Add Region and mid(X::IntervalBox, alpha) (#148)

* Add Region and mid(X::IntervalBox, alpha)

* Fixes requested changes

* Remove unnecessary parametrization

Author: Kolaru

src/IntervalArithmetic.jl

@@ -69,6 +69,9 @@ export
     interval_part, decoration, DecoratedInterval,
     com, dac, def, trv, ill
 
+## Union type
+export
+    Region
 
 
 
@@ -94,5 +97,9 @@ include("plot_recipes/plot_recipes.jl")
 
 include("deprecated.jl")
 
+"""
+    Region{T} = Union{Interval{T}, IntervalBox{T}}
+"""
+const Region{T} = Union{Interval{T}, IntervalBox{T}}
 
 end # module IntervalArithmetic

src/multidim/intervalbox.jl

@@ -37,7 +37,14 @@ eltype(::Type{IntervalBox{N,T}}) where {N,T} = Interval{T} # Note that this is d
 
 ## arithmetic operations
 # Note that standard arithmetic operations are implemented automatically by FixedSizeArrays.jl
+"""
+    mid(X::IntervalBox, α=0.5)
+
+Return a vector of the `mid` of each interval composing the `IntervalBox`.
 
+See `mid(X::Interval, α=0.5)` for more informations.
+"""
+mid(X::IntervalBox, α) = mid.(X, α)
 mid(X::IntervalBox) = mid.(X)
 mid(X::IntervalBox, α) = mid.(X, α)
 

test/multidim_tests/multidim.jl

@@ -134,6 +134,8 @@ end
     @test length(Y) == 3
     @test Y == IntervalBox(Interval(0, 2), Interval(3, 5), Interval(4, 8))
     @test diam(Y) == 4
+
+    @test mid(IntervalBox(0..1, 3), 0.75) == [0.75, 0.75, 0.75]
 end
 
 @testset "Constructing multidimensional IntervalBoxes" begin