Origin (ZeroSet)
LazySets.ZeroSet
— TypeZeroSet{N} <: AbstractSingleton{N}
Type that represents the zero set, i.e., the set that only contains the origin.
Fields
dim
– the ambient dimension of this zero set
LazySets.dim
— Methoddim(Z::ZeroSet)
Return the ambient dimension of this zero set.
Input
Z
– a zero set, i.e., a set that only contains the origin
Output
The ambient dimension of the zero set.
LazySets.σ
— Methodσ(d::AbstractVector, Z::ZeroSet)
Return the support vector of a zero set.
Input
d
– directionZ
– a zero set, i.e., a set that only contains the origin
Output
The returned value is the origin since it is the only point that belongs to this set.
LazySets.ρ
— Methodρ(d::AbstractVector, Z::ZeroSet)
Evaluate the support function of a zero set in a given direction.
Input
d
– directionZ
– a zero set, i.e., a set that only contains the origin
Output
0
.
Base.:∈
— Method∈(x::AbstractVector, Z::ZeroSet)
Check whether a given point is contained in a zero set.
Input
x
– point/vectorZ
– 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
Base.rand
— Methodrand(::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 dispatchN
– (optional, default:Float64
) numeric typedim
– (optional, default: 2) dimensionrng
– (optional, default:GLOBAL_RNG
) random number generatorseed
– (optional, default:nothing
) seed for reseeding
Output
The (only) zero set of the given numeric type and dimension.
LazySets.element
— Methodelement(S::ZeroSet{N}) where {N}
Return the element of a zero set.
Input
S
– zero set
Output
The element of the zero set, i.e., a zero vector.
LazySets.element
— Methodelement(S::ZeroSet{N}, ::Int) where {N}
Return the i-th entry of the element of a zero set.
Input
S
– zero seti
– dimension
Output
The i-th entry of the element of the zero set, i.e., 0.
LazySets.linear_map
— Methodlinear_map(M::AbstractMatrix, Z::ZeroSet)
Concrete linear map of a zero set.
Input
M
– matrixZ
– zero set
Output
The zero set whose dimension matches the output dimension of the given matrix.
LazySets.translate
— Methodtranslate(Z::ZeroSet, v::AbstractVector)
Translate (i.e., shift) a zero set by a given vector.
Input
Z
– zero setv
– translation vector
Output
A singleton containing the vector v
.
LazySets.center
— Methodcenter(Z::ZeroSet{N}, i::Int) where {N}
Return the center along a given dimension of a zero set.
Input
Z
– zero seti
– dimension of interest
Output
The center along a given dimension of the zero set.
LazySets.Arrays.rectify
— Methodrectify(Z::ZeroSet)
Concrete rectification of a zero set.
Input
Z
– zero set
Output
The same set.
Inherited from LazySet
:
Inherited from AbstractPolytope
:
Inherited from AbstractCentrallySymmetricPolytope
:
Inherited from AbstractZonotope
:
Inherited from AbstractHyperrectangle
:
Inherited from AbstractSingleton
: