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

Virgil Stokes vs@it.uu...
Tue Nov 20 17:10:19 CST 2012


On 2012-11-20 23:57, Charles R Harris wrote:
>
>
> On Tue, Nov 20, 2012 at 3:49 PM, Virgil Stokes <vs@it.uu.se 
> <mailto:vs@it.uu.se>> wrote:
>
>     On 2012-11-20 23:13, Skipper Seabold wrote:
>     > On Tue, Nov 20, 2012 at 5:03 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.
>     >>
>     > 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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>     Ok Skipper,
>     Unfortunately, things are worse than I had hoped, numpy sometimes
>     returns the negative of the q,r and other times the same as MATLAB!
>     Thus, as someone has already mentioned in this discussion, the "sign"
>     seems to depend on the matrix being decomposed. This could be a
>     nightmare to track down.
>
>     I hope that I can return to some older versions of numpy/scipy to work
>     around this problem until this problem is fixed. Any suggestions
>     on how
>     to recover earlier versions would be appreciated.
>
>
> But why is it a problem? Why is Matlab "right"? What is the property 
> that you
> need to have in the decomposition?
I have already posted an answer to your first question, Chuck.

MATLAB is correct because the results of my application (Kalman filter 
using QR factorization of the covariance matrix) are correct -- I have 
verified this. The QR factorization is used to propagate the R matrix 
and clearly if the "sign" of R changes in an unpredictable manner (at 
least I have been unable to predict the "sign" changes that occur in 
numpy), then the answer is unlikely to be correct.

I believe that I have answered your questions. If not, then you might 
look at a paper/tutorial/book that discusses the "square-root Kalman 
filter". Then, if you have any additional questions on my application, I 
will try my best to answer them for you.
>
> Chuck
>
>
>
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