[SciPy-User] qr decompostion gives negative q, r ?
Virgil Stokes
vs@it.uu...
Tue Nov 20 16:59:00 CST 2012
On 2012-11-20 23:43, Charles R Harris wrote:
>
>
> On Tue, Nov 20, 2012 at 3:03 PM, Virgil Stokes <vs@it.uu.se
> <mailto:vs@it.uu.se>> wrote:
>
> On 2012-11-20 22:33, Da?id wrote:
> > The QR descomposition is finding two matrices with certain
> properties such that:
> >
> > A = Q·R
> >
> > But, if both Q and R are multiplied by -1, (-Q)·(-R) = Q·R = A,
> still
> > the same matrix. If Q is orthogonal, -Q is also. The sign is,
> > therefore, arbitrary.
> >
> > On Tue, Nov 20, 2012 at 12:01 AM, Virgil Stokes <vs@it.uu.se
> <mailto:vs@it.uu.se>> wrote:
> >> I am using the latest versions of numpy (from
> >> numpy-1.7.0b2-win32-superpack-python2.7.exe) and scipy (from
> >> scipy-0.11.0-win32-superpack-python2.7.exe ) on a windows 7
> (32-bit)
> >> platform.
> >>
> >> I have used
> >>
> >> import numpy as np
> >> q,r = np.linalg.qr(A)
> >>
> >> and compared the results to what I get from MATLAB (R2010B)
> >>
> >> [q,r] = qr(A)
> >>
> >> The q,r returned from numpy are both the negative of the q,r
> returned
> >> from MATLAB for the same matrix A. I believe that theq,r
> returned from
> >> MATLAB are correct. Why am I getting their negative from numpy?
> >>
> >> Note, I have tried this on several different matrices ---
> numpy always
> >> gives the negative of MATLAB's.
> >>
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> Thanks David,
> I am well aware of this; but, I am using the QR decomposition for a
> convariance (PD matrix) and the negative R is not very useful in this
> case and the numpy result, IMHO should not be the default.
>
>
> What is your application?
My application is the propagation of the factorized R matrix in the
Kalman filter, where the QR factorization is for the covariance matrix
in the KF recursions.
> I don't see that it should matter for most things, you
> are just using a slightly different set of basis vectors in the q. Is
> orientation something you
> are concerned about?
And it does make a lot of difference!
I now have found that sometimes the "sign" of the factorization switches
(wrt to the MATLAB version). The MATLAB QR factorization (however it may
differ from that of numpy) is consistent in the sense there is no sign
switching and the results obtained from the KF are correct (this I have
verified). On the other hand, it is very unlikely that one can obtain
the correct results with the current implementation of the QR
factorization in Python.
>
> <snip>
>
> Chuck
>
>
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