How can I add a method to Eigen3 library for solving an equation system - eigen3

Question

I am new with Eigen3 and I think it is very good C++ implementation for linear algebra. I would like to add some extra methods to the standard Matrix class for simplifying the use, for instance, for solving an equations system we can make (from the Eigen web):
Matrix3f A;
Vector3f b;
A << 1,2,3, 4,5,6, 7,8,10;
b << 3, 3, 4;
cout << "Here is the matrix A:\n" << A << endl;
cout << "Here is the vector b:\n" << b << endl;
Vector3f x = A.colPivHouseholderQr().solve(b);
cout << "The solution is:\n" << x << endl;
And it solve the equations system:
Here is the matrix A:
1 2 3
4 5 6
7 8 10
Here is the vector b:
3
3
4
The solution is:
-2
1
1
It is ok. I would like to create a new method named solveSystem() to the
Matrix class. For that I have discovered that it can be done creating an
extra header with the new methods and then use the define #define EIGEN_MATRIXBASE_PLUGIN "MatrixBaseAddons.h". Then I try to code this as:
template<typename OtherDerived>
MatrixBase<Derived> solveQr(const Eigen::MatrixBase<OtherDerived>& b)
{
MatrixXd solution = this->colPivHouseholderQr().solve(b);
return solution;
}
I have a lot of compilation errors in multiple templates. I suposse it is because I am doing something wrong. Anyone knows how pass properly other matrices and return a matrix and how to program this simple method?
Thanks in advance.
Pedro

Answer 1

The problem with your plugin is that it tries to convert a MatrixXd to a MatrixBase<Matrix3f> (if you apply it to the problem at the top).
Generally, you can't create pure MatrixBase<...> classes (these are just to be used as base classes). Also, you can't implicitly convert a double matrix to a float matrix.
To solve your problem, something like this should work:
template<typename OtherDerived>
Matrix<Scalar, RowsAtCompileTime, OtherDerived::ColsAtCompileTime> solveQr(const MatrixBase<OtherDerived>& b)
{
return this->colPivHouseholderQr().solve(b);
}
If you want to mix real matrices and complex b, you need to write something more sophisticated.