The change in tutorial.rst is bigger than this PR. It used to state that input is always cast to float64 but that is no longer true. I think a better change to the tutorial would be to mention the rule (of thumb) that lets a user know if or if not the dtype will be changed. However, I don't know if there is a rule like that.

Can/should we add an example where the dtype is changed (in addition to the one that is there now where the dtype is preserved)?

Can/should we add an example where the dtype is changed (in addition to the one that is there now where the dtype is preserved)?

I don't think so because over time those remaining float64 only estimators might disappear and we don't want to have to find a new example each time we fix the one we used as an example in the tutorial.

I think that it is also worth adding a test to check that the fitted attributes are also 32 bits floating-point. This would not be covered by the common test.

I think that it is also worth adding a test to check that the fitted attributes are also 32 bits floating-point. This would not be covered by the common test.

And another test checking that the transformed arrays from float32 and float64 inputs are close up to some tolerance (from sklearn.utils._testing import assert_allclose).

I've added a test to check that the attributes are float32/float64 and that the results are allclose. Not sure if the allclose test is meaningful though, ideas for more realistic Xs to use?

Changed to global dtype and applied review suggestions.

I think this is ready to roll :D

Thanks for all the help and comments!