Introduce AdjointFactorization not subtyping AbstractMatrix

[dkarrasch]

I have long been bugged by the fact that, on the one hand, you can wrap anything by Adjoint, even types that don't subtype to AbstractMatrix, but once wrapped, they are back in the AbstractMatrix hierarchy. It turns out that this subtyping basically doesn't lead to any usage of fallbacks, except for size(::Adjoint{Factorization}, ::Int)! So, this disentangles that, and even restricts Adjoint/Transpose to wrap only AbstractVecOrMat, which is not necessary. Anyway, it shows that it can be done. Obviously, this is breaking, but I assume it breaks only a few basic packages, but we'll see in a nanosoldier run.

This is a "companion" PR to #46196 and #46233.

[dkarrasch]

😉

[dkarrasch]

@nanosoldier runtests(ALL, vs = ":master")

[dkarrasch]

I guess if we don't restrict Adjoint to AbsVecOrMat, then this is actually "not" breaking (unless people define functions for Adjoint{<:Any,<:F} where F is a subtype to some factorization from LinearAlgebra). I see usage as in GenericLinearAlgebra for Householder and HouseholderBlock, which both don't subtype to AbstractMatrix, even though their behavior is "matrix-like", e.g., size(H, i) returns 1 if i > 2. If we wanted to restrict Adjoint to AbsVecOrMat, what would we do with Householder[Block]? (1) Introduce a minimal AdjointHouseholder type? (2) Subtype Householder <: AbstractMatrix? Or is that an indication that we shouldn't add the restriction? Do we care that Adoint{Householder} is an AbstractMatrix? @andreasnoack

[dkarrasch]

@nanosoldier runtests(ALL, vs = ":master")

[nanosoldier]

Your package evaluation job has completed - possible new issues were detected. A full report can be found here.

[dkarrasch]

@nanosoldier runtests()

[nanosoldier]

Your package evaluation job has completed - possible new issues were detected.
A full report can be found here.

[dkarrasch]

I believe the ecosystem is ready for this. Shall we wait until all PRs are merged and run another pkgeval test or can we merge this right away?

[dkarrasch]

Perhaps this needs a NEWS entry.

[dkarrasch]

@nanosoldier runtests(["SparseMatricesCSR", "RecursiveFactorization", "KLU", "UpdatableQRFactorizations", "SuperLU", "Juniper", "Infernal", "QuantumTomography", "BandedMatrices"])

[nanosoldier]

Your job failed. Consult the server logs for more details (cc @maleadt).

[maleadt]

error during bootstrap:
LoadError("sysimg.jl", 19, LoadError("/source/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/LinearAlgebra.jl", 3, LoadError("/source/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/factorization.jl", 32, LoadError("/source/usr/share/julia/stdlib/v1.10/LinearAlgebra/src/factorization.jl", 32, ErrorException("parsing command `    adjoint(F::Factorization) -> AdjointFactorization\n\nLazy adjoint (conjugate transposition) of the factorization `F`.\n`: special characters \"#{}()[]<>|&*?~;\" must be quoted in commands")))))

[dkarrasch]

@nanosoldier runtests(["SparseMatricesCSR", "RecursiveFactorization", "KLU", "UpdatableQRFactorizations", "SuperLU", "Juniper", "Infernal", "QuantumTomography", "BandedMatrices"])

[nanosoldier]

Your package evaluation job has completed - possible new issues were detected.
A full report can be found here.

[dkarrasch]

The remaining failing packages have open PRs, so I think this is finally ready to go?

[dkarrasch]

The only failing test is unrelated. Let's go!