NLR：利用非线性回归，梯度下降法求出学习参数θ，进而求得Cost函数最优值——Jason niu

import numpy as np    
import random         
  
def genData(numPoints,bias,variance):    
    x = np.zeros(shape=(numPoints,2))   
    y = np.zeros(shape=(numPoints))    
    for i in range(0,numPoints):      
        x[i][0]=1                  
        x[i][1]=i                    
        y[i]=(i+bias)+random.uniform(0,1)%variance   
    return x,y  
  
def gradientDescent(x,y,theta,alpha,m,numIterations):   
    xTran = np.transpose(x)           
    for i in range(numIterations):  
        hypothesis = np.dot(x,theta)   
        loss = hypothesis-y        
        cost = np.sum(loss**2)/(2*m)   
        gradient=np.dot(xTran,loss)/m  
        theta = theta-alpha*gradient   
        print ("Iteration %d | cost :%f" %(i,cost))  
    return theta  
  
x,y = genData(100, 25, 10)  #100行，  
print ("x:")  
print (x)  
print ("y:")  
print (y)  
  
m,n = np.shape(x)  
n_y = np.shape(y)    
    
print("m:"+str(m)+" n:"+str(n)+" n_y:"+str(n_y))  
    
numIterations = 100000      
alpha = 0.0005             
theta = np.ones(n)      
theta= gradientDescent(x, y, theta, alpha, m, numIterations)  
print(theta)