%
% We'll test the conclusion of $O(n^3)$ flops experimentally
%

clear
clf
format compact

nn = (400:40:880)';
l = length(nn);
tt = zeros(l, 1);
nrep = 1;
for i = 1:l
    n = nn(i);
    A = randn(n, n);  
    tic()  % start a timer
    for j = 1:nrep   % repeat nrep times for more precise timing
        lufact(A);  
    end
    tt(i) = toc()/nrep 
end

%%
% We 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(nn, tt, 'ro-')
hold on
loglog(nn, tt(end)*(nn/nn(end)).^3, 'k--')
axis tight
xlabel('size of matrix')
ylabel('time (sec)')
title('Timing of LU factorization')
legend('lu','O(n^3)','location','southeast')
grid on
hold off