激活函数 sigmoid

# author: Roy.G
import dataset
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D as a3d
xs,ys=dataset.get_beans(100)

# plt.scatter(xs,ys)
b = 0.1
w = 0.1
# z = w*xs+b
# a = 1/(1+np.exp(-z))
# plt.plot(xs,a)
# plt.show()

for k in range(50000):
    for i in range(100):
        x = xs[i]
        y = ys[i]
        #对e=（y-sigmoid(z)**2 的函数进行分解：
        z = w*x+b
        a = 1 / (1 + np.exp(-z))
        e = (y-a)**2
        #分别对每个分解函数进行求导,求de_dw
        de_da = -2*(y-a)
        da_dz = a*(1-a)
        dz_dw = x
        dz_db = 1
        # 求w，b 偏导数
        de_dw = de_da*da_dz*dz_dw
        de_db = de_da*da_dz*dz_db

        alpha=0.05
        w = w - alpha * de_dw
        b = b - alpha * de_db
        z = w * xs + b
        a = 1 / (1 + np.exp(-z))
    if k%100 == 0:
        plt.clf()
        plt.scatter(xs, ys)
        plt.title("size-toxicity function")
        plt.xlabel("beans-size")
        plt.ylabel("toxicity")
        plt.xlim(0,1.5)
        plt.ylim(0,1.5)
        plt.plot(xs,a)
        plt.pause(0.1)