Python利用给定的一组坐标，实现三次Hermite差值曲线绘制的函数

下面是利用Python实现三次Hermite差值曲线绘制的函数：

import numpy as np
import matplotlib.pyplot as plt

def hermite_cubic_interpolation(x, y, m):
    """
    :param x: 数据点的横坐标，array_like
    :param y: 数据点的纵坐标，array_like
    :param m: 数据点处的导数，array_like
    :return: 返回插值函数 f(x)
    """
    n = len(x)
    h = np.diff(x)
    alpha = np.zeros(n)
    for i in range(1, n-1):
        alpha[i] = 3/h[i]*(y[i+1]-y[i]) - 3/h[i-1]*(y[i]-y[i-1])
    l = np.zeros(n)
    mu = np.zeros(n)
    z = np.zeros(n)
    l[0] = 1
    mu[0] = 0
    z[0] = 0
    for i in range(1, n-1):
        l[i] = 2*(x[i+1]-x[i-1])-h[i-1]*mu[i-1]
        mu[i] = h[i]/l[i]
        z[i] = (alpha[i]-h[i-1]*z[i-1])/l[i]
    l[n-1] = 1
    z[n-1] = 0
    c = np.zeros(n)
    b = np.zeros(n-1)
    d = np.zeros(n-1)
    for j in range(n-2, -1, -1):
        c[j] = z[j]-mu[j]*c[j+1]
        b[j] = (y[j+1]-y[j])/h[j] - h[j]*(c[j+1]+2*c[j])/3
        d[j] = (c[j+1]-c[j])/(3*h[j])
    def f(t):
        """
        :param t: 自变量，scalar or array_like
        :return: 因变量 f(t)，scalar or array_like
        """
        idx = np.searchsorted(x, t)
        if idx == 0:
            return y[0] + m[0]*(t-x[0])
        elif idx == n:
            return y[-1] + m[-1]*(t-x[-1])
        else:
            i = idx - 1
            return y[i] + m[i]*(t-x[i]) + b[i]*(t-x[i])**2 + c[i]*(t-x[i])**3 + d[i]*(t-x[i])**3*(t-x[i+1])
    return f

# 示例
x = np.array([0, 1, 2, 3, 4, 5])
y = np.array([0, 1, 3, 2, 1, 2])
m = np.array([1, 2, 3, 4, 5, 6])
f = hermite_cubic_interpolation(x, y, m)
t = np.linspace(0, 5, 1000)
plt.plot(x, y, 'o', t, f(t), '-')
plt.show()

其中，`x` 是数据点的横坐标，`y` 是数据点的纵坐标，`m` 是数据点处的导数。函数返回一个函数对象 `f`，通过调用 `f(t)` 可以得到自变量为 `t` 时的因变量值。示例中的数据点和导数都是随意构造的，可以根据具体需求进行修改。