On Thu, 14 Jan 2010 09:29:33 -0600, Barry Smith <bsmith at mcs.anl.gov> wrote: > Do you want this so you know when the function is being called > directly vs when it is being called in computing a Jacobian derivative > with finite differencing? Do you want the function to do something > different in the two cases?
Actually, here's a use case where it would be good to know. Suppose that F does some caching of intermediate quantities needed to apply J, or that make assembly of J cheaper. For example, I apply full-accuracy Jacobians unassembled, and assemble something else for preconditioning. But suppose I wanted to use a preconditioning matrix computed by coloring, that perhaps also discards some coupling. For example, we might precondition a 3-component STENCIL_BOX discretization with STENCIL_STAR where inter-field coupling has been discarded [1]. Since I have a fast full-accuracy Jacobian, I wouldn't want to use the inexact thing as the real Jacobian, and caching the intermediate terms isn't a lot of work, but it might add 20% to the cost of evaluating F(x) and thus be worthwhile if the line search typically needs less than 5 steps or so. But perhaps more importantly, if I'm recaching J while computing the preconditioner with FD, then J will be evaluated at x+eps*y instead of at x which may hurt quadratic convergence. Jed [1] STENCIL_STAR preconditioning isn't just hypothetical, I have a nice 2D p-Laplacian example where -snes_mf_operator with STENCIL_STAR preconditioning beats the analytic (STENCIL_BOX) Jacobian in every measure.
