multiply matrix from and out to files using vectors

matrix_multiply.cpp

#include <cctype>
#include <istream>
#include <algorithm>
#include <bits/chrono.h>
#include <ctime>
#include <iostream>
#include <chrono>
#include <fstream>
#include <string>
#include <vector>



std :: vector<std::vector<int>> matrix_mult (std :: vector<std::vector<int>> a,std :: vector<std::vector<int>> b ) ;
int main (){

    std :: ifstream matrix_file  = std::ifstream ("matrix.txt") ; 
    std :: ifstream vector_file  = std::ifstream ("vector.txt") ; 
    std:: vector<std::vector<int>> matrix  ; 
    std:: vector<std::vector<int>> vector ; 
    if (matrix_file.is_open()){
	int index = 0  ;
	while (matrix_file){
	    std :: string line  , input = ""; 
	    std::getline(matrix_file,line);  
	    if (line.size() != 0 ){
		matrix.push_back({});
		for (auto c : line){
		    if (c  == ',')
		    {
			matrix[index].push_back(std::stoi((input)));
			input.clear();  
		    }
		    else if (std::isdigit(c)){
			input.push_back(c);
		    }
		}
		matrix[index].push_back(std::stoi((input)));
		index++;
	    }
	}
    }
    if (vector_file.is_open()){
	int index = 0  ;
	while (vector_file){
	    std :: string line  , input = ""; 
	    std::getline(vector_file,line);  
	    if (line.size() != 0 ){
		vector.push_back({});
		for (auto c : line){
		    if (c  == ',')
		    {
			vector[index].push_back(std::stoi((input)));
			input.clear();  
		    }
		    else if (std::isdigit(c)){
			input.push_back(c);
		    }
		}
		vector[index].push_back(std::stoi((input)));
		index++;
	    }
	}
    }
    auto out = matrix_mult (matrix , vector);
	// for(auto x  : matrix ){
	//     for (auto y : x ){
	// 	std :: cout << "x" <<y;
	//     }
	//     std :: cout << '\n';
	// }
    std :: ofstream output_file = std::ofstream ("output.txt");
    if (output_file.is_open())
    {
	for(auto x  : out ){
	    output_file << "[";
	    for (auto y : x ){
		output_file <<y<< "," ;
	    }
	output_file<< "]\n";
	}
    }
}
std::vector<std::vector<int>> matrix_mult(std::vector<std::vector<int>> m1, std::vector<std::vector<int>> m2) {
    std::vector<std::vector<int>> out(m1.size(), std::vector<int>(m2[0].size() , 0));

    for (std::size_t row = 0; row < out.size(); row++) {
        for (std::size_t col = 0; col < out[0].size(); col++) {
            for (std::size_t inner = 0; inner < m2.size(); inner++) {
                 out[row][col] += m1[row][inner] * m2[inner][col];
            }
        }
    }
    return out;
}