Merge pull request #115 from JuliaReach/mforets/templates

Update templates

src/Flowpipes/reachsets.jl

@@ -605,14 +605,24 @@ end
 # Template reach set
 # ================================================================
 
+using LazySets.Approximations: AbstractDirections
+
 """
-    TemplateReachSet{N, VN<:AbstractVector{N}} <: AbstractReachSet{N}
+    TemplateReachSet{N, VN, TN<:AbstractDirections{N, VN}, SN<:AbstractVector{N}} <: AbstractLazyReachSet{N}
 
 Reach set that stores the support function of a set at a give set of directions.
 
 ### Notes
 
-The parameter `N` refers to the numerical type of the representation.
+The struct has the following parameters:
+
+- `N`  -- refers to the numerical type of the representation.
+- `VN` -- refers to the vector type of the template
+- `TN` -- refers to the template type
+- `SN` -- vector type that holds the support function evaluations
+
+Concrete subtypes of `AbstractDirections` are defined in the `LazySets` library.
+
 This reach-set implicitly represents a set by a set of directions and support
 functions. `set(R::TemplateReachSet)` returns a polyhedron in half-space
 representation.
@@ -624,29 +634,47 @@ the following methods are available:
 - `sup_func(R)`    -- return the vector of support function evaluations
 - `sup_func(R, i)` -- return the `i`-th coordinate of the vector of support function evaluatons
 """
-struct TemplateReachSet{N, VN<:AbstractVector{N}} <: AbstractReachSet{N}
-    dirs::Vector{VN} # TODO: consider more general types eg. AbstractDirections ?
-    sf::Vector{N}
+struct TemplateReachSet{N, VN, TN<:AbstractDirections{N, VN}, SN<:AbstractVector{N}} <: AbstractLazyReachSet{N}
+    dirs::TN
+    sf::SN
     Δt::TimeInterval
 end
 
+# constructor from a given set (may overapproximate)
+function TemplateReachSet(dirs::AbstractDirections, X::LazySet, Δt::TimeInterval)
+    sfunc = [ρ(d, X) for d in dirs]
+    return TemplateReachSet(dirs, sfunc, Δt)
+end
+
+# constructor from a given reach-set (may overapproximate)
+function TemplateReachSet(dirs::AbstractDirections, R::AbstractLazyReachSet)
+    return TemplateReachSet(dirs, set(R), tspan(R))
+end
+
 # implement abstract reachset interface
 # TODO: use HPolyhedron or HPolytope if the set is bounded or not
-set(R::TemplateReachSet) = HPolytope([HalfSpace(R.dirs[i], R.sf[i]) for i in eachindex(R.sf)])
+set(R::TemplateReachSet) = HPolytope([HalfSpace(di, R.sf[i]) for (i, di) in enumerate(R.dirs)])
 setrep(::Type{TemplateReachSet{N, VN}}) where {N, VN} = HPolyhedron{N, VN}
 setrep(::TemplateReachSet{N, VN}) where {N, VN} = HPolyhedron{N, VN}
 tspan(R::TemplateReachSet) = R.Δt
 tstart(R::TemplateReachSet) = inf(R.Δt)
 tend(R::TemplateReachSet) = sup(R.Δt)
-dim(R::TemplateReachSet) = length(first(R.dirs))
-vars_idx(R::TemplateReachSet) = Tuple(Base.OneTo(dim(R)),)
+dim(R::TemplateReachSet) = dim(R.dirs)
+vars_idx(R::TemplateReachSet) = Tuple(Base.OneTo(dim(R)),) # TODO rename to vars ?
 
-directions(R::TemplateReachSet) = R.dirs
-sup_func(R::TemplateReachSet) = R.sf
+directions(R::TemplateReachSet) = R.dirs # TODO rename to dirs ?
+sup_func(R::TemplateReachSet) = R.sf # TODO rename?
 sup_func(R::TemplateReachSet, i) = R.sf[i]
 
+# overapproximate a given reach set with the template, concretely
+#= TODO: remove?
 function overapproximate(R::AbstractLazyReachSet, dirs::Vector{VN}) where {VN}
     Δt = tspan(R)
     sup_func = map(d -> ρ(d, R), dirs)
     return TemplateReachSet(dirs, sup_func, Δt)
 end
+=#
+
+# convenience functions to get support directions of a given set
+_getdirs(X::LazySet) = [c.a for c in constraints_list(X)]
+LazySets.CustomDirections(X::LazySet) = CustomDirections(_getdirs(X), dim(X)) # TODO may use isboundedtype trait