梯度下降法是非常常见的优化方法，在神经网络的深度学习中更是必会方法，但是直接从深度学习去实现，会比较复杂。本文试图使用梯度下降来优化最简单的LSR线性回归问题，作为进一步学习的基础。

import numpy as npimport pandas as pdfrom numpy import *from pandas import *import matplotlib.pyplot as pltx = np.array([[1,2],[2,1],[3,2.5],[4,3],              [5,4],[6,5],[7,2.7],[8,4.5],              [9,2]])m, n = np.shape(x)x_data = np.ones((m,n))x_data[:,:-1] = x[:,:-1]y_data = x[:,-1]print(x_data.shape)print(y_data.shape)m, n = np.shape(x_data)theta = np.ones(n)def batchGradientDescent(maxiter,x,y,theta,alpha):    xTrains = x.transpose()    for i in range(0,maxiter):        hypothesis = np.dot(x,theta)        loss = (hypothesis-y)        gradient = np.dot(xTrains,loss)/m        theta = theta - alpha * gradient        cost = 1.0/2*m*np.sum(np.square(np.dot(x,np.transpose(theta))-y))        print("cost: %f"%cost)    return thetaresult = batchGradientDescent(10,x_data,y_data,theta,0.01)print(result)newy = np.dot(x_data,result)fig, ax = plt.subplots()ax.plot(x[:,0],newy, 'k--')ax.plot(x[:,0],x[:,1], 'ro')plt.show()print("final: " + result)