I have just noticed that the LDLT decomposition is broken with the latest Intel compiler.
The installation I have access to reports for icpc -v:
icpc version 18.0.1 (gcc version 6.4.0 compatibility)
Comparing the solutions for a random SPD matrix obtained with FullPivLU, PartialPivLU, LLT and LDLT shows that the latter is broken. You can find the code for this test on GitHub: https://github.com/robertodr/eigen-cholesky