#include #include #include #include #define INNODE 2 // 输入层神经元个数 #define HIDENODE 10 // 隐藏层神经元个数 #define OUTNODE 1 // 输出层神经元个数 /** * 步长(学习率) */ double StudyRate = 1.6; /** * 允许最大误差 */ double threshold = 1e-4; /** * 最大迭代次数 */ int mostTimes = 1e6; /** * 训练集大小 */ int trainSize = 0; /** * 测试集大小 */ int testSize = 0; /** * 样本 */ typedef struct Sample{ double out[30][OUTNODE]; // 输出 double in[30][INNODE]; // 输入 }Sample; /** * 神经元结点 */ typedef struct Node{ double value; // 当前神经元结点输出的值 double bias; // 当前神经元结点偏偏置值 double bias_delta; // 当前神经元结点偏置值的修正值 double *weight; // 当前神经元结点向下一层结点传播的权值 double *weight_delta; // 当前神经元结点向下一层结点传播的权值的修正值 }Node; /** * 输入层 */ Node inputLayer[INNODE]; /** * 隐藏层 */ Node hideLayer[HIDENODE]; /** * 输出层 */ Node outLayer[OUTNODE]; double Max(double a, double b){ return a > b ? a : b; } /** * 激活函数sigmoid * @param x 输入值 * @return 输出值 */ double sigmoid(double x){ //请补全sigmod函数的计算结果 double S=2/(1+exp(-2*x))-1; return S; } /** * 读取训练集 * @param filename 文件名 * @return 训练集 */ Sample * getTrainData(const char * filename){ Sample * result = (Sample*)malloc(sizeof (Sample)); FILE * file = fopen(filename, "r"); if(file != NULL){ int count = 0; while (fscanf(file, "%lf %lf %lf", &result->in[count][0], &result->in[count][1], &result->out[count][0]) != EOF){ ++count; } trainSize = count; printf("%s The file has been successfully read!\n", filename); fclose(file); return result; } else{ fclose(file); printf("%s Encountered an error while opening the file!\n\a", filename); return NULL; } } /** * 读取测试集 * @param filename 文件名 * @return 测试集 */ Sample * getTestData(const char * filename){ /*在内存中分配足够的空间来存储一个Sample结构,并将指向该内存块的指针存储在result变量中*/ Sample * result = (Sample*)malloc(sizeof (Sample)); FILE * file = fopen(filename, "r");//打开文件 if(file != NULL){ int count=0; // 初始化一个整数变量count,用于跟踪读取的数据行数; while (fscanf(file, "%lf %lf", &result->in[count][0], &result->in[count][1]) != EOF){ ++count; } /*利用while循环从测试集文件中逐行读取两个浮点数,直到读取到文件末尾。 每次成功读取一行数据后,递增count;*/ testSize = count; //将最终的count的值存储在名为testSize的全局变量中,以便后续使用 printf("%s The file has been successfully read!\n", filename); fclose(file); return result; //返回result }else{ fclose(file); printf("%s Encountered an error while opening the file!\n\a", filename); return NULL; } } /** * 打印样本 * @param data 要打印的样本 * @param size 样本大小 */ void printData(Sample * data, int size){ if(data==NULL) printf("Sample is empty!"); else{ for(int i=0;iin[i][0],data->in[i][1],data->out[i][0]); } } /** * 初始化函数 */ void init(){ // 设置时间戳为生成随机序列的种子 srand(time(NULL)); // 输入层的初始化 for (int i = 0; i < INNODE; ++i) { inputLayer[i].weight = (double *)malloc(sizeof (double ) * HIDENODE); inputLayer[i].weight_delta = (double *) malloc(sizeof (double ) * HIDENODE); inputLayer[i].bias = 0.0; inputLayer[i].bias_delta = 0.0; } // 输出层权值初始化 for (int i = 0; i < INNODE; ++i) { for (int j = 0; j < HIDENODE; ++j) { inputLayer[i].weight[j] = rand() % 10000 / (double )10000 * 2 - 1.0; inputLayer[i].weight_delta[j] = 0.0; } } // 初始化隐藏层结点 for (int i = 0; i < HIDENODE; ++i) { /*为隐藏层节点 i 分配了一个 double 类型的数组,用于存储该节点向下一层节点传播的权重。 使用malloc 函数在堆内存中分配足够的空间,以存储 OUTNODE 个 double 类型的权重值。 */ hideLayer[i].weight = (double *)malloc(sizeof (double ) * OUTNODE); /*为隐藏层节点 i 分配了一个用于存储权重修正值的数组。这个数组将在神经网络的训练过程中用于存储权重的更新值。 使用malloc 函数在堆内存中分配足够的空间,以存储 OUTNODE 个 double 类型的权重值。 */ hideLayer[i].weight_delta = (double *) malloc(sizeof (double ) * OUTNODE); /*为隐藏层节点 i 初始化了一个随机的偏置值。 这个值通常是一个在 -1.0 到 1.0 之间的随机数,用于调整该节点的激活函数的阈值。 */ hideLayer[i].bias = rand() % 10000 / (double )10000 * 2 - 1.0; /*初始化了隐藏层节点 i 的偏置值修正值,初始值为0.0。*/ hideLayer[i].bias_delta = 0.0; } // 初始化隐藏层权值 for (int i = 0; i < HIDENODE; ++i) { for (int j = 0; j < OUTNODE; ++j) { hideLayer[i].weight[j] = rand() % 10000 / (double )10000 * 2 - 1.0; hideLayer[i].weight_delta[j] = 0.0; } } for (int i = 0; i < OUTNODE; ++i) { outLayer[i].bias = rand() % 10000 / (double )10000 * 2 - 1.0; outLayer[i].bias_delta = 0.0; } } /** * 重置修正值 */ void resetDelta(){ for (int i = 0; i < INNODE; ++i) { for (int j = 0; j < HIDENODE; ++j) { inputLayer[i].weight_delta[j] = 0.0; } } for (int i = 0; i < HIDENODE; ++i) { hideLayer[i].bias_delta = 0.0; for (int j = 0; j < OUTNODE; ++j) { hideLayer[i].weight_delta[j] = 0.0; } } for (int i = 0; i < OUTNODE; ++i) { outLayer[i].bias_delta = 0.0; } } int main() { // 初始化 init(); // 获取训练集 Sample * trainSample = getTrainData("TrainData.txt"); // printData(trainSample, trainSize); for (int trainTime = 0; trainTime < mostTimes; ++trainTime) { // 重置梯度信息 resetDelta(); // 当前训练最大误差 double error_max = 0.0; // 开始训练(累计bp) for (int currentTrainSample_Pos = 0; currentTrainSample_Pos < trainSize; ++currentTrainSample_Pos) { // 输入自变量 for (int inputLayer_Pos = 0; inputLayer_Pos < INNODE; ++inputLayer_Pos) { inputLayer[inputLayer_Pos].value = trainSample->in[currentTrainSample_Pos][inputLayer_Pos]; } /** ----- 开始正向传播 ----- */ for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) { double sum = 0.0; for (int inputLayer_Pos = 0; inputLayer_Pos < INNODE; ++inputLayer_Pos) { sum += inputLayer[inputLayer_Pos].value * inputLayer[inputLayer_Pos].weight[hideLayer_Pos]; } sum -= hideLayer[hideLayer_Pos].bias; hideLayer[hideLayer_Pos].value = sigmoid(sum); } for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE ; ++outLayer_Pos) { double sum = 0.0; for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) { //计算每一个隐藏层节点的value和权值的乘积,相加得到sum sum += hideLayer[hideLayer_Pos].value * hideLayer[hideLayer_Pos].weight[outLayer_Pos]; } //更新sum,使sum减去偏置值; sum -= outLayer[outLayer_Pos].bias; //利用sigmod函数对得到的sum进行激活,把激活后的结果赋值给对应的输出层节点value(outLayer[outLayer_Pos].value) outLayer[outLayer_Pos].value = sigmoid(sum); } /** ----- 计算误差 ----- */ double error = 0.0; for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) { double temp = fabs(outLayer[outLayer_Pos].value - trainSample->out[currentTrainSample_Pos][outLayer_Pos]); // 损失函数 error += temp * temp / 2.0; } error_max = Max(error_max, error); /** ----- 反向传播 ----- */ for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) { double bias_delta = -(trainSample->out[currentTrainSample_Pos][outLayer_Pos] - outLayer[outLayer_Pos].value) * outLayer[outLayer_Pos].value * (1.0 - outLayer[outLayer_Pos].value); outLayer[outLayer_Pos].bias_delta += bias_delta; } for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) { for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) { double weight_delta = (trainSample->out[currentTrainSample_Pos][outLayer_Pos] - outLayer[outLayer_Pos].value) * outLayer[outLayer_Pos].value * (1.0 - outLayer[outLayer_Pos].value) * hideLayer[hideLayer_Pos].value; hideLayer[hideLayer_Pos].weight_delta[outLayer_Pos] += weight_delta; } } // for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) { double