BP神经网络C语言实现

以下是一个简单的BP神经网络的C语言实现，其中包括了前向传播和反向传播两个过程：

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

#define INPUT_NUM 2 // 输入层节点数
#define HIDDEN_NUM 3 // 隐藏层节点数
#define OUTPUT_NUM 1 // 输出层节点数
#define LEARNING_RATE 0.5 // 学习率
#define EPOCHS 10000 // 迭代次数

// sigmoid函数
double sigmoid(double x) {
    return 1.0 / (1.0 + exp(-x));
}

// 前向传播
void forward(double input[INPUT_NUM], double hidden[HIDDEN_NUM], double output[OUTPUT_NUM], double w1[INPUT_NUM][HIDDEN_NUM], double w2[HIDDEN_NUM][OUTPUT_NUM]) {
    // 计算隐藏层节点的值
    for (int i = 0; i < HIDDEN_NUM; i++) {
        double sum = 0.0;
        for (int j = 0; j < INPUT_NUM; j++) {
            sum += input[j] * w1[j][i];
        }
        hidden[i] = sigmoid(sum);
    }
    // 计算输出层节点的值
    for (int i = 0; i < OUTPUT_NUM; i++) {
        double sum = 0.0;
        for (int j = 0; j < HIDDEN_NUM; j++) {
            sum += hidden[j] * w2[j][i];
        }
        output[i] = sigmoid(sum);
    }
}

// 反向传播
void backward(double input[INPUT_NUM], double hidden[HIDDEN_NUM], double output[OUTPUT_NUM], double target[OUTPUT_NUM], double w1[INPUT_NUM][HIDDEN_NUM], double w2[HIDDEN_NUM][OUTPUT_NUM]) {
    double delta_output[OUTPUT_NUM];
    double delta_hidden[HIDDEN_NUM];
    // 计算输出层的误差
    for (int i = 0; i < OUTPUT_NUM; i++) {
        delta_output[i] = (target[i] - output[i]) * output[i] * (1.0 - output[i]);
    }
    // 计算隐藏层的误差
    for (int i = 0; i < HIDDEN_NUM; i++) {
        double sum = 0.0;
        for (int j = 0; j < OUTPUT_NUM; j++) {
            sum += delta_output[j] * w2[i][j];
        }
        delta_hidden[i] = hidden[i] * (1.0 - hidden[i]) * sum;
    }
    // 更新权重
    for (int i = 0; i < INPUT_NUM; i++) {
        for (int j = 0; j < HIDDEN_NUM; j++) {
            w1[i][j] += LEARNING_RATE * delta_hidden[j] * input[i];
        }
    }
    for (int i = 0; i < HIDDEN_NUM; i++) {
        for (int j = 0; j < OUTPUT_NUM; j++) {
            w2[i][j] += LEARNING_RATE * delta_output[j] * hidden[i];
        }
    }
}

int main() {
    // 初始化权重
    double w1[INPUT_NUM][HIDDEN_NUM];
    double w2[HIDDEN_NUM][OUTPUT_NUM];
    for (int i = 0; i < INPUT_NUM; i++) {
        for (int j = 0; j < HIDDEN_NUM; j++) {
            w1[i][j] = (double)rand() / RAND_MAX - 0.5;
        }
    }
    for (int i = 0; i < HIDDEN_NUM; i++) {
        for (int j = 0; j < OUTPUT_NUM; j++) {
            w2[i][j] = (double)rand() / RAND_MAX - 0.5;
        }
    }
    // 训练数据
    double input[4][INPUT_NUM] = {{0, 0}, {0, 1}, {1, 0}, {1, 1}};
    double target[4][OUTPUT_NUM] = {{0}, {1}, {1}, {0}};
    // 迭代训练
    for (int epoch = 0; epoch < EPOCHS; epoch++) {
        double error = 0.0;
        for (int i = 0; i < 4; i++) {
            double hidden[HIDDEN_NUM];
            double output[OUTPUT_NUM];
            forward(input[i], hidden, output, w1, w2);
            backward(input[i], hidden, output, target[i], w1, w2);
            error += 0.5 * (target[i][0] - output[0]) * (target[i][0] - output[0]);
        }
        if (epoch % 1000 == 0) {
            printf("Epoch %d, error = %f\n", epoch, error);
        }
    }
    // 测试数据
    double test_input[4][INPUT_NUM] = {{0, 0}, {0, 1}, {1, 0}, {1, 1}};
    for (int i = 0; i < 4; i++) {
        double hidden[HIDDEN_NUM];
        double output[OUTPUT_NUM];
        forward(test_input[i], hidden, output, w1, w2);
        printf("%f %f -> %f\n", test_input[i][0], test_input[i][1], output[0]);
    }
    return 0;
}