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https://github.com/p1x/toeplitz
Implementation of the Zohar-Trench algorithm for solving a set of linear Toeplitz equations.
https://github.com/p1x/toeplitz
algorithm c-sharp c-sharp-library dotnet dotnet-standard2 equation-solver equations-set linear-algebra math mathematics matrix matrix-calculations matrix-library
Last synced: 2 days ago
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Implementation of the Zohar-Trench algorithm for solving a set of linear Toeplitz equations.
- Host: GitHub
- URL: https://github.com/p1x/toeplitz
- Owner: p1x
- License: mit
- Created: 2020-11-28T17:40:07.000Z (about 4 years ago)
- Default Branch: master
- Last Pushed: 2020-12-09T14:09:24.000Z (about 4 years ago)
- Last Synced: 2024-04-28T06:45:49.017Z (10 months ago)
- Topics: algorithm, c-sharp, c-sharp-library, dotnet, dotnet-standard2, equation-solver, equations-set, linear-algebra, math, mathematics, matrix, matrix-calculations, matrix-library
- Language: C#
- Homepage:
- Size: 49.8 KB
- Stars: 2
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
## About
This 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.
For more info on the algorithm and its limitations see the referenced paper. There is also many papers about algorithm numerical stability.
## Performance
The 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:
``` ini
BenchmarkDotNet=v0.12.0, OS=Windows 10.0.18363
Intel Core i5-6600 CPU 3.30GHz (Skylake), 1 CPU, 4 logical and 4 physical cores
.NET Core SDK=3.1.302
[Host] : .NET Core 3.1.6 (CoreCLR 4.700.20.26901, CoreFX 4.700.20.31603), X64 RyuJIT
DefaultJob : .NET Core 3.1.6 (CoreCLR 4.700.20.26901, CoreFX 4.700.20.31603), X64 RyuJIT
```
| Method | N | Mean | Error | StdDev | Median | Ratio | Gen 0 | Gen 1 | Gen 2 | Allocated |
|----------------- |---- |---------------:|-------------:|-------------:|---------------:|------:|---------:|---------:|---------:|----------:|
| **MainSolver** | **8** | **621.0 ns** | **3.36 ns** | **2.98 ns** | **621.7 ns** | **0.11** | **0.1707** | **-** | **-** | **536 B** |
| MathNetNativeMkl | 8 | 5,594.6 ns | 20.61 ns | 18.27 ns | 5,589.4 ns | 1.00 | 0.3052 | - | - | 968 B |
| | | | | | | | | | | |
| **MainSolver** | **32** | **11,690.5 ns** | **126.34 ns** | **118.17 ns** | **11,641.2 ns** | **0.33** | **0.2899** | **-** | **-** | **920 B** |
| MathNetNativeMkl | 32 | 35,077.0 ns | 256.05 ns | 239.51 ns | 35,094.7 ns | 1.00 | 1.5259 | - | - | 4904 B |
| | | | | | | | | | | |
| **MainSolver** | **128** | **72,167.5 ns** | **378.92 ns** | **316.42 ns** | **72,159.9 ns** | **0.39** | **0.7324** | **-** | **-** | **2457 B** |
| MathNetNativeMkl | 128 | 185,198.8 ns | 1,108.50 ns | 1,036.89 ns | 184,818.0 ns | 1.00 | 20.5078 | - | - | 66728 B |
| | | | | | | | | | | |
| **MainSolver** | **512** | **219,324.7 ns** | **1,027.25 ns** | **910.63 ns** | **219,068.5 ns** | **0.17** | **2.6855** | **-** | **-** | **8603 B** |
| 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 |