How are the parameters for GTR20 infered?

[benjamin-lieser]

I am trying to understand how you would get estimations of the rate matrices.
I am especially interested in the computational complexity.
For example for GTR20 I could imagine that you can calculate gradients with respect to the likelihood under a given tree. But this seems nasty because of the matrix exp involved.
I have tried to get this information from the code, but failed. I would be grateful for a short explanation of the computation or a reference to it.