[eigen] Using Cholmods LDLT factorization with eigen.

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I have a case where I need both the LDLT factorization and permutation corresponding to the factorization; i.e., I need eigen matrices corresponding to L, D, and P in
    P * A * P' = L * D * L'
In addition, I wish to ensure that factorization corresponds to the corresponding cholmod routine.

Looking at the specifications for
I see that the Eigen simplicial LDLT routine can return the necessary information. But looking at
I do not see member functions for obtaining L, D, and P. On the other hand I do see the text 'This simplicial variant is equivalent to Eigens's built-in SimplicialLDLT class.'

Are the L, D, and P matrices accessible from CholmodSimplicialLDLT ?

If not, under what conditions can I be certain that cholmod is being used for the factorization when I use the SimplicialLDLT class ?

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