using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Diagnostics;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows.Forms;
using MathNet.Numerics.LinearAlgebra;
using MathNet.Numerics.LinearAlgebra.Double;
using MathNet.Numerics.LinearAlgebra.Factorization;
using MathNet.Numerics.LinearRegression;

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

        private void Form1_Load(object sender, EventArgs e)
        {
            var xs = new double[ ] { 1, 1, 8, 22,30,32,35 };
            var ys = new double[] { 2, 10, 22, 33, 37,44,50 };
            var res = Polyfit(xs, ys, 4);//.Select(ee => Math.Round(ee, 10).ToString("N0")).ToList();

            var eq = String.Format("x=1, y= ({0})x^4 + ({1})x^3 + ({2})x^2 +({3})x +({4})", res[4], res[3], res[2], res[1], res[0]);
            Clipboard.SetText(eq);
            Process.Start("https://www.wolframalpha.com/input/?i=" + Uri.EscapeDataString(eq));
        }

        public static double[] Polynomial(double[] x, double[] y, int order)
        {
            var design = Matrix<double>.Build.Dense(x.Length, order + 1, (i, j) => Math.Pow(x[i], j));
            return MultipleRegression.QR(design, Vector<double>.Build.Dense(y)).ToArray();
        }
        public static double[] Polyfit(double[] x, double[] y, int degree)
        {
            // Vandermonde matrix
            var v = new DenseMatrix(x.Length, degree + 1);
            for (int i = 0; i < v.RowCount; i++)
                for (int j = 0; j <= degree; j++) v[i, j] = Math.Pow(x[i], j);
            var yv = new DenseVector(y).ToColumnMatrix();
            QR<double> qr = v.QR();
            // Math.Net doesn't have an "economy" QR, so:
            // cut R short to square upper triangle, then recompute Q
            var r = qr.R.SubMatrix(0, degree + 1, 0, degree + 1);
            var q = v.Multiply(r.Inverse());
            var p = r.Inverse().Multiply(q.TransposeThisAndMultiply(yv));
            return p.Column(0).ToArray();
        }
    }
}