Merge pull request #3906 from JuliaReach/schillic/is_interior_point_hyperrectangle

Fix and improve `is_interior_point` for `AbstractHyperrectangle`

Author: schillic

docs/src/lib/interfaces/AbstractHyperrectangle.md

@@ -243,6 +243,7 @@ CurrentModule = LazySets.API
 * [`low`](@ref low(::LazySet))
 * [`low`](@ref low(::LazySet, ::Int))
 * [`distance`](@ref distance(::AbstractVector, ::LazySet))
+* [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::LazySet))
 * [`project`](@ref project(::LazySet, ::AbstractVector{Int}))
 * [`ρ`](@ref ρ(::AbstractVector, ::LazySet))
 * [`cartesian_product`](@ref cartesian_product(::LazySet, ::LazySet))
@@ -272,7 +273,6 @@ Inherited from [`LazySet`](@ref):
 * [`vertices`](@ref vertices(::LazySet))
 * [`affine_map`](@ref affine_map(::AbstractMatrix, ::LazySet, ::AbstractVector))
 * [`exponential_map`](@ref exponential_map(::AbstractMatrix, ::LazySet))
-* [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::LazySet))
 * [`sample`](@ref sample(::LazySet, ::Int=1))
 * [`scale`](@ref scale(::Real, ::LazySet))
 * [`translate`](@ref translate(::LazySet, ::AbstractVector))

docs/src/lib/interfaces/AbstractSingleton.md

@@ -134,7 +134,6 @@ Inherited from [`LazySet`](@ref):
 * [`triangulate_faces`](@ref triangulate_faces(::LazySet))
 * [`affine_map`](@ref affine_map(::AbstractMatrix, ::LazySet, ::AbstractVector))
 * [`exponential_map`](@ref exponential_map(::AbstractMatrix, ::LazySet))
-* [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::LazySet))
 * [`sample`](@ref sample(::LazySet, ::Int=1))
 * [`scale`](@ref scale(::Real, ::LazySet))
 * [`translate`](@ref translate(::LazySet, ::AbstractVector))
@@ -181,6 +180,7 @@ Inherited from [`AbstractHyperrectangle`](@ref):
 * [`rectify`](@ref rectify(::AbstractHyperrectangle))
 * [`volume`](@ref volume(::AbstractHyperrectangle))
 * [`distance`](@ref distance(::AbstractVector, ::AbstractHyperrectangle; ::Real=2.0))
+* [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::AbstractHyperrectangle))
 * [`difference`](@ref difference(::AbstractHyperrectangle, ::AbstractHyperrectangle))
 * [`minkowski_difference`](@ref minkowski_difference(::AbstractHyperrectangle, ::AbstractHyperrectangle))
 

docs/src/lib/sets/BallInf.md

@@ -131,7 +131,6 @@ Inherited from [`LazySet`](@ref):
 * [`vertices`](@ref vertices(::LazySet))
 * [`affine_map`](@ref affine_map(::AbstractMatrix, ::LazySet, ::AbstractVector))
 * [`exponential_map`](@ref exponential_map(::AbstractMatrix, ::LazySet))
-* [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::LazySet))
 * [`sample`](@ref sample(::LazySet, ::Int))
 * [`translate`](@ref translate(::LazySet, ::AbstractVector))
 * [`convex_hull`](@ref convex_hull(::LazySet, ::LazySet))
@@ -180,6 +179,7 @@ Inherited from [`AbstractHyperrectangle`](@ref):
 * [`rectify`](@ref rectify(::AbstractHyperrectangle))
 * [`vertices_list`](@ref vertices_list(::AbstractHyperrectangle))
 * [`∈`](@ref ∈(::AbstractVector, ::AbstractHyperrectangle))
+* [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::AbstractHyperrectangle))
 * [`cartesian_product`](@ref cartesian_product(::AbstractHyperrectangle, ::AbstractHyperrectangle))
 * [`difference`](@ref difference(::AbstractHyperrectangle, ::AbstractHyperrectangle))
 * [`distance`](@ref distance(::AbstractHyperrectangle, ::AbstractHyperrectangle))

docs/src/lib/sets/Hyperrectangle.md

@@ -93,7 +93,6 @@ Inherited from [`LazySet`](@ref):
 * [`vertices`](@ref vertices(::LazySet))
 * [`affine_map`](@ref affine_map(::AbstractMatrix, ::LazySet, ::AbstractVector))
 * [`exponential_map`](@ref exponential_map(::AbstractMatrix, ::LazySet))
-* [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::LazySet))
 * [`sample`](@ref sample(::LazySet, ::Int=1))
 * [`convex_hull`](@ref convex_hull(::LazySet, ::LazySet))
 * [`exact_sum`](@ref exact_sum(::LazySet, ::LazySet))
@@ -152,6 +151,7 @@ Inherited from [`AbstractHyperrectangle`](@ref):
 * [`volume`](@ref volume(::AbstractHyperrectangle))
 * [`distance`](@ref distance(::AbstractVector, ::AbstractHyperrectangle))
 * [`∈`](@ref ∈(::AbstractVector, ::AbstractHyperrectangle))
+* [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::AbstractHyperrectangle))
 * [`project`](@ref project(::AbstractHyperrectangle, ::AbstractVector{Int}))
 * [`split`](@ref split(::AbstractHyperrectangle, ::AbstractVector{Int}))
 * [`ρ`](@ref ρ(::AbstractVector, ::AbstractHyperrectangle))

