An Efficient overloaded implementation of forward mode automatic differentiation in MATLAB

Abstract

The Mad package described here facilitates the evaluation of first derivatives of multi-dimensional functions that are defined by computer codes written in MATLAB. The underlying algorithm is the well-known forward mode of automatic differentiation implemented via operator overloading on variables of the class fmad. The main distinguishing feature of this MATLAB implementation is the separation of the linear combination of derivative vectors into a separate derivative vector class derivvec. This allows for the straightforward performance optimisation of the overall package. Additionally by internally using a matrix (two-dimensional) representation of arbitrary dimension directional derivatives we may utilise MATLAB"s sparse matrix class to propagate sparse directional derivatives for MATLAB code which uses arbitrary dimension arrays. On several examples the package is shown to be more efficient than Verma"s ADMAT package.© ACM, 2006. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Mathematical Software (TOMS) Volume 32 , Issue 2 (June 2006) 195 - 222, 2006 ISSN:0098-3500 http://doi.acm.org/10.1145/1141885.1141888