Empirically estimating big-oh time efficiency

Question

Background

I\'d like to estimate the big-oh performance of some methods in a library through benchmarks. I don\'t need precision -- it suffices to show that someth

Answer 1

Wanted to share my experiments as well. Nothing new from the theoretical standpoint, but it's a fully functional Python module that can easily be extended.

Main points:

• It's based on scipy Python library curve_fit function that allows to fit any function into the given set of points minimizing sum of square differences;

• Since tests are done increasing the problem size exponentially points closer to the start will kind of have a bigger weight, which does not help to identify the correct approximation, so it seems to me that simple linear interpolation to redestribute points evenly does help;

• The set of approximations we are trying to fit is fully under our control; I've added the following ones:

        def fn_linear(x, k, c):
            return k * x + c

        def fn_squared(x, k, c):
            return k * x ** 2 + c

        def fn_pow3(x, k, c):
            return k * x ** 3 + c

        def fn_log(x, k, c):
            return k * np.log10(x) + c

        def fn_nlogn(x, k, c):
            return k * x * np.log10(x) + c

Here is a fully functional Python module to play with: https://gist.github.com/gubenkoved/d9876ccf3ceb935e81f45c8208931fa4, and some pictures it produces (please note -- 4 graphs per sample with different axis scales).