https://github.com/juliaapproximation/semiclassicalorthogonalpolynomials.jl

A Julia repository for semiclassical orthogonal polynomials
https://github.com/juliaapproximation/semiclassicalorthogonalpolynomials.jl

Last synced: over 1 year ago
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A Julia repository for semiclassical orthogonal polynomials

• Host: GitHub
• URL: https://github.com/juliaapproximation/semiclassicalorthogonalpolynomials.jl
• Owner: JuliaApproximation
• License: mit
• Created: 2020-02-11T14:31:02.000Z (over 6 years ago)
• Default Branch: master
• Last Pushed: 2025-02-12T22:04:13.000Z (over 1 year ago)
• Last Synced: 2025-02-12T23:20:33.815Z (over 1 year ago)
• Language: Julia
• Size: 224 KB
• Stars: 7
• Watchers: 8
• Forks: 3
• Open Issues: 13
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# SemiclassicalOrthogonalPolynomials.jl

A Julia repository for semiclassical orthogonal polynomials

[![Build Status](https://github.com/JuliaApproximation/SemiclassicalOrthogonalPolynomials.jl/workflows/CI/badge.svg)](https://github.com/JuliaApproximation/SemiclassicalOrthogonalPolynomials.jl/actions)

[![codecov](https://codecov.io/gh/JuliaApproximation/SemiclassicalOrthogonalPolynomials.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaApproximation/SemiclassicalOrthogonalPolynomials.jl)

This package implements `SemiclassicalJacobi`, a family of orthogonal 

polynomials orthogonal with respect to the weight `x^a * (1-x)^b * (t-x)^c`. 

This builds on top of [ClassicalOrthogonalPolynomials.jl](https://github.com/JuliaApproximation/ClassicalOrthogonalPolynomials.jl) and usage is similar.

For example, the following gives a half-range Chebyshev polynomial:

```julia

julia> using SemiclassicalOrthogonalPolynomials

julia> T = SemiclassicalJacobi(2, -1/2, 0, -1/2)

SemiclassicalJacobi with weight x^-0.5 * (1-x)^0.0 * (2.0-x)^-0.5 on 0..1

julia> T[0.1,1:10] # evaluate first 10 OPs at 0.1

10-element Array{Float64,1}:

  1.0

 -0.855801766003832

  0.19083013661761547

  0.5574589013555691

 -1.085921276099753

  1.181713489691121

 -0.8056271765695796

  0.10748539771183807

  0.6338334369113602

 -1.1219700834800677

julia> U = SemiclassicalJacobi(2, 1/2, 0, 1/2, T) # last argument reuses computation from T

SemiclassicalJacobi with weight x^0.5 * (1-x)^0.0 * (2.0-x)^0.5 on 0..1

```