import numpy as np

def generate_laguerre_basis(poles:list|np.ndarray, s: np.ndarray):
    basis = np.zeros((len(poles)+1,len(s)),dtype=complex)

    product = np.ones(len(s),dtype=complex)

    basis[0] = np.ones(len(s),dtype=complex)  # φ_0 = 1
    i = 0
    while i < len(poles):
        if np.real(poles[i]) >= 0:
            raise ValueError(f"极点必须在左半平面: {poles[i]}")

        # 复对首 (正虚部)
        if np.iscomplex(poles[i]) and np.imag(poles[i]) > 0:
            if i + 1 >= len(poles):
                raise ValueError("复极点缺少共轭")
            pc = poles[i + 1]
            if not np.isclose(pc, np.conj(poles[i])):
                raise ValueError("复极点未按 (p, p*) 顺序排列 (正虚部在前)")
            sigma = -np.real(poles[i])           # >0
            scale = np.sqrt(2 * sigma)
            r = np.abs(poles[i])
            denom = (s - poles[i]) * (s - pc)

            # 两个基函数
            phi_p  = scale * (s - r) / denom * product
            phi_pc = scale * (s + r) / denom * product

            # product 先乘 (s + p^*)/(s - p)，再乘 (s + p)/(s - p^*)
            product = product * (s + pc) / (s - poles[i])
            product = product * (s + poles[i])  / (s - pc)

            basis[i + 1] = phi_p
            basis[i + 2] = phi_pc
            i += 2
            continue

        # 复对次 (负虚部) —— 应该被首元素处理，出现表示顺序错误
        if np.iscomplex(poles[i]) and np.imag(poles[i]) < 0:
            raise ValueError("检测到负虚部复极点但其共轭尚未处理，请将正虚部成员放在前面。")

        # 实极点
        sigma = -np.real(poles[i])
        if sigma <= 0:
            raise ValueError("实极点实部应为负 (稳定)。")
        scale = np.sqrt(2 * sigma)
        phi = scale / (s - poles[i]) * product
        # 更新乘积
        product = product * (s + poles[i]) / (s - poles[i])
        i += 1
        basis[i + 1] = phi
    return basis