[Dune] [#729] Singularity detection in FieldMatrix' LU decomposition buggy (Attachment added)

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FS#729 - Singularity detection in FieldMatrix' LU decomposition buggy
User who did this - Christian Engwer (christi)

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Andreas, you can just change the threshold to 0 in your application.

0) just call Dune::FMatrixPrecision<>::set_singular_limit(0.0);

1) Rescaling is the way to go if the matrix is like in your case, although you should better scale the last line by 1e-9.

2) Full pivoting would be the proper fix, but your suggested fix isn't a fix at all.

If you just force dune to invert your matrix, you A*A^-1 is a lot worse compared to the scaled version (see code attached):

============orig=============
1 0 0 6.53252e-21
9.04729e-24 1 4.69256e-19 -1.55248e-27
0 0 1 0
-3.41061e-13 0 0 1

============scaled=============
1 0 0 0
2.67283e-23 1 1.07997e-19 -1.70084e-18
0 0 1 0
1.12579e-21 7.75205e-18 7.72219e-18 1

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