// <copyright file="NewtonRaphson.cs" company="Math.NET">
|
// Math.NET Numerics, part of the Math.NET Project
|
// http://numerics.mathdotnet.com
|
// http://github.com/mathnet/mathnet-numerics
|
//
|
// Copyright (c) 2009-2020 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.
|
// </copyright>
|
|
using System;
|
|
namespace IStation.Numerics.RootFinding
|
{
|
/// <summary>
|
/// Pure Secant root-finding algorithm without any recovery measures in cases it behaves badly.
|
/// The algorithm aborts immediately if the root leaves the bound interval.
|
/// </summary>
|
/// <seealso cref="Brent"/>
|
public static class Secant
|
{
|
/// <summary>Find a solution of the equation f(x)=0.</summary>
|
/// <param name="f">The function to find roots from.</param>
|
/// <param name="guess">The first guess of the root within the bounds specified.</param>
|
/// <param name="secondGuess">The second guess of the root within the bounds specified.</param>
|
/// <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>
|
/// <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>
|
/// <param name="accuracy">Desired accuracy. The root will be refined until the accuracy or the maximum number of iterations is reached. Default 1e-8. Must be greater than 0.</param>
|
/// <param name="maxIterations">Maximum number of iterations. Default 100.</param>
|
/// <returns>Returns the root with the specified accuracy.</returns>
|
/// <exception cref="NonConvergenceException"></exception>
|
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)
|
{
|
double root;
|
if (TryFindRoot(f, guess, secondGuess, lowerBound, upperBound, accuracy, maxIterations, out root))
|
{
|
return root;
|
}
|
|
throw new NonConvergenceException("The algorithm has failed, exceeded the number of iterations allowed or there is no root within the provided bounds.");
|
}
|
|
/// <summary>Find a solution of the equation f(x)=0.</summary>
|
/// <param name="f">The function to find roots from.</param>
|
/// <param name="guess">The first guess of the root within the bounds specified.</param>
|
/// <param name="secondGuess">The second guess of the root within the bounds specified.</param>
|
/// <param name="lowerBound">The low value of the range where the root is supposed to be. Aborts if it leaves the interval.</param>
|
/// <param name="upperBound">The low value of the range where the root is supposed to be. Aborts if it leaves the interval.</param>
|
/// <param name="accuracy">Desired accuracy. The root will be refined until the accuracy or the maximum number of iterations is reached. Example: 1e-14. Must be greater than 0.</param>
|
/// <param name="maxIterations">Maximum number of iterations. Example: 100.</param>
|
/// <param name="root">The root that was found, if any. Undefined if the function returns false.</param>
|
/// <returns>True if a root with the specified accuracy was found, else false</returns>
|
public static bool TryFindRoot(Func<double, double> f, double guess, double secondGuess, double lowerBound, double upperBound, double accuracy, int maxIterations, out double root)
|
{
|
if (accuracy <= 0)
|
{
|
throw new ArgumentOutOfRangeException(nameof(accuracy), "Must be greater than zero.");
|
}
|
|
root = secondGuess;
|
|
// Either guess is outside of bounds
|
if (guess <= lowerBound || guess >= upperBound || secondGuess <= lowerBound || secondGuess >= upperBound)
|
{
|
return false;
|
}
|
|
// Evaluation
|
double fguess = f(guess);
|
double froot = f(root);
|
|
for (int i = 0; i <= maxIterations && root >= lowerBound && root <= upperBound; i++)
|
{
|
// Secant step
|
double step = froot * (root - guess) / (froot - fguess);
|
|
guess = root;
|
fguess = froot;
|
|
root -= step;
|
froot = f(root);
|
|
if (Math.Abs(step) < accuracy && Math.Abs(froot) < accuracy)
|
{
|
return true;
|
}
|
}
|
|
return false;
|
}
|
}
|
}
|
