//Author : Md Al Masum Bhuiyan

#include <iostream>
#include <cmath>
using namespace std;

#define N 100

class my_matrix
{	//variable declaration
    int max_entries;
    double matrix[N][N];
    double column[N];
    double row[N];
    
  public: 
  	//functions declaration
    void set_values (int _max_entries);
    void set_entries () ; //using prototype
    double norm1 () ;
    double norm2 () ;
    double norm_infinity();
};

void my_matrix::set_values (int _max_entries)
{
  max_entries = _max_entries ;
}

void my_matrix::set_entries ()
{
   //declaring the entries of the 2 dimensional array.
    for (int i = 0 ; i < max_entries ; ++i )
        for (int j = 0 ; j <  max_entries ;++j)
            cin >> matrix[i][j]  ;
}

double my_matrix::norm1()
{
    double max1=0;
    double norm1 =0;
    column[max_entries] = 0;
    for(int i = 0; i < max_entries; ++i){
        for( int j = 0; j < max_entries; ++j){
            column[j] = column[j] + abs(matrix[i][j]); //sum of absolute column entries
        }
    }
   
    for(int i = 0; i < max_entries; ++i){
        if(column[i]>max1){
            max1=column[i];   // the maximum absolute column sum
        }
    }
    return max1; 
}
 
double my_matrix::norm2()
{
    double norm2 =0;
    double  k = 0;
    for (int i = 0 ; i < max_entries ; ++ i){
        for (int j = 0 ; j <  max_entries ;++j){
            k +=matrix[i][j]* matrix[i][j];
        }
	}
	norm2 +=norm2+ sqrt(k);  // the square root of the sum of all the squares
    return norm2;
}

double my_matrix::norm_infinity()
{
    double max=0;
    row[max_entries] = 0;
    for(int i = 0; i < max_entries; ++i){
        for( int j = 0; j < max_entries; ++j){
            row[i] = row[i] + abs(matrix[i][j]); // sum of row entries
        }
    }
        
    for(int i = 0; i < max_entries; ++i){
        if(row[i]>max){
            max=row[i];  // the maximum absolute row sum.
        }
    }
    return max;
}
 

int main (){
  int n ;
  my_matrix mat; // creating object
    
    cout << " This program calculates the norms of a matrix. " << endl;
    cout << " Please enter the dimension of the matrix: " ;
    cin >> n;
    
    mat.set_values (n);

    mat.set_entries();
    
    //calling member functions
    cout << "norm1 of the matrix = " << mat.norm1() << endl;
    cout << "norm2 of the matrix = " << mat.norm2() << endl;
    cout << "norm_inifnity of the matrix = " << mat.norm_infinity() << endl;
    
return 0; 
}