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richard-churchman
cc0a2bee21
Included open-source Accord.net library code natively to the solution given the deprecated state of that project. Accord.net will be supported inside Jube for own needs (such as upgrading to .Net 7+). Accord.net libraries modified to compile to .Net 6. Modified Accord.net libraries to better support Newtonsoft Json.net serialisation. Included annotations in the Accord.net libraries to house important dependency statistics. Serialised json can be used independently of Jube to recall a Neural Network. Removal of Binary Serializer totally as a precursor to the projects support of .Net 7+. Extensive bug fixing in crucial functions of Neural Network training and recall. While this part of the system remains in Alpha, it is substantially more fit for purpose.
302 lines
11 KiB
C#
302 lines
11 KiB
C#
// Accord Statistics Library
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// The Accord.NET Framework
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// http://accord-framework.net
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//
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// Copyright © César Souza, 2009-2017
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// cesarsouza at gmail.com
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//
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// This library is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 2.1 of the License, or (at your option) any later version.
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//
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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// Lesser General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License along with this library; if not, write to the Free Software
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// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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//
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namespace Accord.Statistics.Distributions.Univariate
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{
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using System;
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using Accord.Statistics.Distributions.Fitting;
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using Accord.Compat;
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using System.Numerics;
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/// <summary>
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/// Wrapped Cauchy Distribution.
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/// </summary>
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///
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/// <remarks>
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/// <para>
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/// In probability theory and directional statistics, a wrapped Cauchy distribution
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/// is a wrapped probability distribution that results from the "wrapping" of the
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/// Cauchy distribution around the unit circle. The Cauchy distribution is sometimes
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/// known as a Lorentzian distribution, and the wrapped Cauchy distribution may
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/// sometimes be referred to as a wrapped Lorentzian distribution.</para>
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///
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/// <para>
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/// The wrapped Cauchy distribution is often found in the field of spectroscopy where
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/// it is used to analyze diffraction patterns (e.g. see Fabry–Pérot interferometer)</para>.
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///
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/// <para>
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/// References:
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/// <list type="bullet">
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/// <item><description><a href="http://en.wikipedia.org/wiki/Directional_statistics">
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/// Wikipedia, The Free Encyclopedia. Directional statistics. Available on:
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/// http://en.wikipedia.org/wiki/Directional_statistics </a></description></item>
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/// <item><description><a href="http://en.wikipedia.org/wiki/Wrapped_Cauchy_distribution">
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/// Wikipedia, The Free Encyclopedia. Wrapped Cauchy distribution. Available on:
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/// http://en.wikipedia.org/wiki/Wrapped_Cauchy_distribution </a></description></item>
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/// </list></para>
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/// </remarks>
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///
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/// <example>
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/// <code>
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/// // Create a Wrapped Cauchy distribution with μ = 0.42, γ = 3
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/// var dist = new WrappedCauchyDistribution(mu: 0.42, gamma: 3);
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///
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/// // Common measures
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/// double mean = dist.Mean; // 0.42
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/// double var = dist.Variance; // 0.950212931632136
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///
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/// // Probability density functions
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/// double pdf = dist.ProbabilityDensityFunction(x: 0.42); // 0.1758330112785475
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/// double lpdf = dist.LogProbabilityDensityFunction(x: 0.42); // -1.7382205338929015
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///
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/// // String representation
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/// string str = dist.ToString(); // "WrappedCauchy(x; μ = 0,42, γ = 3)"
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/// </code>
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/// </example>
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///
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/// <seealso cref="CauchyDistribution"/>
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///
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public class WrappedCauchyDistribution : UnivariateContinuousDistribution,
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IFittableDistribution<double, CauchyOptions>
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{
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private double mu;
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private double gamma;
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/// <summary>
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/// Initializes a new instance of the <see cref="WrappedCauchyDistribution"/> class.
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/// </summary>
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///
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/// <param name="mu">The mean resultant parameter μ.</param>
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/// <param name="gamma">The gamma parameter γ.</param>
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///
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public WrappedCauchyDistribution([Real] double mu, [Positive] double gamma)
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{
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if (gamma <= 0)
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throw new ArgumentOutOfRangeException("gamma", "Gamma must be positive.");
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this.mu = mu;
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this.gamma = gamma;
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}
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/// <summary>
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/// Gets the mean for this distribution.
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/// </summary>
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///
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/// <value>
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/// The distribution's mean value.
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/// </value>
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///
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public override double Mean
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{
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get { return mu; }
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set {} //Not Implemented.
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}
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/// <summary>
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/// Gets the variance for this distribution.
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/// </summary>
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///
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/// <value>
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/// The distribution's variance.
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/// </value>
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///
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public override double Variance
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{
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get { return 1 - Math.Exp(-gamma); }
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set {} //Not Implemented.
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}
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/// <summary>
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/// Not supported.
