Singleton

LazySets.SingletonType
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

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])
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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.

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LazySets.elementMethod
element(S::Singleton)

Return the element of a singleton.

Input

  • S – singleton

Output

The element of the singleton.

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LazySets.elementMethod
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.

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LazySets.translateMethod
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.

Notes

See also translate!(::Singleton, ::AbstractVector) for the in-place version.

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LazySets.translate!Method
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.

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

Concrete rectification of a singleton.

Input

  • S – singleton

Output

The Singleton that corresponds to the rectification of S.

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LazySets.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.

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Inherited from ConvexSet:

Inherited from AbstractPolytope:

Inherited from AbstractCentrallySymmetricPolytope:

Inherited from AbstractZonotope:

Inherited from AbstractHyperrectangle:

Inherited from AbstractSingleton: