Merge pull request #2963 from JuliaReach/schillic/2947

center for lazy operations

docs/src/lib/interfaces.md

@@ -462,6 +462,7 @@ an_element(::AbstractAffineMap)
 isempty(::AbstractAffineMap)
 isbounded(::AbstractAffineMap)
 ∈(::AbstractVector, ::AbstractAffineMap)
+center(::AbstractAffineMap)
 vertices_list(::AbstractAffineMap)
 constraints_list(::AbstractAffineMap)
 linear_map(::AbstractMatrix, ::AbstractAffineMap)

docs/src/lib/lazy_operations/CartesianProduct.md

@@ -17,6 +17,7 @@ dim(::CartesianProduct)
 isbounded(::CartesianProduct)
 ∈(::AbstractVector, ::CartesianProduct)
 isempty(::CartesianProduct)
+center(::CartesianProduct)
 constraints_list(::CartesianProduct)
 vertices_list(cp::CartesianProduct{N}) where {N}
 linear_map(M::AbstractMatrix, cp::CartesianProduct)
@@ -41,6 +42,7 @@ dim(::CartesianProductArray)
 isbounded(::CartesianProductArray)
 ∈(::AbstractVector, ::CartesianProductArray)
 isempty(::CartesianProductArray)
+center(::CartesianProductArray)
 constraints_list(cpa::CartesianProductArray{N}) where {N}
 vertices_list(::CartesianProductArray{N}) where {N}
 linear_map(M::AbstractMatrix, cpa::CartesianProductArray)

