I spent some time today profiling a Brownian dynamics simulation written in Python to see how I could make it faster before starting some long runs on a Linux cluster. In the sections below, I have attempted to quantify the speed improvements due to various changes. Keep in mind that the actual speed improvement in your code will vary, depending on where the actual bottlenecks occur. See my post about profiling Python code. Another caveat: I am running Python 2.4.4 because it’s installed on our cluster.

Numerical programming frequently requires the use of look-up tables. A look-up table is a collection of pre-computed values. When given an “x” value, the table returns a pre-computed “y” value. Look-up tables can be used to speed up numerical codes, when it is faster to look up a value in the table than it is to compute the value. They are also used when the data in the table cannot be computed–for example, experimental data or averaged results from an ensemble of Monte Carlo simulations. Another application is to compute a value when a function cannot be solved algebraically. Assume that you have a formula for a function q(h). You need the value of h for a given value of q, but the formula cannot be algebraically solved to get h(q). Instead, choose a range of h values, compute the function q(h), and store each value in a look-up table. Now you can get h(q) for any value stored in the table. The major limitation of a look-up table is that it cannot return valid results for any value of q which is outside the range of those stored in the table. Depending on its implementation, the table may be able to interpolate to return values between known points.