// Решение СЛАУ методом Гауса
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace HM51
{
    class Program
    {
        static void Main(string[] args)
        {
            const int n = 4;
            double[,] A = new double[n, n]
            {
                {0.0, 0.0, 0.0, 1.0},
                {0.0, 0.0, 1.0,0.0},
                {0.0,1.0, 0.0, 0.0},
                {1.0, 0.0, 0.0, 0.0}
            };
            double[] B = new double[n] { 1.0, 1.0, 1.0, 1.0 };
            double[] X = new double[n];
            PrintM("Matrix A                                Vector B", A, B, n);
            Gusev(X, A, B, n);
            Console.WriteLine("Vecrot X");
            for (int i = 0; i < n; i++) Console.WriteLine("{0,8:F2}", X[i]);
            Console.ReadKey();
        }
        //-------------------------------------------------------------------------
        static void PrintM(string text, double[,] A, double[] B, int n)
        {
            Console.WriteLine(text);
            for (int i = 0; i < n; i++)
            {
                for (int g = 0; g < n; g++) Console.Write("{0,8:F2}", A[i, g]);
                Console.WriteLine("{0,14:F2}", B[i]);
            }
        }
        //------------------------------------------------------------------------
        static void Gusev(double[] x, double[,] z, double[] y, int n)
        {
            double[,] a = new double[n, n];
            Array.Copy(z, a, z.Length);
            double[] b = new double[n];
            Array.Copy(y, b, y.Length);
            PrintM("Matrix A                                Vector B", a, b, n);
            for (int k = 0; k < n - 1; k++)                         //цыкл перебора столбцов
            {
                int l = k+1;
                while (a[k, k] == 0)
                    {
                        for (int i = 0; i <l;i++ ) SdvigStrokiVverh(a, b, l, n);
                        l += 1;
                    }
                for (int i = k + 1; i < n; i++)                       //цыкл зануления всех элементов под элементом главной диагонали к текущем столбце
                {
                    double r = a[i, k] / a[k, k];
                    for (int g = k; g < n; g++) a[i, g] -= r * a[k, g];
                    b[i] -= r * b[k];
                }
                PrintM("Gusev", a, b, n);
            }
            //Вычисление корней системы
            x[n - 1] = b[n - 1] / a[n - 1, n - 1];
            for (int i = n - 2; i >= 0; i--)
            {
                double s = 0.0;
                for (int g = i + 1; g < n; g++) s += a[i, g] * x[g];
                x[i] = (b[i] - s) / a[i, i];
            }
        }
        static void SdvigStrokiVverh(double [,] a,double [] b, int l, int n)
        {
            for (int i = 0; i < n; i++)
            {
                double r = a[l,i];
                a[l, i] = a[l-1,i];
                a[l - 1, i] = r;
            }
            double s = b[l];
            b[l] = b[l - 1];
            b[l - 1] = s;
        }
    }
}