24 October 2006

Updated Scheme Code for Derivatives

I've updated my functional differential geometry code to use the same techniques I've been writing about these past few days in OCaml for computing derivatives. It should (haven't rigorously tested this) improve the performance of computing structure constants (which involve the commutator of two tangent vectors in the group, and therefore taking second derivatives, and therefore multiple tags in the derivative objects, which the tree structure handles more efficiently) and anywhere else in the code where I need multiple derivatives. Issuing darcs get http://web.mit.edu/farr/www/SchemeCode/ should get the new version, or you can just download the code at that web address. Scheme can really be a breath of fresh air (compare the implementation of the macro define-binary-derivative in derivatives.ss to the repeated pattern which appears in the OCaml code), but the performance leaves something to be desired for large-scale numerical work. (The OCaml code runs *much* faster than the Scheme code, and still takes a couple of hours to measure the non-symplecticity in a 25-body simulation.)

As always, comments from my user(s?) are definitely welcome at farr@mit.edu.

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