| public static Cholesky ( Matrix m ) : Matrix | ||
| m | Matrix | Input Matrix. |
| return | Matrix | |
/// <summary>
/// Solves Ax = b for x If A is not square or the system is overdetermined, this operation solves
/// the linear least squares A.T * A x = A.T * b.
/// </summary>
/// <exception cref="InvalidOperationException">Thrown when the requested operation is invalid.</exception>
/// <param name="A">Matrix A.</param>
/// <param name="b">Vector b.</param>
/// <returns>x.</returns>
public static Vector operator /(Matrix A, Vector b)
{
if (A.Rows != b.Length)
{
throw new InvalidOperationException("Matrix row count does not match vector length!");
}
// LLS
if (A.Rows != A.Cols)
{
Matrix C = A.T * A;
Matrix L = C.Cholesky();
Vector d = (A.T * b).ToVector();
Vector z = Forward(L, d);
Vector x = Backward(L.T, z);
return(x);
}
// regular solve
else
{
// need to be smarter here....
return(((A ^ -1) * b).ToVector());
}
}
/// <summary>A Matrix extension method that choleskies the given m.</summary>
/// <param name="m">Matrix.</param>
/// <returns>A Matrix.</returns>
public static Matrix Cholesky(this Matrix m)
{
return(Matrix.Cholesky(m));
}
