Hello,
I was curious how long it would take my laptop to solve Ax = b for square A as a function of the problem size. I tried to profile it using BenchmarkTools:
ns = [1,2,3,5,7,10,20,30,50,70,100,200,300,500,700,1000,2000,3000,5000,7000,10000]
ts = Array{Float64}(undef, length(ns))
for (i,n) in enumerate(ns)
b = @benchmark $(rand(n,n)) \ $(rand(n))
ts[i] = median(b).time
end
and found that it seems to grow quadratically, in O(n^2). I expected it to grow in O(n^3).
The gray trendline is n^2 / 10^7.
I’m running Julia single-threaded and the matrices are dense, so I am not sure why this would be. Is there something wrong with how I am benchmarking it? Is there some property of positive dense matrices that I am missing? Is it actually using multiple threads under the hood?
Thank you!
