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)