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<2007-04-11> by Lorenzo Bolla

Numerical computing: Matlab vs Python + numpy + weave

Recently, I've discovered the power of Python for numerical computing. Being a slave of Matlab for many years, I've decided to give Python (and it's numerical module numpy) a try, comparing its number crunching capabilities versus Matlab's.

The tests are heavily inspired by Prabhu Ramachandran. I've only added Matlab to complete his comparisons.

Here is a short description of the test, taken from here:

The example we will consider is a very simple (read, trivial) case of solving the 2D Laplace equation using an iterative finite difference scheme (four point averaging, Gauss-Seidel or Gauss-Jordan). The formal specification of the problem is as follows.

We are required to solve for some unknown function u(x,y) such that nabla^2 u = 0 with a boundary condition specified. For convenience the domain of interest is considered to be a rectangle and the boundary values at the sides of this rectangle are given.

All the tests have been run on a Pentium IV Xeon 2GHz, with 1Gb of RAM. Here is the Matlab script I used laplace.m (it's a doc file: sorry for that, but I'm only allowed to upload docs and images on this blog).

time.png

Figure 1: time spent by different solvers

factor.png

Figure 2: speed factor with respect to matlab

blitz is roughly twice as fast as Matlab. inline, fastinline, fortran and pyrex only differ appreciably for small grids: for 500x500 grids they are around 10x faster than Matlab.

Here is some other digits, not included in the graphs:

Pretty amazing, if you think that optimizing Python, most of the time, is really trivial. Moreover, Python is free and easily parallelizable with MPI (I'll show some performances in a future post).

Tests have been run also on an SGI Altix with Itanium2 processors, on a single CPU. The graphs are reported in the following thumbnails.

pico_time.png pico_factor.png