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

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 = 0
    for k in range(l):
        xxx=xx.copy()
        x_k = xxx[k]
        xxx.pop(k)
        l_k = 1
        for i in range(len(xxx)):
            l_k *= (x - xxx[i]) / (x_k -xxx[i])
        l_n += y[k] * l_k
    return expand(l_n)  
lagrange_interpolation_polynomial = lagrange(xx, y)
print("拉格朗日插值多項式為:",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)
#繪制散點圖,逼近函數
plt.figure(figsize=(8,4))
plt.scatter(xx,y,c='red')
plt.plot(x2,y1,'-')
plt.show()