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(::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.

rectify(S::Singleton)

Concrete rectification of a singleton.

Input

• S – singleton

Output

The Singleton that corresponds to the rectification of S.

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.

linear_map(M::AbstractMatrix, S::Singleton)

Concrete linear map of a singleton.

Input

• M – matrix
• S – singleton

Output

A singleton.

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.

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.

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

Translate (i.e., shift) a singleton by a given vector, in-place.

Input

• S – singleton
• v – translation vector

Output

The singleton S translated by v.

Algorithm

We add the vector to the point in the singleton.

Notes

See also translate(::Singleton, ::AbstractVector) for the out-of-place version.