// <copyright file="NumericalJacobian.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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// 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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// Software is furnished to do so, subject to the following
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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 Jacobian of a 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 NumericalJacobian
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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 Jacobian object with a three point central difference method.
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/// </summary>
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public NumericalJacobian() : this(3, 1) { }
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/// <summary>
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/// Creates a numerical Jacobian with a specified differentiation scheme.
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/// </summary>
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/// <param name="points">Number of points for Jacobian evaluation.</param>
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/// <param name="center">Center point for differentiation.</param>
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public NumericalJacobian(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 Jacobian of scalar univariate function f at point 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 Jacobian.</param>
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/// <returns>Jacobian vector.</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, 1) };
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}
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/// <summary>
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/// Evaluates the Jacobian of a multivariate function f at vector x.
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/// </summary>
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/// <remarks>
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/// This function assumes that the length of vector x consistent with the argument count of f.
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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 Jacobian.</param>
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/// <returns>Jacobian vector.</returns>
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public double[] Evaluate(Func<double[], double> f, double[] x)
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{
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var jacobian = new double[x.Length];
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for (var i = 0; i < jacobian.Length; i++)
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jacobian[i] = _df.EvaluatePartialDerivative(f, x, i, 1);
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return jacobian;
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}
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/// <summary>
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/// Evaluates the Jacobian of a multivariate function f at vector x given a current function value.
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/// </summary>
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/// <remarks>
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/// To minimize the number of function evaluations, a user can supply the current value of the function
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/// to be used in computing the Jacobian. This value must correspond to the "center" location for the
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/// finite differencing. If a scheme is used where the center value is not evaluated, this will provide no
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/// added efficiency. This method also assumes that the length of vector x consistent with the argument count of f.
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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 Jacobian.</param>
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/// <param name="currentValue">Current function value at finite difference center.</param>
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/// <returns>Jacobian vector.</returns>
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public double[] Evaluate(Func<double[], double> f, double[] x, double currentValue)
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{
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var jacobian = new double[x.Length];
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for (var i = 0; i < jacobian.Length; i++)
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jacobian[i] = _df.EvaluatePartialDerivative(f, x, i, 1, currentValue);
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return jacobian;
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}
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/// <summary>
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/// Evaluates the Jacobian of a multivariate function array f at vector x.
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/// </summary>
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/// <param name="f">Multivariate function array handle.</param>
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/// <param name="x">Vector at which to evaluate Jacobian.</param>
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/// <returns>Jacobian matrix.</returns>
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public double[,] Evaluate(Func<double[], double>[] f, double[] x)
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{
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var jacobian = new double[f.Length, x.Length];
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for (int i = 0; i < f.Length; i++)
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{
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var gradient = Evaluate(f[i], x);
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for (int j = 0; j < gradient.Length; j++)
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jacobian[i, j] = gradient[j];
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}
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return jacobian;
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}
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/// <summary>
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/// Evaluates the Jacobian of a multivariate function array f at vector x given a vector of current function values.
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/// </summary>
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/// <remarks>
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/// To minimize the number of function evaluations, a user can supply a vector of current values of the functions
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/// to be used in computing the Jacobian. These value must correspond to the "center" location for the
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/// finite differencing. If a scheme is used where the center value is not evaluated, this will provide no
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/// added efficiency. This method also assumes that the length of vector x consistent with the argument count of f.
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/// </remarks>
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/// <param name="f">Multivariate function array handle.</param>
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/// <param name="x">Vector at which to evaluate Jacobian.</param>
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/// <param name="currentValues">Vector of current function values.</param>
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/// <returns>Jacobian matrix.</returns>
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public double[,] Evaluate(Func<double[], double>[] f, double[] x, double[] currentValues)
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{
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var jacobian = new double[f.Length, x.Length];
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for (int i = 0; i < f.Length; i++)
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{
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var gradient = Evaluate(f[i], x, currentValues[i]);
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for (int j = 0; j < gradient.Length; j++)
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jacobian[i, j] = gradient[j];
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}
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return jacobian;
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}
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/// <summary>
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/// Resets the function evaluation counter for the Jacobian.
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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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