#2646 - Add intersection between star set and halfspace

[SebastianGuadalupe]

Closes #2646.

[mforets]

lgtm if tests pass

we could also add a check of the in-place transformation.

[SebastianGuadalupe]

The new test doesn't pass in my machine, but I don't see why it wouldn't

[schillic]

Looks good in general!

[mforets]

👍 let's wait until tests & docs pass..

[schillic]

This in-place intersection is problematic if the constraints use a vector type different from Vector. For example convert(HPolyhedron, ::BallInf) creates an HPolyhedron with SingleEntryVector constraints. The new constraint that we want to add does not use this vector type and hence you cannot add it.

julia> using LazySets
julia> N = Float64;
julia> S = Star(N[3, 3], N[1 0; 0 1], BallInf(N[0, 0], N(1)));
julia> H = HalfSpace(N[0, 1], N(0));
julia> I = intersection(S, H)
ERROR: MethodError: Cannot `convert` an object of type 
  HalfSpace{Float64{},Vector{Float64}} to an object of type 
  HalfSpace{Float64{},LazySets.Arrays.SingleEntryVector{Float64}}

I do not see an easy way out. I suggest that in the method

function intersection(X::STAR{N, VN, MN, PT}, H::HalfSpace) where {N, VN, MN, PT<:Union{HPoly, HPolygon, HPolygonOpt}}
    return intersection!(copy(X), H)
end

we check whether the vector type is Vector and if not we first convert X to a STAR with that type.

[schillic]

Apart from my comment here this looks good!

[mforets]

LazySets.Star: Test Failed at /home/travis/build/JuliaReach/LazySets.jl/test/Sets/Star.jl:47
  Expression: isequivalent(S, P)
Stacktrace:
 [1] top-level scope at /home/travis/build/JuliaReach/LazySets.jl/test/Sets/Star.jl:47
 [2] include(::String) at ./client.jl:457
 [3] macro expansion at /home/travis/build/JuliaReach/LazySets.jl/test/runtests.jl:136 [inlined]
 [4] macro expansion at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.5/Test/src/Test.jl:1119 [inlined]
 [5] macro expansion at /home/travis/build/JuliaReach/LazySets.jl/test/runtests.jl:136 [inlined]
 [6] macro expansion at ./timing.jl:174 [inlined]
 [7] top-level scope at /home/travis/build/JuliaReach/LazySets.jl/test/runtests.jl:136
LazySets.Star: Test Failed at /home/travis/build/JuliaReach/LazySets.jl/test/Sets/Star.jl:47
  Expression: isequivalent(S, P)

[mforets]

┌ Error: 1 docstring not included in the manual:
│ 
│     LazySets.intersection :: Tuple{AffineMap{N,PT,N,MN,VN} where PT<:AbstractPolyhedron{N} where MN<:AbstractArray{N,2} where VN<:AbstractArray{N,1} where N,HalfSpace}
│ 
│ 
│ These are docstrings in the checked modules (configured with the modules keyword)
│ that are not included in @docs or @autodocs blocks.
└ @ Documenter.DocChecks ~/.julia/packages/Documenter/6vUwN/src/DocChecks.jl:69
[ Info: Populate: populating indices.
ERROR: LoadError: `makedocs` encountered an error. Terminating build
Stacktrace:
 [1] error(::String) at ./error.jl:33
 [2] runner(::Type{Documenter.Builder.RenderDocument}, ::Documenter.Documents.Document) at /home/travis/.julia/packages/Documenter/6vUwN/src/Builder.jl:255
 [3] dispatch(::Type{Documenter.Builder.DocumentPipeline}, ::Documenter.Documents.Document) at /home/travis/.julia/packages/Documenter/6vUwN/src/Utilities/Selectors.jl:170
 [4] #2 at /home/travis/.julia/packages/Documenter/6vUwN/src/Documenter.jl:247 [inlined]
 [5] cd(::Documenter.var"#2#3"{Documenter.Documents.Document}, ::String) at ./file.jl:104
 [6] #makedocs#1 at /home/travis/.julia/packages/Documenter/6vUwN/src/Documenter.jl:246 [inlined]
 [7] top-level scope at /home/travis/build/JuliaReach/LazySets.jl/docs/make.jl:7
 [8] include(::Function, ::Module, ::String) at ./Base.jl:380