Add missing set operations involving IntervalBoxes, with tests (#262)

* Add missing set operations involving `IntervalBox`es, with tests

* Use metaprograming and add negative tests

Author: lbenet

src/multidim/arithmetic.jl

@@ -31,11 +31,8 @@ Base.size(X::IntervalBox{2,Float64}) = (2,)
 @inline broadcasted(f, x, y, Z::IntervalBox) = wrap(f.(x, y, Z.v))
 @inline broadcasted(f, x, Y::IntervalBox, z) = wrap(f.(x, Y.v, z))
 
-for op in (:+, :-, :∩, :∪, :⊆, :isinterior, :dot, :setdiff, :×)
+for op in (:+, :-, :∩, :∪, :⊆, :⊂, :⊃, :isinterior, :dot, :setdiff, :×)
     @eval $(op)(a::SVector, b::IntervalBox) = $(op)(IntervalBox(a), b)
-end
-
-for op in (:+, :-, :∩, :∪, :⊆, :isinterior, :dot, :setdiff, :×)
     @eval $(op)(a::IntervalBox, b::SVector) = $(op)(a, IntervalBox(b))
 end
 

src/multidim/intervalbox.jl

@@ -65,8 +65,9 @@ big(X::IntervalBox) = big.(X)
 ## set operations
 
 # TODO: Update to use generator
-⊆(X::IntervalBox{N,T}, Y::IntervalBox{N,T}) where {N,T} =
-    all(X.v .⊆ Y.v)
+for (op, dotop) in ((:⊆, :.⊆), (:⊂, :.⊂), (:⊃, :.⊃))
+    @eval $(op)(X::IntervalBox{N,T}, Y::IntervalBox{N,T}) where {N,T} = all($(dotop)(X, Y))
+end
 
 ∩(X::IntervalBox{N,T}, Y::IntervalBox{N,T}) where {N,T} =
     IntervalBox(X.v .∩ Y.v)

test/multidim_tests/multidim.jl

@@ -35,9 +35,26 @@ let X, A  # avoid problems with global variables
     @test A .^ 2 == IntervalBox(1..4, 9..16)
     @test B .^ 0.5 == IntervalBox(@interval(0,sqrt(2)), @interval(sqrt(3),sqrt(6)))
 
+    @test A ⊆ A
     @test A ⊆ B
     @test A.v ⊆ B
+    @test A ⊂ B.v
+    @test !(A ⊂ A)
+    @test A ⊂ B
+    @test A.v ⊂ B
     @test A ⊆ B.v
+    @test !(B ⊆ A)
+    @test !(B ⊂ A)
+    @test B ⊇ B
+    @test B ⊇ A
+    @test B.v ⊇ A
+    @test B ⊇ A.v
+    @test !(B ⊃ B)
+    @test B ⊃ A
+    @test B.v ⊃ A
+    @test B ⊃ A.v
+    @test !(A ⊇ B)
+    @test !(A ⊃ B)
 
     @test A ∩ B == A
     @test A.v ∩ B == A