JuliaReach · schillic · Mar 16, 2024 · Mar 10, 2024
diff --git a/docs/src/lib/reachsets.md b/docs/src/lib/reachsets.md
@@ -27,7 +27,7 @@ shift(::AbstractReachSet)
 
 ```@docs
 AbstractLazyReachSet
-project(::AbstractLazyReachSet, ::NTuple{D,M}; check_vars::Bool=true) where {D,M<:Integer}
+project(::AbstractLazyReachSet, ::NTuple{D,Int}; check_vars::Bool=true) where {D}
 ```
 
 ## Reachable set

diff --git a/src/Flowpipes/Flowpipe.jl b/src/Flowpipes/Flowpipe.jl
@@ -130,7 +130,7 @@ function (fp::Flowpipe)(dt::TimeInterval)
 end
 
 # concrete projection of a flowpipe along variables `vars`
-function project(fp::Flowpipe, vars::NTuple{D,T}) where {D,T<:Integer}
+function project(fp::Flowpipe, vars::NTuple{D,Int}) where {D}
     Xk = array(fp)
     πfp = map(X -> project(X, vars), Xk)
     return Flowpipe(πfp, fp.ext)
@@ -243,13 +243,13 @@ Base.:⊆(F::Flowpipe, X::LazySet) = all(R ⊆ X for R in F)
 Base.:⊆(F::Flowpipe, Y::AbstractLazyReachSet) = all(R ⊆ set(Y) for R in F)
 
 # lazy projection of a flowpipe
-function Projection(F::Flowpipe, vars::NTuple{D,T}) where {D,T<:Integer}
+function Projection(F::Flowpipe, vars::NTuple{D,Int}) where {D}
     Xk = array(F)
     out = map(X -> Projection(X, vars), Xk)
     return Flowpipe(out)
 end
 Projection(F::Flowpipe; vars) = Projection(F, Tuple(vars))
-Projection(F::Flowpipe, vars::AbstractVector{M}) where {M<:Integer} = Projection(F, Tuple(vars))
+Projection(F::Flowpipe, vars::AbstractVector{Int}) = Projection(F, Tuple(vars))
 
 # membership test
 function ∈(x::AbstractVector{N}, fp::Flowpipe{N,<:AbstractLazyReachSet{N}}) where {N}

diff --git a/src/Flowpipes/MappedFlowpipe.jl b/src/Flowpipes/MappedFlowpipe.jl
@@ -16,7 +16,7 @@ struct MappedFlowpipe{FT<:AbstractFlowpipe,ST} <: AbstractFlowpipe
 end
 
 """
-    Projection(fp::AbstractFlowpipe, vars::NTuple{D, T}) where {D, T<:Integer}
+    Projection(fp::AbstractFlowpipe, vars::NTuple{D,Int}) where {D}
 
 Return the lazy projection of a flowpipe.
 
@@ -30,7 +30,7 @@ The projection is lazy, and consists of mapping each set
 `X` in the flowpipe to `MX`, where `M` is the projection matrix associated with
 the given variables `vars`.
 """
-function LazySets.Projection(fp::AbstractFlowpipe, vars::NTuple{D,T}) where {D,T<:Integer}
+function LazySets.Projection(fp::AbstractFlowpipe, vars::NTuple{D,Int}) where {D}
     # TODO: assert that vars belong to the variables of the flowpipe
     M = projection_matrix(collect(vars), dim(F), Float64)
     func = @map(x -> M * x)

diff --git a/src/Flowpipes/ShiftedFlowpipe.jl b/src/Flowpipes/ShiftedFlowpipe.jl
@@ -45,7 +45,7 @@ end
 project(fp::ShiftedFlowpipe, vars::AbstractVector) = project(fp, Tuple(vars))
 project(fp::ShiftedFlowpipe; vars) = project(fp, Tuple(vars))
 
-function project(fp::ShiftedFlowpipe, vars::NTuple{D,T}) where {D,T<:Integer}
+function project(fp::ShiftedFlowpipe, vars::NTuple{D,Int}) where {D}
     Xk = array(fp)
     # TODO: use projection of the reachsets
     if 0 ∈ vars # projection includes "time"
@@ -60,7 +60,7 @@ end
 
