IntervalLinearAlgebra.jl

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Pkg Info	Build status	Documentation	Citation	Contributing

Overview

This package contains routines to perform numerical linear algebra using interval arithmetic. This can be used both for rigorous computations and uncertainty propagation.

If you use this package in your work, please cite it as

@software{ferranti2021interval,
author = {
            Luca Feranti and
            Marcelo Forets and
            David P. Sanders
         },
title  = {IntervalLinearAlgebra.jl: linear algebra done rigorously},
month  = {9},
year   = {2021},
doi    = {10.5281/zenodo.5363563},
url    = {https://github.com/juliaintervals/IntervalLinearAlgebra.jl}
}

Features

Note: The package is still under active development and things evolve quickly (or at least should)

• enclosure of the solution of interval linear systems
• exact characterization of the solution set of interval linear systems using Oettli-Präger
• verified solution of floating point linear systems
• enclosure of eigenvalues of interval matrices
• verified computation of eigenvalues and eigenvectors of floating point matrices

Installation

Open a Julia session and enter

using Pkg; Pkg.add("IntervalLinearAlgebra")

this will download the package and all the necessary dependencies for you. Next you can import the package with

using IntervalLinearAlgebra

and you are ready to go.

Documentation

• STABLE -- Documentation of the latest release
• DEV -- Documentation of the current version on main (work in progress)

The package was also presented at JuliaCon 2021! The video is available here and the slides here

Quickstart

Here is a quick demo about solving an interval linear system.

using IntervalLinearAlgebra, LazySets, Plots

A = [2..4 -1..1;-1..1 2..4]
b = [-2..2, -1..1]

Xenclose = solve(A, b)
polytopes = solve(A, b, LinearOettliPrager())

plot(UnionSetArray(polytopes), ratio=1, label="solution set", legend=:top)
plot!(IntervalBox(Xenclose), label="enclosure")

Contributing

If you spot something strange in the software (something doesn't work or doesn't behave as expected) do not hesitate to open a bug issue.

If have an idea of how to make the package better (a new feature, a new piece of documentation, an idea to improve some existing feature), you can open an enhancement issue.

If you feel like your issue does not fit any of the above mentioned templates (e.g. you just want to ask something), you can also open a blank issue.

Pull requests are also very welcome! More details in the contributing guidelines

The core developers of the package can be found in the #intervals channel in the Julia slack or zulip, links to join the platforms can be found here. Come to chat with us!

References

An excellent introduction to interval linear algebra is J. Horácek, Interval Linear and Nonlinear Systems, 2019, available here

See also the complete list of references for the concepts and algorithms used in this package.

Related packages

• IntervalArithmetic.jl -- Interval computations in Julia
• IntervalMatrices.jl -- Matrices with interval coefficients in Julia.

Acknowledgment

The development of this package started during the Google Summer of Code (GSoC) 2021 program for the Julia organisation. The author wishes to thank his mentors David Sanders and Marcelo Forets for the constant guidance and feedback. During the GSoC program, this project was financially supported by Google.