using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows.Forms;
using MathNet.Numerics.LinearAlgebra;
using System.Windows.Forms.DataVisualization.Charting;

namespace SystemsOfLinearEquations
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();
        }

        void Button1_Click(object sender, EventArgs e)
        {
            Close();
        }

        public void ClearForm()
        {
            chart1.Series.Clear();
            richTextBox1.Clear();
        }

        double F(double x)
        {
            return Math.Log(x) / (Math.Sin(2.0 * x) + 1.5) - Math.Cos(x / 5.0);
        }

        double IF(double x, Vector<double> A)
        {
            double temp = 0;
            double differences = 1;
            double differences1 = x;
            double result = differences * A[0] + differences1 * A[1];
            for (int row = 2; row < A.Count; row++)
            {
                temp = 2 * x * differences1 - differences;
                result += temp * A[row];
                differences = differences1;
                differences1 = temp;
            }
            return result;
        }

        void Chebyshev(double[] xValues)
        {
            Vector<double> X = Vector<double>.Build.DenseOfArray(xValues);
            Vector<double> A = Vector<double>.Build.Dense(X.Count);
            Vector<double> Y = Vector<double>.Build.Dense(X.Count);
            Matrix<double> N = Matrix<double>.Build.Dense(X.Count, X.Count, 0);

            for (int row = 0; row < X.Count; row++)
            {
                // Y reikšmės apskaičiavimas

                Y[row] = F(X[row]);

                // N matricos eilutės apskaičiavimas

                N[row, 0] = 1;
                N[row, 1] = X[row];
                for (int column = 2; column < X.Count; column++)
                {
                    N[row, column] = 2 * X[row] * N[row, column - 1] - N[row, column - 2];
                }
            }

            // A reikšmės apskaičiavimas
            // A = N.Inverse() * Y;
            Matrix<double> Nn = N.Inverse();
            for (int row = 0; row < X.Count; row++)
            {
                for (int column = 0; column < X.Count; column++) {
                    A[row] += Nn[row, column] * Y[column];
                   }
            }

            Series Original = chart1.Series.Add("Original");
            Series Interpolated = chart1.Series.Add("Interpolated");
            Series Difference = chart1.Series.Add("Difference");
            Series Points = chart1.Series.Add("Points");

            Original.ChartType = SeriesChartType.Line;
            Interpolated.ChartType = SeriesChartType.Line;
            Difference.ChartType = SeriesChartType.Line;
            Points.ChartType = SeriesChartType.Point;

            Original.BorderWidth = 3;
            Interpolated.BorderWidth = 3;
            Difference.BorderWidth = 3;

            for (int i = 0; i < X.Count; i++)
            {
                Points.Points.AddXY(X[i], F(X[i]));
            }

            for (double x = 2; x <= 10; x += 0.1)
            {
                double originalY = F(x);
                double interpolatedY = IF(x, A);
                double differenceY = originalY - interpolatedY;

                Original.Points.AddXY(x, originalY);
                Interpolated.Points.AddXY(x, interpolatedY);
                Difference.Points.AddXY(x, differenceY);
            }
        }

        void Button2_Click(object sender, EventArgs e)
        {
            ClearForm();
            Chebyshev(new double[] { 2, 3, 4, 5, 6, 7, 8, 9, 10 });
        }

        void Button3_Click(object sender, EventArgs e)
        {
            ClearForm();
            double a = 2;
            double b = 10;
            int n = 10;
            double[] xValues = new double[n]; // Mazgai ties Čiobyševo abscisėmis
            for (int i = 0; i < n; i++){
                xValues[i] = (b - a) / 2 * Math.Cos(Math.PI * (2 * i + 1) / (2 * n)) + (b + a) / 2;
            }
            Chebyshev(xValues.ToArray());
        }
    }
}