Merge pull request #899 from JuliaReach/schillic/support_function

Fast support function for `TemplateReachSet`

Author: schillic

src/Flowpipes/AbstractFlowpipe.jl

@@ -33,7 +33,7 @@ In this fallback implementation, the flowpipe behaves like the union of the
 reach-sets, i.e. the implementation is analogue to that of a `LazySet.UnionSetArray`.
 """
 function LazySets.ρ(d::AbstractVector, fp::AbstractFlowpipe)
-    return maximum(map(Ri -> ρ(d, set(Ri)), array(fp)))
+    return maximum(ρ(d, Ri) for Ri in array(fp))
 end
 
 """

src/Initialization/init.jl

@@ -28,7 +28,7 @@ using LazySets: Interval, radius, sample, ∅, dim, scale, scale!, ⊂, matrix
 
 # JuliaReach internal functions
 using ReachabilityBase.Arrays: projection_matrix, SingleEntryVector,
-                               isinvertible, vector_type
+                               isinvertible, samedir, vector_type
 using ReachabilityBase.Comparison: _leq, _geq
 using ReachabilityBase.Require: @required
 using LazySets.Approximations: AbstractDirections

src/ReachSets/TemplateReachSet.jl

@@ -93,3 +93,23 @@ end
 function overapproximate(R::AbstractLazyReachSet, dirs::Vector{VN}) where {VN}
     return TemplateReachSet(CustomDirections(dirs), R)
 end
+
+function LazySets.ρ(d::AbstractVector, R::TemplateReachSet)
+    # efficient implementation when direction is identical with some template direction
+    for (i, di) in enumerate(R.dirs)
+        if d == di
+            return support_functions(R, i)
+        end
+    end
+
+    # efficient implementation when direction is multiple of some template direction
+    for (i, di) in enumerate(R.dirs)
+        issamedir, factor = samedir(d, di)
+        if issamedir
+            return support_functions(R, i) * factor
+        end
+    end
+
+    # fall back to polyhedral support function
+    return ρ(d, set(R))
+end

test/reachsets/reachsets.jl

@@ -1,4 +1,4 @@
-using ReachabilityAnalysis: zeroI
+using ReachabilityAnalysis: zeroI, TimeInterval
 using TaylorModels: set_variables,
                     Taylor1,
                     TaylorModel1
@@ -19,6 +19,17 @@ using TaylorModels: set_variables,
     @test tspan(R) == interval(1.0)
 end
 
+@testset "Reach-set support function" begin
+    dirs = CustomDirections([[1.0, 0.0]])
+    sf = [2.0]
+    Δt = TimeInterval(0.0, 1.0)
+    R = TemplateReachSet(dirs, sf, Δt)
+    d = [1.0, 0.0]
+    @test ρ(d, R) == 2.0
+    d = 2 * d
+    @test ρ(d, R) == 4.0
+end
+
 @testset "Reach-set projections" begin
     X = BallInf(zeros(5), 1.0)
     B = BallInf(zeros(2), 1.0)