Automatic Differentiation for MATLAB Programs

Abstract

Derivative information is required in numerous applications, including sensitivity analysis and numerical optimization. For simple functions, symbolic differentiation–done either manually or with a computer algebra system–can provide the derivatives, whereas divided differences (DD) have been used traditionally for functions defined by (potentially very complex) computer programs, even if only approximate values can be obtained this way. An alternative approach for such functions is automatic differentiation (AD), yielding exact derivatives at often lower cost than DD, and without restrictions on the program complexity. In this paper we compare the functionality and describe the use of ADMIT/ADMAT and ADiMat. These two AD tools provide derivatives for programs written in the MATLAB language, which is widely used for prototype and production software in scientific and engineering applications. While ADMIT/ADMAT implements a pure operator overloading approach of AD, ADiMat also employes source transformation techniques.