AbstractPolynomialZonotope: add linear_combination and convex_hull

docs/src/lib/interfaces/AbstractPolynomialZonotope.md

@@ -35,6 +35,7 @@ This interface defines the following functions:
 ```@docs
 ngens(::AbstractPolynomialZonotope)
 order(::AbstractPolynomialZonotope)
+convex_hull(::AbstractPolynomialZonotope, ::AbstractPolynomialZonotope)
 ```
 
 ```@meta
@@ -44,10 +45,12 @@ CurrentModule = LazySets.API
 Undocumented implementations:
 
 * [`center`](@ref center(::LazySet, ::Int))
+* [`convex_hull`](@ref convex_hull(::LazySet))
 * [`dim`](@ref dim(::LazySet))
 * [`isboundedtype`](@ref isboundedtype(::Type{LazySet}))
 * [`isempty`](@ref isempty(::LazySet))
 * [`isuniversal`](@ref isuniversal(::LazySet))
+* [`linear_combination`](@ref linear_combination(::LazySet, ::LazySet))
 
 ```@meta
 CurrentModule = LazySets
@@ -60,7 +63,6 @@ Inherited from [`LazySet`](@ref):
 * [`complement`](@ref complement(::LazySet))
 * [`concretize`](@ref concretize(::LazySet))
 * [`constraints`](@ref constraints(::LazySet))
-* [`convex_hull`](@ref convex_hull(::LazySet))
 * `copy(::Type{LazySet})`
 * [`diameter`](@ref diameter(::LazySet, ::Real=Inf))
 * [`eltype`](@ref eltype(::Type{<:LazySet}))
@@ -93,7 +95,6 @@ Inherited from [`LazySet`](@ref):
 * [`ρ`](@ref ρ(::AbstractVector, ::LazySet))
 * [`translate`](@ref translate(::LazySet, ::AbstractVector))
 * [`cartesian_product`](@ref cartesian_product(::LazySet, ::LazySet))
-* [`convex_hull`](@ref convex_hull(::LazySet, ::LazySet))
 * [`exact_sum`](@ref exact_sum(::LazySet, ::LazySet))
 * [`≈`](@ref ≈(::LazySet, ::LazySet))
 * [`isdisjoint`](@ref isdisjoint(::LazySet, ::LazySet))

docs/src/lib/sets/DensePolynomialZonotope.md

@@ -37,7 +37,6 @@ Inherited from [`LazySet`](@ref):
 * [`complement`](@ref complement(::LazySet))
 * [`concretize`](@ref concretize(::LazySet))
 * [`constraints`](@ref constraints(::LazySet))
-* [`convex_hull`](@ref convex_hull(::LazySet))
 * `copy(::Type{LazySet})`
 * [`diameter`](@ref diameter(::LazySet, ::Real=Inf))
 * [`eltype`](@ref eltype(::Type{<:LazySet}))
@@ -70,23 +69,24 @@ Inherited from [`LazySet`](@ref):
 * [`ρ`](@ref ρ(::AbstractVector, ::LazySet))
 * [`translate`](@ref translate(::LazySet, ::AbstractVector))
 * [`cartesian_product`](@ref cartesian_product(::LazySet, ::LazySet))
-* [`convex_hull`](@ref convex_hull(::LazySet, ::LazySet))
 * [`exact_sum`](@ref exact_sum(::LazySet, ::LazySet))
 * [`≈`](@ref ≈(::LazySet, ::LazySet))
 * [`isdisjoint`](@ref isdisjoint(::LazySet, ::LazySet))
 * [`==`](@ref ==(::LazySet, ::LazySet))
 * [`isequivalent`](@ref isequivalent(::LazySet, ::LazySet))
 * [`⊂`](@ref ⊂(::LazySet, ::LazySet))
 * [`⊆`](@ref ⊆(::LazySet, ::LazySet))
-* [`linear_combination`](@ref linear_combination(::LazySet, ::LazySet))
 * [`minkowski_difference`](@ref minkowski_difference(::LazySet, ::LazySet))
 * [`minkowski_sum`](@ref minkowski_sum(::LazySet, ::LazySet))
 
 Inherited from [`AbstractPolynomialZonotope`](@ref):
 * [`center`](@ref center(::AbstractPolynomialZonotope, ::Int))
+* [`convex_hull`](@ref convex_hull(::AbstractPolynomialZonotope))
 * [`dim`](@ref dim(::AbstractPolynomialZonotope))
 * [`isboundedtype`](@ref isboundedtype(::Type{AbstractPolynomialZonotope}))
 * [`isempty`](@ref isempty(::AbstractPolynomialZonotope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolynomialZonotope))
 * [`ngens`](@ref ngens(::AbstractPolynomialZonotope))
 * [`order`](@ref dim(::AbstractPolynomialZonotope))
+* [`convex_hull`](@ref convex_hull(::AbstractPolynomialZonotope, ::AbstractPolynomialZonotope))
+* [`linear_combination`](@ref linear_combination(::AbstractPolynomialZonotope, ::AbstractPolynomialZonotope))

docs/src/lib/sets/SimpleSparsePolynomialZonotope.md

@@ -84,18 +84,6 @@ CurrentModule = LazySets.SimpleSparsePolynomialZonotopeModule
 cartesian_product(::SimpleSparsePolynomialZonotope, ::SimpleSparsePolynomialZonotope)
 ```
 ```@meta
-CurrentModule = LazySets
-```
-```@docs; canonical=false
-convex_hull(::LazySet, ::LazySet)
-```
-```@meta
-CurrentModule = LazySets.SimpleSparsePolynomialZonotopeModule
-```
-```@docs
-convex_hull(::SimpleSparsePolynomialZonotope, ::SimpleSparsePolynomialZonotope)
-```
-```@meta
 CurrentModule = LazySets.API
 ```
 ```@docs; canonical=false
@@ -182,7 +170,6 @@ Inherited from [`LazySet`](@ref):
 * [`isequivalent`](@ref isequivalent(::LazySet, ::LazySet))
 * [`⊂`](@ref ⊂(::LazySet, ::LazySet))
 * [`⊆`](@ref ⊆(::LazySet, ::LazySet))
-* [`linear_combination`](@ref linear_combination(::LazySet, ::LazySet))
 * [`minkowski_difference`](@ref minkowski_difference(::LazySet, ::LazySet))
 
 Inherited from [`AbstractPolynomialZonotope`](@ref):
@@ -192,6 +179,7 @@ Inherited from [`AbstractPolynomialZonotope`](@ref):
 * [`isempty`](@ref isempty(::AbstractPolynomialZonotope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolynomialZonotope))
 * [`order`](@ref order(::AbstractPolynomialZonotope))
+* [`convex_hull`](@ref convex_hull(::AbstractPolynomialZonotope, ::AbstractPolynomialZonotope))
 
 Inherited from [`AbstractSparsePolynomialZonotope`](@ref):
 * [`ngens_dep`](@ref ngens_dep(::AbstractSparsePolynomialZonotope))

docs/src/lib/sets/SparsePolynomialZonotope.md

@@ -104,7 +104,6 @@ Inherited from [`LazySet`](@ref):
 * [`complement`](@ref complement(::LazySet))
 * [`concretize`](@ref concretize(::LazySet))
 * [`constraints`](@ref constraints(::LazySet))
-* [`convex_hull`](@ref convex_hull(::LazySet))
 * `copy(::Type{LazySet})`
 * [`diameter`](@ref diameter(::LazySet, ::Real=Inf))
 * [`eltype`](@ref eltype(::Type{<:LazySet}))
@@ -134,24 +133,25 @@ Inherited from [`LazySet`](@ref):
 * [`sample`](@ref sample(::LazySet, ::Int=1))
 * [`scale`](@ref scale(::Real, ::LazySet))
 * [`σ`](@ref σ(::AbstractVector, ::LazySet))
-* [`convex_hull`](@ref convex_hull(::LazySet, ::LazySet))
 * [`≈`](@ref ≈(::LazySet, ::LazySet))
 * [`isdisjoint`](@ref isdisjoint(::LazySet, ::LazySet))
 * [`==`](@ref ==(::LazySet, ::LazySet))
 * [`isequivalent`](@ref isequivalent(::LazySet, ::LazySet))
 * [`⊂`](@ref ⊂(::LazySet, ::LazySet))
 * [`⊆`](@ref ⊆(::LazySet, ::LazySet))
-* [`linear_combination`](@ref linear_combination(::LazySet, ::LazySet))
 * [`minkowski_difference`](@ref minkowski_difference(::LazySet, ::LazySet))
 
 Inherited from [`AbstractPolynomialZonotope`](@ref):
 * [`center`](@ref center(::AbstractPolynomialZonotope, ::Int))
+* [`convex_hull`](@ref convex_hull(::AbstractPolynomialZonotope))
 * [`dim`](@ref dim(::AbstractPolynomialZonotope))
 * [`isboundedtype`](@ref isboundedtype(::Type{AbstractPolynomialZonotope}))
 * [`isempty`](@ref isempty(::AbstractPolynomialZonotope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolynomialZonotope))
 * [`ngens`](@ref ngens(::AbstractPolynomialZonotope))
 * [`order`](@ref order(::AbstractPolynomialZonotope))
+* [`convex_hull`](@ref convex_hull(::AbstractPolynomialZonotope, ::AbstractPolynomialZonotope))
+* [`linear_combination`](@ref linear_combination(::AbstractPolynomialZonotope, ::AbstractPolynomialZonotope))
 
