mathnet-numerics/examples/examples-csharp/Integration.cs

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using System;
using MathNet.Numerics;

namespace Examples
{
    /// <summary>
    /// Numeric Integration (Quadrature)
    /// </summary>
    /// <seealso cref="http://reference.wolfram.com/mathematica/ref/Integrate.html"/>
    public class Integration : IExample
    {
        /// <summary>
        /// Gets the name of this example
        /// </summary>
        public string Name
        {
            get
            {
                return "Numeric Integration";
            }
        }

        /// <summary>
        /// Gets the description of this example
        /// </summary>
        public string Description
        {
            get
            {
                return "Analytic integration of smooth functions with no discontinuitie or derivative discontinuities and no poles inside the interval";
            }
        }

        /// <summary>
        /// Run example
        /// </summary>
        /// <seealso cref="http://en.wikipedia.org/wiki/Trapezoidal_rule">Trapezoidal rule</seealso>
        public void Run()
        {
            // 1. Integrate x*x on interval [0, 10]
            Console.WriteLine(@"1. Integrate x*x on interval [0, 10]");
            var result = Integrate.OnClosedInterval(x => x * x, 0, 10);
            Console.WriteLine(result);
            Console.WriteLine();

            // 2. Integrate 1/(x^3 + 1) on interval [0, 1]
            Console.WriteLine(@"2. Integrate 1/(x^3 + 1) on interval [0, 1]");
            result = Integrate.OnClosedInterval(x => 1 / (Math.Pow(x, 3) + 1), 0, 1);
            Console.WriteLine(result);
            Console.WriteLine();

            // 3. Integrate f(x) = exp(-x/5) (2 + sin(2 * x)) on [0, 10]
            Console.WriteLine(@"3. Integrate f(x) = exp(-x/5) (2 + sin(2 * x)) on [0, 10]");
            result = Integrate.OnClosedInterval(x => Math.Exp(-x / 5) * (2 + Math.Sin(2 * x)), 0, 100);
            Console.WriteLine(result);
            Console.WriteLine();

            // 4. Integrate target function with absolute error = 1E-4
            Console.WriteLine(@"4. Integrate target function with absolute error = 1E-4 on [0, 10]");
            Console.WriteLine(@"public static double TargetFunctionA(double x)
{
    return Math.Exp(-x / 5) * (2 + Math.Sin(2 * x));
}");
            result = Integrate.OnClosedInterval(TargetFunctionA, 0, 100, 1e-4);
            Console.WriteLine(result);
            Console.WriteLine();
        }

        /// <summary>
        /// Test Function: f(x) = exp(-x/5) (2 + sin(2 * x))
        /// </summary>
        /// <param name="x">X parameter value</param>
        /// <returns>Calculation result</returns>
        public static double TargetFunctionA(double x)
        {
            return Math.Exp(-x / 5) * (2 + Math.Sin(2 * x));
        }
    }
}