 # this method is analogue to project(::AbstractLazyReachSet, vars; check_vars=true)
 # TODO add check_vars ?
-function project(fp::ShiftedFlowpipe, i::Int, vars::NTuple{D,M}) where {D,M<:Integer}
+function project(fp::ShiftedFlowpipe, i::Int, vars::NTuple{D,Int}) where {D}
     t0 = time_shift(fp)
     R = fp[i]
     if 0 ∈ vars

diff --git a/src/Flowpipes/clustering.jl b/src/Flowpipes/clustering.jl
@@ -40,10 +40,11 @@ the third to tenth reach-sets in another cluster.
 """
 abstract type AbstractClusteringMethod{P} end
 
-_partition(method::AbstractClusteringMethod{Missing}, idx) = nfolds(idx, 1)
-_partition(method::AbstractClusteringMethod{<:Integer}, idx) = nfolds(idx, partition(method))
-function _partition(method::AbstractClusteringMethod{VT},
-                    idx) where {D<:Integer,VTi<:AbstractVector{D},VT<:AbstractVector{VTi}}
+_partition(::AbstractClusteringMethod{Missing}, idx) = nfolds(idx, 1)
+
+_partition(method::AbstractClusteringMethod{Int}, idx) = nfolds(idx, partition(method))
+
+function _partition(method::AbstractClusteringMethod{<:AbstractVector{<:AbstractVector{Int}}}, idx)
     return [idx[vi] for vi in partition(method)]
 end
 
@@ -95,11 +96,10 @@ end
 partition(method::LazyClustering) = method.partition
 
 LazyClustering(; convex::Bool=true) = LazyClustering(missing, Val(convex))
-function LazyClustering(nchunks::D; convex::Bool=true) where {D<:Integer}
-    return LazyClustering{D,typeof(Val(convex))}(nchunks, Val(convex))
+function LazyClustering(nchunks::Int; convex::Bool=true)
+    return LazyClustering{Int,typeof(Val(convex))}(nchunks, Val(convex))
 end
-function LazyClustering(partition::VT) where {D<:Integer,VTi<:AbstractVector{D},
-                                              VT<:AbstractVector{VTi}}
+function LazyClustering(partition::VT) where {VT<:AbstractVector{<:AbstractVector{Int}}}
     return LazyClustering{VT,typeof(Val(convex))}(partition, Val(convex))
 end
 
@@ -156,18 +156,16 @@ end
 partition(method::BoxClustering) = method.inpartition
 
 BoxClustering() = BoxClustering(missing, missing)
-BoxClustering(nchunks::D) where {D<:Integer} = BoxClustering{D,Missing}(nchunks, missing)
-function BoxClustering(partition::VT) where {D<:Integer,VTi<:AbstractVector{D},
-                                             VT<:AbstractVector{VTi}}
+BoxClustering(nchunks::Int) = BoxClustering{Int,Missing}(nchunks, missing)
+function BoxClustering(partition::VT) where {VT<:AbstractVector{<:AbstractVector{Int}}}
     return BoxClustering{VT,Missing}(partition, missing)
 end
 
-_out_partition(method::BoxClustering{PI,Missing}, idx, n) where {PI} = fill(1, n)
-function _out_partition(method::BoxClustering{PI,<:Integer}, idx, n) where {PI}
+_out_partition(::BoxClustering{PI,Missing}, idx, n) where {PI} = fill(1, n)
+function _out_partition(method::BoxClustering{PI,Int}, idx, n) where {PI}
     return fill(method.outpartition, n)
 end
-function _out_partition(method::BoxClustering{PI,VT}, idx,
-                        n) where {PI,D<:Integer,VT<:AbstractVector{D}}
+function _out_partition(method::BoxClustering{PI,<:AbstractVector{Int}}, idx, n) where {PI}
     return method.outpartition
 end
 
@@ -350,14 +348,12 @@ end
 partition(method::UnionClustering) = method.partition
 
 UnionClustering() = UnionClustering(missing)
-UnionClustering(nchunks::D) where {D<:Integer} = UnionClustering{D}(nchunks)
-function UnionClustering(partition::VT) where {D<:Integer,VTi<:AbstractVector{D},
-                                               VT<:AbstractVector{VTi}}
+UnionClustering(nchunks::Int) = UnionClustering{Int}(nchunks)
+function UnionClustering(partition::VT) where {VT<:AbstractVector{<:AbstractVector{Int}}}
     return UnionClustering{VT}(partition)
 end
 
