Concretely type linear constraint arrays

[mforets]

The type parameter of the normal direction in the half-space type was not added from the beginning. As a consequence there are methods which return non-concretely-typed containers where they shouldn't. For instance,

julia> x = rand(Hyperrectangle)
Hyperrectangle{Float64,Array{Float64,1},Array{Float64,1}}([0.6356749195435474, -0.7138079011876447], [0.6689691491156268, 0.32291592190199064])

julia> constraints_list(x)
4-element Array{HalfSpace{Float64,VN} where VN<:AbstractArray{Float64,1},1}:
 HalfSpace{Float64,LazySets.Arrays.SingleEntryVector{Float64}}([1.0, 0.0], 1.304644068659174)   
 HalfSpace{Float64,LazySets.Arrays.SingleEntryVector{Float64}}([0.0, 1.0], -0.39089197928565406)
 HalfSpace{Float64,LazySets.Arrays.SingleEntryVector{Float64}}([-1.0, 0.0], 0.03329422957207939)
 HalfSpace{Float64,LazySets.Arrays.SingleEntryVector{Float64}}([0.0, -1.0], 1.0367238230896354) 

Searching for LinearConstraint{N} reveals other places.

For ref: https://docs.julialang.org/en/v1/manual/performance-tips/index.html#Avoid-containers-with-abstract-type-parameters-1

[mforets]

h = rand(Hyperrectangle)
m = minkowski_difference(h, h)

HPolytope{Float64}(HalfSpace{Float64,VN} where VN<:AbstractArray{Float64,1}[HalfSpace{Float64,Array{Float64,1}}([1.0, 0.0], 0.0), HalfSpace{Float64,Array{Float64,1}}([0.0, 1.0], 0.0), HalfSpace{Float64,Array{Float64,1}}([-1.0, 0.0], 0.0), HalfSpace{Float64,Array{Float64,1}}([0.0, -1.0], 0.0)])

[mforets]

function overapproximate(X::LazySet{N}, dir::AbstractDirections{N}) where {N}
    halfspaces = Vector{LinearConstraint{N}}() # ??
    sizehint!(halfspaces, length(dir))
    T = isbounding(dir) ? HPolytope : HPolyhedron
    H = T(halfspaces)
    for d in dir
        addconstraint!(H, LinearConstraint(d, ρ(d, X)))
    end
    return H
end