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using System;
using System.Collections.Generic;
using IStation.Numerics.Random;

namespace IStation.Numerics.Distributions
{
    /// <summary>
    /// Discrete Univariate Zipf distribution.
    /// Zipf's law, an empirical law formulated using mathematical statistics, refers to the fact
    /// that many types of data studied in the physical and social sciences can be approximated with
    /// a Zipfian distribution, one of a family of related discrete power law probability distributions.
    /// For details about this distribution, see
    /// <a href="http://en.wikipedia.org/wiki/Zipf%27s_law">Wikipedia - Zipf distribution</a>.
    /// </summary>
    public class Zipf : IDiscreteDistribution
    {
        System.Random _random;

        /// <summary>
        /// The s parameter of the distribution.
        /// </summary>
        readonly double _s;

        /// <summary>
        /// The n parameter of the distribution.
        /// </summary>
        readonly int _n;

        /// <summary>
        /// Initializes a new instance of the <see cref="Zipf"/> class.
        /// </summary>
        /// <param name="s">The s parameter of the distribution.</param>
        /// <param name="n">The n parameter of the distribution.</param>
        public Zipf(double s, int n)
        {
            if (!IsValidParameterSet(s, n))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            _random = SystemRandomSource.Default;
            _s = s;
            _n = n;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="Zipf"/> class.
        /// </summary>
        /// <param name="s">The s parameter of the distribution.</param>
        /// <param name="n">The n parameter of the distribution.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
        public Zipf(double s, int n, System.Random randomSource)
        {
            if (!IsValidParameterSet(s, n))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            _random = randomSource ?? SystemRandomSource.Default;
            _s = s;
            _n = n;
        }

        /// <summary>
        /// A string representation of the distribution.
        /// </summary>
        /// <returns>a string representation of the distribution.</returns>
        public override string ToString()
        {
            return $"Zipf(S = {_s}, N = {_n})";
        }

        /// <summary>
        /// Tests whether the provided values are valid parameters for this distribution.
        /// </summary>
        /// <param name="s">The s parameter of the distribution.</param>
        /// <param name="n">The n parameter of the distribution.</param>
        public static bool IsValidParameterSet(double s, int n)
        {
            return n > 0 && s > 0.0;
        }

        /// <summary>
        /// Gets or sets the s parameter of the distribution.
        /// </summary>
        public double S => _s;

        /// <summary>
        /// Gets or sets the n parameter of the distribution.
        /// </summary>
        public int N => _n;

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

        /// <summary>
        /// Gets the mean of the distribution.
        /// </summary>
        public double Mean => SpecialFunctions.GeneralHarmonic(_n, _s - 1.0)/SpecialFunctions.GeneralHarmonic(_n, _s);

        /// <summary>
        /// Gets the variance of the distribution.
        /// </summary>
        public double Variance
        {
            get
            {
                if (_s <= 3)
                {
                    throw new NotSupportedException();
                }

                var ghns = SpecialFunctions.GeneralHarmonic(_n, _s);
                return (SpecialFunctions.GeneralHarmonic(_n, _s - 2)*SpecialFunctions.GeneralHarmonic(_n, _s))
                       - (Math.Pow(SpecialFunctions.GeneralHarmonic(_n, _s - 1), 2)/(ghns*ghns));
            }
        }

        /// <summary>
        /// Gets the standard deviation of the distribution.
        /// </summary>
        public double StdDev => Math.Sqrt(Variance);

        /// <summary>
        /// Gets the entropy of the distribution.
        /// </summary>
        public double Entropy
        {
            get
            {
                double sum = 0;
                for (var i = 0; i < _n; i++)
                {
                    sum += Math.Log(i + 1)/Math.Pow(i + 1, _s);
                }

                return ((_s/SpecialFunctions.GeneralHarmonic(_n, _s))*sum) + Math.Log(SpecialFunctions.GeneralHarmonic(_n, _s));
            }
        }

        /// <summary>
        /// Gets the skewness of the distribution.
        /// </summary>
        public double Skewness
        {
            get
            {
                if (_s <= 4)
                {
                    throw new NotSupportedException();
                }

                return ((SpecialFunctions.GeneralHarmonic(_n, _s - 3)*Math.Pow(SpecialFunctions.GeneralHarmonic(_n, _s), 2)) - (SpecialFunctions.GeneralHarmonic(_n, _s - 1)*((3*SpecialFunctions.GeneralHarmonic(_n, _s - 2)*SpecialFunctions.GeneralHarmonic(_n, _s)) - Math.Pow(SpecialFunctions.GeneralHarmonic(_n, _s - 1), 2))))/Math.Pow((SpecialFunctions.GeneralHarmonic(_n, _s - 2)*SpecialFunctions.GeneralHarmonic(_n, _s)) - Math.Pow(SpecialFunctions.GeneralHarmonic(_n, _s - 1), 2), 1.5);
            }
        }

        /// <summary>
        /// Gets the mode of the distribution.
        /// </summary>
        public int Mode => 1;

        /// <summary>
        /// Gets the median of the distribution.
        /// </summary>
        public double Median => throw new NotSupportedException();

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

        /// <summary>
        /// Gets the largest element in the domain of the distributions which can be represented by an integer.
        /// </summary>
        public int Maximum => _n;

