I am happy to announce PolyChaos.jl , a collection of functions for orthogonal polynomials , quadrature rules , and polynomial chaos expansions . What’s the idea? Let’s say you have some non-negative function w: \Omega \longrightarrow \mathbb{R} and you would like to find the polynomals that are ortho…

Nice! This’ll be a good starting place for SPDE expansions!

Yes! A similar to-do is this : auto-generate Galerkin projections of ODEs. In the documentation of PolyChaos I did it by hand for a scalar linear ODE .

Awesome stuff and great tutorials too. I’ve never used these types of approaches but I’ve looked into them in the past. Your documentation gives one of the most approachable introductions to the topic that I’ve seen.

Good news: PolyChaos.jl v0.1.1 is out. The improvements as summarized in NEWS.md : improved performance of recurrence coefficients, quadrature rules, evaluation of orthogonal polynomials added considerable number of tests for recurrence coefficients and quadrature rules added code coverage added GN…

Is there any particular reason you chose GPL? In the Julia community it is more usual to use MIT.

The GaussQuadrature.jl package can generate all of the classical Gauss rules in multiple precision (as BigFloat arrays), and also rules for a log weight function.

It’s mostly because my bosses said so (great reason, I know…). I am aware of the discussions about the licenses and I am doing by best to persuade them. :slight_smile:

This is great, thanks! I have to admit that our focus was not so much on arbitrary precision of quadrature rules, but having a workflow from weight → recursion coefficients → quadrature rule → polynomial chaos. It just so happened that quadrature rules became an important part. PolyChaos also has su…

My GaussQuadrature.jl package is mostly a re-write of a Fortran 95 code descended from the original implementation gaussq.f of the Golub-Welsch algorithm.

Announcing `PolyChaos.jl`

Package Announcements

swissr March 4, 2019, 9:24am 10

(offtopic) Another discussion about licenses: Bitcoin.jl released as GPL, later switched to MIT.

Topic		Replies	Views
Polychaos.jl for uncertainty propagation - avoiding manual operations with tensors New to Julia question , package , uncertainty-quantifi	8	725	March 21, 2024
Julia analog to R's poly function, orthogonal polynomials by QR decomposition New to Julia question , linearalgebra , r , polynomials , qr	24	1109	April 22, 2026
What is the best way to get orthogonal polynomials for a regression like R's poly function General Usage	1	1553	July 20, 2021
Obtaining readable polynomial chaos surrogate model using Surrogates.jl Modelling & Simulations	1	349	May 26, 2023
Degree modification of multivariate polynomial chaos surrogate model Modelling & Simulations question	2	311	July 13, 2022

Announcing `PolyChaos.jl`

Related topics