mathnet-numerics/src/Numerics/Distributions/Rayleigh.cs

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using System;
using System.Collections.Generic;
using MathNet.Numerics.Properties;
using MathNet.Numerics.Random;
using MathNet.Numerics.Threading;

namespace MathNet.Numerics.Distributions
{
    /// <summary>
    /// Continuous Univariate Rayleigh distribution.
    /// The Rayleigh distribution (pronounced /ˈreɪli/) is a continuous probability distribution. As an
    /// example of how it arises, the wind speed will have a Rayleigh distribution if the components of
    /// the two-dimensional wind velocity vector are uncorrelated and normally distributed with equal variance.
    /// For details about this distribution, see
    /// <a href="http://en.wikipedia.org/wiki/Rayleigh_distribution">Wikipedia - Rayleigh distribution</a>.
    /// </summary>
    public class Rayleigh : IContinuousDistribution
    {
        System.Random _random;

        double _scale;

        /// <summary>
        /// Initializes a new instance of the <see cref="Rayleigh"/> class.
        /// </summary>
        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
        /// <exception cref="ArgumentException">If <paramref name="scale"/> is negative.</exception>
        public Rayleigh(double scale)
        {
            _random = SystemRandomSource.Default;
            SetParameters(scale);
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Rayleigh"/> class.
        /// </summary>
        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
        /// <exception cref="ArgumentException">If <paramref name="scale"/> is negative.</exception>
        public Rayleigh(double scale, System.Random randomSource)
        {
            _random = randomSource ?? SystemRandomSource.Default;
            SetParameters(scale);
        }

        /// <summary>
        /// A string representation of the distribution.
        /// </summary>
        /// <returns>a string representation of the distribution.</returns>
        public override string ToString()
        {
            return "Rayleigh(σ = " + _scale + ")";
        }

        /// <summary>
        /// Sets the parameters of the distribution after checking their validity.
        /// </summary>
        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
        /// <exception cref="ArgumentOutOfRangeException">When the parameters are out of range.</exception>
        void SetParameters(double scale)
        {
            if (scale <= 0.0 || Double.IsNaN(scale))
            {
                throw new ArgumentException(Resources.InvalidDistributionParameters);
            }

            _scale = scale;
        }

        /// <summary>
        /// Gets or sets the scale (σ) of the distribution. Range: σ > 0.
        /// </summary>
        public double Scale
        {
            get { return _scale; }
            set { SetParameters(value); }
        }

        /// <summary>
        /// Gets or sets the random number generator which is used to draw random samples.
        /// </summary>
        public System.Random RandomSource
        {
            get { return _random; }
            set { _random = value ?? SystemRandomSource.Default; }
        }

        /// <summary>
        /// Gets the mean of the distribution.
        /// </summary>
        public double Mean
        {
            get { return _scale*Math.Sqrt(Constants.PiOver2); }
        }

        /// <summary>
        /// Gets the variance of the distribution.
        /// </summary>
        public double Variance
        {
            get { return (2.0 - Constants.PiOver2)*_scale*_scale; }
        }

        /// <summary>
        /// Gets the standard deviation of the distribution.
        /// </summary>
        public double StdDev
        {
            get { return Math.Sqrt(2.0 - Constants.PiOver2)*_scale; }
        }

        /// <summary>
        /// Gets the entropy of the distribution.
        /// </summary>
        public double Entropy
        {
            get { return 1.0 + Math.Log(_scale/Constants.Sqrt2) + (Constants.EulerMascheroni/2.0); }
        }

        /// <summary>
        /// Gets the skewness of the distribution.
        /// </summary>
        public double Skewness
        {
            get { return (2.0*Math.Sqrt(Constants.Pi)*(Constants.Pi - 3.0))/Math.Pow(4.0 - Constants.Pi, 1.5); }
        }

        /// <summary>
        /// Gets the mode of the distribution.
        /// </summary>
        public double Mode
        {
            get { return _scale; }
        }

        /// <summary>
        /// Gets the median of the distribution.
        /// </summary>
        public double Median
        {
            get { return _scale*Math.Sqrt(Math.Log(4.0)); }
        }

        /// <summary>
        /// Gets the minimum of the distribution.
        /// </summary>
        public double Minimum
        {
            get { return 0.0; }
        }

        /// <summary>
        /// Gets the maximum of the distribution.
        /// </summary>
        public double Maximum
        {
            get { return Double.PositiveInfinity; }
        }

        /// <summary>
        /// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
        /// </summary>
        /// <param name="x">The location at which to compute the density.</param>
        /// <returns>the density at <paramref name="x"/>.</returns>
        /// <seealso cref="PDF"/>
        public double Density(double x)
        {
            return (x/(_scale*_scale))*Math.Exp(-x*x/(2.0*_scale*_scale));
        }

        /// <summary>
        /// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
        /// </summary>
        /// <param name="x">The location at which to compute the log density.</param>
        /// <returns>the log density at <paramref name="x"/>.</returns>
        /// <seealso cref="PDFLn"/>
        public double DensityLn(double x)
        {
            return Math.Log(x/(_scale*_scale)) - (x*x/(2.0*_scale*_scale));
        }

