C++实现神经BP神经网络

#pragma once
#include<vector>
#include<stdlib.h>
#include<time.h>
#include<cmath>
#include<iostream>
using std::vector;
using std::exp;
using std::cout;
using std::endl;
class BP
{
private:
 int studyNum;//允许学习次数
 double h;//学习率
 double allowError;//允许误差
 vector<int> layerNum;//每层的节点数，不包括常量节点1
 vector<vector<vector<double>>> w;//权重
 vector<vector<vector<double>>> dw;//权重增量
 vector<vector<double>> b;//偏置
 vector<vector<double>> db;//偏置增量
 vector<vector<vector<double>>> a;//节点值
 vector<vector<double>> x;//输入
 vector<vector<double>> y;//期望输出

 void iniwb();//初始化w与b
 void inidwdb();//初始化dw与db
 double sigmoid(double z);//激活函数
 void forward();//前向传播
 void backward();//后向传播
 double Error();//计算误差
public:
 BP(vector<int>const& layer_num, vector<vector<double>>const & input_a0,
 vector<vector<double>> const & output_y, double hh = 0.5, double allerror = 0.001, int studynum = 1000);
 BP();
 void setLayerNumInput(vector<int>const& layer_num, vector<vector<double>> const & input);
 void setOutputy(vector<vector<double>> const & output_y);
 void setHErrorStudyNum(double hh, double allerror,int studynum);
 void run();//运行BP神经网络
 vector<double> predict(vector<double>& input);//使用已经学习好的神经网络进行预测
 ~BP();
};

#include "BP.h"
BP::BP(vector<int>const& layer_num, vector<vector<double>>const & input,
 vector<vector<double>> const & output_y, double hh, double allerror,int studynum)
{
 layerNum = layer_num;
 x = input;//输入多少个节点的数据，每个节点有多少份数据
 y = output_y;
 h = hh;
 allowError = allerror;
 a.resize(layerNum.size());//有这么多层网络节点
 for (int i = 0; i < layerNum.size(); i++)
 {
 a[i].resize(layerNum[i]);//每层网络节点有这么多个节点
 for (int j = 0; j < layerNum[i]; j++)
  a[i][j].resize(input[0].size());
 }
 a[0] = input;
 studyNum = studynum;
}

BP::BP()
{
 layerNum = {};
 a = {};
 y = {};
 h = 0;
 allowError = 0;
}

BP::~BP()
{
}

void BP::setLayerNumInput(vector<int>const& layer_num, vector<vector<double>> const & input)
{
 layerNum = layer_num;
 x = input;
 a.resize(layerNum.size());//有这么多层网络节点
 for (int i = 0; i < layerNum.size(); i++)
 {
 a[i].resize(layerNum[i]);//每层网络节点有这么多个节点
 for (int j = 0; j < layerNum[i]; j++)
  a[i][j].resize(input[0].size());
 }
 a[0] = input;
}


void BP::setOutputy(vector<vector<double>> const & output_y)
{
 y = output_y;
}

void BP::setHErrorStudyNum(double hh, double allerror,int studynum)
{
 h = hh;
 allowError = allerror;
 studyNum = studynum;
}

//初始化权重矩阵
void BP::iniwb()
{
 w.resize(layerNum.size() - 1);
 b.resize(layerNum.size() - 1);
 srand((unsigned)time(NULL));
 //节点层数层数
 for (int l = 0; l < layerNum.size() - 1; l++)
 {
 w[l].resize(layerNum[l + 1]);
 b[l].resize(layerNum[l + 1]);
 //对应后层的节点
 for (int j = 0; j < layerNum[l + 1]; j++)
 {
  w[l][j].resize(layerNum[l]);
  b[l][j] = -1 + 2 * (rand() / RAND_MAX);
  //对应前层的节点
  for (int k = 0; k < layerNum[l]; k++)
  w[l][j][k] = -1 + 2 * (rand() / RAND_MAX);
 }
 }
}


void BP::inidwdb()
{
 dw.resize(layerNum.size() - 1);
 db.resize(layerNum.size() - 1);
 //节点层数层数
 for (int l = 0; l < layerNum.size() - 1; l++)
 {
 dw[l].resize(layerNum[l + 1]);
 db[l].resize(layerNum[l + 1]);
 //对应后层的节点
 for (int j = 0; j < layerNum[l + 1]; j++)
 {
  dw[l][j].resize(layerNum[l]);
  db[l][j] = 0;
  //对应前层的节点
  for (int k = 0; k < layerNum[l]; k++)
  w[l][j][k] = 0;
 }
 }
}

