Singleton

Singleton{N, VN<:AbstractVector{N}} <: AbstractSingleton{N}

Type that represents a singleton, that is, a set with a single element.

Fields

• element – the only element of the set

Examples

julia> Singleton([1.0, 2.0])
Singleton{Float64, Vector{Float64}}([1.0, 2.0])

julia> Singleton(1.0, 2.0)  # convenience constructor from numbers
Singleton{Float64, Vector{Float64}}([1.0, 2.0])

element(S::Singleton)

Return the element of a singleton.

Input

• S – singleton

Output

The element of the singleton.

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.

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

Algorithm

The element is a normally distributed vector with entries of mean 0 and standard deviation 1.

singleton_list(P::LazySet)

Return the vertices of a polytopic set as a list of singletons.

Input

• P – polytopic set

Output

A list of the vertices of P as Singletons.

Notes

This function relies on vertices_list, which raises an error if the set is not polytopic (e.g., unbounded).

singleton_list(S::Singleton)

Return the vertices of a singleton as a list of singletons.

Input

• S – singleton

Output

The list of vertices of S, as Singleton.

translate!(X::LazySet, v::AbstractVector)

Translate a set with a vector by modifying it.

Input

• X – set
• v – vector

Output

The translated set representing $X + \{v\}$.

Extended help

translate!(S::Singleton, v::AbstractVector)

Algorithm

We add the vector to the point in the singleton.