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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 rule(self):
 """ Return finite differencing rule. The rule is for a nominal unit step size, and must be scaled later to reflect the local step size. Member methods used _fd_matrix Member variables used n order method """

        step_ratio = self.step_ratio
        method = self.method
        if method in ('multicomplex', ) or self.n == 0:
            return np.ones((1,))

        order, method_order = self.n - 1, self._method_order
        parity = self._parity(method, order, method_order)
        step = self._richardson_step()
        num_terms, ix = (order + method_order) // step, order // step
        fd_rules = FD_RULES.get((step_ratio, parity, num_terms))
        if fd_rules is None:
            fd_mat = self._fd_matrix(step_ratio, parity, num_terms)
            fd_rules = linalg.pinv(fd_mat)
            FD_RULES[(step_ratio, parity, num_terms)] = fd_rules

        if self._flip_fd_rule:
            return -fd_rules[ix]
        return fd_rules[ix]