mathnet-numerics/src/Numerics/Distributions/Geometric.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>
    /// Discrete Univariate Geometric distribution.
    /// The Geometric distribution is a distribution over positive integers parameterized by one positive real number.
    /// This implementation of the Geometric distribution will never generate 0's.
    /// <a href="http://en.wikipedia.org/wiki/Geometric_distribution">Wikipedia - geometric distribution</a>.
    /// </summary>
    public class Geometric : IDiscreteDistribution
    {
        System.Random _random;

        readonly double _p;

        /// <summary>
        /// Initializes a new instance of the Geometric class.
        /// </summary>
        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
        public Geometric(double p)
        {
            if (!IsValidParameterSet(p))
            {
                throw new ArgumentException(Resources.InvalidDistributionParameters);
            }

            _random = SystemRandomSource.Default;
            _p = p;
        }

        /// <summary>
        /// Initializes a new instance of the Geometric class.
        /// </summary>
        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
        public Geometric(double p, System.Random randomSource)
        {
            if (!IsValidParameterSet(p))
            {
                throw new ArgumentException(Resources.InvalidDistributionParameters);
            }

            _random = randomSource ?? SystemRandomSource.Default;
            _p = p;
        }

        /// <summary>
        /// Returns a <see cref="System.String"/> that represents this instance.
        /// </summary>
        /// <returns>A <see cref="System.String"/> that represents this instance.</returns>
        public override string ToString()
        {
            return "Geometric(p = " + _p + ")";
        }

        /// <summary>
        /// Tests whether the provided values are valid parameters for this distribution.
        /// </summary>
        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
        public static bool IsValidParameterSet(double p)
        {
            return p >= 0.0 && p <= 1.0;
        }

        /// <summary>
        /// Gets the probability of generating a one. Range: 0 ≤ p ≤ 1.
        /// </summary>
        public double P
        {
            get { return _p; }
        }

        /// <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/_p; }
        }

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

        /// <summary>
        /// Gets the standard deviation of the distribution.
        /// </summary>
        public double StdDev
        {
            get { return Math.Sqrt(1.0 - _p)/_p; }
        }

        /// <summary>
        /// Gets the entropy of the distribution.
        /// </summary>
        public double Entropy
        {
            get { return ((-_p*Math.Log(_p, 2.0)) - ((1.0 - _p)*Math.Log(1.0 - _p, 2.0)))/_p; }
        }

        /// <summary>
        /// Gets the skewness of the distribution.
        /// </summary>
        /// <remarks>Throws a not supported exception.</remarks>
        public double Skewness
        {
            get { return (2.0 - _p)/Math.Sqrt(1.0 - _p); }
        }

        /// <summary>
        /// Gets the mode of the distribution.
        /// </summary>
        public int Mode
        {
            get { return 1; }
        }

        /// <summary>
        /// Gets the median of the distribution.
        /// </summary>
        public double Median
        {
            get { return _p == 0.0 ? double.PositiveInfinity : _p == 1.0 ? 1.0 : Math.Ceiling(-Constants.Ln2/Math.Log(1 - _p)); }
        }

        /// <summary>
        /// Gets the smallest element in the domain of the distributions which can be represented by an integer.
        /// </summary>
        public int Minimum
        {
            get { return 1; }
        }

        /// <summary>
        /// Gets the largest element in the domain of the distributions which can be represented by an integer.
        /// </summary>
        public int Maximum
        {
            get { return int.MaxValue; }
        }

        /// <summary>
        /// Computes the probability mass (PMF) at k, i.e. P(X = k).
        /// </summary>
        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
        public double Probability(int k)
        {
            if (k <= 0)
            {
                return 0.0;
            }

            return Math.Pow(1.0 - _p, k - 1)*_p;
        }

        /// <summary>
        /// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
        /// </summary>
        /// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
        public double ProbabilityLn(int k)
        {
            if (k <= 0)
            {
                return double.NegativeInfinity;
            }

            return ((k - 1)*Math.Log(1.0 - _p)) + Math.Log(_p);
        }

        /// <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>
        public double CumulativeDistribution(double x)
        {
            return 1.0 - Math.Pow(1.0 - _p, x);
        }

