{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/an-mathcal-o-n-algorithm-for-generating","title":"An O(n) algorithm for generating uniform random vectors in n-dimensional cones","arxiv_id":"2101.00936","date":"2021-01-04","proceeding":null,"authors":["Arun I.","Murugesan Venkatapathi"],"abstract":"Unbiased random vectors i.e. distributed uniformly in n-dimensional space, are widely applied and the computational cost of generating a vector increases only linearly with n. On the other hand, generating uniformly distributed random vectors in its subspaces typically involves the inefficiency of rejecting vectors falling outside, or re-weighting a non-uniformly distributed set of samples. Both approaches become severely ineffective as n increases. We present an efficient algorithm to generate uniformly distributed random directions in n-dimensional cones, to aid searching and sampling tasks in high dimensions.","url_abs":"https://arxiv.org/abs/2101.00936v2","url_pdf":"https://arxiv.org/pdf/2101.00936v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"an-mathcal-o-n-algorithm-for-generating","repo_url":"https://gitlab.com/arunisaac/nsmc","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}