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recommend robust method for iteratively calculated functions #170
Description
I have a computation that solves an implicit equation using iterative numerical methods (bisection, Brent, etc). I would like to use FiniteDifferences.jl for unit testing partials I write for ChainRulesCore.
The problem is that since the calculated function is not technically continuous, using eg central_fdm(5, 1) gives me bogus results (occasionally off by a factor of 5--10). I had some success with a high number of grid points, eg central_fdm(20, 1), but too much adaptation (eg 2 steps) makes things go bad again.
I would appreciate recommendations on how to deal with this in a robust way for unit testing. Since it is for testing, it does not have to be super-fast, just robust.
Activity
wesselb commentedon Jun 4, 2021
Hey @tpapp,
How do the results look like it you set
factorto a high number, e.g.central_fdm(5, 1; factor=1e4)?tpapp commentedon Jun 4, 2021
Improved, compared to
central_fdm(5, 1), butcentral_fdm(20, 1)is still better (2-3 digits more accuracy).factor = 1e6works fine though. Is that what I should do in this case, instead of more gridpoints?wesselb commentedon Jun 4, 2021
If
factor=1e6works fine, then that would be the more robust solution, I think.factorcontrols how much error derives from the function evaluations and is relative to the machine epsilon. You can even try something likecentral_fdm(10, 1; factor=1e6).oxinabox commentedon Jun 4, 2021
Aside: If you are not already I recomment using ChainRulesTestUtils, which wraps FiniteDifferences.jl.
The default fdm in ChainRulesTestUtils is
central_fdm(5, 1; max_range=1e-2)That might not work for you (you can pass your own fdm into
test_rruleto overwritewesselb commentedon Jun 8, 2021
Hey @tpapp! Would you be able to confirm whether you've found a satisfactory way to compute finite differences? If so, we'll add a recommendation to the README. :)
tpapp commentedon Jun 8, 2021
@wesselb: I am in the process of finishing up the unit tests for the relevant package, it seems to be working for now but I will get back here once I am done.
wesselb commentedon Jun 8, 2021
Thanks for responding quickly! No need to rush at all, of course. :)
tpapp commentedon Jun 8, 2021
@wesselb: I am done, and I can confirm that
central_fdm(5, 1; factor = 1e6)works reasonably for my purposes. I can even combine it withmax_rangeto bound away from singularities.You may close this issue, or keep it as a reminder for the readme change if you prefer.
Thanks for all the help everyone. I appreciate it, and also this great package.
wesselb commentedon Jun 10, 2021
That's fantastic to hear! I've opened a PR to add a small section to the README (#174).
tpapp commentedon Sep 29, 2025
This was closed by #174.