"""
Bollinger Bands 计算函数

Author: 张飞 翼德
Date: 2026-05-31
"""

import math
from typing import List, Tuple


def calc_bollinger(
    closes: List[float],
    period: int = 20,
    num_std: float = 2.0,
) -> Tuple[List[float], List[float], List[float]]:
    """计算布林带指标。

    Args:
        closes: 收盘价序列
        period: SMA 周期，默认 20
        num_std: 标准差倍数，默认 2.0

    Returns:
        (upper, middle, lower) 三列表。
        数据不足 period 时返回 ([], [], [])。
    """
    n = len(closes)
    if period <= 0 or n < period:
        return [], [], []

    upper: List[float] = []
    middle: List[float] = []
    lower: List[float] = []

    for i in range(period - 1, n):
        window = closes[i - period + 1 : i + 1]
        avg = sum(window) / period
        variance = sum((x - avg) ** 2 for x in window) / period
        std = math.sqrt(variance)

        middle.append(avg)
        upper.append(avg + num_std * std)
        lower.append(avg - num_std * std)

    return upper, middle, lower