diff --git a/src/Numerics/Numerics.csproj b/src/Numerics/Numerics.csproj index b6004e90..6369d13e 100644 --- a/src/Numerics/Numerics.csproj +++ b/src/Numerics/Numerics.csproj @@ -112,6 +112,7 @@ + diff --git a/src/Numerics/OdeSolvers/OdeSolvers.cs b/src/Numerics/OdeSolvers/OdeSolvers.cs new file mode 100644 index 00000000..dd3ab6fe --- /dev/null +++ b/src/Numerics/OdeSolvers/OdeSolvers.cs @@ -0,0 +1,156 @@ +// +// Math.NET Numerics, part of the Math.NET Project +// http://numerics.mathdotnet.com +// http://github.com/mathnet/mathnet-numerics +// +// Copyright (c) 2009-2016 Math.NET +// +// Permission is hereby granted, free of charge, to any person +// obtaining a copy of this software and associated documentation +// files (the "Software"), to deal in the Software without +// restriction, including without limitation the rights to use, +// copy, modify, merge, publish, distribute, sublicense, and/or sell +// copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following +// conditions: +// +// The above copyright notice and this permission notice shall be +// included in all copies or substantial portions of the Software. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, +// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES +// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND +// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT +// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, +// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR +// OTHER DEALINGS IN THE SOFTWARE. +// + +using MathNet.Numerics.LinearAlgebra; +using System; + +namespace MathNet.Numerics.OdeSolvers +{ + /// + /// ODE Solver Algorithms + /// + public static class RungeKutta + { + /// + /// Second Order Runge-Kutta method + /// + /// initial value + /// start time + /// end time + /// Number of subintervals + /// ode function + /// approximations + public static double[] SecondOrder(double y0, double start, double end, int N, Func f) + { + double dt = (end - start) / (N - 1); + double k1 = 0; + double k2 = 0; + double t = start; + double[] y = new double[N]; + y[0] = y0; + for (int i = 1; i < N; i++) + { + k1 = f(t, y0); + k2 = f(t + dt, y0 + k1 * dt); + y[i] = y0 + dt * 0.5 * (k1 + k2); + t += dt; + y0 = y[i]; + } + return y; + } + + /// + /// Fourth Order Runge-Kutta method + /// + /// initial value + /// start time + /// end time + /// number of subintervals + /// ode function + /// approximations + public static double[] FourthOrder(double y0, double start, double end, int N, Func f) + { + double dt = (end - start) / (N - 1); + double k1 = 0; + double k2 = 0; + double k3 = 0; + double k4 = 0; + double t = start; + double[] y = new double[N]; + y[0] = y0; + for (int i = 1; i < N; i++) + { + k1 = f(t, y0); + k2 = f(t + dt / 2, y0 + k1 * dt / 2); + k3 = f(t + dt / 2, y0 + k2 * dt / 2); + k4 = f(t + dt, y0 + k3 * dt); + y[i] = y0 + dt / 6 * (k1 + 2 * k2 + 2 * k3 + k4); + t += dt; + y0 = y[i]; + } + return y; + } + + /// + /// Second Order Runge-Kutta to solve ODE SYSTEM + /// + /// initial vector + /// start time + /// end time + /// number of subintervals + /// ode function + /// approximations + public static Vector[] SecondOrder(Vector y0, double start, double end, int N, Func, Vector> f) + { + double dt = (end - start) / (N - 1); + Vector k1, k2; + Vector[] y = new Vector[N]; + double t = start; + y[0] = y0; + for (int i = 1; i < N; i++) + { + k1 = f(t, y0); + k2 = f(t, y0 + k1 + dt); + y[i] = y0 + 0.5 * (k1 + k2); + t += dt; + y0 = y[i]; + } + return y; + } + + /// + /// Fourth Order Runge-Kutta to solve ODE SYSTEM + /// + /// initial vector + /// start time + /// end time + /// number of subintervals + /// ode function + /// approximations + public static Vector[] FourthOrder(Vector y0, double start, double end, int N, Func, Vector> f) + { + double dt = (end - start) / (N - 1); + Vector k1, k2, k3, k4; + Vector[] y = new Vector[N]; + double t = start; + y[0] = y0; + for (int i = 1; i < N; i++) + { + k1 = f(t, y0); + k2 = f(t + dt / 2, y0 + k1 * dt / 2); + k3 = f(t + dt / 2, y0 + k2 * dt / 2); + k4 = f(t + dt, y0 + k3 * dt); + y[i] = y0 + dt / 6 * (k1 + 2 * k2 + 2 * k3 + k4); + t += dt; + y0 = y[i]; + } + return y; + } + } +} \ No newline at end of file diff --git a/src/UnitTests/OdeSolvers/OdeSolverTest.cs b/src/UnitTests/OdeSolvers/OdeSolverTest.cs new file mode 100644 index 00000000..d8b3542b --- /dev/null +++ b/src/UnitTests/OdeSolvers/OdeSolverTest.cs @@ -0,0 +1,91 @@ +// +// Math.NET Numerics, part of the Math.NET Project +// http://numerics.mathdotnet.com +// http://github.com/mathnet/mathnet-numerics +// +// Copyright (c) 2009-2016 Math.NET +// +// Permission is hereby granted, free of charge, to any person +// obtaining a copy of this software and associated documentation +// files (the "Software"), to deal in the Software without +// restriction, including without limitation the rights to use, +// copy, modify, merge, publish, distribute, sublicense, and/or sell +// copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following +// conditions: +// +// The above copyright notice and this permission notice shall be +// included in all copies or substantial portions of the Software. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, +// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES +// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND +// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT +// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, +// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR +// OTHER DEALINGS IN THE SOFTWARE. +// + +using NUnit.Framework; +using System; +using MathNet.Numerics.OdeSolvers; +using System.Linq; + +namespace MathNet.Numerics.UnitTests.OdeSolvers +{ + /// + /// ODE Solver tests. + /// + [TestFixture, Category("OdeSolver")] + public class OdeSolverTest + { + /// + /// Runge-Kutta second order method for first order ODE. + /// + [Test] + public void RK2Test() + { + Func ode = (t, y) => t + 2 * y * t; + Func sol = (t) => 0.5 * (Math.Exp(t * t) - 1); + double ratio = double.NaN; + double error = 0; + double oldError = 0; + for (int k = 0; k < 4; k++) + { + double y0 = 0; + double[] y_t = RungeKutta.SecondOrder(y0, 0, 2, Convert.ToInt32(Math.Pow(2, k + 6)), ode); + error = Math.Abs(sol(2) - y_t.Last()); + if (oldError != 0) + ratio = Math.Log(oldError / error, 2); + oldError = error; + Console.WriteLine(string.Format("{0}, {1}", error, ratio)); + } + Assert.AreEqual(2, ratio, 0.01);// Check error convergence order + } + + /// + /// Runge-Kutta fourth order method for first order ODE. + /// + [Test] + public void RK4Test() + { + Func ode = (t, y) => t + 2 * y * t; + Func sol = (t) => 0.5 * (Math.Exp(t * t) - 1); + double ratio = double.NaN; + double error = 0; + double oldError = 0; + for (int k = 0; k < 4; k++) + { + double y0 = 0; + double[] y_t = RungeKutta.FourthOrder(y0, 0, 2, Convert.ToInt32(Math.Pow(2, k + 6)), ode); + error = Math.Abs(sol(2) - y_t.Last()); + if (oldError != 0) + ratio = Math.Log(oldError / error, 2); + oldError = error; + Console.WriteLine(string.Format("{0}, {1}", error, ratio)); + } + Assert.AreEqual(4, ratio, 0.01);// Check error convergence order + } + } +} \ No newline at end of file diff --git a/src/UnitTests/UnitTests.csproj b/src/UnitTests/UnitTests.csproj index 735d4a80..e07050ea 100644 --- a/src/UnitTests/UnitTests.csproj +++ b/src/UnitTests/UnitTests.csproj @@ -362,6 +362,7 @@ +