We'll test the conclusion of flops experimentally, using the built-in lu function instead of the purely instructive lufact.

n_ = (200:100:2400)';

t_ = 0*n_;

for i = 1:length(n_)

n = n_(i);

A = randn(n,n);

tic % start a timer

for j = 1:6, [L,U] = lu(A); end

t = toc; % read the timer

t_(i) = t/6;

end

We plot the performance on a log-log graph and compare it to . The result could vary significantly from machine to machine.

loglog(n_,t_,'.-')

hold on, loglog(n_,t_(end)*(n_/n_(end)).^3,'--')

axis tight

xlabel('size of matrix'), ylabel('time (sec)')

title('Timing of LU factorization')

legend('lu','O(n^3)','location','southeast')