#2213 - Port zonotope splitting implementation from RA

[SebastianGuadalupe]

Closes #2213.

[mforets]

Lgtm

[mforets]

A comparison between static vs non-static implementation:

julia> using Revise, LazySets, StaticArrays, BenchmarkTools
[ Info: Precompiling LazySets [b4f0291d-fe17-52bc-9479-3d1a343d9043]

julia> Z = Zonotope(@SVector(rand(2)), @SMatrix(rand(2, 2)))
Zonotope{Float64,SArray{Tuple{2},Float64,1,2},SArray{Tuple{2,2},Float64,2,4}}([0.6088108765998801, 0.5135386852090658], [0.666497673074505
6 0.9542751369371558; 0.5158563660350037 0.5883345234682646])

julia> split(Z, 2)
(Zonotope{Float64,SArray{Tuple{2},Float64,1,2},SArray{Tuple{2,2},Float64,2,4}}([0.13167330813130218, 0.21937142347493344], [0.666497673074
5056 0.4771375684685779; 0.5158563660350037 0.2941672617341323]), Zonotope{Float64,SArray{Tuple{2},Float64,1,2},SArray{Tuple{2,2},Float64,
2,4}}([1.085948445068458, 0.8077059469431981], [0.6664976730745056 0.4771375684685779; 0.5158563660350037 0.2941672617341323]))

julia> @btime split($Z, 2);
  35.733 ns (4 allocations: 160 bytes)

julia> Z2 = Zonotope(Vector(Z.center), Matrix(Z.generators));

julia> split(Z2, 2)
(Zonotope{Float64,Array{Float64,1},Array{Float64,2}}([0.13167330813130218, 0.21937142347493344], [0.6664976730745056 0.4771375684685779; 0
.5158563660350037 0.2941672617341323]), Zonotope{Float64,Array{Float64,1},Array{Float64,2}}([1.085948445068458, 0.8077059469431981], [0.66
64976730745056 0.4771375684685779; 0.5158563660350037 0.2941672617341323]))

julia> @btime split($Z2, 2);
  120.027 ns (4 allocations: 416 bytes)

runtime in master using regular arrays (errors with sarrays)

julia> @btime split($Z2, 2);
  196.267 ns (9 allocations: 704 bytes)

[mforets]

Thanks @SebastianGuadalupe to help porting this code from RA. Also, we can now begin adding optional parts for use with StaticArrays. Should we merge this? @schillic

[schillic]

Before merging, can you add a test for the two split methods for one of the other zonotopic types (e.g., BallInf), please?

There is an issue with mixed array types. I guess that _split_ret for the two other combinations (where only one component is an MArray) would be needed. You can either fix it or open an issue.
We should also open an issue that in the conversion to zonotopes from static arrays we should use a static generator matrix.

julia> B = BallInf(SVector{2}(1., 1.), 1.)
BallInf{Float64,SArray{Tuple{2},Float64,1,2}}([1.0, 1.0], 1.0)

julia> convert(Zonotope, B)
Zonotope{Float64,SArray{Tuple{2},Float64,1,2},Array{Float64,2}}([1.0, 1.0], [1.0 0.0; 0.0 1.0])
# note that only the center is a static vector; the generators are a normal matrix

julia> split(B, [1], [1])
ERROR: MethodError: Cannot `convert` an object of type 
  Zonotope{Float64{},MArray{Tuple{2},Float64,1,2},Array{Float64{},2}} to an object of type 
  Zonotope{Float64{},SArray{Tuple{2},Float64,1,2},Array{Float64{},2}}
Closest candidates are:
  convert(::Type{T}, ::T) where T at essentials.jl:171
Stacktrace:
 [1] setindex!(::Array{Zonotope{Float64,SArray{Tuple{2},Float64,1,2},Array{Float64,2}},1}, ::Zonotope{Float64,MArray{Tuple{2},Float64,1,2},Array{Float64,2}}, ::Int64) at ./array.jl:826
 [2] _append! at ./array.jl:968 [inlined]
 [3] append! at ./array.jl:960 [inlined]
 [4] _split(::Zonotope{Float64,SArray{Tuple{2},Float64,1,2},Array{Float64,2}}, ::Array{Int64,1}, ::Array{Int64,1}) at .julia/dev/LazySets/src/Sets/Zonotope.jl:402
 [5] split(::BallInf{Float64,SArray{Tuple{2},Float64,1,2}}, ::Array{Int64,1}, ::Array{Int64,1}) at .julia/dev/LazySets/src/Interfaces/AbstractZonotope.jl:652