# Singleton

LazySets.SingletonModule.SingletonType
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])
source

## Operations

LazySets.elementMethod
element(S::Singleton)

Return the element of a singleton.

Input

• S – singleton

Output

The element of the singleton.

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

Create a random singleton.

Input

• Singleton – 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

A random singleton.

Algorithm

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

source
ReachabilityBase.Arrays.rectifyMethod
rectify(S::Singleton)

Concrete rectification of a singleton.

Input

• S – singleton

Output

The Singleton that corresponds to the rectification of S.

source
LazySets.singleton_listMethod
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.

source
LazySets.API.linear_mapMethod
linear_map(M::AbstractMatrix, S::Singleton)

Concrete linear map of a singleton.

Input

• M – matrix
• S – singleton

Output

A singleton.

source
SparseArrays.permuteMethod
permute(S::Singleton, p::AbstractVector{Int})

Permute the dimensions according to a permutation vector.

Input

• S – singleton
• p – permutation vector

Output

A new Singleton with the permuted dimensions.

source
LazySets.API.projectMethod
project(S::Singleton, block::AbstractVector{Int}; kwargs...)

Concrete projection of a singleton.

Input

• S – singleton
• block – block structure, a vector with the dimensions of interest

Output

A set representing the projection of the singleton S on the dimensions specified by block.

source

Inherited from LazySet:

Inherited from ConvexSet:

Inherited from AbstractPolyhedron:

Inherited from AbstractPolytope:

Inherited from AbstractCentrallySymmetricPolytope:

Inherited from AbstractZonotope:

Inherited from AbstractHyperrectangle:

Inherited from AbstractSingleton: