add 'linear_map_inverse' for EmptySet (#3887)

Author: schillic

src/Sets/EmptySet/EmptySetModule.jl

@@ -20,7 +20,7 @@ using ReachabilityBase.Require: require
                         intersection, ≈, isdisjoint, ⊆, linear_combination,
                         minkowski_difference, minkowski_sum
 @reexport import ..LazySets: chebyshev_center_radius, constrained_dimensions,
-                             rationalize, triangulate
+                             linear_map_inverse, rationalize, triangulate
 import ..LazySets: plot_recipe
 import Base: convert, copy
 @reexport using ..API
@@ -55,6 +55,7 @@ include("exponential_map.jl")
 include("in.jl")
 include("is_interior_point.jl")
 include("linear_map.jl")
+include("linear_map_inverse.jl")
 include("permute.jl")
 include("project.jl")
 include("scale.jl")

src/Sets/EmptySet/linear_map_inverse.jl

@@ -0,0 +1,6 @@
+function linear_map_inverse(Minv::AbstractMatrix{N}, ∅::EmptySet{N}) where {N}
+    @assert size(Minv, 1) == dim(∅) "a linear map of size $(size(Minv)) " *
+                                    "cannot be applied to a set of dimension $(dim(∅))"
+    n = size(Minv, 2)
+    return EmptySet{N}(n)
+end

test/Sets/EmptySet.jl

@@ -233,9 +233,8 @@ for N in @tN([Float64, Float32, Rational{Int}])
     @test isidentical(E3, E2)
 
     # linear_map_inverse
-    @test_broken LazySets.linear_map_inverse(ones(N, 2, 3), E)  # TODO this should maybe change
-    # E2 = LazySets.linear_map_inverse(ones(N, 2, 3), E)
-    # @test isidentical(E3, E2)
+    E2 = LazySets.linear_map_inverse(ones(N, 2, 3), E)
+    @test isidentical(E3, E2)
 
     # permute
     @test_throws DimensionMismatch permute(E, [1])