Taking the Inverse of a Matrix Using Gauss-Jordan Method - Prepared for AGU EEE Coma Capsule Integrated Project#1

inverse.cpp

#include <iostream>

/*
    used vectors instead of arrays.
    It's easier to work with vectors
    because of their dynamic size.
    ~ barbarbar338
*/
#include <vector>

using namespace std;

void printMatrix(const vector<vector<double>> &matrix)
{
    for (const auto &row : matrix)
    {
        cout << "| ";
        for (const auto &elem : row)
        {
            cout << elem << "\t";
        }
        cout << "|" << endl;
    }
}

int main()
{
    int n;      // matrix size
    int choice; // user's choice (1, input matrix elements manually; 2, generate random numbers)

    cout << "This program finds the inverse of a square matrix using Gauss-Jordan elimination.";

    // ask for use input to create nxn matrix
    cout << "Enter the square matrix size (n => nxn): ";
    cin >> n;

    cout << n << "x" << n << " matrix will be created. Would you like to enter all the elements by yourself (1) or generate random numbers (2)? (1/2): ";
    cin >> choice;

    // create matrix
    vector<vector<double>> matrix(n, vector<double>(n, 0.0));

    if (choice == 2)
    {
        // Create random elements for the matrix
        srand(time(NULL));
        for (int i = 0; i < n; i++)
            for (int k = 0; k < n; k++)
                matrix[i][k] = rand() % 100;
    }
    else
    {
        // Get all elements from the user
        for (int i = 0; i < n; i++)
        {
            cout << "Enter the elements of the " << i + 1 << ". row:";
            for (int k = 0; k < n; k++)
                cin >> matrix[i][k];
        }
    }

    // Pretty-print the matrix in a table
    cout << "The matrix is:" << endl;
    printMatrix(matrix);

    // Create the nxn identity matrix
    vector<vector<double>> identity(n, vector<double>(n, 0.0));

    for (int i = 0; i < n; i++)
        identity[i][i] = 1.0;

    // Pretty-print the identity matrix in a table
    cout << "The identity matrix is:" << endl;
    printMatrix(identity);

    // Create the augmented [A I] matrix
    vector<vector<double>> augmented(n, vector<double>(n * 2, 0.0));

    for (int i = 0; i < n; i++)
        for (int k = 0; k < n; k++)
            augmented[i][k] = matrix[i][k];

    for (int i = 0; i < n; i++)
        for (int k = n; k < n * 2; k++)
            augmented[i][k] = identity[i][k - n];

    // Pretty-Print the augmented matrix
    cout << "The augmented matrix is:" << endl;
    printMatrix(augmented);

    // Gauss-Jordan elimination to find the inverse matrix
    for (int i = 0; i < n; i++)
    {
        // Scale the current row to make the diagonal element 1
        double scale = augmented[i][i];
        for (int j = 0; j < 2 * n; j++)
            augmented[i][j] /= scale;

        // Eliminate non-diagonal elements in the current column
        for (int j = 0; j < n; j++)
        {
            if (j != i)
            {
                double factor = augmented[j][i];
                for (int k = 0; k < 2 * n; k++)
                    augmented[j][k] -= factor * augmented[i][k];
            }
        }
    }

    // Extract the inverse matrix from the augmented matrix
    vector<vector<double>> inverse(n, vector<double>(n, 0.0));

    for (int i = 0; i < n; i++)
        for (int j = 0; j < n; j++)
            inverse[i][j] = augmented[i][j + n];

    // Pretty-Print the inverse matrix
    cout << "The inverse matrix is:" << endl;
    printMatrix(inverse);

    cout << "This program is prepared by Barış DEMİRCİ & Nuri İNCEÖZ for AGU EEE COMA Capsule Integrated Project 1";
    cout << "Thanks for using our program <3" << endl;
    return 0;
}