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

namespace IStation.Numerics.Distributions
{
    public class Burr : IContinuousDistribution
    {
        System.Random _random;

        /// <summary>
        /// Gets the scale (a) of the distribution. Range: a > 0.
        /// </summary>
        public double a { get; }

        /// <summary>
        /// Gets the first shape parameter (c) of the distribution. Range: c > 0.
        /// </summary>
        public double c { get; }

        /// <summary>
        /// Gets the second shape parameter (k) of the distribution. Range: k > 0.
        /// </summary>
        public double k { get; }

        /// <summary>
        /// Initializes a new instance of the Burr Type XII class.
        /// </summary>
        /// <param name="a">The scale parameter a of the Burr distribution. Range: a > 0.</param>
        /// <param name="c">The first shape parameter c of the Burr distribution. Range: c > 0.</param>
        /// <param name="k">The second shape parameter k of the Burr distribution. Range: k > 0.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples. Optional, can be null.</param>
        public Burr(double a, double c, double k, System.Random randomSource = null)
        {
            if (!IsValidParameterSet(a, c, k))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }
            _random = randomSource ?? SystemRandomSource.Default;
            this.a = a;
            this.c = c;
            this.k = k;
        }

        /// <summary>
        /// A string representation of the distribution.
        /// </summary>
        /// <returns>a string representation of the distribution.</returns>
        public override string ToString()
        {
            return $"Burr(a = {a}, c = {c}, k = {k})";
        }

        /// <summary>
        /// Tests whether the provided values are valid parameters for this distribution.
        /// </summary>
        /// <param name="a">The scale parameter a of the Burr distribution. Range: a > 0.</param>
        /// <param name="c">The first shape parameter c of the Burr distribution. Range: c > 0.</param>
        /// <param name="k">The second shape parameter k of the Burr distribution. Range: k > 0.</param>
        public static bool IsValidParameterSet(double a, double c, double k)
        {
            var allFinite = a.IsFinite() && c.IsFinite() && k.IsFinite();
            return allFinite && a > 0.0 && c > 0.0 && k > 0.0;
        }

        /// <summary>
        /// Gets 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 Burr distribution.
        /// </summary>
        public double Mean => (1 / SpecialFunctions.Gamma(k)) * a * SpecialFunctions.Gamma(1 + 1 / c) * SpecialFunctions.Gamma(k - 1 / c);

        /// <summary>
        /// Gets the variance of the Burr distribution.
        /// </summary>
        public double Variance =>
            (1 / SpecialFunctions.Gamma(k)) * Math.Pow(a, 2) * SpecialFunctions.Gamma(1 + 2 / c) * SpecialFunctions.Gamma(k - 2 / c)
            - Math.Pow((1 / SpecialFunctions.Gamma(k)) * a * SpecialFunctions.Gamma(1 + 1 / c) * SpecialFunctions.Gamma(k - 1 / c), 2);

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

        /// <summary>
        /// Gets the mode of the Burr distribution.
        /// </summary>
        public double Mode => a * Math.Pow((c - 1) / (c * k + 1), 1 / c);

        /// <summary>
        /// Gets the minimum of the Burr distribution.
        /// </summary>
        public double Minimum => 0.0;

        /// <summary>
        /// Gets the maximum of the Burr distribution.
        /// </summary>
        public double Maximum => double.PositiveInfinity;

        /// <summary>
        /// Gets the entropy of the Burr distribution (currently not supported).
        /// </summary>
        public double Entropy => throw new NotSupportedException();

        /// <summary>
        /// Gets the skewness of the Burr distribution.
        /// </summary>
        public double Skewness
        {
            get
            {
                var mean = Mean;
                var variance = Variance;
                var std = StdDev;
                return (GetMoment(3) - 3 * mean * variance - mean * mean * mean) / (std * std * std);
            }
        }

        /// <summary>
        /// Gets the median of the Burr distribution.
        /// </summary>
        public double Median => a * Math.Pow(Math.Pow(2, 1 / k) - 1, 1 / c);

        /// <summary>
        /// Generates a sample from the Burr distribution.
        /// </summary>
        /// <returns>a sample from the distribution.</returns>
        public double Sample()
        {
            return SampleUnchecked(_random, a, c, k);
        }

        /// <summary>
        /// Fills an array with samples generated from the distribution.
        /// </summary>
        /// <param name="values">The array to fill with the samples.</param>
        public void Samples(double[] values)
        {
            SamplesUnchecked(_random, values, a, c, k);
        }

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

        /// <summary>
        /// Generates a sample from the Burr distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="a">The scale parameter a of the Burr distribution. Range: a > 0.</param>
        /// <param name="c">The first shape parameter c of the Burr distribution. Range: c > 0.</param>
        /// <param name="k">The second shape parameter k of the Burr distribution. Range: k > 0.</param>
        /// <returns>a sample from the distribution.</returns>
        public static double Sample(System.Random rnd, double a, double c, double k)
        {
            if (!IsValidParameterSet(a, c, k))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }
            return SampleUnchecked(rnd, a, c, k);
        }

