// <copyright file="InverseGamma.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
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using System;
using System.Collections.Generic;
using System.Linq;
using IStation.Numerics.Random;
using IStation.Numerics.Threading;

namespace IStation.Numerics.Distributions
{
    /// <summary>
    /// Continuous Univariate Inverse Gamma distribution.
    /// The inverse Gamma distribution is a distribution over the positive real numbers parameterized by
    /// two positive parameters.
    /// <a href="http://en.wikipedia.org/wiki/Inverse-gamma_distribution">Wikipedia - InverseGamma distribution</a>.
    /// </summary>
    public class InverseGamma : IContinuousDistribution
    {
        System.Random _random;

        readonly double _shape;
        readonly double _scale;

        /// <summary>
        /// Initializes a new instance of the <see cref="InverseGamma"/> class.
        /// </summary>
        /// <param name="shape">The shape (α) of the distribution. Range: α > 0.</param>
        /// <param name="scale">The scale (β) of the distribution. Range: β > 0.</param>
        public InverseGamma(double shape, double scale)
        {
            if (!IsValidParameterSet(shape, scale))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            _random = SystemRandomSource.Default;
            _shape = shape;
            _scale = scale;
        }

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

            _random = randomSource ?? SystemRandomSource.Default;
            _shape = shape;
            _scale = scale;
        }

        /// <summary>
        /// A string representation of the distribution.
        /// </summary>
        /// <returns>a string representation of the distribution.</returns>
        public override string ToString()
        {
            return $"InverseGamma(α = {_shape}, β = {_scale})";
        }

        /// <summary>
        /// Tests whether the provided values are valid parameters for this distribution.
        /// </summary>
        /// <param name="shape">The shape (α) of the distribution. Range: α > 0.</param>
        /// <param name="scale">The scale (β) of the distribution. Range: β > 0.</param>
        public static bool IsValidParameterSet(double shape, double scale)
        {
            return shape > 0.0 && scale > 0.0;
        }

        /// <summary>
        /// Gets or sets the shape (α) parameter. Range: α > 0.
        /// </summary>
        public double Shape => _shape;

        /// <summary>
        /// Gets or sets The scale (β) parameter. Range: β > 0.
        /// </summary>
        public double Scale => _scale;

        /// <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 (_shape <= 1)
                {
                    throw new NotSupportedException();
                }

                return _scale/(_shape - 1.0);
            }
        }

        /// <summary>
        /// Gets the variance of the distribution.
        /// </summary>
        public double Variance
        {
            get
            {
                if (_shape <= 2)
                {
                    throw new NotSupportedException();
                }

                return _scale*_scale/((_shape - 1.0)*(_shape - 1.0)*(_shape - 2.0));
            }
        }

        /// <summary>
        /// Gets the standard deviation of the distribution.
        /// </summary>
        public double StdDev => _scale/(Math.Abs(_shape - 1.0)*Math.Sqrt(_shape - 2.0));

        /// <summary>
        /// Gets the entropy of the distribution.
        /// </summary>
        public double Entropy => _shape + Math.Log(_scale) + SpecialFunctions.GammaLn(_shape) - ((1 + _shape)*SpecialFunctions.DiGamma(_shape));

        /// <summary>
        /// Gets the skewness of the distribution.
        /// </summary>
        public double Skewness
        {
            get
            {
                if (_shape <= 3)
                {
                    throw new NotSupportedException();
                }

                return (4*Math.Sqrt(_shape - 2))/(_shape - 3);
            }
        }

        /// <summary>
        /// Gets the mode of the distribution.
        /// </summary>
        public double Mode => _scale/(_shape + 1.0);

        /// <summary>
        /// Gets the median of the distribution.
        /// </summary>
        /// <remarks>Throws <see cref="NotSupportedException"/>.</remarks>
        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 x < 0.0 ? 0.0 : Math.Pow(_scale, _shape)*Math.Pow(x, -_shape - 1.0)*Math.Exp(-_scale/x)/SpecialFunctions.Gamma(_shape);
        }

        /// <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.GammaUpperRegularized(_shape, _scale/x);
        }

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

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

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

        static double SampleUnchecked(System.Random rnd, double shape, double scale)
        {
            return 1.0/Gamma.SampleUnchecked(rnd, shape, scale);
        }

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

        static IEnumerable<double> SamplesUnchecked(System.Random rnd, double shape, double scale)
        {
            return Gamma.SamplesUnchecked(rnd, shape, scale).Select(z => 1.0/z);
        }

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

            return x < 0.0 ? 0.0 : Math.Pow(scale, shape)*Math.Pow(x, -shape - 1.0)*Math.Exp(-scale/x)/SpecialFunctions.Gamma(shape);
        }

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

            return SpecialFunctions.GammaUpperRegularized(shape, scale/x);
        }

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

            return SampleUnchecked(rnd, shape, scale);
        }

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

            return SamplesUnchecked(rnd, shape, scale);
        }

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

            SamplesUnchecked(rnd, values, shape, scale);
        }

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

            return SampleUnchecked(SystemRandomSource.Default, shape, scale);
        }

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

            return SamplesUnchecked(SystemRandomSource.Default, shape, scale);
        }

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

            SamplesUnchecked(SystemRandomSource.Default, values, shape, scale);
        }
    }
}