Improve mince and add method for non-uniform partition of IntervalBox

src/intervals/arithmetic.jl

@@ -575,7 +575,7 @@ convert(::Type{Integer}, a::Interval) = isinteger(a) ?
 Splits `x` in `n` intervals of the same diameter, which are returned
 as a vector.
 """
-function mince(x::Interval, n)
+@inline function mince(x::Interval, n)
     nodes = range(x.lo, x.hi, length = n+1)
-    return [Interval(nodes[i], nodes[i+1]) for i in 1:length(nodes)-1]
+    return Interval.(nodes[1:n], nodes[2:n+1])
 end

src/multidim/intervalbox.jl

@@ -115,29 +115,33 @@ Base.:(==)(x::IntervalBox, y::IntervalBox) = x.v == y.v
 
 
 """
-    mince(x::IntervalBox, n)
+    mince(x::IntervalBox, n::Int)
 
 Splits `x` in `n` intervals in each dimension of the same diameter. These
 intervals are combined in all possible `IntervalBox`-es, which are returned
 as a vector.
 """
-@generated function mince(x::IntervalBox{N,T}, n) where {N,T}
-    quote
-        nodes_matrix = Array{Interval{T},2}(undef, n, N)
-        for i in 1:N
-            nodes_matrix[1:n,i] .= mince(x[i], n)
-        end
-
-        nodes = IntervalBox{$N,T}[]
-        Base.Cartesian.@nloops $N i _->(1:n) begin
-            Base.Cartesian.@nextract $N ival d->nodes_matrix[i_d, d]
-            ibox = Base.Cartesian.@ncall $N IntervalBox ival
-            push!(nodes, ibox)
-        end
-        nodes
+@inline mince(x::IntervalBox{N,T}, n::Int) where {N,T} = 
+    mince(x, ntuple(_ -> n, N))
+
+"""
+    mince(x::IntervalBox, ncuts::::NTuple{N,Int})
+
+Splits `x[i]` in `ncuts[i]` intervals . These intervals are 
+combined in all possible `IntervalBox`-es, which are returned
+as a vector.
+"""
+@inline function mince(x::IntervalBox{N,T}, ncuts::NTuple{N,Int}) where {N,T}
+    minced_intervals = [mince(x[i], ncuts[i]) for i in 1:N]
+    minced_boxes = Vector{IntervalBox{N,T}}(undef, prod(ncuts))
+
+    for (k, cut_indices) in enumerate(CartesianIndices(ncuts))
+        minced_boxes[k] = IntervalBox([minced_intervals[i][cut_indices[i]] for i in 1:N])
     end
+    return minced_boxes
 end
 
+
 hull(a::IntervalBox{N,T}, b::IntervalBox{N,T}) where {N,T} = IntervalBox(hull.(a[:], b[:]))
 hull(a::Vector{IntervalBox{N,T}}) where {N,T} = hull(a...)
 

test/multidim_tests/multidim.jl

@@ -306,18 +306,28 @@ end
     @test vb2 == vv
     @test hull(vb2...) == ib2
     @test hull(vb2) == ib2
+    @test mince(ib2, (4,4)) == vb2
+    @test mince(ib2, (1,4)) == [ (-1 .. 1)×(-1 .. -0.5), (-1 .. 1)×(-0.5 .. 0),
+        (-1 .. 1)×(0 .. 0.5), (-1 .. 1)×(0.5 .. 1)]
+    @test hull(mince(ib2, (1,4))) == ib2
 
     ib3 = IntervalBox(-1..1, 3)
     vb3 = mince(ib3, 4)
     @test length(vb3) == 4^3
     @test hull(vb3...) == ib3
     @test hull(vb3) == ib3
+    @test mince(ib3, (4,4,4)) == vb3
+    @test mince(ib3, (2,1,1)) == [(-1 .. 0)×(-1 .. 1)×(-1 .. 1), 
+        (0 .. 1)×(-1 .. 1)×(-1 .. 1)]
+    @test hull(mince(ib3, (2,1,1))) == ib3
 
     ib4 = IntervalBox(-1..1, 4)
     vb4 = mince(ib4, 4)
     @test length(vb4) == 4^4
     @test hull(vb4...) == ib4
     @test hull(vb4) == ib4
+    @test mince(ib4,(4,4,4,4)) == vb4
+    @test mince(ib4,(1,1,1,1)) == [ib4]
 end
 
 @testset "Special box constructors" begin