{"id":20500559,"url":"https://github.com/juliaapproximation/equilibriummeasures.jl","last_synced_at":"2026-03-08T12:31:39.645Z","repository":{"id":35355916,"uuid":"39618532","full_name":"JuliaApproximation/EquilibriumMeasures.jl","owner":"JuliaApproximation","description":"Calculate equilibrium measures from potentials","archived":false,"fork":false,"pushed_at":"2025-02-13T00:55:50.000Z","size":131,"stargazers_count":2,"open_issues_count":22,"forks_count":1,"subscribers_count":8,"default_branch":"master","last_synced_at":"2025-02-20T21:41:19.690Z","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":"2015-07-24T07:42:34.000Z","updated_at":"2024-12-01T06:31:06.000Z","dependencies_parsed_at":"2025-01-16T06:50:11.293Z","dependency_job_id":"eb7b2cf2-5f12-439e-94bc-b3dbb602aed5","html_url":"https://github.com/JuliaApproximation/EquilibriumMeasures.jl","commit_stats":null,"previous_names":[],"tags_count":3,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FEquilibriumMeasures.jl","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FEquilibriumMeasures.jl/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FEquilibriumMeasures.jl/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/JuliaApproximation%2FEquilibriumMeasures.jl/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/JuliaApproximation","download_url":"https://codeload.github.com/JuliaApproximation/EquilibriumMeasures.jl/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":242092197,"owners_count":20070480,"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":"2024-11-15T18:21:30.318Z","updated_at":"2026-03-08T12:31:39.619Z","avatar_url":"https://github.com/JuliaApproximation.png","language":"Julia","funding_links":[],"categories":[],"sub_categories":[],"readme":"# EquilbriumMeasures\nCalculate equilibrium measures from potentials\n\n[![Build Status](https://github.com/JuliaApproximation/EquilibriumMeasures.jl/workflows/CI/badge.svg)](https://github.com/JuliaApproximation/EquilibriumMeasures.jl/actions)\n[![codecov](https://codecov.io/gh/JuliaApproximation/EquilibriumMeasures.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaApproximation/EquilibriumMeasures.jl)\n[![DOI](https://zenodo.org/badge/39618532.svg)](https://zenodo.org/badge/latestdoi/39618532)\n\nIn potential theory, the equilibrium measure is the limiting distribution of charges in a potential field that minimises energy, see [Saff and Totic 1997](https://www.springer.com/gp/book/9783540570783) and [Deift 1999](https://bookstore.ams.org/cln-3). These distributions also describe the distribution of\n1. Zeros of orthogonal polynomials\n2. Fekete (near optimal interpolation) points\n3. Eigenvalues of random matrices\nThis package facilitates their computation, and is based on [RHPackage](https://github.com/dlfivefifty/RHPackage).\n\n```julia\nusing EquilibriumMeasures, Plots\nplot(equilibriummeasure(x -\u003e x^2); label=\"Semicircle\", legend=:topleft)\nplot!(equilibriummeasure(x -\u003e x^4); label=\"x^4\")\nplot!(equilibriummeasure(x -\u003e x^100); label=\"x^100\")\nplot!(equilibriummeasure(x -\u003e exp(x) - x); label=\"exp(x) - x\")\n```\n\u003cimg src=https://github.com/JuliaApproximation/EquilibriumMeasures.jl/raw/master/images/ems.svg\u003e\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjuliaapproximation%2Fequilibriummeasures.jl","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fjuliaapproximation%2Fequilibriummeasures.jl","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjuliaapproximation%2Fequilibriummeasures.jl/lists"}