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Accord Statistics Library\r","// The Accord.NET Framework\r","// http://accord-framework.net\r","//\r","// Copyright © César Souza, 2009-2017\r","// cesarsouza at gmail.com\r","//\r","// This library is free software; you can redistribute it and/or\r","// modify it under the terms of the GNU Lesser General Public\r","// License as published by the Free Software Foundation; either\r","// version 2.1 of the License, or (at your option) any later version.\r","//\r","// This library is distributed in the hope that it will be useful,\r","// but WITHOUT ANY WARRANTY; without even the implied warranty of\r","// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU\r","// Lesser General Public License for more details.\r","//\r","// You should have received a copy of the GNU Lesser General Public\r","// License along with this library; if not, write to the Free Software\r","// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA\r","//\r","\r","namespace Accord.Statistics.Distributions.Multivariate\r","{\r"," using System;\r"," using Accord.Math;\r"," using Accord.Math.Decompositions;\r"," using Accord.Statistics.Distributions;\r"," using Accord.Statistics.Distributions.Fitting;\r"," using Accord.Statistics.Distributions.Univariate;\r"," using System.Runtime.CompilerServices;\r"," using Accord.Math.Random;\r"," using Accord.Compat;\r","\r"," /// \r"," /// Uniform distribution inside a n-dimensional ball.\r"," /// \r"," /// \r"," /// \r"," /// \r"," [Serializable]\r"," public class UniformSphereDistribution : MultivariateContinuousDistribution,\r"," ISampleableDistribution\r"," {\r","\r"," private const double rtol = 1e-5;\r","\r"," // Distribution parameters\r"," private double[] center;\r"," private double radius;\r","\r"," private double surface;\r","\r","\r","\r"," /// \r"," /// Initializes a new instance of the class.\r"," /// \r"," /// \r"," /// The number of dimensions in the n-dimensional sphere.\r"," /// \r"," public UniformSphereDistribution(int dimension)\r"," : this(new double[dimension])\r"," {\r"," }\r","\r"," /// \r"," /// Initializes a new instance of the class.\r"," /// \r"," /// \r"," /// The sphere's mean.\r"," /// The sphere's radius.\r"," /// \r"," public UniformSphereDistribution(double[] mean, double radius = 1)\r"," : base(mean.Length)\r"," {\r"," this.center = mean;\r"," this.radius = radius;\r","\r"," double n = mean.Length;\r"," double num = Math.Pow(2 * Math.PI, (n + 1.0) / 2.0);\r"," double den = Gamma.Function((n + 1) / 2.0);\r"," surface = num / den * Math.Pow(radius, n);\r"," }\r","\r"," /// \r"," /// Gets the sphere radius.\r"," /// \r"," /// \r"," public double Radius { get { return radius; } }\r","\r"," /// \r"," /// Gets the sphere volume.\r"," /// \r"," /// \r"," public double Surface { get { return surface; } }\r","\r"," /// \r"," /// Gets the sphere center (mean) vector.\r"," /// \r"," /// A vector containing the mean values for the distribution.\r"," public override double[] Mean\r"," {\r"," get { return center; }\r"," }\r","\r"," /// \r"," /// Gets the variance for this distribution.\r"," /// \r"," /// A vector containing the variance values for the distribution.\r"," public override double[] Variance\r"," {\r"," get { return Vector.Create(Dimension, radius); }\r"," }\r","\r"," /// \r"," /// Gets the variance-covariance matrix for this distribution.\r"," /// \r"," /// A matrix containing the covariance values for the distribution.\r"," public override double[,] Covariance\r"," {\r"," get { return Matrix.Diagonal(Variance); }\r"," }\r","\r"," /// \r"," /// Not implemented.\r"," /// \r"," /// \r"," protected internal override double InnerDistributionFunction(params double[] x)\r"," {\r"," throw new NotImplementedException();\r"," }\r","\r","\r"," /// \r"," /// Gets the probability density function (pdf) for\r"," /// this distribution evaluated at point x.\r"," /// \r"," /// A single point in the distribution range. For a\r"," /// univariate distribution, this should be a single\r"," /// double value. For a multivariate distribution,\r"," /// this should be a double array.\r"," /// The probability of x occurring\r"," /// in the current distribution.\r"," /// The Probability Density Function (PDF) describes the\r"," /// probability that a given value x will occur.\r"," protected internal override double InnerProbabilityDensityFunction(params double[] x)\r"," {\r"," double distance = Distance.Euclidean(x, center);\r"," if (distance.IsEqual(radius, rtol: rtol))\r"," return 1 / surface;\r"," return 0;\r"," }\r","\r"," /// \r"," /// Gets the log-probability density function (pdf)\r"," /// for this distribution evaluated at point x.\r"," /// \r"," /// A single point in the distribution range. For a\r"," /// univariate distribution, this should be a single\r"," /// double value. For a multivariate distribution,\r"," /// this should be a double array.\r"," /// The logarithm of the probability of x\r"," /// occurring in the current distribution.\r"," protected internal override double InnerLogProbabilityDensityFunction(params double[] x)\r"," {\r"," double distance = Distance.Euclidean(x, center);\r"," if (distance.IsEqual(radius, rtol: rtol))\r"," return -Math.Log(surface);\r"," return Double.NegativeInfinity;\r"," }\r","\r"," /// \r"," /// Creates a new object that is a copy of the current instance.