cat SMatrices returns Arrays

Hi!

I was trying to compute a static block matrix using static sub matrices and saw that the result is not a StaticArray.

julia> m1 = @SMatrix rand(2,3);

julia> m2 = @SMatrix rand(2,3);

julia> cat(m1, m2, dims = (1, 2))
4×6 Array{Float64,2}:
 0.611586  0.396562  0.30208    0.0       0.0       0.0
 0.574913  0.909981  0.0731041  0.0       0.0       0.0
 0.0       0.0       0.0        0.495477  0.512808  0.232148
 0.0       0.0       0.0        0.880756  0.449617  0.305318

Also, trying simpler examples yield to Arrays as well:

julia> cat(m1, m2, dims = 1)
4×3 Array{Float64,2}:
 0.611586  0.396562  0.30208
 0.574913  0.909981  0.0731041
 0.495477  0.512808  0.232148
 0.880756  0.449617  0.305318

julia> cat(m1, m2, dims = 2)
2×6 Array{Float64,2}:
 0.611586  0.396562  0.30208    0.495477  0.512808  0.232148
 0.574913  0.909981  0.0731041  0.880756  0.449617  0.305318

The result is different if we just use hcat or vcat.

julia> hcat(m1, m2)
2×6 SArray{Tuple{2,6},Float64,2,12} with indices SOneTo(2)×SOneTo(6):
 0.611586  0.396562  0.30208    0.495477  0.512808  0.232148
 0.574913  0.909981  0.0731041  0.880756  0.449617  0.305318

julia> vcat(m1, m2)
4×3 SArray{Tuple{4,3},Float64,2,12} with indices SOneTo(4)×SOneTo(3):
 0.611586  0.396562  0.30208
 0.574913  0.909981  0.0731041
 0.495477  0.512808  0.232148
 0.880756  0.449617  0.305318

However, I still need to find a method that computes a block matrix using submatrices.

I have a function that computes several static matrices in the body that need to be concatenated as a block static matrix (which is then returned). Should I create static sub-matrices filled with zeros and use hcat and vcat then?

Also, in the slack channel, @mcabbott suggested using generated functions:

I guess this might end up more efficient. I think it ought to be possible to re-use cat by making arrays of expressions like :(args[n][i,j]) and cat-ing those… The one thing I contributed to StaticArrays is like that: https://github.com/JuliaArrays/StaticArrays.jl/blob/0a7f3f7eae1fab11a50699fe33332d5099534be9/src/abstractarray.jl#L218

Please, notice that the sub matrices might have different sizes as well.

Any ideas?

Thanks!

Reproduce the cat, hcat, and vcat examples with static matrices, then inspect src/abstractarray.jl at the referenced concatenation implementation. Determine how concatenation should preserve static results, including inputs with different sizes, and add tests showing the expected StaticArray output.