挑战题：

import matplotlib.pyplot as plt
import numpy as np
import json

def load_data():
    # 从文件导入数据
    datafile = './work/housing.data'
    data = np.fromfile(datafile, sep=' ')

    feature_names = [ 'CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV' ]
    feature_num = len(feature_names)

    # 将原始数据进行Reshape，变成[N, 14]这样的形状
    data = data.reshape([data.shape[0] // feature_num, feature_num])

    # 将原数据集拆分成训练集和测试集
    # 这里使用80%的数据做训练，20%的数据做测试
    # 测试集和训练集必须是没有交集的
    ratio = 0.8
    offset = int(data.shape[0] * ratio)
    training_data = data[:offset]

    # 计算train数据集的最大值，最小值，平均值
    maximums, minimums, avgs = training_data.max(axis=0), training_data.min(axis=0), training_data.sum(axis=0) / training_data.shape[0]

    # 对数据进行归一化处理
    for i in range(feature_num):
        #print(maximums[i], minimums[i], avgs[i])
        data[:, i] = (data[:, i] - avgs[i]) / (maximums[i] - minimums[i])

    # 训练集和测试集的划分比例
    training_data = data[:offset]
    test_data = data[offset:]
    return training_data, test_data

# 获取数据
training_data, test_data = load_data()
x = training_data[:, :-1]
y = training_data[:, -1:]


class Network_two_layer(object):
    def __init__(self, num_of_weights):
        np.random.seed(0)
        self.w0 = np.random.randn(num_of_weights, 13)
        self.b0 = np.zeros((1,13))
        self.w1 = np.random.randn(13, 1)
        self.b1 = 0.
        
    def forward(self, x):
        x = np.dot(x, self.w0) + self.b0
        z = np.dot(x, self.w1) + self.b1 
        self.x1 = x
        return z
    
    def loss(self, z, y):
        error = z - y
        num_samples = error.shape[0]
        cost = error * error
        cost = np.sum(cost) / num_samples
        return cost
    
    def gradient(self, x, y):
        z = self.forward(x)
        N = x.shape[0]
        gradient_x1 = 1. / N * np.dot((z-y),self.w1.T)
        self.gradient_w1 = 1. / N * np.dot(self.x1.T,z-y)
        self.gradient_b1 = 1. / N * np.sum(z-y)
        self.gradient_w0 = np.dot(x.T,gradient_x1)
        self.gradient_b0 = np.sum(gradient_x1,axis=0)
        self.gradient_b0 = self.gradient_b0[np.newaxis,:]
    
    def update(self, eta = 0.01):
        self.w1 = self.w1 - eta * self.gradient_w1
        self.b1 = self.b1 - eta * self.gradient_b1
        self.w0 = self.w0 - eta * self.gradient_w0
        self.b0 = self.b0 - eta * self.gradient_b0
            
                
    def train(self, training_data, num_epoches, batch_size=10, eta=0.01):
        n = len(training_data)
        losses = []
        for epoch_id in range(num_epoches):
            # 在每轮迭代开始之前，将训练数据的顺序随机的打乱，
            # 然后再按每次取batch_size条数据的方式取出
            np.random.shuffle(training_data)
            # 将训练数据进行拆分，每个mini_batch包含batch_size条的数据
            mini_batches = [training_data[k:k+batch_size] for k in range(0, n, batch_size)]
            for iter_id, mini_batch in enumerate(mini_batches):
                #print(self.w.shape)
                #print(self.b)
                x = mini_batch[:, :-1]
                y = mini_batch[:, -1:]
                a = self.forward(x)
                loss = self.loss(a, y)
                self.gradient(x, y)
                self.update(eta)
                losses.append(loss)
                print('Epoch {:3d} / iter {:3d}, loss = {:.4f}'.
                                 format(epoch_id, iter_id, loss))
        
        return losses

# 获取数据
train_data, test_data = load_data()

# 创建网络
net = Network_two_layer(13)
# 启动训练
losses = net.train(train_data, num_epoches=50, batch_size=100, eta=0.1)

# 画出损失函数的变化趋势
plot_x = np.arange(len(losses))
plot_y = np.array(losses)
plt.plot(plot_x, plot_y)
plt.show()