Sparse polynomial zonotope sets (AbstractSparsePolynomialZonotope)

AbstractSparsePolynomialZonotope{N} <: AbstractPolynomialZonotope{N}

Abstract type for sparse polynomial zonotope sets.

Notes

See SparsePolynomialZonotope for a standard implementation of this interface.

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

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.

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.

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.

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.