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using System;
using System.Collections.Generic;
using System.Linq;
using IStation.Numerics.Random;
using IStation.Numerics.Statistics;
using IStation.Numerics.Threading;

namespace IStation.Numerics.Distributions
{
    /// <summary>
    /// Continuous Univariate Log-Normal distribution.
    /// For details about this distribution, see
    /// <a href="http://en.wikipedia.org/wiki/Log-normal_distribution">Wikipedia - Log-Normal distribution</a>.
    /// </summary>
    public class LogNormal : IContinuousDistribution
    {
        System.Random _random;

        readonly double _mu;
        readonly double _sigma;

        /// <summary>
        /// Initializes a new instance of the <see cref="LogNormal"/> class.
        /// The distribution will be initialized with the default <seealso cref="System.Random"/>
        /// random number generator.
        /// </summary>
        /// <param name="mu">The log-scale (μ) of the logarithm of the distribution.</param>
        /// <param name="sigma">The shape (σ) of the logarithm of the distribution. Range: σ ≥ 0.</param>
        public LogNormal(double mu, double sigma)
        {
            if (!IsValidParameterSet(mu, sigma))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            _random = SystemRandomSource.Default;
            _mu = mu;
            _sigma = sigma;
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="LogNormal"/> class.
        /// The distribution will be initialized with the default <seealso cref="System.Random"/>
        /// random number generator.
        /// </summary>
        /// <param name="mu">The log-scale (μ) of the distribution.</param>
        /// <param name="sigma">The shape (σ) of the distribution. Range: σ ≥ 0.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
        public LogNormal(double mu, double sigma, System.Random randomSource)
        {
            if (!IsValidParameterSet(mu, sigma))
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            _random = randomSource ?? SystemRandomSource.Default;
            _mu = mu;
            _sigma = sigma;
        }

        /// <summary>
        /// Constructs a log-normal distribution with the desired mu and sigma parameters.
        /// </summary>
        /// <param name="mu">The log-scale (μ) of the distribution.</param>
        /// <param name="sigma">The shape (σ) of the distribution. Range: σ ≥ 0.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples. Optional, can be null.</param>
        /// <returns>A log-normal distribution.</returns>
        public static LogNormal WithMuSigma(double mu, double sigma, System.Random randomSource = null)
        {
            return new LogNormal(mu, sigma, randomSource);
        }

        /// <summary>
        /// Constructs a log-normal distribution with the desired mean and variance.
        /// </summary>
        /// <param name="mean">The mean of the log-normal distribution.</param>
        /// <param name="var">The variance of the log-normal distribution.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples. Optional, can be null.</param>
        /// <returns>A log-normal distribution.</returns>
        public static LogNormal WithMeanVariance(double mean, double var, System.Random randomSource = null)
        {
            var sigma2 = Math.Log(var/(mean*mean) + 1.0);
            return new LogNormal(Math.Log(mean) - sigma2/2.0, Math.Sqrt(sigma2), randomSource);
        }

        /// <summary>
        /// Estimates the log-normal distribution parameters from sample data with maximum-likelihood.
        /// </summary>
        /// <param name="samples">The samples to estimate the distribution parameters from.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples. Optional, can be null.</param>
        /// <returns>A log-normal distribution.</returns>
        /// <remarks>MATLAB: lognfit</remarks>
        public static LogNormal Estimate(IEnumerable<double> samples, System.Random randomSource = null)
        {
            var muSigma = samples.Select(s => Math.Log(s)).MeanStandardDeviation();
            return new LogNormal(muSigma.Item1, muSigma.Item2, randomSource);
        }

        /// <summary>
        /// A string representation of the distribution.
        /// </summary>
        /// <returns>a string representation of the distribution.</returns>
        public override string ToString()
        {
            return $"LogNormal(μ = {_mu}, σ = {_sigma})";
        }

        /// <summary>
        /// Tests whether the provided values are valid parameters for this distribution.
        /// </summary>
        /// <param name="mu">The log-scale (μ) of the distribution.</param>
        /// <param name="sigma">The shape (σ) of the distribution. Range: σ ≥ 0.</param>
        public static bool IsValidParameterSet(double mu, double sigma)
        {
            return sigma >= 0.0 && !double.IsNaN(mu);
        }

        /// <summary>
        /// Gets the log-scale (μ) (mean of the logarithm) of the distribution.
        /// </summary>
        public double Mu => _mu;

