text: import numpy as np
  import pandas as pd
  import matplotlib
  matplotlib.use('TkAgg')
  import matplotlib.pyplot as plt
  import ui
  from scipy.io import loadmat
  
  print("经典的 MNIST 手写数字识别")
  ui.split_line1()
  print("载入数据")
  data = loadmat('data/ex3data1.mat')
  print("预览载入的数据")
  print(data)
  print("数据的 X 和 y 的尺寸")
  print(data['X'].shape, data['y'].shape)
  print("定义 sigmoid 函数，cost 函数和向量化的梯度函数")
  def sigmoid(z):
      return 1 / (1 + np.exp(-z))
  
  def cost(theta, X, y, learningRate):
      theta = np.matrix(theta)
      X = np.matrix(X)
      y = np.matrix(y)
      first = np.multiply(-y, np.log(sigmoid(X * theta.T)))
      second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))
      reg = (learningRate / (2 * len(X))) * np.sum(np.power(theta[:,1:theta.shape[1]], 2))
      return np.sum(first - second) / len(X) + reg
  
  def gradient(theta, X, y, learningRate):
      theta = np.matrix(theta)
      X = np.matrix(X)
      y = np.matrix(y)
      
      parameters = int(theta.ravel().shape[1])
      error = sigmoid(X * theta.T) - y
      
      grad = ((X.T * error) / len(X)).T + ((learningRate / len(X)) * theta)
      
      # intercept gradient is not regularized
      grad[0, 0] = np.sum(np.multiply(error, X[:,0])) / len(X)
      
      return np.array(grad).ravel()
  
  ui.split_line2()
  print("实现一对一全分类方法，其中具有k个不同类的标签就有k个分类器，每个分类器在“类别 i”和“不是 i”之间")
  print("决定。 我们将把分类器训练包含在一个函数中，该函数计算10个分类器中的每个分类器的最终权重，并将权重")
  print("返回为k x（n + 1）数组，其中n是参数数量。")
  from scipy.optimize import minimize
  def one_vs_all(X, y, num_labels, learning_rate):
      rows = X.shape[0]
      params = X.shape[1]
      
      # k X (n + 1) array for the parameters of each of the k classifiers
      all_theta = np.zeros((num_labels, params + 1))
      
      # insert a column of ones at the beginning for the intercept term
      X = np.insert(X, 0, values=np.ones(rows), axis=1)
      
      # labels are 1-indexed instead of 0-indexed
      for i in range(1, num_labels + 1):
          theta = np.zeros(params + 1)
          y_i = np.array([1 if label == i else 0 for label in y])
          y_i = np.reshape(y_i, (rows, 1))
          
          # minimize the objective function
          fmin = minimize(fun=cost, x0=theta, args=(X, y_i, learning_rate), method='TNC', jac=gradient)
          all_theta[i-1,:] = fmin.x
      
      return all_theta
  
  print("准备训练数据")
  rows = data['X'].shape[0]
  params = data['X'].shape[1]
  
  all_theta = np.zeros((10, params + 1))
  
  X = np.insert(data['X'], 0, values=np.ones(rows), axis=1)
  
  theta = np.zeros(params + 1)
  
  y_0 = np.array([1 if label == 0 else 0 for label in data['y']])
  y_0 = np.reshape(y_0, (rows, 1))
  print("X, y, theta, all_theta 的大小")
  print(X.shape, y_0.shape, theta.shape, all_theta.shape)
  print("独立的标签数量")
  print(np.unique(data['y']))
  print("进行训练")
  all_theta = one_vs_all(data['X'], data['y'], 10, 1)
  print(all_theta)
  print("预测每个图像的标签")
  
  def predict_all(X, all_theta):
      rows = X.shape[0]
      params = X.shape[1]
      num_labels = all_theta.shape[0]
      
      # same as before, insert ones to match the shape
      X = np.insert(X, 0, values=np.ones(rows), axis=1)
      
      # convert to matrices
      X = np.matrix(X)
      all_theta = np.matrix(all_theta)
      
      # compute the class probability for each class on each training instance
      h = sigmoid(X * all_theta.T)
      
      # create array of the index with the maximum probability
      h_argmax = np.argmax(h, axis=1)
      
      # because our array was zero-indexed we need to add one for the true label prediction
      h_argmax = h_argmax + 1
      
      return h_argmax
  
  print("得到准确率")
  y_pred = predict_all(data['X'], all_theta)
  correct = [1 if a == b else 0 for (a, b) in zip(y_pred, data['y'])]
  accuracy = (sum(map(int, correct)) / float(len(correct)))
  print ('accuracy = {0}%'.format(accuracy * 100))