【数值分析】牛顿差商法 -Python实现

本篇为数值分析课程代码实现-牛顿差商法 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
  @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 Newton():
  
      def __init__(self):
          
          self.W = None
          self.X = None
          
      def fit(self, X, y):#0-n-1
          
          if type(X) != np.ndarray:
              X=np.array(X)
          if type(y) != np.ndarray:
              y=np.array(y)
          W = np.zeros([len(X),len(X)+1])
          W_list=[]
          W[:,0] = X
          W[:,1] = y
          #针对每列
          W_list.append(W[0,1])
          for j in range(2,W.shape[1]):
              #对每行
              for i in range(j-1,W.shape[0]):
                  W[i,j] = (W[i,j-1] - W[i-1,j-1]) / (W[i,0] - W[i-j+1,0])
              W_list.append(W[j-1,j])
          self.W =np.array(W_list)
          self.X = np.concatenate([[1],X[:-1]],axis=0)
          return self
    
      def predict(self, X_pre):
          
          if type(X_pre)!=np.ndarray:
              X_pre = np.array(X_pre)
          def fun(x):
              sum=0
              for i in range(len(self.W)):
                  w=self.W[i]
                  c=1
                  for j in range(i):
                      c*=(x-self.X[j+1])
                  sum+=(w*c)
              return sum
  
          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=Newton()
  model.fit(fit_x,fit_y)
  W_fit=model.W
  y_pre=model.predict(sca_x)
  plt.subplot(2,1,2)
  plt.xlabel('X')
  plt.ylabel('Y')
  plt.title('牛顿插值图像')
  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！