```import numpy as np
import pandas as pd
import matplotlib
matplotlib.use('TkAgg')
import matplotlib.pyplot as plt
import ui

print("经典的 MNIST 手写数字识别")
ui.split_line1()
print("载入数据")
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

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)

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))```