// <copyright file="FisherSnedecor.cs" company="Math.NET">
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using System;
using System.Collections.Generic;
using IStation.Numerics.Random;
using IStation.Numerics.RootFinding;
using IStation.Numerics.Threading;

namespace IStation.Numerics.Distributions
{
    /// <summary>
    /// Continuous Univariate F-distribution, also known as Fisher-Snedecor distribution.
    /// For details about this distribution, see
    /// <a href="http://en.wikipedia.org/wiki/F-distribution">Wikipedia - FisherSnedecor distribution</a>.
    /// </summary>
    public class FisherSnedecor : IContinuousDistribution
    {
        System.Random _random;

        readonly double _freedom1;
        readonly double _freedom2;

        /// <summary>
        /// Initializes a new instance of the <see cref="FisherSnedecor"/> class.
        /// </summary>
        /// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
        /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
        public FisherSnedecor(double d1, double d2)
        {
            if (!IsValidParameterSet(d1, d2))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            _random = SystemRandomSource.Default;
            _freedom1 = d1;
            _freedom2 = d2;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="FisherSnedecor"/> class.
        /// </summary>
        /// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
        /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
        public FisherSnedecor(double d1, double d2, System.Random randomSource)
        {
            if (!IsValidParameterSet(d1, d2))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            _random = randomSource ?? SystemRandomSource.Default;
            _freedom1 = d1;
            _freedom2 = d2;
        }

        /// <summary>
        /// A string representation of the distribution.
        /// </summary>
        /// <returns>a string representation of the distribution.</returns>
        public override string ToString()
        {
            return $"FisherSnedecor(d1 = {_freedom1}, d2 = {_freedom2})";
        }

        /// <summary>
        /// Tests whether the provided values are valid parameters for this distribution.
        /// </summary>
        /// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
        /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
        public static bool IsValidParameterSet(double d1, double d2)
        {
            return d1 > 0.0 && d2 > 0.0;
        }

        /// <summary>
        /// Gets the first degree of freedom (d1) of the distribution. Range: d1 > 0.
        /// </summary>
        public double DegreesOfFreedom1 => _freedom1;

        /// <summary>
        /// Gets the second degree of freedom (d2) of the distribution. Range: d2 > 0.
        /// </summary>
        public double DegreesOfFreedom2 => _freedom2;

        /// <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
        {
            get
            {
                if (_freedom2 <= 2)
                {
                    throw new NotSupportedException();
                }

                return _freedom2/(_freedom2 - 2.0);
            }
        }

        /// <summary>
        /// Gets the variance of the distribution.
        /// </summary>
        public double Variance
        {
            get
            {
                if (_freedom2 <= 4)
                {
                    throw new NotSupportedException();
                }

                return (2.0*_freedom2*_freedom2*(_freedom1 + _freedom2 - 2.0))/(_freedom1*(_freedom2 - 2.0)*(_freedom2 - 2.0)*(_freedom2 - 4.0));
            }
        }

        /// <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 => throw new NotSupportedException();

        /// <summary>
        /// Gets the skewness of the distribution.
        /// </summary>
        public double Skewness
        {
            get
            {
                if (_freedom2 <= 6)
                {
                    throw new NotSupportedException();
                }

                return (((2.0*_freedom1) + _freedom2 - 2.0)*Math.Sqrt(8.0*(_freedom2 - 4.0)))/((_freedom2 - 6.0)*Math.Sqrt(_freedom1*(_freedom1 + _freedom2 - 2.0)));
            }
        }

        /// <summary>
        /// Gets the mode of the distribution.
        /// </summary>
        public double Mode
        {
            get
            {
                if (_freedom1 <= 2)
                {
                    throw new NotSupportedException();
                }

                return (_freedom2*(_freedom1 - 2.0))/(_freedom1*(_freedom2 + 2.0));
            }
        }

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

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

        /// <summary>
        /// Gets the maximum of the distribution.
        /// </summary>
        public double Maximum => 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 Math.Sqrt(Math.Pow(_freedom1*x, _freedom1)*Math.Pow(_freedom2, _freedom2)/Math.Pow((_freedom1*x) + _freedom2, _freedom1 + _freedom2))/(x*SpecialFunctions.Beta(_freedom1/2.0, _freedom2/2.0));
        }

        /// <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(Density(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 SpecialFunctions.BetaRegularized(_freedom1/2.0, _freedom2/2.0, _freedom1*x/((_freedom1*x) + _freedom2));
        }

        /// <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"/>
        /// <remarks>WARNING: currently not an explicit implementation, hence slow and unreliable.</remarks>
        public double InverseCumulativeDistribution(double p)
        {
            return InvCDF(_freedom1, _freedom2, p);
        }

        /// <summary>
        /// Generates a sample from the <c>FisherSnedecor</c> distribution.
        /// </summary>
        /// <returns>a sample from the distribution.</returns>
        public double Sample()
        {
            return SampleUnchecked(_random, _freedom1, _freedom2);
        }

