[eigen] 3x3 symmetric eigenvalues Problem |

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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