\r"," /// \r"," /// \r"," /// \r"," /// A new object that is a copy of this instance.\r"," /// \r"," /// \r"," public override object Clone()\r"," {\r"," return new UniformSphereDistribution(center.Copy(), radius);\r"," }\r","\r"," /// \r"," /// Generates a random vector of observations from the current distribution.\r"," /// \r"," /// \r"," /// The number of samples to generate.\r"," /// The location where to store the samples.\r"," /// The random number generator to use as a source of randomness. \r"," /// Default is to use .\r"," /// \r"," /// A random vector of observations drawn from this distribution.\r"," /// \r"," public override double[][] Generate(int samples, double[][] result, Random source)\r"," {\r"," return Random(samples, center, radius, result, source);\r"," }\r","\r"," /// \r"," /// Generates a random vector of observations from the current distribution.\r"," /// \r"," /// \r"," /// The number of samples to generate.\r"," /// The location where to store the samples.\r"," /// The sphere's mean.\r"," /// The sphere's radius.\r"," /// \r"," /// A random vector of observations drawn from this distribution.\r"," /// \r"," public static double[][] Random(int samples, double[] mean, double radius, double[][] result)\r"," {\r"," return Random(samples, mean, radius, result, Accord.Math.Random.Generator.Random);\r"," }\r","\r"," /// \r"," /// Generates a random vector of observations from the current distribution.\r"," /// \r"," /// \r"," /// The number of samples to generate.\r"," /// The location where to store the samples.\r"," /// The sphere's mean.\r"," /// The sphere's radius.\r"," /// The random number generator to use as a source of randomness. \r"," /// Default is to use .\r"," /// \r"," /// A random vector of observations drawn from this distribution.\r"," /// \r"," public static double[][] Random(int samples, double[] mean, double radius, double[][] result, Random source)\r"," {\r"," Random(samples, mean.Length, result, source);\r","\r"," for (int i = 0; i < result.Length; i++)\r"," for (int j = 0; j < mean.Length; j++)\r"," result[i][j] = result[i][j] * radius + mean[j];\r","\r"," return result;\r"," }\r","\r"," /// \r"," /// Generates a random vector of observations from the current distribution.\r"," /// \r"," /// \r"," /// The number of samples to generate.\r"," /// The number of dimensions in the n-dimensional sphere.\r"," /// \r"," /// A random vector of observations drawn from this distribution.\r"," /// \r"," public static double[][] Random(int samples, int dimension)\r"," {\r"," return Random(samples, dimension, Jagged.Zeros(samples, dimension));\r"," }\r","\r"," /// \r"," /// Generates a random vector of observations from the current distribution.\r"," /// \r"," /// \r"," /// The number of samples to generate.\r"," /// The number of dimensions in the n-dimensional sphere.\r"," /// The random number generator to use as a source of randomness. \r"," /// Default is to use .\r"," /// \r"," /// A random vector of observations drawn from this distribution.\r"," /// \r"," public static double[][] Random(int samples, int dimension, Random source)\r"," {\r"," return Random(samples, dimension, Jagged.Zeros(samples, dimension), source);\r"," }\r","\r"," /// \r"," /// Generates a random vector of observations from the current distribution.\r"," /// \r"," /// \r"," /// The number of samples to generate.\r"," /// The number of dimensions in the n-dimensional sphere.\r"," /// The location where to store the samples.\r"," /// \r"," /// A random vector of observations drawn from this distribution.\r"," /// \r"," public static double[][] Random(int samples, int dimension, double[][] result)\r"," {\r"," return Random(samples, dimension, result, Accord.Math.Random.Generator.Random);\r"," }\r","\r"," /// \r"," /// Generates a random vector of observations from the current distribution.\r"," /// \r"," /// \r"," /// The number of samples to generate.\r"," /// The number of dimensions in the n-dimensional sphere.\r"," /// The location where to store the samples.\r"," /// The random number generator to use as a source of randomness. \r"," /// Default is to use .\r"," /// \r"," /// A random vector of observations drawn from this distribution.\r"," /// \r"," public static double[][] Random(int samples, int dimension, double[][] result, Random source)\r"," {\r"," for (int i = 0; i < result.Length; i++)\r"," {\r"," // Generate independent normally-distributed vectors\r"," NormalDistribution.Random(dimension, result: result[i], source: source);\r"," result[i].Normalize(inPlace: true); // make unit norm\r"," }\r","\r"," return result;\r"," }\r","\r"," /// \r"," /// Returns a that represents this instance.\r"," /// \r"," /// \r"," /// The format.\r"," /// The format provider.\r"," /// \r"," /// \r"," /// A that represents this instance.\r"," /// \r"," /// \r"," public override string ToString(string format, IFormatProvider formatProvider)\r"," {\r"," return String.Format(formatProvider, \"UniformSphere(X; μ, r)\");\r"," }\r","\r"," 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