Merge pull request #2957 from JuliaReach/schillic/2111

#2111 - Volume for polytopes
JuliaReach · Apr 11, 2022 · 501c2d2 · 501c2d2
2 parents 393e67c + 0afdd1e
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diff --git a/docs/src/lib/interfaces.md b/docs/src/lib/interfaces.md
@@ -237,6 +237,7 @@ This interface defines the following functions:
 isbounded(::AbstractPolytope)
 isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N}
 isempty(::AbstractPolytope)
+volume(::AbstractPolytope)
 ```
 
 ### Implementations

diff --git a/docs/src/lib/sets/Ball1.md b/docs/src/lib/sets/Ball1.md
@@ -25,6 +25,7 @@ Inherited from [`LazySet`](@ref):
 Inherited from [`AbstractPolytope`](@ref):
 * [`isbounded`](@ref isbounded(::AbstractPolytope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`volume`](@ref volume(::AbstractPolytope))
 
 Inherited from [`AbstractCentrallySymmetricPolytope`](@ref):
 * [`dim`](@ref dim(::AbstractCentrallySymmetricPolytope))

diff --git a/docs/src/lib/sets/HParallelotope.md b/docs/src/lib/sets/HParallelotope.md
@@ -27,6 +27,7 @@ Inherited from [`LazySet`](@ref):
 Inherited from [`AbstractPolytope`](@ref):
 * [`isbounded`](@ref isbounded(::AbstractPolytope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`volume`](@ref volume(::AbstractPolytope))
 
 Inherited from [`AbstractCentrallySymmetricPolytope`](@ref):
 * [`dim`](@ref dim(::AbstractCentrallySymmetricPolytope))

diff --git a/docs/src/lib/sets/HPolygon.md b/docs/src/lib/sets/HPolygon.md
@@ -21,6 +21,7 @@ Inherited from [`AbstractPolyhedron`](@ref):
 Inherited from [`AbstractPolytope`](@ref):
 * [`isempty`](@ref isempty(::AbstractPolytope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`volume`](@ref volume(::AbstractPolytope))
 
 Inherited from [`AbstractPolygon`](@ref):
 * [`dim`](@ref dim(::AbstractPolygon))

diff --git a/docs/src/lib/sets/HPolygonOpt.md b/docs/src/lib/sets/HPolygonOpt.md
@@ -18,6 +18,7 @@ Inherited from [`LazySet`](@ref):
 Inherited from [`AbstractPolytope`](@ref):
 * [`isempty`](@ref isempty(::AbstractPolytope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`volume`](@ref volume(::AbstractPolytope))
 
 Inherited from [`AbstractPolygon`](@ref):
 * [`dim`](@ref dim(::AbstractPolygon))

diff --git a/docs/src/lib/sets/HPolytope.md b/docs/src/lib/sets/HPolytope.md
@@ -24,3 +24,4 @@ isbounded(::HPolytope, ::Bool=true)
 
 Inherited from [`AbstractPolytope`](@ref):
 * [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`volume`](@ref volume(::AbstractPolytope))
diff --git a/docs/src/lib/sets/LineSegment.md b/docs/src/lib/sets/LineSegment.md
@@ -29,6 +29,7 @@ Inherited from [`LazySet`](@ref):
 Inherited from [`AbstractPolytope`](@ref):
 * [`isbounded`](@ref isbounded(::AbstractPolytope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolytope, ::Bool=false))
+* [`volume`](@ref volume(::AbstractPolytope))
 
 Inherited from [`AbstractCentrallySymmetricPolytope`](@ref):
 * [`isempty`](@ref isempty(::AbstractCentrallySymmetricPolytope))

diff --git a/docs/src/lib/sets/RotatedHyperrectangle.md b/docs/src/lib/sets/RotatedHyperrectangle.md
@@ -26,6 +26,7 @@ Inherited from [`LazySet`](@ref):
 Inherited from [`AbstractPolytope`](@ref):
 * [`isbounded`](@ref isbounded(::AbstractPolytope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`volume`](@ref volume(::AbstractPolytope))
 
 Inherited from [`AbstractCentrallySymmetricPolytope`](@ref):
 * [`isempty`](@ref isempty(::AbstractCentrallySymmetricPolytope))

diff --git a/docs/src/lib/sets/VPolygon.md b/docs/src/lib/sets/VPolygon.md
@@ -32,6 +32,7 @@ Inherited from [`AbstractPolytope`](@ref):
 * [`isbounded`](@ref isbounded(::AbstractPolytope))
 * [`isempty`](@ref isempty(::AbstractPolytope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`volume`](@ref volume(::AbstractPolytope))
 
 Inherited from [`AbstractPolygon`](@ref):
 * [`dim`](@ref dim(::AbstractPolygon))
diff --git a/docs/src/lib/sets/VPolytope.md b/docs/src/lib/sets/VPolytope.md
@@ -33,3 +33,4 @@ Inherited from [`AbstractPolytope`](@ref):
 * [`isbounded`](@ref isbounded(::AbstractPolytope))
 * [`isempty`](@ref isempty(::AbstractPolytope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`volume`](@ref volume(::AbstractPolytope))
diff --git a/docs/src/lib/sets/Zonotope.md b/docs/src/lib/sets/Zonotope.md
@@ -33,6 +33,7 @@ Inherited from [`LazySet`](@ref):
 Inherited from [`AbstractPolytope`](@ref):
 * [`isbounded`](@ref isbounded(::AbstractPolytope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`volume`](@ref volume(::AbstractPolytope))
 
 Inherited from [`AbstractCentrallySymmetricPolytope`](@ref):
 * [`dim`](@ref dim(::AbstractCentrallySymmetricPolytope))

diff --git a/src/Interfaces/AbstractPolytope.jl b/src/Interfaces/AbstractPolytope.jl
@@ -152,3 +152,33 @@ end
 function _vertices_list(P::AbstractPolytope, backend)
     return vertices_list(P)
 end
+
+"""
+    volume(P::AbstractPolytope; backend=default_polyhedra_backend(P))
+
+Compute the volume of a polytope.
+
+### Input
+
+- `P`       -- polytope
+- `backend` -- (optional, default: `default_polyhedra_backend(P)`) the backend
+               for polyhedral computations; see [Polyhedra's
+               documentation](https://juliapolyhedra.github.io/) for further
+               information
+
+### Output
+
+The volume of `P`.
+
+### Algorithm
+
+The volume is computed by the `Polyhedra` library.
+"""
+function volume(P::AbstractPolytope; backend=nothing)
+    require(:Polyhedra; fun_name="volume")
+    if isnothing(backend)
+        backend = default_polyhedra_backend(P)
+    end
+
+    return Polyhedra.volume(polyhedron(P; backend=backend))
+end
diff --git a/test/Sets/Polytope.jl b/test/Sets/Polytope.jl
@@ -145,6 +145,7 @@ for N in [Float64, Rational{Int}, Float32]
             # ρ(::Vector{Float64}, ::HPolytope{Float32})
         end
     end
+
     # -----
     # V-rep
     # -----
@@ -190,6 +191,9 @@ for N in [Float64, Rational{Int}, Float32]
         Pe = polyhedron(Vempty, relative_dimension=2)
     end
 
+    # volume
+    @test volume(p) == N(1//2)
+
     # translation
     @test translate(p, N[1, 2]) == VPolytope([N[1, 2], N[2, 2], N[1, 3]])
     pp = copy(p)