The MAD (MATLAB Automatic Differentiation) Project

Investigators:

• Dr Shaun Forth, Cranfield University (Shrivenham Campus), School of Defence Technology, UK

Introduction:

Automatic Differentiation (AD) software tools are available for a range of programming languages (see list at www.autodiff.org), but progress on developing AD tools for MATLAB has been much slower. 

Project Aim: In this project we aim to carefully implement the standard (and hopefully not so standard) algorithms of AD by operator overloading in MATLAB.  We will pay particular attention to achieving good performance and robustness so that the software can be used on genuine applications and not just carefully coded test cases.

Progress:

•  We have implemented the standard forward mode of AD via operator overloading in the fmad class with linear combinations of directional derivatives performed by the optimized derivvec class.  Details may be found in An Efficient Implementation of Forward Mode Automatic Differentiation in MATLAB and the User Guide.
• In collaboration with the TOMLAB company, we have integrated MAD into TOMLAB's suite of optimization software for MATLAB. 
• We are working with Prof. Larry Shampine on investigating the integration of MAD into the ODE solvers provided by MATLAB. See the ADenODES project for more details.

Journal Papers:

• An Efficient Implementation of Forward Mode Automatic Differentiation in MATLAB, Shaun A Forth, ACM Transactions on Mathematical Software (TOMS) Accepted (August 2005).
• Using AD to solve BVPs in MATLAB, Larry F. Shampine, Robert Ketzscher & Shaun A Forth, ACM Transactions on Mathematical Software (TOMS) Volume 31, Issue 1 (March 2005), pp 79-94.

Conference Papers:

• High-Level Interfaces for the MAD (Matlab Automatic Differentiation) Package , Shaun A Forth & Robert Ketzscher, 4th European Congress on Computational Methods in Applied Sciences & Engineering (ECCOMAS).
• Improved Fitting of Constrained Multivariate Regression Models using Automatic Differentiation , Trevor J Ringrose & Shaun A Forth, Published in 
  Proceedings of the 15th Symposium on Computational Statistics.

User Guide

• User Guide for MAD - A Matlab Automatic Differentiation Package, TOMLAB/MAD, Version 1.2 The Forward Mode, Shaun Forth and Marcus Edvall.

Software Availability:

The MAD package is available for academic and commercial use for a modest license fee (after a 21 day trial) from the TOMLAB company at www.tomopt.com. 

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