Merge pull request #3663 from JuliaReach/schillic/emptyset

`EmptySet` minor revision

docs/src/lib/sets/EmptySet.md

@@ -12,32 +12,9 @@ EmptySet
 ## Operations
 
 ```@docs
-an_element(::EmptySet)
-area(::EmptySet)
 chebyshev_center_radius(::EmptySet; kwargs...)
 complement(::EmptySet{N}) where {N}
-diameter(::EmptySet, ::Real=Inf)
-dim(::EmptySet)
-high(::EmptySet)
-high(::EmptySet, ::Int)
-isbounded(::EmptySet)
-isempty(::EmptySet)
-isuniversal(::EmptySet{N}, ::Bool=false) where {N}
-low(::EmptySet)
-low(::EmptySet, ::Int)
-norm(::EmptySet, ::Real=Inf)
-radius(::EmptySet, ::Real=Inf)
 rand(::Type{EmptySet})
-rectify(::EmptySet)
-reflect(::EmptySet)
-vertices_list(::EmptySet)
-vertices(::EmptySet)
-volume(::EmptySet{N}) where {N}
-∈(::AbstractVector, ::EmptySet)
-linear_map(::AbstractMatrix, ::EmptySet)
-ρ(::AbstractVector, ::EmptySet)
-σ(::AbstractVector, ::EmptySet)
-translate(::EmptySet, ::AbstractVector)
 plot_recipe(::EmptySet{N}, ::Any=zero(N)) where {N}
 ```
 
@@ -46,15 +23,36 @@ CurrentModule = LazySets.API
 ```
 
 Undocumented implementations:
+
+* [`an_element`](@ref an_element(::LazySet))
+* [`area`](@ref area(::LazySet))
 * [`convex_hull`](@ref convex_hull(::LazySet))
+* [`diameter`](@ref diameter(::LazySet, ::Real=Inf))
+* [`dim`](@ref dim(::LazySet))
+* [`high`](@ref high(::LazySet))
+* [`high`](@ref high(::LazySet, ::Int))
+* [`isbounded`](@ref isbounded(::LazySet))
 * [`isboundedtype`](@ref isboundedtype(::Type{LazySet}))
 * [`isconvextype`](@ref isconvextype(::Type{LazySet}))
+* [`isempty`](@ref isempty(::LazySet))
 * [`isoperationtype`](@ref isoperationtype(::Type{LazySet}))
-* [`affine_map`](@ref affine_map(::AbstractMatrix, ::LazySet, ::AbstractVector))
-* [`exponential_map`](@ref exponential_map(::AbstractMatrix, ::LazySet))
-* [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::LazySet))
+* [`isuniversal`](@ref isuniversal(::LazySet, ::Bool=false))
+* [`low`](@ref low(::LazySet))
+* [`low`](@ref low(::LazySet, ::Int))
+* [`norm`](@ref norm(::LazySet, ::Real=Inf))
+* [`radius`](@ref radius(::LazySet, ::Real=Inf))
+* [`rectify`](@ref rectify(::LazySet))
+* [`reflect`](@ref reflect(::LazySet))
+* [`vertices_list`](@ref vertices_list(::LazySet))
+* [`vertices`](@ref vertices(::LazySet))
+* [`volume`](@ref volume(::LazySet))
+* [`∈`](@ref ∈(::AbstractVector, ::LazySet))
+* [`linear_map`](@ref linear_map(::AbstractMatrix, ::LazySet))
+* [`ρ`](@ref ρ(::AbstractVector, ::LazySet))
+* [`σ`](@ref σ(::AbstractVector, ::LazySet))
 * [`scale`](@ref scale(::Real, ::LazySet))
 * [`scale!`](@ref scale!(::Real, ::LazySet))
+* [`translate`](@ref translate(::LazySet, ::AbstractVector))
 * [`translate!`](@ref translate!(::LazySet, ::AbstractVector))
 * [`convex_hull`](@ref convex_hull(::LazySet, ::LazySet))
 * [`intersection`](@ref isequivalent(::LazySet, ::LazySet))
@@ -75,6 +73,9 @@ Inherited from [`LazySet`](@ref):
 * [`ispolyhedral`](@ref ispolyhedral(::LazySet))
 * [`singleton_list`](@ref singleton_list(::LazySet))
 * [`surface`](@ref surface(::LazySet))
+* [`affine_map`](@ref affine_map(::AbstractMatrix, ::LazySet, ::AbstractVector))
+* [`exponential_map`](@ref exponential_map(::AbstractMatrix, ::LazySet))
+* [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::LazySet))
 * [`cartesian_product`](@ref cartesian_product(::LazySet, ::LazySet))
 * [`≈`](@ref ≈(::LazySet, ::LazySet))
 * [`==`](@ref ==(::LazySet, ::LazySet))

src/Sets/EmptySet/an_element.jl

@@ -1,16 +1,3 @@
-"""
-    an_element(∅::EmptySet)
-
-Return some element of an empty set.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-An error.
