训练逻辑与门和逻辑或门
作业要求
作业正文
1. 训练一个逻辑与门和逻辑或门,结果及代码形成博客
逻辑与门样本
X1 |
0 |
0 |
1 |
1 |
X2 |
0 |
1 |
0 |
1 |
Y |
0 |
0 |
0 |
1 |
逻辑或门样本
X1 |
0 |
0 |
1 |
1 |
X2 |
0 |
1 |
0 |
1 |
Y |
0 |
1 |
1 |
1 |
代码展示
import numpy as np
import matplotlib.pyplot as plt
import math
def And_Or(key):
X1 =np.array([0,0,1,1])
X2 = np.array([0,1,0,1])
X = np.vstack((X1, X2))
if (key == 'And'):
Y = np.array([0,0,0,1])
elif (key == 'Or'):
Y = np.array([0,1,1,1])
return X, Y
def Initialize(X, m, n):
W = np.zeros((1,n))
B = np.zeros((1,1))
eta = 0.8
max_epoch = 10000
return W, B, eta, max_epoch
def Sigmiod(x):
A = 1/(1+np.exp(-x))
return A
def ForwardCal(W, X, B):
Z = np.dot(W,X) + B
A = Sigmiod(Z)
return Z, A
def CheckLoss(Y, A, m):
p1 = 1 - Y
p2 = np.log(A)
p3 = np.log(1-A)
p4 = np.multiply(Y, p2)
p5 = np.multiply(p1, p3)
Loss = np.sum(-(p4 + p5))
loss = Loss / m
return loss
def BackwardCal(X, Y, A, m):
dZ = A - Y
dB = dZ.sum(axis = 1, keepdims = True)/m
dW = np.dot(dZ, X.T)/m
return dW, dB
def UpdateWeights(eta, dW, dB, W, B):
W = W - eta*dW
B = B - eta*dB
return W, B
def train(key):
X, Y = And_Or(key)
n = X.shape[0]
m = X.shape[1]
W, B, eta, max_epoch = Initialize(X, m, n)
epoch = 0
# while (True):
# epoch = epoch + 1
for epoch in range(max_epoch):
Z, A = ForwardCal(W, X, B)
dW, dB = BackwardCal(X, Y, A, m)
W, B = UpdateWeights(eta, dW, dB, W, B)
loss = CheckLoss(Y, A, m)
if loss <= 1e-2:
break
print(W, B)
print(loss)
print(epoch)
ShowFigure(X, Y, W, B, m)
def ShowFigure(X, Y, W, B, m):
for i in range(m):
if Y[i] == 0:
plt.plot(X[0,i], X[1,i], '.', c='r')
elif Y[i] == 1:
plt.plot(X[0,i], X[1,i], '^', c='g')
a = - (W[0,0] / W[0,1])
b = - (B[0,0] / W[0,1])
x = np.linspace(-0.1,1.1,100)
y = a * x + b
plt.plot(x,y)
plt.axis([-0.1,1.1,-0.1,1.1])
plt.show()
if __name__=='__main__':
key = 'Or' #逻辑与门将Or换为And
train(key)
训练结果
- 逻辑或门
w = [8.51697047, 8.51697047]
b = -3.79279452
loss = 0.009999219577877546
epoch = 1163
![](https://img2018.cnblogs.com/blog/1612789/201904/1612789-20190407173200217-836439622.png)
- 逻辑与门
w = [8.53544939, 8.53544939]
b = -12.97388027
loss = 0.009999210510001869
epoch = 2171
![](https://img2018.cnblogs.com/blog/1612789/201904/1612789-20190407173515324-1836848475.png)