// <copyright file="LogLinear.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) 2009-2014 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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using System.Linq;
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using IStation.Numerics.Threading;
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namespace IStation.Numerics.Interpolation
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{
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/// <summary>
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/// Piece-wise Log-Linear Interpolation
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/// </summary>
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/// <remarks>This algorithm supports differentiation, not integration.</remarks>
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public class LogLinear : IInterpolation
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{
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/// <summary>
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/// Internal Spline Interpolation
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/// </summary>
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readonly LinearSpline _spline;
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/// <param name="x">Sample points (N), sorted ascending</param>
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/// <param name="logy">Natural logarithm of the sample values (N) at the corresponding points</param>
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public LogLinear(double[] x, double[] logy)
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{
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_spline = LinearSpline.InterpolateSorted(x, logy);
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}
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/// <summary>
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/// Create a piecewise log-linear interpolation from a set of (x,y) value pairs, sorted ascendingly by x.
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/// </summary>
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public static LogLinear InterpolateSorted(double[] x, double[] y)
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{
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if (x.Length != y.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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var logy = new double[y.Length];
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CommonParallel.For(0, y.Length, 4096, (a, b) =>
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{
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for (int i = a; i < b; i++)
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{
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logy[i] = Math.Log(y[i]);
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}
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});
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return new LogLinear(x, logy);
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}
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/// <summary>
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/// Create a piecewise log-linear interpolation from an unsorted set of (x,y) value pairs.
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/// WARNING: Works in-place and can thus causes the data array to be reordered and modified.
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/// </summary>
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public static LogLinear InterpolateInplace(double[] x, double[] y)
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{
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if (x.Length != y.Length)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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Sorting.Sort(x, y);
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CommonParallel.For(0, y.Length, 4096, (a, b) =>
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{
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for (int i = a; i < b; i++)
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{
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y[i] = Math.Log(y[i]);
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}
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});
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return new LogLinear(x, y);
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}
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/// <summary>
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/// Create a piecewise log-linear interpolation from an unsorted set of (x,y) value pairs.
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/// </summary>
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public static LogLinear Interpolate(IEnumerable<double> x, IEnumerable<double> y)
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{
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// note: we must make a copy, even if the input was arrays already
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return InterpolateInplace(x.ToArray(), y.ToArray());
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}
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/// <summary>
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/// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
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/// </summary>
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bool IInterpolation.SupportsDifferentiation => true;
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/// <summary>
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/// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
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/// </summary>
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bool IInterpolation.SupportsIntegration => false;
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/// <summary>
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/// Interpolate at point t.
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/// </summary>
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/// <param name="t">Point t to interpolate at.</param>
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/// <returns>Interpolated value x(t).</returns>
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public double Interpolate(double t)
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{
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return Math.Exp(_spline.Interpolate(t));
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}
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/// <summary>
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/// Differentiate at point t.
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/// </summary>
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/// <param name="t">Point t to interpolate at.</param>
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/// <returns>Interpolated first derivative at point t.</returns>
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public double Differentiate(double t)
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{
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return Interpolate(t)*_spline.Differentiate(t);
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}
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/// <summary>
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/// Differentiate twice at point t.
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/// </summary>
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/// <param name="t">Point t to interpolate at.</param>
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/// <returns>Interpolated second derivative at point t.</returns>
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public double Differentiate2(double t)
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{
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var linearFirstDerivative = _spline.Differentiate(t);
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var linearSecondDerivative = _spline.Differentiate2(t);
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var secondDerivative = Differentiate(t)*linearFirstDerivative +
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Interpolate(t)*linearSecondDerivative;
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return secondDerivative;
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}
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/// <summary>
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/// Indefinite integral at point t.
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/// </summary>
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/// <param name="t">Point t to integrate at.</param>
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double IInterpolation.Integrate(double t)
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{
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throw new NotSupportedException();
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}
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/// <summary>
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/// Definite integral between points a and b.
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/// </summary>
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/// <param name="a">Left bound of the integration interval [a,b].</param>
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/// <param name="b">Right bound of the integration interval [a,b].</param>
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double IInterpolation.Integrate(double a, double b)
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{
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throw new NotSupportedException();
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}
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}
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}
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