intervals.md

+++ title = "Intervals" +++

Intervals

There are several Julia packages for interval sets and interval arithmetic.

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Overview

IntervalSets.jl and Intervals.jl both focus on working with interval sets, in a mathematical sense (as opposed to a numerical sense). While there have been discussions on merging the two (see IntervalSets.jl#67 and Intervals.jl#94), they currently still exist as separate packages.

IntervalArithmetic.jl on the other hand focuses on interval arithmetic, i.e. carrying out operations like $a+b$ where $a$ or $b$ (or both!) are intervals instead of numbers. There were issues to add an dependency on IntervalSets.jl, but this also has not yet been realized.

• IntervalArithmetic#345
• IntervalArithmetic#366

Packages

IntervalSets.jl

{{badge IntervalSets}}

Intervals.jl

{{badge Intervals}}

IntervalArithmetic.jl

{{badge IntervalArithmetic}} Example of adding an interval and a number:

julia> a = 1;

julia> b = interval(3, 4)
[3.0, 4.0]_com

julia> a+b
[4.0, 5.0]_com_NG

Examples of applying a function to an interval:

julia> f(interval(3, 4))
[9.0, 16.0]_com

julia> f(interval(-3, 4))
[0.0, 16.0]_com

To quote from the intro of the IntervalArithmetic.jl docs:

Since f(x) does not contain 0, the true range of the function $f$ over the interval $[3,4]$ is guaranteed not to contain 00, and hence we obtain the following property.

Theorem: $f$ has no root in the interval $[3,4]$.

This theorem has been obtained using floating-point computations!

Star History

{{star_history IntervalSets Intervals IntervalArithmetic}}