replace ambiguous scale! methods

[Sacha0]

Discussion in #16772 revealed some dubious scale! methods. For example (#16772 (comment)), determining what either of

scale!(A::AbstractArray{T<:Any,2}, b::AbstractArray{T<:Any,1}) at linalg/generic.jl:477
scale!(b::AbstractArray{T<:Any,1}, A::AbstractArray{T<:Any,2}) at linalg/generic.jl:478

does requires reading the associated code. And as @Keno suggests, expressing these operations as e.g. A*Diagonal(B) might be better. Best!

[Sacha0]

Moreover we should consider whether scale! should exist at all: Two-argument scale! methods are just in-place multiplication, and (the undocumented) three-argument scale! methods are just out-of-place multiplication. If we address #16772 (comment), all scale! methods could then simply disappear into in-place and out-of-place multiplication. Best!

[andreasnoack]

The fundamental question here is exactly the same as in #16772 so let's keep the general discussion in that issue. Whatever we decide and as you point out, it makes sense to deprecate these in favor of mutating multiplication. The methods are already defined in

julia/base/linalg/diagonal.jl

Lines 233 to 238 in 0385a60

	A_mul_B!(A::Diagonal,B::AbstractMatrix) = scale!(A.diag,B)
	At_mul_B!(A::Diagonal,B::AbstractMatrix) = scale!(A.diag,B)
	Ac_mul_B!(A::Diagonal,B::AbstractMatrix) = scale!(conj(A.diag),B)
	A_mul_B!(A::AbstractMatrix,B::Diagonal) = scale!(A,B.diag)
	A_mul_Bt!(A::AbstractMatrix,B::Diagonal) = scale!(A,B.diag)
	A_mul_Bc!(A::AbstractMatrix,B::Diagonal) = scale!(A,conj(B.diag))

.

[Sacha0]

The fundamental question here is exactly the same as in #16772 so let's keep the general discussion in that issue.

Yes, apart from the additional question of whether scale! should exist all :).

[Sacha0]

Triage settled on deprecating scale! in favor of mul! once the in-place/out-of-place mul! question is settled. Best!

[JeffBezanson]

That implies that mul1! and mul2! should be exported, since scale! currently is.

[JeffBezanson]

Is anybody working on this, or should I take a crack at it?

[andreasnoack]

Let me do it.