写一个c++代码：以cnn为基础的数字识别

好的，以下是一个基于CNN的数字识别的C++代码示例：

#include <iostream>
#include <fstream>
#include <cmath>
#include <vector>

using namespace std;

// 图像大小
const int IMAGE_SIZE = 28;

// 卷积层参数
const int CONV_KERNEL_SIZE = 5; // 卷积核大小
const int CONV_KERNEL_NUM = 8; // 卷积核数量
const int CONV_STRIDE = 1; // 卷积步长
const int CONV_PADDING = 2; // 卷积填充

// 池化层参数
const int POOL_KERNEL_SIZE = 2; // 池化核大小
const int POOL_STRIDE = 2; // 池化步长

// 全连接层参数
const int FC_INPUT_SIZE = 12 * 12 * 8; // 全连接层输入大小
const int FC_HIDDEN_SIZE = 10; // 全连接层隐藏层大小
const int FC_OUTPUT_SIZE = 10; // 全连接层输出大小

// 激活函数
double relu(double x) {
    return max(x, 0.0);
}

// 卷积操作
void convolution(vector<vector<double>>& input, vector<vector<double>>& output,
                 vector<vector<vector<double>>>& kernels, int kernel_num) {
    int input_size = input.size();
    int kernel_size = kernels[0].size();
    int output_size = output.size();
    for (int i = 0; i < output_size; i++) {
        for (int j = 0; j < output_size; j++) {
            double sum = 0.0;
            for (int k = 0; k < kernel_size; k++) {
                for (int l = 0; l < kernel_size; l++) {
                    sum += input[i * CONV_STRIDE + k][j * CONV_STRIDE + l] *
                           kernels[kernel_num][k][l];
                }
            }
            output[i][j] = relu(sum);
        }
    }
}

// 池化操作
void pooling(vector<vector<double>>& input, vector<vector<double>>& output) {
    int input_size = input.size();
    int output_size = output.size();
    for (int i = 0; i < output_size; i++) {
        for (int j = 0; j < output_size; j++) {
            double max_val = 0.0;
            for (int k = 0; k < POOL_KERNEL_SIZE; k++) {
                for (int l = 0; l < POOL_KERNEL_SIZE; l++) {
                    max_val = max(max_val, input[i * POOL_STRIDE + k][j * POOL_STRIDE + l]);
                }
            }
            output[i][j] = max_val;
        }
    }
}

// 全连接层操作
void fully_connected(vector<double>& input, vector<double>& output,
                     vector<vector<double>>& weights, vector<double>& biases) {
    for (int i = 0; i < FC_HIDDEN_SIZE; i++) {
        double sum = 0.0;
        for (int j = 0; j < FC_INPUT_SIZE; j++) {
            sum += input[j] * weights[j][i];
        }
        output[i] = relu(sum + biases[i]);
    }
    for (int i = 0; i < FC_OUTPUT_SIZE; i++) {
        double sum = 0.0;
        for (int j = 0; j < FC_HIDDEN_SIZE; j++) {
            sum += output[j] * weights[FC_INPUT_SIZE + j][i];
        }
        output[i] = sum + biases[FC_HIDDEN_SIZE + i];
    }
}

// 加载模型参数
void load_model(vector<vector<vector<double>>>& conv_kernels, vector<vector<double>>& fc_weights,
                vector<double>& fc_biases) {
    ifstream in_conv_kernels("conv_kernels.bin", ios::binary);
    for (int i = 0; i < CONV_KERNEL_NUM; i++) {
        vector<vector<double>> kernel(CONV_KERNEL_SIZE, vector<double>(CONV_KERNEL_SIZE));
        for (int j = 0; j < CONV_KERNEL_SIZE; j++) {
            for (int k = 0; k < CONV_KERNEL_SIZE; k++) {
                in_conv_kernels.read((char*)&kernel[j][k], sizeof(double));
            }
        }
        conv_kernels.push_back(kernel);
    }
    ifstream in_fc_weights("fc_weights.bin", ios::binary);
    for (int i = 0; i < FC_INPUT_SIZE + FC_HIDDEN_SIZE; i++) {
        vector<double> weight(FC_OUTPUT_SIZE);
        for (int j = 0; j < FC_OUTPUT_SIZE; j++) {
            in_fc_weights.read((char*)&weight[j], sizeof(double));
        }
        fc_weights.push_back(weight);
    }
    ifstream in_fc_biases("fc_biases.bin", ios::binary);
    for (int i = 0; i < FC_HIDDEN_SIZE + FC_OUTPUT_SIZE; i++) {
        double bias;
        in_fc_biases.read((char*)&bias, sizeof(double));
        fc_biases.push_back(bias);
    }
}

int main() {
    // 读取图像数据
    vector<vector<double>> image(IMAGE_SIZE, vector<double>(IMAGE_SIZE));
    ifstream in_image("image.bin", ios::binary);
    for (int i = 0; i < IMAGE_SIZE; i++) {
        for (int j = 0; j < IMAGE_SIZE; j++) {
            in_image.read((char*)&image[i][j], sizeof(double));
        }
    }

    // 定义卷积层、池化层、全连接层输出
    vector<vector<vector<double>>> conv_outputs(CONV_KERNEL_NUM, vector<vector<double>>(IMAGE_SIZE, vector<double>(IMAGE_SIZE)));
    vector<vector<double>> pool_output(IMAGE_SIZE / POOL_STRIDE, vector<double>(IMAGE_SIZE / POOL_STRIDE));
    vector<double> fc_output(FC_OUTPUT_SIZE);

    // 加载模型参数
    vector<vector<vector<double>>> conv_kernels;
    vector<vector<double>> fc_weights;
    vector<double> fc_biases;
    load_model(conv_kernels, fc_weights, fc_biases);

    // 卷积层、池化层、全连接层前向传播
    for (int i = 0; i < CONV_KERNEL_NUM; i++) {
        convolution(image, conv_outputs[i], conv_kernels, i);
    }
    pooling(conv_outputs[0], pool_output);
    fully_connected(vector<double>(pool_output.begin(), pool_output.end()).data(),
                    fc_output, fc_weights, fc_biases);

    // 输出预测结果
    int pred_digit = 0;
    double max_prob = 0.0;
    for (int i = 0; i < FC_OUTPUT_SIZE; i++) {
        if (fc_output[i] > max_prob) {
            pred_digit = i;
            max_prob = fc_output[i];
        }
    }
    cout << "Predicted digit: " << pred_digit << endl;

    return 0;
}

这段代码实现了一个简单的基于CNN的数字识别模型，包括卷积层、池化层和全连接层。模型参数通过从文件中读取得到，在程序中进行前向传播，最终输出预测结果。注意，由于缺少预处理和后处理的代码，该模型并不能直接用于实际应用，仅供参考。