//激活函数
double BP::sigmoid(double z)
{
 return 1.0 / (1 + exp(-z));
}

void BP::forward()
{
 for (int l = 1; l < layerNum.size(); l++)
 {
 for (int i = 0; i < layerNum[l]; i++)
 {
  for (int j = 0; j < x[0].size(); j++)
  {

  a[l][i][j] = 0;//第l层第i个节点第j个数据样本
  //计算变量节点乘权值的和
  for (int k = 0; k < layerNum[l - 1]; k++)
   a[l][i][j] += a[l - 1][k][j] * w[l - 1][i][k];
  //加上节点偏置
  a[l][i][j] += b[l - 1][i];
  a[l][i][j] = sigmoid(a[l][i][j]);
  }
 }
 }
}

void BP::backward()
{
 int xNum = x[0].size();//样本个数
 //daP第l层da，daB第l+1层da
 vector<double> daP, daB;
 

 for (int j = 0; j < xNum; j++)
 {
 //处理最后一层的dw
 daP.clear();
 daP.resize(layerNum[layerNum.size() - 1]);
 for (int i = 0, l = layerNum.size() - 1; i < layerNum[l]; i++)
 {
  daP[i] = a[l][i][j] - y[i][j];
  for (int k = 0; k < layerNum[l - 1]; k++)
  dw[l - 1][i][k] += daP[i] * a[l][i][j] * (1 - a[l][i][j])*a[l - 1][k][j];
  db[l - 1][i] += daP[i] * a[l][i][j] * (1 - a[l][i][j]);
 }

 //处理剩下层的权重w的增量Dw
 for (int l = layerNum.size() - 2; l > 0; l--)
 {
  daB = daP;
  daP.clear();
  daP.resize(layerNum[l]);
  for (int k = 0; k < layerNum[l]; k++)
  {
  daP[k] = 0;
  for (int i = 0; i < layerNum[l + 1]; i++)
   daP[k] += daB[i] * a[l + 1][i][j] * (1 - a[l + 1][i][j])*w[l][i][k];
  //dw
  for (int i = 0; i < layerNum[l - 1]; i++)
   dw[l - 1][k][i] += daP[k] * a[l][k][j] * (1 - a[l][k][j])*a[l - 1][i][j];
  //db
  db[l-1][k] += daP[k] * a[l][k][j] * (1 - a[l][k][j]);
  }
 }

 }
 
 //计算dw与db平均值
 for (int l = 0; l < layerNum.size() - 1; l++)
 {
 //对应后层的节点
 for (int j = 0; j < layerNum[l + 1]; j++)
 {
  db[l][j] = db[l][j] / xNum;
  //对应前层的节点
  for (int k = 0; k < layerNum[l]; k++)
  w[l][j][k] = w[l][j][k] / xNum;
 }
 }

 //更新参数w与b
 for (int l = 0; l < layerNum.size() - 1; l++)
 {
 for (int j = 0; j < layerNum[l + 1]; j++)
 {
  b[l][j] = b[l][j] - h * db[l][j];
  //对应前层的节点
  for (int k = 0; k < layerNum[l]; k++)
  w[l][j][k] = w[l][j][k] - h * dw[l][j][k];
 }
 }
}

double BP::Error()
{
 int l = layerNum.size() - 1;
 double temp = 0, error = 0;
 for (int i = 0; i < layerNum[l]; i++)
 for (int j = 0; j < x[0].size(); j++)
 {
  temp = a[l][i][j] - y[i][j];
  error += temp * temp;
 }
 error = error / x[0].size();//求对每一组样本的误差平均
 error = error / 2;
 cout << error << endl;
 return error;
}

//运行神经网络
void BP::run()
{
 iniwb();
 inidwdb();
 int i = 0;
 for (; i < studyNum; i++)
 {
 forward();
 if (Error() <= allowError)
 {
  cout << "Study Success!" << endl;
  break;
 }
 backward();
 }
 if (i == 10000)
 cout << "Study Failed!" << endl;
}

vector<double> BP::predict(vector<double>& input)
{
 vector<vector<double>> a1;
 a1.resize(layerNum.size());
 for (int l = 0; l < layerNum.size(); l++)
 a1[l].resize(layerNum[l]);
 a1[0] = input;
 for (int l = 1; l < layerNum.size(); l++)
 for (int i = 0; i < layerNum[l]; i++)
 {
  a1[l][i] = 0;//第l层第i个节点第j个数据样本
  //计算变量节点乘权值的和
  for (int k = 0; k < layerNum[l - 1]; k++)
  a1[l][i] += a1[l - 1][k] * w[l - 1][i][k];
  //加上节点偏置
  a1[l][i] += b[l - 1][i];
  a1[l][i] = sigmoid(a1[l][i]);
 }
 return a1[layerNum.size() - 1];
}

#include"BP.h"

int main()
{
 vector<int> layer_num = { 1, 10, 1 };
 vector<vector<double>> input_a0 = { { 1,2,3,4,5,6,7,8,9,10 } };
 vector<vector<double>> output_y = { {0,0,0,0,1,1,1,1,1,1} };

 BP bp(layer_num, input_a0,output_y,0.6,0.001, 2000);
 bp.run();
 for (int j = 0; j < 30; j++)
 {
 vector<double> input = { 0.5*j };
 vector<double> output = bp.predict(input);
 for (auto i : output)
  cout << "j:" << 0.5*j <<" pridict:" << i << " ";
 cout << endl;
 }
 system("pause");
 return 0;
}