Fix computation of eigenvectors of singular matrices

The eigenvector algorithm for symmetric FieldMatrices was buggy, it does not handle singular matrices well. Add a test and fix the bug.

changed the description

The 3d code still produces a wrong result when it is passed a singular matrix. @lukas.renelt , you wrote the code: Can you please have a look?

I am not actively working on DUNE anymore, therefore it might take some time until I can look at this. I suppose the issues arise when calculating eigenvectors? In that case we should be able to identify zero eigenvalues and add a special case for the eigenvectors

Yes, it's the eigenvector part that fails. The updated test uses the matrix

1 0 0
0 0 0
0 0 0

The eigenvalues are correctly determined to be 0 0 1, but the computed eigenvectors are

1 0 0
0 1 0
0 0 1

(which is correct expect for the ordering -- no idea whether that's a coincidence.)

added 3 commits

• 6afc1614 - Fix eigenvector computation for singular 2x2 matrices
• 6a7ad532 - Fix eigenvector computation for diagonal 3x3 matrices
• ac551b65 - Test eigenvector computation for singular matrices

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resolved all threads

added 1 commit

• 35daeab5 - Test eigenvector computation for singular matrices

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enabled an automatic merge when the pipeline for 35daeab5 succeeds

merged

mentioned in commit 4adb48c3