数学建模之：BP神经网络模型Python代码

# -*- 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[j] * 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 j 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()