High-level Interfaces for the Mad (matlab Automatic Differentiation) Package

Presently, the MAD Automatic Differentiation package for matlab comprises an overloaded implementation of forward mode AD via the fmad class. A key design feature of the fmad class is a separation of the storage and manipulation of directional derivatives into a separate derivvec class. Within the derivvec class, directional derivatives are stored as matrices (2-D arrays) allowing for the use of either full or sparse matrix storage. All manipulation of directional derivatives is performed using high-level matrix operations thus assuring efficiency. In this paper: we briefly review implementation of the fmad class; we then present our implementation of high-level interfaces allowing users to utilise MAD in conjunction with stiff ODE solvers and numerical optimization routines; we then demonstrate the ease and utility of this approach via several examples; we conclude with a road-map for future developments.