fix conflicts and rebase

Project_tmp

@@ -1,21 +1,23 @@
 # basic package information
 name = "LazySets"
 uuid = "b4f0291d-fe17-52bc-9479-3d1a343d9043"
-version = "1.3.0"
+version = "1.5.2"
 author = ["Marcelo Forets",
           "Christian Schilling",
           "Frédéric Viry"]
 
 [deps]
 # add dependencies here
 Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
+Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 Expokit = "a1e7a1ef-7a5d-5822-a38c-be74e1bb89f4"
 GLPKMathProgInterface = "3c7084bd-78ad-589a-b5bb-dbd673274bea"
 IntervalArithmetic = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
 MathProgBase = "fdba3010-5040-5b88-9595-932c9decdf73"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
 Requires = "ae029012-a4dd-5104-9daa-d747884805df"
+SharedArrays = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [compat]

docs/Project.toml

@@ -0,0 +1,5 @@
+[deps]
+Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+
+[compat]
+Documenter = "~0.19.7"

docs/make.jl

@@ -21,15 +21,18 @@ makedocs(
         "A Reachability Algorithm" => "man/reach_zonotopes.md",
         "A Hybrid Reachability Algorithm" => "man/reach_zonotopes_hybrid.md",
         "Concrete Polyhedra" => "man/concrete_polyhedra.md",
+        "Parallel Approximations" => "man/parallel_approximations.md"
         ],
         "Library" => Any[
         "Set Interfaces" => "lib/interfaces.md",
         "Common Set Representations" => "lib/representations.md",
         "Common Set Operations" => "lib/operations.md",
-        "Conversion between set representations" => "lib/conversion.md",
+        "Comparisons" => "lib/comparisons.md",
+        "Conversions between set representations" => "lib/conversion.md",
         "Binary Functions on Sets" => "lib/binary_functions.md",
         "Approximations" => "lib/approximations.md",
         "Utility Functions" => "lib/utils.md",
+        "Parallel" => "lib/parallel.md"
         ],
         "About" => "about.md"
     ]

docs/make_doctests_only.jl

@@ -1,4 +1,4 @@
-using Documenter, LazySets
+using Documenter, LazySets, Polyhedra, Optim
 
 makedocs(
     doctest = true,

docs/src/about.md

@@ -104,8 +104,8 @@ approximations computed with [SpaceEx](http://spaceex.imag.fr/).
 These persons have contributed to `LazySets.jl` (in alphabetic order):
 
 - Tomer Arnon
-- [Marcelo Forets](http://marcelo-forets.fr)
+- [Marcelo Forets](http://main.marcelo-forets.fr/)
 - [Christian Schilling](https://schillic.github.io/)
 - Frédéric Viry
 
-We are also grateful to Goran Frehse for enlightening discussions.
+We are also grateful to [Goran Frehse](https://sites.google.com/site/frehseg/) for enlightening discussions.

docs/src/index.md

@@ -185,9 +185,11 @@ Pages = [
     "man/iterative_refinement.md",
     "man/interval_hulls.md",
     "man/convex_hulls.md",
+    "man/set_operations.md",
     "man/reach_zonotopes.md",
     "man/reach_zonotopes_hybrid.md",
-    "man/concrete_polyhedra.md"
+    "man/concrete_polyhedra.md",
+    "man/parallel_approximations.md"
 ]
 Depth = 2
 ```
@@ -199,9 +201,12 @@ Pages = [
     "lib/interfaces.md",
     "lib/representations.md",
     "lib/operations.md",
+    "lib/comparisons.md",
     "lib/conversion.md",
+    "lib/binary_functions.md",
     "lib/approximations.md",
-    "lib/utils.md"
+    "lib/utils.md",
+    "lib/parallel.md"
 ]
 Depth = 2
 ```