-function cluster(F::Flowpipe{N,<:AbstractLazyReachSet}, idx,
-                 method::UnionClustering{Missing}) where {N}
+function cluster(F::Flowpipe{N,<:AbstractLazyReachSet}, idx, ::UnionClustering{Missing}) where {N}
     Fidx = view(F, idx)
     Δt = tspan(Fidx)
     Uidx = UnionSetArray([set(R) for R in Fidx])

diff --git a/src/Flowpipes/recipes.jl b/src/Flowpipes/recipes.jl
@@ -177,8 +177,7 @@ end
 
 # TODO use LazySets._plot_singleton_list_1D if the reach-sets are stored as a struct
 # array. Otherwise, we could use pass the list through x -> set(x)
-function _plot_singleton_list_1D(list::Union{Flowpipe{N},AbstractVector{RN}}) where {N,
-                                                                                     RN<:AbstractReachSet{N}}
+function _plot_singleton_list_1D(list::Union{Flowpipe{N},AbstractVector{<:AbstractReachSet{N}}}) where {N}
     m = length(list)
 
     x = Vector{N}(undef, m)
@@ -191,8 +190,7 @@ function _plot_singleton_list_1D(list::Union{Flowpipe{N},AbstractVector{RN}}) wh
     return x, y
 end
 
-function _plot_singleton_list_2D(list::Union{Flowpipe{N},AbstractVector{RN}}) where {N,
-                                                                                     RN<:AbstractReachSet{N}}
+function _plot_singleton_list_2D(list::Union{Flowpipe{N},AbstractVector{<:AbstractReachSet{N}}}) where {N}
     m = length(list)
     x = Vector{N}(undef, m)
     y = Vector{N}(undef, m)
@@ -256,10 +254,10 @@ end
 # Flowpipe plot recipes
 # ========================
 
-@recipe function plot_list(list::Union{Flowpipe{N},AbstractVector{RN}};
+@recipe function plot_list(list::Union{Flowpipe{N},AbstractVector{<:AbstractReachSet{N}}};
                            vars=nothing,
                            ε=N(PLOT_PRECISION),
-                           Nφ=PLOT_POLAR_DIRECTIONS) where {N,RN<:AbstractReachSet{N}}
+                           Nφ=PLOT_POLAR_DIRECTIONS) where {N}
     _check_vars(vars)
 
     label --> DEFAULT_LABEL
@@ -280,11 +278,10 @@ end
 end
 
 # composite flowpipes
-@recipe function plot_list(fp::Union{HF,MF};
+@recipe function plot_list(fp::Union{<:HybridFlowpipe{N},<:MixedFlowpipe{N}};
                            vars=nothing,
                            ε=Float64(PLOT_PRECISION),
-                           Nφ=PLOT_POLAR_DIRECTIONS) where {N,HF<:HybridFlowpipe{N},
-                                                            MF<:MixedFlowpipe{N}}
+                           Nφ=PLOT_POLAR_DIRECTIONS) where {N}
     _check_vars(vars)
 
     label --> DEFAULT_LABEL
@@ -313,10 +310,10 @@ end
 # Solution plot recipes
 # ========================
 
-@recipe function plot_list(sol::ReachSolution{FT};
+@recipe function plot_list(sol::ReachSolution{<:Flowpipe{N}};
                            vars=nothing,
                            ε=Float64(PLOT_PRECISION),
-                           Nφ=PLOT_POLAR_DIRECTIONS) where {N,FT<:Flowpipe{N}}
+                           Nφ=PLOT_POLAR_DIRECTIONS) where {N}
     _check_vars(vars)
 
     label --> DEFAULT_LABEL
@@ -338,13 +335,11 @@ end
 end
 
 # compound solution flowpipes
-@recipe function plot_list(sol::Union{SMF,SHF};
+@recipe function plot_list(sol::Union{ReachSolution{<:MixedFlowpipe{N}},
+                                      ReachSolution{<:HybridFlowpipe{N}}};
                            vars=nothing,
                            ε=Float64(PLOT_PRECISION),
-                           Nφ=PLOT_POLAR_DIRECTIONS) where {N,MF<:MixedFlowpipe{N},
-                                                            HF<:HybridFlowpipe{N},
-                                                            SMF<:ReachSolution{MF},
-                                                            SHF<:ReachSolution{HF}}
+                           Nφ=PLOT_POLAR_DIRECTIONS) where {N}
     _check_vars(vars)
 
     label --> DEFAULT_LABEL
@@ -435,15 +430,15 @@ end
 # plot each variable vs time
 @recipe function plot_reachset(R::AbstractLazyReachSet{N};
                                ε::N=N(PLOT_PRECISION)
-                               ) where {N<:Real, D, M<:Integer}
+                               ) where {N}
     error("not implemented yet")
 end
 
