Non-uniform split of hyperrectangles

Project.toml

@@ -24,7 +24,7 @@ IntervalArithmetic = "0.15 - 0.21, =0.21.2"  # v0.22 removed IntervalBox
 JuMP = "0.21 - 0.23, 1"
 LinearAlgebra = "<0.0.1, 1.6"
 Random = "<0.0.1, 1.6"
-ReachabilityBase = "0.2.1"
+ReachabilityBase = "0.2.5"
 RecipesBase = "0.6 - 0.8, 1"
 Reexport = "0.2, 1"
 Requires = "0.5, 1"

src/Interfaces/AbstractHyperrectangle.jl

@@ -666,6 +666,38 @@ function split(H::AbstractHyperrectangle{N},
     return result
 end
 
+# non-uniform partition
+function split(H::AbstractHyperrectangle{N},
+               bounds::AbstractVector{<:AbstractVector{<:Real}}) where {N}
+    @assert length(bounds) == dim(H) "the bounds ($(length(bounds))) must be " *
+                                     "specified in each dimension ($(dim(H)))"
+    lo = low(H)
+    hi = high(H)
+    n = length(lo)
+
+    bs = [length(b) + 1 for b in bounds]
+    total_number = prod(bs)
+    result = Vector{Hyperrectangle{N,Vector{N},Vector{N}}}(undef, total_number)
+    for (j, vj) in enumerate(CartesianIterator(bs, false))
+        l = Vector{N}(undef, n)
+        h = Vector{N}(undef, n)
+        for (i, ei) in enumerate(vj)
+            if ei == 1
+                l[i] = lo[i]
+            else
+                l[i] = bounds[i][ei-1]
+            end
+            if ei == bs[i]
+                h[i] = hi[i]
+            else
+                h[i] = bounds[i][ei]
+            end
+        end
+        result[j] = Hyperrectangle(low=l, high=h)
+    end
+    return result
+end
+
 """
     rectify(H::AbstractHyperrectangle)
 

test/Sets/Hyperrectangle.jl

@@ -173,6 +173,33 @@ for N in [Float64, Rational{Int}, Float32]
     H = Hyperrectangle(SA[N(0), N(0)], SA[N(1), N(2)])
     S = split(H, [2, 2])
     @test S isa Vector{typeof(H)}
+    # split with non-uniform partition
+    H = Hyperrectangle(low=N[1, 2], high=N[5, 6])
+    S = split(H, [N[3], N[4]])
+    @test ispermutation(S, [Hyperrectangle(low=N[1, 2], high=N[3, 4]),
+                            Hyperrectangle(low=N[3, 2], high=N[5, 4]),
+                            Hyperrectangle(low=N[1, 4], high=N[3, 6]),
+                            Hyperrectangle(low=N[3, 4], high=N[5, 6])])
+    S = split(H, [N[2, 3], N[4, 5]])
+    @test ispermutation(S, [Hyperrectangle(low=N[1, 2], high=N[2, 4]),
+                            Hyperrectangle(low=N[2, 2], high=N[3, 4]),
+                            Hyperrectangle(low=N[3, 2], high=N[5, 4]),
+                            Hyperrectangle(low=N[1, 4], high=N[2, 5]),
+                            Hyperrectangle(low=N[2, 4], high=N[3, 5]),
+                            Hyperrectangle(low=N[3, 4], high=N[5, 5]),
+                            Hyperrectangle(low=N[1, 5], high=N[2, 6]),
+                            Hyperrectangle(low=N[2, 5], high=N[3, 6]),
+                            Hyperrectangle(low=N[3, 5], high=N[5, 6])])
+    H = Hyperrectangle(low=N[1, 2, 3], high=N[5, 6, 7])
+    S = split(H, [N[3], N[4], N[5]])
+    @test ispermutation(S, [Hyperrectangle(low=N[1, 2, 3], high=N[3, 4, 5]),
+                            Hyperrectangle(low=N[1, 2, 5], high=N[3, 4, 7]),
+                            Hyperrectangle(low=N[1, 4, 3], high=N[3, 6, 5]),
+                            Hyperrectangle(low=N[1, 4, 5], high=N[3, 6, 7]),
+                            Hyperrectangle(low=N[3, 2, 3], high=N[5, 4, 5]),
+                            Hyperrectangle(low=N[3, 2, 5], high=N[5, 4, 7]),
+                            Hyperrectangle(low=N[3, 4, 3], high=N[5, 6, 5]),
+                            Hyperrectangle(low=N[3, 4, 5], high=N[5, 6, 7])])
 
     # subset
     H1 = Hyperrectangle(N[1, 3], N[0.5, 0.5])