        /// <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="a">The scale parameter a of the Burr distribution. Range: a > 0.</param>
        /// <param name="c">The first shape parameter c of the Burr distribution. Range: c > 0.</param>
        /// <param name="k">The second shape parameter k of the Burr distribution. Range: k > 0.</param>
        public static void Samples(System.Random rnd, double[] values, double a, double c, double k)
        {
            if (!IsValidParameterSet(a, c, k))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }
            SamplesUnchecked(rnd, values, a, c, k);
        }

        /// <summary>
        /// Generates a sequence of samples from the Burr distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="a">The scale parameter a of the Burr distribution. Range: a > 0.</param>
        /// <param name="c">The first shape parameter c of the Burr distribution. Range: c > 0.</param>
        /// <param name="k">The second shape parameter k of the Burr distribution. Range: k > 0.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static IEnumerable<double> Samples(System.Random rnd, double a, double c, double k)
        {
            if (!IsValidParameterSet(a, c, k))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }
            return SamplesUnchecked(rnd, a, c, k);
        }

        internal static double SampleUnchecked(System.Random rnd, double a, double c, double k)
        {
            var k_inv = 1 / k;
            var c_inv = 1 / c;
            double u = rnd.NextDouble();
            return a * Math.Pow(Math.Pow(1 - u, -k_inv) - 1, c_inv);
        }

        internal static void SamplesUnchecked(System.Random rnd, double[] values, double a, double c, double k)
        {
            if (values.Length == 0)
            {
                return;
            }
            var k_inv = 1 / k;
            var c_inv = 1 / c;
            double[] u = rnd.NextDoubles(values.Length);

            for (var j = 0; j < values.Length; ++j)
            {
                values[j] = a * Math.Pow(Math.Pow(1 - u[j], -k_inv) - 1, c_inv);
            }
        }

        internal static IEnumerable<double> SamplesUnchecked(System.Random rnd, double a, double c, double k)
        {
            while (true)
            {
                yield return SampleUnchecked(rnd, a, c, k);
            }
        }

        /// <summary>
        /// Gets the n-th raw moment of the distribution.
        /// </summary>
        /// <param name="n">The order (n) of the moment. Range: n ≥ 1.</param>
        /// <returns>the n-th moment of the distribution.</returns>
        public double GetMoment(double n)
        {
            if (n > k * c)
            {
                throw new ArgumentException("The chosen parameter set is invalid (probably some value is out of range).");
            }
            var lambda_n = (n / c) * SpecialFunctions.Gamma(n / c) * SpecialFunctions.Gamma(k - n / c);
            return Math.Pow(a, n) * lambda_n / SpecialFunctions.Gamma(k);
        }

        /// <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 DensityImpl(a, c, k, 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 DensityLnImpl(a, c, k, 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 CumulativeDistributionImpl(a, c, k, x);
        }

        /// <summary>
        /// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
        /// </summary>
        /// <param name="a">The scale parameter a of the Burr distribution. Range: a > 0.</param>
        /// <param name="c">The first shape parameter c of the Burr distribution. Range: c > 0.</param>
        /// <param name="k">The second shape parameter k of the Burr distribution. Range: k > 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 a, double c, double k, double x)
        {
            if (!IsValidParameterSet(a, c, k))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }
            return DensityImpl(a, c, k, x);
        }

        /// <summary>
        /// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
        /// </summary>
        /// <param name="a">The scale parameter a of the Burr distribution. Range: a > 0.</param>
        /// <param name="c">The first shape parameter c of the Burr distribution. Range: c > 0.</param>
        /// <param name="k">The second shape parameter k of the Burr distribution. Range: k > 0.</param>
        /// <param name="x">The location at which to compute the log density.</param>
        /// <returns>the log density at <paramref name="x"/>.</returns>
        /// <seealso cref="DensityLn"/>
        public static double PDFLn(double a, double c, double k, double x)
        {
            if (!IsValidParameterSet(a, c, k))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }
            return DensityLnImpl(a, c, k, x);
        }

        /// <summary>
        /// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
        /// </summary>
        /// <param name="a">The scale parameter a of the Burr distribution. Range: a > 0.</param>
        /// <param name="c">The first shape parameter c of the Burr distribution. Range: c > 0.</param>
        /// <param name="k">The second shape parameter k of the Burr distribution. Range: k > 0.</param>
        /// <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="CumulativeDistribution"/>
        public static double CDF(double a, double c, double k, double x)
        {
            if (!IsValidParameterSet(a, c, k))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }
            return CumulativeDistributionImpl(a, c, k, x);
        }

        internal static double DensityImpl(double a, double c, double k, double x)
        {
            var numerator = (k * c / a) * Math.Pow(x / a, c - 1);
            var denominator = Math.Pow(1 + Math.Pow(x / a, c), k + 1);
            return numerator / denominator;
        }

        internal static double DensityLnImpl(double a, double c, double k, double x)
        {
            return Math.Log(DensityImpl(a, c, k, x));
        }

        internal static double CumulativeDistributionImpl(double a, double c, double k, double x)
        {
            var denominator = Math.Pow(1 + Math.Pow(x / a, c), k);
            return 1 - 1 / denominator;
        }
    }
}