EmptySet: add 'linear_combination'

src/ConcreteOperations/linear_combination.jl

@@ -1,3 +1,12 @@
 function linear_combination(X::ConvexSet, Y::ConvexSet)
     return convex_hull(X, Y)
 end
+
+@commutative function linear_combination(∅::EmptySet, X::LazySet)
+    return _linear_combination_emptyset(∅, X)
+end
+
+# disambiguation
+@commutative function linear_combination(∅::EmptySet, X::ConvexSet)
+    return _linear_combination_emptyset(∅, X)
+end

src/LazySets.jl

@@ -122,8 +122,8 @@ include("Sets/EmptySet/EmptySetModule.jl")
 @reexport using ..EmptySetModule: EmptySet, ∅
 using ..EmptySetModule: _difference_emptyset, _difference_emptyset2, _distance_emptyset,
                         _isdisjoint_emptyset, _issubset_emptyset, _issubset_emptyset2,
-                        _minkowski_difference_emptyset, _minkowski_difference_emptyset2,
-                        _minkowski_sum_emptyset
+                        _linear_combination_emptyset, _minkowski_difference_emptyset,
+                        _minkowski_difference_emptyset2, _minkowski_sum_emptyset
 
 include("Sets/HParallelotope/HParallelotopeModule.jl")
 @reexport using ..HParallelotopeModule: HParallelotope,

src/Sets/EmptySet/EmptySetModule.jl

@@ -17,7 +17,7 @@ using ReachabilityBase.Require: require
                         ρ, σ, surface, translate, translate!, vertices,
                         vertices_list, volume, cartesian_product, convex_hull,
                         difference, distance, intersection, ≈, isdisjoint, ⊆,
-                        minkowski_difference, minkowski_sum
+                        linear_combination, minkowski_difference, minkowski_sum
 @reexport import ..LazySets: chebyshev_center_radius
 import ..LazySets: plot_recipe
 import Base: convert, copy
@@ -68,6 +68,7 @@ include("intersection.jl")
 include("isapprox.jl")
 include("isdisjoint.jl")
 include("issubset.jl")
+include("linear_combination.jl")
 include("minkowski_difference.jl")
 include("minkowski_sum.jl")
 

src/Sets/EmptySet/linear_combination.jl

@@ -0,0 +1,10 @@
+function linear_combination(∅₁::EmptySet, ∅₂::EmptySet)
+    return _linear_combination_emptyset(∅₁, ∅₂)
+end
+
+# the empty set is absorbing for the linear combination
+function _linear_combination_emptyset(∅::EmptySet, X::LazySet)
+    @assert dim(∅) == dim(X) "the dimensions of the given sets should match, " *
+                             "but they are $(dim(∅)) and $(dim(X)), respectively"
+    return ∅
+end