mathnet-numerics/src/Numerics/RootFinding/Algorithms/Bisection.cs

// <copyright file="Bisection.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://numerics.mathdotnet.com
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// http://mathnetnumerics.codeplex.com
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using System;
using MathNet.Numerics.Properties;

namespace MathNet.Numerics.RootFinding.Algorithms
{
    public static class Bisection
    {
        /// <summary>Find a solution of the equation f(x)=0.</summary>
        /// <exception cref="NonConvergenceException"></exception>
        public static double FindRootExpand(Func<double, double> f, double guessLowerBound, double guessUpperBound, double accuracy = 1e-8, double expandFactor = 1.6, int maxExpandIteratons = 100)
        {
            ZeroCrossingBracketing.Expand(f, ref guessLowerBound, ref guessUpperBound, expandFactor, maxExpandIteratons);
            return FindRoot(f, guessLowerBound, guessUpperBound, accuracy);
        }

        /// <summary>Find a solution of the equation f(x)=0.</summary>
        /// <exception cref="NonConvergenceException"></exception>
        public static double FindRoot(Func<double, double> f, double lowerBound, double upperBound, double accuracy = 1e-8)
        {
            double fmin = f(lowerBound);
            double fmax = f(upperBound);

            if (fmin == 0.0) return lowerBound;
            if (fmax == 0.0) return upperBound;

            if (Math.Sign(fmin) == Math.Sign(fmax))
            {
                throw new NonConvergenceException(Resources.RootMustBeBracketedByBounds);
            }

            while (Math.Abs(fmax - fmin) > 0.5 * accuracy || Math.Abs(upperBound - lowerBound) > 0.5 * Precision.DoubleMachinePrecision)
            {
                double midpoint = 0.5*(upperBound + lowerBound);
                double midval = f(midpoint);

                if (Math.Sign(midval) == Math.Sign(fmin))
                {
                    lowerBound = midpoint;
                    fmin = midval;
                }
                else if (Math.Sign(midval) == Math.Sign(fmax))
                {
                    upperBound = midpoint;
                    fmax = midval;
                }
                else
                {
                    return midpoint;
                }
            }

            return 0.5*(lowerBound + upperBound);
        }
    }
}