Timing of LU factorization

using FundamentalsNumericalComputation

We’ll test the conclusion of \(O(n^3)\) flops experimentally, using the built-in lu function instead of the purely instructive lufact.

lu(randn(3,3));  # throwaway to force compilation

n = 200:100:2400
t = zeros(size(n))
for (i,n) in enumerate(n) 
    A = randn(n,n)  
    t[i] = @elapsed for j = 1:6; lu(A); end

We plot the timings on a log-log graph and compare it to \(O(n^3)\). The result could vary significantly from machine to machine.

    xaxis=(:log10,"\$n\$"), yaxis=(:log10,"elapsed time"), label="data", leg=:topleft)