spezialized conj of Transpose/Adjoint

[simeonschaub]

I brought this up on Slack and it received quite positive feedback, so I put this together as a PR. The implementation is very minimal. Two things to maybe think about:

• For AbstractArray{<:Real}, conj is generally a no-op, this breaks this assumption. We still differentiate between Adjoint and Transpose for real matrices though, so I think this is fine.
• Do we want something similar for broadcasted conj? – Probably not worth it?

I am also not quite sure, how breaking one should consider this change. It will definitely break code, that relies on conj returning a copy here.

[StefanKarpinski]

Clever. This makes sense to me (although it took me a second).

[dkarrasch]

LGTM. I don't have own experience with the lazy vs copy issue of conj. At some point, @andreasnoack suggested to consider to introduce a lazy conj type, in the style of Adjoint and Transpose. This PR kind of introduces that for a very specific situation. Everywhere else, conj does create a copy, and people might rely on that, but I don't know how to check that. OTOH, many people who care seem to be in favor of it, so why not.

[simeonschaub]

Thanks for the quick review, @dkarrasch! I've added another test case, that checks, whether we do the right thing for custom matrix types, that have a different implementation for adjoint. The lazy Conj idea is something that occurred to me as well. (You can kind of have that with adjoint(transpose(A)), but that's definitely not an efficient way.) Would make for some more symmetry, so I might open an issue at some point.

[kshyatt]

Win32 failure is a no-output timeout. Is this good to go?

[dkarrasch]

I think so, from the code point of view. The question is whether someone with an actual working experience with complex linear algebra should step up and make a personal statement regarding the lazy vs. copy aspect?

[andreasnoack]

I think this is fine. We generally try to avoid copies and ask people to rely on implicit copies.