[SciPy-User] qr decompostion gives negative q, r ?

Charles R Harris charlesr.harris@gmail....
Tue Nov 20 16:43:05 CST 2012


On Tue, Nov 20, 2012 at 3:03 PM, Virgil Stokes <vs@it.uu.se> wrote:

> On 2012-11-20 22:33, Daπid 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> 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? 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?

<snip>

Chuck
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