MatFlat 0.8.0

.NET 8.0 
dotnet add package MatFlat --version 0.8.0
NuGet\Install-Package MatFlat -Version 0.8.0
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="MatFlat" Version="0.8.0" />
For projects that support PackageReference, copy this XML node into the project file to reference the package. 
paket add MatFlat --version 0.8.0
#r "nuget: MatFlat, 0.8.0"
#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 MatFlat as a Cake Addin
#addin nuget:?package=MatFlat&version=0.8.0

// Install MatFlat as a Cake Tool
#tool nuget:?package=MatFlat&version=0.8.0

MatFlat

This library aims to provide a pure C# implementation of reasonably fast low-level routines for linear algebra operations.

This library was created as a matrix decomposition implementation for NumFlat, a comprehensive numerical computing library written in pure C#. If you're interested in numerical computing with C#, please check out NumFlat.

This library is based on the following great projects:

Currently the following routines are implemented:

  • LU decomposition
  • Cholesky decomposition
  • QR decomposition
  • Singular value decomposition
  • Eigenvalue decomposition
  • Generalized eigenvalue decomposition
  • Forward and backward substitution
  • Inverse matrix
  • Matrix-vector multiplication
  • Matrix-matrix multiplication
  • Dot and outer product
  • Vector norm

Features

  • Supports float, double, and Complex matrices.
  • Faster than the managed matrix decompositions in Math.NET in many cases.
  • Small code size, with no dependencies other than .NET 8.
  • No internal multi-threaded optimization, making it safe to use in any multi-threaded code.
  • BLAS and LAPACK-like interface that allows arbitrary leading dimension.

Limitations

  • Unsafe pointers are required, similar to the original BLAS and LAPACK routines.
  • Only column-major order is supported.
  • EVD and GEVD support only symmetric (Hermitian) matrices.

Installation

.NET 8 is required.

The NuGet package is available.

Install-Package MatFlat

All the classes are in the MatFlat namespace.

using MatFlat;

Performance

The following is a performance comparison with the managed implementation in Math.NET Numerics. The execution times of various double matrix decompositions for square matrices were measured. The matrix sizes range from 5x5 to 200x200.

Measurement condition

The benchmarks were run under the following conditions:

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.3296/23H2/2023Update/SunValley3)
12th Gen Intel Core i7-12700K, 1 CPU, 20 logical and 12 physical cores
.NET SDK 8.0.202
  [Host]     : .NET 8.0.3 (8.0.324.11423), X64 RyuJIT AVX2
  DefaultJob : .NET 8.0.3 (8.0.324.11423), X64 RyuJIT AVX2

LU decomposition

Method Order Mean Error StdDev Gen0 Allocated
MathNet 5 79.40 ns 0.139 ns 0.130 ns 0.0049 64 B
MatFlat 5 95.05 ns 0.226 ns 0.200 ns - -
MathNet 10 357.11 ns 2.120 ns 1.983 ns 0.0076 104 B
MatFlat 10 315.61 ns 3.603 ns 3.370 ns - -
MathNet 20 1,919.06 ns 12.070 ns 11.290 ns 0.0114 184 B
MatFlat 20 1,477.05 ns 7.740 ns 7.240 ns - -
MathNet 50 25,544.68 ns 125.243 ns 117.152 ns 0.0305 424 B
MatFlat 50 14,749.34 ns 23.885 ns 21.174 ns - -
MathNet 100 178,305.77 ns 664.818 ns 621.871 ns - 824 B
MatFlat 100 103,991.50 ns 237.204 ns 198.076 ns - -
MathNet 200 1,363,118.63 ns 3,265.866 ns 3,054.893 ns - 1625 B
MatFlat 200 797,660.58 ns 3,207.267 ns 2,843.159 ns - 1 B

Cholesky decomposition

Method Order Mean Error StdDev Gen0 Allocated
MathNet 5 57.38 ns 0.202 ns 0.189 ns 0.0263 344 B
MatFlat 5 34.32 ns 0.077 ns 0.068 ns - -
MathNet 10 196.48 ns 0.446 ns 0.417 ns 0.0508 664 B
MatFlat 10 145.42 ns 0.302 ns 0.283 ns - -
MathNet 20 1,058.98 ns 3.243 ns 3.033 ns 0.0992 1304 B
MatFlat 20 786.09 ns 1.664 ns 1.556 ns - -
MathNet 50 13,813.05 ns 54.198 ns 50.697 ns 0.2441 3224 B
MatFlat 50 7,687.34 ns 32.545 ns 30.442 ns - -
MathNet 100 106,477.52 ns 478.292 ns 447.395 ns 0.4883 6424 B
MatFlat 100 47,260.82 ns 259.007 ns 242.275 ns - -
MathNet 200 847,155.59 ns 14,113.388 ns 13,201.672 ns 0.9766 12824 B
MatFlat 200 364,254.50 ns 1,320.133 ns 1,102.371 ns - -

