AMOR REPORT 2005/01 Source Transformation for MATLAB Automatic Differentiation

Abstract. This report describes MSAD, a tool that applies source transformation automatic differentiation to MATLAB programs involving arbitrary vector-valued functions. The transformed programs compute both the results of the original program and the first derivatives. The current version of MSAD performs a complete source transformation for the forward mode of AD by specialising and inlining operations from the fmad and derivvec classes of the MAD package. This implementation benefits by eliminating overheads due to operator overloading in MAD while preserving the optimised derivative combination operations from thederivvec class. MSAD also inherits from MAD the use of MATLAB’s sparse data-type to propagate directional derivatives. To aid the process of specialising routines during differentiation, a simple forward activity, shape and type propagation mechanism is used. Compared to MAD and the previous hybrid of source transformation and operator overloading approach in MSAD, we find a marked improvement in derivative computations using source transformation, even on large problem sizes. On most smaller problems we observe an order of magnitude savings over MAD. We have also tested the tool on several problems from the MINPACK-2, MATLAB ODE/optimisation and CWI IVP test suites, some of these results are presented here.