title: Eigen - directly compute log determinant of huge sparse matrix
body: <p>I would like to compute the log-determinant of a very large matrix (5e6 x 5e6). It is, however, highly sparse - there are only 6 nonzero entries on each row (7 counting the diagonal). It's also symmetrical and positive definite.</p>
  
  <p>In Eigen I've tried to use the Cholesky decomposition: <code>SimplicialLDLT&lt;SparseMatrix&lt;double&gt;&gt;</code> followed by summing the log-values of the diagonal (accessible by <code>SimplicialLDLT::vectorD()</code>) But the decomposition runs for a very long time without finishing. Any better approaches? I don't actually need any sort of decomposition, just the log-determinant itself (or a good estimate).</p>