吴裕雄 python深度学习与实践(11)
import numpy as np
from matplotlib import pyplot as plt A = np.array([[5],[4]])
C = np.array([[4],[6]])
B = A.T.dot(C)
AA = np.linalg.inv(A.T.dot(A))
l=AA.dot(B)
P=A.dot(l)
x=np.linspace(-2,2,10)
x.shape=(1,10)
xx=A.dot(x)
fig = plt.figure()
ax= fig.add_subplot(111)
ax.plot(xx[0,:],xx[1,:])
ax.plot(A[0],A[1],'ko') ax.plot([C[0],P[0]],[C[1],P[1]],'r-o')
ax.plot([0,C[0]],[0,C[1]],'m-o') ax.axvline(x=0,color='black')
ax.axhline(y=0,color='black') margin=0.1
ax.text(A[0]+margin, A[1]+margin, r"A",fontsize=20)
ax.text(C[0]+margin, C[1]+margin, r"C",fontsize=20)
ax.text(P[0]+margin, P[1]+margin, r"P",fontsize=20)
ax.text(0+margin,0+margin,r"O",fontsize=20)
ax.text(0+margin,4+margin, r"y",fontsize=20)
ax.text(4+margin,0+margin, r"x",fontsize=20)
plt.xticks(np.arange(-2,3))
plt.yticks(np.arange(-2,3)) ax.axis('equal')
plt.show()
x = [(2, 0, 3), (1, 0, 3), (1, 1, 3), (1,4, 2), (1, 2, 4)]
y = [5, 6, 8, 10, 11] alpha = 0.02
diff = [0, 0]
error0 = 0
error1 = 0
w0 = 0
w1 = 0
w2 = 0 cnt = 0
while True:
cnt += 1
for i in range(len(x)):
diff[0] = (w0 * x[i][0] + w1 * x[i][1] + w2 * x[i][2]) - y[i]
w0 -= alpha * diff[0] * x[i][0]
w1 -= alpha * diff[0] * x[i][1]
w2 -= alpha * diff[0] * x[i][2]
error1 = 0
for lp in range(len(x)):
error1 += (y[lp] - (w0 + w1 * x[lp][1] + w2 * x[lp][2])) ** 2 / 2
if abs(error1 - error0) < 0.002:
break
else:
error0 = error1 print('theta0 : %f, theta1 : %f, theta2 : %f, error1 : %f' % (w0, w1, w2, error1))
print('Done: theta0 : %f, theta1 : %f, theta2 : %f' % (w0, w1, w2))
print('迭代次数: %d' % cnt)
import math
import random
import numpy as np def rand(a, b):
return (b - a) * random.random() + a def make_matrix(m,n,fill=0.0):
mat = []
for i in range(m):
mat.append([fill] * n)
return mat def sigmoid(x):
return 1.0 / (1.0 + math.exp(-x)) def sigmod_derivate(x):
return x * (1 - x) class BPNeuralNetwork: def __init__(self):
self.input_n = 0
self.hidden_n = 0
self.output_n = 0
self.input_cells = []
self.hidden_cells = []
self.output_cells = []
self.input_weights = []
self.output_weights = [] def setup(self,ni,nh,no):
self.input_n = ni + 1
self.hidden_n = nh
self.output_n = no self.input_cells = [1.0] * self.input_n
self.hidden_cells = [1.0] * self.hidden_n
self.output_cells = [1.0] * self.output_n self.input_weights = make_matrix(self.input_n,self.hidden_n)
self.output_weights = make_matrix(self.hidden_n,self.output_n) # random activate
for i in range(self.input_n):
for h in range(self.hidden_n):
self.input_weights[i][h] = rand(-0.2, 0.2)
for h in range(self.hidden_n):
for o in range(self.output_n):
self.output_weights[h][o] = rand(-2.0, 2.0) def predict(self,inputs):
for i in range(self.input_n - 1):
self.input_cells[i] = inputs[i] for j in range(self.hidden_n):
total = 0.0
for i in range(self.input_n):
total += self.input_cells[i] * self.input_weights[i][j]
self.hidden_cells[j] = sigmoid(total) for k in range(self.output_n):
total = 0.0
for j in range(self.hidden_n):
total += self.hidden_cells[j] * self.output_weights[j][k]
self.output_cells[k] = sigmoid(total) return self.output_cells[:] def back_propagate(self,case,label,learn): self.predict(case)
#计算输出层的误差
output_deltas = [0.0] * self.output_n
for k in range(self.output_n):
error = label[k] - self.output_cells[k]
output_deltas[k] = sigmod_derivate(self.output_cells[k]) * error #计算隐藏层的误差
hidden_deltas = [0.0] * self.hidden_n
for j in range(self.hidden_n):
error = 0.0
for k in range(self.output_n):
error += output_deltas[k] * self.output_weights[j][k]
hidden_deltas[j] = sigmod_derivate(self.hidden_cells[j]) * error #更新输出层权重
for j in range(self.hidden_n):
for k in range(self.output_n):
self.output_weights[j][k] += learn * output_deltas[k] * self.hidden_cells[j] #更新隐藏层权重
for i in range(self.input_n):
for j in range(self.hidden_n):
self.input_weights[i][j] += learn * hidden_deltas[j] * self.input_cells[i] error = 0
for o in range(len(label)):
error += 0.5 * (label[o] - self.output_cells[o]) ** 2 return error def train(self,cases,labels,limit = 100,learn = 0.05):
for i in range(limit):
error = 0
for i in range(len(cases)):
label = labels[i]
case = cases[i]
error += self.back_propagate(case, label, learn)
pass def test(self):
cases = [
[0, 0],
[0, 1],
[1, 0],
[1, 1],
]
labels = [[0], [1], [1], [0]]
self.setup(2, 5, 1)
self.train(cases, labels, 100000, 0.001)
for case in cases:
print(self.predict(case)) if __name__ == '__main__':
nn = BPNeuralNetwork()
nn.test()
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