// <copyright file="HybridMC.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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// 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.Linq;
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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 multivariate distributions.
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/// </summary>
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public class HybridMC : HybridMCGeneric<double[]>
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{
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/// <summary>
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/// Number of parameters in the density function.
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/// </summary>
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private readonly int _length;
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/// <summary>
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/// Distribution to sample momentum from.
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/// </summary>
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private Normal _pDistribution;
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/// <summary>
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/// Standard deviations used in the sampling of different components of the
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/// momentum.
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/// </summary>
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private double[] _mpSdv;
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/// <summary>
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/// Gets or sets the standard deviations used in the sampling of different components of the
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/// momentum.
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/// </summary>
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/// <exception cref="ArgumentOutOfRangeException">When the length of pSdv is not the same as Length.</exception>
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public double[] MomentumStdDev
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{
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get => (double[])_mpSdv.Clone();
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set
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{
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CheckVariance(value);
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_mpSdv = (double[])value.Clone();
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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 components of the momentum will be sampled from a normal distribution with standard deviation
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/// 1 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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/// <exception cref="ArgumentOutOfRangeException">When the number of burnInterval iteration is negative.</exception>
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public HybridMC(double[] x0, DensityLn<double[]> pdfLnP, int frogLeapSteps, double stepSize, int burnInterval = 0)
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: this(x0, pdfLnP, frogLeapSteps, stepSize, burnInterval, new double[x0.Length], SystemRandomSource.Default, Grad)
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{
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for (int i = 0; i < _length; i++)
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{
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_mpSdv[i] = 1;
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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 components of 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 deviations of the normal distributions that are used to sample
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/// the components of the momentum.</param>
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/// <exception cref="ArgumentOutOfRangeException">When the number of burnInterval iteration is negative.</exception>
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public HybridMC(double[] x0, DensityLn<double[]> pdfLnP, int frogLeapSteps, double stepSize, int burnInterval, double[] pSdv)
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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 multivariate probability distribution.
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/// The components of the momentum will be sampled from a normal distribution with standard deviation
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/// specified by pSdv using the a random number generator provided by the user.
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/// 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 deviations of the normal distributions that are used to sample
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/// the components of the momentum.</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 HybridMC(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 components of the momentum will be sampled from a normal distribution with standard deviations
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/// given by pSdv. This constructor will set the burn interval, the method used for
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/// numerical differentiation and the random number generator.
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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 deviations of the normal distributions that are used to sample
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/// the components of the momentum.</param>
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/// <param name="randomSource">Random number generator used for sampling the momentum.</param>
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/// <param name="diff">The method used for numerical differentiation.</param>
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/// <exception cref="ArgumentOutOfRangeException">When the number of burnInterval iteration is negative.</exception>
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/// <exception cref="ArgumentOutOfRangeException">When the length of pSdv is not the same as x0.</exception>
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public HybridMC(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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_length = x0.Length;
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MomentumStdDev = pSdv;
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Initialize(x0);
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Burn(BurnInterval);
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}
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/// <summary>
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/// Initialize parameters.
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/// </summary>
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/// <param name="x0">The current location of the sampler.</param>
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private void Initialize(double[] x0)
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{
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Current = (double[])x0.Clone();
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_pDistribution = new Normal(0.0, 1.0, RandomSource);
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}
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/// <summary>
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/// Checking that the location and the momentum are of the same dimension and that each component is positive.
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/// </summary>
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/// <param name="pSdv">The standard deviations used for sampling the momentum.</param>
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/// <exception cref="ArgumentOutOfRangeException">When the length of pSdv is not the same as Length or if any
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/// component is negative.</exception>
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/// <exception cref="ArgumentNullException">When pSdv is null.</exception>
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private void CheckVariance(double[] pSdv)
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{
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if (pSdv == null)
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{
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throw new ArgumentNullException(nameof(pSdv), "Standard deviation cannot be null.");
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}
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if (pSdv.Length != _length)
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{
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throw new ArgumentOutOfRangeException(nameof(pSdv), "Standard deviation of momentum must have same length as sample.");
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}
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if (pSdv.Any(sdv => sdv < 0))
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{
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throw new ArgumentOutOfRangeException(nameof(pSdv), "Standard deviation must be positive.");
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}
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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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var destination = new double[_length];
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Array.Copy(source, 0, destination, 0, _length);
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return destination;
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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 new double[_length];
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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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for (int i = 0; i < _length; i++)
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{
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first[i] += factor * second[i];
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}
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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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for (int i = 0; i < _length; i++)
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{
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first[i] -= factor * second[i];
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}
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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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double prod = 0;
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for (int i = 0; i < _length; i++)
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{
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prod += first[i] * second[i];
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}
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return prod;
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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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for (int j = 0; j < _length; j++)
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{
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p[j] = _mpSdv[j] * _pDistribution.Sample();
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}
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}
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/// <summary>
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/// The default method used for computing the gradient. Uses a simple three point estimation.
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/// </summary>
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/// <param name="function">Function which the gradient is to be evaluated.</param>
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/// <param name="x">The location where the gradient is to be evaluated.</param>
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/// <returns>The gradient 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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int length = x.Length;
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var returnValue = new double[length];
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var increment = new double[length];
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var decrement = new double[length];
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Array.Copy(x, 0, increment, 0, length);
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Array.Copy(x, 0, decrement, 0, length);
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for (int i = 0; i < length; i++)
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{
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double y = x[i];
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double h = Math.Max(10e-4, (10e-7) * y);
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increment[i] += h;
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decrement[i] -= h;
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returnValue[i] = (function(increment) - function(decrement)) / (2 * h);
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increment[i] = y;
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decrement[i] = y;
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}
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return returnValue;
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}
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}
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}
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