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Sparse polynomial zonotope sets (AbstractSparsePolynomialZonotope)

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

Abstract type for sparse polynomial zonotope sets.

Notes

Every concrete AbstractSparsePolynomialZonotope must define the following functions:

  • expmat(::AbstractSparsePolynomialZonotope) – return the exponent matrix (sparse PZ only)

  • genmat_dep(::AbstractSparsePolynomialZonotope) – return the matrix of dependent generators

  • genmat_indep(::AbstractSparsePolynomialZonotope) – return the matrix of independent generators

The subtypes of AbstractSparsePolynomialZonotope (including abstract interfaces):

julia> subtypes(AbstractSparsePolynomialZonotope)
2-element Vector{Any}:
 SimpleSparsePolynomialZonotope
 SparsePolynomialZonotope
source

This interface requires to implement the following functions:

LazySets.expmat — Method
expmat(P::AbstractSparsePolynomialZonotope)

Return the matrix of exponents of a sparse polynomial zonotope.

Input

  • P – sparse polynomial zonotope

Output

The matrix of exponents, where each column is a multidegree.

Notes

In the exponent matrix, each row corresponds to a parameter ($αₖ$ in the definition) and each column corresponds to a monomial.

source
LazySets.genmat_dep — Method
genmat_dep(P::AbstractSparsePolynomialZonotope)

Return the matrix of dependent generators of a sparse polynomial zonotope.

Input

  • P – sparse polynomial zonotope

Output

The matrix of dependent generators.

source
LazySets.genmat_indep — Method
genmat_indep(P::AbstractSparsePolynomialZonotope)

Return the matrix of independent generators of a sparse polynomial zonotope.

Input

  • P – sparse polynomial zonotope

Output

The matrix of independent generators.

source

This interface defines the following functions:

LazySets.nparams — Method
nparams(P::AbstractSparsePolynomialZonotope)

Return the number of dependent parameters in the polynomial representation of a sparse polynomial zonotope.

Input

  • P – sparse polynomial zonotope

Output

The number of dependent parameters in the polynomial representation.

Notes

This number corresponds to the number of rows in the exponent matrix.

source

Implementations