docs/src/lib/binary_functions.md

@@ -14,26 +14,6 @@ DocTestSetup = quote
 end
 ```
 
-## Subset check
-
-```@docs
-⊆(::LazySet{N}, ::AbstractHyperrectangle{N}, ::Bool=false) where {N<:Real}
-⊆(::AbstractPolytope{N}, ::LazySet{N}, ::Bool=false) where {N<:Real}
-⊆(::AbstractPolytope{N}, ::AbstractHyperrectangle, ::Bool=false) where {N<:Real}
-⊆(::AbstractHyperrectangle{N}, ::AbstractHyperrectangle{N}, ::Bool=false) where {N<:Real}
-⊆(::LazySet{N}, ::Union{AbstractPolytope{N}, HPolyhedron{N}, HalfSpace{N}}, ::Bool=false) where {N<:Real}
-⊆(::AbstractSingleton{N}, ::LazySet{N}, ::Bool=false) where {N<:Real}
-⊆(::AbstractSingleton{N}, ::AbstractHyperrectangle{N}, ::Bool=false) where {N<:Real}
-⊆(::AbstractSingleton{N}, ::AbstractSingleton{N}, ::Bool=false) where {N<:Real}
-⊆(::Ball2{N}, ::Ball2{N}, ::Bool=false) where {N<:AbstractFloat}
-⊆(::Union{Ball2{N}, Ballp{N}}, ::AbstractSingleton{N}, ::Bool=false) where {N<:AbstractFloat}
-⊆(::LineSegment{N}, ::LazySet{N}, ::Bool=false) where {N<:Real}
-⊆(::LineSegment{N}, ::AbstractHyperrectangle{N}, ::Bool=false) where {N<:Real}
-⊆(::Interval, ::Interval)
-⊆(::EmptySet{N}, ::LazySet{N}, ::Bool=false) where {N<:Real}
-⊆(::LazySet{N}, ::EmptySet{N}, ::Bool=false) where {N<:Real}
-```
-
 ## Check for emptiness of intersection
 
 ```@docs
@@ -53,6 +33,14 @@ is_intersection_empty(::LazySet{N}, ::Union{HPolyhedron{N}, HPolytope{N}, Abstra
 is_intersection_empty(::HPolytope{N}, ::HPolytope{N}, ::Bool=false) where {N<:Real}
 ```
 
+## Convex hull
+
+```@docs
+convex_hull(::HPoly{N}, ::HPoly{N}) where {N<:Real}
+convex_hull(::VPolytope{N}, ::VPolytope{N}) where {N<:Real}
+convex_hull(::VPolygon{N}, ::VPolygon{N}) where {N<:Real}
+```
+
 ## Intersection of two sets
 
