Added real and Fourier space spliner base classes

[PicoCentauri]

As given in the title this PR adds two new base clases:

1. RealSpaceRadialIntegralSplinerBase
2. FourierSpaceRadialIntegralSplinerBase

With these base classes constructing (almost) any radial integral becomes quite easy. A developer/user only has to implement the method for her/his radial basis in a child class. The actual integral is performed numerically with quad. Also I added the option to (ortho)normalize the radial integral.

For RealSpaceRadialIntegralSplinerBase I added support for delta atomic densities and Gaussian atomic densities. The support for custom atomic densities is prepared, but the logic is missing. Since the integral is a more complex we should do this in an upcoming PR.

FourierSpaceRadialIntegralSplinerBase already works for any atomic density and radial basis.

TODO

I still have to document and test everything. Especially the equations for the radial integral should be added.

As a test I suggest that I add a GTO child class for LODE and SOAP and compare this to the analytical results which we already implemented in rust.

I would happy about some comments if the class structure makes sense and is understandable :-).

---

:books: Documentation preview :books:: https://rascaline--235.org.readthedocs.build/en/235/

[github-actions[bot]]

Here is a pre-built version of the code in this pull request: wheels.zip, you can install it locally by unzipping wheels.zip and using pip to install the file matching your system

[Luthaf]

Regarding the class structure, should we have separate classes for atomic density and basis functions instead of putting everyone inside the spliner? Something like

class GaussianDensity(AtomicDensityBase):
    ...

class DeltaDensity(AtomicDensityBase):
    ...

class RadiallyVaryingDensity(AtomicDensityBase):
    ...

class GTOBasis(RadialBasis):
    ...

class MonomialBasis(RadialBasis):
    ...

class RealSpaceSpliner():
    def __init__(self, density: AtomicDensityBase, basis: RadialBasis):
        ...

class KSpaceSpliner():
    def __init__(self, density: AtomicDensityBase, basis: RadialBasis):
        ...

This way RealSpaceSpliner and KSpaceSpliner can be concrete classes, and the users only need to customize the part they care about (density and/or basis).

---

A partially unrelated thing I find weird is making the abstractmethod functions private (starting with an _). If they are part of the abstract interface, they should be public IMO.

Which is also solved by the API above, using composition instead of inheritance for the density & basis functions!

[PicoCentauri]

Yes, we can split this up even more. Shouldn't we then use inheritance, i.e.

class GTORealSpaceSpliner(RealSpaceSpliner, GTOBasis, GaussianDensity):
    ....

[Luthaf]

I think composition is going to be much clearer than multiple inheritance here

[PicoCentauri]

Yeah might be. First of all if to fix the code that it is actually working. Currently, I run into infinite loops when doing the integrals.

[PicoCentauri]

@Luthaf sorry for the delay but I continued the work on the spliner classes. Splitting the AtomicDensities and the RadialBasis was a very good idea. Looks much cleaner now. There is still a lot of docs missing, but maybe you can another look?

The LODE part is already working and agrees with the analytical implementation that we did in rust as the test_fourier_space_spliner() is showing. 🥳

I will continue the work on the real space part next week.

[PicoCentauri]

After some rounds of debugging the implementation is working. The main and most important tests are testing that the Numerical implementation for the special case of GTOs + Gaussian densities agrees with the analytical implementation in rust for GTOs + Gaussian densities.

In addition I already added some more interesting densities and basis classes.

The theory part was written by @kvhuguenin 🙏. I just ported this from a LaTeX document to rst.

[PicoCentauri]

Thanks again for the feedback @Luthaf. If you want to give the docs another round of improvements I am happy if you provide a commit. Otherwise we can also proceed in another PR. This is already quite big...

[Luthaf]

CI error is pulling from host quay.io failed with status code [manifests latest]: 500 Internal Server Error, I'll try to re-run later.