-"""
 function an_element(::EmptySet)
-    return error("an empty set does not contain any element")
+    throw(ArgumentError("an empty set does not contain any element"))
 end

src/Sets/EmptySet/area.jl

@@ -1,16 +1,3 @@
-"""
-    area(∅::EmptySet)
-
-Return the area of an empty set.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-``0``.
-"""
 function area(∅::EmptySet)
     N = eltype(∅)
     return zero(N)

src/Sets/EmptySet/chebyshev_center_radius.jl

@@ -14,5 +14,5 @@ and the corresponding radius of an empty set.
 An error.
 """
 function chebyshev_center_radius(∅::EmptySet; kwargs...)
-    return error("the Chebyshev center and radius of an empty set are undefined")
+    throw(ArgumentError("the Chebyshev center and radius of an empty set are undefined"))
 end

src/Sets/EmptySet/complement.jl

@@ -1,15 +1,11 @@
 """
-    complement(∅::EmptySet{N}) where {N}
-
-Return the complement of an empty set.
+# Extended help
 
-### Input
-
-- `∅` -- empty set
+    complement(∅::EmptySet{N}) where {N}
 
 ### Output
 
-The universe of the same dimension.
+The [`Universe`](@ref) of the same dimension.
 """
 function complement(∅::EmptySet{N}) where {N}
     require(@__MODULE__, :LazySets; fun_name="complement")

src/Sets/EmptySet/convex_hull.jl

@@ -1 +1,9 @@
-convex_hull(∅::EmptySet, ::EmptySet) = ∅
+function convex_hull(∅::EmptySet)
+    return ∅
+end
+
+function convex_hull(∅₁::EmptySet, ∅₂::EmptySet)
+    @assert dim(∅₁) == dim(∅₂) "cannot take the convex hull between two " *
+                               "empty sets of dimensions $(dim(∅₁)) and $(dim(∅₂))"
+    return ∅₁
+end

src/Sets/EmptySet/diameter.jl

@@ -1,20 +1,3 @@
-"""
-    diameter(∅::EmptySet, [p]::Real=Inf)
-
-Return the diameter of an empty set.
-It is the maximum distance between any two elements of the set or, equivalently,
-the diameter of the enclosing ball (of the given ``p``-norm) of minimal volume
-with the same center.
-
-### Input
-
-- `∅` -- empty set
-- `p` -- (optional, default: `Inf`) norm
-
-### Output
-
-An error.
-"""
 function diameter(::EmptySet, ::Real=Inf)
-    return error("the diameter of an empty set is undefined")
+    throw(ArgumentError("the diameter of an empty set is undefined"))
 end

src/Sets/EmptySet/dim.jl

@@ -1,16 +1,3 @@
-"""
-    dim(∅::EmptySet)
-
-Return the dimension of an empty set.
-
-### Input
-
-- `∅` -- an empty set
-
-### Output
-
-The dimension of the empty set.
-"""
 function dim(∅::EmptySet)
     return ∅.dim
 end

src/Sets/EmptySet/high.jl

@@ -1,39 +1,7 @@
-"""
-    high(∅::EmptySet)
-
-Return a vector with the highest coordinates of an empty set in each canonical
-direction.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-An error.
-
-### Notes
-
-See also [`high(∅::EmptySet, i::Int)`](@ref).
-"""
 function high(::EmptySet)
-    return error("the upper bound of an empty set is undefined")
+    throw(ArgumentError("the upper bound of an empty set is undefined"))
 end
 
-"""
-    high(∅::EmptySet, i::Int)
-
-Return the highest coordinate of an empty set in the given direction.
