center of lazy translation and bloating (#2949)

* add center for lazy bloating

* add center for lazy translation

Author: mforets

docs/src/lib/lazy_operations/Bloating.md

@@ -13,6 +13,7 @@ isbounded(::Bloating)
 isempty(::Bloating)
 an_element(::Bloating)
 constraints_list(::Bloating)
+center(::Bloating)
 ```
 
 Inherited from [`LazySet`](@ref):

docs/src/lib/lazy_operations/Translation.md

@@ -14,6 +14,7 @@ an_element(::Translation)
 constraints_list(::Translation)
 linear_map(::AbstractMatrix, ::Translation)
 ∈(::AbstractVector, ::Translation)
+center(::Translation)
 ```
 Inherited from [`AbstractAffineMap`](@ref):
 * [`dim`](@ref dim(::AbstractAffineMap))

src/LazyOperations/Bloating.jl

@@ -1,7 +1,7 @@
 export Bloating
 
 """
-    Bloating{N, S<:LazySet{N}} <:LazySet{N}
+    Bloating{N, S<:LazySet{N}} <: LazySet{N}
 
 Type that represents a uniform expansion of a set in a given norm (also
 known as *bloating*).
@@ -21,7 +21,7 @@ of `X` and a ball in the `p`-norm of radius `ε` centered in the origin `O`
 The `Bloating` operation preserves convexity: if `X` is convex, then any
 bloating of `X` is convex as well.
 """
-struct Bloating{N, S<:LazySet{N}} <:LazySet{N}
+struct Bloating{N, S<:LazySet{N}} <: LazySet{N}
     X::S
     ε::N
     p::N
@@ -192,3 +192,20 @@ function constraints_list(B::Bloating)
 
     return constraints_list(MinkowskiSum(B.X, _bloating_ball(B)))
 end
+
+"""
+    center(B::Bloating)
+
+Return the center of a bloated set.
+
+### Input
+
+- `B` -- bloated set
+
+### Output
+
+The center of the wrapped set.
+"""
+function center(B::Bloating)
+    center(B.X)
+end

src/LazyOperations/Translation.jl

@@ -3,7 +3,8 @@ import Base: isempty
 export Translation,
        an_element,
        constraints_list,
-       linear_map
+       linear_map,
+       center
 
 """
     Translation{N, S<:LazySet{N}, VN<:AbstractVector{N}} <: AbstractAffineMap{N, S}
@@ -375,3 +376,20 @@ end
 function concretize(tr::Translation)
     return translate(concretize(tr.X), tr.v)
 end
+
+"""
+    center(tr::Translation)
+
+Return the center of the translation of a set.
+
+### Input
+
+- `tr` -- translation of a set
+
+### Output
+
+The translation of the center of the wrapped set by the translation vector.
+"""
+function center(tr::Translation)
+    center(tr.X) + tr.v
+end

test/LazyOperations/Bloating.jl

@@ -29,6 +29,9 @@ for N in [Float64, Float32]
     end
     @test_throws ErrorException an_element(Y)
 
+    # center
+    @test center(X) == center(B)
+
     # tests for different norms
     for p in N[1, 2, Inf]
         B = BallInf(zeros(N, 2), N(1))

test/LazyOperations/Translation.jl

@@ -60,6 +60,9 @@ for N in [Float64, Rational{Int}, Float32]
     # concretize
     @test concretize(tr) == translate(B, v)
 
+    # center
+    @test center(tr) == center(B) + v
+
     # ==================================
     # Type-specific methods
     # ==================================