mathnet-numerics/examples/examples-csharp/Signals/Chebyshev.cs

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using System;
using MathNet.Numerics;

namespace Examples.SignalsExamples
{
    /// <summary>
    /// Example of generic function sampling and quantization provider
    /// </summary>
    public class Chebyshev : IExample
    {
              /// <summary>
        /// Gets the name of this example
        /// </summary>
        public string Name
        {
            get
            {
                return "Sampling - Chebyshev";
            }
        }

        /// <summary>
        /// Gets the description of this example
        /// </summary>
        public string Description
        {
            get
            {
                return "Samples a function at the roots of the Chebyshev polynomial";
            }
        }

        /// <summary>
        /// Run example
        /// </summary>
        public void Run()
        {
            // 1. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of the first kind within interval [0, 10] 
            var roots = FindRoots.ChebychevPolynomialFirstKind(20, 0, 10);
            var result = Generate.Map(roots, Function);
            Console.WriteLine(@"1. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of the first kind within interval [0, 10]");
            for (var i = 0; i < result.Length; i++)
            {
                Console.Write(result[i].ToString("N") + @" ");
            }

            Console.WriteLine();
            Console.WriteLine();

            // 2. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of the second kind within interval [0, 10]
            roots = FindRoots.ChebychevPolynomialSecondKind(20, 0, 10);
            result = Generate.Map(roots, Function);
            Console.WriteLine(@"2. Get 20 samples of f(x) = (x * x) / 2 at the roots of the Chebyshev polynomial of the second kind within interval [0, 10]");
            for (var i = 0; i < result.Length; i++)
            {
                Console.Write(result[i].ToString("N") + @" ");
            }

            Console.WriteLine();
        }

        /// <summary>
        /// Fucntion f(x) = (x * x) / 2
        /// </summary>
        /// <param name="x">Input value</param>
        /// <returns>Calculation result</returns>
        public double Function(double x)
        {
            return Math.Pow(x, 2) / 2;
        }
    }
}