Fast Ad Jacobians by Compact Lu Factorization

For a vector function, coded without branches or loops, 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 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 LNCS vol. 2330, 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.