话不多说,直接上代码
所有的说明均在代码中
首先是头文件BPNetWork.h
#ifndef BPNETWORK_H #define BPNETWORK_H //所需头文件 #include<math.h> #include<stdio.h> #include<stdlib.h> #include<string.h> #define f(x) Sigmoid(x)//激活函数设定 #define f_(x) Sigmoidf(x)//导函数 typedef struct { double* ws;//权重矩阵 double* bs;//偏置数组 double* os;//输出数组 double* ss;//误差(总误差关于加权和的偏导) } Layer; typedef struct { int lns;//层数 int* ns;//每层神经元的数量 double* is;//神经网络输入 double* ts;//理想输出 Layer* las;//神经网络各个层(不包括输入层) double ln;//学习率 }BPNetWork; //创建神经网络 BPNetWork* BPCreate(int* nums, int len,double ln); //运行一次神经网络 void RunOnce(BPNetWork* network); //载入训练集 void LoadIn(BPNetWork* network, double* input, double* putout); //反向传播一次(训练一次) void TrainOnce(BPNetWork* network); //输出总误差 double ETotal(BPNetWork* network); //sigmoid激活函数 #define Sigmoid(x) (1 / (1 + exp(-(x)))) //sigmoid激活函数的导函数,输入为sigmoid输出 #define Sigmoidf(f) ((f) * (1 - (f))) #define Tanh(x) ((2 / (1 + exp(-2 * (x))))-1) #define Tanhf(f) ((1+(f))*(1-(f))) #endif
然后是程序本体BPNetWork.c
宏定义
#include"BPNetWork.h" //神经网络的层数 #define LS network->lns //输入层神经元的数量 #define INNS network->ns[0] //输入层的第a个输入 #define INS(a) network->is[a-1] //第a个理想输出 #define TAS(a) network->ts[a-1] //输出层神经元的数量 #define OUTNS network->ns[LS-1] //第n层神经元的数量 #define NS(n) network->ns[n-1] //第n层第a个神经元的第p个权重 #define WF(n,a,p) network->las[n-2].ws[(p-1)+(a-1)*NS(n-1)] //第n层的第a个神经元的偏置 #define BF(n,a) network->las[n-2].bs[a-1] //第n层第a个神经元的输出 #define OF(n,a) network->las[n-2].os[a-1] //第n层第a个神经元的误差 #define SF(n,a) network->las[n-2].ss[a-1] //学习率 #define LN network->ln
BPCreate函数:
BPNetWork* BPCreate(int* nums, int len,double ln) { BPNetWork* network = malloc(sizeof(BPNetWork)); network->lns = len; network->ns = malloc(len * sizeof(int)); network->ln = ln; memcpy(network->ns, nums, len * sizeof(int)); // network->is = malloc(nums[0] * sizeof(double)); network->las = malloc(sizeof(Layer) * (len - 1)); network->ts = malloc(sizeof(double) * nums[len - 1]); srand(&network);//用networkd的内存地址做为随机数种子 for (int p = 0; p < len - 1; p++) { int lastnum = nums[p];//上一层的神经元数量 int num = nums[p + 1];//当前层的神经元数量 network->las[p].bs = malloc(sizeof(double) * num); // network->las[p].ws = malloc(sizeof(double) * num * lastnum); // network->las[p].os = malloc(sizeof(double) * num); // network->las[p].ss = malloc(sizeof(double) * num); for (int pp = 0; pp < num; pp++) { //这里rand()/2.0的意思是把整数除整数转换为浮点数除整数 //如果是整数除整数,输出则为带余的商 network->las[p].bs[pp] = rand() / 2.0 / RAND_MAX; for (int ppp = 0; ppp < lastnum; ppp++) { network->las[p].ws[ppp + pp * lastnum] = rand() / 2.0 / RAND_MAX; } } } return network; }
RunOnce函数:
