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Polynomial zonotope sets (AbstractPolynomialZonotope)

LazySets.AbstractPolynomialZonotope — Type
AbstractPolynomialZonotope{N} <: LazySet{N}

Abstract type for polynomial zonotope sets.

Notes

Polynomial zonotopes are in general non-convex. They are always bounded.

Every concrete AbstractPolynomialZonotope must define the following functions:

  • center(::AbstractPolynomialZonotope) – return the center

  • polynomial_order(::AbstractPolynomialZonotope) – return the polynomial order

  • ngens_dep – return the number of dependent generators

  • ngens_indep – return the number of independent generators

The subtypes of AbstractPolynomialZonotope (including abstract interfaces):

julia> subtypes(AbstractPolynomialZonotope)
2-element Vector{Any}:
 AbstractSparsePolynomialZonotope
 DensePolynomialZonotope
source

This interface requires to implement the following functions:

LazySets.API.center — Method
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.

source
LazySets.ngens_dep — Method
ngens_dep(P::AbstractPolynomialZonotope)

Determine the number of dependent generators of a polynomial zonotope.

Input

  • P – polynomial zonotope

Output

A nonnegative integer representing the number of dependent generators.

source
LazySets.ngens_indep — Method
ngens_indep(P::AbstractPolynomialZonotope)

Determine the number of independent generators of a polynomial zonotope.

Input

  • P – polynomial zonotope

Output

A nonnegative integer representing the number of independent generators.

source
LazySets.polynomial_order — Method
polynomial_order(P::AbstractPolynomialZonotope)

Determine the polynomial order of a polynomial zonotope.

Input

  • P – polynomial zonotope

Output

A nonnegative integer representing the polynomial order.

Notes

The polynomial order is the maximum sum of all monomials' parameter exponents.

source

This interface defines the following functions:

LazySets.API.dim — Method
dim(PZ::AbstractPolynomialZonotope)

Return the ambient dimension of a polynomial zonotope.

Input

  • PZ – polynomial zonotope

Output

An integer representing the ambient dimension of the polynomial zonotope.

source
LazySets.ngens — Method
ngens(P::AbstractPolynomialZonotope)

Return the number of generators of a polynomial zonotope.

Input

  • P – polynomial zonotope

Output

The total number of generators of P.

source
LazySets.order — Method
order(P::AbstractPolynomialZonotope)

Return the order of a polynomial zonotope.

Input

  • P – polynomial zonotope

Output

The order, defined as the quotient between the total number of generators and the ambient dimension, as a Rational number.

source

Implementations