Singletons (AbstractSingleton)

AbstractSingleton{N} <: AbstractHyperrectangle{N}

Abstract type for sets with a single value.

Notes

See Singleton for a standard implementation of this interface.

julia> subtypes(AbstractSingleton)
2-element Vector{Any}:
 Singleton
 ZeroSet

reflect(X::LazySet)

Compute the reflection of a set in the origin.

Input

• X – set

Output

A set representing the reflection $-X$.

Extended help

reflect(S::AbstractSingleton)

Output

A Singleton.

in(x::AbstractVector, X::LazySet)

Check whether a point lies in a set.

Input

• x – point/vector
• X – set

Output

true iff $x ∈ X$.

Extended help

in(x::AbstractVector, S::AbstractSingleton)

Notes

This implementation performs an approximate comparison to account for imprecision in floating-point computations.

σ(d::AbstractVector, X::LazySet)

Compute a support vector of a set in a given direction.

Input

• d – direction
• X – set

Output

A support vector of X in direction d.

Notes

The convenience alias support_vector is also available.

Extended help

σ(d::AbstractVector, S::AbstractSingleton)

Algorithm

The support vector is the set's vector itself, irrespective of the given direction.