P1X.Toeplitz 0.1.0

.NET Standard 2.0 This package targets .NET Standard 2.0. The package is compatible with this framework or higher. 
dotnet add package P1X.Toeplitz --version 0.1.0                

                    
                

            
NuGet\Install-Package P1X.Toeplitz -Version 0.1.0
This command is intended to be used within the Package Manager Console in Visual Studio, as it uses the NuGet module's version of Install-Package. 
<PackageReference Include="P1X.Toeplitz" Version="0.1.0" />
For projects that support PackageReference, copy this XML node into the project file to reference the package. 
paket add P1X.Toeplitz --version 0.1.0                

                    
                

            
#r "nuget: P1X.Toeplitz, 0.1.0"
#r directive can be used in F# Interactive and Polyglot Notebooks. Copy this into the interactive tool or source code of the script to reference the package. 
// Install P1X.Toeplitz as a Cake Addin
#addin nuget:?package=P1X.Toeplitz&version=0.1.0

// Install P1X.Toeplitz as a Cake Tool
#tool nuget:?package=P1X.Toeplitz&version=0.1.0

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:

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
Product Compatible and additional computed target framework versions.
.NET net5.0 was computed.  net5.0-windows was computed.  net6.0 was computed.  net6.0-android was computed.  net6.0-ios was computed.  net6.0-maccatalyst was computed.  net6.0-macos was computed.  net6.0-tvos was computed.  net6.0-windows was computed.  net7.0 was computed.  net7.0-android was computed.  net7.0-ios was computed.  net7.0-maccatalyst was computed.  net7.0-macos was computed.  net7.0-tvos was computed.  net7.0-windows was computed.  net8.0 was computed.  net8.0-android was computed.  net8.0-browser was computed.  net8.0-ios was computed.  net8.0-maccatalyst was computed.  net8.0-macos was computed.  net8.0-tvos was computed.  net8.0-windows was computed. 
.NET Core netcoreapp2.0 was computed.  netcoreapp2.1 was computed.  netcoreapp2.2 was computed.  netcoreapp3.0 was computed.  netcoreapp3.1 was computed. 
.NET Standard netstandard2.0 is compatible.  netstandard2.1 was computed. 
.NET Framework net461 was computed.  net462 was computed.  net463 was computed.  net47 was computed.  net471 was computed.  net472 was computed.  net48 was computed.  net481 was computed. 
MonoAndroid monoandroid was computed. 
MonoMac monomac was computed. 
MonoTouch monotouch was computed. 
Tizen tizen40 was computed.  tizen60 was computed. 
Xamarin.iOS xamarinios was computed. 
Xamarin.Mac xamarinmac was computed. 
Xamarin.TVOS xamarintvos was computed. 
Xamarin.WatchOS xamarinwatchos was computed. 
Compatible target framework(s)
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NuGet packages

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GitHub repositories

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Version Downloads Last updated
0.1.0 451 12/9/2020