sum = 0.0; for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) { sum += -(trainSample->out[currentTrainSample_Pos][outLayer_Pos] - outLayer[outLayer_Pos].value) * outLayer[outLayer_Pos].value * (1.0 - outLayer[outLayer_Pos].value) * hideLayer[hideLayer_Pos].weight[outLayer_Pos]; } hideLayer[hideLayer_Pos].bias_delta += sum * hideLayer[hideLayer_Pos].value * (1.0 - hideLayer[hideLayer_Pos].value); } for (int inputLayer_Pos = 0; inputLayer_Pos < INNODE; ++inputLayer_Pos) { for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) { double sum = 0.0; for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) { sum += (trainSample->out[currentTrainSample_Pos][outLayer_Pos] - outLayer[outLayer_Pos].value) * outLayer[outLayer_Pos].value * (1.0 - outLayer[outLayer_Pos].value) * hideLayer[hideLayer_Pos].weight[outLayer_Pos]; } inputLayer[inputLayer_Pos].weight_delta[hideLayer_Pos] += sum * hideLayer[hideLayer_Pos].value * (1.0 - hideLayer[hideLayer_Pos].value) * inputLayer[inputLayer_Pos].value; } } } // 判断误差是否达到允许误差范围 if(error_max < threshold){ printf("\a Training completed!Total training count:%d, maximum error is:%f\n", trainTime + 1, error_max); break; } // 误差无法接受,开始修正 for (int inputLayer_Pos = 0; inputLayer_Pos < INNODE; ++inputLayer_Pos) { for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) { inputLayer[inputLayer_Pos].weight[hideLayer_Pos] += StudyRate * inputLayer[inputLayer_Pos].weight_delta[hideLayer_Pos] / (double) trainSize; } } for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) { hideLayer[hideLayer_Pos].bias += StudyRate * hideLayer[hideLayer_Pos].bias_delta / (double )trainSize; for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) { hideLayer[hideLayer_Pos].weight[outLayer_Pos] += StudyRate * hideLayer[hideLayer_Pos].weight_delta[outLayer_Pos] / (double )trainSize; } } for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) { outLayer[outLayer_Pos].bias += StudyRate * outLayer[outLayer_Pos].bias_delta / (double )trainSize; } } // 训练完成,读取测试集 Sample * testSample = getTestData("TestData.txt"); printf("The predicted results are as follows:\n"); for (int currentTestSample_Pos = 0; currentTestSample_Pos < testSize; ++currentTestSample_Pos) { for (int inputLayer_Pos = 0; inputLayer_Pos < INNODE; ++inputLayer_Pos) { inputLayer[inputLayer_Pos].value = testSample->in[currentTestSample_Pos][inputLayer_Pos]; } for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) { double sum = 0.0; for (int inputLayer_Pos = 0; inputLayer_Pos < INNODE; ++inputLayer_Pos) { sum += inputLayer[inputLayer_Pos].value * inputLayer[inputLayer_Pos].weight[hideLayer_Pos]; } sum -= hideLayer[hideLayer_Pos].bias; hideLayer[hideLayer_Pos].value = sigmoid(sum); } for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) { double sum = 0.0; for (int hideLayer_Pos = 0; hideLayer_Pos < HIDENODE; ++hideLayer_Pos) { sum += hideLayer[hideLayer_Pos].value * hideLayer[hideLayer_Pos].weight[outLayer_Pos]; } sum -= outLayer[outLayer_Pos].bias; outLayer[outLayer_Pos].value = sigmoid(sum); } for (int outLayer_Pos = 0; outLayer_Pos < OUTNODE; ++outLayer_Pos) { testSample->out[currentTestSample_Pos][outLayer_Pos] = outLayer[outLayer_Pos].value; } } printData(testSample, testSize); return 0; }