AbstractPolynomialZonotope: add 'linear_combination'

Author: schillic

docs/src/lib/interfaces/AbstractPolynomialZonotope.md

@@ -60,6 +60,7 @@ Undocumented implementations:
 * [`isboundedtype`](@ref isboundedtype(::Type{LazySet}))
 * [`isempty`](@ref isempty(::LazySet))
 * [`isuniversal`](@ref isuniversal(::LazySet))
+* [`linear_combination`](@ref linear_combination(::LazySet, ::LazySet))
 
 ```@meta
 CurrentModule = LazySets

docs/src/lib/sets/DensePolynomialZonotope.md

@@ -77,7 +77,6 @@ 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))
 * [`minkowski_sum`](@ref minkowski_sum(::LazySet, ::LazySet))
 
@@ -90,3 +89,4 @@ Inherited from [`AbstractPolynomialZonotope`](@ref):
 * [`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

@@ -170,7 +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):

docs/src/lib/sets/SparsePolynomialZonotope.md

@@ -140,7 +140,6 @@ 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):
@@ -152,6 +151,7 @@ Inherited from [`AbstractPolynomialZonotope`](@ref):
 * [`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/linear_combination.jl

@@ -29,3 +29,10 @@ 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

test/Sets/SparsePolynomialZonotope.jl

@@ -141,6 +141,18 @@ 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]
 end
 
 for N in [Float64]