python实现拉格朗日插值及作图

作者: 随遇而安O30846076
来源: 51数据库
2021-07-28

本文实例为大家分享了python实现拉格朗日插值及作图，供大家参考，具体内容如下

python代码

import numpy as np
import matplotlib.pyplot as plt

x = input("x的值：").split(' ')
y = input("y的值：").split(' ')
x = input("要预测的值：")
print('\n')

x = np.array(x).astype(np.float64)
y = np.array(y).astype(np.float64)
x = np.array(x).astype(np.float64)

n = len(x)

# 原函数
def fun(x):
 return np.sin(x)

# 累乘函数
def t(x, i, x):
 t_i = 1
 for x_i in x:
  if x[i] == x_i:
   continue
  t_i = t_i * (x-x_i)
 return t_i

# 插值基函数
def p(i, x, x, y):
 p_i = t(x, i, x)/t(x[i], i, x) * y[i]
 return p_i

# 计算预测值
def l(x, x, y):
 result = 0
 for i in range(n):
  result = result + p(i, x, x, y)
 return result

y = l(x, x, y) 
  
print("预测结果：" + str(y) + '\n')
print("误差：" + str(fun(x) - y))

# 画图
x_n = np.linspace(0, 1, 50)
y_n = fun(x_n)

x_n = np.linspace(0, 1, 50)
y_n = l(x_n, x, y)

l1, = plt.plot(x_n, y_n, label='theory')
l2, = plt.plot(x_n, y_n, label='prediction',linestyle='--')
plt.legend(handles=[l1,l2,],labels=['theory','prediction'], loc='best')

plt.show()

代码测试结果（输入方式如图所示）：