[SparseArrays] Respect order of mul in (l)mul!(::Diagonal,::Sparse)

[dkarrasch]

Fixes JuliaLang/LinearAlgebra.jl#589 .

[andreasnoack]

We actually have

julia/stdlib/LinearAlgebra/test/generic.jl

Lines 10 to 32 in 6b2d211

	struct Quaternion{T<:Real} <: Number
	s::T
	v1::T
	v2::T
	v3::T
	end
	Quaternion(s::Real, v1::Real, v2::Real, v3::Real) = Quaternion(promote(s, v1, v2, v3)...)
	Base.abs2(q::Quaternion) = q.s*q.s + q.v1*q.v1 + q.v2*q.v2 + q.v3*q.v3
	Base.abs(q::Quaternion) = sqrt(abs2(q))
	Base.real(::Type{Quaternion{T}}) where {T} = T
	Base.conj(q::Quaternion) = Quaternion(q.s, -q.v1, -q.v2, -q.v3)
	Base.isfinite(q::Quaternion) = isfinite(q.s) & isfinite(q.v1) & isfinite(q.v2) & isfinite(q.v3)
	(-)(ql::Quaternion, qr::Quaternion) =
	Quaternion(ql.s - qr.s, ql.v1 - qr.v1, ql.v2 - qr.v2, ql.v3 - qr.v3)
	(*)(q::Quaternion, w::Quaternion) = Quaternion(q.s*w.s - q.v1*w.v1 - q.v2*w.v2 - q.v3*w.v3,
	q.s*w.v1 + q.v1*w.s + q.v2*w.v3 - q.v3*w.v2,
	q.s*w.v2 - q.v1*w.v3 + q.v2*w.s + q.v3*w.v1,
	q.s*w.v3 + q.v1*w.v2 - q.v2*w.v1 + q.v3*w.s)
	(*)(q::Quaternion, r::Real) = Quaternion(q.s*r, q.v1*r, q.v2*r, q.v3*r)
	(*)(q::Quaternion, b::Bool) = b * q # remove method ambiguity
	(/)(q::Quaternion, w::Quaternion) = q * conj(w) * (1.0 / abs2(w))
	(\)(q::Quaternion, w::Quaternion) = conj(q) * w * (1.0 / abs2(q))

exactly for testing this. Maybe we should move the definition to https://github.com/JuliaLang/julia/tree/ca7a692f9f1099ba042ed75e5d83236ec523608a/test/testhelpers where e.g. Furlong already lives such that we can use it here.

[dkarrasch]

Ok, cool, I have tests which pass (and wouldn't pass on master for exactly the commutativity issue). It looks like this:

for n in (1, 10)
    v = Quaternion.(rand(n), rand(n), rand(n), rand(n))
    D = Diagonal(v)
    Avals = Quaternion.(rand(2n), rand(2n), rand(2n), rand(2n))
    A = sparse(rand(1:n, 2n), rand(1:n, 2n), Avals, n, n)
    Am = convert(Matrix, A) # test versus dense matrix to make sure different code paths are taken
    @test A * D ≈ Am * D
    @test D * A ≈ D * Am
    @test rmul!(copy(A), D) ≈ Am * D
    @test lmul!(D, copy(A)) ≈ D * Am
end

Comments are welcome. To get this running, I needed to define

Base.zero(::Type{Quaternion{T}}) where T = Quaternion{T}(zero(T), zero(T), zero(T), zero(T))

(+)(ql::Quaternion, qr::Quaternion) =
 Quaternion(ql.s + qr.s, ql.v1 + qr.v1, ql.v2 + qr.v2, ql.v3 + qr.v3)

in addition to what is defined in @andreasnoack 's snippet above. I didn't understand the "move the code" comment above. Should I just add the definitions where the others are and the tests somewhere in the usual test section? Would the tests know about Quaternions?

[KristofferC]

To move the code you can cut and paste the existing Quaternion definition into test/testhelpers/Quaternions.jl. Then you can include that file where it is used in the LinearAlgebra test and also include that file for your sparse multiplication test. You can look at how the other test helpers (like Furlong) is used.

[fredrikekre]

Could be good to squash this into two commits: one with the move of Quaternion and one with the bugfix, but does not matter much.

[dkarrasch]

Yes, I'll see if I can find a git expert to help me with that.

On a different note: this PR affects #29296, which is labelled as "backport pending 1.0".

[andreasnoack]

On a different note: this PR affects #29296, which is labelled as "backport pending 1.0".

I think it should be safe to mark this PR for backport as well.

[dkarrasch]

That was the adventure of my life, but I managed to clean up my commit mess (with the help of my colleague... well, he dictated, I was typing). Result: two beautiful, nicely sorted commits. 🎉

[chriscoey]

can this be merged?

[ViralBShah]

I believe so - but I am wondering if we need to wait for the 1.1 release process.

[dkarrasch]

can this be merged?

Yes. I wasn't sure if I needed to give another "I'm done" signal, since I felt that was obvious and didn't want to put pressure on anyone.

[KristofferC]

Can change behavior so should not be backported