@system should not convert matrices to Matrix

[schillic]

Currently @system calls hcat on every matrix, which yields a Matrix even if the input already was an AbstractMatrix.

MathematicalSystems.jl/src/macros.jl

Lines 599 to 611 in c1b8b06

	if state == var
	push!(params, (Expr(:call, :hcat, array), :A))
	# obtain "state_dim" for later using in IdentityMultiple
	state_dim = Expr(:call, :size, :($array), 1)
	got_state_dim = true
	num_state_assignments += 1
	elseif input == var
	push!(params, (Expr(:call, :hcat, array), :B))
	num_input_assignments += 1
	elseif noise == var
	push!(params, (Expr(:call, :hcat, array), :D))

I think this is not good because you may for instance want to work with a sparse matrix.

This change was added in #175 with the motivation to handle scalar inputs.

A simple solution would be to check whether the input has type AbstractMatrix and in that case not call hcat.

This would be mildly breaking.

[blegat]

I'm not sure to understand, hcat does not turn sparse matrices into dense ones:

julia> using SparseArrays

julia> A = spzeros(2, 2)
2×2 SparseMatrixCSC{Float64, Int64} with 0 stored entries:
  ⋅    ⋅ 
  ⋅    ⋅ 

julia> hcat(A)
2×2 SparseMatrixCSC{Float64, Int64} with 0 stored entries:
  ⋅    ⋅ 
  ⋅    ⋅ 

julia> hcat(A, A)
2×4 SparseMatrixCSC{Float64, Int64} with 0 stored entries:
  ⋅    ⋅    ⋅    ⋅ 
  ⋅    ⋅    ⋅    ⋅

[schillic]

Indeed! I saw that it converts an IdentityMultiple (defined in this library). So I guess it does that for AbstractMatrix when no custom hcat method is implemented.

julia> A = Id(2)
IdentityMultiple{Float64} of value 1.0 and order 2

julia> hcat(A)
2×2 Matrix{Float64}:
 1.0  0.0
 0.0  1.0

[blegat]

I see, I guess the use of this hcat is to turn vectors to matrices so we can just create a vector_to_matrix function that calls hcat on AbstractVector and does nothing on matrices