More efficient intersection and union for boxes (#196)

* More efficient intersection and union for boxes

* Improve subset for boxes

* Add a couple of tests for intersection and union

* Make union(a,b) and hull(a,b) more specific to only work with intervals

* Fix union and hull

* Import union from Base!

Author: dpsanders

src/ValidatedNumerics.jl

@@ -20,7 +20,7 @@ import Base:
     union, intersect, isempty,
     convert, promote_rule, eltype,
     BigFloat, float, widen, big,
-    ∩, ⊆, eps,
+    ∩, ∪, ⊆, eps,
     floor, ceil, trunc, sign, round,
     expm1, log1p,
     precision,

src/intervals/set_operations.jl

@@ -69,7 +69,7 @@ all of `a` and `b`.
 """
 hull{T}(a::Interval{T}, b::Interval{T}) = Interval{T}(min(a.lo, b.lo), max(a.hi, b.hi))
 
-hull(a, b) = hull(promote(a, b)...)
+hull{T,S}(a::Interval{T}, b::Interval{S}) = hull(promote(a, b)...)
 
 """
     union(a, b)
@@ -80,7 +80,7 @@ to `hull(a,b)`.
 """
 union{T}(a::Interval{T}, b::Interval{T}) = hull(a, b)
 
-union(a, b) = union(promote(a, b)...)
+union{T,S}(a::Interval{T}, b::Interval{S}) = union(promote(a, b)...)
 
 
 doc"""

src/multidim/intervalbox.jl

@@ -19,15 +19,25 @@ mid(X::IntervalBox) = [mid(x) for x in X]
 
 ## set operations
 
-⊆(X::IntervalBox, Y::IntervalBox) = all([x ⊆ y for (x,y) in zip(X, Y)])
+# TODO: Update to use generator
+⊆{N,T}(X::IntervalBox{N,T}, Y::IntervalBox{N,T}) = all(i->(X[i] ⊆ Y[i]), 1:N)
+# all(X[i] ⊆ Y[i] for i in 1:N)  # on Julia 0.6
+
+∩{N,T}(X::IntervalBox{N,T}, Y::IntervalBox{N,T}) = IntervalBox(ntuple(i -> X[i] ∩ Y[i], Val{N}))
+∪{N,T}(X::IntervalBox{N,T}, Y::IntervalBox{N,T}) = IntervalBox(ntuple(i -> X[i] ∪ Y[i], Val{N}))
+
+#=
+On Julia 0.6 can now write
+∩{N,T}(X::IntervalBox{N,T}, Y::IntervalBox{N,T}) = IntervalBox(NTuple{N, Interval{Float64}}( (X[i] ∩ Y[i]) for i in 1:N))
+=#
 
-∩(X::IntervalBox, Y::IntervalBox) = IntervalBox([x ∩ y for (x,y) in zip(X, Y)]...)
 
 isempty(X::IntervalBox) = any(isempty, X)
 
+# TODO: Replace with generator in 0.5:
 diam(X::IntervalBox) = maximum([diam(x) for x in X])
 
-emptyinterval(X::IntervalBox) = IntervalBox(map(emptyinterval, X))
+emptyinterval{N,T}(X::IntervalBox{N,T}) = IntervalBox(ntuple(i->emptyinterval(T), Val{N}))
 
 
 import Base.×

test/multidim_tests/multidim.jl

@@ -10,11 +10,18 @@ facts("Operations on boxes") do
     @fact dot(A, B) --> @interval(9, 28)
 
     @fact A ⊆ B --> true
+    @fact A ∩ B --> A
+    @fact A ∪ B --> B
 
     X = IntervalBox(1..2, 3..4)
     Y = IntervalBox(3..4, 3..4)
 
     @fact isempty(X ∩ Y) --> true
+    @fact X ∪ Y --> IntervalBox(1..4, 3..4)
+
+    X = IntervalBox(2..4, 3..5)
+    Y = IntervalBox(3..5, 4..17)
+    @fact X ∩ Y --> IntervalBox(3..4, 4..5)
 
     v = [@interval(i, i+1) for i in 1:10]
     V = IntervalBox(v...)