clear
%%
% Test the conclusion of O(n^3) flops experimentally, using the
% built-in lu function
n = (1000:200:4000)';
t = 0*n;
seed = 1;
rng(seed);
nrep = 6;
for i = 1:length(n)
    m = n(i);
    A = randn(m, m);  
    tic()       % start a timer
    for j = 1:nrep
        [L, U] = lu(A);  
    end
    t(i) = toc()/nrep;  % read the timer
end

%%
% Plot the performance on a log-log graph and compare it to O(n^3).
% The result could vary significantly from machine to machine. 
loglog(n, t, '.-')
hold on
loglog(n, t(end)*(n/n(end)).^3, '--')
xlabel('size of matrix')
ylabel('time (sec)')
title('Timing of LU factorization')
legend('lu', 'O(n^3)', 'location','southeast')
grid on