using System;

public class Program

{

    static int MAX = 100;

    static String s = "";

    static Tuple<int[,],int[,]> luDecomposition(int[, ] mat, int n)

    {

        // https://www.geeksforgeeks.org/doolittle-algorithm-lu-decomposition/

        int[, ] lower = new int[n, n];

        int[, ] upper = new int[n, n];

        // Decomposing matrix into Upper and Lower

        // triangular matrix

        for (int i = 0; i < n; i++) 

        {

            // Upper Triangular

            for (int k = i; k < n; k++) 

            {

                // Summation of L(i, j) * U(j, k)

                int sum = 0;

                for (int j = 0; j < i; j++)

                    sum += (lower[i, j] * upper[j, k]);

                // Evaluating U(i, k)

                upper[i, k] = mat[i, k] - sum;

            }

            // Lower Triangular

            for (int k = i; k < n; k++) 

            {

                if (i == k)

                    lower[i, i] = 1; // Diagonal as 1

                else

                {

                    // Summation of L(k, j) * U(j, i)

                    int sum = 0;

                    for (int j = 0; j < i; j++)

                        sum += (lower[k, j] * upper[j, i]);

                    // Evaluating L(k, i)

                    lower[k, i]

                        = (mat[k, i] - sum) / upper[i, i];

                }

            }

        }

        return Tuple.Create(lower,upper);

​

    }

    static String setw(int noOfSpace)

    {

        s = "";

        for (int i = 0; i < noOfSpace; i++)

            s += " ";

        return s;

    }

    static void printmatrix(int[,] mat, int n)

    {

        for (int i = 0; i < n; i++) 

        {

            for (int j = 0; j < n; j++)

            {

                Console.Write(setw(4) + mat[i, j] + "\t");

            }

            Console.Write("\n");

        }   

    }

​

    public static void Main()

    {

​

        int[, ] mat = { { 2, -1, -2 },

                        { -4, 6, 3 },

                        { -4, -2, 8 } };

        var outTuple = luDecomposition(mat, mat.GetLength((0)));

        int[,] L = outTuple.Item1;

        int[,] U = outTuple.Item2;

        Console.WriteLine("A");

        printmatrix(mat, mat.GetLength(0));

        Console.WriteLine("\nL");

        printmatrix(L, L.GetLength(0));

        Console.WriteLine("\nU");

        printmatrix(U, U.GetLength(0));

    }

}