// <copyright file="SimpsonRule.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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// 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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// included in all copies or substantial portions of the Software.
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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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// </copyright>
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using System;
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namespace IStation.Numerics.Integration
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{
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/// <summary>
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/// Approximation algorithm for definite integrals by Simpson's rule.
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/// </summary>
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public static class SimpsonRule
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{
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/// <summary>
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/// Direct 3-point approximation of the definite integral in the provided interval by Simpson's rule.
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/// </summary>
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/// <param name="f">The analytic smooth function to integrate.</param>
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/// <param name="intervalBegin">Where the interval starts, inclusive and finite.</param>
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/// <param name="intervalEnd">Where the interval stops, inclusive and finite.</param>
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/// <returns>Approximation of the finite integral in the given interval.</returns>
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public static double IntegrateThreePoint(Func<double, double> f, double intervalBegin, double intervalEnd)
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{
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if (f == null)
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{
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throw new ArgumentNullException(nameof(f));
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}
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double midpoint = (intervalEnd + intervalBegin)/2;
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return (intervalEnd - intervalBegin)/6*(f(intervalBegin) + f(intervalEnd) + (4*f(midpoint)));
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}
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/// <summary>
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/// Composite N-point approximation of the definite integral in the provided interval by Simpson's rule.
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/// </summary>
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/// <param name="f">The analytic smooth function to integrate.</param>
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/// <param name="intervalBegin">Where the interval starts, inclusive and finite.</param>
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/// <param name="intervalEnd">Where the interval stops, inclusive and finite.</param>
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/// <param name="numberOfPartitions">Even number of composite subdivision partitions.</param>
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/// <returns>Approximation of the finite integral in the given interval.</returns>
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public static double IntegrateComposite(Func<double, double> f, double intervalBegin, double intervalEnd, int numberOfPartitions)
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{
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if (f == null)
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{
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throw new ArgumentNullException(nameof(f));
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}
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if (numberOfPartitions <= 0)
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{
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throw new ArgumentOutOfRangeException(nameof(numberOfPartitions), "Value must be positive (and not zero).");
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}
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if (numberOfPartitions.IsOdd())
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{
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throw new ArgumentException("Value must be even.", nameof(numberOfPartitions));
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}
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double step = (intervalEnd - intervalBegin)/numberOfPartitions;
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double factor = step/3;
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double offset = step;
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int m = 4;
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double sum = f(intervalBegin) + f(intervalEnd);
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for (int i = 0; i < numberOfPartitions - 1; i++)
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{
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// NOTE (cdrnet, 2009-01-07): Do not combine intervalBegin and offset (numerical stability)
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sum += m*f(intervalBegin + offset);
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m = 6 - m;
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offset += step;
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}
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return factor*sum;
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}
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}
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}
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