-@recipe function plot_list(list::AbstractVector{RN};
+@recipe function plot_list(list::AbstractVector{<:AbstractReachSet{N}};
                            ε::N=N(PLOT_PRECISION),
                            Nφ::Int=PLOT_POLAR_DIRECTIONS,
                            fast::Bool=true
-                          ) where {N<:Real, RN<:AbstractReachSet{N}}
+                          ) where {N}
     error("not implemented yet")
 end
 =#

diff --git a/src/Flowpipes/setops.jl b/src/Flowpipes/setops.jl
@@ -179,11 +179,11 @@ end
 # =========================
 
 # extend LazySets concrete projection for other arguments
-LazySets.project(X::LazySet, vars::NTuple{D,<:Integer}) where {D} = project(X, collect(vars))
+LazySets.project(X::LazySet, vars::NTuple{D,Int}) where {D} = project(X, collect(vars))
 LazySets.project(X::LazySet; vars) = project(X, vars)
 
 # extend LazySets lazy projection for other arguments
-LazySets.Projection(X::LazySet, vars::NTuple{D,<:Integer}) where {D} = Projection(X, collect(vars))
+LazySets.Projection(X::LazySet, vars::NTuple{D,Int}) where {D} = Projection(X, collect(vars))
 LazySets.Projection(X::LazySet; vars) = Projection(X, vars)
 
 # ===============================

diff --git a/src/Hybrid/solve.jl b/src/Hybrid/solve.jl
@@ -327,11 +327,10 @@ end
 
 # the initial states are passed as a vector-of-tuples, each tuple being of the form
 # (loc, X) where loc is an integer that corresponds to the mode and X is a set
-function _distribute(ivp::InitialValueProblem{HS,Vector{Tuple{M,ST}}};
+function _distribute(ivp::InitialValueProblem{<:HybridSystem,Vector{Tuple{Int,ST}}};
                      intersection_method=nothing,
                      check_invariant=false,
-                     intersect_invariant=false) where {HS<:HybridSystem,M<:Integer,
-                                                       ST<:AdmissibleSet}
+                     intersect_invariant=false) where {ST<:AdmissibleSet}
     H = system(ivp)
     X0vec = initial_state(ivp) #  distributed initial states
 
@@ -342,7 +341,6 @@ function _distribute(ivp::InitialValueProblem{HS,Vector{Tuple{M,ST}}};
         STwl = ST
     end
 
-    N = eltype(ST)
     WL = WaitingList{TimeInterval,STwl,Int,StateInLocation{STwl,Int}}
 
     if !check_invariant && !intersect_invariant
@@ -356,11 +354,10 @@ end
 
 # "duck-typing" the initial states passed as a vector-of-tuples, each tuple being
 # of the form (X, loc) where loc is an integer that corresponds to the mode and X is a set
-function _distribute(ivp::InitialValueProblem{HS,Vector{Tuple{ST,M}}};
+function _distribute(ivp::InitialValueProblem{HS,Vector{Tuple{ST,Int}}};
                      intersection_method=nothing,
                      check_invariant=false,
-                     intersect_invariant=false) where {HS<:HybridSystem,ST<:AdmissibleSet,
-                                                       M<:Integer}
+                     intersect_invariant=false) where {HS<:HybridSystem,ST<:AdmissibleSet}
     H = system(ivp)
     X0vec = initial_state(ivp) #  distributed initial states
 
@@ -371,7 +368,6 @@ function _distribute(ivp::InitialValueProblem{HS,Vector{Tuple{ST,M}}};
         STwl = ST
     end
 
-    N = eltype(ST)
     WL = WaitingList{TimeInterval,STwl,Int,StateInLocation{STwl,Int}}
 
     if !check_invariant && !intersect_invariant
@@ -414,7 +410,7 @@ end
 # optionally it is checked that each set has a non-empty intersction with loc_i's invariant
 function _distribute(ivp::InitialValueProblem{HS, VQT};
                      check_invariant=false) where {HS<:HybridSystem,
-                     ST, QT<:Tuple{<:Integer, ST}, VQT<:AbstractVector{QT}}
+                     ST, QT<:Tuple{Int}, ST}, VQT<:AbstractVector{QT}}
     initial_states = WaitingList{Int, ST}()
     for loc in states(S)
         if check_invariant

diff --git a/src/Hybrid/waiting_list.jl b/src/Hybrid/waiting_list.jl
@@ -3,7 +3,7 @@
 # =====================================
 
