Singleton

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

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

Fields

• element – the only element of the set

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.

element(S::Singleton)

Return the element of a singleton.

Input

• S – singleton

Output

The element of the singleton.

element(S::Singleton, i::Int)

Return the i-th entry of the element of a singleton.

Input

• S – singleton
• i – dimension

Output

The i-th entry of the element of the singleton.

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

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

Input

• S – singleton
• v – translation vector

Output

A translated singleton.

Algorithm

We add the vector to the point in the singleton.

rectify(S::Singleton)

Concrete rectification of a singleton.

Input

• S – singleton

Output

The Singleton that corresponds to the rectification of S.

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.