// <copyright file="UnivariateHybridMC.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) 2009-2010 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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// 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 IStation.Numerics.Distributions;
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using IStation.Numerics.Random;
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namespace IStation.Numerics.Statistics.Mcmc
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{
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/// <summary>
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/// A hybrid Monte Carlo sampler for univariate distributions.
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/// </summary>
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public class UnivariateHybridMC : HybridMCGeneric<double>
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{
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/// <summary>
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/// Distribution to sample momentum from.
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/// </summary>
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private readonly Normal _distribution;
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/// <summary>
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/// Standard deviations used in the sampling of the
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/// momentum.
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/// </summary>
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private double _sdv;
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/// <summary>
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/// Gets or sets the standard deviation used in the sampling of the
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/// momentum.
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/// </summary>
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/// <exception cref="ArgumentOutOfRangeException">When standard deviation is negative.</exception>
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public double MomentumStdDev
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{
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get => _sdv;
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set
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{
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if (_sdv != value)
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{
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_sdv = SetPositive(value);
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}
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}
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}
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/// <summary>
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/// Constructs a new Hybrid Monte Carlo sampler for a univariate probability distribution.
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/// The momentum will be sampled from a normal distribution with standard deviation
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/// specified by pSdv using the default <see cref="System.Random"/> random
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/// number generator. A three point estimation will be used for differentiation.
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/// This constructor will set the burn interval.
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/// </summary>
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/// <param name="x0">The initial sample.</param>
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/// <param name="pdfLnP">The log density of the distribution we want to sample from.</param>
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/// <param name="frogLeapSteps">Number frog leap simulation steps.</param>
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/// <param name="stepSize">Size of the frog leap simulation steps.</param>
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/// <param name="burnInterval">The number of iterations in between returning samples.</param>
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/// <param name="pSdv">The standard deviation of the normal distribution that is used to sample
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/// the momentum.</param>
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/// <exception cref="ArgumentOutOfRangeException">When the number of burnInterval iteration is negative.</exception>
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public UnivariateHybridMC(double x0, DensityLn<double> pdfLnP, int frogLeapSteps, double stepSize, int burnInterval = 0, double pSdv = 1)
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: this(x0, pdfLnP, frogLeapSteps, stepSize, burnInterval, pSdv, SystemRandomSource.Default)
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{
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}
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/// <summary>
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/// Constructs a new Hybrid Monte Carlo sampler for a univariate probability distribution.
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/// The momentum will be sampled from a normal distribution with standard deviation
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/// specified by pSdv using a random
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/// number generator provided by the user. A three point estimation will be used for differentiation.
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/// This constructor will set the burn interval.
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/// </summary>
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/// <param name="x0">The initial sample.</param>
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/// <param name="pdfLnP">The log density of the distribution we want to sample from.</param>
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/// <param name="frogLeapSteps">Number frog leap simulation steps.</param>
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/// <param name="stepSize">Size of the frog leap simulation steps.</param>
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/// <param name="burnInterval">The number of iterations in between returning samples.</param>
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/// <param name="pSdv">The standard deviation of the normal distribution that is used to sample
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/// the momentum.</param>
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/// <param name="randomSource">Random number generator used to sample the momentum.</param>
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/// <exception cref="ArgumentOutOfRangeException">When the number of burnInterval iteration is negative.</exception>
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public UnivariateHybridMC(double x0, DensityLn<double> pdfLnP, int frogLeapSteps, double stepSize, int burnInterval, double pSdv, System.Random randomSource)
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: this(x0, pdfLnP, frogLeapSteps, stepSize, burnInterval, pSdv, randomSource, Grad)
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{
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}
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/// <summary>
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/// Constructs a new Hybrid Monte Carlo sampler for a multivariate probability distribution.
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/// The momentum will be sampled from a normal distribution with standard deviation
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/// given by pSdv using a random
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/// number generator provided by the user. This constructor will set both the burn interval and the method used for
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/// numerical differentiation.
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/// </summary>
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/// <param name="x0">The initial sample.</param>
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/// <param name="pdfLnP">The log density of the distribution we want to sample from.</param>
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/// <param name="frogLeapSteps">Number frog leap simulation steps.</param>
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/// <param name="stepSize">Size of the frog leap simulation steps.</param>
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/// <param name="burnInterval">The number of iterations in between returning samples.</param>
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/// <param name="pSdv">The standard deviation of the normal distribution that is used to sample
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/// the momentum.</param>
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/// <param name="diff">The method used for numerical differentiation.</param>
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/// <param name="randomSource">Random number generator used for sampling the momentum.</param>
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/// <exception cref="ArgumentOutOfRangeException">When the number of burnInterval iteration is negative.</exception>
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public UnivariateHybridMC(double x0, DensityLn<double> pdfLnP, int frogLeapSteps, double stepSize, int burnInterval, double pSdv, System.Random randomSource, DiffMethod diff)
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: base(x0, pdfLnP, frogLeapSteps, stepSize, burnInterval, randomSource, diff)
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{
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MomentumStdDev = pSdv;
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_distribution = new Normal(0.0, MomentumStdDev, RandomSource);
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Burn(BurnInterval);
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}
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/// <summary>
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/// Use for copying objects in the Burn method.
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/// </summary>
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/// <param name="source">The source of copying.</param>
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/// <returns>A copy of the source object.</returns>
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protected override double Copy(double source)
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{
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return source;
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}
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/// <summary>
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/// Use for creating temporary objects in the Burn method.
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/// </summary>
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/// <returns>An object of type T.</returns>
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protected override double Create()
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{
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return 0;
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}
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/// <inheritdoc/>
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protected override void DoAdd(ref double first, double factor, double second)
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{
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first += factor * second;
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}
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/// <inheritdoc/>
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protected override double DoProduct(double first, double second)
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{
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return first * second;
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}
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/// <inheritdoc/>
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protected override void DoSubtract(ref double first, double factor, double second)
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{
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first -= factor * second;
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}
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/// <summary>
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/// Samples the momentum from a normal distribution.
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/// </summary>
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/// <param name="p">The momentum to be randomized.</param>
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protected override void RandomizeMomentum(ref double p)
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{
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p = _distribution.Sample();
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}
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/// <summary>
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/// The default method used for computing the derivative. Uses a simple three point estimation.
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/// </summary>
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/// <param name="function">Function for which the derivative is to be evaluated.</param>
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/// <param name="x">The location where the derivative is to be evaluated.</param>
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/// <returns>The derivative of the function at the point x.</returns>
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static double Grad(DensityLn<double> function, double x)
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{
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double h = Math.Max(10e-4, (10e-7) * x);
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double increment = x + h;
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double decrement = x - h;
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return (function(increment) - function(decrement)) / (2 * h);
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}
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}
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}
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