 """
-    StateInLocation{ST, M<:Integer}
+    StateInLocation{ST,M}
 
 Struct that associates a set with a hybrid automaton's location index,
 usually an integer.
@@ -135,7 +135,7 @@ end
 
 # conversion from vector-of-tuples to waiting list
 function Base.convert(::Type{TW},
-                      Q::Vector{Tuple{M,ST}}) where {TW<:WaitingList,M<:Integer,ST<:AdmissibleSet}
+                      Q::Vector{Tuple{Int,ST}}) where {TW<:WaitingList,ST<:AdmissibleSet}
     waiting_list = TW()
     for Qi in Q # no intersection chcks
         q, Xi = Qi
@@ -146,7 +146,7 @@ end
 
 # "duck-typing" conversion from vector-of-tuples to waiting list
 function Base.convert(::Type{TW},
-                      Q::Vector{Tuple{ST,M}}) where {TW<:WaitingList,ST<:AdmissibleSet,M<:Integer}
+                      Q::Vector{Tuple{ST,Int}}) where {TW<:WaitingList,ST<:AdmissibleSet}
     waiting_list = TW()
     for Qi in Q # no intersection chcks
         Xi, q = Qi

diff --git a/src/ReachSets/AbstractLazyReachSet.jl b/src/ReachSets/AbstractLazyReachSet.jl
@@ -95,8 +95,8 @@ end
 # ------------------------------------
 
 """
-    project(R::AbstractLazyReachSet, variables::NTuple{D, M};
-            check_vars::Bool=true) where {D, M<:Integer}
+    project(R::AbstractLazyReachSet, variables::NTuple{D,Int};
+            check_vars::Bool=true) where {D}
 
 Projects a reach-set onto the subspace spanned by the given variables.
 
@@ -129,8 +129,8 @@ associated with the given variables `vars`.
 To project onto the time variable, use the index `0`. For instance, `(0, 1)` projects
 onto the time variable and the first variable in `R`.
 """
-function project(R::AbstractLazyReachSet, variables::NTuple{D,M};
-                 check_vars::Bool=true) where {D,M<:Integer}
+function project(R::AbstractLazyReachSet, variables::NTuple{D,Int};
+                 check_vars::Bool=true) where {D}
     vR = vars(R)
     vRvec = collect(vR)
 
@@ -162,7 +162,7 @@ function project(R::AbstractLazyReachSet, variable::Int; check_vars::Bool=true)
 end
 
 # concrete projection overloads
-function project(R::AbstractLazyReachSet, vars::AbstractVector{M}) where {M<:Integer}
+function project(R::AbstractLazyReachSet, vars::AbstractVector{Int})
     return project(R, Tuple(vars))
 end
 project(R::AbstractLazyReachSet; vars) = project(R, Tuple(vars))
@@ -178,8 +178,8 @@ project(R::SubArray{<:AbstractLazyReachSet}; vars) = _project_vec(R, vars)
 # Lazy projection of a reach-set
 # -------------------------------
 
-function Projection(R::AbstractLazyReachSet, variables::NTuple{D,M},
-                    check_vars::Bool=true) where {D,M<:Integer}
+function Projection(R::AbstractLazyReachSet, variables::NTuple{D,Int},
+                    check_vars::Bool=true) where {D}
     vR = vars(R)
     vRvec = collect(vR)
 
@@ -202,7 +202,7 @@ function Projection(R::AbstractLazyReachSet, variables::NTuple{D,M},
 end
 
 # handle generic vars vector
-function Projection(R::AbstractLazyReachSet, vars::AbstractVector{M}) where {M<:Integer}
+function Projection(R::AbstractLazyReachSet, vars::AbstractVector{Int})
     return Projection(R, Tuple(vars))
 end
 

diff --git a/src/ReachSets/ReachSet.jl b/src/ReachSets/ReachSet.jl
@@ -64,7 +64,7 @@ end
 
 #=
 # specialized concrete projection of zonotopic set by removing zero generators
-function linear_map(R::ReachSet{N, <:AbstractZonotope{N}}, variables::NTuple{D, M}; check_vars::Bool=true) where {D, M<:Integer}
+function linear_map(R::ReachSet{N, <:AbstractZonotope{N}}, variables::NTuple{D,Int}; check_vars::Bool=true) where {D}
     πR = linear(R, variables, check_vars)
     X = remove_zero_generators(set(πR))
     SparseReachSet(proj, tspan(R), variables)