better isstrictsubset for Interval

docs/src/lib/sets/Interval.md

@@ -84,6 +84,7 @@ Undocumented implementations:
 * [`convex_hull`](@ref convex_hull(::LazySet, ::LazySet))
 * [`≈`](@ref ≈(::LazySet, ::LazySet))
 * [`isequivalent`](@ref isequivalent(::LazySet, ::LazySet))
+* [`⊂`](@ref ⊂(::LazySet, ::LazySet))
 
 ```@meta
 CurrentModule = LazySets
@@ -99,7 +100,6 @@ Inherited from [`LazySet`](@ref):
 * [`vertices`](@ref vertices(::LazySet))
 * [`sample`](@ref sample(::LazySet, ::Int))
 * [`==`](@ref ==(::LazySet, ::LazySet))
-* [`⊂`](@ref ⊂(::LazySet, ::LazySet))
 
 Inherited from [`AbstractPolyhedron`](@ref):
 * [`is_polyhedral`](@ref is_polyhedral(::AbstractPolyhedron))

src/Sets/Interval/IntervalModule.jl

@@ -16,7 +16,7 @@ import IntervalArithmetic as IA
                         is_interior_point, isoperationtype, linear_map, low, norm, permute,
                         project, rand, rectify, reflect, scale, ρ, σ, translate,
                         vertices_list, volume,
-                        difference, intersection, ≈, isdisjoint, isequivalent, ⊆,
+                        difference, intersection, ≈, isdisjoint, isequivalent, ⊂, ⊆,
                         minkowski_difference, minkowski_sum
 @reexport import ..LazySets: chebyshev_center_radius, isflat, ngens, plot_recipe,
                              radius_hyperrectangle, split
@@ -67,6 +67,7 @@ include("intersection.jl")
 include("isapprox.jl")
 include("isdisjoint.jl")
 include("isequivalent.jl")
+include("isstrictsubset.jl")
 include("issubset.jl")
 include("minkowski_difference.jl")
 include("minkowski_sum.jl")

src/Sets/Interval/isstrictsubset.jl

@@ -0,0 +1,11 @@
+function ⊂(X::Interval, Y::Interval, witness::Bool=false)
+    if min(X) < min(Y) || max(X) > max(Y)
+        return _witness_result_empty(witness, false, X, Y)
+    end
+    if min(X) > min(Y)
+        return witness ? (true, low(Y)) : true
+    elseif max(Y) > max(X)
+        return witness ? (true, high(Y)) : true
+    end
+    return _witness_result_empty(witness, false, X, Y)
+end

test/Sets/Interval.jl

@@ -261,12 +261,23 @@ for N in [Float64, Float32, Rational{Int}]
     I13 = Interval(N(1), N(3))
     I02 = Interval(N(0), N(2))
     I24 = Interval(N(2), N(4))
+    I03 = Interval(N(0), N(3))
+    I14 = Interval(N(1), N(4))
     for I in (I02, I24)
         res, w = ⊆(I13, I, true)
         @test !(⊆(I13, I)) && !res && w ∈ I13 && w ∉ I
     end
     res, w = ⊆(I13, I13, true)
     @test ⊆(I13, I13) && res && w == N[]
+    # isstrictsubset
+    for I in (I02, I24, I13)
+        res, w = ⊂(I13, I, true)
+        @test !(⊂(I13, I)) && !res && w == N[]
+    end
+    for I in (I03, I14)
+        res, w = ⊂(I13, I, true)
+        @test ⊂(I13, I) && res && w ∈ I && w ∉ I13
+    end
 
     # permute
     @test permute(x, [1]) == x