#58 - modified AbstractPointSymmetricPolytope types

src/Ball1.jl

@@ -3,7 +3,7 @@ import Base.∈
 export Ball1
 
 """
-    Ball1 <: LazySet
+    Ball1{N<:Real} <: AbstractPointSymmetricPolytope{N}
 
 Type that represents a ball in the 1-norm, also known as Manhattan or Taxicab
 norm.
@@ -40,7 +40,7 @@ julia> σ([0.,1], B)
  1.0
 ```
 """
-struct Ball1{N<:Real} <: LazySet
+struct Ball1{N<:Real} <: AbstractPointSymmetricPolytope{N}
     center::Vector{N}
     radius::N
 
@@ -51,39 +51,67 @@ end
 # type-less convenience constructor
 Ball1(center::Vector{N}, radius::N) where {N<:Real} = Ball1{N}(center, radius)
 
+
+# --- AbstractPointSymmetric interface functions ---
+
+
 """
-    dim(B::Ball1)::Int
+    center(B::Ball1{N})::Vector{N} where {N<:Real}
 
-Return the dimension of a `Ball1`.
+Return the center of a ball in the 1-norm.
 
 ### Input
 
-- `B` -- a ball in the 1-norm
+- `B` -- ball in the 1-norm
 
 ### Output
 
-The ambient dimension of the ball.
+The center of the ball in the 1-norm.
 """
-function dim(B::Ball1)::Int
-    return length(B.center)
+function center(B::Ball1{N})::Vector{N} where {N<:Real}
+    return B.center
 end
 
+
+# --- AbstractPolytope interface functions ---
+
+
+"""
+    vertices_list(B::Ball1{N})::Vector{Vector{N}} where {N<:Real}
+
+Return the list of vertices of a ball in the 1-norm.
+
+### Input
+
+- `B` -- ball in the 1-norm
+
+### Output
+
+A list containing only a single vertex.
+"""
+function vertices_list(B::Ball1{N})::Vector{Vector{N}} where {N<:Real}
+    error("this function is not implemented yet, see issue #84")
+end
+
+
+# --- LazySet interface functions ---
+
+
 """
     σ(d::AbstractVector{N}, B::Ball1)::AbstractVector{N} where {N<:Real}
 
-Return the support vector of a `Ball1` in a given direction.
+Return the support vector of a ball in the 1-norm in a given direction.
 
 ### Input
 
-- `d` -- a direction
-- `B` -- a ball in the p-norm
+- `d` -- direction
+- `B` -- ball in the 1-norm
 
 ### Output
 
 Support vector in the given direction.
 """
-function σ(d::AbstractVector{N},
-           B::Ball1)::AbstractVector{N} where {N<:AbstractFloat}
+function σ(d::AbstractVector{N}, B::Ball1{N})::AbstractVector{N} where {N<:Real}
     res = copy(B.center)
     imax = indmax(abs.(d)) 
     res[imax] = sign(d[imax]) * B.radius

src/Zonotope.jl

@@ -1,11 +1,10 @@
 import Base.∈
 
 export Zonotope,
-       vertices_list,
        order
 
 """
-    Zonotope{N<:Real} <: LazySet
+    Zonotope{N<:Real} <: AbstractPointSymmetricPolytope{N}
 
 Type that represents a zonotope.
 
@@ -32,7 +31,8 @@ ball in ``\\mathbb{R}^n`` by an affine transformation.
             generators::AbstractMatrix{N}) where {N<:Real}`
 
 - `Zonotope(center::AbstractVector{N},
-            generators_list::AbstractVector{T}) where {N<:Real, T<:AbstractVector{N}}`
+            generators_list::AbstractVector{T}
+           ) where {N<:Real, T<:AbstractVector{N}}`
 
 ### Examples
 
@@ -76,7 +76,7 @@ julia> Z.generators
  0.0  1.0  1.0
 ```
 """
-struct Zonotope{N<:Real} <: LazySet
+struct Zonotope{N<:Real} <: AbstractPointSymmetricPolytope{N}
     center::AbstractVector{N}
     generators::AbstractMatrix{N}
 end
@@ -85,43 +85,31 @@ Zonotope(center::AbstractVector{N},
          generators_list::AbstractVector{T}) where {N<:Real, T<:AbstractVector{N}} =
     Zonotope(center, hcat(generators_list...))
 
-"""
-    dim(Z::Zonotope)::Int
 
-Return the dimension of a zonotope.
+# --- AbstractPointSymmetric interface functions ---
 
-### Input
 
-- `Z` -- zonotope
-
-### Output
-
-The ambient dimension of the zonotope.
 """
-function dim(Z::Zonotope)::Int
-    return length(Z.center)
-end
+    center(Z::Zonotope{N})::Vector{N} where {N<:Real}
 
-"""
-    σ(d::AbstractVector{<:Real}, Z::Zonotope)::AbstractVector{<:Real}
-
-Return the support vector of a zonotope in a given direction.
+Return the center of a zonotope.
 
 ### Input
 
-- `d` -- direction
 - `Z` -- zonotope
 
 ### Output
 
-Support vector in the given direction.
-If the direction has norm zero, the vertex with ``ξ_i = 1 \\ \\ ∀ i = 1,…, p``
-is returned.
+The center of the zonotope.
 """
-function σ(d::AbstractVector{<:Real}, Z::Zonotope)::AbstractVector{<:Real}
-    return Z.center .+ Z.generators * sign_cadlag.(Z.generators.' * d)
+function center(Z::Zonotope{N})::Vector{N} where {N<:Real}
+    return Z.center
 end
 
+
+# --- AbstractPolytope interface functions ---
+
+
 """
     vertices_list(Z::Zonotope{N})::Vector{Vector{N}} where {N<:Real}
 
@@ -154,26 +142,28 @@ function vertices_list(Z::Zonotope{N})::Vector{Vector{N}} where {N<:Real}
     return convex_hull!(vlist)
 end
 
+
+# --- LazySet interface functions ---
+
+
 """
-    order(Z::Zonotope)::Rational
+    σ(d::AbstractVector{<:Real}, Z::Zonotope)::AbstractVector{<:Real}
 
-Return the order of a zonotope.
+Return the support vector of a zonotope in a given direction.
 
 ### Input
 
+- `d` -- direction
 - `Z` -- zonotope
 
 ### Output
 
-A rational number representing the order of the zonotope.
-
-### Notes
-
-The order of a zonotope is defined as the quotient of its number of generators
-and its dimension.
+Support vector in the given direction.
+If the direction has norm zero, the vertex with ``ξ_i = 1 \\ \\ ∀ i = 1,…, p``
+is returned.
 """
-function order(Z::Zonotope)::Rational
-    return size(Z.generators, 2) // dim(Z)
+function σ(d::AbstractVector{<:Real}, Z::Zonotope)::AbstractVector{<:Real}
+    return Z.center .+ Z.generators * sign_cadlag.(Z.generators.' * d)
 end
 
 """
@@ -239,3 +229,29 @@ function ∈(x::AbstractVector{N}, Z::Zonotope{N})::Bool where {N<:Real}
         return false
     end
 end
+
+
+# --- Zonotope functions ---
+
+
+"""
+    order(Z::Zonotope)::Rational
+
+Return the order of a zonotope.
+
+### Input
+
+- `Z` -- zonotope
+
+### Output
+
+A rational number representing the order of the zonotope.
+
+### Notes
+
+The order of a zonotope is defined as the quotient of its number of generators
+and its dimension.
+"""
+function order(Z::Zonotope)::Rational
+    return size(Z.generators, 2) // dim(Z)
+end