Math.NET Numerics


Math.NET Numerics

Math.NET Numerics aims to provide methods and algorithms for numerical computations in science, engineering and every day use. Covered topics include special functions, linear algebra, probability models, random numbers, interpolation, integration, regression, optimization problems and more.

Math.NET Numerics is part of the Math.NET initiative and is the result of merging dnAnalytics with Math.NET Iridium, replacing both. It targets Microsoft .Net 4, .Net 3.5 and Mono (Windows, Linux and Mac), Silverlight 5, WindowsPhone 8, Windows 8/Store (PCL 47, 136) and Android/iOS (Xamarin). In addition to a purely managed implementation it also supports native hardware optimization. Available for free under the MIT/X11 License.

NuGet Packages

The recommended way to get Math.NET Numerics is to use NuGet. The following packages are provided and maintained in the public NuGet Gallery. Alternatively you can also download the binaries in Zip packages, available on CodePlex.

Core Package:

Alternative Provider Packages (optional):

Data/IO Packages for reading and writing data (optional):

Platform Support and Dependencies

  • .Net 4.0, .Net 3.5 and Mono: Windows, Linux and Mac.
  • PCL Portable Profiles 7, 47, 78, 259 and 328: Windows 8, Silverlight 5, Windows Phone/SL 8, Windows Phone 8.1.
  • Xamarin: Android, iOS

The F# extensions support a slightly reduced platform set:

  • .Net 4.0, .Net 3.5 and Mono: Windows, Linux and Mac.
  • PCL Portable Profile 47: Windows 8, Silverlight 5
  • Xamarin: Android, iOS

Package Dependencies:

Framework Dependencies (part of the .NET Framework):

  • .Net 4.0 and higher, Mono, PCL profiles 7 and 47: System.Numerics
  • .Net 3.5, PCL profiles 78, 259 and 328: None

Using Math.NET Numerics with C#

Being written in it, Math.NET Numerics works very well with C# and related .Net languages. When using Visual Studio or another IDE with built-in NuGet support, you can get started quickly by adding a reference to the MathNet.Numerics NuGet package. Alternatively you can grab that package with the command line tool with nuget.exe install MathNet.Numerics -Pre or simply download the Zip package.

let's say we have a matrix \(\mathrm{A}\) and want to find an orthonormal basis of the kernel or null-space of that matrix, such that \(\mathrm{A}x = 0\) for all \(x\) in that subspace.

using MathNet.Numerics.LinearAlgebra;
using MathNet.Numerics.LinearAlgebra.Double;

Matrix<double> A = DenseMatrix.OfArray(new double[,] {
        {1,1,1,1},
        {1,2,3,4},
        {4,3,2,1}});
Vector<double>[] nullspace = A.Kernel();

// verify: the following should be approximately (0,0,0)
(A * (2*nullspace[0] - 3*nullspace[1]))

F# and F# Interactive

Even though the core of Math.NET Numerics is written in C#, it aims to support F# just as well. In order to achieve this we recommend to reference the MathNet.Numerics.FSharp package as well (in addition to MathNet.Numerics) which adds a few modules to make it more idiomatic and includes arbitrary precision types (BigInteger, BigRational).

It also works well in the interactive F# environment (REPL) which can be launched with fsharpi on all platforms (including Linux). As a start let's enter the following lines into F# interactive. Append ;; to the end of a line to run all code up to there immediately and print the result to the output. Use the tab key for auto-completion or #help;; for help. For convenience our F# packages include a small script that sets everything up properly:

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#load "../packages/MathNet.Numerics.FSharp.3.0.0/MathNet.Numerics.fsx"

open MathNet.Numerics
SpecialFunctions.Gamma(0.5)

open MathNet.Numerics.LinearAlgebra
let m : Matrix<float> = DenseMatrix.randomStandard 50 50
(m * m.Transpose()).Determinant()

Visual Basic

Let's use Visual Basic to find the polynomial roots \(x\) such that \(2x^2 - 2x - 2 = 0\) numerically. We already know there are two roots, one between -2 and 0, the other between 0 and 2:

Imports MathNet.Numerics.RootFinding

Dim f As Func(Of Double, Double) = Function(x) 2*x^2 - 2*x - 2

Bisection.FindRoot(f, 0, 2) ' returns 1.61803398874989
Bisection.FindRoot(f, -2, 0) ' returns -0.618033988749895

' Alternative to directly compute the roots for this special case:
FindRoots.Quadratic(-2, -2, 2)

Linux with Mono

You need a recent version of Mono in order to use Math.NET Numerics on anything other than Windows. Luckily there has been great progress lately to make both Mono and F# available as proper Debian packages. In Debian testing and Ubuntu 14.04 (trusty/universe) you can install both of them with APT:

sudo apt-get update
sudo apt-get install mono-complete
sudo apt-get install fsharp

If you don't have NuGet yet:

sudo mozroots --import --sync
curl -L http://nuget.org/nuget.exe -o nuget.exe

Then you can use NuGet to fetch the latest binaries in your working directory. The -Pre argument causes it to include pre-releases, omit it if you want stable releases only.

mono nuget.exe install MathNet.Numerics -Pre -OutputDirectory packages
# or if you intend to use F#:
mono nuget.exe install MathNet.Numerics.FSharp -Pre -OutputDirectory packages

In practice you'd probably use the Monodevelop IDE instead which can take care of fetching and updating NuGet packages and maintain assembly references. But for completeness let's use the compiler directly this time. Let's create a C# file Start.cs:

using System;
using MathNet.Numerics;
using MathNet.Numerics.LinearAlgebra;

class Program
{
    static void Main(string[] args)
    {
        // Evaluate a special function
        Console.WriteLine(SpecialFunctions.Erf(0.5));

        // Solve a random linear equation system with 500 unknowns
        var m = Matrix<double>.Build.Random(500, 500);
        var v = Vector<double>.Build.Random(500);
        var y = m.Solve(v);
        Console.WriteLine(y);
    }
}

Compile and run:

# single line:
mcs -optimize -lib:packages/MathNet.Numerics.3.0.0-alpha8/lib/net40/
              -r:MathNet.Numerics.dll Start.cs -out:Start
# launch:
mono Start

Which will print something like the following to the output:

0.520499877813047
DenseVector 500-Double
   -0.181414     -1.25024    -0.607136      1.12975     -3.31201     0.344146
    0.934095     -2.96364      1.84499      1.20752     0.753055      1.56942
    0.472414      6.10418    -0.359401     0.613927    -0.140105       2.6079
    0.163564     -3.04402    -0.350791      2.37228     -1.65218     -0.84056
     1.51311     -2.17326    -0.220243   -0.0368934    -0.970052     0.580543
    0.755483     -1.01755    -0.904162     -1.21824     -2.24888      1.42923
   -0.971345     -3.16723    -0.822723      1.85148     -1.12235    -0.547885
    -2.01044      4.06481    -0.128382      0.51167     -1.70276          ...

See Intel MKL for details how to use native providers on Linux.

val m : obj

Full name: index.m
Multiple items
val float : value:'T -> float (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.float

--------------------
type float = System.Double

Full name: Microsoft.FSharp.Core.float

--------------------
type float<'Measure> = float

Full name: Microsoft.FSharp.Core.float<_>