        /// <summary>
        /// Fills an array with samples generated from the distribution.
        /// </summary>
        public void Samples(double[] values)
        {
            SamplesUnchecked(_random, values, _freedom1, _freedom2);
        }

        /// <summary>
        /// Generates a sequence of samples from the <c>FisherSnedecor</c> distribution.
        /// </summary>
        /// <returns>a sequence of samples from the distribution.</returns>
        public IEnumerable<double> Samples()
        {
            return SamplesUnchecked(_random, _freedom1, _freedom2);
        }

        /// <summary>
        /// Generates one sample from the <c>FisherSnedecor</c> distribution without parameter checking.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
        /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
        /// <returns>a <c>FisherSnedecor</c> distributed random number.</returns>
        static double SampleUnchecked(System.Random rnd, double d1, double d2)
        {
            return (ChiSquared.Sample(rnd, d1)*d2)/(ChiSquared.Sample(rnd, d2)*d1);
        }

        static void SamplesUnchecked(System.Random rnd, double[] values, double d1, double d2)
        {
            var values2 = new double[values.Length];
            ChiSquared.SamplesUnchecked(rnd, values, d1);
            ChiSquared.SamplesUnchecked(rnd, values2, d2);
            CommonParallel.For(0, values.Length, 4096, (a, b) =>
            {
                for (int i = a; i < b; i++)
                {
                    values[i] = (values[i]*d2)/(values2[i]*d1);
                }
            });
        }

        static IEnumerable<double> SamplesUnchecked(System.Random rnd, double d1, double d2)
        {
            while (true)
            {
                yield return SampleUnchecked(rnd, d1, d2);
            }
        }

        /// <summary>
        /// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
        /// </summary>
        /// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
        /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 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 d1, double d2, double x)
        {
            if (d1 <= 0.0 || d2 <= 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return Math.Sqrt(Math.Pow(d1*x, d1)*Math.Pow(d2, d2)/Math.Pow((d1*x) + d2, d1 + d2))/(x*SpecialFunctions.Beta(d1/2.0, d2/2.0));
        }

        /// <summary>
        /// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
        /// </summary>
        /// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
        /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 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 d1, double d2, double x)
        {
            return Math.Log(PDF(d1, d2, 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="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
        /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
        /// <seealso cref="CumulativeDistribution"/>
        public static double CDF(double d1, double d2, double x)
        {
            if (d1 <= 0.0 || d2 <= 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return SpecialFunctions.BetaRegularized(d1/2.0, d2/2.0, d1*x/(d1*x + d2));
        }

        /// <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="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
        /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
        /// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
        /// <seealso cref="InverseCumulativeDistribution"/>
        /// <remarks>WARNING: currently not an explicit implementation, hence slow and unreliable.</remarks>
        public static double InvCDF(double d1, double d2, double p)
        {
            if (d1 <= 0.0 || d2 <= 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return Brent.FindRoot(
                x => SpecialFunctions.BetaRegularized(d1/2.0, d2/2.0, d1*x/(d1*x + d2)) - p,
                0, 1000, accuracy: 1e-12);
        }

        /// <summary>
        /// Generates a sample from the distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
        /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
        /// <returns>a sample from the distribution.</returns>
        public static double Sample(System.Random rnd, double d1, double d2)
        {
            if (d1 <= 0.0 || d2 <= 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return SampleUnchecked(rnd, d1, d2);
        }

        /// <summary>
        /// Generates a sequence of samples from the distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
        /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static IEnumerable<double> Samples(System.Random rnd, double d1, double d2)
        {
            if (d1 <= 0.0 || d2 <= 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return SamplesUnchecked(rnd, d1, d2);
        }

        /// <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="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
        /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static void Samples(System.Random rnd, double[] values, double d1, double d2)
        {
            if (d1 <= 0.0 || d2 <= 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            SamplesUnchecked(rnd, values, d1, d2);
        }

        /// <summary>
        /// Generates a sample from the distribution.
        /// </summary>
        /// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
        /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
        /// <returns>a sample from the distribution.</returns>
        public static double Sample(double d1, double d2)
        {
            if (d1 <= 0.0 || d2 <= 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return SampleUnchecked(SystemRandomSource.Default, d1, d2);
        }

        /// <summary>
        /// Generates a sequence of samples from the distribution.
        /// </summary>
        /// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
        /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static IEnumerable<double> Samples(double d1, double d2)
        {
            if (d1 <= 0.0 || d2 <= 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return SamplesUnchecked(SystemRandomSource.Default, d1, d2);
        }

        /// <summary>
        /// Fills an array with samples generated from the distribution.
        /// </summary>
        /// <param name="values">The array to fill with the samples.</param>
        /// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
        /// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static void Samples(double[] values, double d1, double d2)
        {
            if (d1 <= 0.0 || d2 <= 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            SamplesUnchecked(SystemRandomSource.Default, values, d1, d2);
        }
    }
}