Re: Fwd: [eigen] 3x3 symmetric eigenvalues Problem

[Benjamin Schindler <bschindler@xxxxxxxxxxx>]

Hi

Actually, I didn't think before replying, sorry. The matrix I found the error with is not positive semi-definite, correct. However, the example I posted, the matrix IS positive definitie actually (diag(2000, 1, 1)).
So, I have the impression that the code for solving the 3x3 equation system is plain buggy...

Cheers
Benjamin


If you take my example which clearly does not work
On 31.10.2011 22:10, Suat Gedikli wrote:

Hi,

thank you for the report.
This method (even if the name is misleading) is for symmetric positive semi-definite matrices _only_ => non-negative eigenvalues.
If in your case the largest eingenvalue is zero, then this would mean that for a positive-semidefinite matrix the smallest one is also zero => the first if would apply in line 195:
if((evals(2)-evals(0))<=Eigen::NumTraits<Scalar>::epsilon())
        {
            // all three equal
            evecs.setIdentity();
        }

so, the matrix you're using can not produce correct results, since its negative definite. If it should be a covariance matrix (as used for the normal estimation) check the code where you're calculating the matrix. If not, just use the SelfAdjoint Solver from Eigen which should give you correct results, but is also much slower.

Cheers,
Suat


On 10/31/2011 11:14 AM, Radu B. Rusu wrote:

Could be interesting for you :)

Cheers,

Radu.

Begin forwarded message:

From: Benjamin Schindler <bschindler@xxxxxxxxxxx>
Date: October 31, 2011 9:52:44 PDT
To: "eigen@xxxxxxxxxxxxxxxxxxx" <eigen@xxxxxxxxxxxxxxxxxxx>
Cc: <gael.guennebaud@xxxxxxxxx>
Subject: [eigen] 3x3 symmetric eigenvalues Problem
Reply-To: eigen@xxxxxxxxxxxxxxxxxxx

Hi

I just stumbled over a problem in the analytic 3x3
eigenvalue/eigenvector for symmetric matrices.
I have a matrix, where all row vectors are parallel to each other and
there is a zero eigenvalue as the largest eigenvalue. What happens is that:

Vector cross01 = tmp.row (0).cross (tmp.row (1));
Vector cross02 = tmp.row (0).cross (tmp.row (2));
Scalar n01 = cross01.squaredNorm();
Scalar n02 = cross02.squaredNorm();

here, both n01 and n02 become zero and as a result, the entire
eigenvector matrix becomes nan's.

Reproducing it is easy. Its a different case, but shows the same behavior:

   Matrix3f m = Matrix3f::Zero();
   m.diagonal() = Vector3f(2000, 1, 0);
   Matrix3f evecs;
   Vector3f eivs;
   eigenSymm33(m, evecs, eivs);
   std::cout << evecs << std::endl << eivs.transpose() << std::endl;

Output is:

-nan -nan -nan
-nan -nan -nan
-nan -nan -nan
0.0110269 0.98902    2000

Now, one might think that 2000,1,0 is exploiting numerics. But in fact
its not. Test 2, 1, 1 as the diagonal. The routine will give out the
correct result, but if you look closely on what happens, both n01 and
n02 will be extremely small, like 1e-15, bot not zero. But analytically,
zero would be the correct value! So nan's are simply prevented because
of numerical errors.

Cheers
Benjamin