User guide for MAD - a Matlab automatic differentiation toolbox

Mad is a Matlab library of functions and utilities for the automatic differentiation of Matlab func-tions/statements via operator and function overloading. Currently the forward mode of automatic differentia-tion is supported via the fmad class. For a single directional derivative objects of the fmad class use Matlab arrays of the same size for a variable’s value and its directional derivative. Multiple directional derivatives are stored in objects of the derivvec class allowing for an internal 2-D, matrix storage so allowing the use of sparse matrix storage for derivatives and ensuring efficient linear combination of derivative vectors via high-level Matlab functions. This user guide covers: • installation of Mad on UNIX and PC platforms, • using TOMLAB /MAD, • basic use of the forward mode for differentiating expressions and functions • advanced use of the forward mode including: – dynamic propagation of sparse derivatives, – sparse derivatives via compression, – differentiating implicitly defined functions