Octave and Matlab tricks
Below are notes on a few programming issues that crop up a lot. You might also want to check out my much longer page on efficient Matlab/Octave programming. See also Tom Minka’s lightspeed Matlab toolbox. (Personally I’ve stuck with an old version of lightspeed, which has a more liberal MIT-style license.) Also see my own modest toolbox of Octave/Matlab code.
Not all vectorizations are equal:
Terrible: A = trace(V*V'); % I have been guilty of this(!)
Better: A = sum(sum(V.*V));
Best: A = V(:)'*V(:);
Don’t compute things you don’t need (if you can help it). Check .*’s inside sums to see if they can be changed into a * without the sum.
Not great: w = inv(X)*y;
Better: w = X\y
See also functions in Lightspeed.
Inefficient for huge matrices: X = X + diag(y); % where y is a vector
Better: X = plus_diag(X, y);
Debugging out-of-bound numbers:
dbstop if naninf; will let you catch NaN’s and Inf’s at source. Caveats: naninf does not work in Octave yet and in Matlab only works for functions, not scripts.
Complex numbers are also a pain when not intended. Get log and sqrt to throw errors rather than create complex numbers with: log=@reallog; sqrt=@realsqrt; — in octave you'll have to provide reallog.m and realsqrt.m.
If memory is too tight for a naive repmat: have a look at bsxfun, it may be useful. The alternative is to start chunking the operation up in loops, or writing mex files. Having a new standard Matlab function (now in Octave too) for avoiding this mess is nice.
Actually, use bsxfun routinely: I have found it very useful; bsxfun often gives cleaner, faster code than using repmat. If you send your code to someone with an old version of Matlab, they can use this simple replacement, which is implemented with repmat.
Update 2019: you don't need bsxfun either: both Matlab and Octave have now supported broadcasting for a while, making bsxfun crufty line-noise of the past.