Origin (ZeroSet)

LazySets.ZeroSetModule.ZeroSetType
ZeroSet{N} <: AbstractSingleton{N}

Type that represents the zero set, i.e., the set that only contains the origin.

Fields

  • dim – the ambient dimension of the set
source

Operations

LazySets.API.dimMethod
dim(Z::ZeroSet)

Return the ambient dimension of a zero set.

Input

  • Z – zero set

Output

The ambient dimension of the zero set.

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LazySets.elementMethod
element(Z::ZeroSet{N}) where {N}

Return the element of a zero set.

Input

  • Z – zero set

Output

The element of the zero set, i.e., a zero vector.

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LazySets.elementMethod
element(Z::ZeroSet{N}, ::Int) where {N}

Return the i-th entry of the element of a zero set.

Input

  • Z – zero set
  • i – dimension

Output

The i-th entry of the element of the zero set, i.e., 0.

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

Create a zero set (note that there is nothing to randomize).

Input

  • ZeroSet – 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

The (only) zero set of the given numeric type and dimension.

source
LazySets.API.reflectMethod
reflect(Z::ZeroSet)

Concrete reflection of a zero set Z, resulting in the reflected set -Z.

Input

  • Z – zero set

Output

The same zero set.

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Base.:∈Method
∈(x::AbstractVector, Z::ZeroSet)

Check whether a given point is contained in a zero set.

Input

  • x – point/vector
  • Z – zero set

Output

true iff $x ∈ Z$.

Examples

julia> Z = ZeroSet(2);

julia> [1.0, 0.0] ∈ Z
false
julia> [0.0, 0.0] ∈ Z
true
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LazySets.API.linear_mapMethod
linear_map(M::AbstractMatrix, Z::ZeroSet)

Concrete linear map of a zero set.

Input

  • M – matrix
  • Z – zero set

Output

The zero set whose dimension matches the output dimension of the given matrix.

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LazySets.API.ρMethod
ρ(d::AbstractVector, Z::ZeroSet)

Evaluate the support function of a zero set in a given direction.

Input

  • d – direction
  • Z – zero set

Output

0.

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LazySets.API.translateMethod
translate(Z::ZeroSet, v::AbstractVector)

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

Input

  • Z – zero set
  • v – translation vector

Output

A singleton containing the vector v.

source

Undocumented implementations:

Inherited from LazySet:

Inherited from ConvexSet:

Inherited from AbstractPolyhedron:

Inherited from AbstractPolytope:

Inherited from AbstractCentrallySymmetricPolytope:

Inherited from AbstractZonotope:

Inherited from AbstractHyperrectangle:

Inherited from AbstractSingleton: