Rotated hyperrectangle (RotatedHyperrectangle)

RotatedHyperrectangle{N, MN<:AbstractMatrix{N},
                      HT<:AbstractHyperrectangle{N}} <: AbstractZonotope{N}

Type that represents a hyperrectangle that is not necessarily axis aligned.

Fields

• M – matrix (not necessarily invertible)
• box – axis-aligned hyperrectangle

Notes

The matrix M is typically a rotation matrix and hence invertible, but this type does not require that and any matrix that is compatible with the dimension of box is allowed.

dim(R::RotatedHyperrectangle)

Return the ambient dimension of a rotated hyperrectangle.

Input

• R – rotated hyperrectangle

Output

The ambient dimension of the rotated hyperrectangle.

ρ(d::AbstractVector, R::RotatedHyperrectangle)

Evaluate the support function of a rotated hyperrectangle in a given direction.

Input

• d – direction
• R – rotated hyperrectangle

Output

Evaluation of the support function in the given direction.

σ(d::AbstractVector, R::RotatedHyperrectangle)

Return a support vector of a rotated hyperrectangle in a given direction.

Input

• d – direction
• R – rotated hyperrectangle

Output

A support vector in the given direction.

center(R::RotatedHyperrectangle)

Return the center of a rotated hyperrectangle.

Input

• R – rotated hyperrectangle

Output

The center of the rotated hyperrectangle.

generators(R::RotatedHyperrectangle)

Return an iterator over the generators of a rotated hyperrectangle.

Input

• R – rotated hyperrectangle

Output

An iterator over the generators of R.

genmat(R::RotatedHyperrectangle)

Return the generator matrix of a rotated hyperrectangle.

Input

• R – rotated hyperrectangle

Output

A matrix where each column represents one generator of R.

linear_map(M::AbstractMatrix, R::RotatedHyperrectangle)

Compute the concrete linear map of a rotated hyperrectangle.

Input

• M – matrix
• R – rotated hyperrectangle

Output

A new rotated hyperrectangle.

Notes

If M is not a square matrix, the result is not necessarily a rotated hyperrectangle. The type still represents the correct set, but it is suggested to only apply square linear maps to it.

vertices_list(R::RotatedHyperrectangle)

Return the list of vertices of a rotated hyperrectangle.

Input

• R – rotated hyperrectangle

Output

A list of the vertices.

constraints_list(R::RotatedHyperrectangle)

Return the list of constraints of a rotated hyperrectangle.

Input

• R – rotated hyperrectangle

Output

A list of the linear constraints.