一、拉格朗日的基本思想：

 二、线性插值

 

三、多个点

 四、代码实现

def lagrange(xx,y):l=len(y)l_n = 0for k in range(l):xxx=xx.copy()x_k = xxx[k]xxx.pop(k)l_k = 1for i in range(len(xxx)):l_k *= (x - xxx[i]) / (x_k -xxx[i])l_n += y[k] * l_kreturn expand(l_n) 

 五、完整代码

import matplotlib.pyplot as plt
import numpy as np 
import pandas as pd
from sympy import expand
from sympy.abc import x
xx=[]
for i in range(7):xx.append(data['x'][i])
y=[]
for j in range(7):y.append(data['y'][j])
def lagrange(xx,y):l=len(y)l_n = 0for k in range(l):xxx=xx.copy()x_k = xxx[k]xxx.pop(k)l_k = 1for i in range(len(xxx)):l_k *= (x - xxx[i]) / (x_k -xxx[i])l_n += y[k] * l_kreturn expand(l_n)  
lagrange_interpolation_polynomial = lagrange(xx, y)
print("拉格朗日插值多项式为:",lagrange_interpolation_polynomial)
x2=np.linspace(-1,4,100)
y1=[]
for i in range(len(x2)):y1.append(lagrange_interpolation_polynomial.subs(x,x2[i]))
print(y1)
#绘制散点图,逼近函数
plt.figure(figsize=(8,4))
plt.scatter(xx,y,c='red')
plt.plot(x2,y1,'-')
plt.show()

六、pop（）函数

 七、结果展示