Implementing automatic differentiation efficiently

摘要

The automatic differentiation of computer arithmetic has been investigated since before 1960. Most of this effort has been centered on the forward mode of derivative evaluation. Speelpenning, Iri and Kubota, and Horwedel et al. have all implemented the more efficient reverse mode of evaluating derivatives in their respective Fortran precompilers. The reverse mode requires information about a computation to be stored in order that derivatives may be calculated after the function evaluation has been completed. This additional storage cost may be prohibitive. The goals of our research have been to implement an automatic differentiation package that gracefully handles the storage issue and to generate a parallel implementation of derivative evaluation in the reverse mode. This paper discusses results of both research efforts, specifically those involving the ADOL-C package. 10 refs., 4 figs.