mul! of sparse and diagonal for non-commutative eltypes?

[dkarrasch]

Here (and in the corresponding rmul!/lmul!)

https://github.com/JuliaLang/julia/blob/58c0ed57dc796a9bb0759ce49781d97b8474eee3/stdlib/SparseArrays/src/linalg.jl#L1165-L1192

we assume that multiplication of the eltypes of D and A is commutative, whereas we do care about the order of multiplication here:

https://github.com/JuliaLang/julia/blob/58c0ed57dc796a9bb0759ce49781d97b8474eee3/stdlib/SparseArrays/src/linalg.jl#L1194-L1218

I don't have a use/test case for matrix multiplication with non-commutative eltypes, so somebody should tell if there is an issue here (with an easy fix). @Jutho ?

[andreasnoack]

It's only the second of the methods and lmul!(D::Diagonal, A::SparseMatrixCSC) that have the problem, right?

[Jutho]

No I don't have a use case. But it's easy enough to make the implementation respect the order that corresponds to the definition. I think the more challenging case if scalar factors alpha and beta are involved, as in the other discussion. There I think it is fine to assume commutativity, otherwise the number of options just explodes.

[dkarrasch]

@andreasnoack: Yes, that's right, sorry for being imprecise. I'll prepare a PR with a fix.

@Jutho: I just remembered your comment in the other discussion on how you learned to appreciate rmul! and lmul! in the non-commutative case, and that made me check this situation here.