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Merge pull request #216 from JuliaReach/schillic/63
#63 - refactoring LazySet & an_element default implementation
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| import Base.LinAlg:norm | ||
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| export LazySet, | ||
| ρ, support_function, | ||
| σ, support_vector, | ||
| dim, | ||
| norm, | ||
| radius, | ||
| diameter, | ||
| an_element | ||
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| """ | ||
| LazySet{N} | ||
| Abstract type for convex sets, i.e., sets characterized by a (possibly infinite) | ||
| intersection of halfspaces, or equivalently, sets ``S`` such that for any two | ||
| elements ``x, y ∈ S`` and ``0 ≤ λ ≤ 1`` it holds that ``λ x + (1-λ) y ∈ S``. | ||
| ### Notes | ||
| `LazySet` types should be parameterized with a type `N`, typically | ||
| `N<:Real`, for using different numeric types. | ||
| Every concrete `LazySet` must define the following functions: | ||
| - `σ(d::AbstractVector{N}, S::LazySet)::AbstractVector{N}` -- the | ||
| support vector of `S` in a given direction `d` | ||
| - `dim(S::LazySet)::Int` -- the ambient dimension of `S` | ||
| ```jldoctest | ||
| julia> subtypes(LazySet) | ||
| 15-element Array{Union{DataType, UnionAll},1}: | ||
| LazySets.AbstractPointSymmetric | ||
| LazySets.AbstractPolytope | ||
| LazySets.CartesianProduct | ||
| LazySets.CartesianProductArray | ||
| LazySets.ConvexHull | ||
| LazySets.ConvexHullArray | ||
| LazySets.EmptySet | ||
| LazySets.ExponentialMap | ||
| LazySets.ExponentialProjectionMap | ||
| LazySets.HalfSpace | ||
| LazySets.Hyperplane | ||
| LazySets.Intersection | ||
| LazySets.LinearMap | ||
| LazySets.MinkowskiSum | ||
| LazySets.MinkowskiSumArray | ||
| ``` | ||
| """ | ||
| abstract type LazySet{N} end | ||
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| # --- common LazySet functions --- | ||
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| """ | ||
| ρ(d::AbstractVector{N}, S::LazySet{N})::N where {N<:Real} | ||
| Evaluate the support function of a set in a given direction. | ||
| ### Input | ||
| - `d` -- direction | ||
| - `S` -- convex set | ||
| ### Output | ||
| The support function of the set `S` for the direction `d`. | ||
| """ | ||
| function ρ(d::AbstractVector{N}, S::LazySet{N})::N where {N<:Real} | ||
| return dot(d, σ(d, S)) | ||
| end | ||
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| """ | ||
| support_function | ||
| Alias for the support function ρ. | ||
| """ | ||
| const support_function = ρ | ||
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| """ | ||
| σ | ||
| Function to compute the support vector σ. | ||
| """ | ||
| function σ end | ||
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| """ | ||
| support_vector | ||
| Alias for the support vector σ. | ||
| """ | ||
| const support_vector = σ | ||
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| """ | ||
| norm(S::LazySet, [p]::Real=Inf) | ||
| Return the norm of a convex set. | ||
| It is the norm of the enclosing ball (of the given ``p``-norm) of minimal volume | ||
| that is centered in the origin. | ||
| ### Input | ||
| - `S` -- convex set | ||
| - `p` -- (optional, default: `Inf`) norm | ||
| ### Output | ||
| A real number representing the norm. | ||
| """ | ||
| function norm(S::LazySet, p::Real=Inf) | ||
| if p == Inf | ||
| return norm(Approximations.ballinf_approximation(S), p) | ||
| else | ||
| error("the norm for this value of p=$p is not implemented") | ||
| end | ||
| end | ||
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| """ | ||
| radius(S::LazySet, [p]::Real=Inf) | ||
| Return the radius of a convex set. | ||
| It is the radius of the enclosing ball (of the given ``p``-norm) of minimal | ||
| volume with the same center. | ||
| ### Input | ||
| - `S` -- convex set | ||
| - `p` -- (optional, default: `Inf`) norm | ||
| ### Output | ||
| A real number representing the radius. | ||
| """ | ||
| function radius(S::LazySet, p::Real=Inf) | ||
| if p == Inf | ||
| return radius(Approximations.ballinf_approximation(S)::BallInf, p) | ||
| else | ||
| error("the radius for this value of p=$p is not implemented") | ||
| end | ||
| end | ||
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| """ | ||
| diameter(S::LazySet, [p]::Real=Inf) | ||
| Return the diameter of a convex set. | ||
| It is the maximum distance between any two elements of the set, or, | ||
| equivalently, the diameter of the enclosing ball (of the given ``p``-norm) of | ||
| minimal volume with the same center. | ||
| ### Input | ||
| - `S` -- convex set | ||
| - `p` -- (optional, default: `Inf`) norm | ||
| ### Output | ||
| A real number representing the diameter. | ||
| """ | ||
| function diameter(S::LazySet, p::Real=Inf) | ||
| if p == Inf | ||
| return radius(S, p) * 2 | ||
| else | ||
| error("the diameter for this value of p=$p is not implemented") | ||
| end | ||
| end | ||
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| """ | ||
| an_element(S::LazySet{N})::AbstractVector{N} where {N<:Real} | ||
| Return some element of a convex set. | ||
| ### Input | ||
| - `S` -- convex set | ||
| ### Output | ||
| An element of a convex set. | ||
| """ | ||
| function an_element(S::LazySet{N})::AbstractVector{N} where {N<:Real} | ||
| return σ(sparsevec([1], [one(N)], dim(S)), S) | ||
| end |
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