Sparse jacobian computation in automatic differentiation by static program analysis

Abstract

A major diffculty in quickly computing Jacobians by Automatic Dierentiation is to deal with the nonzero structures of sparse matrices. We propose to detect the sparsity structure of Jacobians by static program analysis. The method consists in traversing the data dependence graph extended with the control-flow of the program and computing relations between array regions. Then, we safely extract informations about the dependences from program inputs to program outputs. The generation of the derived program uses these informations to produce a better result. We eventually, introduce the Automatic Differentiation tool Odyssfee and present some benchmark tests. © 1998 Springer-Verlag Berlin Heidelberg.