mathnet-numerics/examples/examples-csharp/Interpolation/LinearBetweenPoints.cs

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using System;
using MathNet.Numerics;
using MathNet.Numerics.Random;

namespace Examples.InterpolationExamples
{
    /// <summary>
    /// Interpolation example
    /// </summary>
    /// <seealso cref="http://reference.wolfram.com/mathematica/ref/Interpolation.html"/>
    public class LinearBetweenPoints : IExample
    {
        /// <summary>
        /// Gets the name of this example
        /// </summary>
        public string Name
        {
            get
            {
                return "Interpolation - Linear Between Points";
            }
        }

        /// <summary>
        /// Gets the description of this example
        /// </summary>
        public string Description
        {
            get
            {
                return "Linear Spline Interpolation Algorithm";
            }
        }

        /// <summary>
        /// Run example
        /// </summary>
        /// <seealso cref="http://en.wikipedia.org/wiki/Spline_interpolation">Spline interpolation</seealso>
        public void Run()
        {
            // 1. Generate 20 samples of the function x*x-2*x on interval [0, 10]
            Console.WriteLine(@"1. Generate 20 samples of the function x*x-2*x on interval [0, 10]");
            double[] points = Generate.LinearSpaced(20, 0, 10);
            var values = Generate.Map(points, TargetFunction);
            Console.WriteLine();

            // 2. Create a linear spline interpolation based on arbitrary points 
            var method = Interpolate.Linear(points, values);
            Console.WriteLine(@"2. Create a linear spline interpolation based on arbitrary points");
            Console.WriteLine();

            // 3. Check if interpolation support integration
            Console.WriteLine(@"3. Support integration = {0}", method.SupportsIntegration);
            Console.WriteLine();

            // 4. Check if interpolation support differentiation
            Console.WriteLine(@"4. Support differentiation = {0}", method.SupportsDifferentiation);
            Console.WriteLine();

            // 5. Differentiate at point 5.2
            Console.WriteLine(@"5. Differentiate at point 5.2 = {0}", method.Differentiate(5.2));
            Console.WriteLine();

            // 6. Integrate at point 5.2
            Console.WriteLine(@"6. Integrate at point 5.2 = {0}", method.Integrate(5.2));
            Console.WriteLine();

            // 7. Interpolate ten random points and compare to function results
            Console.WriteLine(@"7. Interpolate ten random points and compare to function results");
            var rng = new MersenneTwister(1);
            for (var i = 0; i < 10; i++)
            {
                // Generate random value from [0, 10]
                var point = rng.NextDouble() * 10;
                Console.WriteLine(@"Interpolate at {0} = {1}. Function({0}) = {2}", point.ToString("N05"), method.Interpolate(point).ToString("N05"), TargetFunction(point).ToString("N05"));
            }

            Console.WriteLine();
        }

        /// <summary>
        /// Test Function: f(x) = x * x - 2 * x
        /// </summary>
        /// <param name="x">X parameter value</param>
        /// <returns>Calculation result</returns>
        public static double TargetFunction(double x)
        {
            return (x * x) - (2 * x);
        }
    }
}