Merge pull request #3667 from JuliaReach/schillic/emptyset_radius

`EmptySet`: redefine `norm`/`radius`/`diameter`

Author: schillic

src/API/Unary/diameter.jl

@@ -16,6 +16,6 @@ A real number representing the diameter.
 
 The diameter of a set is the maximum distance between any two elements of the
 set, or, equivalently, the diameter of the enclosing ball (of the given
-``p``-norm) of minimal volume with the same center.
+``p``-norm) of minimal volume.
 """
 function diameter(::LazySet, ::Real=Inf) end

src/API/Unary/radius.jl

@@ -15,6 +15,6 @@ A real number representing the radius.
 ### Notes
 
 The radius of a set is the radius of the enclosing ball (of the given
-``p``-norm) of minimal volume with the same center.
+``p``-norm) of minimal volume.
 """
 function radius(::LazySet, ::Real=Inf) end

src/Sets/EmptySet/diameter.jl

@@ -1,3 +1,4 @@
-function diameter(::EmptySet, ::Real=Inf)
-    throw(ArgumentError("the diameter of an empty set is undefined"))
+function diameter(∅::EmptySet, ::Real=Inf)
+    N = eltype(∅)
+    return zero(N)
 end

src/Sets/EmptySet/norm.jl

@@ -1,3 +1,4 @@
-function norm(::EmptySet, ::Real=Inf)
-    throw(ArgumentError("the norm of an empty set is undefined"))
+function norm(∅::EmptySet, ::Real=Inf)
+    N = eltype(∅)
+    return zero(N)
 end

src/Sets/EmptySet/radius.jl

@@ -1,3 +1,4 @@
-function radius(::EmptySet, ::Real=Inf)
-    throw(ArgumentError("the radius of an empty set is undefined"))
+function radius(∅::EmptySet, ::Real=Inf)
+    N = eltype(∅)
+    return zero(N)
 end

test/Sets/EmptySet.jl

@@ -80,9 +80,8 @@ for N in [Float64, Float32, Rational{Int}]
     end
 
     # diameter
-    @test_throws ArgumentError diameter(E)  # TODO this should maybe change
-    # res = diameter(E)
-    # @test res isa N && res == N(0)
+    res = diameter(E)
+    @test res isa N && res == N(0)
 
     # dim
     @test dim(E) == 2
@@ -129,19 +128,17 @@ for N in [Float64, Float32, Rational{Int}]
     @test_throws ArgumentError low(E, 1)
 
     # norm
-    @test_throws ArgumentError norm(E)  # TODO this should maybe change
-    # res = norm(E)
-    # @test res isa N && res == N(0)
+    res = norm(E)
+    @test res isa N && res == N(0)
 
     # polyhedron
     if test_suite_polyhedra
         @test_throws MethodError polyhedron(E)  # TODO this should maybe change
     end
 
     # radius
-    @test_throws ArgumentError radius(E)  # TODO this should maybe change
-    # res = radius(E)
-    # @test res isa N && res == N(0)
+    res = radius(E)
+    @test res isa N && res == N(0)
 
     # rand
     E2 = rand(EmptySet; N=N)