Numerical benchmarks for Julia, Python.

We try to avoid trivial and nonsense benchmarks (for people doing numerics!) like fibonacci, sorting and so on.

We put ourself in the shoes of a typical Matlab or Matlab-like programmer, writing quite short but numerically intensive programs.

Are Python and Julia easy to use and efficient? We compare them with a C++ optimized implementation (and sometimes with a Fortran one)..

The benchmark(s):

• 🆕 Callback: callbacks of small and not so small functions.

• Gaussian: Gaussian elimination with partial pivoting.

• FeStiff: compute the stiffness matrix, for the Poisson equation, discretized with P2 finite elements on triangles.

• Weno: a classical solver for hyperbolic equations, in dimension 1, with application to Burghers equation and to Convection.

• Sparse: building a sparse matrix and doing a sparse matrix x vector product.

• MicroBenchmarks: very simple benchmarks to show the importance of different programing styles.

We will add other numerical significative benchmarks in the (near) future.

Dependencies:

What you need to install:

• python3
• pip (pip3)
• g++ (and/or clang++)
• gfortran
• lapack
• openblas
• cmake
• gnuplot

You can install them using your distribution tool (apt...).

• julia

❗ Julia ❗ since 2018-10-08 programs need at least version Version 1.1 (stable version in 2018-10); note that all programs needed adaptation when moving to this version, and will not run with former ones.

Note also that the version packaged with Ubuntu 18-04 is older. Install the stable version from here. Note also that Julia is evolving, and it is possible that the codes need some adaptation to run with later versions of the language.

You also need:

• pythran
• scipy
• Numpy
• numba

to install them, you can just do:

pip install pythran

and so on...

You can also install them from conda.

Note that, for Pythran it seems necessary to create a .pythranrc file in the home directory, to describe which blas is used:

[compiler]
blas=openblas

How to run the Benchmarks ?

-1: First solution: Enter the directories CallBack/, FeStiff/, Gaussian/, MicroBenchmarks/, Sparse/ or Weno/. Then read the README.md, which explains how to run the (local) benchmark.

-2: Second solution: In each of these directories, you will find a script: runAllTests.sh . This script will run the benchmark, for every language (and variant).

The first solution is certainly the safest.

Results:

Have a look at the wiki, where you can find results obtained on my personal computer, as well as some considerations on the different benchmarks and on optimizations implemented.