用Python实现插值算法

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
data = pd.read_excel('data.xlsx')

import scipy
from scipy.interpolate import lagrange
x = np.linspace(0,10,6)      #0~10等差插入11个数，需要预测的值
y = np.sin(x)
x_new = np.linspace(0,10,200)  #用于绘制图形
y_new = np.sin(x_new)
plt.plot(x,y,'ro')
plt.plot(x_new,y_new,'b')

f1 = lagrange(x,y)
plt.plot(x,y,'ro')
plt.plot(x_new,y_new,'b')
plt.plot(x_new,f1(x_new),'g')

f4 = scipy.interpolate.interp1d(x,y,kind='linear')
plt.plot(x,y,'ro')
plt.plot(x_new,y_new,'b')
plt.plot(x_new,f4(x_new),'g')

f5 = scipy.interpolate.interp1d(x,y,kind='quadratic')    #三次就是cubic
plt.plot(x,y,'ro')
plt.plot(x_new,y_new,'b')
plt.plot(x_new,f5(x_new),'g')

f5 = scipy.interpolate.interp1d(x,y,kind='quadratic')    #三次就是cubic
plt.plot(x,y,'ro')
plt.plot(x_new,y_new,'b')
plt.plot(x_new,f5(x_new),'g')

f3 = scipy.interpolate.CubicSpline(x,y)
plt.plot(x,y,'ro')
plt.plot(x_new,y_new,'b')
plt.plot(x_new,f3(x_new),'g')

y = np.array(data)[:,1]
x = np.linspace(2009,2018,10)
x_new = np.array([2019,2020,2021])
f2 = scipy.interpolate.PchipInterpolator(x,y)
f3 = scipy.interpolate.CubicSpline(x,y)
 
#coding:utf-8
plt.rcParams['font.sans-serif']=['SimHei'] #用来正常显示中文标签
plt.rcParams['axes.unicode_minus']=False #用来正常显示负号
 
plt.plot(x,y,color='black',marker='o',label='样本点')
plt.plot(x_new,f2(x_new),'b-',marker='x',label='分段三次埃米尔特')
plt.plot(x_new,f3(x_new),'r-',marker='x',label='三次样条插值')
plt.xticks(range(2009,2022,1))     #调整x轴间距
plt.legend()
plt.show()