EmptySet: shorten docs & throw ArgumentErrors

docs/src/lib/sets/EmptySet.md

@@ -36,7 +36,7 @@ Undocumented implementations:
 * [`isconvextype`](@ref isconvextype(::Type{LazySet}))
 * [`isempty`](@ref isempty(::LazySet))
 * [`isoperationtype`](@ref isoperationtype(::Type{LazySet}))
-* [`isuniversal`](@ref isuniversal(::LazySet{N}, ::Bool=false) where {N})
+* [`isuniversal`](@ref isuniversal(::LazySet, ::Bool=false))
 * [`low`](@ref low(::LazySet))
 * [`low`](@ref low(::LazySet, ::Int))
 * [`norm`](@ref norm(::LazySet, ::Real=Inf))
@@ -45,7 +45,7 @@ Undocumented implementations:
 * [`reflect`](@ref reflect(::LazySet))
 * [`vertices_list`](@ref vertices_list(::LazySet))
 * [`vertices`](@ref vertices(::LazySet))
-* [`volume`](@ref volume(::LazySet{N}) where {N})
+* [`volume`](@ref volume(::LazySet))
 * [`∈`](@ref ∈(::AbstractVector, ::LazySet))
 * [`linear_map`](@ref linear_map(::AbstractMatrix, ::LazySet))
 * [`ρ`](@ref ρ(::AbstractVector, ::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/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

src/Sets/EmptySet/radius.jl

@@ -1,19 +1,3 @@
-"""
-    radius(∅::EmptySet, [p]::Real=Inf)
-
-Return the radius of an empty set.
-It is the radius 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 radius(::EmptySet, ::Real=Inf)
-    return error("the radius of an empty set is undefined")
+    throw(ArgumentError("the radius of an empty set is undefined"))
 end

src/Sets/EmptySet/rand.jl

@@ -1,20 +1,12 @@
 """
+# Extended help
+
     rand(::Type{EmptySet}; [N]::Type{<:Real}=Float64, [dim]::Int=2,
          [rng]::AbstractRNG=GLOBAL_RNG, [seed]::Union{Int, Nothing}=nothing)
 
-Create an empty set (note that there is nothing to randomize).
-
-### Input
-
-- `EmptySet` -- type for dispatch
-- `N`        -- (optional, default: `Float64`) numeric type
-- `dim`      -- (optional, default: 2) dimension
-- `rng`      -- (optional, default: `GLOBAL_RNG`) random number generator
-- `seed`     -- (optional, default: `nothing`) seed for reseeding
-
 ### Output
 
-The (only) empty set of the given numeric type and dimension.
+The (unique) empty set of the given numeric type and dimension.
 """
 function rand(::Type{EmptySet};
               N::Type{<:Real}=Float64,

src/Sets/EmptySet/rectify.jl

@@ -1,16 +1,3 @@
-"""
-    rectify(∅::EmptySet)
-
-Concrete rectification of an empty set.
-
-### Input
-
-- `∅` -- empty set
-
-### Output
-
-The empty set.
-"""
 function rectify(∅::EmptySet)
     return ∅
 end