An automatic differentiation system, GRAD, is described. Given a Fortran subprogram for computing a function, it generates a subprogram that computes partial derivatives. The APL computer language was used in the implementation.
The performance of automatic differentiation in fitting growth models for intensively managed forest plantations is examined. The models consist of a system of stochastic differential equations, and parameters are estimated by maximum-likelihood using a general-purpose variable-metric optimization procedure. Compared to central difference approximations, the use of derivatives generated by GRAD in the optimization reduced computing time by a factor of 4 on an 80386/80387 microcomputer and by a factor of 6 on a MicroVAX 3500. GRAD was found superior to JAKEF in this type of problem.
GRAD combines the forward mode of automatic differentiation with symbolic manipulation. A conceptual framework capable of describing these hybrid strategies is presented, and their advantages are discussed.
Keywords: Automatic differentiation, symbolic differentiation, computer algebra, statistics, estimation, optimization, forestry, maximum-likelihood, stochastic differential equations, APL, GRAD, JAKEF.