Centrally symmetric polytopes (AbstractCentrallySymmetricPolytope)

AbstractCentrallySymmetricPolytope{N} <: AbstractPolytope{N}

Abstract type for centrally symmetric, polytopic sets. It combines the AbstractCentrallySymmetric and AbstractPolytope interfaces. Such a type combination is necessary as long as Julia does not support multiple inheritance.

Notes

Every concrete AbstractCentrallySymmetricPolytope must define the following AbstractCentrallySymmetric method, in addition to the AbstractPolytope methods:

• center(::AbstractCentrallySymmetricPolytope) – return the center point

The subtypes of AbstractCentrallySymmetricPolytope (including abstract interfaces):

julia> subtypes(AbstractCentrallySymmetricPolytope)
2-element Vector{Any}:
 AbstractZonotope
 Ball1

center(X::LazySet)

Compute the center of a centrally symmetric set.

Input

• X – centrally symmetric set

Output

A vector with the center, or midpoint, of X.

constraints_list(X::LazySet)

Compute a list of linear constraints of a polyhedral set.

Input

• X – polyhedral set

Output

A list of the linear constraints of X.

vertices_list(X::LazySet)

Compute a list of vertices of a polytopic set.

Input

• X – polytopic set

Output

A list of the vertices of X.

Extended help

an_element(S::AbstractCentrallySymmetricPolytope)

Output

The center of the centrally symmetric set.

Extended help

extrema(S::AbstractCentrallySymmetricPolytope)

Notes

The result is equivalent to (low(S), high(S)).

Algorithm

We compute high(S) and then compute the lowest coordinates with the help of center(S) (which is assumed to be cheaper to obtain).

Extended help

extrema(S::AbstractCentrallySymmetricPolytope, i::Int)

Notes

The result is equivalent to (low(S, i), high(S, i)).

Algorithm

We compute high(S, i) and then compute the lowest coordinates with the help of center(S, i) (which is assumed to be cheaper to obtain).

Extended help

isuniversal(S::AbstractCentrallySymmetricPolytope, [witness]::Bool=false)

Algorithm

A witness is obtained by computing the support vector in direction d = [1, 0, …, 0] and adding d on top.