#121 - Replace 'IterTools.product' -> 'Iterators.product'

[schillic]

See #121.

In v0.7 we could drop the dependency on IterTools.jl, but for now we still have it for v0.6.

[mforets]

in 0.7,

julia> using LazySets
[ Info: Recompiling stale cache file /Users/mforets/.julia/compiled/v0.7/LazySets/NjrGc.ji for LazySets [b4f0291d-fe17-52bc-9479-3d1a343d9043]

julia> H2 = Hyperrectangle(rand(2), rand(2))
Hyperrectangle{Float64}([0.11199, 0.300178], [0.726638, 0.382507])

julia> vertices_list(H2)
ERROR: MethodError: no method matching Array{Array{Float64,1},1}(::Array{Array{Float64,1},2})
Closest candidates are:
  Array{Array{Float64,1},1}(::AbstractArray{S,N}) where {T, N, S} at array.jl:497
  Array{Array{Float64,1},1}(::Any) where T<:AbstractArray at abstractarray.jl:22
  Array{Array{Float64,1},1}() where T at boot.jl:413
  ...
Stacktrace:
 [1] Array{Array{Float64,1},1}(::Array{Array{Float64,1},2}) at ./abstractarray.jl:22
 [2] convert(::Type{Array{Array{Float64,1},1}}, ::Array{Array{Float64,1},2}) at ./array.jl:489
 [3] vertices_list(::Hyperrectangle{Float64}) at /Users/mforets/.julia/dev/LazySets/src/AbstractHyperrectangle.jl:54
 [4] top-level scope at none:0

the problem is that the return types of IterTools.product and Iterators.product are different iirc

[mforets]

i had this idea, that works both on 0.6 and 0.7:

function vk(H::AbstractHyperrectangle{N})::Vector{Vector{N}} where {N<:Real}
    R = Iterators.repeated(N[1, -1], dim(H))
    vlist = Vector{Vector{N}}(undef, 2^dim(H))
    c, r = center(H), radius_hyperrectangle(H)
    @inbounds for (i, si) in enumerate(Iterators.product(R...))
        vlist[i] = c .+ si[1] .* r
    end
    return vlist
end

but (??) in 0.6 this version is much slower than the current one but in 0.7 it takes the same time

in 0.6

julia> H5 = Hyperrectangle(rand(5), rand(5));
 
julia> @btime vertices_list($H5);
43.424 μs (239 allocations: 19.38 KiB)

julia> @btime vertices_list($H10);
  1.416 ms (7188 allocations: 809.72 KiB)

  julia> @btime vk($H5);
    1.432 ms (2105 allocations: 110.47 KiB)

    julia> @btime vk($H10);
  54.450 ms (99642 allocations: 12.59 MiB)

in 0.7

  julia> @btime vk($H5);
  39.413 μs (329 allocations: 19.39 KiB)

[schillic]

My new solution is easier and more efficient (do not ask why, I just tried out).

v0.6:

julia> @btime vk($H5);
  804.768 μs (2105 allocations: 110.47 KiB)
julia> @btime vertices_list($H5);
  4.009 μs (53 allocations: 5.72 KiB)

v0.7:

julia> @btime vk($H5);
  23.813 μs (329 allocations: 19.39 KiB)
julia> @btime vertices_list($H5);
  1.940 μs (45 allocations: 5.53 KiB)

[mforets]

this was neat, well done