Math.Net system of linear equations with a 0 value in solution

问题

I am trying to solve a Matrix in Math.Net when one of the actual solutions to the matrix is 0, but I am getting -NaN- as results.

Here is an example matrix which has already been reduced for simplicity.

1 0  1 | 10000 
0 1 -1 | 1000
0 0  0 | 0

Code example:

public void DoExample()
{
    Matrix<double> A = Matrix<double>.Build.DenseOfArray(new double[,] {
        { 1, 0, 1 }, 
        { 0, 1, -1 }, 
        { 0, 0, 0 }, 
    });

    Vector<double> B = Vector<double>.Build.Dense(new double[] { 10000, 1000, 0 });

    var result = A.Solve(B);
}

The solution I am hoping to get to is [ 10000, 1000, 0 ].

As you can see, the result I want is already the augment vector. This is because I simplified the matrix to reduced row echelon form (RREF) by hand using Gauss-Jordan for this example. If I could somehow use a Gauss-Jordan operations within Math.Net to do this, I could check for the scenario where an all 0 row exists in the RREF matrix. Can this be done?

Otherwise, is there any way I can recognize when 0 is the only possible solution for one of the variables using the existing Math.Net linear algebra solver operations?

Thanks!

回答1:

The iterative solver can actually handle this, for example

using MathNet.Numerics.LinearAlgebra.Double.Solvers;
A.SolveIterative(B, new MlkBiCgStab());

returns

[10000, 1000, 0]

Interestingly, with the MKL Native Provider this also works with the normal Solve routine, but not with the managed provider (as you have found out) nor with e.g. the OpenBLAS native provider.

回答2:

This is degenerate matrix with rank 2, and you cannot expect to get true solution (there are infinity number of solutions)

来源：https://stackoverflow.com/questions/43908740/math-net-system-of-linear-equations-with-a-0-value-in-solution

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