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
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.
plot(n,t,m=:o,
xaxis=(:log10,"\$n\$"), yaxis=(:log10,"elapsed time"), label="data", leg=:topleft)
plot!(n,(n/n[3]).^3*t[5],l=:dash,label="\$O(n^3)\$")