Christoph Ruegg
11 years ago
4 changed files with 200 additions and 0 deletions
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// <copyright file="NewtonRaphson.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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// http://mathnetnumerics.codeplex.com
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//
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// Copyright (c) 2009-2013 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System; |
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using MathNet.Numerics.Properties; |
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namespace MathNet.Numerics.RootFinding |
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{ |
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/// <summary>
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/// Pure Secant root-finding algorithm without any recovery measures in cases it behaves badly.
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/// The algorithm aborts immediately if the root leaves the bound interval.
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/// </summary>
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/// <seealso cref="Brent"/>
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public static class Secant |
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{ |
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/// <summary>Find a solution of the equation f(x)=0.</summary>
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/// <param name="f">The function to find roots from.</param>
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/// <param name="guess">The first guess of the root within the bounds specified.</param>
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/// <param name="secondGuess">The second guess of the root within the bounds specified.</param>
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/// <param name="lowerBound">The low value of the range where the root is supposed to be. Aborts if it leaves the interval. Default MinValue.</param>
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/// <param name="upperBound">The high value of the range where the root is supposed to be. Aborts if it leaves the interval. Default MaxValue.</param>
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/// <param name="accuracy">Desired accuracy. The root will be refined until the accuracy or the maximum number of iterations is reached. Default 1e-8.</param>
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/// <param name="maxIterations">Maximum number of iterations. Default 100.</param>
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/// <returns>Returns the root with the specified accuracy.</returns>
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/// <exception cref="NonConvergenceException"></exception>
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public static double FindRoot(Func<double, double> f, double guess, double secondGuess, double lowerBound = double.MinValue, double upperBound = double.MaxValue, double accuracy = 1e-8, int maxIterations = 100) |
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{ |
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double root; |
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if (TryFindRoot(f, guess, secondGuess, lowerBound, upperBound, accuracy, maxIterations, out root)) |
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{ |
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return root; |
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} |
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throw new NonConvergenceException(Resources.RootFindingFailed); |
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} |
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/// <summary>Find a solution of the equation f(x)=0.</summary>
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/// <param name="f">The function to find roots from.</param>
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/// <param name="guess">The first guess of the root within the bounds specified.</param>
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/// <param name="secondGuess">The second guess of the root within the bounds specified.</param>
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/// <param name="lowerBound">The low value of the range where the root is supposed to be. Aborts if it leaves the interval.</param>
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/// <param name="upperBound">The low value of the range where the root is supposed to be. Aborts if it leaves the interval.</param>
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/// <param name="accuracy">Desired accuracy. The root will be refined until the accuracy or the maximum number of iterations is reached. Example: 1e-14.</param>
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/// <param name="maxIterations">Maximum number of iterations. Example: 100.</param>
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/// <param name="root">The root that was found, if any. Undefined if the function returns false.</param>
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/// <returns>True if a root with the specified accuracy was found, else false</returns>
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public static bool TryFindRoot(Func<double, double> f, double guess, double secondGuess, double lowerBound, double upperBound, double accuracy, int maxIterations, out double root) |
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{ |
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root = secondGuess; |
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// Either guess is outside of bounds
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if (guess <= lowerBound || guess >= upperBound || secondGuess <= lowerBound || secondGuess >= upperBound) |
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{ |
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return false; |
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} |
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// Evaluation
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double fguess = f(guess); |
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double froot = f(root); |
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for (int i = 0; i <= maxIterations && root >= lowerBound && root <= upperBound; i++) |
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{ |
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// Secant step
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double step = froot * (root - guess) / (froot - fguess); |
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guess = root; |
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fguess = froot; |
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root -= step; |
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froot = f(root); |
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if (Math.Abs(step) < accuracy && Math.Abs(froot) < accuracy) |
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{ |
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return true; |
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} |
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} |
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return false; |
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} |
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} |
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} |
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// <copyright file="BrentTest.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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// http://mathnetnumerics.codeplex.com
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//
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// Copyright (c) 2009-2013 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System; |
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using MathNet.Numerics.RootFinding; |
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using NUnit.Framework; |
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namespace MathNet.Numerics.UnitTests.RootFindingTests |
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{ |
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[TestFixture, Category("RootFinding")] |
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public class SecantTest |
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{ |
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[Test] |
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public void MultipleRoots() |
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{ |
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// Roots at -2, 2
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Func<double, double> f1 = x => x * x - 4; |
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Assert.AreEqual(0, f1(Secant.FindRoot(f1, 0, 6, -10, 10, 1e-14))); |
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Assert.AreEqual(-2, Secant.FindRoot(f1, -3, 0, -10, 10, 1e-14)); |
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Assert.AreEqual(2, Secant.FindRoot(f1, 1, 4, -10, 10, 1e-14)); |
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Assert.AreEqual(0, f1(Secant.FindRoot(x => f1(x), -6, 0, -10, 10, 1e-14))); |
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Assert.AreEqual(-2, Secant.FindRoot(x => f1(x), -5, -1, -10, 10, 1e-14)); |
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Assert.AreEqual(2, Secant.FindRoot(x => f1(x), 1, 4, -10, 10, 1e-14)); |
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// Roots at 3, 4
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Func<double, double> f2 = x => (x - 3) * (x - 4); |
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Assert.AreEqual(0, f2(Secant.FindRoot(f2, 3.5, 6, 0, 10, 1e-14))); |
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Assert.AreEqual(3, Secant.FindRoot(f2, -5, 3.5, -10, 10, 1e-14)); |
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Assert.AreEqual(4, Secant.FindRoot(f2, 3.2, 4.2, 0, 10, 1e-14)); |
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Assert.AreEqual(3, Secant.FindRoot(f2, 2.1, 3.1, 0, 10, 0.001, 50), 0.001); |
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Assert.AreEqual(3, Secant.FindRoot(f2, 2.1, 3.4, 0, 10, 0.001, 50), 0.001); |
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} |
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[Test] |
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public void LocalMinima() |
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{ |
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Func<double, double> f1 = x => x * x * x - 2 * x + 2; |
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Assert.AreEqual(0, f1(Secant.FindRoot(f1, -5, 6, -10, 10, 1e-14))); |
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} |
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[Test] |
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public void Cubic() |
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{ |
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// with complex roots (looking for the real root only): 3x^3 + 4x^2 + 5x + 6
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Func<double, double> f1 = x => Evaluate.Polynomial(x, 6, 5, 4, 3); |
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Assert.AreEqual(-1.265328088928, Secant.FindRoot(f1, -2, -1, -10, 10, 1e-10), 1e-6); |
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Assert.AreEqual(-1.265328088928, Secant.FindRoot(f1, -5, 6, -10, 10, 1e-10), 1e-6); |
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// real roots only: 2x^3 + 4x^2 - 50x + 6
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Func<double, double> f2 = x => Evaluate.Polynomial(x, 6, -50, 4, 2); |
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Assert.AreEqual(-6.1466562197069, Secant.FindRoot(f2, -8, -5, -10, 10, 1e-10), 1e-6); |
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Assert.AreEqual(0.12124737195841, Secant.FindRoot(f2, -1, 1, -10, 10, 1e-10), 1e-6); |
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Assert.AreEqual(4.0254088477485, Secant.FindRoot(f2, 3, 5, 0, 10, 1e-10), 1e-6); |
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} |
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[Test] |
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public void NoRoot() |
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{ |
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Func<double, double> f1 = x => x * x + 4; |
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Assert.That(() => Secant.FindRoot(f1, -5, 5, -10, 10, 1e-14, 50), Throws.TypeOf<NonConvergenceException>()); |
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} |
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} |
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} |
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