docs/src/lib/sets/Interval.md

@@ -192,7 +192,6 @@ Inherited from [`LazySet`](@ref):
 * [`singleton_list`](@ref singleton_list(::LazySet))
 * [`tosimplehrep`](@ref tosimplehrep(::LazySet))
 * [`vertices`](@ref vertices(::LazySet))
-* [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::LazySet))
 * [`sample`](@ref sample(::LazySet, ::Int))
 * [`==`](@ref ==(::LazySet, ::LazySet))
 
@@ -223,6 +222,7 @@ Inherited from [`AbstractZonotope`](@ref):
 Inherited from [`AbstractHyperrectangle`](@ref):
 * [`generators`](@ref generators(::AbstractHyperrectangle))
 * [`genmat`](@ref genmat(::AbstractHyperrectangle))
+* [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::AbstractHyperrectangle))
 * [`cartesian_product`](@ref cartesian_product(::AbstractHyperrectangle, ::AbstractHyperrectangle))
 
 Some additional functionality is available for `IntervalArithmetic.Interval`s:

src/Interfaces/AbstractHyperrectangle.jl

@@ -637,3 +637,13 @@ function chebyshev_center_radius(H::AbstractHyperrectangle)
     r = minimum(radius_hyperrectangle(H, i) for i in 1:dim(H))
     return c, r
 end
+
+@validate function is_interior_point(v::AbstractVector{N}, H::AbstractHyperrectangle{N};
+                                     p=N(Inf), ε=_rtol(N)) where {N<:Real}
+    @inbounds for (i, vi) in enumerate(v)
+        if low(H, i) + ε >= v[i] || v[i] >= high(H, i) - ε
+            return false
+        end
+    end
+    return true
+end

test/ConcreteOperations/interior.jl

@@ -6,30 +6,30 @@ if !isdefined(@__MODULE__, Symbol("@tN"))
 end
 
 for N in @tN([Float64, Float32, Rational{Int}])
-    P = BallInf(zeros(N, 2), N(1 // 10))
-    d = N[1 // 10, 1 // 10]
+    B = Ball1(zeros(N, 2), N(1 // 10))
+    x = N[1 // 10, 1 // 10]
     if N <: AbstractFloat
-        @test !is_interior_point(d, P)
+        @test !is_interior_point(x, B)
     else
-        @test_throws ArgumentError is_interior_point(d, P)
-        @test !is_interior_point(d, P; ε=1 // 100)
+        @test_throws ArgumentError is_interior_point(x, B)
+        @test !is_interior_point(x, B; ε=N(1 // 100))
     end
-    @test !is_interior_point(d, P; ε=N(1))
-    @test_throws ArgumentError is_interior_point(d, P; ε=N(0))
+    @test !is_interior_point(x, B; ε=N(1))
+    @test_throws ArgumentError is_interior_point(x, B; ε=N(0))
 
-    d = N[1 // 10, 1 // 10] .- LazySets._rtol(N)
+    x = N[1 // 10, 1 // 10] .- LazySets._rtol(N)
     if N <: AbstractFloat
-        @test is_interior_point(d, P)
+        @test !is_interior_point(x, B)
     else
-        @test !is_interior_point(d, P; ε=1 // 100)
+        @test !is_interior_point(x, B; ε=N(1 // 100))
     end
 end
 
 for N in @tN([Float64, Float32])
-    P = BallInf(zeros(N, 2), N(1 // 10))
-    d = N[1 // 10, 1 // 10]
-    @test !is_interior_point(d, P; p=N(2))
+    B = Ball1(zeros(N, 2), N(1 // 10))
+    x = N[1 // 10, 1 // 10]
+    @test !is_interior_point(x, B; p=N(2))
 
-    d = N[1 // 10, 1 // 10] .- LazySets._rtol(N)
-    @test is_interior_point(d, P; p=N(2))
+    x = N[1 // 10, 1 // 10] .- LazySets._rtol(N)
+    @test !is_interior_point(x, B; p=N(2))
 end

test/Sets/Interval.jl

@@ -330,12 +330,11 @@ for N in @tN([Float64, Float32, Rational{Int}])
     @test_throws ArgumentError is_interior_point(N[0], X; p=N(1 // 2))
     if N <: AbstractFloat
         @test is_interior_point(N[1], X)
-        if N == Float64
-            @test_broken !is_interior_point(N[2], X)  # TODO fix
-        else
-            @test !is_interior_point(N[2], X)
-        end
+        @test !is_interior_point(N[2], X)
         @test !is_interior_point(N[3], X)
+        @test is_interior_point(N[1], X; p=N(2))
+        @test is_interior_point(N[1], X; p=N(2), ε=N(1//2))
+        @test !is_interior_point(N[1], X; ε=N(1))
     else
         @test_throws ArgumentError is_interior_point(N[1], X)
         @test is_interior_point(N[1], X; ε=1 // 100)