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

namespace ConsoleApplication1
{
    public class Interpolacja_funkcje_sklejane
    {

        private static double eps = 1e-10;
        private static double[] xi = { -4, -2, 0, 2, 4 };

        public double pkt(double xx, double[] x)
        {
            int lp = 0;
            double w = 0;
            for (int i = 0; i < xi.Length - 1; i++)
            {
                if (xx >= xi[i] && xx < xi[i + 1])
                {
                    lp = i + 1;
                }
            }

            for (int i = 0; i < 4; i++)
            {
                w += x[i] * Math.Pow(xx, i);
            }
            for (int j = 4; j < 4 + lp - 1; j++)
            {
                w += x[j] * Math.Pow((xx - xi[j - 3]), 3);
            }
            return w;
        }

        public double[] gauss(double[][] tabA, double[] tabB)
        {
            int N = tabB.Length;

            for (int p = 0; p < N; p++)
            {


                int max = p;
                for (int i = p + 1; i < N; i++)
                {
                    if (Math.Abs(tabA[i][p]) > Math.Abs(tabA[max][p]))
                    {
                        max = i;
                    }
                }
                double[] temp = tabA[p];
                tabA[p] = tabA[max];
                tabA[max] = temp;

                double t = tabB[p];
                tabB[p] = tabB[max];
                tabB[max] = t;



                for (int i = p + 1; i < N; i++)
                {
                    double alpha = tabA[i][p] / tabA[p][p];
                    tabB[i] -= alpha * tabB[p];
                    for (int j = p; j < N; j++)
                    {
                        tabA[i][j] -= alpha * tabA[p][j];
                    }
                }
            }


            double[] x = new double[N];
            for (int i = N - 1; i >= 0; i--)
            {
                double sum = 0.0;
                for (int j = i + 1; j < N; j++)
                {
                    sum += tabA[i][j] * x[j];
                }
                x[i] = (tabB[i] - sum) / tabA[i][i];
            }
            return x;
        }
    }





    class Program
    {
        static void Main(string[] args)
        {
            double[] xi = { -4, -2, 0, 2, 4 };
            double[] xii = { -332, -24, 4, -8, -204, 312, -216 };
            double pochodna1 = -4;
            double pochodna2 = 4;
            double wynik = 0;
            int n = xi.Length;
            double[][] S = new double [(n + 2)][n + 2];
            int i, j;
            Interpolacja_funkcje_sklejane funkcyjka = new Interpolacja_funkcje_sklejane();
            for (i = 0; i < n; i++)
            {
                for (j = 0; j < n - 1; j++)
                {
                    S[i][j] = Math.Pow(xi[i], j);

                }
            }

            for (i = 5; i < S.Length - 1; i++)
            {

                for (j = 0; j < S.Length - 3; j++)

                {

                    S[i][j] = j * (Math.Pow(pochodna1, j - 1));

                }

            }

            for (i = 2; i < S.Length - 2; i++)
            {
                double xx;
                xx = xi[i];


                for (j = 4; j < S.Length; j++)

                {
                    S[i][j] = Math.Pow(xx - xi[j - 3], 3);

                }



            }

            for (i = 5; i < S.Length - 1; i++)
            {

                for (j = 0; j < S.Length - 3; j++)

                {

                    S[i][j] = j * (Math.Pow(pochodna1, j - 1));
                }

            }


            for (i = 6; i < S.Length; i++)
            {

                for (j = 0; j < S.Length - 2; j++)

                {

                    S[i][j] = j * (Math.Pow(pochodna2, j - 1));

                }

            }


            for (i = 6; i < S.Length; i++)
            {

                for (j = 4; j < S.Length; j++)
                {
                    S[i][j] = (3 * Math.Pow((pochodna2 - xi[j - 3]), 2));

                }

            }

            for (i = 0; i < S.Length; i++)
            {
                for (j = 0; j < S.Length; j++)
                {
                    S[2][6] = 0;
                    Console.Write("  " + S[i][j]);
                }
                Console.WriteLine("  ");
            }
            double[] x = funkcyjka.gauss(S[][], xii);
            Console.WriteLine("-------------------");
            for (i = 0; i < S.Length; i++)
            {
                for (j = 0; j < S.Length; j++)
                {

                    Console.Write("  " + S[i][j]);
                }
                Console.WriteLine("  ");
            }

            double podajx = 3;
            for (i = 0; i < x.Length; i++)
            {
                wynik += x[i] * Math.Pow(podajx, i);
            }
            wynik = funkcyjka.pkt(podajx, x);

            Console.WriteLine("wynik: " + wynik);
        }
    }
}