This is an annoying case here.

Supposedly, we should be raising an error if both sparse and sparse_output are set to non-default values. However, to detect it we need to add a None option to sparse_output that defaults to True by default. However, we don't want None and we also need to depreciate it at the inclusion such that we remove it. It means that in practice we will always be raising a warning and force users to set it to a bool.

@jeremiedbb I recall that we had a similar pattern somewhere else (DictionaryLearning of NMF). How did we do it?

@lorentzenchr @thomasjpfan do you see a better way?

To keep it simple, I would raise in the following case

if self.sparse != "deprecated" and self.sparse != self.sparse_output:
    raise ValueError("Some informative message")

This doesn't work because you don't want to raise when the user sets sparse to a value different than the default of sparse_output.

To me the appropriate way is to do as explained in our docs, i.e. if a user sets sparse we raise a warning saying that it's deprecated and that sparse_output should be used instead and is ignored, and then use the value of sparse.
We don't really need to raise when both are set, the future warning is enough

To keep it simple, I would raise in the following case

if self.sparse != "deprecated" and self.sparse != self.sparse_output:
    raise ValueError("Some informative message")