Empty set (EmptySet)

EmptySet{N} <: ConvexSet{N}

Type that represents the empty set, i.e., the set with no elements.

∅

Alias for EmptySet{Float64}.

chebyshev_center_radius(∅::EmptySet; [kwargs]...)

Compute a Chebyshev center and the corresponding radius of an empty set.

Input

• ∅ – empty set
• kwargs – further keyword arguments (ignored)

Output

An error.

complement(X::LazySet)

Compute the complement of a set.

Input

• X – set

Output

A set representing the complement of X.

Extended help

complement(∅::EmptySet)

Output

The Universe of the same dimension.

rand(T::Type{<:LazySet}; [N]::Type{<:Real}=Float64, [dim]::Int=2,
     [rng]::AbstractRNG=GLOBAL_RNG, [seed]::Union{Int, Nothing}=nothing
    )

Create a random set of the given set type.

Input

• T – set type
• 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

A random set of the given set type.

Extended help

rand(::Type{EmptySet}; [N]::Type{<:Real}=Float64, [dim]::Int=2,
     [rng]::AbstractRNG=GLOBAL_RNG, [seed]::Union{Int, Nothing}=nothing)

Output

The (unique) empty set of the given numeric type and dimension.

plot_recipe(∅::EmptySet{N}, [ε]=zero(N)) where {N}

Convert an empty set to a sequence of points for plotting. In the special case of an empty set, the sequence is empty.

Input

• ∅ – empty set
• ε – (optional, default: 0) ignored, used for dispatch

Output

An empty array.