        /// <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)
        {
            return (1.0/Math.Pow(k, _s))/SpecialFunctions.GeneralHarmonic(_n, _s);
        }

        /// <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)
        {
            return Math.Log(Probability(k));
        }

        /// <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)
        {
            if (x < 1)
            {
                return 0.0;
            }

            return SpecialFunctions.GeneralHarmonic((int)x, _s)/SpecialFunctions.GeneralHarmonic(_n, _s);
        }

        /// <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="s">The s parameter of the distribution.</param>
        /// <param name="n">The n parameter of the distribution.</param>
        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
        public static double PMF(double s, int n, int k)
        {
            if (!(n > 0 && s > 0.0))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return (1.0/Math.Pow(k, s))/SpecialFunctions.GeneralHarmonic(n, s);
        }

        /// <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="s">The s parameter of the distribution.</param>
        /// <param name="n">The n parameter of the distribution.</param>
        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
        public static double PMFLn(double s, int n, int k)
        {
            if (!(n > 0 && s > 0.0))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return Math.Log(PMF(s, n, k));
        }

        /// <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="s">The s parameter of the distribution.</param>
        /// <param name="n">The n parameter of the distribution.</param>
        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
        /// <seealso cref="CumulativeDistribution"/>
        public static double CDF(double s, int n, double x)
        {
            if (!(n > 0 && s > 0.0))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            if (x < 1)
            {
                return 0.0;
            }

            return SpecialFunctions.GeneralHarmonic((int)x, s)/SpecialFunctions.GeneralHarmonic(n, s);
        }

        /// <summary>
        /// Generates a sample from the Zipf distribution without doing parameter checking.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="s">The s parameter of the distribution.</param>
        /// <param name="n">The n parameter of the distribution.</param>
        /// <returns>a random number from the Zipf distribution.</returns>
        static int SampleUnchecked(System.Random rnd, double s, int n)
        {
            var r = 0.0;
            while (r == 0.0)
            {
                r = rnd.NextDouble();
            }

            var p = 1.0/SpecialFunctions.GeneralHarmonic(n, s);
            int i;
            var sum = 0.0;
            for (i = 1; i <= n; i++)
            {
                sum += p/Math.Pow(i, s);
                if (sum >= r)
                {
                    break;
                }
            }

            return i;
        }

        static void SamplesUnchecked(System.Random rnd, int[] values, double s, int n)
        {
            for (int i = 0; i < values.Length; i++)
            {
                values[i] = SampleUnchecked(rnd, s, n);
            }
        }

        static IEnumerable<int> SamplesUnchecked(System.Random rnd, double s, int n)
        {
            while (true)
            {
                yield return SampleUnchecked(rnd, s, n);
            }
        }

        /// <summary>
        /// Draws a random sample from the distribution.
        /// </summary>
        /// <returns>a sample from the distribution.</returns>
        public int Sample()
        {
            return SampleUnchecked(_random, _s, _n);
        }

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

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

        /// <summary>
        /// Samples a random variable.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="s">The s parameter of the distribution.</param>
        /// <param name="n">The n parameter of the distribution.</param>
        public static int Sample(System.Random rnd, double s, int n)
        {
            if (!(n > 0 && s > 0.0))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return SampleUnchecked(rnd, s, n);
        }

        /// <summary>
        /// Samples a sequence of this random variable.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="s">The s parameter of the distribution.</param>
        /// <param name="n">The n parameter of the distribution.</param>
        public static IEnumerable<int> Samples(System.Random rnd, double s, int n)
        {
            if (!(n > 0 && s > 0.0))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return SamplesUnchecked(rnd, s, n);
        }

        /// <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="s">The s parameter of the distribution.</param>
        /// <param name="n">The n parameter of the distribution.</param>
        public static void Samples(System.Random rnd, int[] values, double s, int n)
        {
            if (!(n > 0 && s > 0.0))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            SamplesUnchecked(rnd, values, s, n);
        }

        /// <summary>
        /// Samples a random variable.
        /// </summary>
        /// <param name="s">The s parameter of the distribution.</param>
        /// <param name="n">The n parameter of the distribution.</param>
        public static int Sample(double s, int n)
        {
            if (!(n > 0 && s > 0.0))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return SampleUnchecked(SystemRandomSource.Default, s, n);
        }

        /// <summary>
        /// Samples a sequence of this random variable.
        /// </summary>
        /// <param name="s">The s parameter of the distribution.</param>
        /// <param name="n">The n parameter of the distribution.</param>
        public static IEnumerable<int> Samples(double s, int n)
        {
            if (!(n > 0 && s > 0.0))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return SamplesUnchecked(SystemRandomSource.Default, s, n);
        }

        /// <summary>
        /// Fills an array with samples generated from the distribution.
        /// </summary>
        /// <param name="values">The array to fill with the samples.</param>
        /// <param name="s">The s parameter of the distribution.</param>
        /// <param name="n">The n parameter of the distribution.</param>
        public static void Samples(int[] values, double s, int n)
        {
            if (!(n > 0 && s > 0.0))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            SamplesUnchecked(SystemRandomSource.Default, values, s, n);
        }
    }
}