# -*- coding: utf-8 -*-
"""
Created on Mon Oct 1 22:15:54 2018
@author: Heisenberg
"""
import numpy as np
import math
import random
import string
import matplotlib as mpl
import matplotlib.pyplot as plt
#random.seed(0) #当我们设置相同的seed，每次生成的随机数相同。如果不设置seed，则每次会生成不同的随机数
#参考https://blog.csdn.net/jiangjiang_jian/article/details/79031788
#生成区间[a,b]内的随机数
def random_number(a,b):
return (b-a)*random.random()+a
#生成一个矩阵，大小为m*n,并且设置默认零矩阵
def makematrix(m, n, fill=0.0):
a = []
for i in range(m):
a.append([fill]*n)
return a
#函数sigmoid(),这里采用tanh，因为看起来要比标准的sigmoid函数好看
def sigmoid(x):
return math.tanh(x)
#函数sigmoid的派生函数
def derived_sigmoid(x):
return 1.0 - x**2
#构造三层BP网络架构
class BPNN:
def __init__(self, num_in, num_hidden, num_out):
#输入层，隐藏层，输出层的节点数
self.num_in = num_in + 1 #增加一个偏置结点
self.num_hidden = num_hidden + 1 #增加一个偏置结点
self.num_out = num_out
#激活神经网络的所有节点（向量）
self.active_in = [1.0]*self.num_in
self.active_hidden = [1.0]*self.num_hidden
self.active_out = [1.0]*self.num_out
#创建权重矩阵
self.wight_in = makematrix(self.num_in, self.num_hidden)
self.wight_out = makematrix(self.num_hidden, self.num_out)
#对权值矩阵赋初值
for i in range(self.num_in):
for j in range(self.num_hidden):
self.wight_in[i][j] = random_number(-0.2, 0.2)
for i in range(self.num_hidden):
for j in range(self.num_out):
self.wight_out[i][j] = random_number(-0.2, 0.2)
#最后建立动量因子（矩阵）
self.ci = makematrix(self.num_in, self.num_hidden)
self.co = makematrix(self.num_hidden, self.num_out)
#信号正向传播
def update(self, inputs):
if len(inputs) != self.num_in-1:
raise ValueError('与输入层节点数不符')
#数据输入输入层
for i in range(self.num_in - 1):
#self.active_in[i] = sigmoid(inputs[i]) #或者先在输入层进行数据处理
self.active_in[i] = inputs[i] #active_in[]是输入数据的矩阵
#数据在隐藏层的处理
for i in range(self.num_hidden - 1):
sum = 0.0
for j in range(self.num_in):
sum = sum + self.active_in[i] * self.wight_in[j][i]
self.active_hidden[i] = sigmoid(sum) #active_hidden[]是处理完输入数据之后存储，作为输出层的输入数据
#数据在输出层的处理
for i in range(self.num_out):
sum = 0.0
for j in range(self.num_hidden):
sum = sum + self.active_hidden[j]*self.wight_out[j][i]
self.active_out[i] = sigmoid(sum) #与上同理
return self.active_out[:]
#误差反向传播
def errorbackpropagate(self, targets, lr, m): #lr是学习率， m是动量因子
if len(targets) != self.num_out:
raise ValueError('与输出层节点数不符！')
#首先计算输出层的误差
out_deltas = [0.0]*self.num_out
for i in range(self.num_out):
error = targets[i] - self.active_out[i]
out_deltas[i] = derived_sigmoid(self.active_out[i])*error
#然后计算隐藏层误差
hidden_deltas = [0.0]*self.num_hidden
for i in range(self.num_hidden):
error = 0.0
for j in range(self.num_out):
error = error + out_deltas[j]* self.wight_out[i][j]
hidden_deltas[i] = derived_sigmoid(self.active_hidden[i])*error
#首先更新输出层权值
for i in range(self.num_hidden):
for j in range(self.num_out):
change = out_deltas[j]*self.active_hidden[i]
self.wight_out[i][j] = self.wight_out[i][j] + lr*change + m*self.co[i][j]
self.co[i][j] = change
#然后更新输入层权值
for i in range(self.num_in):
for i in range(self.num_hidden):
change = hidden_deltas[j]*self.active_in[i]
self.wight_in[i][j] = self.wight_in[i][j] + lr*change + m* self.ci[i][j]
self.ci[i][j] = change
#计算总误差
error = 0.0
for i in range(len(targets)):
error = error + 0.5*(targets[i] - self.active_out[i])**2
return error
#测试
def test(self, patterns):
for i in patterns:
print(i[0], '->', self.update(i[0]))
#权重
def weights(self):
print("输入层权重")
for i in range(self.num_in):
print(self.wight_in[i])
print("输出层权重")
for i in range(self.num_hidden):
print(self.wight_out[i])
def train(self, pattern, itera=100000, lr = 0.1, m=0.1):
for i in range(itera):
error = 0.0
for j in pattern:
inputs = j[0]
targets = j[1]
self.update(inputs)
error = error + self.errorbackpropagate(targets, lr, m)
if i % 100 == 0:
print('误差 %-.5f' % error)
#实例
def demo():
patt = [
[[1,2,5],[0]],
[[1,3,4],[1]],
[[1,6,2],[1]],
[[1,5,1],[0]],
[[1,8,4],[1]]
]
#创建神经网络，3个输入节点，3个隐藏层节点，1个输出层节点
n = BPNN(3, 3, 1)
#训练神经网络
n.train(patt)
#测试神经网络
n.test(patt)
#查阅权重值
n.weights()
if __name__ == '__main__':
demo()