docs/src/lib/lazy_operations/MinkowskiSum.md

@@ -16,6 +16,7 @@ dim(::MinkowskiSum)
 σ(::AbstractVector, ::MinkowskiSum)
 isbounded(::MinkowskiSum)
 isempty(::MinkowskiSum)
+center(::MinkowskiSum)
 constraints_list(::MinkowskiSum)
 ∈(::AbstractVector, ::MinkowskiSum{N, S1, S2}) where {N, S1<:AbstractSingleton, S2<:LazySet}
 vertices_list(::MinkowskiSum)
@@ -37,6 +38,7 @@ dim(::MinkowskiSumArray)
 isbounded(::MinkowskiSumArray)
 isempty(::MinkowskiSumArray)
 array(::MinkowskiSumArray)
+center(::MinkowskiSumArray)
 ```
 Inherited from [`LazySet`](@ref):
 * [`norm`](@ref norm(::LazySet, ::Real))

src/Interfaces/AbstractAffineMap.jl

@@ -209,6 +209,23 @@ function ∈(x::AbstractVector, am::AbstractAffineMap)
     return matrix(am) \ (x - vector(am)) ∈ set(am)
 end
 
+"""
+    center(am::AbstractAffineMap)
+
+Return the center of an affine map of a centrally-symmetric set.
+
+### Input
+
+- `cp` -- affine map of a centrally-symmetric set
+
+### Output
+
+The center of the affine map.
+"""
+function center(am::AbstractAffineMap)
+    matrix(am) * center(set(am)) + vector(am)
+end
+
 """
     vertices_list(am::AbstractAffineMap; [apply_convex_hull]::Bool)
 

src/LazyOperations/CartesianProduct.jl

@@ -227,6 +227,23 @@ function isempty(cp::CartesianProduct)
     return isempty(cp.X) || isempty(cp.Y)
 end
 
+"""
+    center(cp::CartesianProduct)
+
+Return the center of a Cartesian product of centrally-symmetric sets.
+
+### Input
+
+- `cp` -- Cartesian product of centrally-symmetric sets
+
+### Output
+
+The center of the Cartesian product.
+"""
+function center(cp::CartesianProduct)
+    vcat(center(cp.X), center(cp.Y))
+end
+
 """
     constraints_list(cp::CartesianProduct)
 

src/LazyOperations/CartesianProductArray.jl

@@ -277,6 +277,23 @@ function isempty(cpa::CartesianProductArray)
    return any(isempty, array(cpa))
 end
 
+"""
+    center(cpa::CartesianProductArray)
+
+Return the center of a Cartesian product array of centrally-symmetric sets.
+
+### Input
+
+- `cpa` -- Cartesian product array of centrally-symmetric sets
+
+### Output
+
+The center of the Cartesian product array.
+"""
+function center(cpa::CartesianProductArray)
+    reduce(vcat, center(X) for X in array(cpa))
+end
+
 """
    constraints_list(cpa::CartesianProductArray{N}) where {N}
 

src/LazyOperations/MinkowskiSum.jl

@@ -196,6 +196,23 @@ function isempty(ms::MinkowskiSum)
     return isempty(ms.X) || isempty(ms.Y)
 end
 
+"""
+    center(ms::MinkowskiSum)
+
+Return the center of a Minkowski sum of centrally-symmetric sets.
+
+### Input
+
+- `ms` -- Minkowski sum of centrally-symmetric sets
+
+### Output
+
+The center of the Minkowski sum.
+"""
+function center(ms::MinkowskiSum)
+    center(ms.X) + center(ms.Y)
+end
+
 """
     constraints_list(ms::MinkowskiSum)
 

src/LazyOperations/MinkowskiSumArray.jl

@@ -176,6 +176,23 @@ function isempty(msa::MinkowskiSumArray)
    return any(isempty, array(msa))
 end
 
+"""
+    center(msa::MinkowskiSumArray)
+
+Return the center of a Minkowski sum array of centrally-symmetric sets.
+
+### Input
+
+- `msa` -- Minkowski sum array of centrally-symmetric sets
+
+### Output
+
+The center of the Minkowski sum array.
+"""
+function center(msa::MinkowskiSumArray)
+    sum(center(X) for X in array(msa))
+end
+
 function concretize(msa::MinkowskiSumArray)
     a = array(msa)
     @assert !isempty(a) "an empty Minkowski sum is not allowed"

test/LazyOperations/CartesianProduct.jl

@@ -49,6 +49,9 @@ for N in [Float64, Float32, Rational{Int}]
     # isempty
     @test !isempty(cp)
 
+    # center
+    @test center(cp) == N[0, 0, 0]
+
     # Cartesian Product of a not-centered 1D BallInf and a not-centered 2D BallInf
     # Here a Hyperrectangle where c = [1, -3, 4] and r = [3, 2, 2]
     b1 = BallInf(N[1], N(3))
@@ -244,6 +247,9 @@ for N in [Float64, Float32, Rational{Int}]
         @test ρ(dd, cpa) == ρ(ds, cpa) == dot(svec, dd)
     end
 
+    # center
+    @test center(cpa) == N[1, 2, 3, 4]
+
     # boundedness
     @test isbounded(cpa) && isboundedtype(typeof(cpa))
     cpa2 = CartesianProductArray([Singleton(N[1]), HalfSpace(N[1], N(1))])

test/LazyOperations/LinearMap.jl

@@ -17,6 +17,8 @@ for N in [Float64, Rational{Int}, Float32]
     @test σ(d, lm1) == N[-3, 0]
     d = N[1, -1]
     @test σ(d, lm1) == N[-1, 0]
+    # center
+    @test center(lm1) == N[-2, 1]
 
     # 2D -> 1D Projection
     b = BallInf(N[1, 2], N(1))

test/LazyOperations/MinkowskiSum.jl

@@ -45,6 +45,9 @@ for N in [Float64, Rational{Int}, Float32]
     v = σ(d, s)
     @test v[2] == N(2)
 
+    # center
+    @test center(s) == N[0, 5]
+
     # Sum of array of LazySet
     # 2-elements
     ms = MinkowskiSum(Singleton(N[1]), Singleton(N[2]))
@@ -147,6 +150,9 @@ for N in [Float64, Rational{Int}, Float32]
     # isempty
     @test !isempty(msa)
 
+    # center
+    @test center(msa) == N[0, 5]
+
     # convert m-sum of m-sum array to m-sum array (#1678)
     s = Singleton(N[1, 2, 3])
     X  = s ⊕ MinkowskiSumArray([s, s])