void RunOnce(BPNetWork* network) { //计算输入层到第二层 for (int a = 1; a <= NS(2); a++) { double net = 0; double* o = &OF(2,a);//获取第2层的输出值for (int aa = 1; aa <= INNS; aa++) { net += INS(aa) * WF(2, a, aa);//INS(aa) * WF(2, a, aa); } *o = f(net + BF(2,a)); } for (int n = 2; n <= LS-1; n++) { for (int a = 1; a <= NS(n + 1); a++) {//下一层的神经网络 double net = 0; double* o = &OF(n+1,a);for (int aa = 1; aa <= NS(n); aa++) {//当前层的神经网络 double oo = OF(n, aa); double* ww = &WF(n + 1, a, aa); net += oo * (*ww); } *o = f(net + BF(n + 1, a)); } } }
TrainOnce函数:
void TrainOnce(BPNetWork* network) { //计算输出层的误差函数 for (int a = 1; a <= OUTNS; a++) { double* s = &SF(LS,a);//获取第a个神经元的误差double* b = &BF(LS, a);//获取第a个神经元的偏置 double o = OF(LS, a);//获取第a个神经元的输出 *s = (2.0 / OUTNS) * (o - TAS(a))* f_(o); *b = *b - LN * (*s);//更新偏置 //更新权重 for (int aa = 1; aa <=NS(LS-1) ; aa++) { double* w = &WF(LS, a, aa); *w = *w - LN * (*s) * OF(LS-1, aa); } } //计算隐藏层的误差 for (int a = LS-1; a > 2; a--) { //开始计算第a层每个神经元的误差 for (int n = 1; n <= NS(a); n++) {//当前层 double* s = &SF(a, n);//获取第a个神经元的误差 *s = 0; double* b = &BF(a, n);//获取第a个神经元的偏置 double o = OF(a, n);//获取第a个神经元的输出 for (int nn = 1; nn <= NS(a+1); nn++) {//下一层 double lw = WF(a + 1, nn, n);//获取下一层到当前神经元的偏置 double ls = SF(a + 1, nn);//获取下一层第nn个神经元的误差 *s += ls * lw * f_(o); } *b = *b - LN * (*s);//更新偏置 //更新权重 for (int nn = 1; nn <= NS(a - 1); nn++) {//上一层 double* w = &WF(a, n, nn); *w = *w - LN * (*s) *OF(a - 1, nn); } } } //计算第2层的误差函数 for (int n = 1; n <= NS(2); n++) {//当前层 double* s = &SF(2, n);//获取第a个神经元的误差 *s = 0; double* b = &BF(2, n);//获取第a个神经元的偏置 double o = OF(2, n);//获取第a个神经元的输出 for (int nn = 1; nn <= NS(3); nn++) {//下一层 double lw = WF(3, nn, n);//获取下一层到当前神经元的偏置 double ls = SF(3, nn);//获取下一层第nn个神经元的误差 *s += ls * lw * f_(o); } *b = *b - LN * (*s);//更新偏置 //更新权重 for (int nn = 1; nn <= INNS; nn++) {//上一层 double* w = &WF(2, n, nn); *w = *w - LN * (*s) * INS(nn); } } }
LoadIn函数:
void LoadIn(BPNetWork* network,double* input,double* putout) { memcpy(network->is, input, INNS*sizeof(double)); memcpy(network->ts, putout, OUTNS*sizeof(double)); }
ETotal函数:
double ETotal(BPNetWork* network) { double val = 0; for (int a = 1; a <= OUTNS; a++) { val += ((OF(LS, a) - TAS(a)) * (OF(LS, a) - TAS(a))) / OUTNS; } return val; }
入口函数:
int main() { int a[] = { 1,20,20,1 };//4层神经元,数量分别为1,20,20,1 double in[1] = { 0.9 };//训练样本输入1 double in1[1] = { 0.1 };//训练样本输入2 double in2[1] = { 0.5 };//训练样本输入3 double out[1] = { 0.1 };//理想输出 //神经网络训练目标: //输入任意值,输出0.1 BPNetWork* network = BPCreate(a, 4, 0.5); int c = 1000;//训练1000次 while (c--) { LoadIn(network, in, out); RunOnce(network); TrainOnce(network); LoadIn(network, in1, out); RunOnce(network); TrainOnce(network); LoadIn(network, in2, out); RunOnce(network); TrainOnce(network); } //训练完后来一波测试 double t[1] = { 0.7 };//输入 double o[1] = { 0.2 };//凑数 LoadIn(network, t, o); RunOnce(network); printf("OK\n"); printf("%g\n", ETotal(network)); printf("%g", OF(4, 1)); return 0; }
训练目标:
输入任意数,输出总为0.1
经过1000次训练后的输出:
OK 0.0101097//最终误差 0.0994528//输入0.7,输出约为0.1
