Created attachment 646 [details] testcase The attached testcase crashes when compiled without NDEBUG on this assertion: IncompleteCholesky.h:155: void Eigen::IncompleteCholesky<Scalar, _UpLo, _OrderingType>::_solve_impl(const Rhs&, Dest&) const [with Rhs = Eigen::Matrix<double, -1, 1>; Dest = Eigen::Matrix<double, -1, 1>; Scalar = double; int _UpLo = 1; _OrderingType = Eigen::AMDOrdering<int>]: Assertion `m_factorizationIsOk && "factorize() should be called first"' failed. With N < 10, the assertion does not trigger.
This is because the solver failed, as reported by: solver.info() and more precisely, the preconditioner failed to factorize the matrix: solver.preconditioner().info() Of course, ILLT should not fail on a SPD matrix, so let's see what's going wrong.
OK, so we probably need to restart with a larger shift until the factorization succeed, as in algorithm 3.1 of: http://ftp.mcs.anl.gov/pub/tech_reports/reports/P682.pdf Should be straightforward. Patch welcome ;)
https://bitbucket.org/eigen/eigen/commits/08afec829f35/ Summary: Bug 1150: make IncompleteCholesky more robust by iteratively increase the shift until the factorization succeed (with at most 10 attempts).
(In reply to Gael Guennebaud from comment #3) > https://bitbucket.org/eigen/eigen/commits/08afec829f35/ > Summary: Bug 1150: make IncompleteCholesky more robust by iteratively > increase the shift until the factorization succeed (with at most 10 > attempts). Thanks for fixing it. Is there still a risk of failure with the shift increment strategy ? If yes, would it occur on specific cases like big matricies, ill conditioned matricies, ... ?
Yes there is still a risk (e.g., with a large negative eigenvalue). It performs a maximum of 10 iteration, doubling the shift each time. If it still fails, you can increase the initial shift with the respective method, but with such a large shift, better use another preconditioning technique.
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