/*28/09/2022 By Eong Koungmeng*/
#include <iostream>
#include <vector>

std::vector<std::vector<float>> GaussianElimination(std::vector<std::vector<float>> matrix)
{
    int rows = matrix.size();
    int cols = matrix[0].size();
    for (int i = 0; i < rows; i++)
    {
        float coefficient1 = matrix[i][i];
        for (int j = 0; j < cols; j++)
        {
            matrix[i][j] /= coefficient1;
        }

        for (int j = 0; j < rows; j++)
        {
            if (j == i) continue;

            float coefficient2 = matrix[j][i];
            for (int k = 0; k < cols; k++)
            {
                matrix[j][k] -=  coefficient2 * matrix[i][k];
            }
        }
    }

    return matrix;
}

void PrintMatrix(std::vector<std::vector<float>> matrix)
{
    for (int i = 0; i < matrix.size(); i++)
    {
        for (int j = 0; j < matrix[0].size(); j++)
        {
            std::cout.width(5); std::cout << matrix[i][j] << "    ";
        }
        std::cout << std::endl;
    }
}

void PrintSE(std::vector<std::vector<float>> matrix)
{
    std::cout << "X = ";
    for (int i = 0; i < matrix.size()-1; i++)
    {
        std::cout << matrix[i][matrix[0].size()-1] << ", ";
    }
    std::cout << matrix[matrix.size() - 1][matrix[0].size() - 1];
    std::cout << std::endl;
}

void PrintInverse(std::vector<std::vector<float>> matrix)
{
    std::cout << "The inverse matrix is\n";
    int rows = matrix.size();
    int cols = matrix[0].size();
    for (int i = 0; i < rows; i++)
    {
        for (int j = rows; j < cols; j++)
        {
            std::cout.width(5); std::cout << matrix[i][j] << "    ";
        }
        std::cout << std::endl;
    }
    std::cout << std::endl;
}
int main()
{
    std::cout << "Result of simultaneous equations with Gaussian Elimination" << std::endl;
    std::vector<std::vector<float>>(matrixA) = { {1, -4, -2, 21}, {2, 1, 2, 3 }, {3, 2, -1, -2} };
    std::vector<std::vector<float>>(ResultMatrixA) = GaussianElimination(matrixA);
    PrintMatrix(ResultMatrixA);
    PrintSE(ResultMatrixA);

    std::cout << std::endl;
    std::cout << std::endl;

    std::cout << "Result of inverse matrix with Gaussian Elimination" << std::endl;
    std::vector<std::vector<float>>(matrixB) = { {-1, 8, -2, 1, 0, 0}, {-6, 49, -10, 0, 1, 0}, {-4, 34, -5, 0, 0, 1} };
    std::vector<std::vector<float>>(ResultMatrixB) = GaussianElimination(matrixB);
    PrintMatrix(ResultMatrixB);
    PrintInverse(ResultMatrixB);

    std::cin.get();

}