BP.h
#pragma once
#include
#include
#include
#include
#include
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 layerNum;
//每层的节点数，不包括常量节点1
vector>> w;
//权重
vector>> dw;
//权重增量
vector> b;
//偏置
vector> db;
//偏置增量
vector>> a;
//节点值
vector> x;
//输入
vector> 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(vectorconst& layer_num, vector>const & input_a0,
vector> const & output_y, double hh = 0.5, double allerror = 0.001, int studynum = 1000);
BP();
void setLayerNumInput(vectorconst& layer_num, vector> const & input);
void setOutputy(vector> const & output_y);
void setHErrorStudyNum(double hh, double allerror,int studynum);
void run();
//运行BP神经网络
vector predict(vector& input);
//使用已经学习好的神经网络进行预测
~BP();
};
BP.cpp
#include "BP.h"
BP::BP(vectorconst& layer_num, vector>const & input,
vector> 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(vectorconst& layer_num, vector> 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> 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 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 BP::predict(vector& input)
{
vector> 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];
} 验证程序：
#include"BP.h"int main()
{
vector layer_num = { 1, 10, 1 };
vector> input_a0 = { { 1,2,3,4,5,6,7,8,9,10 } };
vector> 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 input = { 0.5*j };
vector output = bp.predict(input);
for (auto i : output)
cout << "j:" << 0.5*j <<" pridict:" << i << " ";
cout << endl;
}
system("pause");
return 0;
}
【C++|C++ 实现神经BP神经网络】输出：
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