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Use .NETLink to call the MathNet library

Posted 10 years ago

Wolfram Language(WL) provides several useful interfaces to link itself to libraries written in other language. NETLink and JLink are such very powerful tools that bridge WL to the strong objective-oriented languages. I am going to show briefly an example about how to call a NuGet library for C sharp from WL. is a project on NuGet that promotes the numerical computing power of C sharp. It does lots of things like what BLAS and LAPACK does for linear algebra and numeric solvers. Of course Mathematica and MATLAB(R) are much more mature products than this library. I use this library simply to show how you can call an external library.

I am writing this example with Mathematica 10 + Windows 7 + Visual Studio 2012.

  1. Follow this link to install the MathNet assembly into any open project or clone the git drive
  2. You can locate the assembly on your machine by right-clicking the entry in Solution Explorer (VS 2012): reference->MathNet.Numeric->Properties

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Now you can open Mathematica and load the .NETLink package.


You can launch the runtime link connection with


Assume things are going well, here is what you see:

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If you have targeted the location of MathNet.Numerics.dll in your project, you can load the assembly with LoadNETAssembly


Of course your absolute path may be different, here it is just my location to store the dll file. As in the VS2012, you have a xml tree about the build-in classes and objects in this MathNet package:

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The same view can be generated within Mathematica by NETTypeInfo function:

enter image description here provides the following example code ( Using's are omitted ):

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

This is where Mathematica has to call a different method. The Vector generic type is valid and can be loaded into Mathematica without problem:

In:= netType=LoadNETType["MathNet.Numerics.LinearAlgebra.Vector<int>"]
Out:= NETType[MathNet.Numerics.LinearAlgebra.Vector`1[System.Int32],16]

However NETNew cannot create a vector object:

enter image description here

because there is no constructor with this type. The workaround is from taking a look at class list of the NETTypeInfo of the MathNet assembly:

enter image description here

NETInfo[assem, "Classes", "*Dense*"] is a call of such funciton with pattern match. I use this function when I notice that the C Sharp code in the online example calls the Dense.Build method to create a dynamic (a fancy way of using new) vector or matrix object. The dense method stores every item of the array. Contrary, the sparse method only store the non-zero entries.

The ....DenseVector type contains public constructors:

enter image description here

(Notice that NETTypeInfo can take the string name of the class/type/assembly as well)

To create a vector in the runtime, you just put a regular Mathematica vector of real numbers into the place of arguments:

In:= a = NETNew[ "MathNet.Numerics.LinearAlgebra.Double.DenseVector", {1, 2, 3, 4}] 
Out:= <<NETObject[MathNet.Numerics.LinearAlgebra.Double.DenseVector]>>

In:= b = NETNew[ "MathNet.Numerics.LinearAlgebra.Double.DenseVector", 10] 
Out:= <<NETObject[MathNet.Numerics.LinearAlgebra.Double.DenseVector]>>
(* b is {0,0,...,0} *)

In:= c = NETNew["MathNet.Numerics.LinearAlgebra.Double.DenseMatrix", 2, 2, {1,2,3,4}]
Out:= <<NETObject[MathNet.Numerics.LinearAlgebra.Double.DenseMatrix]>>
(* c is a col-major matrix: {{1,3},{2,4}}*)

To get the result back to Mathematica, use the method associated with these types:

 In:= a@ToArray[]
 Out= {1.,2.,3.,4.}

 In:= c@ToArray[]
 Out= {{1.,3.},{2.,4.}}

I can do this because the return type of the ToArray is double[] or double[,], which are basic System type in C sharp and Mathematica can convert these type to Real automatically. One more thing to say here is that Mathematica kernel is smart enough to avoid namespace/context clashing:

In:= res=(c@Transpose[])@Inverse[] (*MathNet's Transpose and Inverse*)
Out= « NETObject[MathNet.Numerics.LinearAlgebra.Double.DenseMatrix]»

Check the result:

In:= res@ToArray[]
Out= {{-2.,1.},{1.5,-0.5}}

which is the same as the familiar Mathematica implementation:

In:= Inverse[Transpose[c@ToArray[]]] (*the Mathematica Inverse and Transpose*)
Out= {{-2.,1.},{1.5,-0.5}}
POSTED BY: Shenghui Yang
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