 Inherited from [`AbstractSparsePolynomialZonotope`](@ref):
 * [`ngens_dep`](@ref ngens_dep(::AbstractSparsePolynomialZonotope))

src/ConcreteOperations/convex_hull.jl

@@ -485,3 +485,16 @@ end
 @commutative function convex_hull(X::LazySet, ∅::EmptySet)
     return EmptySetModule._convex_hull_emptyset(∅, X)
 end
+
+"""
+# Extended help
+
+    convex_hull(PZ1::AbstractPolynomialZonotope, PZ2::AbstractPolynomialZonotope)
+
+### Output
+
+The tightest convex polynomial zonotope containing `P1` and `P2`.
+"""
+function convex_hull(PZ1::AbstractPolynomialZonotope, PZ2::AbstractPolynomialZonotope)
+    return linear_combination(convex_hull(PZ1), convex_hull(PZ2))
+end

src/ConcreteOperations/linear_combination.jl

@@ -29,3 +29,14 @@ end
 @commutative function linear_combination(∅::EmptySet, X::ConvexSet)
     return _linear_combination_emptyset(∅, X)
 end
+
+function linear_combination(P1::AbstractPolynomialZonotope,
+                            P2::AbstractPolynomialZonotope)
+    SSPZ1 = convert(SimpleSparsePolynomialZonotope, P1)
+    SSPZ2 = convert(SimpleSparsePolynomialZonotope, P2)
+    return linear_combination(SSPZ1, SSPZ2)
+end
+
+@commutative function linear_combination(Z::AbstractZonotope, P::AbstractPolynomialZonotope)
+    return linear_combination(convert(SparsePolynomialZonotope, Z), P)
+end

src/Interfaces/AbstractPolynomialZonotope.jl

@@ -128,3 +128,7 @@ dim(PZ::AbstractPolynomialZonotope) = length(center(PZ))
 isempty(PZ::AbstractPolynomialZonotope) = false
 
 isuniversal(PZ::AbstractPolynomialZonotope) = false
+
+function convex_hull(PZ::AbstractPolynomialZonotope)
+    return convex_hull(convert(SimpleSparsePolynomialZonotope, PZ))
+end

src/Sets/SimpleSparsePolynomialZonotope/convex_hull.jl

@@ -10,17 +10,3 @@ The tightest convex simple sparse polynomial zonotope containing `P`.
 function convex_hull(P::SimpleSparsePolynomialZonotope)
     return linear_combination(P, P)
 end
-
-"""
-# Extended help
-
-    convex_hull(P1::SimpleSparsePolynomialZonotope,
-                P2::SimpleSparsePolynomialZonotope)
-
-### Output
-
-The tightest convex simple sparse polynomial zonotope containing `P1` and `P2`.
-"""
-function convex_hull(P1::SimpleSparsePolynomialZonotope, P2::SimpleSparsePolynomialZonotope)
-    return linear_combination(linear_combination(P1, P1), linear_combination(P2, P2))
-end

test/Sets/SparsePolynomialZonotope.jl

@@ -141,6 +141,21 @@ for N in [Float64, Float32, Rational{Int}]
     @test isequivalent(overapproximate(PZ, Zonotope), Z)
     SSPZ2 = convert(SimpleSparsePolynomialZonotope, PZ)
     @test isequivalent(overapproximate(SSPZ2, Zonotope, dom2), Z)
+
+    # Example 3.1.29 from thesis
+    PZ1 = SparsePolynomialZonotope(N[-5, 0], N[2 0 2; 0 2 2], Matrix{N}(undef, 2, 0), [1 0 1; 0 1 1])
+    PZ2 = SparsePolynomialZonotope(N[3, 3], N[1 -2 2; 2 3 1], hcat(N[1//2; 0]), [1 0 2; 0 1 1])
+    PZ_lc = linear_combination(PZ1, PZ2)
+    # no reasonable tests available here
+    @test PZ_lc isa SimpleSparsePolynomialZonotope{N}
+    @test center(PZ_lc) == N[-1, 3//2]
+    PZ_ch = convex_hull(PZ1, PZ2)
+    # no reasonable tests available here
+    @test PZ_ch isa SimpleSparsePolynomialZonotope{N}
+    @test center(PZ_ch) == N[-1, 3//2]
+    # mixed linear_combination
+    PZ_lc = linear_combination(PZ1, ZeroSet{N}(2))
+    @test PZ_lc isa SimpleSparsePolynomialZonotope{N}
 end
 
 for N in [Float64]