Perform gradient checks for SBML test suite

[dweindl]

Motivated by #1230

Should be done for both forward and adjoint sensitivities (#18).

[paulstapor]

We used to have an FD implementation with automatic step-size detection in PESTO. maybe it would be good to have something like that as a little python file/package also within AMICI? This way, pyPESTO could use it right away, because this would also be helpful there...
Alternatively: Would it make sense writing a C++ code for that? Maybe this could save some cpu time... Ideally by exploiting openMP...
I would also be happy trying to code something for this in Rust. However, I doubt it's advisable to mingle the AMICI source code with another compiled language... 🤔

[yannikschaelte]

FD with automatic step-size should definitely be implemented, not sure whether it makes more sense in AMICI or pyPESTO (where the final objective function is defined) 🤔

[paulstapor]

Depends on the definition of "final"... Would argue for AMICI:

• I think we can assume priors to be correctly implemented, so it should suffice to care about the AMICI part
• We want to use this also for sbml-only models, where no PEtab whatsover is involved...
• Still, one could write it in Python... However, I think there will be some (little) computational benefit of doing it in C++. When doing this for >1000 models in the SBML test suite, this benefit might be desirable...

[dweindl]

For me also fine to have that as a (tiny) separate package. Might be useful elsewhere. Good if it's usable in pyPESTO without having to install AMICI. And I'd strongly argue for not creating circular dependencies between AMICI and pyPESTO, so rather not putting it into pyPESTO.

Regarding C++ vs Python: I'd guess that the benefit of using C++ there is not big enough to justify two implementations, once in C++ for AMICI stuff and once for in Python for functions beyond single AMICI simulations.

[FFroehlich]

https://github.com/wesselb/fdm might help with this