zgh,
You should post the problem you are working on or at least a minimum working example of what you have tried so others can help you. See here.
I can’t directly answer your question but I can provide a temporary work around.
Personally I encountered this same exact question a few months ago when I wanted to obtain the principle components of a symmetric stress tensor after essentially solving the Fenics tutorial for elasticity example.
-\nabla * \sigma(u) = f in \Omega
The closest I got was iterating through each of the vertices, getting the correct eigenvalues and eigenvectors using Numpy, but was unable to correctly project back onto the solution space. So as for doing this programmatically I am unable to help.
However, if you need this soon, the way I got around this was to export the projected solution \sigma(u) onto a TensorFunctionSpace and output as a “.xdmf”. I then opened this in Paraview and exported the tensor from the spreadsheet view as a “.csv”. Using another software (Matlab), I then could easily grab the stress tensor - calculate the components - and then generate a spreadsheet where I project the eigen values and vectors back onto the original solution space (to be view in ParaView). I found this to be optimal especially since my application involved 500k+ elements and even with MPI this became cumbersome to try in Python. This is my personal experience take it or leave it - I’m welcome to provide further detail if this is of interest.
-Sven