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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def predict_jacobian(self, Xnew, kern=None, full_cov=False):
 """ Compute the derivatives of the posterior of the GP. Given a set of points at which to predict X* (size [N*,Q]), compute the mean and variance of the derivative. Resulting arrays are sized: dL_dX* -- [N*, Q ,D], where D is the number of output in this GP (usually one). Note that this is the mean and variance of the derivative, not the derivative of the mean and variance! (See predictive_gradients for that) dv_dX* -- [N*, Q], (since all outputs have the same variance) If there is missing data, it is not implemented for now, but there will be one output variance per output dimension. :param X: The points at which to get the predictive gradients. :type X: np.ndarray (Xnew x self.input_dim) :param kern: The kernel to compute the jacobian for. :param boolean full_cov: whether to return the cross-covariance terms between the N* Jacobian vectors :returns: dmu_dX, dv_dX :rtype: [np.ndarray (N*, Q ,D), np.ndarray (N*,Q,(D)) ] """

        if kern is None:
            kern = self.kern

        mean_jac = np.empty((Xnew.shape[0],Xnew.shape[1],self.output_dim))

        for i in range(self.output_dim):
            mean_jac[:,:,i] = kern.gradients_X(self.posterior.woodbury_vector[:,i:i+1].T, Xnew, self._predictive_variable)

        dK_dXnew_full = np.empty((self._predictive_variable.shape[0], Xnew.shape[0], Xnew.shape[1]))
        one = np.ones((1,1))
        for i in range(self._predictive_variable.shape[0]):
            dK_dXnew_full[i] = kern.gradients_X(one, Xnew, self._predictive_variable[[i]])

        if full_cov:
            dK2_dXdX = kern.gradients_XX(one, Xnew)
        else:
            dK2_dXdX = kern.gradients_XX_diag(one, Xnew)
            #dK2_dXdX = np.zeros((Xnew.shape[0], Xnew.shape[1], Xnew.shape[1]))
            #for i in range(Xnew.shape[0]):
            #    dK2_dXdX[i:i+1,:,:] = kern.gradients_XX(one, Xnew[i:i+1,:])

        def compute_cov_inner(wi):
            if full_cov:
                var_jac = dK2_dXdX - np.einsum('qnm,msr->nsqr', dK_dXnew_full.T.dot(wi), dK_dXnew_full) # n,s = Xnew.shape[0], m = pred_var.shape[0]
            else:
                var_jac = dK2_dXdX - np.einsum('qnm,mnr->nqr', dK_dXnew_full.T.dot(wi), dK_dXnew_full)
            return var_jac

        if self.posterior.woodbury_inv.ndim == 3: # Missing data:
            if full_cov:
                var_jac = np.empty((Xnew.shape[0],Xnew.shape[0],Xnew.shape[1],Xnew.shape[1],self.output_dim))
                for d in range(self.posterior.woodbury_inv.shape[2]):
                    var_jac[:, :, :, :, d] = compute_cov_inner(self.posterior.woodbury_inv[:, :, d])
            else:
                var_jac = np.empty((Xnew.shape[0],Xnew.shape[1],Xnew.shape[1],self.output_dim))
                for d in range(self.posterior.woodbury_inv.shape[2]):
                    var_jac[:, :, :, d] = compute_cov_inner(self.posterior.woodbury_inv[:, :, d])
        else:
            var_jac = compute_cov_inner(self.posterior.woodbury_inv)
        return mean_jac, var_jac