User Guide for MAD - A Matlab Automatic Differentiation Package, TOMLAB/MAD, Version 1.4 The Forward Mode

Shaun A. Forth & Marcus Edvall 

Abstract 
MAD is a Matlab library of functions and utilities for the automatic differentiation of Matlab functions/statements via operator and function overloading. Currently the forward mode of automatic differentiation 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, control of dependencies,
• use of high-level interfaces for solving ODEs and optimization problems outside of the TOMLAB framework,
• differentiating black-box functions for which derivatives are known.

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