[eigen] Improve CUDA compatibility

[Andrea Bocci <andrea.bocci@xxxxxxx>]

Dear Eigen developers,

we are in the process of porting some of the algorithms we are using in the CMS experiment [1] reconstruction software [2] to CUDA.

We use Eigen for operations on small matrices (4x4, 5x5, up to 19x19), and we are interested in using it also inside the CUDA kernels.

In the past weeks we have come up with the minimal set of changes to get 4x4 matrix inversion and self-adjoint solver working on CUDA devices.

After spending some time to learn to use mercurial, I finally submitted the changes in https://bitbucket.org/eigen/eigen/pull-requests/408 .

I will be happy to address any comments regarding those changes, and maybe discuss if there are any plans to further extend the use of Eigen in CUDA device code.

Thank you,

Andrea Bocci, from the "Patatrack" team [3]

[1] https://cms.cern/

[2] https://github.com/cms-sw/cmssw

[3] https://patatrack.web.cern.ch/patatrack/