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/// </summary>
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///
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public override double Median
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{
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get { throw new NotSupportedException(); }
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}
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/// <summary>
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/// Not supported.
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/// </summary>
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///
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public override double Mode
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{
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get { throw new NotSupportedException(); }
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set { } //Not Implemented.
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}
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/// <summary>
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/// Gets the support interval for this distribution.
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/// </summary>
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///
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/// <value>
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/// A <see cref="DoubleRange" /> containing
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/// the support interval for this distribution.
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/// </value>
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///
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public override DoubleRange Support
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{
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get { return new DoubleRange(-Math.PI, Math.PI); }
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set {} //Not Implemented.
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}
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/// <summary>
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/// Gets the entropy for this distribution.
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/// </summary>
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///
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/// <value>
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/// The distribution's entropy.
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/// </value>
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///
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public override double Entropy
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{
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get { return Math.Log(2 * Math.PI * (1 - Math.Exp(-2 * gamma))); }
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set {} //Not Implemented.
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}
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/// <summary>
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/// Not supported.
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/// </summary>
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///
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protected internal override double InnerDistributionFunction(double x)
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{
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throw new NotSupportedException();
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}
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/// <summary>
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/// Gets the probability density function (pdf) for
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/// this distribution evaluated at point <c>x</c>.
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/// </summary>
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///
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/// <param name="x">A single point in the distribution range.</param>
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///
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/// <returns>
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/// The probability of <c>x</c> occurring
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/// in the current distribution.
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/// </returns>
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///
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protected internal override double InnerProbabilityDensityFunction(double x)
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{
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double constant = (1.0 / (2 * Math.PI));
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return constant * Math.Sinh(gamma) / (Math.Cosh(gamma) - Math.Cos(x - mu));
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}
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/// <summary>
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/// Gets the log-probability density function (pdf) for
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/// this distribution evaluated at point <c>x</c>.
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/// </summary>
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///
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/// <param name="x">A single point in the distribution range.</param>
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///
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/// <returns>
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/// The logarithm of the probability of <c>x</c>
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/// occurring in the current distribution.
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/// </returns>
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///
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protected internal override double InnerLogProbabilityDensityFunction(double x)
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{
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return Math.Log(ProbabilityDensityFunction(x));
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}
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/// <summary>
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/// Creates a new object that is a copy of the current instance.
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/// </summary>
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///
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/// <returns>
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/// A new object that is a copy of this instance.
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/// </returns>
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///
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public override object Clone()
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{
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return new WrappedCauchyDistribution(mu, gamma);
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}
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/// <summary>
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/// Fits the underlying distribution to a given set of observations.
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/// </summary>
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///
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/// <param name="observations">The array of observations to fit the model against. The array
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/// elements can be either of type double (for univariate data) or
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/// type double[] (for multivariate data).</param>
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/// <param name="weights">The weight vector containing the weight for each of the samples.</param>
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/// <param name="options">Optional arguments which may be used during fitting, such
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/// as regularization constants and additional parameters.</param>
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///
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public void Fit(double[] observations, int[] weights, CauchyOptions options)
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{
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if (weights != null)
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throw new ArgumentException("This distribution does not support weighted samples.", "weights");
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Fit(observations, (double[])null, options);
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}
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/// <summary>
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/// Fits the underlying distribution to a given set of observations.
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/// </summary>
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///
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/// <param name="observations">The array of observations to fit the model against. The array
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/// elements can be either of type double (for univariate data) or
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/// type double[] (for multivariate data).</param>
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/// <param name="weights">The weight vector containing the weight for each of the samples.</param>
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/// <param name="options">Optional arguments which may be used during fitting, such
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/// as regularization constants and additional parameters.</param>
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///
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public void Fit(double[] observations, double[] weights, CauchyOptions options)
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{
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if (weights != null)
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throw new ArgumentException("This distribution does not support weighted samples.", "weights");
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double sin = 0, cos = 0;
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for (int i = 0; i < observations.Length; i++)
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{
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sin += Math.Sin(observations[i]);
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cos += Math.Cos(observations[i]);
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}
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mu = new Complex(sin, cos).Phase;
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double N = observations.Length;
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double R2 = (cos / N) * (cos / N) + (sin / N) * (sin / N);
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double R2e = N / (N - 1) * (R2 - 1.0 / N);
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gamma = Math.Log(1.0 / R2e) / 2.0;
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}
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/// <summary>
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/// Returns a <see cref="System.String"/> that represents this instance.
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/// </summary>
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///
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/// <returns>
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/// A <see cref="System.String"/> that represents this instance.
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/// </returns>
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///
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public override string ToString(string format, IFormatProvider formatProvider)
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{
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return String.Format(formatProvider, "WrappedCauchy(x; μ = {0}, γ = {1})",
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mu.ToString(format, formatProvider),
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gamma.ToString(format, formatProvider));
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}
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}
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}
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