I'm trying to solve a non square linear system with Math.net. But I get an error Matrix dimensions must agree: 3x7.
Here is some example code:
using MathNet.Numerics.LinearAlgebra;
var mBuilder = Matrix<double>.Build;
var vBuilder = Vector<double>.Build;
var A = mBuilder.DenseOfArray(new double[,]
{
{ 3, 2, 1, 5, -1, 0, 0 },
{ 2, 1, 1, 2, 0, -1, 0 },
{ 5, 1, 3, 4, 0, 0, -1 }
});
var b = vBuilder.DenseOfArray(new double[] { -3, -5, -2 });
Vector<double> x;
x = A.Solve(b);
Cleary the system has a solution (e.g. X = {0, 0, 0, 0, 3, 5, 2}
).
How can I solve such a system with Math.Net?
You can not use the Matrix.Solve function with a non-square matrix because there is no inverse and no unique solutions for a rectangular matrix. Google "inverse of rectangular matrix" for explanations galore. You can use pseudoinverse however, as shown below.
var mBuilder = Matrix<double>.Build;
var A = mBuilder.DenseOfArray(new double[,]
{
{ 3, 2, 1, 5, -1, 0, 0 },
{ 2, 1, 1, 2, 0, -1, 0 },
{ 5, 1, 3, 4, 0, 0, -1 }
});
Matrix<double> b = Matrix<double>.Build.Dense(3, 1);
b[0, 0] = -3.0;
b[1, 0] = -5.0;
b[2, 0] = -2.0;
var p = A.PseudoInverse();
var x = p * b;
// verify
var o = A * x;