Implement low level accelerators for the GGCE backend

[matthewcarbone]

This is a major endeavor that will require a lot of work/thought. Essentially we want to do the following: Replace everything in ggce.models and ggce.engine.system with low level language accelerators. For example, by using pybind11 as a submodule we should be able to create Python-importable binaries.

As funny as it is, I think that the current solvers we use in NumPy, SciPy and (obviously) PETSc are faster than most of what we could try to get working in a lower level language! So for now, we can stick with those. But the steps of generating the basis are incredibly time-consuming and could be dramatically sped up.

This idea is still very much in the abstract but I want to document that we want to do it. I'm also closing #6 in favor of this, since this feature will do more than just generate the basis, it will also hook into the modules in e.g. ggce.engine.terms.

[Chiffafox]

This is really important. Having optimized basis construction -- dare I say, even a parallelizable one?? -- would make our code fully scalable and enable us to do crazy things.

[matthewcarbone]

Yeah it's not going to be straightforward though. I'm not super comfortable/familiar with building projects that are not pure Python. The good news is that whatever C++ code we use should be pure C++ plus pybind11 for the Python bindings, so we shouldn't have to worry about including a bunch of other header files or something.

That said, I am not entirely sure yet how to properly build the wheels for everything we'd need. If you have any ideas I'm all ears.

[Chiffafox]

Same here, I am not too experienced with this at the moment. That said, I'd definitely be keen to learn more about Python-C++ integration, so I'd love to work on this together if you think that would be helpful!

[matthewcarbone]

@Chiffafox your help on this would be amazing. Check out the new master branch. I've pushed the relevant build scripts (to scripts) and I use flit to build the package.

When we include C++ code for example, we will need to build that (make ...), then link it via pybind11, and somehow package all that into a wheel. The system dependencies gets a bit crazy at that point.

I am happy to write most of the C++ code (in fact we more or less already have a lot of it in GMA2 or whatever that old repo was), if you can help me figure out how to package it!

[matthewcarbone]

This looks extremely promising as a way to do exactly what we want: https://github.com/pybind/python_example