I want to use a least squares problem with the use of Eigen library. My options are 2,

sysAAA.jacobiSvd( Eigen::ComputeThinU | Eigen::ComputeThinV ).solve( sysBBB )
sysAAA.colPivHouseholderQr().solve( sysBBB );
I was using the first in the beginning, but it proved to be very slow (1)(2).

So I went to the second solution (other methods aren't appropriate for my case, because they require special matrices (2) )

Does colPivHouseholderQr().solve give a least squares solution?

My impression is that it doesn't (3), but I want to be sure before looking for a "workaround".

1 - viewtopic.php?f=74&t=102088
2 - http://eigen.tuxfamily.org/dox/TopicLin ... tions.html
3 - http://eigen.tuxfamily.org/dox/Tutorial ... astsquares

PS - it was asked also here , but the only answer provided didn't give any source as proof

Yes, colPivHouseholderQr().solve() does LS solving, as a proof:

Code: Select all

   |Ax-b|^2 = min
 => 2 A^T (Ax-b) = 0
    A^T A x = A^T b
If A = QR (with Q and R corresponding to the "thin" QR, so R is square), then we have:
    R^T Q^T Q R x = R^T Q^T b
    R^T R x = R^T Q^T b
Assuming R is full rank:
    R x = Q^T b
    x = R-1 Q^T b


that is what *QR::solve does.

thanx ggael