[Dune] [#778] MatrixHelper::detAAT is unstable

[Dune]

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A new Flyspray task has been opened.  Details are below. 

User who did this - Oliver Sander (sander) 

Attached to Project - Dune
Summary - MatrixHelper::detAAT is unstable
Task Type - Bug Report
Category - Grid
Status - New
Assigned To - 
Operating System - Unspecified / All
Severity - Low
Priority - Normal
Reported Version - SVN (pre2.1)
Due in Version - Undecided
Due Date - Undecided
Details - For certain almost singular matrices, for example 

    A[0][0] =  0.099999999999999867;
    A[0][1] = -0.010000000000002118;
    A[1][0] =  0.099999999999999867;
    A[1][1] = -0.0099999999999998979;

the method detAAT in genericgeometries/matrix.hh aborts with 

testmatrix: ../matrix.hh:243: static void Dune::GenericGeometry::MatrixHelper<Traits>::cholesky_L(const typename Traits::Matrix<n, n>::type&, typename Traits::Matrix<n, n>::type&) [with int n = 2, Traits = Dune::GenericGeometry::DuneCoordTraits<double>]: Assertion `x > FieldType( 0 )' failed.

rather than computing something close to zero.

This is not an artificial example.  I found it when integrating over remote intersections between two unrelated grids.

A test case has been added in the file genericgeometries/test/testmatrix.cc.


More information can be found at the following URL:
http://www.dune-project.org/flyspray/index.php?do=details&task_id=778

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