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

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

namespace MathNet.Numerics.Distributions
{
    /// <summary>
    /// Continuous Univariate Exponential distribution.
    /// The exponential distribution is a distribution over the real numbers parameterized by one non-negative parameter.
    /// <a href="http://en.wikipedia.org/wiki/Exponential_distribution">Wikipedia - exponential distribution</a>.
    /// </summary>
    public class Exponential : IContinuousDistribution
    {
        System.Random _random;

        double _rate;

        /// <summary>
        /// Initializes a new instance of the <see cref="Exponential"/> class.
        /// </summary>
        /// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
        public Exponential(double rate)
        {
            _random = SystemRandomSource.Default;
            SetParameters(rate);
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Exponential"/> class.
        /// </summary>
        /// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
        public Exponential(double rate, System.Random randomSource)
        {
            _random = randomSource ?? SystemRandomSource.Default;
            SetParameters(rate);
        }

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

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

            _rate = rate;
        }

        /// <summary>
        /// Gets or sets the rate (λ) parameter of the distribution. Range: λ ≥ 0.
        /// </summary>
        public double Rate
        {
            get { return _rate; }
            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 1.0/_rate; }
        }

        /// <summary>
        /// Gets the variance of the distribution.
        /// </summary>
        public double Variance
        {
            get { return 1.0/(_rate*_rate); }
        }

        /// <summary>
        /// Gets the standard deviation of the distribution.
        /// </summary>
        public double StdDev
        {
            get { return 1.0/_rate; }
        }

        /// <summary>
        /// Gets the entropy of the distribution.
        /// </summary>
        public double Entropy
        {
            get { return 1.0 - Math.Log(_rate); }
        }

        /// <summary>
        /// Gets the skewness of the distribution.
        /// </summary>
        public double Skewness
        {
            get { return 2.0; }
        }

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

        /// <summary>
        /// Gets the median of the distribution.
        /// </summary>
        public double Median
        {
            get { return Math.Log(2.0)/_rate; }
        }

        /// <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 < 0.0 ? 0.0 : _rate*Math.Exp(-_rate*x);
        }

        /// <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(_rate) - (_rate*x);
        }

        /// <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 x < 0.0 ? 0.0 : 1.0 - Math.Exp(-_rate*x);
        }

        /// <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 p >= 1.0 ? double.PositiveInfinity : -Math.Log(1 - p)/_rate;
        }

        /// <summary>
        /// Draws a random sample from the distribution.
        /// </summary>
        /// <returns>A random number from this distribution.</returns>
        public double Sample()
        {
            return SampleUnchecked(_random, _rate);
        }

        /// <summary>
        /// Generates a sequence of samples from the Exponential distribution.
        /// </summary>
        /// <returns>a sequence of samples from the distribution.</returns>
        public IEnumerable<double> Samples()
        {
            return SamplesUnchecked(_random, _rate);
        }

        /// <summary>
        /// Samples the distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
        /// <returns>a random number from the distribution.</returns>
        static double SampleUnchecked(System.Random rnd, double rate)
        {
            var r = rnd.NextDouble();
            while (r == 0.0)
            {
                r = rnd.NextDouble();
            }

            return -Math.Log(r)/rate;
        }

        static IEnumerable<double> SamplesUnchecked(System.Random rnd, double rate)
        {
            return rnd.NextDoubleSequence().Where(r => r != 0.0).Select(r => -Math.Log(r)/rate);
        }

        static void SamplesUnchecked(System.Random rnd, double[] values, double rate)
        {
            rnd.NextDoubles(values);
            CommonParallel.For(0, values.Length, 4096, (a, b) =>
            {
                for (int i = a; i < b; i++)
                {
                    // this happens very rarely
                    var r = values[i];
                    while (r == 0.0)
                    {
                        r = rnd.NextDouble();
                    }
                    values[i] = -Math.Log(r)/rate;
                }
            });
        }

        /// <summary>
        /// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
        /// </summary>
        /// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 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 rate, double x)
        {
            if (rate < 0.0) throw new ArgumentException(Resources.InvalidDistributionParameters);

            return x < 0.0 ? 0.0 : rate*Math.Exp(-rate*x);
        }

        /// <summary>
        /// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
        /// </summary>
        /// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 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 rate, double x)
        {
            if (rate < 0.0) throw new ArgumentException(Resources.InvalidDistributionParameters);

            return Math.Log(rate) - (rate*x);
        }

        /// <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="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
        /// <seealso cref="CumulativeDistribution"/>
        public static double CDF(double rate, double x)
        {
            if (rate < 0.0) throw new ArgumentException(Resources.InvalidDistributionParameters);

            return x < 0.0 ? 0.0 : 1.0 - Math.Exp(-rate*x);
        }

        /// <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="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
        /// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
        /// <seealso cref="InverseCumulativeDistribution"/>
        public static double InvCDF(double rate, double p)
        {
            if (rate < 0.0) throw new ArgumentException(Resources.InvalidDistributionParameters);

            return p >= 1.0 ? double.PositiveInfinity : -Math.Log(1 - p)/rate;
        }

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

            return SampleUnchecked(rnd, rate);
        }

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

            return SamplesUnchecked(rnd, rate);
        }

        /// <summary>
        /// Fills an array with samples generated from the distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="values">The array to fill with the samples.</param>
        /// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static void Samples(System.Random rnd, double[] values, double rate)
        {
            if (rate < 0.0) throw new ArgumentException(Resources.InvalidDistributionParameters);

            SamplesUnchecked(rnd, values, rate);
        }

        /// <summary>
        /// Draws a random sample from the distribution.
        /// </summary>
        /// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
        /// <returns>A random number from this distribution.</returns>
        public static double Sample(double rate)
        {
            if (rate < 0.0) throw new ArgumentException(Resources.InvalidDistributionParameters);

            return SampleUnchecked(SystemRandomSource.Default, rate);
        }

        /// <summary>
        /// Generates a sequence of samples from the Exponential distribution.
        /// </summary>
        /// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static IEnumerable<double> Samples(double rate)
        {
            if (rate < 0.0) throw new ArgumentException(Resources.InvalidDistributionParameters);

            return SamplesUnchecked(SystemRandomSource.Default, rate);
        }

        /// <summary>
        /// Fills an array with samples generated from the distribution.
        /// </summary>
        /// <param name="values">The array to fill with the samples.</param>
        /// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static void Samples(double[] values, double rate)
        {
            if (rate < 0.0) throw new ArgumentException(Resources.InvalidDistributionParameters);

            SamplesUnchecked(SystemRandomSource.Default, values, rate);
        }
    }
}