-
-### Input
-
-- `∅` -- empty set
-- `i` -- dimension of interest
-
-### Output
-
-An error.
-"""
 function high(::EmptySet, ::Int)
-    return error("the upper bound of an empty set is undefined")
+    throw(ArgumentError("the upper bound of an empty set is undefined"))
 end

src/Sets/EmptySet/in.jl

@@ -1,24 +1,3 @@
-"""
-    ∈(x::AbstractVector, ∅::EmptySet)
-
-Check whether a given point is contained in an empty set.
-
-### Input
-
-- `x` -- point/vector
-- `∅` -- empty set
-
-### Output
-
-`false`.
-
-### Examples
-
-```jldoctest
-julia> [1.0, 0.0] ∈ ∅(2)
-false
-```
-"""
 function ∈(::AbstractVector, ::EmptySet)
     return false
 end

src/Sets/EmptySet/isbounded.jl

@@ -1,16 +1,3 @@
-"""
-    isbounded(∅::EmptySet)
-
-Check whether an empty set is bounded.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-`true`.
-"""
 function isbounded(::EmptySet)
     return true
 end

src/Sets/EmptySet/isempty.jl

@@ -1,16 +1,3 @@
-"""
-    isempty(∅::EmptySet)
-
-Check if the empty set is empty.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-`true`.
-"""
 function isempty(::EmptySet)
     return true
 end

src/Sets/EmptySet/isuniversal.jl

@@ -1,18 +1,3 @@
-"""
-    isuniversal(∅::EmptySet{N}, [witness]::Bool=false) where {N}
-
-Check whether an empty set is universal.
-
-### Input
-
-- `∅`       -- empty set
-- `witness` -- (optional, default: `false`) compute a witness if activated
-
-### Output
-
-* If `witness` option is deactivated: `false`
-* If `witness` option is activated: `(false, v)` where ``v ∉ S``
-"""
 function isuniversal(∅::EmptySet{N}, witness::Bool=false) where {N}
     if witness
         return (false, zeros(N, dim(∅)))

src/Sets/EmptySet/linear_map.jl

@@ -1,21 +1,7 @@
-"""
-    linear_map(M::AbstractMatrix{N}, ∅::EmptySet{N}) where {N}
-
-Return the linear map of an empty set.
-
-### Input
-
-- `M` -- matrix
-- `∅` -- empty set
-
-### Output
-
-An empty set.
-"""
 function linear_map(M::AbstractMatrix, ∅::EmptySet)
-    N = eltype(∅)
     @assert size(M, 2) == dim(∅) "cannot apply a $(size(M))-dimensional " *
                                  "matrix to a $(dim(∅))-dimensional set"
 
+    N = eltype(∅)
     return EmptySet{N}(size(M, 1))
 end

src/Sets/EmptySet/low.jl

@@ -1,39 +1,7 @@
-"""
-    low(∅::EmptySet)
-
-Return a vector with the lowest coordinates of an empty set in each canonical
-direction.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-An error.
-
-### Notes
-
-See also [`low(∅::EmptySet, i::Int)`](@ref).
-"""
 function low(::EmptySet)
-    return error("the lower bound of an empty set is undefined")
+    throw(ArgumentError("the lower bound of an empty set is undefined"))
 end
 
-"""
-    low(∅::EmptySet, i::Int)
-
-Return the lowest coordinate of an empty set in the given direction.
-
-### Input
-
-- `∅` -- empty set
-- `i` -- dimension of interest
-
-### Output
-
-An error.
-"""
 function low(::EmptySet, ::Int)
-    return error("the lower bound of an empty set is undefined")
+    throw(ArgumentError("the lower bound of an empty set is undefined"))
 end

src/Sets/EmptySet/norm.jl

@@ -1,19 +1,3 @@
-"""
-    norm(∅::EmptySet, [p]::Real=Inf)
-
-Return the norm of an empty set.
-It is the norm of the enclosing ball (of the given ``p``-norm) of minimal volume
-that is centered in the origin.
-
-### Input
-
-- `∅` -- empty set
-- `p` -- (optional, default: `Inf`) norm
-
-### Output
-
-An error.
-"""
 function norm(::EmptySet, ::Real=Inf)
-    return error("the norm of an empty set is undefined")
+    throw(ArgumentError("the norm of an empty set is undefined"))
 end