python+numpy+matplotalib实现梯度下降法

import numpy as npimport matplotlib.pyplot as pltfrom mpl_toolkits.mplot3d import axes3dfrom matplotlib import style  #构造数据def get_data(sample_num=10000):  """  拟合函数为  y = 5*x1 + 7*x2  :return:  """  x1 = np.linspace(0, 9, sample_num)  x2 = np.linspace(4, 13, sample_num)  x = np.concatenate(([x1], [x2]), axis=0).T  y = np.dot(x, np.array([5, 7]).T)   return x, y#梯度下降法def GD(samples, y, step_size=0.01, max_iter_count=1000):  """  :param samples: 样本  :param y: 结果value  :param step_size: 每一接迭代的步长  :param max_iter_count: 最大的迭代次数  :param batch_size: 随机选取的相对于总样本的大小  :return:  """  #确定样本数量以及变量的个数初始化theta值  m, var = samples.shape  theta = np.zeros(2)  y = y.flatten()  #进入循环内  print(samples)  loss = 1  iter_count = 0  iter_list=[]  loss_list=[]  theta1=[]  theta2=[]  #当损失精度大于0.01且迭代此时小于最大迭代次数时，进行  while loss > 0.001 and iter_count < max_iter_count:    loss = 0    #梯度计算    theta1.append(theta[0])    theta2.append(theta[1])    for i in range(m):      h = np.dot(theta,samples[i].T)      #更新theta的值,需要的参量有：步长，梯度      for j in range(len(theta)):        theta[j] = theta[j] - step_size*(1/m)*(h - y[i])*samples[i,j]    #计算总体的损失精度，等于各个样本损失精度之和    for i in range(m):      h = np.dot(theta.T, samples[i])      #每组样本点损失的精度      every_loss = (1/(var*m))*np.power((h - y[i]), 2)      loss = loss + every_loss     print("iter_count: ", iter_count, "the loss:", loss)        iter_list.append(iter_count)    loss_list.append(loss)        iter_count += 1  plt.plot(iter_list,loss_list)  plt.xlabel("iter")  plt.ylabel("loss")  plt.show()  return theta1,theta2,theta,loss_listdef painter3D(theta1,theta2,loss):  style.use('ggplot')  fig = plt.figure()  ax1 = fig.add_subplot(111, projection='3d')  x,y,z = theta1,theta2,loss  ax1.plot_wireframe(x,y,z, rstride=5, cstride=5)  ax1.set_xlabel("theta1")  ax1.set_ylabel("theta2")  ax1.set_zlabel("loss")  plt.show()def predict(x, theta):  y = np.dot(theta, x.T)  return y    if __name__ == '__main__':  samples, y = get_data()  theta1,theta2,theta,loss_list = GD(samples, y)  print(theta) # 会很接近[5, 7]   painter3D(theta1,theta2,loss_list)  predict_y = predict(theta, [7,8])  print(predict_y)