These preconditioners are implemented by the IFPACK library, by classes Ifpack_IC, Ifpack_ICT, Ifpack_ILU, Ifpack_ILUT.
These preconditioners are used for symmetric and positive definite matrices (IC and ICT), or non-symmetric matrices (ILU and ILUT). The dropping for IC and ILU factorizations is based on a prescribed pattern, while ICT and ILUT the dropping is based on element magnitude. Typically, IC and ILU are faster but less effective than ICT and ILUT. The level-of-fill is specified by different parameters, so be sure that you are selecting the appropriate one. If you want to analyze the performances of these preconditioners, first click on Incomplete Factorization Preconditioners to visualize the list of parameters, then set to Yes one or more of the following: IC, ICT, ILU, ILUT.