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.f_u function is for internal usage only and is not intended to be called by the user.
.f_u(eps, Pdat, muhat1, muhat2, sigmahat1, sigmahat2, pi_hat, muhat1_est, muhat2_est, sigmahat1_est, sigmahat2_est, pi_hat_est, ll, W, Z, INERiter, N)