I am trying to shuffle rows and columns in C++ 11, where the aim is to retain the rows and column names. I am able to generate the shuffled matrix, but the names are not retained.

#include <iostream>
#include <fstream>
#include <vector>
#include <string>
#include <random>
#include <algorithm>
#include <sstream>  // For std::istringstream
#include "util/base.hpp"




void writeMatrix(const std::vector<std::vector<double>>& matrix, const std::string& out_file_name) {
    std::ofstream file(out_file_name);
    for (const auto& row : matrix) {
        for (size_t i = 0; i < row.size(); i++) {
            file << row[i];
            if (i != row.size() - 1) file << "t"; // Use tab as delimiter
        }
        file << "n";
    }
    file.close();
}


// Function to permute a matrix
void permuteMatrix(std::vector<std::vector<double>>& matrix, std::mt19937& g) {
    for (auto& row : matrix) {
        std::shuffle(row.begin(), row.end(), g);
    }
}

int main(int argc, char* argv[]) {
    if (argc < 5) {
        std::cerr << "Usage: " << argv[0] << " <input file> <output file base> <number of permutations> <seed>n";
        return 1;
    }

    std::string inputFile = argv[1];
    std::string outputFileBase = argv[2];
    int numPermutations = std::stoi(argv[3]);
    int seed = std::stoi(argv[4]);
    

    // read file
    std::vector<std::string> annotation_vec;
    std::vector<std::string> gene_name_vec;
    std::vector<std::vector<double>> matrix;
    load(inputFile, annotation_vec, gene_name_vec, matrix);


    // Create a random number generator
    std::mt19937 g(seed);

    // Perform permutations and write to files
    for (int i = 0; i < numPermutations; ++i) {
        auto permutedMatrix = matrix;  // Copy original matrix to preserve it
        permuteMatrix(permutedMatrix, g); // Shuffle each row

        // Create a filename for each permutation
        std::string out_file_name = outputFileBase + "_permutation" + std::to_string(i + 1) + ".txt";
        writeMatrix(permutedMatrix, out_file_name);
    }

    return 0;
}

The base.hpp can be found on github, essentially the aim is to undertake random permutations of the original matrix, and then to undertake pearson/spearman correlation and investigate if the fdr of the random permutated correlation pairs are higher than from a biological sample, as a measure to address the null hypothesis.