        /// <summary>
        /// Gets the shape (σ) (standard deviation of the logarithm) of the distribution. Range: σ ≥ 0.
        /// </summary>
        public double Sigma => _sigma;

        /// <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 mu of the log-normal distribution.
        /// </summary>
        public double Mean => Math.Exp(_mu + (_sigma*_sigma/2.0));

        /// <summary>
        /// Gets the variance of the log-normal distribution.
        /// </summary>
        public double Variance
        {
            get
            {
                var sigma2 = _sigma*_sigma;
                return (Math.Exp(sigma2) - 1.0)*Math.Exp(_mu + _mu + sigma2);
            }
        }

        /// <summary>
        /// Gets the standard deviation of the log-normal distribution.
        /// </summary>
        public double StdDev
        {
            get
            {
                var sigma2 = _sigma*_sigma;
                return Math.Sqrt((Math.Exp(sigma2) - 1.0)*Math.Exp(_mu + _mu + sigma2));
            }
        }

        /// <summary>
        /// Gets the entropy of the log-normal distribution.
        /// </summary>
        public double Entropy => 0.5 + Math.Log(_sigma) + _mu + Constants.LogSqrt2Pi;

        /// <summary>
        /// Gets the skewness of the log-normal distribution.
        /// </summary>
        public double Skewness
        {
            get
            {
                var expsigma2 = Math.Exp(_sigma*_sigma);
                return (expsigma2 + 2.0)*Math.Sqrt(expsigma2 - 1);
            }
        }

        /// <summary>
        /// Gets the mode of the log-normal distribution.
        /// </summary>
        public double Mode => Math.Exp(_mu - (_sigma*_sigma));

        /// <summary>
        /// Gets the median of the log-normal distribution.
        /// </summary>
        public double Median => Math.Exp(_mu);

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

        /// <summary>
        /// Gets the maximum of the log-normal 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)
        {
            if (x < 0.0)
            {
                return 0.0;
            }

            var a = (Math.Log(x) - _mu)/_sigma;
            return Math.Exp(-0.5*a*a)/(x*_sigma*Constants.Sqrt2Pi);
        }

        /// <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)
        {
            if (x < 0.0)
            {
                return double.NegativeInfinity;
            }

            var a = (Math.Log(x) - _mu)/_sigma;
            return (-0.5*a*a) - Math.Log(x*_sigma) - Constants.LogSqrt2Pi;
        }

        /// <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 x < 0.0 ? 0.0
                : 0.5*SpecialFunctions.Erfc((_mu - Math.Log(x))/(_sigma*Constants.Sqrt2));
        }

        /// <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"/>
        public double InverseCumulativeDistribution(double p)
        {
            return p <= 0.0 ? 0.0 : p >= 1.0 ? double.PositiveInfinity
                : Math.Exp(_mu - _sigma*Constants.Sqrt2*SpecialFunctions.ErfcInv(2.0*p));
        }

        /// <summary>
        /// Generates a sample from the log-normal distribution using the <i>Box-Muller</i> algorithm.
        /// </summary>
        /// <returns>a sample from the distribution.</returns>
        public double Sample()
        {
            return SampleUnchecked(_random, _mu, _sigma);
        }

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

        /// <summary>
        /// Generates a sequence of samples from the log-normal distribution using the <i>Box-Muller</i> algorithm.
        /// </summary>
        /// <returns>a sequence of samples from the distribution.</returns>
        public IEnumerable<double> Samples()
        {
            return SamplesUnchecked(_random, _mu, _sigma);
        }

        static double SampleUnchecked(System.Random rnd, double mu, double sigma)
        {
            return Math.Exp(Normal.SampleUnchecked(rnd, mu, sigma));
        }

        static IEnumerable<double> SamplesUnchecked(System.Random rnd, double mu, double sigma)
        {
            return Normal.SamplesUnchecked(rnd, mu, sigma).Select(Math.Exp);
        }

        static void SamplesUnchecked(System.Random rnd, double[] values, double mu, double sigma)
        {
            Normal.SamplesUnchecked(rnd, values, mu, sigma);
            CommonParallel.For(0, values.Length, 4096, (a, b) =>
            {
                for (int i = a; i < b; i++)
                {
                    values[i] = Math.Exp(values[i]);
                }
            });
        }

