BibTeX
@ARTICLE{
         Forth2006AEO,
       author = "Shaun A. Forth",
       title = "An Efficient Overloaded Implementation of Forward Mode Automatic Differentiation in
         {MATLAB}",
       journal = "{ACM} Transactions on Mathematical Software",
       volume = "32",
       number = "2",
       pages = "195--222",
       year = "2006",
       URL = "http://doi.acm.org/10.1145/1141885.1141888",
       abstract = "The {\sc 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 {\tt 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 {\tt 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.",
       month = "jun",
       ad_tools = "TOMLAB /MAD"
}