def derivatives(self, x, y, theta_E, ratio, w_c1, w_t1, e11, e21, w_c2, w_t2, e12, e22, center_x=0, center_y=0):
        """

        :param amp:
        :param ratio:
        :param w_c1:
        :param w_t1:
        :param e11:
        :param e21:
        :param w_c2:
        :param w_t2:
        :param e12:
        :param e22:
        :param center_x:
        :param center_y:
        :return:
        """
        f_x1, f_y1 = self.chameleon.derivatives(x, y, theta_E / (1. + 1./ratio), w_c1, w_t1, e11, e21, center_x, center_y)
        f_x2, f_y2 = self.chameleon.derivatives(x, y, theta_E / (1. + ratio), w_c2, w_t2, e12, e22, center_x, center_y)
        return f_x1 + f_x2, f_y1 + f_y2
def derivatives ( self , x , y , theta_E , ratio , w_c1 , w_t1 , e11 , e21 , w_c2 , w_t2 , e12 , e22 , center_x = 0 , center_y = 0 ) : f_x1 , f_y1 = self . chameleon . derivatives ( x , y , theta_E / ( 1. + 1. / ratio ) , w_c1 , w_t1 , e11 , e21 , center_x , center_y ) f_x2 , f_y2 = self . chameleon . derivatives ( x , y , theta_E / ( 1. + ratio ) , w_c2 , w_t2 , e12 , e22 , center_x , center_y ) return f_x1 + f_x2 , f_y1 + f_y2
:param amp:
        :param ratio:
        :param w_c1:
        :param w_t1:
        :param e11:
        :param e21:
        :param w_c2:
        :param w_t2:
        :param e12:
        :param e22:
        :param center_x:
        :param center_y:
        :return: