Python Least squares leastsq function implementation

Code modified from http://www.cnblogs.com/NanShan2016/p/5493429.html

Baidu on the Internet a bit, mainly two examples, a use of polynomial functions, one is this. Some of the details are not understood, mainly to ignore the P is an array of parameters instead of a number (python basic problem), tangled up with notes to make a note

  
 

   
  

  
# 修改自 http://www.cnblogs.com/NanShan2016/p/5493429.html
   
  

  

   
  

  

   
  

  
### 最小二乘法 python leastsq###
   
  

  
import numpy as np
   
  

  
from scipy.optimize import leastsq
   
  

  

   
  

  
###采样点(Xi,Yi)###
   
  

  
Xi=np.array([8.19,2.72,6.39,8.71,4.7,2.66,3.78])
   
  

  
Yi=np.array([7.01,2.78,6.47,6.71,4.1,4.23,4.05])
   
  

  

   
  

  

   
  

  

   
  

  

   
  

  
# p是个数组，表示所有参数!!!
   
  

  
### 定义误差函数，拟合y=kx+b，p[0]表示k，p[1]表示b
   
  

  
def error(p,x,y):
   
  

  

   
  

  
 return (p[0]*x+p[1])-y #x、y都是列表，故返回值也是个列表
   
  

  

   
  

  

   
  

  

   
  

  

   
  

  
###主函数从此开始###
   
  

  
# 可能是使用梯度下降法而非矩阵运算，因此需要给定初始参数p0
   
  

  
p0=[2,2]
   
  

  

   
  

  
Para=leastsq(error,p0,args=(Xi,Yi)) #把error函数中除了p以外的参数打包到args中
   
  

  
k = Para[0][0]
   
  

  
b = Para[0][1]
   
  

  
print("k=",k,‘\n‘,"b=",b)
   
  

  

   
  

  
###绘图，看拟合效果###
   
  

  
import matplotlib.pyplot as plt
   
  

  

   
  

  

   
  

  
  plt    scatter   ( xi   yi  Span class= "pun",  color  =   "red"   label  =   "Sample Point"   linewidth  =  3      #画样本点   
   
  

  
x=np.linspace(0,10,100)
   
  

  
y=k*x+b
   
  

  
plt.plot(x,y,color="orange",label="Fitting Line",linewidth=2) #画拟合直线
   
  

  
plt.legend()
   
  

  
plt.show()
  
 

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Python Least squares leastsq function implementation