# IntervalContractors.jl

**Repository Path**: Julialang/IntervalContractors.jl

## Basic Information

- **Project Name**: IntervalContractors.jl
- **Description**: No description available
- **Primary Language**: Unknown
- **License**: MIT
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2018-03-12
- **Last Updated**: 2024-08-15

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# IntervalContractors

[![travis badge][travis_badge]][travis_url]
[![appveyor badge][appveyor_badge]][appveyor_url]
[![codecov badge][codecov_badge]][codecov_url]

## Documentation

- [**STABLE**][documenter_stable] — **most recently tagged version of the documentation.**
- [**LATEST**][documenter_latest] — *in-development version of the documentation.*

[travis_badge]: https://travis-ci.org/JuliaIntervals/IntervalContractors.jl.svg?branch=master
[travis_url]: https://travis-ci.org/JuliaIntervals/IntervalContractors.jl

[appveyor_badge]: https://ci.appveyor.com/api/projects/status/github/JuliaIntervals/IntervalContractors.jl?svg=true&branch=master
[appveyor_url]: https://ci.appveyor.com/project/JuliaIntervals/intervalcontractors-jl

[codecov_badge]: http://codecov.io/github/JuliaIntervals/IntervalContractors.jl/coverage.svg?branch=master
[codecov_url]: http://codecov.io/github/JuliaIntervals/IntervalContractors.jl?branch=master

[documenter_stable]: https://juliaintervals.github.io/IntervalContractors.jl/stable
[documenter_latest]: https://juliaintervals.github.io/IntervalContractors.jl/latest

## About `IntervalContractors.jl`

`IntervalContractors.jl` provides contractors and reverse functions (also called backward functions or relational functions) for interval arithmetic.

### Reverse functions

The reverse function of a function `f` calculates the (interval hull of) its inverse function, `f⁻¹`.

For example, `sin_rev(Y::Interval, X::Interval)` calculates the (interval hull of) those `x ∈ X` such that `sin(x) ∈ Y`. This can also be thought of as an inverse function, calculating `X_new := sin⁻¹(Y) ∩ X`.
The return value is `(Y, X_new)`.

Functions such as `mul_rev(C::Interval, A::Interval, B::Interval)` take three arguments, and correspond to `C = A * B`; they return `(C, A_new, B_new)`, with `A_new` and `B_new` similarly defined to be the corresponding inverse images of the multiplication operator in each component.

### Contractors

Functions like `sin!` (currently non-exported) are contractors for the set `{(x, y): y = sin(x)}`.

The list of available functions may be found in the documentation.

These functions are designed to be used inside the [`IntervalConstraintProgramming.jl`]( https://github.com/JuliaIntervals/IntervalConstraintProgramming.jl) library,
and (eventually) to satisfy the section on reverse functions in the IEEE-1788 2015 standard on interval arithmetic.

## Author

- [David P. Sanders](http://sistemas.fciencias.unam.mx/~dsanders),
Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM)


## References:
- *Applied Interval Analysis*, Luc Jaulin, Michel Kieffer, Olivier Didrit, Eric Walter (2001)

- IBEX library documentation: http://www.ibex-lib.org/doc/interval.html#backward-arithmetic



## Acknowledements
Financial support is acknowledged from DGAPA-UNAM PAPIIT grant IN-117117. The author thanks Luc Jaulin and Jordan Ninin for the [IAMOOC](http://iamooc.ensta-bretagne.fr/) online course, which introduced him to this subject, and Zenna Tavares for a helpful conversation.