import numpy as np

 A = np.eye(5)

 print(A)

 import numpy as np

 import matplotlib.pyplot as plt

 from mpl_toolkits.mplot3d import Axes3D

 #-----------------计算代价值函数-----------------------

 def computeCost(X, y, theta):

     m = np.size(X[:,0])

     J = 1/(2*m)*np.sum((np.dot(X,theta)-y)**2)

     return J

 #----------------根据人口预测利润----------------------

 #读取数据集中数据，第一列是人口数据，第二列是利润数据

 data = np.loadtxt('ex1data1.txt',delimiter=",",dtype="float")

 m = np.size(data[:,0])

 # print(data)

 #------------------绘制样本点--------------------------

 X = data[:,0:1]

 y = data[:,1:2]

 plt.plot(X,y,"rx")

 plt.xlabel('Population of City in 10,000s')

 plt.ylabel('Profit in $10,000s')

 # plt.show()

 #-----------------梯度下降计算局部最优解----------------

 #添加第一列1

 one = np.ones(m)

 X = np.insert(X,0,values=one,axis=1)

 # print(X)

 #设置α、迭代次数、θ

 theta = np.zeros((2,1))

 iterations = 1500

 alpha = 0.01

 #梯度下降，并显示线性回归

 J_history = np.zeros((iterations,1))

 for iter in range(0,iterations):

     theta = theta - alpha/m*np.dot(X.T,(np.dot(X,theta)-y))

     J_history[iter] = computeCost(X,y,theta)

 plt.plot(data[:,0],np.dot(X,theta),'-')

 plt.show()

 # print(theta)

 # print(J_history)

 #--------------------显示三维图------------------------

 theta0 = np.linspace(-10,10,100)

 theta1 = np.linspace(-1,4,100)

 J_vals = np.zeros((np.size(theta0),np.size(theta1)))

 for i in range(0,np.size(theta0)):

     for j in range(0,np.size(theta1)):

         t = np.asarray([theta0[i],theta1[j]]).reshape(2,1)

         J_vals[i,j] = computeCost(X,y,t)

 # print(J_vals)

 J_vals = J_vals.T    #需要转置一下，否则轴会反

 fig1 = plt.figure()

 ax = Axes3D(fig1)

 ax.plot_surface(theta0,theta1,J_vals,rstride=1,cstride=1,cmap=plt.get_cmap('rainbow'))

 ax.set_xlabel('theta0')

 ax.set_ylabel('theta1')

 ax.set_zlabel('J')

 plt.show()

 #--------------------显示轮廓图-----------------------

 lines = np.logspace(-2,3,20)

 plt.contour(theta0,theta1,J_vals,levels = lines)

 plt.xlabel('theta0')

 plt.ylabel('theta1')

 plt.plot(theta[0],theta[1],'rx')

 plt.show()

 import numpy as np

 import matplotlib.pyplot as plt

 #-----------------计算代价值函数-----------------------

 def computeCost(X, y, theta):

     m = np.size(X[:,0])

     J = 1/(2*m)*np.sum((np.dot(X,theta)-y)**2)

     return J

 #-------------------根据面积和卧室数量预测房价----------

 #读取数据集中数据，第一列是面积数据，第二列是卧室数量，第三列是房价

 data = np.loadtxt('ex1data2.txt',delimiter=",",dtype="float")

 m = np.size(data[:,0])

 # print(data)

 X = data[:,0:2]

 y = data[:,2:3]

 #----------------------均值归一化---------------------

 mu = np.mean(X,0)

 sigma = np.std(X,0)

 X_norm = np.divide(np.subtract(X,mu),sigma)

 one = np.ones(m)   #添加第一列1

 X_norm = np.insert(X_norm,0,values=one,axis=1)

 # print(mu)

 # print(sigma)

 # print(X_norm)

 #----------------------梯度下降-----------------------

 alpha = 0.05

 num_iters = 100

 theta = np.zeros((3,1));

 J_history = np.zeros((num_iters,1))

 for iter in range(0,num_iters):

     theta = theta - alpha/m*np.dot(X_norm.T,(np.dot(X_norm,theta)-y))

     J_history[iter] = computeCost(X_norm,y,theta)

 # print(theta)

 x_col = np.arange(0,num_iters)

 plt.plot(x_col,J_history,'-b')

 plt.xlabel('Number of iterations')

 plt.ylabel('Cost J')

 plt.show()

 #----------使用上述结果对[1650,3]的数据进行预测--------

 test1 = [1,1650,3]

 test1[1:3] = np.divide(np.subtract(test1[1:3],mu),sigma)

 price = np.dot(test1,theta)

 print(price)        #输出预测结果[292455.63375132]

 #-------------使用正规方程法求解----------------------

 one = np.ones(m)

 X = np.insert(X,0,values=one,axis=1)

 theta = np.dot(np.dot(np.linalg.pinv(np.dot(X.T,X)),X.T),y)

 # print(theta)

 price = np.dot([1,1650,3],theta)

 print(price)       #输出预测结果[293081.46433497]