更新所有实验程序到正确绘图版本

Author: tsycnh

p2 SGD.py

@@ -0,0 +1,133 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from mpl_toolkits.mplot3d import Axes3D
+import random
+# 本代码是一个最简单的线形回归问题，优化函数为经典的 SGD
+rate = 0.2 # learning rate
+def da(y,y_p,x):
+    return (y-y_p)*(-x)
+
+def db(y,y_p):
+    return (y-y_p)*(-1)
+def calc_loss(a,b,x,y):
+    tmp = y - (a * x + b)
+    tmp = tmp ** 2  # 对矩阵内的每一个元素平方
+    SSE = sum(tmp) / (2 * len(x))
+    return SSE
+def draw_hill(x,y):
+    a = np.linspace(-20,20,100)
+    print(a)
+    b = np.linspace(-20,20,100)
+    x = np.array(x)
+    y = np.array(y)
+
+    allSSE = np.zeros(shape=(len(a),len(b)))
+    for ai in range(0,len(a)):
+        for bi in range(0,len(b)):
+            a0 = a[ai]
+            b0 = b[bi]
+            SSE = calc_loss(a=a0,b=b0,x=x,y=y)
+            allSSE[ai][bi] = SSE
+
+    a,b = np.meshgrid(a, b)
+
+    return [a,b,allSSE]
+
+def shuffle_data(x,y):
+    # 随机打乱x，y的数据，并且保持x和y一一对应
+    seed = random.random()
+    random.seed(seed)
+    random.shuffle(x)
+    random.seed(seed)
+    random.shuffle(y)
+#  模拟数据
+x = [30	,35,37,	59,	70,	76,	88,	100]
+y = [1100,	1423,	1377,	1800,	2304,	2588,	3495,	4839]
+
+# 数据归一化
+x_max = max(x)
+x_min = min(x)
+y_max = max(y)
+y_min = min(y)
+
+for i in range(0,len(x)):
+    x[i] = (x[i] - x_min)/(x_max - x_min)
+    y[i] = (y[i] - y_min)/(y_max - y_min)
+
+[ha,hb,hallSSE] = draw_hill(x,y)
+hallSSE = hallSSE.T# 重要，将所有的losses做一个转置。原因是矩阵是以左上角至右下角顺序排列元素，而绘图是以左下角为原点。
+# 初始化a,b值
+a = 10.0
+b = -20.0
+fig = plt.figure(1, figsize=(12, 8))
+
+# 绘制图1的曲面
+ax = fig.add_subplot(2, 2, 1, projection='3d')
+ax.set_top_view()
+ax.plot_surface(ha, hb, hallSSE, rstride=2, cstride=2, cmap='rainbow')
+
+# 绘制图2的等高线图
+plt.subplot(2,2,2)
+ta = np.linspace(-20, 20, 100)
+tb = np.linspace(-20, 20, 100)
+plt.contourf(ha,hb,hallSSE,15,alpha=0.5,cmap=plt.cm.hot)
+C = plt.contour(ha,hb,hallSSE,15,colors='black')
+plt.clabel(C,inline=True)
+plt.xlabel('a')
+plt.ylabel('b')
+
+plt.ion() # iteration on
+
+all_loss = []
+all_step = []
+last_a = a
+last_b = b
+step = 1
+while step <= 500:
+    loss = 0
+    all_da = 0
+    all_db = 0
+    shuffle_data(x,y)
+    for i in range(0,len(x)):
+        y_p = a*x[i] + b
+        loss = (y[i] - y_p)*(y[i] - y_p)/2
+        all_da = da(y[i],y_p,x[i])
+        all_db = db(y[i],y_p)
+    #loss_ = calc_loss(a = a,b=b,x=np.array(x),y=np.array(y))
+    #loss = loss/len(x)
+
+        # 绘制图1中的loss点
+        ax.scatter(a, b, loss, color='black')
+        # 绘制图2中的loss点
+        plt.subplot(2, 2, 2)
+        plt.scatter(a,b,s=5,color='blue')
+        plt.plot([last_a,a],[last_b,b],color='aqua')
+        # 绘制图3中的回归直线
+        plt.subplot(2, 2, 3)
+        plt.plot(x, y)
+        plt.plot(x, y, 'o')
+        x_ = np.linspace(0, 1, 2)
+        y_draw = a * x_ + b
+        plt.plot(x_, y_draw)
+        # 绘制图4的loss更新曲线
+        all_loss.append(loss)
+        all_step.append(step)
+        plt.subplot(2,2,4)
+        plt.plot(all_step,all_loss,color='orange')
+        plt.xlabel("step")
+        plt.ylabel("loss")
+
+        last_a = a
+        last_b = b
+
+        # 更新参数
+        a = a - rate*all_da
+        b = b - rate*all_db
+
+        if step%1 == 0:
+            print("step: ", step, " loss: ", loss)
+            plt.show()
+            plt.pause(0.01)
+        step = step + 1
+plt.show()
+plt.pause(99999999999)