Implement a uniform interface to automatic differentiation libraries

[jppelteret]

This commit adds the classes that give users a uniform interface to the Adol-C and Sacado automatic differentiation libraries. Also added are a selection of tests that give a indication of how the classes are used. I have many other tests that verify the actual implementation (about 27 other tests for Adol-C and 14 for Sacado), but I reckon that those are best left to another PR.

TODO list:

• Doxygen documentation must be finished (include code snippets)
• Documentation must be checked for relevance (it was written before I added support for Sacado)
• Change lazy implementation of assertions (ExcInternalError) where applicable
• Ensure that there is verification of mechanisms put in place to prevent data corruption / initialisation errors work correctly for all number types (maybe for the next PR with other tests).

[bangerth]

Uh, that's about 5000 new lines of code! I'm afraid that's beyond my ability to review for the next few weeks. Does anyone else have the necessary expertise? (Which, in fact, I don't actually have -- knowing very little about AD...)

[bangerth]

you're in a header file -- just leave these things in the internal namespace, instead of an anonymous one

[jppelteret]

Fair enough. I didn't realise it was quite so much. Would you prefer me to add one class at a time (there's 1 main base class and 4 derived)? Either way, I just wanted to put this out there before I go on holiday next week -- I probably couldn't attend to many comments during December anyway. I planned to spend that time extending the documentation.

[bangerth]

I don't have a good solution. I just don't have the time to review such a massive amount of code, regardless of how it is packaged, in the near future :-) I'm hoping that others can look at least at parts.

[jppelteret]

Ok, well let's collectively come up with a plan on how we can best tackle this. But tomorrow or sometime later though ;-) I'm really not in a rush to get this in since I've got plenty to keep me busy too.

[jppelteret]

I've decided to close this PR, and instead I'll focus on tidying up the documentation and implementation during the upcoming vacation. I'll then try to figure out how to introduce all of this in smaller chunks. I can always refer back to this closed PR to give context to what I'm doing.

[bangerth]

OK. But I do think this is great work that should be merged. Please don't take my lack of time to review as lack of appreciation for your work!

[jppelteret]

OK. But I do think this is great work that should be merged. Please don't take my lack of time to review as lack of appreciation for your work!

Thanks! I do intend on pushing forward with this. It didn't strike me that the first commit was going to be as large as it was, because in my head I have packaged these PR in the smallest logical chunks. So, I must apologise for that. I was also hoping to get some general feedback on the overall structure of the code, in case it was expected that I overhaul the implementation in some massive way.

Anyway, I'm busy stripping out some of the code into smaller pieces to be submitted individually. I'm not sure that they'll make sense without the full context, but lets try anyway :-)