// <copyright file="HybridMCGeneric.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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// </copyright>
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namespace IStation.Numerics.Statistics.Mcmc
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{
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using System;
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using Distributions;
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/// <summary>
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/// The Hybrid (also called Hamiltonian) Monte Carlo produces samples from distribution P using a set
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/// of Hamiltonian equations to guide the sampling process. It uses the negative of the log density as
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/// a potential energy, and a randomly generated momentum to set up a Hamiltonian system, which is then used
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/// to sample the distribution. This can result in a faster convergence than the random walk Metropolis sampler
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/// (<seealso cref="MetropolisSampler{T}"/>).
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/// </summary>
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/// <typeparam name="T">The type of samples this sampler produces.</typeparam>
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public abstract class HybridMCGeneric<T> : McmcSampler<T>
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{
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/// <summary>
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/// The delegate type that defines a derivative evaluated at a certain point.
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/// </summary>
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/// <param name="f">Function to be differentiated.</param>
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/// <param name="x">Value where the derivative is computed.</param>
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public delegate T DiffMethod(DensityLn<T> f, T x);
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/// <summary>
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/// Evaluates the energy function of the target distribution.
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/// </summary>
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readonly DensityLn<T> _energy;
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/// <summary>
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/// The current location of the sampler.
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/// </summary>
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protected T Current;
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/// <summary>
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/// The number of burn iterations between two samples.
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/// </summary>
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int _burnInterval;
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/// <summary>
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/// The size of each step in the Hamiltonian equation.
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/// </summary>
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double _stepSize;
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/// <summary>
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/// The number of iterations in the Hamiltonian equation.
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/// </summary>
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int _frogLeapSteps;
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/// <summary>
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/// The algorithm used for differentiation.
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/// </summary>
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readonly DiffMethod _diff;
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/// <summary>
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/// Gets or sets the number of iterations in between returning samples.
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/// </summary>
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/// <exception cref="ArgumentOutOfRangeException">When burn interval is negative.</exception>
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public int BurnInterval
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{
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get => _burnInterval;
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set => _burnInterval = SetNonNegative(value);
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}
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/// <summary>
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/// Gets or sets the number of iterations in the Hamiltonian equation.
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/// </summary>
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/// <exception cref="ArgumentOutOfRangeException">When frog leap steps is negative or zero.</exception>
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public int FrogLeapSteps
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{
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get => _frogLeapSteps;
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set => _frogLeapSteps = SetPositive(value);
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}
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/// <summary>
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/// Gets or sets the size of each step in the Hamiltonian equation.
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/// </summary>
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/// <exception cref="ArgumentOutOfRangeException">When step size is negative or zero.</exception>
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public double StepSize
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{
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get => _stepSize;
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set => _stepSize = SetPositive(value);
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}
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/// <summary>
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/// Constructs a new Hybrid Monte Carlo sampler.
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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="randomSource">Random number generator used for sampling the momentum.</param>
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/// <param name="diff">The method used for differentiation.</param>
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/// <exception cref="ArgumentOutOfRangeException">When the number of burnInterval iteration is negative.</exception>
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/// <exception cref="ArgumentNullException">When either x0, pdfLnP or diff is null.</exception>
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protected HybridMCGeneric(T x0, DensityLn<T> pdfLnP, int frogLeapSteps, double stepSize, int burnInterval, Random randomSource, DiffMethod diff)
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{
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_energy = x => -pdfLnP(x);
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FrogLeapSteps = frogLeapSteps;
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StepSize = stepSize;
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BurnInterval = burnInterval;
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Current = x0;
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_diff = diff;
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RandomSource = randomSource;
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}
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/// <summary>
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/// Returns a sample from the distribution P.
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/// </summary>
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public override T Sample()
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{
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Burn(_burnInterval + 1);
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return Current;
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}
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/// <summary>
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/// This method runs the sampler for a number of iterations without returning a sample
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/// </summary>
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protected void Burn(int n)
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{
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T p = Create();
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double e = _energy(Current);
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T gradient = _diff(_energy, Current);
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for (int i = 0; i < n; i++)
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{
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RandomizeMomentum(ref p);
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double h = Hamiltonian(p, e);
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T mNew = Copy(Current);
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T gNew = Copy(gradient);
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for (int j = 0; j < _frogLeapSteps; j++)
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{
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HamiltonianEquations(ref gNew, ref mNew, ref p);
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}
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double enew = _energy(mNew);
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double hnew = Hamiltonian(p, enew);
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double dh = hnew - h;
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Update(ref e, ref gradient, mNew, gNew, enew, dh);
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Samples++;
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}
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}
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/// <summary>
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/// Method used to update the sample location. Used in the end of the loop.
