msmle.py 文件源码

def _uwham_obj_grad(self, f_i):
        """Return the log-likelihood (scalar objective function) and its
        gradient (wrt the free energies) for a given value of the free
        energies.  Note that this expects one less free energy than there are
        states, since we always solve under the constraint that f_1 = 0.
        """
        _f_i = hstack((zeros(1), asarray(f_i)))
        # For numerical stability, use log quantities.
        logQ_nj = _f_i - self._u_nj_m
        logNorm_n = logsumexp(logQ_nj, 1, self.PIsdiag[newaxis, :])
        W_nj = exp(logQ_nj - logNorm_n[:, newaxis])
        # Compute matrix products and sums (equivalent to multiplying by
        # appropriate vector of ones). Note that using dot() with ndarrays is
        # _much_ faster than multiplying matrix objects.
        PIW = self.PIs.dot(W_nj.T)
        WPI = W_nj.dot(self.PIs)
        g = PIW.mean(axis=1) # used in gradient and Hessian computation
        kappa = logNorm_n.mean() - (self.PIsdiag.dot(_f_i)).sum()
        grad = (g - self.PIsdiag)[1:]
        self._hess = (diagflat(g) - PIW.dot(WPI) / self.total_samples)[1:, 1:]
        return kappa, grad