        /// <summary>
        /// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
        /// </summary>
        /// <param name="x">The location at which to compute the cumulative distribution function.</param>
        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
        /// <seealso cref="CDF"/>
        public double CumulativeDistribution(double x)
        {
            return 1.0 - Math.Exp(-x*x/(2.0*_scale*_scale));
        }

        /// <summary>
        /// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
        /// at the given probability. This is also known as the quantile or percent point function.
        /// </summary>
        /// <param name="p">The location at which to compute the inverse cumulative density.</param>
        /// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
        /// <seealso cref="InvCDF"/>
        public double InverseCumulativeDistribution(double p)
        {
            return _scale*Math.Sqrt(-2*Math.Log(1 - p));
        }

        /// <summary>
        /// Draws a random sample from the distribution.
        /// </summary>
        /// <returns>A random number from this distribution.</returns>
        public double Sample()
        {
            return _scale*Math.Sqrt(-2.0*Math.Log(_random.NextDouble()));
        }

        /// <summary>
        /// Generates a sequence of samples from the Rayleigh distribution.
        /// </summary>
        /// <returns>a sequence of samples from the distribution.</returns>
        public IEnumerable<double> Samples()
        {
            while (true)
            {
                yield return _scale*Math.Sqrt(-2.0*Math.Log(_random.NextDouble()));
            }
        }

        static void SampleUnchecked(System.Random rnd, double[] values, double scale)
        {
            rnd.NextDoubles(values);
            CommonParallel.For(0, values.Length, 4096, (a, b) =>
            {
                for (int i = a; i < b; i++)
                {
                    values[i] = scale*Math.Sqrt(-2.0*Math.Log(values[i]));
                }
            });
        }

        /// <summary>
        /// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
        /// </summary>
        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
        /// <param name="x">The location at which to compute the density.</param>
        /// <returns>the density at <paramref name="x"/>.</returns>
        /// <seealso cref="Density"/>
        public static double PDF(double scale, double x)
        {
            if (scale <= 0.0) throw new ArgumentException(Resources.InvalidDistributionParameters);

            return (x/(scale*scale))*Math.Exp(-x*x/(2.0*scale*scale));
        }

        /// <summary>
        /// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
        /// </summary>
        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
        /// <param name="x">The location at which to compute the density.</param>
        /// <returns>the log density at <paramref name="x"/>.</returns>
        /// <seealso cref="DensityLn"/>
        public static double PDFLn(double scale, double x)
        {
            if (scale <= 0.0) throw new ArgumentException(Resources.InvalidDistributionParameters);

            return Math.Log(x/(scale*scale)) - (x*x/(2.0*scale*scale));
        }

        /// <summary>
        /// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
        /// </summary>
        /// <param name="x">The location at which to compute the cumulative distribution function.</param>
        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
        /// <seealso cref="CumulativeDistribution"/>
        public static double CDF(double scale, double x)
        {
            if (scale <= 0.0) throw new ArgumentException(Resources.InvalidDistributionParameters);

            return 1.0 - Math.Exp(-x*x/(2.0*scale*scale));
        }

        /// <summary>
        /// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
        /// at the given probability. This is also known as the quantile or percent point function.
        /// </summary>
        /// <param name="p">The location at which to compute the inverse cumulative density.</param>
        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
        /// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
        /// <seealso cref="InverseCumulativeDistribution"/>
        public static double InvCDF(double scale, double p)
        {
            if (scale <= 0.0) throw new ArgumentException(Resources.InvalidDistributionParameters);

            return scale*Math.Sqrt(-2*Math.Log(1 - p));
        }

        /// <summary>
        /// Generates a sample from the distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
        /// <returns>a sample from the distribution.</returns>
        public static double Sample(System.Random rnd, double scale)
        {
            if (scale <= 0.0) throw new ArgumentException(Resources.InvalidDistributionParameters);

            return scale*Math.Sqrt(-2.0*Math.Log(rnd.NextDouble()));
        }

        /// <summary>
        /// Generates a sequence of samples from the distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static IEnumerable<double> Samples(System.Random rnd, double scale)
        {
            if (scale <= 0.0) throw new ArgumentException(Resources.InvalidDistributionParameters);

            while (true)
            {
                yield return scale*Math.Sqrt(-2.0*Math.Log(rnd.NextDouble()));
            }
        }

        /// <summary>
        /// Generates a sample from the distribution.
        /// </summary>
        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
        /// <returns>a sample from the distribution.</returns>
        public static double Sample(double scale)
        {
            return Sample(SystemRandomSource.Default, scale);
        }

        /// <summary>
        /// Generates a sequence of samples from the distribution.
        /// </summary>
        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static IEnumerable<double> Samples(double scale)
        {
            return Samples(SystemRandomSource.Default, scale);
        }
    }
}