LDLT decomposition works for DENSE semi-definite matrices but not for sparse ones (note the documentation is clear on that point).
Please could you update the implementation for the SPARSE semi-definite matrices?
That will not be as easy as it may sound. SimplicialLDLT determined its permutation solely on the sparsity pattern with the goal of reducing fill-in, i.e., before doing any numerical operations, whereas dense LDLt makes pivoting on-the-fly to determine the permutation.
You can try using (the slower but rank-revealing) SparseQR if you have non-definite matrices. If your matrix origins from a normal-equation (A.transpose()*A), you can even work on the original A matrix for extra numerical accuracy.
Of course, that feature can be added to Sparse Cholesky decompositions, but don't rely on that happening very soon.
Ah ok, what a pity! Thank you anyway.