分段线性差值Python

分段线性插值是一种插值方法，它将插值区间分成若干个小区间，每个小区间内使用线性函数进行插值。下面是Python实现分段线性插值的代码：

import numpy as np
import matplotlib.pyplot as plt

def piecewise_linear_interpolation(x, xs, ys):
    """
    分段线性插值
    :param x: 待插值的点
    :param xs: 插值区间的横坐标
    :param ys: 插值区间的纵坐标
    :return: 插值结果
    """
    n = len(xs)
    for i in range(n - 1):
        if xs[i] <= x <= xs[i + 1]:
            k = (ys[i + 1] - ys[i]) / (xs[i + 1] - xs[i])
            b = ys[i] - k * xs[i]
            return k * x + b

# 测试代码
xs = [1, 2, 3, 4, 5]
ys = [1, 4, 9, 16, 25]
x = np.linspace(1, 5, 100)
y = [piecewise_linear_interpolation(i, xs, ys) for i in x]
plt.plot(x, y)
plt.scatter(xs, ys)
plt.show()

以上代码实现了分段线性插值，并在测试数据上进行了可视化展示。