Lab

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

namespace ConsoleApplication8
{
    class Program
    {
        const int n = 2;
        const double eps = 1e-11;
        /*Задание функции
         х - столбец значений неизвестных
         i - номер функции в системе*/
        static double func(double[] x, int i)
        {
            switch (i)
            {
                case 0:
                    return (Math.Sin(x[0])+2*(x[1]) - 2); //вычисляем значение первой функции
                case 1:
                    return (Math.Cos(x[1] - 1) + x[0] -0.7);   //вычисляем значение второй функции
            }
            throw new ArgumentException();
        }
        /*Задание якобиана
         * х - столбец значений неизвестных
         * i,j индексы элементов якобиана
         * i - номер строки
         * j - номер столбца
         */
        static double jacobian(double[] x, int i, int j)
        {
            switch (i)
            {
                case 0:
                    switch (j)
                    {
                        case 0:
                            return (Math.Cos(x[0]));
                        case 1:
                            return (2);
                    }
                    break;
                case 1:
                    switch (j)
                    {
                        case 0:
                            return(1);
                        case 1:
                            return(-1 * Math.Sin(x[1] - 1));
                    }
                    break;

            }
            throw new ArgumentException();
        }
        //вывод вектора
        static void vivod_vectr(double[] vect)
        {
            for (int j = 0; j < n; j++)
            {
                Console.WriteLine("x{0} = {1}", j, vect[j]);
            }
        }

        static void simq(int nn, double[,] a, double[] bb)
        {
            const double eps1 = 1e-21;
            double max, u, v;
            int ks, k1;
            double[,] aa = new double[n,n+1];
            for (int i = 0; i < nn; i++)
            {
                aa[i, nn + 1] = bb[i];
            }
            for (int i = 0; i < nn; i++)
            {
                for (int j = 0; j < nn; j++)
                {
                    aa[i, j] = a[i, j];
                }
            }
            for (int i = 0; i < nn; i++)
            {
                max = Math.Abs(aa[i,i]);
                k1 = i;
                for (int l = (i+1); l < nn ; l++)
                {
                    if (Math.Abs(aa[l, i]) > max)
                    {
                        max = Math.Abs(aa[l,i]);
                        k1 = l;
                    }
                }
                if (max < eps1)
                {
                    ks = 1;
                    break;
                }
                else
                    ks = 0;
                if (k1 != i)
                {
                    for (int j = 0; j < (nn+1); j++)
                    {
                        u = aa[i,j];
                        aa[i,j] = aa[k1,j];
                        aa[k1,j] = u;
                    }
                }
                v = aa[i,i];
                for (int j = 0; j < (nn+1); j++)
                {
                   aa[i,j] = aa[i,j]/v;
                }
                for (int l = (i + 1); l < nn; l++)
                {
                    v = aa[l, i];
                    for (int j = (i + 1); j < (nn + 1); j++)
                    {
                        aa[l, j] = aa[l, j] - aa[i, j] * v;
                    }
                }
            }
            bb[nn] = aa[nn, nn + 1];
            for (int i = (nn - 1); i >= 0; i--)
            {
                bb[i] = aa[i, nn + 1];
                for (int j = (i + 1); j < nn; j++)
                {
                    bb[j] = bb[i] - aa[i, j] * bb[j];
                }
            }
        }
        static void Main(string[] args)
        {
            double[,] a = new double[n, n];
            double[] x = new double[n];
            double[] f = new double[n];
            double[] dx = new double[n];
            double max = 0;
            int iter = 0;

            x[0] = 0;
            x[1] = 0;

            do
            {
                vivod_vectr(x);
                Console.WriteLine("nomer iter {0}", iter);
                Console.WriteLine("==============");
                iter++;
                for (int i = 0; i < n; i++)
                {
                    for (int j = 0; j < n; j++)
                    {
                        a[i, j] = jacobian(x,i,j);
                    }
                }
                for (int i = 0; i < n; i++)
                {
                    f[i] = -1 * func(x, i);
                }
                simq(n, a, f);
                dx = f;
                max = Math.Abs(dx[0]);
                for (int i = 0; i < n; i++)
                {
                    if (Math.Abs(dx[i]) > max)
                        max = Math.Abs(dx[i]);
                }
                for (int i = 0; i < n; i++)
                {
                    x[i] = x[i]+dx[i];
                }
            }
            while (max < eps);
        }
    }
}