{"id":23330380,"url":"https://github.com/p1x/toeplitz","last_synced_at":"2025-04-07T10:14:20.208Z","repository":{"id":143370513,"uuid":"316788476","full_name":"p1x/Toeplitz","owner":"p1x","description":"Implementation of the Zohar-Trench algorithm for solving a set of linear Toeplitz equations.","archived":false,"fork":false,"pushed_at":"2020-12-09T14:09:24.000Z","size":51,"stargazers_count":2,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"master","last_synced_at":"2024-04-28T06:45:49.017Z","etag":null,"topics":["algorithm","c-sharp","c-sharp-library","dotnet","dotnet-standard2","equation-solver","equations-set","linear-algebra","math","mathematics","matrix","matrix-calculations","matrix-library"],"latest_commit_sha":null,"homepage":"","language":"C#","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/p1x.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":"2020-11-28T17:40:07.000Z","updated_at":"2023-01-02T06:49:55.000Z","dependencies_parsed_at":null,"dependency_job_id":"84a385dd-1d12-4e6d-89bc-3ffe46e3a11f","html_url":"https://github.com/p1x/Toeplitz","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/p1x%2FToeplitz","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/p1x%2FToeplitz/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/p1x%2FToeplitz/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/p1x%2FToeplitz/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/p1x","download_url":"https://codeload.github.com/p1x/Toeplitz/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":247631833,"owners_count":20970069,"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":["algorithm","c-sharp","c-sharp-library","dotnet","dotnet-standard2","equation-solver","equations-set","linear-algebra","math","mathematics","matrix","matrix-calculations","matrix-library"],"created_at":"2024-12-20T22:16:49.195Z","updated_at":"2025-04-07T10:14:20.170Z","avatar_url":"https://github.com/p1x.png","language":"C#","readme":"## About\nThis is an implementation of the Zohar-Trench algorithm for solving a set of linear Toeplitz equations, based on the original article by S. Zohar \"The Solution of a Toeplitz Set of Linear Equations\" (https://doi.org/10.1145/321812.321822). There is also an option for an iterative solution that gives a valid result for increasing sub-matrix size.\n\nFor more info on the algorithm and its limitations see the referenced paper. There is also many papers about algorithm numerical stability.\n\n## Performance\nThe solution includes a small benchmark to compare with MathNet.Numerics+MKL implementation. Although MathNet does not implement Toeplitz matrices and algorithms optimized for them, it is still worth the comparison. Here are my results:\n\n``` ini\nBenchmarkDotNet=v0.12.0, OS=Windows 10.0.18363\nIntel Core i5-6600 CPU 3.30GHz (Skylake), 1 CPU, 4 logical and 4 physical cores\n.NET Core SDK=3.1.302\n [Host] : .NET Core 3.1.6 (CoreCLR 4.700.20.26901, CoreFX 4.700.20.31603), X64 RyuJIT\n DefaultJob : .NET Core 3.1.6 (CoreCLR 4.700.20.26901, CoreFX 4.700.20.31603), X64 RyuJIT\n```\n| Method | N | Mean | Error | StdDev | Median | Ratio | Gen 0 | Gen 1 | Gen 2 | Allocated |\n|----------------- |---- |---------------:|-------------:|-------------:|---------------:|------:|---------:|---------:|---------:|----------:|\n| **MainSolver** | **8** | **621.0 ns** | **3.36 ns** | **2.98 ns** | **621.7 ns** | **0.11** | **0.1707** | **-** | **-** | **536 B** |\n| MathNetNativeMkl | 8 | 5,594.6 ns | 20.61 ns | 18.27 ns | 5,589.4 ns | 1.00 | 0.3052 | - | - | 968 B |\n| | | | | | | | | | | |\n| **MainSolver** | **32** | **11,690.5 ns** | **126.34 ns** | **118.17 ns** | **11,641.2 ns** | **0.33** | **0.2899** | **-** | **-** | **920 B** |\n| MathNetNativeMkl | 32 | 35,077.0 ns | 256.05 ns | 239.51 ns | 35,094.7 ns | 1.00 | 1.5259 | - | - | 4904 B |\n| | | | | | | | | | | |\n| **MainSolver** | **128** | **72,167.5 ns** | **378.92 ns** | **316.42 ns** | **72,159.9 ns** | **0.39** | **0.7324** | **-** | **-** | **2457 B** |\n| MathNetNativeMkl | 128 | 185,198.8 ns | 1,108.50 ns | 1,036.89 ns | 184,818.0 ns | 1.00 | 20.5078 | - | - | 66728 B |\n| | | | | | | | | | | |\n| **MainSolver** | **512** | **219,324.7 ns** | **1,027.25 ns** | **910.63 ns** | **219,068.5 ns** | **0.17** | **2.6855** | **-** | **-** | **8603 B** |\n| MathNetNativeMkl | 512 | 1,274,336.5 ns | 25,380.10 ns | 47,043.64 ns | 1,249,485.4 ns | 1.00 | 248.0469 | 248.0469 | 248.0469 | 1053296 B |\n","funding_links":[],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fp1x%2Ftoeplitz","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fp1x%2Ftoeplitz","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fp1x%2Ftoeplitz/lists"}