        /// <summary>
        /// Computes the probability mass (PMF) at k, i.e. P(X = k).
        /// </summary>
        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
        public static double PMF(double p, int k)
        {
            if (!(p >= 0.0 && p <= 1.0))
            {
                throw new ArgumentException(Resources.InvalidDistributionParameters);
            }

            if (k <= 0)
            {
                return 0.0;
            }

            return Math.Pow(1.0 - p, k - 1)*p;
        }

        /// <summary>
        /// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
        /// </summary>
        /// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
        public static double PMFLn(double p, int k)
        {
            if (!(p >= 0.0 && p <= 1.0))
            {
                throw new ArgumentException(Resources.InvalidDistributionParameters);
            }

            if (k <= 0)
            {
                return double.NegativeInfinity;
            }

            return ((k - 1)*Math.Log(1.0 - p)) + Math.Log(p);
        }

        /// <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="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
        /// <seealso cref="CumulativeDistribution"/>
        public static double CDF(double p, double x)
        {
            if (!(p >= 0.0 && p <= 1.0))
            {
                throw new ArgumentException(Resources.InvalidDistributionParameters);
            }

            return 1.0 - Math.Pow(1.0 - p, x);
        }

        /// <summary>
        /// Returns one sample from the distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
        /// <returns>One sample from the distribution implied by <paramref name="p"/>.</returns>
        static int SampleUnchecked(System.Random rnd, double p)
        {
            return p == 1.0 ? 1 : (int)Math.Ceiling(Math.Log(1.0 - rnd.NextDouble(), 1.0 - p));
        }

        static void SamplesUnchecked(System.Random rnd, int[] values, double p)
        {
            if (p == 1.0)
            {
                CommonParallel.For(0, values.Length, 4096, (a, b) =>
                {
                    for (int i = a; i < b; i++)
                    {
                        values[i] = 1;
                    }
                });
                return;
            }

            var uniform = rnd.NextDoubles(values.Length);
            double rp = 1.0 - p;
            CommonParallel.For(0, values.Length, 4096, (a, b) =>
            {
                for (int i = a; i < b; i++)
                {
                    values[i] = (int)Math.Ceiling(Math.Log(1.0 - uniform[i], rp));
                }
            });
        }

        static IEnumerable<int> SamplesUnchecked(System.Random rnd, double p)
        {
            if (p == 1.0)
            {
                return Generate.RepeatSequence(1);
            }

            double rp = 1.0 - p;
            return rnd.NextDoubleSequence().Select(r => (int)Math.Ceiling(Math.Log(1.0 - r, rp)));
        }

        /// <summary>
        /// Samples a Geometric distributed random variable.
        /// </summary>
        /// <returns>A sample from the Geometric distribution.</returns>
        public int Sample()
        {
            return SampleUnchecked(_random, _p);
        }

        /// <summary>
        /// Fills an array with samples generated from the distribution.
        /// </summary>
        public void Samples(int[] values)
        {
            SamplesUnchecked(_random, values, _p);
        }

        /// <summary>
        /// Samples an array of Geometric distributed random variables.
        /// </summary>
        /// <returns>a sequence of samples from the distribution.</returns>
        public IEnumerable<int> Samples()
        {
            return SamplesUnchecked(_random, _p);
        }

        /// <summary>
        /// Samples a random variable.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
        public static int Sample(System.Random rnd, double p)
        {
            if (!(p >= 0.0 && p <= 1.0))
            {
                throw new ArgumentException(Resources.InvalidDistributionParameters);
            }

            return SampleUnchecked(rnd, p);
        }

        /// <summary>
        /// Samples a sequence of this random variable.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
        public static IEnumerable<int> Samples(System.Random rnd, double p)
        {
            if (!(p >= 0.0 && p <= 1.0))
            {
                throw new ArgumentException(Resources.InvalidDistributionParameters);
            }

            return SamplesUnchecked(rnd, p);
        }

        /// <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="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
        public static void Samples(System.Random rnd, int[] values, double p)
        {
            if (!(p >= 0.0 && p <= 1.0))
            {
                throw new ArgumentException(Resources.InvalidDistributionParameters);
            }

            SamplesUnchecked(rnd, values, p);
        }

        /// <summary>
        /// Samples a random variable.
        /// </summary>
        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
        public static int Sample(double p)
        {
            if (!(p >= 0.0 && p <= 1.0))
            {
                throw new ArgumentException(Resources.InvalidDistributionParameters);
            }

            return SampleUnchecked(SystemRandomSource.Default, p);
        }

        /// <summary>
        /// Samples a sequence of this random variable.
        /// </summary>
        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
        public static IEnumerable<int> Samples(double p)
        {
            if (!(p >= 0.0 && p <= 1.0))
            {
                throw new ArgumentException(Resources.InvalidDistributionParameters);
            }

            return SamplesUnchecked(SystemRandomSource.Default, p);
        }

        /// <summary>
        /// Fills an array with samples generated from the distribution.
        /// </summary>
        /// <param name="values">The array to fill with the samples.</param>
        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
        public static void Samples(int[] values, double p)
        {
            if (!(p >= 0.0 && p <= 1.0))
            {
                throw new ArgumentException(Resources.InvalidDistributionParameters);
            }

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