#1802 - Concretely type linear constraint arrays (#1803)

* type constraints_list of hyperrectangular set

* type constraints list of Ball1

* constraints list of cpa

* type for constraints list of ResetMap

* add more type annotations

* more type annotations

* update doctest

* fix last doctest

src/Approximations/decompositions.jl

@@ -555,7 +555,7 @@ Now let's take a ball in the infinity norm and remove some constraints:
 julia> B = BallInf(zeros(4), 1.0);
 
 julia> c = constraints_list(B)[1:2]
-2-element Array{HalfSpace{Float64,VN} where VN<:AbstractArray{Float64,1},1}:
+2-element Array{HalfSpace{Float64,LazySets.Arrays.SingleEntryVector{Float64}},1}:
  HalfSpace{Float64,LazySets.Arrays.SingleEntryVector{Float64}}([1.0, 0.0, 0.0, 0.0], 1.0)
  HalfSpace{Float64,LazySets.Arrays.SingleEntryVector{Float64}}([0.0, 1.0, 0.0, 0.0], 1.0)
 

src/Approximations/iterative_refinement.jl

@@ -59,10 +59,11 @@ Type that represents the polygonal approximation of a convex set.
 struct PolygonalOverapproximation{N<:Real}
     S::LazySet{N}
     approx_stack::Vector{LocalApproximation{N}}
-    constraints::Vector{LinearConstraint{N}}
+    constraints::Vector{LinearConstraint{N, Vector{N}}}
 
-    PolygonalOverapproximation(S::LazySet{N}) where {N<:Real} = new{N}(
-        S, Vector{LocalApproximation{N}}(), Vector{LinearConstraint{N}}())
+    function PolygonalOverapproximation(S::LazySet{N}) where {N<:Real}
+        return new{N}(S, Vector{LocalApproximation{N}}(), Vector{LinearConstraint{N,Vector{N}}}())
+    end
 end
 
 """

src/Approximations/overapproximate.jl

@@ -48,7 +48,7 @@ function overapproximate(S::LazySet{N},
                         )::HPolygon where {N<:Real}
     @assert dim(S) == 2
     if ε == Inf
-        constraints = Vector{LinearConstraint{N}}(undef, 4)
+        constraints = Vector{LinearConstraint{N, Vector{N}}}(undef, 4)
         constraints[1] = LinearConstraint(DIR_EAST(N), ρ(DIR_EAST(N), S))
         constraints[2] = LinearConstraint(DIR_NORTH(N), ρ(DIR_NORTH(N), S))
         constraints[3] = LinearConstraint(DIR_WEST(N), ρ(DIR_WEST(N), S))

src/Interfaces/AbstractHyperrectangle.jl

@@ -238,7 +238,7 @@ A list of linear constraints.
 """
 function constraints_list(H::AbstractHyperrectangle{N}) where {N<:Real}
     n = dim(H)
-    constraints = Vector{LinearConstraint{N}}(undef, 2*n)
+    constraints = Vector{LinearConstraint{N, SingleEntryVector{N}}}(undef, 2*n)
     b, c = high(H), -low(H)
     one_N = one(N)
     for i in 1:n

src/LazyOperations/CartesianProduct.jl

@@ -588,7 +588,7 @@ number of sets.
 A list of constraints.
 """
 function constraints_list(cpa::CartesianProductArray{N}) where {N<:Real}
-    clist = Vector{LinearConstraint{N}}()
+    clist = Vector{LinearConstraint{N, SparseVector{N, Int}}}()
     n = dim(cpa)
     sizehint!(clist, n)
     prev_step = 1
@@ -599,8 +599,7 @@ function constraints_list(cpa::CartesianProductArray{N}) where {N<:Real}
             indices = prev_step : (dim(c_low_list[1]) + prev_step - 1)
         end
         for constr in c_low_list
-            new_constr = LinearConstraint(sparsevec(indices, constr.a, n),
-                                          constr.b)
+            new_constr = LinearConstraint(sparsevec(indices, constr.a, n), constr.b)
             push!(clist, new_constr)
         end
         prev_step += dim(c_low_list[1])

src/LazyOperations/ResetMap.jl

@@ -359,7 +359,7 @@ function constraints_list(rm::ResetMap{N, S}
                          ) where {N<:Real, S<:AbstractHyperrectangle}
     H = rm.X
     n = dim(H)
-    constraints = Vector{LinearConstraint{N}}(undef, 2*n)
+    constraints = Vector{LinearConstraint{N, SingleEntryVector{N}}}(undef, 2*n)
     j = 1
     for i in 1:n
         ei = SingleEntryVector(i, n, one(N))

src/LazyOperations/Translation.jl

@@ -130,7 +130,7 @@ whose `constraints_list` is available) can be computed from a lazy translation:
 
 ```jldoctest translation
 julia> constraints_list(tr)
-6-element Array{HalfSpace{Float64,VN} where VN<:AbstractArray{Float64,1},1}:
+6-element Array{HalfSpace{Float64,LazySets.Arrays.SingleEntryVector{Float64}},1}:
  HalfSpace{Float64,LazySets.Arrays.SingleEntryVector{Float64}}([1.0, 0.0, 0.0], 5.0)
  HalfSpace{Float64,LazySets.Arrays.SingleEntryVector{Float64}}([0.0, 1.0, 0.0], 3.0)
  HalfSpace{Float64,LazySets.Arrays.SingleEntryVector{Float64}}([0.0, 0.0, 1.0], 3.0)

src/Sets/Ball1.jl

@@ -245,7 +245,7 @@ all possible ``d_i``, the function `Iterators.product` is used.
 function constraints_list(B::Ball1{N}) where {N<:Real}
     n = LazySets.dim(B)
     c, r = B.center, B.radius
-    clist = Vector{LinearConstraint{N}}(undef, 2^n)
+    clist = Vector{LinearConstraint{N, Vector{N}}}(undef, 2^n)
     for (i, di) in enumerate(Iterators.product([[one(N), -one(N)] for i = 1:n]...))
         d = collect(di) # tuple -> vector
         clist[i] = LinearConstraint(d, dot(d, c) + r)

src/Sets/HPolytope.jl

@@ -147,7 +147,8 @@ return quote
 # see the interface file AbstractPolytope.jl for the imports
 
 function convert(::Type{HPolytope{N}}, P::HRep{N}) where {N}
-    constraints = LinearConstraint{N}[]
+    VT = Polyhedra.hvectortype(P)
+    constraints = Vector{LinearConstraint{N, VT}}()
     for hi in Polyhedra.allhalfspaces(P)
         a, b = hi.a, hi.β
         if isapproxzero(norm(a))

src/convert.jl

@@ -402,7 +402,7 @@ A polygon in constraint representation with the minimal number of constraints
 """
 function convert(::Type{HPOLYGON}, S::AbstractSingleton{N}
                 ) where {N<:Real, HPOLYGON<:AbstractHPolygon}
-    constraints_list = Vector{LinearConstraint{N}}(undef, 3)
+    constraints_list = Vector{LinearConstraint{N, Vector{N}}}(undef, 3)
     o = one(N)
     z = zero(N)
     v = element(S)