Add "in" for IntervalBox (#244)

* Add explicit definition for ∈ of IntervalBox

* Import alias for 'in'

* Throw ArgumentError for  for IntervalBox

* Fix test

* Allow general AbstractVector for membership of IntervalBox; add tests

* Make X in Y an error for X and Y intervals

* Add tests

* Add explicit definition for subseteq of two complex intervals

Author: dpsanders

src/IntervalArithmetic.jl

@@ -28,7 +28,7 @@ import Base:
     union, intersect, isempty,
     convert, promote_rule, eltype, size,
     BigFloat, float, widen, big,
-    ∩, ∪, ⊆, ⊇, eps,
+    ∩, ∪, ⊆, ⊇, ∈, eps,
     floor, ceil, trunc, sign, round,
     expm1, log1p,
     precision,

src/intervals/complex.jl

@@ -1,3 +1,6 @@
+
+⊆(x::Complex{Interval{T}}, y::Complex{Interval{T}}) where T = real(x) ⊆ real(y) && imag(x) ⊆ imag(y)
+
 function ^(x::Complex{Interval{T}}, n::Integer) where {T}
     if n < 0
         return inv(x)^n

src/intervals/set_operations.jl

@@ -13,6 +13,8 @@ function in(x::T, a::Interval) where T<:Real
     a.lo <= x <= a.hi
 end
 
+in(x::Interval, y::Interval) = throw(ArgumentError("$x ∈ $y is not defined"))
+
 in(x::T, a::Complex{<:Interval}) where T<:Real = x ∈ real(a) && 0 ∈ imag(a)
 in(x::Complex{T}, a::Complex{<:Interval}) where T<:Real = real(x) ∈ real(a) && imag(x) ∈ imag(a)
 

src/multidim/intervalbox.jl

@@ -67,6 +67,10 @@ big(X::IntervalBox) = big.(X)
 ∪(X::IntervalBox{N,T}, Y::IntervalBox{N,T}) where {N,T} =
     IntervalBox(X.v .∪ Y.v)
 
+∈(X::AbstractVector, Y::IntervalBox{N,T}) where {N,T} = all(X .∈ Y)
+∈(X, Y::IntervalBox{N,T}) where {N,T} = throw(ArgumentError("$X ∈ $Y is not defined"))
+
+
 #=
 On Julia 0.6 can now write
 ∩{N,T}(X::IntervalBox{N,T}, Y::IntervalBox{N,T}) = IntervalBox(NTuple{N, Interval{Float64}}( (X[i] ∩ Y[i]) for i in 1:N))

test/interval_tests/consistency.jl

@@ -83,6 +83,8 @@ setprecision(Interval, Float64)
         @test 0.1 in @interval(0.1)
         @test !(-Inf ∈ entireinterval())
         @test !(Inf ∈ entireinterval())
+
+        @test_throws ArgumentError (3..4) ∈ (3..4)
     end
 
     @testset "Inclusion tests" begin

test/multidim_tests/multidim.jl

@@ -218,4 +218,18 @@ end
     @test diam.(X) == SVector(diam(X[1]), diam(X[2]))
 end
 
+@testset "∈" begin
+    X = IntervalBox(3..4, 5..6)
+    @test mid(X) ∈ X
+    @test mid(X, 0.75) ∈ X
+
+    @test (zero(mid(X)) ∈ X) == false
+    @test zero(mid(X)) ∉ X
+
+    @test_throws ArgumentError (3..4) ∈ X
+
+    @test_throws ArgumentError [3..4, 5..6] ∈ X
+
+end
+
 end