// <copyright file="NumericalHessian.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) 2009-2015 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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// 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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// 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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using System;
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namespace IStation.Numerics.Differentiation
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{
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/// <summary>
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/// Class for evaluating the Hessian of a smooth continuously differentiable function using finite differences.
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/// By default, a central 3-point method is used.
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/// </summary>
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public class NumericalHessian
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{
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/// <summary>
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/// Number of function evaluations.
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/// </summary>
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public int FunctionEvaluations => _df.Evaluations;
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private readonly NumericalDerivative _df;
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/// <summary>
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/// Creates a numerical Hessian object with a three point central difference method.
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/// </summary>
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public NumericalHessian() : this(3, 1) { }
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/// <summary>
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/// Creates a numerical Hessian with a specified differentiation scheme.
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/// </summary>
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/// <param name="points">Number of points for Hessian evaluation.</param>
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/// <param name="center">Center point for differentiation.</param>
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public NumericalHessian(int points, int center)
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{
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_df = new NumericalDerivative(points, center);
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}
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/// <summary>
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/// Evaluates the Hessian of the scalar univariate function f at points x.
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/// </summary>
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/// <param name="f">Scalar univariate function handle.</param>
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/// <param name="x">Point at which to evaluate Hessian.</param>
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/// <returns>Hessian tensor.</returns>
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public double[] Evaluate(Func<double, double> f, double x)
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{
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return new[] { _df.EvaluateDerivative(f, x, 2) };
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}
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/// <summary>
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/// Evaluates the Hessian of a multivariate function f at points x.
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/// </summary>
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/// <remarks>
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/// This method of computing the Hessian is only valid for Lipschitz continuous functions.
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/// The function mirrors the Hessian along the diagonal since d2f/dxdy = d2f/dydx for continuously differentiable functions.
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/// </remarks>
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/// <param name="f">Multivariate function handle.></param>
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/// <param name="x">Points at which to evaluate Hessian.></param>
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/// <returns>Hessian tensor.</returns>
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public double[,] Evaluate(Func<double[], double> f, double[] x)
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{
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var hessian = new double[x.Length, x.Length];
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// Compute diagonal elements
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for (var row = 0; row < x.Length; row++)
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{
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hessian[row, row] = _df.EvaluatePartialDerivative(f, x, row, 2);
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}
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// Compute non-diagonal elements
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for (var row = 0; row < x.Length; row++)
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{
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for (var col = 0; col < row; col++)
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{
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var mixedPartial = _df.EvaluateMixedPartialDerivative(f, x, new[] { row, col }, 2);
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hessian[row, col] = mixedPartial;
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hessian[col, row] = mixedPartial;
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}
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}
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return hessian;
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}
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/// <summary>
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/// Resets the function evaluation counter for the Hessian.
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/// </summary>
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public void ResetFunctionEvaluations()
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{
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_df.ResetEvaluations();
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}
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}
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}
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