IntervalSets.jl

A Julia package implementing interval sets.

Installation

pkg> add IntervalSets

Quick start

julia> using IntervalSets
julia> i1 = 1.0 .. 3.01.0 .. 3.0
julia> i2 = OpenInterval(0..4)0 .. 4 (open)
julia> i1 ⊆ i2true
julia> i2 ⊆ i1false

Currently this package defines one concrete type, Interval. These define the set spanning from a to b, meaning the interval is defined as the set $\{x \ | \ a ≤ x ≤ b\}$. This is sometimes written $[a,b]$ (mathematics syntax, not Julia syntax) or $a..b$.

Optionally, Interval{L,R} can represent open and half-open intervals. The type parameters L and R correspond to the left and right endpoint respectively. The notation ClosedInterval is short for Interval{:closed,:closed}, while OpenInterval is short for Interval{:open,:open}. For example, the interval Interval{:open,:closed} corresponds to the set $(a,b] = \{x \ | \ a < x ≤ b\}$.

More examples

Constructors

julia> ClosedInterval{Float64}(1,3)1.0 .. 3.0
julia> OpenInterval{Float64}(1,3)1.0 .. 3.0 (open)
julia> Interval{:open, :closed}(1,3)1 .. 3 (open-closed)
julia> OpenInterval(0.5..2.5)  # construct `OpenInterval` from `ClosedInterval`0.5 .. 2.5 (open)

The ± operator and .. creates ClosedInterval instance.

julia> 0.5..2.50.5 .. 2.5
julia> 1.5 ± 1  # \pm<TAB>0.5 .. 2.5

There is also a useful string macro @iv_str to define an interval with mathematical notations such as $(a,b]$.

julia> iv"[1,2]"1 .. 2
julia> iv"[1,2)"1 .. 2 (closed-open)
julia> iv"(1,2]"1 .. 2 (open-closed)
julia> iv"(1,2)"1 .. 2 (open)

Set operations

julia> 1.75 ∈ 1.5±1  # \in<TAB>; can also use `in`true
julia> 0 ∈ 1.5±1false
julia> 1 ∈ OpenInterval(0..1)false
julia> intersect(1..5, 3..7)   # can also use `a ∩ b`, where the symbol is \cap<TAB>3 .. 5
julia> isempty(intersect(1..5, 10..11))true
julia> (0.25..5) ∪ (3..7.4)  # \cup<TAB>; can also use `union()`0.25 .. 7.4
julia> isclosedset(0.5..2.0)true
julia> isopenset(OpenInterval(0.5..2.5))true
julia> isleftopen(2..3)false
julia> (0.25..5) ∪ (6..7.4)  # union of interval must be an intervalERROR: ArgumentError: Cannot construct union of disjoint sets.

Visualization

Intervals can be visulalized with Plots.plot function.

using IntervalSets, Plots
plot(iv"(1,2)")
plot!(iv"[3,6)")
plot!(iv"[5,7)")

The offset keyword argument is useful for avoid duplication.

plot(iv"[1,3]")
plot!(iv"(2,4)"; offset=-0.1, ylims=(-1,1))

Importing the .. operator

To import the .. operator, use import IntervalSets: (..). The parantheses are necessary to avoid parsing issues.

julia> import IntervalSets: (..)
julia> import IntervalSets.(..)  # This is also okay