 ```@docs
@@ -66,3 +54,23 @@ intersection(::HPoly{N}, ::VPolytope{N}) where {N<:Real}
 intersection(::HPoly{N}, ::AbstractPolytope{N}) where {N<:Real}
 intersection(::S1, ::S2) where {N<:Real, S1<:AbstractPolytope{N}, S2<:AbstractPolytope{N}}
 ```
+
+## Subset check
+
+```@docs
+⊆(::LazySet{N}, ::AbstractHyperrectangle{N}, ::Bool=false) where {N<:Real}
+⊆(::AbstractPolytope{N}, ::LazySet{N}, ::Bool=false) where {N<:Real}
+⊆(::AbstractPolytope{N}, ::AbstractHyperrectangle, ::Bool=false) where {N<:Real}
+⊆(::AbstractHyperrectangle{N}, ::AbstractHyperrectangle{N}, ::Bool=false) where {N<:Real}
+⊆(::LazySet{N}, ::Union{AbstractPolytope{N}, HPolyhedron{N}, HalfSpace{N}}, ::Bool=false) where {N<:Real}
+⊆(::AbstractSingleton{N}, ::LazySet{N}, ::Bool=false) where {N<:Real}
+⊆(::AbstractSingleton{N}, ::AbstractHyperrectangle{N}, ::Bool=false) where {N<:Real}
+⊆(::AbstractSingleton{N}, ::AbstractSingleton{N}, ::Bool=false) where {N<:Real}
+⊆(::Ball2{N}, ::Ball2{N}, ::Bool=false) where {N<:AbstractFloat}
+⊆(::Union{Ball2{N}, Ballp{N}}, ::AbstractSingleton{N}, ::Bool=false) where {N<:AbstractFloat}
+⊆(::LineSegment{N}, ::LazySet{N}, ::Bool=false) where {N<:Real}
+⊆(::LineSegment{N}, ::AbstractHyperrectangle{N}, ::Bool=false) where {N<:Real}
+⊆(::Interval, ::Interval)
+⊆(::EmptySet{N}, ::LazySet{N}, ::Bool=false) where {N<:Real}
+⊆(::LazySet{N}, ::EmptySet{N}, ::Bool=false) where {N<:Real}
+```

docs/src/lib/comparisons.md

@@ -0,0 +1,25 @@
+# Comparisons
+
+This section of the manual lists the comparison functions in floating point between scalars and between vectors.
+
+```@contents
+Pages = ["comparisons.md"]
+Depth = 3
+```
+
+```@meta
+CurrentModule = LazySets
+DocTestSetup = quote
+    using LazySets
+end
+```
+
+```@docs
+_leq(x::N, y::N; kwargs...) where {N<:Real}
+_leq(x::N, y::M; kwargs...) where {N<:Real, M<:Real}
+_geq(x::Real, y::Real; kwargs...)
+isapproxzero(x::Real; kwargs...)
+isapproxzero(x::N; ztol::Real=ABSZTOL(N)) where {N<:AbstractFloat}
+_isapprox(x::N, y::N; rtol::Real=Base.rtoldefault(N), ztol::Real=ABSZTOL(N), atol::Real=zero(N)) where {N<:AbstractFloat}
+_leq(x::N, y::N; rtol::Real=Base.rtoldefault(N), ztol::Real=ABSZTOL(N), atol::Real=zero(N)) where {N<:AbstractFloat}
+```

docs/src/lib/interfaces.md

@@ -59,13 +59,19 @@ diameter(::LazySet, ::Real=Inf)
 isbounded(::LazySet)
 isbounded_unit_dimensions(::LazySet{N}) where {N<:Real}
 an_element(::LazySet{N}) where {N<:Real}
-==(::LazySet, ::LazySet)
 RecipesBase.apply_recipe(::Dict{Symbol,Any}, ::LazySet)
 RecipesBase.apply_recipe(::Dict{Symbol,Any}, ::Vector{S}) where {S<:LazySet}
 RecipesBase.apply_recipe(::Dict{Symbol,Any}, ::LazySet, ::Float64)
 RecipesBase.apply_recipe(::Dict{Symbol,Any}, ::Vector{S}, ::Float64) where {S<:LazySet}
 ```
 
