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I haven't looked at this in detail yet. Do you think CUSOLVER_Randomized should be a valid argument for svd_full! given the warning note in the doc string? Wouldn't this make more sense as a svd_trunc! algorithm ?

Could well do better there since for best performance/accuracy k should be much much smaller than min(m,n). I can switch it in the morning.

The reason I didn't do this at first I think is that Xgesvdr expects U, S, and V to be full sized, which is rather annoying...

I do have somewhere on my todo list to make the check_input function also take the algorithm, would that help here?

I think I agree with Jutho though, that this might make more sense as an svd_trunc implementation, with some restrictions on the possible truncation strategies of course.

If we can modify check_input then that seems fine to me! I could do that as part of this PR, even?

CI does now run!