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#include <stdio.h> #include <math.h> #include <stdlib.h> #include <time.h>

#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){ double y;//请补全sigmod函数的计算结果 y=1/(exp(-x)+1); return y; }

/**

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{ return result; 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){ Sample result=(Sample*)malloc(sizeof(Sample));/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/ FILE * file = fopen(filename, "r");//打开文件 if(file != NULL){ int count=0; while(fscanf(file,"%lf %lf",&result->in[count][0],&result->in[count][1])!=EOF) { ++count; } testSize=count; printf("%s The file has been successfully read!\n", filename); fclose(file); return result; } //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

//返回result

else{ fclose(file); printf("%s Encountered an error while opening the file!\n\a", "TextData.txt"); 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{ int i; for(i=0;i<testSize;i++) { printf("%4.3lf %4.3lf %4.3f",data->in[i][0],data->in[i][1],data->out[i][0]); printf("\n"); } } }

/**

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);//开辟了一个数组 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)100002-1.0; /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"); printf("\n"); 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) {
                sum+=hideLayer[hideLayer_Pos].value*hideLayer[hideLayer_Pos].weight[outLayer_Pos];/*计算每一个隐藏层节点的value和权值的乘积，相加得到sum
                
                */
            }
            /*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;

}

步骤6：文字大致描述bp神经网络：通过一些训练数据（包含输入的信息和应该输出的信息），让bp神经网络能够在输入测试数据后，在没有输出范例的情况下按要求输出数据。该训练过程为：先将输入层、隐藏层、输出层的各个数值——值，权重、偏置值等初始化，将输入数据原封不动传递给输入层神经元，每个输入层神经元对于将值按照一定权重传递给隐藏层神经元。每个隐藏层神经元将所接受到的值收集起来，减去事先初始化好的偏置值后，将剩下的值通过sigmod函数映射到【0,1】之间，将映射结果作为自身的值。每一个隐藏层神经元将自身的值按照一定权重传递给输出层神经元，输出层神经元将所接收到的值收集起来，减去自身偏置值后，将剩下的值通过sigmod函数映射到【0,1】之间作为自身的值，即预期输出的值。通过分析该输出与应该输出的数据之间的误差，反向传播，将误差分摊给各个神经元——调整其权重，已达到下一次输入数据后缩小误差的目的。一组训练数据训练完后，倘若最大误差不符合要求，则将进行下一次训练。通过反复训练，将最大误差缩小到要求范围之内，即达成训练学习要求。

实验习题1：适当提高学习率可以加快更新权重值的速度，从而加快训练速度，缩短得到输出数据的时间。实验习题2：适当增加隐藏层神经元个数可以有效减小误差。实验习题3：不同的激活函数直接影响了神经网络的拟合能力和收敛速度。

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