feat: Added numerical integration of generic functions

[s-kuberski]

I have added a routine that allows to numerically integrate a one-dimensional function using scipy.integrate.quad. The parameters of the function, as well as the integration bounds, may be Obs.

@fjosw: I was not completely sure about the magic that is applied when constructing the derived_observable maybe you can check it, the current version seems to do the correct thing.

I think the tests should check the relevant cases as one can very nicely compare the numeric with the analytic integration. I hope that I did not overlook any edge case.

[fjosw]

Looks good! I will do some explicit testing later.

Concerning the interface I would maybe propose to have a separate submodule integrate and then to rename the new function to quad to mimic the scipy interface. This would also make room for potential future implementations of other integration methods.

[s-kuberski]

Thanks for looking into it. I refactored the code and added the new module.

[fjosw]

I played around a bit with the new function and everything looks good.

I made a small correction to the docstring and added two more trivial test cases.

[s-kuberski]

There is one case, where this routine fails, namely when no Obs is involved, at all. In this case, derived_observable throws an exception.
One could circumvent this by adding

if len(derivint) == 0:
    return integration_result

before constructing the derived observable, but maybe you have something smarter in mind?

[fjosw]

There is one case, where this routine fails, namely when no Obs is involved, at all. In this case, derived_observable throws an exception. One could circumvent this by adding

if len(derivint) == 0:
    return integration_result

before constructing the derived observable, but maybe you have something smarter in mind?

That sounds like a good solution, do you want to quickly push it?