ADF95: Tool for automatic differentiation of a FORTRAN code designed for large numbers of independent variables

TL;DR

ADF95 is a FORTRAN tool that automatically computes accurate derivatives for complex functions with many variables, requiring minimal code changes and offering high efficiency especially for sparse systems.

Contribution

It introduces a new data type and operator overloading techniques for automatic differentiation in FORTRAN, optimizing memory and performance for large-scale problems.

Findings

Achieves derivatives within machine precision.

Reduces memory usage compared to existing tools.

Provides significant performance improvements for sparse systems.

Abstract

ADF95 is a tool to automatically calculate numerical first derivatives for any mathematical expression as a function of user defined independent variables. Accuracy of derivatives is achieved within machine precision. ADF95 may be applied to any FORTRAN 77/90/95 conforming code and requires minimal changes by the user. It provides a new derived data type that holds the value and derivatives and applies forward differencing by overloading all FORTRAN operators and intrinsic functions. An efficient indexing technique leads to a reduced memory usage and a substantially increased performance gain over other available tools with operator overloading. This gain is especially pronounced for sparse systems with large number of independent variables. A wide class of numerical simulations, e.g., those employing implicit solvers, can profit from ADF95.