Citation:
10th International Conference on Computational Science, University of Amsterdam,
The Netherlands, http://www.iccs-meeting.org/iccs2010/. The paper has been
submitted to the conference's workshop on Automated Program Generation for
Computational Science http://www.sc.rwth-aachen.de/Events/APGCSatICCS2010/
Abstract:
We review the extended Jacobian approach to automatic di erentiation of a user-
supplied function and highlight the Schur complement form's forward and reverse
variants. We detail a Matlab operator overloaded approach to construct the
extended Jacobian that enables the function Jacobian to be computed using
Matlab's sparse matrix operations. Memory and runtime costs are reduced using a
variant of the hoisting technique of Bischof (Issues in Parallel Automatic Di
erentiation, 1991). On ve of the six mesh-based gradient test problems from The
MINPACK-2 Test Problem Collection (Averick et al, 1992) the reverse variant of
our extended Jacobian technique with hoisting outperforms the sparse storage
forward mode of the MAD package (Forth, ACM T. Math. Software. 32, 2006). For
increasing problems size the ratio of gradient to function cpu time is seen to
be bounded, if not decreasing, in line with Griewank and Walther's (Evaluating
Derivatives, SIAM, 2008) cheap gradient principle.
