The important thing is which dimension will you be iterating with the greatest frequency?

PDL applies operations to whole piddles at a time. If you arrange your matrix so that the longest dimension is its first (leftmost) dimension, then the loop code at the assembler level is likely to be able to use auto-incrementing addressing modes, because the fastest changing dimension will be consecutive addresses. This will be faster, often much faster than if it has to add a large offset to calculate the next address each time. It will also likely benefit from greater cache coherency which again can have a significant impact upon performance.

So if all else is equal to your algorithm, make the first (leftmost) dimension of your piddle the largest. See also the documentation of PDL implicit and explicit 'threading'. It goes right over my head, but seems to be applicable to this discussion.

I'm not sure whether or not I will even be using any threading in the work I'll be doing. I'm mainly using PDL just so I can use matrix multiplication to make my equations simpler. However, I will keep your suggestion in mind, since I may end up using threading if possible to increase speed.

Note: The 'threading' I mentioned is not threading in the sense of multi-tasking, but rather implicit looping. Applying a single equation to a whole piddle, or slice of a piddle. The looping occurs within the PDL libraries rather than explicitly within your Perl program. This is where the greatest benefits of using PDL occur.

See the appropriate section of PDL::Indexing for more information.

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