// <copyright file="ZeroCrossingBracketing.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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//
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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 System.Collections.Generic;
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namespace IStation.Numerics.RootFinding
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{
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public static class ZeroCrossingBracketing
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{
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public static IEnumerable<Tuple<double, double>> FindIntervalsWithin(Func<double, double> f, double lowerBound, double upperBound, int subdivisions)
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{
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// TODO: Consider binary-style search instead of linear scan
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double fmin = f(lowerBound);
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double fmax = f(upperBound);
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if (Math.Sign(fmin) != Math.Sign(fmax))
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{
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yield return new Tuple<double, double>(lowerBound, upperBound);
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yield break;
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}
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double subdiv = (upperBound - lowerBound)/subdivisions;
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double smin = lowerBound;
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int sign = Math.Sign(fmin);
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for (int k = 0; k < subdivisions; k++)
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{
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double smax = smin + subdiv;
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double sfmax = f(smax);
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if (double.IsInfinity(sfmax))
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{
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// expand interval to include pole
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smin = smax;
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continue;
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}
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if (Math.Sign(sfmax) != sign)
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{
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yield return new Tuple<double, double>(smin, smax);
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sign = Math.Sign(sfmax);
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}
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smin = smax;
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}
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}
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/// <summary>Detect a range containing at least one root.</summary>
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/// <param name="f">The function to detect roots from.</param>
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/// <param name="lowerBound">Lower value of the range.</param>
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/// <param name="upperBound">Upper value of the range</param>
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/// <param name="factor">The growing factor of research. Usually 1.6.</param>
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/// <param name="maxIterations">Maximum number of iterations. Usually 50.</param>
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/// <returns>True if the bracketing operation succeeded, false otherwise.</returns>
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/// <remarks>This iterative methods stops when two values with opposite signs are found.</remarks>
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public static bool Expand(Func<double, double> f, ref double lowerBound, ref double upperBound, double factor = 1.6, int maxIterations = 50)
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{
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double originalLowerBound = lowerBound;
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double originalUpperBound = upperBound;
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if (lowerBound >= upperBound)
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{
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throw new ArgumentOutOfRangeException(nameof(upperBound), "xmax must be greater than xmin.");
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}
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double fmin = f(lowerBound);
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double fmax = f(upperBound);
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for (int i = 0; i < maxIterations; i++)
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{
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if (Math.Sign(fmin) != Math.Sign(fmax))
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{
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return true;
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}
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if (Math.Abs(fmin) < Math.Abs(fmax))
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{
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lowerBound += factor*(lowerBound - upperBound);
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fmin = f(lowerBound);
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}
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else
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{
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upperBound += factor*(upperBound - lowerBound);
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fmax = f(upperBound);
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}
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}
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lowerBound = originalLowerBound;
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upperBound = originalUpperBound;
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return false;
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}
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public static bool Reduce(Func<double, double> f, ref double lowerBound, ref double upperBound, int subdivisions = 1000)
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{
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double originalLowerBound = lowerBound;
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double originalUpperBound = upperBound;
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if (lowerBound >= upperBound)
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{
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throw new ArgumentOutOfRangeException(nameof(upperBound), "xmax must be greater than xmin.");
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}
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// TODO: Consider binary-style search instead of linear scan
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double fmin = f(lowerBound);
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double fmax = f(upperBound);
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if (Math.Sign(fmin) != Math.Sign(fmax))
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{
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return true;
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}
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double subdiv = (upperBound - lowerBound) / subdivisions;
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double smin = lowerBound;
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int sign = Math.Sign(fmin);
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for (int k = 0; k < subdivisions; k++)
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{
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double smax = smin + subdiv;
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double sfmax = f(smax);
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if (double.IsInfinity(sfmax))
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{
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// expand interval to include pole
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smin = smax;
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continue;
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}
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if (Math.Sign(sfmax) != sign)
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{
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lowerBound = smin;
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upperBound = smax;
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return true;
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}
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smin = smax;
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}
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lowerBound = originalLowerBound;
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upperBound = originalUpperBound;
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return false;
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}
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public static bool ExpandReduce(Func<double, double> f, ref double lowerBound, ref double upperBound, double expansionFactor = 1.6, int expansionMaxIterations = 50, int reduceSubdivisions = 100)
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{
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return Expand(f, ref lowerBound, ref upperBound, expansionFactor, expansionMaxIterations) || Reduce(f, ref lowerBound, ref upperBound, reduceSubdivisions);
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}
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}
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}
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