More numerical unit tests

[yoricklassmann]

I think we should be more thorough with unit tests, especially when it comes to the numerics. For example, in the case of the OverlapModule, it would be nice to verify that the numerical gradient of the overlap with respect to the momentum of the ket Gaussian equals the analytical integral within some acceptable threshold. I say this not because I somehow doubt the implementation, but because we should really enforce this kind of behavior in the future. Whenever someone implements a new integral or other small formula, I think they should be required to add a unit test to verify the implementation is correct. @danielhollas do you have any opinions on this?

[danielhollas]

@yoricklassmann definitely agree! In fact we discussed doing exactly that with @adamjharrison when he implemented his SPA1 integrals, but I think in the end we ran out of time, He did a verification against Wolfphram alpha, as documented in #7

[yoricklassmann]

I remember reading that yes, I think that's already a good enough check indeed. I just wonder how we could streamline the process. If you want I can add some unit tests for the integrals, just to get us started.

[danielhollas]

If you want I can add some unit tests for the integrals, just to get us started.

Sure, it would be nice to have an example unit tests that others could then take as a template. Thanks!

[danielhollas]

Possibly interesting series of articles about unit testing:
https://matthiasnoback.nl/tags/unit-testing/