TMVA classification separation definition

I am trying to understand the Separation definition in TMVA. I understood that for each classifier a separation is calculated by
equation (1) in https://root.cern.ch/root/htmldoc/guides/tmva/TMVAUsersGuide.pdf Section 3.1.10. But how does giniIndex (if this separation type is chosen) comes into play?

Hi @zhwenyu; I am sure @moneta can answer your question.

Cheers,
J.