Empty intervalbox (#145)

* Add emptyinterval(x::IntervalBox)

* Rewrite a couple of IntervalBox functions; better structure for intervalbox.jl

* Add test for emptyinterval(IntervalBox)

src/multidim/intervalbox.jl

@@ -1,26 +1,36 @@
-# Multidimensional intervals, called IntervalBox
+# This file is part of the ValidatedNumerics.jl package; MIT licensed
 
+doc"""An `IntervalBox` is an $N$-dimensional rectangular box, given
+by a Cartesian product of $N$ `Interval`s.
+"""
 
-doc"""An `IntervalBox` is a Cartesian product of an arbitrary number of `Interval`s,
-representing an $N$-dimensional rectangular IntervalBox."""
-
-immutable IntervalBox{N, T} <: FixedVector{N, Interval{T}} # uses FixedSizeArrays package
+immutable IntervalBox{N, T} <: FixedVector{N, Interval{T}}  # uses FixedSizeArrays.jl package
     _ :: NTuple{N, Interval{T}}
 end
 
 IntervalBox(x::Interval) = IntervalBox( (x,) )  # single interval treated as tuple with one element
 
 
+## arithmetic operations
+# Note that standard arithmetic operations are implemented automatically by FixedSizeArrays.jl
+
 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)])
 
 ∩(X::IntervalBox, Y::IntervalBox) = IntervalBox([x ∩ y for (x,y) in zip(X, Y)]...)
 
-isempty(X::IntervalBox) = any([isempty(x) for x in X])
+isempty(X::IntervalBox) = any(isempty, X)
 
 diam(X::IntervalBox) = maximum([diam(x) for x in X])
 
+emptyinterval(X::IntervalBox) = IntervalBox(map(emptyinterval, X))
+
+
+## printing
 
 function show(io::IO, X::IntervalBox)
     for (i, x) in enumerate(X)

test/multidim_tests/multidim.jl

@@ -35,6 +35,9 @@ facts("@intervalbox tests") do
 
     @intervalbox g(x, y) = x - y
     @fact isa(g(X), IntervalBox) --> true
+
+    @fact emptyinterval(X) --> IntervalBox(∅, ∅)
+
 end
 
 facts("setdiff for IntervalBox") do