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An Implementation of the Forward and Reverse Mode in Maple

SYNOPSIS:

GRAD is a Maple procedure that automates the implementation of the forward and reverse modes of derivative computation on existing Maple procedures.

WHOM TO CONTACT:

Michael B. Monagan
Department of Mathematics and Statistics
Simon Fraser University
Burnaby, B.C. V5A 1S6
Canada
Tel: (604) 291-4279
email: monagan@cecm.sfu.ca

FUNCTIONALITY:

GRAD takes an existing Maple procedure as input and produces a procedure that calculates derivative information as determined by the user. The returned procedure is a new procedure that does not reproduce the original procedure, but is capable of providing derivative information. The user specifies the derivatives and sensitivities to calculate as well as whether to apply the forward or reverse mode.

HIGHLIGHTS:

We have attempted to support a wide class of mathematical procedures that the user would input directly or would be created by Maple automatically. GRAD handles Maple procedures containing

control statements: assignments, if, for, while, next, break, RETURN, ERROR
print statements: lprint, print, printf, etc.
data structures: lists, arrays
recursive calls and calls to local and global procedures

Grad can differentiate formulae containing

any mathematical function known to Maple, including integrals and sums
any mathematical function for which the user has defined its derivative
any unknown function (the differential operator D is used)

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