Convert `eltype` using specific types

[jishnub]

The conversion to float works, so ideally, conversions to specific element types should work as well:

julia> float(0..1)
0.0..1.0

julia> Float64(0..1)
ERROR: MethodError: no method matching Float64(::IntervalSets.ClosedInterval{Int64})

Closest candidates are:
  (::Type{T})(::AbstractChar) where T<:Union{AbstractChar, Number}
   @ Base char.jl:50
  (::Type{T})(::Base.TwicePrecision) where T<:Number
   @ Base twiceprecision.jl:266
  (::Type{T})(::Complex) where T<:Real
   @ Base complex.jl:44
  ...

Stacktrace:
 [1] top-level scope
   @ REPL[67]:1

[hyrodium]

We will not support Float64(0..1) because every method of Float64 should be a constructor that returns Float64.
(Same issue on Unitful.jl: JuliaPhysics/Unitful.jl#358)

I think it would be nice to have a method float(::Type{<:AbstractFloat}, x) in Base. After adding the method in Base, we can add the method float(::Type{<:AbstractFloat}, ::Interval) in this package.

[daanhb]

There are other possible ways of expressing this (all of which work for ranges): Float64.(0..1), convert(Domain{Float64}, 0..1) or map(Float64, 0..1).

[dlfivefifty]

I really like Float64.(0..1)! Note this is the only one that has a Set counterpart:

julia> x = Set([1,2,3])
Set{Int64} with 3 elements:
  2
  3
  1

julia> float(x)
ERROR: MethodError: no method matching AbstractFloat(::Set{Int64})
Closest candidates are:
  (::Type{T})(::AbstractChar) where T<:Union{AbstractChar, Number} at char.jl:50
  (::Type{T})(::Base.TwicePrecision) where T<:Number at twiceprecision.jl:266
  (::Type{T})(::Complex) where T<:Real at complex.jl:44
  ...
Stacktrace:
 [1] float(x::Set{Int64})
   @ Base ./float.jl:269
 [2] top-level scope
   @ REPL[2]:1

julia> Float64.(x)
3-element Vector{Float64}:
 2.0
 3.0
 1.0

julia> map(Float64, x)
ERROR: map is not defined on sets
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:35
 [2] map(f::Type, #unused#::Set{Int64})
   @ Base ./abstractarray.jl:2964
 [3] top-level scope
   @ REPL[4]:1

[jishnub]

I agree that Float64.(0..1) and map(Float64, 0..1) seem like a natural way to express this operation, and these are what I had tried initially, but netiher seem to work:

julia> Float64.(0..1)
ERROR: MethodError: no method matching size(::IntervalSets.ClosedInterval{Int64})

Closest candidates are:
  size(::Union{LinearAlgebra.QR, LinearAlgebra.QRCompactWY, LinearAlgebra.QRPivoted})
   @ LinearAlgebra ~/packages/julias/julia-1.9/share/julia/stdlib/v1.9/LinearAlgebra/src/qr.jl:581
  size(::Union{LinearAlgebra.QR, LinearAlgebra.QRCompactWY, LinearAlgebra.QRPivoted}, ::Integer)
   @ LinearAlgebra ~/packages/julias/julia-1.9/share/julia/stdlib/v1.9/LinearAlgebra/src/qr.jl:580
  size(::Union{LinearAlgebra.QRCompactWYQ, LinearAlgebra.QRPackedQ})
   @ LinearAlgebra ~/packages/julias/julia-1.9/share/julia/stdlib/v1.9/LinearAlgebra/src/qr.jl:584
  ...

Stacktrace:
 [1] axes
   @ ./abstractarray.jl:98 [inlined]
 [2] combine_axes(A::IntervalSets.ClosedInterval{Int64})
   @ Base.Broadcast ./broadcast.jl:513
 [3] instantiate
   @ ./broadcast.jl:294 [inlined]
 [4] materialize(bc::Base.Broadcast.Broadcasted{DomainSets.DomainSetStyle, Nothing, Type{Float64}, Tuple{IntervalSets.ClosedInterval{Int64}}})
   @ Base.Broadcast ./broadcast.jl:873
 [5] top-level scope
   @ REPL[2]:1

julia> map(Float64, 0..1)
ERROR: MethodError: no method matching iterate(::IntervalSets.ClosedInterval{Int64})

Closest candidates are:
  iterate(::Union{LinRange, StepRangeLen})
   @ Base range.jl:880
  iterate(::Union{LinRange, StepRangeLen}, ::Integer)
   @ Base range.jl:880
  iterate(::T) where T<:Union{Base.KeySet{<:Any, <:Dict}, Base.ValueIterator{<:Dict}}
   @ Base dict.jl:698
  ...

Stacktrace:
 [1] iterate
   @ ./generator.jl:44 [inlined]
 [2] grow_to!(dest::Vector{Float64}, itr::Base.Generator{IntervalSets.ClosedInterval{Int64}, Type{Float64}})
   @ Base ./array.jl:855
 [3] collect(itr::Base.Generator{IntervalSets.ClosedInterval{Int64}, Type{Float64}})
   @ Base ./array.jl:779
 [4] map(f::Type, A::IntervalSets.ClosedInterval{Int64})
   @ Base ./abstractarray.jl:3283
 [5] top-level scope
   @ REPL[3]:1

This is what had brought me to Float64(0..1) after discovering float(::Interval), although that's perhaps not analogous, as float evidently works on arrays as well. The convert suggestion is the one that works at present. Perhaps the other routes could also be made to work?

[hyrodium]

There was a discussion on broadcasting: #55

[aplavin]

Another common mathematical operation that makes total and unambiguous sense for intervals (and other domains, btw) is adding/stripping Unitful units.

Here is a pirating snippet that I use for interactive work with unitful intervals:

Base.:*(i::Interval, u::Unitful.Units) = @modify(x -> x*u, x |> Properties())
Unitful.ustrip(x::AbstractInterval) = @modify(ustrip, x |> Properties())
Unitful.ustrip(u::Unitful.Units, x::AbstractInterval) = @modify(f -> ustrip(u, f), x |> Properties())

It allows stuff like i = (1..2)u"m", ustrip(i), ustrip(u"cm", i).
Would be great if something similar was added to IntervalSets itself!

Also, deg2rad and rad2deg.

[daanhb]

Hmm, the broadcast and map syntax would need special support which isn't there, but I was expecting the convert syntax to work for units. It does not:

julia> using IntervalSets, Unitful

julia> T = typeof(1.0u"s")
Quantity{Float64, 𝐓, Unitful.FreeUnits{(s,), 𝐓, nothing}}

julia> convert(Domain{T}, 1..2)
ERROR: DimensionError: s and 1 are not dimensionally compatible.

The reason is a (valid!) difference between conversion and constructor syntax of unit types:

julia> convert(T, 1)
ERROR: DimensionError: s and 1 are not dimensionally compatible.

julia> T(1)
1.0 s

Given this behaviour, I think it is valid that the conversion to an interval fails. But T.(1..2) or map(T, 1..2) could be made to work (for any T), and this example might be motivation to do so.