Resolve ambiguity in multiplying Diagonal kronecker products

[jishnub]

Fixes the following multiplications:

julia> A = randn(4, 4);

julia> B = Array{Float64, 2}([1 2 3;
                4 5 6;
                7 -2 9]);

julia> K = A ⊗ B;

julia> Kd = Diagonal(A) ⊗ Diagonal(B);

julia> Kd2 = Diagonal(B) ⊗ Diagonal(A);

julia> Kd * Kd2 ≈ Diagonal(Kd) * Diagonal(Kd2)
true

julia> Kd2 * Kd ≈ Diagonal(Kd2) * Diagonal(Kd)
true

julia> K * Kd ≈ collect(K) * Diagonal(Kd)
true

julia> Kd * K ≈ Diagonal(Kd) * collect(K)
true

[codecov-commenter]

Codecov Report

Merging #113 (aaa0b29) into master (70fc882) will increase coverage by 0.04%. The diff coverage is 96.87%.

@@            Coverage Diff             @@
##           master     #113      +/-   ##
==========================================
+ Coverage   90.43%   90.48%   +0.04%     
==========================================
  Files          10       10              
  Lines         805      809       +4     
==========================================
+ Hits          728      732       +4     
  Misses         77       77              

Impacted Files	Coverage Δ
src/base.jl	92.88% <96.55%> (+0.28%)	:arrow_up:
src/vectrick.jl	94.53% <100.00%> (-0.29%)	:arrow_down:

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[MichielStock]

I've noticed that Diagonal(K) returns are regular Diagonal matrix rather than a KronProdDiagonal. Would it make sence to also extend this function a la

LinearAlgebra.Diagonal(K::AbstractKronecker) = mapreduce(Diagonal, ⊗, getmatrices(K))

[jishnub]

Diagonal refers to the constructor, therefore it should return an object of the same type. Perhaps we may add a function diagonal to Kronecker that will return the appropriate type? Ideally there could have been such a function in LinearAlgebra that we may overload here, but as of now there's only the constructor that exists.

[MichielStock]

For many cases, the difference between a diagonal or a Kronecker type might be minimal. Though it might be useful to add two Kronecker produces?

Agreed that we should not mess with constructors! LinearAlgebra.diagm might fit the bill though.

[jishnub]

diagm constructs a matrix given the vector that corresponds to the diagonal. Perhaps we're looking for something like diagm ∘ diag, but at that point it's probably easier to define our own function

[MichielStock]

You are right, my bad! I thought it also created a diagonal matrix from a square matrix. If we agree that we want the behaviour as discussed, I am in favor of our own function

diagonal(A::AbstractMatrix) = Diagonal(A)
diagonal(K::AbstractKroneckerProduct) = mapreduce(Diagonal, ⊗, getmatrices(K))