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I see that there are failing tests due to .conj() not being part of the array API. Could possibly fix this by replacing with xp.conj().

Not sure how this would play with array API (cc @OmarManzoor on that), maybe @antoinebaker could check the implementation?

This would also need a changelog.

Thanks for the comment @adrinjalali! I added a changelog entry. Lmk if you need anything else.

I'm not sure that we should include this fix. We've never officially supported complex numbers in any estimator or function. I understand that the fix is small but it would open a door that I don't think we want to open and we've rejected several small fixes like this one in the past.

In addition, note that the fact that it almost worked is the result of randomized_svd not properly validating its input. It's not using check_array as it should imo, and if it did, the function would error early on complex input.

Thanks for the comment @jeremiedbb. I think your point is fair. I get that general support for complex valued data across scikit-learn is out of scope. E.g. #10422 related to complex pca. My argument to include the fix is that it is small, it applies only to a relatively low level utility function (i.e. not a major estimator like PCA), and it makes the behavior of the function more consistent with the standard reference scipy.linalg.svd. Also, I intentionally did not edit the docs to advertise the complex data support, to reduce the risk of expanding the scope more in the future.

At the same time, I get that including the fix creates more surface area for testing, and sets a potential precedent for people to request more complex data support later. So I totally get if you all decide not to include it.

Thanks for the PR @clane9.

The implementation seems okay but I agree with @jeremiedbb that we should probably not support complex inputs in randomized_svd, perhaps raise an error and update the docstring.

I also agree, but since randomized_svd is part of the public API, we should do proper input validation to reject this kind of data explicitly (while also introducing a private version to avoid double input validation).

Ok, sounds good, looks like the consensus is to not include this fix. No worries. My thought then is to close this PR and open a new one with added input validation to reject complex valued data. Thoughts?

Thanks again @clane9. If you want to, you can still publish ComplexPCA and other estimators with complex input support as a scikit-learn-contrib project.

For sure, I will look into that! Thanks for the pointer @antoinebaker. But ok, going ahead and closing.