【数值分析】拉格朗日插值法 -Python实现

本篇为数值分析课程代码实现-拉格朗日插值法的实现

仅供参考

配置环境

• Python3.6
• matplotlib
• numpy

# -*- coding: utf-8 -*-
"""
Created on Tue Dec  4 21:04:35 2018
拉格朗日插值
@author: hhuaf
"""
import matplotlib.pyplot as plt
import numpy as np

#可以显示中文
plt.rcParams["font.sans-serif"] = ["SimHei"]
plt.rcParams['axes.unicode_minus'] = False

# 设置风格
plt.style.use('ggplot')

class Lagrangian():

    def __init__(self):
        self.X = None
        self.y = None
    def fit(self, X, y):#0-n
        if type(X) != np.ndarray:
            X=np.array(X)
        if type(y) != np.ndarray:
            y=np.array(y)
        self.X=X
        self.y=y
        pass
                
    def predict(self, X_pre):
        if type(X_pre) != np.ndarray:
            X_pre = np.array(X_pre)
            
        def fun(x):
            Lx=0
            for i in range(len(self.X)):
                lxk=1
                for j in range(len(self.X)):
                    if i!=j:
                        lxk*=(x-self.X[j])/(self.X[i]-self.X[j])
                Lx+=lxk*self.y[i]
            return Lx
        return np.array([fun(i) for i in X_pre])

def generate_data(start,end,sample_num):
    xx=np.arange(start,end,0.01)
    yy=np.log(xx)
    plt.plot(xx.reshape(-1),yy)
    select_num=np.random.choice(np.arange(len(xx)),[sample_num])
    return xx.reshape(-1),yy,[xx[i] for i in select_num],[yy[i] for i in select_num]


m=int(input("请输入样本量：(越多越好)\n"))
fig = plt.figure(figsize = (8, 12))
plt.subplot(2,1,1)
plt.xlabel('X')
plt.ylabel('Y')
plt.title('原函数图像')
sca_x,sca_y,fit_x,fit_y=generate_data(1,10,m)
model=Lagrangian()
model.fit(fit_x,fit_y)
y_pre=model.predict(sca_x)
plt.subplot(2,1,2)
plt.xlabel('X')
plt.ylabel('Y')
plt.title('拉格朗日插值图像')
plt.scatter(fit_x,fit_y,c='red')
plt.plot(sca_x,y_pre,c='black')
plt.plot(sca_x,sca_y)
plt.legend(['预测','真实'])
plt.show()

欢迎大家批评指正！