用python实现KneeLocator函数，并且curve='concave'

以下是一个用Python实现KneeLocator函数的示例代码，其中curve参数为'concave'：

import math

def KneeLocator(x, y, curve='concave'):
    n = len(x)
    dx = [x[i+1] - x[i] for i in range(n-1)]
    dy = [y[i+1] - y[i] for i in range(n-1)]
    angle = [math.atan2(dy[i], dx[i]) for i in range(n-2)]
    cumdist = [sum(math.hypot(dx[j], dy[j]) for j in range(i)) for i in range(n-1)]

    idx = sorted(range(n-2), key=lambda i: angle[i])

    kneepoint_x = 0.0
    kneepoint_y = 0.0
    kneepoint_dist = 0.0
    max_deviation = 0.0
    threshold = 0.0
    i_max = 0

    for i in range(2, n-1):
        j = idx[i-2]
        deviation = abs(angle[j+1] - angle[j])
        if curve == 'concave':
            deviation = math.pi - deviation
        if deviation > max_deviation:
            max_deviation = deviation
            i_max = i

    threshold = (angle[idx[i_max-2]] + angle[idx[i_max-1]]) / 2.0

    for i in range(n-1):
        if angle[i] > threshold:
            cx = x[i] + (x[i+1] - x[i]) * (threshold - angle[i]) / (angle[i+1] - angle[i])
            cy = y[i] + (y[i+1] - y[i]) * (threshold - angle[i]) / (angle[i+1] - angle[i])
            cd = cumdist[i] + math.hypot(cx - x[i], cy - y[i])
            if cd > kneepoint_dist:
                kneepoint_x = cx
                kneepoint_y = cy
                kneepoint_dist = cd

    return kneepoint_x

该函数接受两个列表x和y作为输入，分别表示曲线上每个点的横坐标和纵坐标。curve参数指定曲线的类型，'concave'表示曲线是凹的，'convex'表示曲线是凸的。函数返回曲线的拐点的横坐标。