+### Set functions that override Base functions
+
+```@docs
+==(::LazySet, ::LazySet)
+copy(::LazySet)
+```
+
 ### Aliases for set types
 
 ```@docs

docs/src/lib/operations.md

@@ -305,3 +305,25 @@ Inherited from [`AbstractHyperrectangle`](@ref):
 * [`vertices_list`](@ref vertices_list(::AbstractHyperrectangle{N}) where {N<:Real})
 * [`high`](@ref high(::AbstractHyperrectangle{N}) where {N<:Real})
 * [`low`](@ref low(::AbstractHyperrectangle{N}) where {N<:Real})
+
+## Union
+
+### Binary Set Union
+
+```@docs
+UnionSet
+∪(::LazySet, ::LazySet)
+dim(::Union)
+σ(::AbstractVector{N}, ::UnionSet{N}; algorithm="support_vector") where {N<:Real}
+ρ(::AbstractVector{N}, ::UnionSet{N}) where {N<:Real}
+```
+
+### ``n``-ary Set Union
+
+```@docs
+UnionSetArray
+dim(::UnionSetArray)
+array(::UnionSetArray{N, S}) where {N<:Real, S<:LazySet{N}}
+σ(::AbstractVector{N}, ::UnionSetArray{N}; algorithm="support_vector") where {N<:Real}
+ρ(::AbstractVector{N}, ::UnionSetArray{N}) where {N<:Real}
+```

docs/src/lib/parallel.md

@@ -0,0 +1,40 @@
+# Parallel
+
+This section of the manual describes the parallel implementation of some
+algorithms in the `LazySets` library. These algorithms are implemented in the
+`LazySets.Parallel` module.
+
+```@contents
+Pages = ["parallel.md"]
+Depth = 3
+```
+
+```@meta
+CurrentModule = LazySets.Parallel
+DocTestSetup = quote
+    using LazySets, LazySets.Parallel
+end
+```
+
+```@docs
+Parallel
+```
+
+## Box approximations
+
+```@docs
+LazySets.Parallel.interval_hull
+LazySets.Parallel.box_approximation
+LazySets.Parallel.symmetric_interval_hull
+LazySets.Parallel.box_approximation_symmetric
+LazySets.Parallel.box_approximation_helper_parallel
+LazySets.Parallel.process_chunk!
+```
+
+## Distributed functions
+
+```@docs
+LazySets.Parallel.assign_chunk!
+LazySets.Parallel.distribute_task!
+LazySets.Parallel._prange
+```

docs/src/lib/representations.md

@@ -79,6 +79,7 @@ center(::Ball1{N}) where {N<:Real}
 rand(::Type{Ball1})
 constraints_list(::Ball1{N}) where {N<:Real}
 ```
+
 Inherited from [`LazySet`](@ref):
 * [`norm`](@ref norm(::LazySet, ::Real))
 * [`radius`](@ref radius(::LazySet, ::Real))
@@ -241,6 +242,8 @@ vertices_list(::Interval{N}) where {N<:Real}
 center(::Interval{N}) where {N<:Real}
 min(::Interval{N}) where {N<:Real}
 max(::Interval{N}) where {N<:Real}
+low(::Interval{N}) where {N<:Real}
+high(::Interval{N}) where {N<:Real}
 radius_hyperrectangle(::Interval{N}) where {N<:Real}
 radius_hyperrectangle(::Interval{N}, ::Int) where {N<:Real}
 +(::Interval{N}, ::Interval{N}) where {N<:Real}
@@ -383,6 +386,8 @@ vertices_list(::VPolygon{N}) where {N<:Real}
 tohrep(::VPolygon{N}, ::Type{HPOLYGON}=HPolygon) where {N<:Real, HPOLYGON<:AbstractHPolygon}
 tovrep(::VPolygon{N}) where {N<:Real}
 constraints_list(::VPolygon{N}) where {N<:Real}
+remove_redundant_vertices(::VPolygon{N}; ::String="monotone_chain") where {N<:Real}
+remove_redundant_vertices!(::VPolygon{N}; ::String="monotone_chain") where {N<:Real}
 ```
 Inherited from [`LazySet`](@ref):
 * [`norm`](@ref norm(::LazySet, ::Real))
@@ -430,11 +435,9 @@ dim(::HPoly{N}) where {N<:Real}
 ∈(::AbstractVector{N}, ::HPoly{N}) where {N<:Real}
 addconstraint!(::HPoly{N}, ::LinearConstraint{N}) where {N<:Real}
 constraints_list(::HPoly{N}) where {N<:Real}
-copy(P::PT) where {N, PT<:HPoly{N}} where {N<:Real}
 tosimplehrep(::HPoly{N}) where {N<:Real}
 tohrep(::HPoly{N}) where {N<:Real}
 isempty(::HPoly{N}) where {N<:Real}
-convex_hull(::HPoly{N}, ::HPoly{N}) where {N<:Real}
 cartesian_product(::HPoly{N}, ::HPoly{N}) where {N<:Real}
 tovrep(::HPoly{N}) where {N<:Real}
 polyhedron(::HPoly{N}) where {N<:Real}
@@ -483,6 +486,7 @@ dim(::VPolytope)
 σ(::AbstractVector{N}, ::VPolytope{N}) where {N<:Real}
 rand(::Type{VPolytope})
 vertices_list(::VPolytope{N}) where {N<:Real}
+remove_redundant_vertices(::VPolytope{N}) where {N<:Real}
 constraints_list(::VPolytope{N}) where {N<:Real}
 tohrep(::VPolytope{N}) where {N<:Real}
 tovrep(::VPolytope)