{"id":20500590,"url":"https://github.com/juliaapproximation/annuliorthogonalpolynomials.jl","last_synced_at":"2026-02-05T23:31:09.777Z","repository":{"id":182135089,"uuid":"668007517","full_name":"JuliaApproximation/AnnuliOrthogonalPolynomials.jl","owner":"JuliaApproximation","description":null,"archived":false,"fork":false,"pushed_at":"2025-03-24T16:06:20.000Z","size":79,"stargazers_count":1,"open_issues_count":3,"forks_count":0,"subscribers_count":2,"default_branch":"main","last_synced_at":"2025-12-17T06:38:50.256Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":"Julia","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/JuliaApproximation.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null}},"created_at":"2023-07-18T19:58:01.000Z","updated_at":"2025-02-15T20:43:46.000Z","dependencies_parsed_at":null,"dependency_job_id":"d907ad17-5a3d-4ddb-9c20-7c2b611f5233","html_url":"https://github.com/JuliaApproximation/AnnuliOrthogonalPolynomials.jl","commit_stats":null,"previous_names":["ioannispapapadopoulos/annuliorthogonalpolynomials.jl","juliaapproximation/annuliorthogonalpolynomials.jl"],"tags_count":6,"template":false,"template_full_name":null,"purl":"pkg:github/JuliaApproximation/AnnuliOrthogonalPolynomials.jl","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FAnnuliOrthogonalPolynomials.jl","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FAnnuliOrthogonalPolynomials.jl/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FAnnuliOrthogonalPolynomials.jl/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FAnnuliOrthogonalPolynomials.jl/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/JuliaApproximation","download_url":"https://codeload.github.com/JuliaApproximation/AnnuliOrthogonalPolynomials.jl/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FAnnuliOrthogonalPolynomials.jl/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":29138375,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-02-05T23:14:48.546Z","status":"ssl_error","status_checked_at":"2026-02-05T23:14:35.724Z","response_time":65,"last_error":"SSL_connect returned=1 errno=0 peeraddr=140.82.121.5:443 state=error: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2024-11-15T18:21:49.707Z","updated_at":"2026-02-05T23:31:09.745Z","avatar_url":"https://github.com/JuliaApproximation.png","language":"Julia","funding_links":[],"categories":[],"sub_categories":[],"readme":"## AnnuliOrthogonalPolynomials.jl\r\n\r\n[![Build Status](https://github.com/JuliaApproximation/AnnuliOrthogonalPolynomials.jl/workflows/CI/badge.svg)](https://github.com/JuliaApproximation/AnnuliOrthogonalPolynomials.jl/actions)\r\n[![codecov.io](http://codecov.io/github/JuliaApproximation/AnnuliOrthogonalPolynomials.jl/coverage.svg?branch=main)](http://codecov.io/github/JuliaApproximation/AnnuliOrthogonalPolynomials.jl?branch=main)\r\n\r\n\r\nA Julia package for orthogonal polynomials on an annulus.\r\n\r\nThis code used to be part of [AlgebraicCurveOrthogonalPolynomials.jl](https://github.com/JuliaApproximation/AlgebraicCurveOrthogonalPolynomials.jl).\r\n\r\n\r\nThis experimental package implements `ZernikeAnnulus` and `ComplexZernikeAnnulus`,\r\nfamilies of orthogonal polynomials on the annulus `{ρ² ≤ x² + y² ≤ 1}`\r\nwith respect to the weight `(r² - ρ²)ᵃ * (1-r²)ᵇ`. This builds on top of\r\n[SemiclassicalOrthogonalPolynomials.jl](https://github.com/JuliaApproximation/SemiclassicalOrthogonalPolynomials.jl) and [MultivariateOrthogonalPolynomials.jl](https://github.com/JuliaApproximation/MultivariateOrthogonalPolynomials.jl).\r\n\r\n```julia\r\njulia\u003e using AnnuliOrthogonalPolynomials, StaticArrays\r\n\r\njulia\u003e ρ, a, b = 0.5, 0.0, 0.0;\r\n\r\njulia\u003e Z = ZernikeAnnulus(ρ, a, b)\r\nZernikeAnnulus{Float64}(0.5, 0.0, 0.0)\r\n\r\njulia\u003e Z[SVector(0.5,0.2), Block.(1:3)] # Blocked by degree\r\n3-blocked 6-element BlockVector{Float64}:\r\n 1.0\r\n ───────────────────\r\n 0.20000000000000004\r\n 0.5000000000000001\r\n ───────────────────\r\n 1.547298721428197\r\n 0.20000000000000007\r\n 0.21000000000000008\r\n\r\njulia\u003e x,y = first.(axes(Z,1)), last.(axes(Z,1));\r\n\r\njulia\u003e u = Z * (Z \\ (exp.(x) .* cos.(y))) # Expand in annulus OPs\r\nZernikeAnnulus{Float64}(0.5, 0.0, 0.0) * [1.0, 9.352800883640776e-18, 0.9999999999999999, -5.2512913921638607e-17, -2.337754850841795e-18, 0.5, 2.153350906504162e-18, 1.1925107582660448e-17, -5.513529126039963e-18, 0.1666666666666666  …  ]\r\n\r\njulia\u003e u[SVector(0.5,0.2)] # Evaluate expansion\r\n1.6158566135891377\r\n```\r\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjuliaapproximation%2Fannuliorthogonalpolynomials.jl","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fjuliaapproximation%2Fannuliorthogonalpolynomials.jl","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjuliaapproximation%2Fannuliorthogonalpolynomials.jl/lists"}