QR decomposition

Method Order Mean Error StdDev Gen0 Gen1 Gen2 Allocated
MathNet 5 6,427.4 ns 43.51 ns 40.70 ns 1.0300 - - 13472 B
MatFlat 5 169.0 ns 0.82 ns 0.73 ns - - - -
MathNet 10 16,323.8 ns 204.25 ns 191.06 ns 2.2583 - - 29404 B
MatFlat 10 673.1 ns 2.95 ns 2.76 ns - - - -
MathNet 20 52,568.1 ns 272.42 ns 254.82 ns 5.2490 0.0610 - 68239 B
MatFlat 20 4,525.4 ns 12.39 ns 10.98 ns - - - -
MathNet 50 288,599.5 ns 1,617.16 ns 1,512.69 ns 14.6484 0.9766 - 201068 B
MatFlat 50 47,460.2 ns 64.49 ns 53.85 ns - - - -
MathNet 100 1,254,514.8 ns 18,105.10 ns 16,935.52 ns 27.3438 3.9063 - 404697 B
MatFlat 100 346,350.8 ns 3,654.23 ns 3,418.17 ns - - - -
MathNet 200 8,275,729.8 ns 12,162.74 ns 10,781.95 ns 125.0000 78.1250 78.1250 947874 B
MatFlat 200 2,853,683.2 ns 6,593.42 ns 5,505.80 ns - - - 2 B

Singular value decomposition

Method Order Mean Error StdDev Gen0 Allocated
MathNet 5 2.237 μs 0.0051 μs 0.0048 μs 0.0305 416 B
MatFlat 5 1.438 μs 0.0054 μs 0.0050 μs - -
MathNet 10 10.165 μs 0.0382 μs 0.0358 μs 0.0763 1136 B
MatFlat 10 6.241 μs 0.0293 μs 0.0274 μs - -
MathNet 20 60.726 μs 0.4373 μs 0.4091 μs 0.2441 3776 B
MatFlat 20 33.963 μs 0.1579 μs 0.1477 μs - -
MathNet 50 661.731 μs 4.1310 μs 3.8642 μs 0.9766 21296 B
MatFlat 50 378.563 μs 2.4080 μs 2.2524 μs - -
MathNet 100 4,782.712 μs 25.1383 μs 23.5144 μs - 82499 B
MatFlat 100 2,906.366 μs 10.7507 μs 10.0563 μs - 3 B
MathNet 200 36,541.626 μs 176.5061 μs 165.1039 μs - 324925 B
MatFlat 200 21,199.226 μs 66.6932 μs 52.0697 μs - 23 B

Todo

  • ✅ LU decomposition
  • ✅ Cholesky decomposition
  • ✅ QR decomposition
  • ✅ Singular value decomposition
  • ✅ Eigenvalue decomposition
  • ✅ Generalized eigenvalue decomposition
  • ✅ Forward and backward substitution
  • ✅ Inverse matrix
  • ✅ Matrix-vector multiplication
  • ✅ Matrix-matrix multiplication
  • ✅ Dot and outer product
  • ✅ Vector norm

License

MatFlat is available under the MIT license.

Product Compatible and additional computed target framework versions.
.NET net8.0 is compatible.  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. 
Compatible target framework(s)
Included target framework(s) (in package)
Learn more about Target Frameworks and .NET Standard.

  • net8.0

    • No dependencies.

NuGet packages (1)

Showing the top 1 NuGet packages that depend on MatFlat:

Package Downloads
NumFlat

A numerical computation library for C#

GitHub repositories

This package is not used by any popular GitHub repositories.

Version Downloads Last updated
0.8.0 105 3/27/2024
0.7.0 81 3/27/2024
0.6.0 78 3/26/2024
0.5.0 91 3/26/2024
0.4.1 74 3/25/2024
0.4.0 70 3/25/2024
0.3.1 91 3/24/2024
0.3.0 70 3/24/2024
0.2.0 93 3/23/2024
0.1.0 78 3/21/2024

https://github.com/sinshu/matflat/blob/main/CHANGELOG.md