        /// <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>
        /// <param name="mu">The log-scale (μ) of the distribution.</param>
        /// <param name="sigma">The shape (σ) of the distribution. Range: σ ≥ 0.</param>
        /// <returns>the density at <paramref name="x"/>.</returns>
        /// <seealso cref="Density"/>
        /// <remarks>MATLAB: lognpdf</remarks>
        public static double PDF(double mu, double sigma, double x)
        {
            if (sigma < 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            if (x < 0.0)
            {
                return 0.0;
            }

            var a = (Math.Log(x) - mu)/sigma;
            return Math.Exp(-0.5*a*a)/(x*sigma*Constants.Sqrt2Pi);
        }

        /// <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 density.</param>
        /// <param name="mu">The log-scale (μ) of the distribution.</param>
        /// <param name="sigma">The shape (σ) of the distribution. Range: σ ≥ 0.</param>
        /// <returns>the log density at <paramref name="x"/>.</returns>
        /// <seealso cref="DensityLn"/>
        public static double PDFLn(double mu, double sigma, double x)
        {
            if (sigma < 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            if (x < 0.0)
            {
                return double.NegativeInfinity;
            }

            var a = (Math.Log(x) - mu)/sigma;
            return (-0.5*a*a) - Math.Log(x*sigma) - Constants.LogSqrt2Pi;
        }

        /// <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="mu">The log-scale (μ) of the distribution.</param>
        /// <param name="sigma">The shape (σ) of the distribution. Range: σ ≥ 0.</param>
        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
        /// <seealso cref="CumulativeDistribution"/>
        /// <remarks>MATLAB: logncdf</remarks>
        public static double CDF(double mu, double sigma, double x)
        {
            if (sigma < 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return x < 0.0 ? 0.0
                : 0.5*(1.0 + SpecialFunctions.Erf((Math.Log(x) - mu)/(sigma*Constants.Sqrt2)));
        }

        /// <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="mu">The log-scale (μ) of the distribution.</param>
        /// <param name="sigma">The shape (σ) of the distribution. Range: σ ≥ 0.</param>
        /// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
        /// <seealso cref="InverseCumulativeDistribution"/>
        /// <remarks>MATLAB: logninv</remarks>
        public static double InvCDF(double mu, double sigma, double p)
        {
            if (sigma < 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return p <= 0.0 ? 0.0 : p >= 1.0 ? double.PositiveInfinity
                : Math.Exp(mu - sigma*Constants.Sqrt2*SpecialFunctions.ErfcInv(2.0*p));
        }

        /// <summary>
        /// Generates a sample from the log-normal distribution using the <i>Box-Muller</i> algorithm.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="mu">The log-scale (μ) of the distribution.</param>
        /// <param name="sigma">The shape (σ) of the distribution. Range: σ ≥ 0.</param>
        /// <returns>a sample from the distribution.</returns>
        public static double Sample(System.Random rnd, double mu, double sigma)
        {
            if (sigma < 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return SampleUnchecked(rnd, mu, sigma);
        }

        /// <summary>
        /// Generates a sequence of samples from the log-normal distribution using the <i>Box-Muller</i> algorithm.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="mu">The log-scale (μ) of the distribution.</param>
        /// <param name="sigma">The shape (σ) of the distribution. Range: σ ≥ 0.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static IEnumerable<double> Samples(System.Random rnd, double mu, double sigma)
        {
            if (sigma < 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return SamplesUnchecked(rnd, mu, sigma);
        }

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

            SamplesUnchecked(rnd, values, mu, sigma);
        }

        /// <summary>
        /// Generates a sample from the log-normal distribution using the <i>Box-Muller</i> algorithm.
        /// </summary>
        /// <param name="mu">The log-scale (μ) of the distribution.</param>
        /// <param name="sigma">The shape (σ) of the distribution. Range: σ ≥ 0.</param>
        /// <returns>a sample from the distribution.</returns>
        public static double Sample(double mu, double sigma)
        {
            if (sigma < 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return SampleUnchecked(SystemRandomSource.Default, mu, sigma);
        }

        /// <summary>
        /// Generates a sequence of samples from the log-normal distribution using the <i>Box-Muller</i> algorithm.
        /// </summary>
        /// <param name="mu">The log-scale (μ) of the distribution.</param>
        /// <param name="sigma">The shape (σ) of the distribution. Range: σ ≥ 0.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static IEnumerable<double> Samples(double mu, double sigma)
        {
            if (sigma < 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            return SamplesUnchecked(SystemRandomSource.Default, mu, sigma);
        }

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

            SamplesUnchecked(SystemRandomSource.Default, values, mu, sigma);
        }
    }
}