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# -*- coding: utf-8 -*-
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"""
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Created on Sun Jun 13 06:23:11 2021
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@author: hzh
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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# 生成100个数据点
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np.random.seed(7)
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X = 2 * np.random.rand(100) # 生成100个随机数，模拟x
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Y = 15 + 3 * X + np.random.randn(100) # 生成100个随机数，模拟y，真实的a=3,b=15
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fig, ax = plt.subplots()
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ax.scatter(X, Y)
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fig.savefig('scatter.pdf')
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fig.show()
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learning_rate = 0.1
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roundN = 7 # 对数据点集的轮数
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np.random.seed(3)
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a = np.random.randn()
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b = np.random.randn()
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print(a)
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print(b)
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# 函数定义求误差的最小值
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def errorCompute(a, b):
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error = 0
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for j in range(len(X)):
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error += 1 / 2 * (a * X[j] + b - Y[j]) ** 2
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return error / len(X)
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# 用梯度下降法求得a,b的值
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# 通过多轮迭代，输出每轮迭代的误差，当误差的变化不大的时候此时的a,b为所求的拟合线的值
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for i in range(roundN):
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for j in range(len(X)):
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if j % 50 == 0:
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print("round=%d,iter=%d,a=%f,b=%f,E=%f" % (i, j, a, b, errorCompute(a, b)))
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gradA = (a * X[j] + b - Y[j]) * X[j] # 对a求偏导的公式
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gradB = a * X[j] + b - Y[j] # 对b求偏导的公式
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a = a - learning_rate * gradA # 迭代公式
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b = b - learning_rate * gradB # 迭代公式
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print(a, b) # 输出a,b的值
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# 下面绘制图形
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maxX = max(X)
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minX = min(X)
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maxY = max(Y)
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minY = min(Y)
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X_fit = np.arange(minX, maxX, 0.01)
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Y_fit = a * X_fit + b # 梯度下降法得到的拟合线的方程
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plt.plot(X, Y, '.') # 散点图100个点
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plt.plot(X_fit, Y_fit, 'r-', label='Gradient Descent') # 拟合线
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plt.plot(X_fit, 15 + 3 * X_fit, 'b-', label='True') # 实际的线
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plt.legend() # 显示图例
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plt.show()
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# 练习题：
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#################begin##################
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# 模拟函数y=10x+30,生成100个数据点坐标。
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# 请用梯度下降法拟合出数据点隐含的线性函数y=ax+b，求出a,b值。
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# 数据拟合2
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# 模拟二元函数f(x,y)=5*x+10*y+30,生成1000个数据点坐标。
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# 用梯度下降法拟合出数据点隐含的线性函数f(x,y)=w1*x+w2*y+b的
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# w1,w2,b值
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# 线性预测
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import numpy as np
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from sklearn.model_selection import train_test_split
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# 数据处理
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data = np.loadtxt('advertising.txt', delimiter=',')
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print(data)
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X = data[:, 0:-1]
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y = data[:, -1]
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X = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0)) # 归一化处理
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# print(X)
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# 分割训练与测试
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X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=42)
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# 梯度下降法，y=w1*x1+w2*x2+w3*x3+b
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# 初始化
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np.random.seed(10)
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w1, w2, w3, w4, b = np.random.randn(5)
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lr = 0.001 # 0.00001
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rounds = 1000 # 300,0.001 ,4.54
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def computeErr(X, y): # 误差计算
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err = 0
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for i in range(len(X)):
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err += 1 / 2 * (X[i, 0] * w1 + X[i, 1] * w2 + X[i, 2] * w3 + b - y[i]) ** 2
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return err / len(X)
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for i in range(rounds): # 梯度下降法拟合训练集
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for j in range(len(X_train)):
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w1 -= lr * (X_train[j, 0] * w1 + X_train[j, 1] * w2 + X_train[j, 2] * w3 + b - y_train[j]) * X_train[j, 0]
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w2 -= lr * (X_train[j, 0] * w1 + X_train[j, 1] * w2 + X_train[j, 2] * w3 + b - y_train[j]) * X_train[j, 1]
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w3 -= lr * (X_train[j, 0] * w1 + X_train[j, 1] * w2 + X_train[j, 2] * w3 + b - y_train[j]) * X_train[j, 2]
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b -= lr * (X_train[j, 0] * w1 + X_train[j, 1] * w2 + X_train[j, 2] * w3 + b - y_train[j])
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if i % 100 == 0:
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print('第%i轮迭代训练集误差=%.2f' % (i, computeErr(X_train, y_train)))
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# 模型评估
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print('测试集误差：', computeErr(X_test, y_test))
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print('权重：', w1, w2, w3)
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print('截距：', b)
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predict = (X_test * np.array([w1, w2, w3])).sum(axis=1) + b
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print(len(predict))
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mse = ((predict - y_test) ** 2).sum() / len(y_test)
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print('rmse=', mse ** 0.5)
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