using System using System Collections Generic using System Linq using

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace LU
{

    class Method
    {
        public double[,] _Amatrix = new double[,]
        {
            { 1, 1, -3, 4 },
            { 3, 5,  6, 9 },
            { 1, 1,  2, 2 },
            { 2, 3, -1, 2 }
        };

        public double[] _Barray = new double[] { 1, 2, 3, 4 };

        public double[] _Xarray;
        public double[] _Yarray;

        public double[,] _Lmatrix = new double[,]
        { 
            { 1, 0, 0 , 0 },
            { 1, 1, 0, 0 },
            { 1, 1, 1, 0 },
            { 1, 1, 1, 1 }
        };

        public double[,] _Umatrix;
         
        public void LU()
        {
            _Umatrix = new double[_Amatrix.GetLength(0), _Amatrix.GetLength(1)];
            _Umatrix = _Amatrix;

            int n = _Amatrix.GetLength(0);

            for (int i = 0; i < n; i++)
            {
                for (int j = i; j < n; j++)
                {
                    _Lmatrix[j, i] = _Umatrix[j, i] / _Umatrix[i, i];
                }
            }

            for (int k = 1; k < n; k++)
            {
                for (int i = k - 1; i < n; i++)
                {
                    for (int j = i; j < n; j++)
                    {
                        _Lmatrix[j, i] = _Umatrix[j, i] / _Umatrix[i, i];
                    }
                }

                for (int i = k; i < n; i++)
                {
                    for (int j = k - 1; j < n; j++)
                    {
                        _Umatrix[i, j] = _Umatrix[i, j] - _Lmatrix[i, k - 1] * _Umatrix[k - 1, j];
                    }
                }
            }
        }

        public void solution()
        {
            _Yarray = new double[_Barray.Length];
            _Xarray = new double[_Barray.Length];

            for (int i = 0; i < _Barray.Length; i++)
            {
                _Yarray[i] = 0;
                _Xarray[i] = 0;
            }

            for (int i = 0; i < _Lmatrix.GetLength(0); ++i)
            {
                double sum = 0;
                for (int k = 0; k < i; ++k)
                {
                    sum += _Lmatrix[i, k] * _Yarray[k];
                }
                _Yarray[i] = (_Barray[i] - sum) / _Lmatrix[i, i];
            }

            for (int i = _Umatrix.GetLength(0) - 1; i >= 0; i--)
            {
                double sum = 0;
                for (int k = _Umatrix.GetLength(0) - 1; k >= i; k--)
                {
                    sum += _Umatrix[i, k] * _Xarray[k];
                }
                _Xarray[i] = (_Yarray[i] - sum) / _Umatrix[i, i];
            }
        }
    }

    class Program
    {
        static void Main(string[] args)
        {
            Method method = new Method();


            Console.WriteLine("Исходная марица:");

            for (int i = 0; i < method._Amatrix.GetLength(0); i++)
            {
                for (int j = 0; j < method._Amatrix.GetLength(1); j++)
                {
                    Console.Write("{0:f1} \t", method._Amatrix[i, j]);
                }
                Console.WriteLine();
            }

            method.LU();

            Console.WriteLine();

            Console.WriteLine();
            Console.WriteLine("L матрица:");

            for (int i = 0; i < method._Amatrix.GetLength(0); i++)
            {
                for (int j = 0; j < method._Amatrix.GetLength(1); j++)
                {
                    Console.Write("{0:f2} \t", method._Lmatrix[i, j]);
                }
                Console.WriteLine();
            }

            Console.WriteLine();
            Console.WriteLine();

            Console.WriteLine("U матрица:");


            for (int i = 0; i < method._Amatrix.GetLength(0); i++)
            {
                for (int j = 0; j < method._Amatrix.GetLength(1); j++)
                {
                    Console.Write("{0:f2} \t", method._Umatrix[i, j]);
                }
                Console.WriteLine();
            }

            Console.WriteLine();
            Console.WriteLine();

            method.solution();

            Console.WriteLine("Корни:");


            for (int i = 0; i < method._Barray.Length; i++)
            {
                Console.WriteLine("{0:f3}" , method._Xarray[i]);
            }

            Console.ReadKey();
        }
    }
}