%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-05-18 22:01:15
 % @LastEditTime: 2021-05-18 22:04:01
%--------------------------
function P = PK1_fast_nonlinear(u, l, F)

    Fdet = det_3rank(F); % 1,m
    JJ   = log(Fdet);

    Finv = inv_3rank(F); % 9,m
    FinvT = Finv([1:3:9, 2:3:9, 3:3:9], :);

    P = u(:)' .* (F - FinvT) + l(:)' .* JJ .* FinvT;    
end