LinearAlgebra.norm(x::Union{Transpose, Adjoint}) should default to norm(parent(x))

[jondeuce]

Currently, if x is the adjoint or transpose of an AbstractVector, then norm(x) will default to norm(parent(x)). This PR extends this behaviour to include AbstractMatrixs, as well.

I don't think this should be consider breaking. It is true by the definition of norm - which is invariant to permutation and/or conjugation of the underlying array elements - that norm(x) == norm(parent(x)) should hold.

For reference, I ran into this issue in the wild. When x is an adjoint of a CuMatrix, norm(x) falls back to the generic implementation and throws an error. While this could easily be patched in CUDA.jl, I think it is more correct and convenient to have this fallback in Base. Currently, it is not possible to fix this in one's own code without type piracy.

[dkarrasch]

Is there any risk that this might be too generic? @andreasnoack @stevengj

[stevengj]

Needs a test?

[jondeuce]

Added some tests for vectors and matrices of common element types, as well as for nested vectors/matrices. Let me know if checking norm(x) ≈ norm(parent(x)) seems sufficient, I can't think of anything else to verify.

[stevengj]

I would check norm(x) == norm(Matrix(x))

[jondeuce]

I would check norm(x) == norm(Matrix(x))

Done 👍

[jondeuce]

Looks like tests sometimes fail when using ==. Possibly the iteration order is different for the transposed/adjoint arrays, leading to floating point differences?

[dkarrasch]

Perhaps a short note in the NEWS file to say that norm of AdjOrTrans always falls back to the norm of the parent, and then this is ready to go. I think this is more of a performance issue than an accuracy issue, so isapprox is fine in the tests.

[jondeuce]

Great, NEWS file is updated now.

[dkarrasch]

One failing test is clearly unrelated, the other one (a segmentation fault) occurs in \ in LinearAlgebra/qr in "old" code, so is unrelated to this PR.

[jondeuce]

Regarding the CUDA issue in the original post, do you have any advice on how to incorporate a patch in the meantime?

@maleadt and I were discussing a patch to GPUArrays (e.g. here) along the lines of:

if VERSION < CUTOFF
    for trtype in (:Transpose, :Adjoint)
        @eval LinearAlgebra.norm(x::$trtype{<:Any, <:AbstractGPUArray}, p::Real = 2) = norm(parent(v), p)
    end
end

But I'm not sure what an appropriate cutoff version would be. For example, is there any chance this patch makes it into 1.9?

[maleadt]

But I'm not sure what an appropriate cutoff version would be. For example, is there any chance this patch makes it into 1.9?

As this isn't really a bugfix, I think, backporting it to 1.9 is unlikely at this point. To find out the exact cutoff, you can use the contrib/commit-name.sh script, passing along the hash of the commit where this got merged (70f6f7f).