{"id":20500596,"url":"https://github.com/juliaapproximation/singularintegrals.jl","last_synced_at":"2025-03-05T19:34:03.801Z","repository":{"id":153880405,"uuid":"622329744","full_name":"JuliaApproximation/SingularIntegrals.jl","owner":"JuliaApproximation","description":"A Julia package for computing singular integrals","archived":false,"fork":false,"pushed_at":"2024-05-22T20:40:10.000Z","size":87,"stargazers_count":6,"open_issues_count":4,"forks_count":4,"subscribers_count":6,"default_branch":"main","last_synced_at":"2024-05-22T20:46:01.297Z","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}},"created_at":"2023-04-01T19:37:03.000Z","updated_at":"2024-08-12T16:55:01.124Z","dependencies_parsed_at":null,"dependency_job_id":"64e73dcf-7a53-4469-8c01-134fdc77c5cd","html_url":"https://github.com/JuliaApproximation/SingularIntegrals.jl","commit_stats":null,"previous_names":[],"tags_count":14,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FSingularIntegrals.jl","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FSingularIntegrals.jl/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FSingularIntegrals.jl/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FSingularIntegrals.jl/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/JuliaApproximation","download_url":"https://codeload.github.com/JuliaApproximation/SingularIntegrals.jl/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":242092444,"owners_count":20070532,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","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":"2024-11-15T18:21:51.967Z","updated_at":"2025-03-05T19:34:03.770Z","avatar_url":"https://github.com/JuliaApproximation.png","language":"Julia","funding_links":[],"categories":[],"sub_categories":[],"readme":"# SingularIntegrals.jl\nA Julia package for computing singular integrals\n\n\n\n[![Build Status](https://github.com/JuliaApproximation/SingularIntegrals.jl/workflows/CI/badge.svg)](https://github.com/JuliaApproximation/SingularIntegrals.jl/actions)\n[![codecov](https://codecov.io/gh/JuliaApproximation/SingularIntegrals.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaApproximation/SingularIntegrals.jl)\n[![](https://img.shields.io/badge/docs-latest-blue.svg)](https://JuliaApproximation.github.io/SingularIntegrals.jl)\n\n\nThis package supports computing singular integrals involving Hilbert/Stieltjes/Cauchy,\nlog, and power law kernels.\n\nSome examples:\n\n```julia\njulia\u003e using SingularIntegrals, ClassicalOrthogonalPolynomials\n\njulia\u003e P = Legendre(); x = axes(P, 1); f = expand(P, exp); #  expand exp(x) in Legendre polynomials\n\njulia\u003e @time inv.(10 .- x') * f # Stieltjes: ∫₋₁¹ exp(x) / (10-x) dx\n  0.000034 seconds (22 allocations: 2.266 KiB)\n0.24332755428373515\n\njulia\u003e @time inv.(0.1+0im .- x') * f - inv.(0.1-0im .- x') * f ≈ -2π*im*exp(0.1) # example of Plemelj\n  0.000052 seconds (49 allocations: 6.031 KiB)\ntrue\n\njulia\u003e @time abs.(10 .- x') .^ 0.2 * f # Power law: ∫₋₁¹ (10-x)^0.2 * exp(x) dx\n  0.000077 seconds (21 allocations: 1.875 KiB)\n3.7006631248289135\n\njulia\u003e @time abs.(0.3 .- x') .^ 0.2 * f # ∫₋₁¹ abs(0.3-x)^0.2 * exp(x) dx\n  0.000040 seconds (25 allocations: 2.172 KiB)\n1.9044201526740234\n\njulia\u003e W = Weighted(ChebyshevU()); f = expand(W, x -\u003e exp(x) * sqrt(1-x^2));\n\njulia\u003e @time log.(abs.(10 .- x')) * f # Log-kernel: ∫₋₁¹ log(10-x) * exp(x) * sqrt(1-x^2) dx\n  0.000040 seconds (14 allocations: 400 bytes)\n4.043032838853287\n\njulia\u003e @time log.(abs.(0.3 .- x')) * f # ∫₋₁¹ log(abs(0.3-x)) * exp(x) * sqrt(1-x^2) dx\n  0.000035 seconds (116 allocations: 6.250 KiB)\n-2.320391559008445\n```\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjuliaapproximation%2Fsingularintegrals.jl","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fjuliaapproximation%2Fsingularintegrals.jl","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjuliaapproximation%2Fsingularintegrals.jl/lists"}