[eigen] Complex symmetric Cholesky factorization

[Trevor Irons <tirons@xxxxxxxxxxxx>]

I apologize if this is a repeat email, I've had trouble actually pushing these to the listserver. 

Greetings, certain symmetric complex (non-Hermitian) matrices admit an LL^T/LDL^T factorization[1] (rather than an LL^H LDL^H). I am working with sparse matrices and the code changes to support this are minimal and are all encompassed in Simplicial_Cholesky_impl.h, in the factorize method, as well as the updated solve calling transpose rather than selfadjointView. I have two questions:

1) Is there any desire to add this functionality to Eigen, or should I just keep these changes local? I would prefer to add this upstream is possible. The actual code changes are minimal, three lines or so. 
2) If so what would be an acceptable way to do this, that would not cause surprise to users? It would seem that a separate template parameter or even function call would make this explicit, such as instead of .factorize() calling .factorizeComplexSymmetric() or something along those lines. 

Thanks,


[1] Bereux, N., 2004, A cholesky algorithm for some complex symmetric systems: CMAP 515, Ecole Polytechnique.
(Available at http://www.cmap.polytechnique.fr/~natacha/CMAP TR 515.pdf).

/*************************************************
* Trevor P. Irons, PhD
* Mobile: +1 720.635.8218
* EM Modelling API: http://lemmasoftware.org
*************************************************/