From bug-octave-request at bevo dot che dot wisc dot edu Thu Oct  3 10:59:11 2002
Subject: Re: Bug in eig()
From: Remy Bruno <remy dot bruno at libertysurf dot fr>
To: bug-octave at bevo dot che dot wisc dot edu
Date: Thu, 3 Oct 2002 17:58:58 +0200

On Thursday 03 October at 09:29, Lippert, Ross A. wrote:
> 
> OK, I have run the example directly in LAPACK-3 and the same bug occurs.
> 
> This is an LAPACK bug.

Ok, so maybe I will contact them directly and forward them our conversation.

Regards,

Rémy
> 
> -r
> 
> -----Original Message-----
> From: Remy Bruno [mailto:remy dot bruno at libertysurf dot fr]
> Sent: Thursday, October 03, 2002 5:58 AM
> To: bug-octave at bevo dot che dot wisc dot edu
> Subject: Re: Bug in eig()
> 
> 
> Hi,
> 
> On Wednesday 02 October at 22:10, A S Hodel wrote:
> > On 10/2/02 6:35 PM, "Remy Bruno" <remy dot bruno at libertysurf dot fr> wrote:
> > 
> > 
> > The problem is your matrix A has a cluster of eigenvalues at or near 0:
> > octave:3> svd(a)
> > ans =
> > 
> >    5.3126e-02
> >    2.2939e-18
> >    9.1084e-35
> >    3.9912e-53
> >    3.4228e-84
> 
> But, well, this is not 4 distinct values, it is 4 zeros! The eig() function
> should take the numerical errors into account! Furthermore, with the matrix
> given, the 4 eigenvalues are *exactly* 0. The matrix *is* diagonalizable:
> The QR decomposition gives (with octave, BTW) :
> A=Q*[x1 x2 x3 x4 x5; zeros(4,5)]
> So:
> A*X=0 gives
> [x1 x2 x3 x4 x5; zeros(4,5)] * X = 0
> which is the equation of a space of dimension 4, so this matrix can be
> written
> A=P*D*inv(P).
> 
> If you are not convinced, take this matrix:
> B=ones(5,5)+1e-20*eye(5);
> eig(B)
> ans =
> 
>    -2.7308e-18
>     3.7252e-50
>     2.4586e-33
>     1.6926e-16
>     5.0000e+00
> So 5 different eigenvalues? But this time, eig() returns correct
> eigenvectors!
> 
> > 
> > Doesn't work.  You'll get exactly the same result from MATLAB.  You've
> > picked a particularly icky problem (from a numerical standpoint).
> 
> Yes, it works, I checked! In my previous mail, I gave the results given by
> matlab, which are correct. So why could matlab do something octave can't?
> 
> > 
> > >> [V,L ] = eig(A);
> > >> rank(V)
> > 
> > ans =
> > 
> >      3
> 
> My matlab gives the correct rank (1)... And octave too!
> rank(A)
> ans = 1
> 
> Regards,
> 
> Remy Bruno
> 
> 
> 
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Octave is freely available under the terms of the GNU GPL.

Octave's home on the web:  http://www.octave.org
How to fund new projects:  http://www.octave.org/funding.html
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