import numpy as np
from dataclasses import dataclass
from typing import List, Dict, Tuple

def generate_starting_poles(n_pairs: int, beta_min: float, beta_max: float, alpha_scale: float = 0.01):
    """
    仅生成复共轭对: p = -alpha + j beta, p*。
    n_pairs: 复对数量 (总极点数 = 2*n_pairs)
    beta_min,beta_max: 想要覆盖的虚部范围 (单位: rad/s)
    alpha_scale: alpha = alpha_scale * beta  (文中 {α_p}=0.01{β_p})
    返回: list[complex] (正虚部先, 后跟共轭)
    """
    betas = 2*np.pi*np.linspace(beta_min, beta_max, n_pairs)
    poles = []
    for b in betas:
        alpha = alpha_scale * b
        p = -alpha + 1j * b
        poles += [p, np.conj(p)]
    print(f"生成 {len(poles)} 个初始极点 (复对) {poles}]")
    return poles