作业五：训练一个逻辑与门和逻辑或门
- 训练数据
| Example |
1 |
2 |
3 |
4 |
| x |
0 |
0 |
1 |
1 |
| y |
0 |
1 |
0 |
1 |
| 逻辑与门 |
0 |
0 |
0 |
1 |
| 逻辑或门 |
0 |
1 |
1 |
1 |
- 检测数据
# test AND gate
input number one:1
input number two:1
[[0.99672156]]
True
# test OR gate
input number one:1
input number two:0
[[0.99822654]]
True
- 代码
import numpy as np
import matplotlib.pyplot as plt
from base import *
# x1=0,x2=0,y=0
# x1=0,x2=1,y=0
# x1=1,x2=0,y=0
# x1=1,x2=1,y=1
def Read_AND_Data(gate):
X = np.array([0, 0, 1, 1, 0, 1, 0, 1]).reshape(2, 4)
if gate == 'and':
Y = np.array([0, 0, 0, 1]).reshape(1, 4)
elif gate == 'or':
Y = np.array([0, 1, 1, 1]).reshape(1, 4)
return X,Y
def Test(W,B):
n1 = input("input number one:")
x1 = float(n1)
n2 = input("input number two:")
x2 = float(n2)
a = ForwardCalculationBatch(W, B, np.array([x1,x2]).reshape(2,1))
print(a)
y = x1 or x2
if np.abs(a-y) < 1e-2:
print("True")
else:
print("False")
if __name__ == '__main__':
# SGD, MiniBatch, FullBatch
# read data X,Y = Read_AND_Data('or')
W, B = train(X, Y, ForwardCalculationBatch, CheckLoss)
print("w=",W)
print("b=",B)
ShowResult(W,B,X,Y,"AND")
# test
while True:
Test(W,B)
import numpy as np
import matplotlib.pyplot as plt
def Sigmoid(x):
s = 1 / (1 + np.exp(-x))
return s
# 前向计算
def ForwardCalculationBatch(W, B, batch_X):
Z = np.dot(W, batch_X) + B
A = Sigmoid(Z)
return A
# 反向计算
def BackPropagationBatch(batch_X, batch_Y, A):
m = batch_X.shape[1]
dZ = A - batch_Y
# dZ列相加，即一行内的所有元素相加
dB = dZ.sum(axis=1, keepdims=True) / m
dW = np.dot(dZ, batch_X.T) / m
return dW, dB
# 更新权重参数
def UpdateWeights(W, B, dW, dB, eta):
W = W - eta * dW
B = B - eta * dB
return W, B
# 计算损失函数值
def CheckLoss(W, B, X, Y):
m = X.shape[1]
A = ForwardCalculationBatch(W, B, X)
p4 = np.multiply(1 - Y, np.log(1 - A))
p5 = np.multiply(Y, np.log(A))
LOSS = np.sum(-(p4 + p5)) # binary classification
loss = LOSS / m
return loss
# 初始化权重值
def InitialWeights(num_input, num_output, method):
W = np.zeros((num_output, num_input))
B = np.zeros((num_output, 1))
return W, B
def train(X, Y, ForwardCalculationBatch, CheckLoss):
num_example = X.shape[1]
num_feature = X.shape[0]
num_category = Y.shape[0]
# hyper parameters
eta = 0.5
max_epoch = 10000
# W(num_category, num_feature), B(num_category, 1)
W, B = InitialWeights(num_feature, num_category, "zero")
# calculate loss to decide the stop condition
loss = 5 # initialize loss (larger than 0)
error = 2e-3 # stop condition
# if num_example=200, batch_size=10, then iteration=200/10=20 for epoch in range(max_epoch):
for i in range(num_example):
# get x and y value for one sample
x = X[:, i].reshape(num_feature, 1)
y = Y[:, i].reshape(1, 1)
# get z from x,y
batch_a = ForwardCalculationBatch(W, B, x)
# calculate gradient of w and b
dW, dB = BackPropagationBatch(x, y, batch_a)
# update w,b
W, B = UpdateWeights(W, B, dW, dB, eta)
# end if
# end for # calculate loss for this batch loss = CheckLoss(W, B, X, Y)
print(epoch, i, loss, W, B)
# end if
if loss < error:
break
# end for
return W, B
def ShowResult(W, B, X, Y, title):
w = -W[0, 0] / W[0, 1]
b = -B[0, 0] / W[0, 1]
x = np.array([0, 1])
y = w * x + b
plt.plot(x, y)
for i in range(X.shape[1]):
if Y[0, i] == 0:
plt.scatter(X[0, i], X[1, i], marker="o", c='b', s=64)
else:
plt.scatter(X[0, i], X[1, i], marker="^", c='r', s=64)
plt.axis([-0.1, 1.1, -0.1, 1.1])
plt.title(title)
plt.show()
- 结果
w= [[11.76694002 11.76546912]]
b= [[-17.81530488]]
w= [[11.74573383 11.74749036]]
b= [[-5.41268583]]
