Use finite-differences where forward-mode not implementable
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- C++
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Description
Description
As discussed over in #2839, the ODE methods are not fvar<T> compatible, and it would be a significant amount of work to do so. This means that any downstream methods depending on fvar<> or higher-order autodiff will fail to compile, a current example of this is the new $hessian() method in cmdstanr.
In these instances it would be great to have a method that "works", even if it's slow - better to have in a limited form than to not have at all (imo).
Boost Math has existing optimised routines for finite-differencing, including the use of the complex step approximation for any complex-compatible functions (allowing for estimating the derivative with a single function evaluation)
Current Version:
v4.4.0
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Start by reviewing the ODE compatibility discussion in #2839 and Boost Math's finite-difference and complex-step documentation. Identify which ODE methods need a fallback for higher-order autodiff, then verify that a downstream use such as cmdstanr's $hessian() works where forward mode is unavailable.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- cpp
- Domain
- backend
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Mostly clear
- Newbie friendliness
- 25/100