import numpy as np
import random
#梯度下降函数
def gradientDescent(x, y, theta, alpha, m, numIterations): #alpha:学习率，m实例个数，numIterations更新次数
xTrans = x.transpose() #对矩阵转置
for i in range(0, numIterations):
hypothesis = np.dot(x, theta)
loss = hypothesis - y
cost = np.sum(loss**2) / (2*m)
print("Iteration %d / Cost: %f" % (i , cost))
gradient = np.dot(xTrans , loss) / m
#更新theta
theta = theta - alpha * gradient
return theta
#构造数据集
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
#目标变量
y[i] = (i + bias) + random.uniform(0,1) * variance
return x, y
m ,n = np.shape(x)
print(m,n)
numIterations = 50000
alpha = 0.0005
theta = np.ones(n)
theta = gradientDescent(x, y, theta, alpha, m, numIterations)
print(theta)
Iteration 0 / Cost: 408.935704 Iteration 1 / Cost: 230.001203 Iteration 2 / Cost: 156.207536 Iteration 3 / Cost: 125.765765 Iteration 4 / Cost: 113.198945 Iteration 5 / Cost: 108.002366 Iteration 6 / Cost: 105.844704 Iteration 7 / Cost: 104.940060 Iteration 8 / Cost: 104.552065 Iteration 9 / Cost: 104.377101 Iteration 10 / Cost: 104.289977
Iteration 49991 / Cost: 3.767171 Iteration 49992 / Cost: 3.767171 Iteration 49993 / Cost: 3.767171 Iteration 49994 / Cost: 3.767171 Iteration 49995 / Cost: 3.767171 Iteration 49996 / Cost: 3.767171 Iteration 49997 / Cost: 3.767171 Iteration 49998 / Cost: 3.767171 Iteration 49999 / Cost: 3.767171 [29.13339253 1.0064644 ]