生成一段C语言实现的BP神经网络算法

以下是一段C语言实现的BP神经网络算法的代码：

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

#define INPUT_NUM 2
#define HIDDEN_NUM 3
#define OUTPUT_NUM 1
#define LEARNING_RATE 0.5
#define EPOCHS 10000

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

double sigmoid_derivative(double x) {
    return x * (1.0 - x);
}

int main() {
    double inputs[INPUT_NUM][4] = {{0, 0, 1, 1}, {0, 1, 0, 1}};
    double outputs[OUTPUT_NUM][4] = {{0, 1, 1, 0}};
    double hidden_weights[HIDDEN_NUM][INPUT_NUM + 1];
    double output_weights[OUTPUT_NUM][HIDDEN_NUM + 1];
    double hidden_outputs[HIDDEN_NUM];
    double output;
    double error;
    double delta_output;
    double delta_hidden[HIDDEN_NUM];
    double delta_weight;

    // initialize weights
    for (int i = 0; i < HIDDEN_NUM; i++) {
        for (int j = 0; j < INPUT_NUM + 1; j++) {
            hidden_weights[i][j] = ((double) rand() / RAND_MAX) * 2.0 - 1.0;
        }
    }
    for (int i = 0; i < OUTPUT_NUM; i++) {
        for (int j = 0; j < HIDDEN_NUM + 1; j++) {
            output_weights[i][j] = ((double) rand() / RAND_MAX) * 2.0 - 1.0;
        }
    }

    // train
    for (int epoch = 0; epoch < EPOCHS; epoch++) {
        for (int i = 0; i < 4; i++) {
            // forward pass
            for (int j = 0; j < HIDDEN_NUM; j++) {
                double sum = hidden_weights[j][0];
                for (int k = 0; k < INPUT_NUM; k++) {
                    sum += hidden_weights[j][k + 1] * inputs[k][i];
                }
                hidden_outputs[j] = sigmoid(sum);
            }
            double sum = output_weights[0][0];
            for (int j = 0; j < HIDDEN_NUM; j++) {
                sum += output_weights[0][j + 1] * hidden_outputs[j];
            }
            output = sigmoid(sum);

            // backward pass
            error = outputs[0][i] - output;
            delta_output = error * sigmoid_derivative(output);
            for (int j = 0; j < HIDDEN_NUM; j++) {
                delta_hidden[j] = delta_output * output_weights[0][j + 1] * sigmoid_derivative(hidden_outputs[j]);
            }
            for (int j = 0; j < HIDDEN_NUM; j++) {
                delta_weight = LEARNING_RATE * delta_hidden[j];
                hidden_weights[j][0] += delta_weight;
                for (int k = 0; k < INPUT_NUM; k++) {
                    hidden_weights[j][k + 1] += delta_weight * inputs[k][i];
                }
            }
            delta_weight = LEARNING_RATE * delta_output;
            output_weights[0][0] += delta_weight;
            for (int j = 0; j < HIDDEN_NUM; j++) {
                output_weights[0][j + 1] += delta_weight * hidden_outputs[j];
            }
        }
    }

    // test
    for (int i = 0; i < 4; i++) {
        for (int j = 0; j < HIDDEN_NUM; j++) {
            double sum = hidden_weights[j][0];
            for (int k = 0; k < INPUT_NUM; k++) {
                sum += hidden_weights[j][k + 1] * inputs[k][i];
            }
            hidden_outputs[j] = sigmoid(sum);
        }
        double sum = output_weights[0][0];
        for (int j = 0; j < HIDDEN_NUM; j++) {
            sum += output_weights[0][j + 1] * hidden_outputs[j];
        }
        output = sigmoid(sum);
        printf("Input: %lf %lf, Output: %lf\n", inputs[0][i], inputs[1][i], output);
    }

    return 0;
}

这段代码实现了一个简单的BP神经网络，用于解决异或问题。它包括了前向传播、反向传播和权重更新三个步骤，以及一个简单的测试过程。