Quadratic map (QuadraticMap)

LazySets.QuadraticMapType
QuadraticMap{N, S<:LazySet{N}, MVT<:AbstractVector{<:AbstractMatrix{N}}} <: LazySet{N}

Type that represents a quadratic map of a set.

Fields

  • Q – matrices
  • X – set

Notes

The quadratic map of a set $X$ given $n$ square matrices $Q^{(i)}$ is defined as

\[\left\{ \lambda | \lambda_i = x^T Q^{(i)} x,~i = 1, \ldots, n,~x \in X \right\}\]

where each coordinate $i$ is influenced by the $i$-th matrix $Q^{(i)}$.

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LazySets.dimMethod
dim(qm::QuadraticMap)

Return the dimension of a quadratic map.

Input

  • qm – quadratic map

Output

The ambient dimension of the quadratic map.

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