I am confused with the function of HouseholderQr.
1. If I have a matrix M with size m * n (let m > n). I want get the orthogonal columns Q of M just like
the Matlab command [Q,R]=qr(M,0). But if I use Q = M.householderQr().matrixQ(), I find that Q
has a size m * m not m * n as expected. So how can I obtain the right Q like Matlab.
2. As the help said, matrixQ() returns a Householder sequence but not a matrix. It seems faster if
we store a Householder sequence, and use Householder reflection instead of using matrix multiplication.
But there is lack of documentation describing how to do this, can any one give an example?

Thanks!!

I'm sorry but by definition the 'right' Q matrix is a squared unitary matrix. Here is an example showing how to compute the 'thin' Q. This example also shows how to directly use the returned householder sequence for matrix products:

Code: Select all

#include <iostream>
#include <Eigen/Dense>
using namespace Eigen;

int main()
{
  MatrixXf A(10,5), thinQ(10,5), Q(10,10);
  A.setRandom();
  HouseholderQR<MatrixXf> qr(A);
  Q = qr.householderQ();
  thinQ.setIdentity();
  thinQ = qr.householderQ() * thinQ;

  std::cout << Q << "\n\n" << thinQ << "\n\n";
}


Thanks!
But can you provide an example on how to compute the product Q*N (N is another matrix)
directly using householder reflection? (Because storing Q of size m * m is hard).

just do qr.householderQ() * N !!