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

Skipper Seabold jsseabold@gmail....
Tue Nov 20 16:13:19 CST 2012


On Tue, Nov 20, 2012 at 5:03 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.
>

Can't you guard against this in your code?

> Why is numpy/Python different from that returned by MATLAB and
> MATHEMATICA? This makes translations rather tricky and one begins to
> wonder if there are other differences.

It can often depend on the version of the underlying LAPACK functions
used (or maybe even where/how it was compiled). In my experience, I've
seen linear algebra functions in MATLAB give different results up to
an arbitrary sign when I know for a fact they were using the same
underling LAPACK routine. I later upgraded the LAPACK that I used to
build scipy and the signs agreed. I do not know if MATLAB does any
kind of normalization after the fact, but you could file an issue or
better yet provide a PR for the sign check in scipy if it's something
you don't want to check for in your code in the future. The beauty of
scipy is that you can look at the code to see why you're getting the
results you're getting. You can find out the LAPACK version and then
look at the helper functions that calls these routines to see what's
going on. Good luck figuring that out with MATLAB, etc.

Skipper

Skipper


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