metatensor-operations finite difference test for add

[agoscinski]

This PR adds utilities for doing finite difference tests for the metatensor-operations and uses them in the simple example of the add operation.
This is the first PR addressing issue #84
The idea of the testing utilities originates from issue #469

In the next run on this PR I want to dispatch the testing utilities so they can also be used for torch, but before that I would like to have some general feedback if this is going in a good direction.

TODOs:

• The documentation is still needs some work. Also would add the testing utils to the doc.
• function cartesian_linear needs to be implemented

Contributor (creator of pull-request) checklist

• Tests updated (for new features and bugfixes)?
• Documentation updated (for new features)?
• Issue referenced (for PRs that solve an issue)?

Reviewer checklist

• CHANGELOG updated with public API or any other important changes?

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📚 Documentation preview 📚: https://metatensor--479.org.readthedocs.build/en/479/

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[github-actions]

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

[DavideTisi]

very good i think it is also very clear

[Luthaf]

How about

Suggested change

	function: Callable[[Union[np.ndarray, TorchTensor], bool], TensorMap],
	function: Callable[[TensorMap], TensorMap],

And then in this function define

def full_function():
    data = cartesian_cubic()
    return function(data)

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This should remove a lot of assumptions from the API!

[Luthaf]

ah, we potentially need multiple inputs:

Suggested change

	function: Callable[[Union[np.ndarray, TorchTensor], bool], TensorMap],
	function: Callable[[TensorMap, TensorMap], TensorMap],

and give the function two different random inputs (the function is free to ignore one of them for e.g. pow). Ideally two inputs with different set of gradient samples would be nice, but we can start with identical set of gradients.

[agoscinski]

I will try it out to see how well this works.

[agoscinski]

I am not sure about the two TensorMap's as input as I don't see for the momemt what kind of bugs this could catch which are not covered by the current version, and adding support for two tensor maps makes everything a bit more cumbersome. The idea in the current implementation is that you still can create two different sets of gradients that inherit from the same input, so the finite difference test is easier to perform. In the test for add we first create two different gradients by applying cartesian_cubic and cartesian_linear on this input to then pass it the TensorMap to add. So we are testing this add(f(X), g(X)). I am not sure what kind of bug add(f(X), g(Y)) would catch in addition.

What I see is missing in the current design is a way to also test operations that affect the samples as sort and reduce over samples does.