Symmetric interval hull (SymmetricIntervalHull)

LazySets.SymmetricIntervalHullType
SymmetricIntervalHull{N, S<:ConvexSet{N}} <: AbstractHyperrectangle{N}

Type that represents the symmetric interval hull of a compact set.

Fields

  • X – compact set
  • cache – partial storage of already computed bounds, organized as mapping from dimension to tuples (bound, valid), where valid is a flag indicating if the bound entry has been computed

Notes

The symmetric interval hull can be computed with $2n$ support vector queries of unit vectors, where $n$ is the dimension of the wrapped set (i.e., two queries per dimension). When asking for the support vector for a direction $d$, one needs $2k$ such queries, where $k$ is the number of non-zero entries in $d$.

However, if one asks for many support vectors in a loop, the number of computations may exceed $2n$. To be most efficient in such cases, this type stores the intermediately computed bounds in the cache field.

The set X must be bounded. The flag check_boundedness (which defaults to true) can be used to elide the boundedness check in the inner constructor. Misuse of this flag can result in incorrect behavior.

The symmetric inteval hull of a set is a hyperrectangle, hence in particular convex.

An alias for this function is .

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LazySets.dimMethod
dim(sih::SymmetricIntervalHull)

Return the dimension of the symmetric interval hull of a set.

Input

  • sih – symmetric interval hull of a set

Output

The ambient dimension of the symmetric interval hull of a set.

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LazySets.σMethod
σ(d::AbstractVector, sih::SymmetricIntervalHull)

Return the support vector of the symmetric interval hull of a set in a given direction.

Input

  • d – direction
  • sih – symmetric interval hull of a set

Output

The support vector of the symmetric interval hull of a set in the given direction. If the direction has norm zero, the origin is returned.

Algorithm

For each non-zero entry in d we need to either look up the bound (if it has been computed before) or compute it, in which case we store it for future queries. One such computation just asks for the support vector of the underlying set for both the positive and negative unit vector in the respective dimension.

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LazySets.centerMethod
center(sih::SymmetricIntervalHull{N}, i::Int) where {N}

Return the center along a given dimension of the symmetric interval hull of a set.

Input

  • sih – symmetric interval hull of a set
  • i – dimension of interest

Output

The center along a given dimension of the symmetric interval hull of a set.

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LazySets.centerMethod
center(sih::SymmetricIntervalHull{N}) where {N}

Return the center of the symmetric interval hull of a set.

Input

  • sih – symmetric interval hull of a set

Output

The origin.

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LazySets.radius_hyperrectangleMethod
radius_hyperrectangle(sih::SymmetricIntervalHull)

Return the box radius of the symmetric interval hull of a set in every dimension.

Input

  • sih – symmetric interval hull of a set

Output

The box radius of the symmetric interval hull of a set.

Notes

This function computes the symmetric interval hull explicitly.

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LazySets.radius_hyperrectangleMethod
radius_hyperrectangle(sih::SymmetricIntervalHull, i::Int)

Return the box radius of the symmetric interval hull of a set in a given dimension.

Input

  • sih – symmetric interval hull of a set
  • i – dimension of interest

Output

The radius in the given dimension. If it was computed before, this is just a look-up, otherwise it requires two support vector computations.

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Inherited from ConvexSet:

Inherited from AbstractPolytope:

Inherited from AbstractCentrallySymmetricPolytope:

Inherited from AbstractZonotope:

Inherited from AbstractHyperrectangle: