Fast Automatic Differentiation Jacobians by Compact LU Factorization

Abstract

For a vector function coded without branches or loops, a code for the Jacobian is generated by interpreting Griewank and Reese's vertex elimination as Gaussian elimination and implementing this as compact LU factorization. Tests on several platforms show such a code is typically 4 to 20 times faster than that produced by tools such as Adifor, Tamc, or Tapenade, on average significantly faster than vertex elimination code produced by the EliAD tool [Tadjouddine et al., in Proceedings of ICCS (2), Lecture Notes in Comput. Sci. 2330, Springer, New York, 2002] and can outperform a hand-coded Jacobian. The LU approach is promising, e.g., for CFD flux functions that are central to assembling Jacobians in finite element or finite volume calculations and, in general, for any inner-loop basic block whose Jacobian is crucial to an overall computation involving derivatives.