## PolyChaos.jl

A Julia package to construct orthogonal polynomials, their quadrature rules, and use it with polynomial chaos expansions.
Popularity
116 Stars
Updated Last
19 Days Ago
Started In
January 2019

# PolyChaos -- Orthogonal Polynomials, Quadrature, and Polynomial Chaos

A Julia package to construct orthogonal polynomials, their quadrature rules, and use it with polynomial chaos expansions.

## Tutorials and Documentation

For information on using the package, see the stable documentation. Use the in-development documentation for the version of the documentation, which contains the unreleased features.

The package requires `Julia 1.3` or newer. In `Julia` switch to the package manager

```using Pkg

This will install PolyChaos and its dependencies. Once that is done, load the package:

`using PolyChaos`

That's it.

Let's take a look at a simple example. We would like to solve the integral

Exploiting the underlying uniform measure, the integration can be done exactly with a 3-point quadrature rule.

``````opq = Uniform01OrthoPoly(3)
integrate(x -> 6x^5, opq)
``````

## Citing

If you like `PolyChaos.jl`, consider citing our paper

``````@ARTICLE{2020arXiv200403970M,
author = {{M{\"u}hlpfordt}, Tillmann and {Zahn}, Frederik and {Hagenmeyer}, Veit and {Faulwasser}, Timm},
title = "{PolyChaos.jl -- A Julia Package for Polynomial Chaos in Systems and Control}",
journal = {arXiv e-prints},
keywords = {Electrical Engineering and Systems Science - Systems and Control, Mathematics - Numerical Analysis, Mathematics - Optimization and Control},
year = 2020,
month = apr,
eid = {arXiv:2004.03970},
pages = {arXiv:2004.03970},
archivePrefix = {arXiv},
eprint = {2004.03970},
primaryClass = {eess.SY},
}
``````