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/// </summary>
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/// <param name="e">The old energy.</param>
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/// <param name="gradient">The old gradient/derivative of the energy.</param>
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/// <param name="mNew">The new sample.</param>
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/// <param name="gNew">The new gradient/derivative of the energy.</param>
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/// <param name="enew">The new energy.</param>
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/// <param name="dh">The difference between the old Hamiltonian and new Hamiltonian. Use to determine
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/// if an update should take place. </param>
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protected void Update(ref double e, ref T gradient, T mNew, T gNew, double enew, double dh)
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{
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if (dh <= 0)
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{
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Current = mNew; gradient = gNew; e = enew; Accepts++;
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}
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else if (Bernoulli.Sample(RandomSource, Math.Exp(-dh)) == 1)
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{
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Current = mNew; gradient = gNew; e = enew; Accepts++;
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}
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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 abstract T Create();
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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 abstract T Copy(T source);
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/// <summary>
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/// Method for doing dot product.
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/// </summary>
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/// <param name="first">First vector/scalar in the product.</param>
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/// <param name="second">Second vector/scalar in the product.</param>
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protected abstract double DoProduct(T first, T second);
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/// <summary>
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/// Method for adding, multiply the second vector/scalar by factor and then
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/// add it to the first vector/scalar.
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/// </summary>
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/// <param name="first">First vector/scalar.</param>
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/// <param name="factor">Scalar factor multiplying by the second vector/scalar.</param>
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/// <param name="second">Second vector/scalar.</param>
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protected abstract void DoAdd(ref T first, double factor, T second);
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/// <summary>
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/// Multiplying the second vector/scalar by factor and then subtract it from
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/// the first vector/scalar.
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/// </summary>
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/// <param name="first">First vector/scalar.</param>
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/// <param name="factor">Scalar factor to be multiplied to the second vector/scalar.</param>
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/// <param name="second">Second vector/scalar.</param>
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protected abstract void DoSubtract(ref T first, double factor, T second);
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/// <summary>
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/// Method for sampling a random momentum.
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/// </summary>
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/// <param name="p">Momentum to be randomized.</param>
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protected abstract void RandomizeMomentum(ref T p);
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/// <summary>
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/// The Hamiltonian equations that is used to produce the new sample.
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/// </summary>
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protected void HamiltonianEquations(ref T gNew, ref T mNew, ref T p)
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{
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DoSubtract(ref p, _stepSize / 2, gNew);
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DoAdd(ref mNew, _stepSize, p);
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gNew = _diff(_energy, mNew);
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DoSubtract(ref p, _stepSize / 2, gNew);
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}
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/// <summary>
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/// Method to compute the Hamiltonian used in the method.
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/// </summary>
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/// <param name="momentum">The momentum.</param>
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/// <param name="e">The energy.</param>
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/// <returns>Hamiltonian=E+p.p/2</returns>
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protected double Hamiltonian(T momentum, double e)
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{
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return e + DoProduct(momentum, momentum) / 2;
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}
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/// <summary>
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/// Method to check and set a quantity to a non-negative value.
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/// </summary>
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/// <param name="value">Proposed value to be checked.</param>
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/// <returns>Returns value if it is greater than or equal to zero.</returns>
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/// <exception cref="ArgumentOutOfRangeException">Throws when value is negative.</exception>
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protected int SetNonNegative(int value)
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{
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if (value < 0)
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{
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throw new ArgumentOutOfRangeException(nameof(value), "Value must not be negative (zero is ok).");
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}
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return value;
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}
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/// <summary>
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/// Method to check and set a quantity to a non-negative value.
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/// </summary>
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/// <param name="value">Proposed value to be checked.</param>
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/// <returns>Returns value if it is greater than to zero.</returns>
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/// <exception cref="ArgumentOutOfRangeException">Throws when value is negative or zero.</exception>
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protected int SetPositive(int value)
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{
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if (value <= 0)
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{
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throw new ArgumentOutOfRangeException(nameof(value), "Value must not be negative (zero is ok).");
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}
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return value;
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}
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/// <summary>
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/// Method to check and set a quantity to a non-negative value.
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/// </summary>
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/// <param name="value">Proposed value to be checked.</param>
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/// <returns>Returns value if it is greater than zero.</returns>
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/// <exception cref="ArgumentOutOfRangeException">Throws when value is negative or zero.</exception>
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protected double SetPositive(double value)
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{
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if (value <= 0)
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{
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throw new ArgumentOutOfRangeException(nameof(value), "Value must not be negative (zero is ok).");
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}
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return value;
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}
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}
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}
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