VcatDomain(ℝ, ℕ) causes MethodError

[msagarpatel]

I may be misunderstanding the intended use of VcatDomain, but I assumed it represents a Cartesian Product based on this code:

DomainSets.jl/src/domains/numbers.jl

Lines 64 to 71 in 3b914a2

	"The space ℝ^1."
	const ℝ1 = VcatDomain(ℝ)
	"The space ℝ^2."
	const ℝ2 = VcatDomain(ℝ, ℝ)
	"The space ℝ^3."
	const ℝ3 = VcatDomain(ℝ, ℝ, ℝ)
	"The space ℝ^4."
	const ℝ4 = VcatDomain(ℝ, ℝ, ℝ, ℝ)

So, I tried to represent $\mathbb{R} \times \mathbb{N} $, but was met with an error:

julia> using DomainSets

julia> VcatDomain(ℝ, ℕ)
ERROR: MethodError: no method matching similardomain(::DomainSets.NaturalNumbers, ::Type{Float64})

Closest candidates are:
  similardomain(::IntersectDomain, ::Type{T}) where T
   @ DomainSets ~/.julia/packages/DomainSets/0afEf/src/generic/setoperations.jl:255
  similardomain(::IndicatorFunction, ::Type{T}) where T
   @ DomainSets ~/.julia/packages/DomainSets/0afEf/src/domains/indicator.jl:35
  similardomain(::EmptySpace, ::Type{T}) where T
   @ DomainSets ~/.julia/packages/DomainSets/0afEf/src/domains/trivial.jl:13
  ...

Stacktrace:
  [1] convert(::Type{Domain{Float64}}, d::DomainSets.NaturalNumbers)
    @ DomainSets ~/.julia/packages/DomainSets/0afEf/src/generic/domain.jl:17
  [2] convert_numtype(d::DomainSets.NaturalNumbers, ::Type{Float64})
    @ DomainSets ~/.julia/packages/DomainSets/0afEf/src/generic/domain.jl:9
  [3] _broadcast_getindex_evalf(::typeof(convert_numtype), ::DomainSets.NaturalNumbers, ::Type)
    @ Base.Broadcast ./broadcast.jl:709
  [4] _broadcast_getindex
    @ Base.Broadcast ./broadcast.jl:697 [inlined]
  [5] (::Base.Broadcast.var"#31#32"{Base.Broadcast.Broadcasted{…}})(k::Int64)
    @ Base.Broadcast ./broadcast.jl:1118
  [6] ntuple
    @ Base ./ntuple.jl:49 [inlined]
  [7] copy(bc::Base.Broadcast.Broadcasted{Base.Broadcast.Style{…}, Nothing, typeof(convert_numtype), Tuple{…}})
    @ Base.Broadcast ./broadcast.jl:1118
  [8] materialize
    @ ./broadcast.jl:903 [inlined]
  [9] (VcatDomain{2, Float64})(::RealNumbers, ::Vararg{Any})
    @ DomainSets ~/.julia/packages/DomainSets/0afEf/src/generic/productdomain.jl:134
 [10] VcatDomain(::RealNumbers, ::Vararg{Any})
    @ DomainSets ~/.julia/packages/DomainSets/0afEf/src/generic/productdomain.jl:128
 [11] top-level scope
    @ REPL[33]:1
Some type information was truncated. Use `show(err)` to see complete types.

[daanhb]

Sorry for the lack of documentation. The VcatDomain will concatenate its elements into a vector, in the process promoting them as in

julia> vcat(2.3, 5)
2-element Vector{Float64}:
 2.3
 5.0

The set of natural numbers can not be promoted to have Float64 type, that is why you're getting an error.

The VcatDomain is a concrete subtype of ProductDomain. The more generic function productdomain decides, based on the arguments, which concrete subtype of ProductDomain is most suited to return. However, that will also fail here, because by default it chooses VcatDomain for domains with scalar eltypes.

The type you're probably after is TupleProductDomain, which represents its elements as a Tuple rather than a Vector and which doesn't promote them:

julia> d = TupleProductDomain(ℝ, ℕ)
RealNumbers() × NaturalNumbers()

julia> eltype(d)
Tuple{Float64, Int64}

julia> (2.3,5) ∈ d
true

Alternatively, you could type ProductDomain{Tuple{Float64,Int}}(ℝ, ℕ).

[msagarpatel]

Thank you, @daanhb! That makes sense.