Remove checkeltype from Adjoint and Transpose

[andyferris]

Fixes JuliaLang/LinearAlgebra.jl#495 (and fixes #25271) and is a better design anyway.

The remaining (somewhat confusing) errors on ""' and [""]' are due to the current design of Adjoint, lowering of ', and so-on. I didn't want to mess with any of that at the moment while @Sacha0 is on such a roll, but my guess of one direction where this will end up is that we can reinstate adjoint and have a "user friendly" error message on adjoint(::Any) reminding users of permutedims. I'm sure there are other solutions too!

Note that this PR competes with #25272 and #25268.

[Sacha0]

I prefer your existing design: Insofar as we can check sanity of these wrapped objects on construction (and immediately emit a clear error message if that check fails), doing so seems preferable to allowing construction of nonsensical objects (and throwing a potentially less-clear error downstream if/when getindex gets called on the result, which may not occur). Thoughts? :)

[andyferris]

Ideally, I would like zero-overhead for these operations (I take adjoints of SVector{3} all the time, which was a no-op, and wouldn't want my geometry calculations to slow down). If we can do that without the pure annotation I'm OK... (honestly I didn't check this yet but I didn't love the checkeltype design - partly because it's easy to circumvent it (Expr(:new, ...) is just one way, there are others involving Refs, etc).

In either case we can add the ::T annotations to getindex. This should avoid breakage of the AbstractArray{T} contract.

(We can also just opt-in to adjoint and have a nice message for adjoint(::Any) to use permutedims, to make it user-friendly).

[Sacha0]

Ideally, I would like zero-overhead for these operations (I take adjoints of SVector{3} all the time, which was a no-op, and wouldn't want my geometry calculations to slow down). If we can do that without the pure annotation I'm OK... (honestly I didn't check this yet

Hopefully the annotation was not necessary for compile-time evaluation of the check :).

[JeffBezanson]

Bump.

[dkarrasch]

Is this still of interest? I applied the same changes to the current master, and the only tests that fail are those where the Adjoint/Transpose constructors are called directly with mismatching types, rather than calling adjoint or transpose. I'd think package authors/users would overwrite adjoint and transpose and, in case they use the wrapper types, make sure the eltype determination is correct?

[vtjnash]

Yes, if you rebase this, I'll approve and merge