def predict(self, u):
        '''Predicts the output value at u from the fitted polynomial expansion.
        Therefore the method train() must be called first.

        :param numpy.ndarray u: input value at which to predict the output.

        :return: q_approx - the predicted value of the output at u

        :rtype: float

        *Sample Usage*::

            >>> thePC = PolySurrogate(dimensions=2)
            >>> U = thePC.getQuadraturePoints()
            >>> Q = [myFunc(u) for u in U]
            >>> thePC.train(U, Q)
            >>> thePC.predict([0, 1])

        '''
        y, ysub = 0, np.zeros(self.N_poly)
        for ip in range(self.N_poly):
            inds = tuple(self.index_polys[ip])
            ysub[ip] = self.coeffs[inds]*eval_poly(u, inds, self.J_list)
            y += ysub[ip]

        self.response_components = ysub
        return y
Predicts the output value at u from the fitted polynomial expansion.
        Therefore the method train() must be called first.

        :param numpy.ndarray u: input value at which to predict the output.

        :return: q_approx - the predicted value of the output at u

        :rtype: float

        *Sample Usage*::

            >>> thePC = PolySurrogate(dimensions=2)
            >>> U = thePC.getQuadraturePoints()
            >>> Q = [myFunc(u) for u in U]
            >>> thePC.train(U, Q)
            >>> thePC.predict([0, 1])