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

Virgil Stokes vs@it.uu...
Wed Nov 21 01:46:31 CST 2012


On 21-Nov-2012 02:30, Alex Leach wrote:
>
> On Wednesday 21 Nov 2012 01:36:08 Virgil Stokes wrote:
>
> >
>
> > I have the following matrix, A:
>
> >
>
> > array([[ 7.07106781e+02, 5.49702852e-04, 1.66675481e-19],
>
> > [ -3.53553391e+01, 7.07104659e+01, 1.66675481e-19],
>
> > [ 0.00000000e+00, -3.97555166e+00, 7.07106781e-03],
>
> > [ -7.07106781e+02, -6.48214647e-04, 1.66675481e-19],
>
> > [ 3.53553391e+01, -7.07104226e+01, 1.66675481e-19],
>
> > [ 0.00000000e+00, 3.97560687e+00, -7.07106781e-03],
>
> > [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
>
> > [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
>
> > [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00]])
>
> >
>
> >
>
> > Using np.linalg.qr(A) I get the following for R (3x3) which is
>
> > "square-root" of the covariance matrix:
>
> >
>
> > array([[ -1.00124922e+03, 4.99289918e+00, 0.00000000e+00],
>
> > [ 0.00000000e+00, -1.00033071e+02, 5.62045938e-04],
>
> > [ 0.00000000e+00, 0.00000000e+00, -9.98419272e-03]])
>
> >
>
> I thought this would be down to the Lapack library you have linked against, as 
> numpy uses Lapack's [zd]gqrf internally. I know Matlab comes distributed with 
> Intel's MKL, so I imagine Matlab would use Intel's MKL routines internally.
>
> Without knowing anything about the math, here are some test cases on Linux and 
> Mac OS X. Looks like it's dependent on platform, from these results...
>
> >>> a = np.array( ... )
>
> >>> q, r = np.linalg.qr( a )
>
> >>> r
>
> **Linux**
>
> Intel MKL:
>
> array([[ -1.00124922e+03, 4.99289919e+00, 2.40741243e-35],
>
> [ 0.00000000e+00, -1.00033071e+02, 5.62045938e-04],
>
> [ 0.00000000e+00, 0.00000000e+00, -9.98419272e-03]])
>
> ATLAS Lapack:
>
> array([[ -1.00124922e+03, 4.99289919e+00, -2.40741243e-35],
>
> [ 0.00000000e+00, -1.00033071e+02, 5.62045938e-04],
>
> [ 0.00000000e+00, 0.00000000e+00, -9.98419272e-03]])
>
> **Mac OS X**:
>
> Accelerate Framework:-
>
> array([[ 1.00124922e+03, -4.99289919e+00, 2.40741243e-35],
>
> [ 0.00000000e+00, 1.00033071e+02, -5.62045938e-04],
>
> [ 0.00000000e+00, 0.00000000e+00, 9.98419272e-03]])
>
> ATLAS Lapack:-
>
> array([[ 1.00124922e+03, -4.99289919e+00, 2.40741243e-35],
>
> [ 0.00000000e+00, 1.00033071e+02, -5.62045938e-04],
>
> [ 0.00000000e+00, 0.00000000e+00, 9.98419272e-03]])
>
> Cheers,
>
> Alex
>
>
>
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Very interesting Alex --- Guess I should get a Mac :-)

How can I force the use of the Lapack (on my Win32 system) that is being used by 
the Mac OS X?
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