: sin and sin2 ...');
sample = sin(linspace(-pi,pi,256));
assert(all(abs(functor(sample) - fft(sample))<1e-10));
sample = sin(2*linspace(-pi,pi,256));
assert(all(abs(functor(sample) - fft(sample))<1e-10));
fprintf('\tpassed\n');

Ns = 10:25;
times = zeros(length(Ns),1);
FFTtimes = zeros(length(Ns),1);

% Time complexity test
for k=Ns
    fprintf('\tEvaluating step %d \n', k);
    sample = exp(-linspace(-4,4,2^k).^2)';
    % functor time
    tic;
    functor(sample);
    times(k-Ns(1)+1) = toc;
    % fft time
    tic;
    fft(sample);
    FFTtimes(k-Ns(1)+1) = toc;
end

Ns = 2.^Ns

% output to external file
fout = fopen("output/complexTimeFFT.out", 'w');
fprintf(fout, "N  T FFT\n")
for k = 1:length(Ns)
    fprintf(fout, "%g  %g  %g\n", Ns(k), times(k), FFTtimes(k))
end
fclose(fout);

% show graph
figure
grid on
xlabel('N')
ylabel('Elapsed time')
loglog(Ns, times, Ns, FFTtimes)

fprintf('All tests passed!\n');