Sunday, April 12, 2009

Maxima Latex Listings

The listings package is a really nice way to include typeset source-code listings in Latex documents. I wanted to include an appendix in one of my documents to show the Maxima calculations I used to arrive at some results shown in the paper. Unfortunately Maxima is not one of the (many, many) built-in languages recognized by the package. I tried using C, because the comments in Maxima are like C comments, but it doesn't handle single quotes (used to get noun forms like 'diff()) well. So, how to include listings of Maxima code in Latex?

It turns out to be really easy to define your own language in the preamble of the document.


All this definition does is italicize comments and bold face the keywords, which is sufficient to make the code more readable and pleasant looking. Here's an example screenshot of the results:

Thursday, April 2, 2009

Performance optimization (allocation inside a for loop)

An interesting discussion about an old topic just popped up on the Octave lists. It's not interesting because someone noticed that failing to pre-allocate a vector before entering a loop is slow (doesn't anyone RTFM?), but because of the follow-up discussion on indexing and range objects.

Here's the interesting bit:

octave:1> tic(); n=1e5; retval=1:n; toc()
Elapsed time is 0.000528962 seconds.
octave:2> tic(); n=1e5; retval = (1:n)(1:n); toc
Elapsed time is 0.00593709 seconds.
octave:3> tic();n=1e5;retval=[1:n]; toc
Elapsed time is 0.010952 seconds.

Why the significant difference in performance? According to jwe:

In Octave, an expression like 1:n creates a range object, which contains only the base, limit, and increment as double precision values, so no matter how many elements are in the range, it only takes a few bytes of storage (24 for the data plus some overhead for the internal octave_value object itself).

If you write [1:n], you force a Matrix object with N elements to be created. It will require 8*N bytes of storage, plus the overhead for the internal octave_value object itself.

Similar to the difference between range() and xrange() in Python.