Update README.md

README.md

@@ -1,2 +1,58 @@
 # python
+from numpy import *
 
+
+# 数据集大小 即20个数据点
+m = 20
+# x的坐标以及对应的矩阵
+X0 = ones((m, 1))  # 生成一个m行1列的向量，也就是x0，全是1
+X1 = arange(1, m+1).reshape(m, 1)  # 生成一个m行1列的向量，也就是x1，从1到m
+X = hstack((X0, X1))  # 按照列堆叠形成数组，其实就是样本数据
+# 对应的y坐标
+Y = array([
+    3, 4, 5, 5, 2, 4, 7, 8, 11, 8, 12,
+    11, 13, 13, 16, 17, 18, 17, 19, 21
+]).reshape(m, 1)
+# 学习率
+alpha = 0.01
+
+# 定义代价函数
+def cost_function(theta, X, Y):
+    diff = dot(X, theta) - Y  # dot() 数组需要像矩阵那样相乘，就需要用到dot()
+    return (1/(2*m)) * dot(diff.transpose(), diff)
+
+
+# 定义代价函数对应的梯度函数
+def gradient_function(theta, X, Y):
+    diff = dot(X, theta) - Y
+    return (1/m) * dot(X.transpose(), diff)
+
+######Begin######
+# 梯度下降迭代
+def gradient_descent(X, Y, alpha):
+    theta = array([1, 1]).reshape(2, 1)
+    gradient = gradient_function(theta, X, Y)
+    while not all(abs(gradient) <= 1e-5):
+        theta = theta - alpha * gradient
+        gradient = gradient_function(theta, X, Y)
+    return theta
+
+optimal = gradient_descent(X, Y, alpha)
+print('optimal:', optimal)
+print('cost function:', cost_function(optimal, X, Y)[0][0])
+#######End#######
+
+# 根据数据画出对应的图像
+def plot(X, Y, theta):
+    import matplotlib.pyplot as plt
+    ax = plt.subplot(1,1,1)  
+    ax.scatter(X, Y, s=30, c="red", marker="s")
+    plt.xlabel("X")
+    plt.ylabel("Y")
+    x = arange(0, 21, 0.2)  # x的范围
+    y = theta[0] + theta[1]*x
+    ax.plot(x, y)
+    plt.show()
+
+
+plot(X1, Y, optimal)