Are there methods or considerations for real-time Gelman-Rubin diagnosis while running multiple mcmc chains in parallel?

Question

I have a Metropolis-Hastings algorithm in Python and I parallelized it with the multiprocessing library. However, at this moment I can only do Gelman-Rubin diagnosis when all generated parallel chains have ended (at a certain number of iterations set from the beginning).

I want to do the Gelman-Rubin diagnosis every 1000 iterations of the Metropolis-Hastings algorithm and stop all processes (chains) in case a certain criteria is met in Gelman-Rubin.

• Are there any considerations I should take?

• On the other hand, could you recommend me a convenient pythonic way to do it?

Thank you.