// <copyright file="Weibull.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 Weibull distribution.
    /// For details about this distribution, see
    /// <a href="http://en.wikipedia.org/wiki/Weibull_distribution">Wikipedia - Weibull distribution</a>.
    /// </summary>
    /// <remarks>
    /// The Weibull distribution is parametrized by a shape and scale parameter.
    /// </remarks>
    public class Weibull : IContinuousDistribution
    {
        System.Random _random;

        readonly double _shape;
        readonly double _scale;

        /// <summary>
        /// Reusable intermediate result 1 / (_scale ^ _shape)
        /// </summary>
        /// <remarks>
        /// By caching this parameter we can get slightly better numerics precision
        /// in certain constellations without any additional computations.
        /// </remarks>
        readonly double _scalePowShapeInv;

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

            _random = SystemRandomSource.Default;
            _shape = shape;
            _scale = scale;
            _scalePowShapeInv = Math.Pow(scale, -shape);
        }

        /// <summary>
        /// Initializes a new instance of the Weibull class.
        /// </summary>
        /// <param name="shape">The shape (k) of the Weibull distribution. Range: k > 0.</param>
        /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 0.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
        public Weibull(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;
            _scalePowShapeInv = Math.Pow(scale, -shape);
        }

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

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

        /// <summary>
        /// Gets the shape (k) of the Weibull distribution. Range: k > 0.
        /// </summary>
        public double Shape => _shape;

        /// <summary>
        /// Gets the scale (λ) of the Weibull distribution. Range: λ > 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 Weibull distribution.
        /// </summary>
        public double Mean => _scale*SpecialFunctions.Gamma(1.0 + (1.0/_shape));

        /// <summary>
        /// Gets the variance of the Weibull distribution.
        /// </summary>
        public double Variance => (_scale*_scale*SpecialFunctions.Gamma(1.0 + (2.0/_shape))) - (Mean*Mean);

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

        /// <summary>
        /// Gets the entropy of the Weibull distribution.
        /// </summary>
        public double Entropy => (Constants.EulerMascheroni*(1.0 - (1.0/_shape))) + Math.Log(_scale/_shape) + 1.0;

        /// <summary>
        /// Gets the skewness of the Weibull distribution.
        /// </summary>
        public double Skewness
        {
            get
            {
                double mu = Mean;
                double sigma = StdDev;
                double sigma2 = sigma*sigma;
                double sigma3 = sigma2*sigma;
                return ((_scale*_scale*_scale*SpecialFunctions.Gamma(1.0 + (3.0/_shape))) - (3.0*sigma2*mu) - (mu*mu*mu))/sigma3;
            }
        }

        /// <summary>
        /// Gets the mode of the Weibull distribution.
        /// </summary>
        public double Mode
        {
            get
            {
                if (_shape <= 1.0)
                {
                    return 0.0;
                }

                return _scale*Math.Pow((_shape - 1.0)/_shape, 1.0/_shape);
            }
        }

        /// <summary>
        /// Gets the median of the Weibull distribution.
        /// </summary>
        public double Median => _scale*Math.Pow(Constants.Ln2, 1.0/_shape);

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

        /// <summary>
        /// Gets the maximum of the Weibull 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>
        public double Density(double x)
        {
            if (x >= 0.0)
            {
                if (x == 0.0 && _shape == 1.0)
                {
                    return _shape/_scale;
                }

                return _shape*Math.Pow(x/_scale, _shape - 1.0)*Math.Exp(-Math.Pow(x, _shape)*_scalePowShapeInv)/_scale;
            }

            return 0.0;
        }

        /// <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>
        public double DensityLn(double x)
        {
            if (x >= 0.0)
            {
                if (x == 0.0 && _shape == 1.0)
                {
                    return Math.Log(_shape) - Math.Log(_scale);
                }

                return Math.Log(_shape) + ((_shape - 1.0)*Math.Log(x/_scale)) - (Math.Pow(x, _shape)*_scalePowShapeInv) - Math.Log(_scale);
            }

            return double.NegativeInfinity;
        }

        /// <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 < 0.0)
            {
                return 0.0;
            }

            return -SpecialFunctions.ExponentialMinusOne(-Math.Pow(x, _shape)*_scalePowShapeInv);
        }

        /// <summary>
        /// Generates a sample from the Weibull distribution.
        /// </summary>
        /// <returns>a sample from the 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 Weibull 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)
        {
            var x = rnd.NextDouble();
            return scale*Math.Pow(-Math.Log(x), 1.0/shape);
        }

        static IEnumerable<double> SamplesUnchecked(System.Random rnd, double shape, double scale)
        {
            var exponent = 1.0/shape;
            return rnd.NextDoubleSequence().Select(x => scale*Math.Pow(-Math.Log(x), exponent));
        }

        static void SamplesUnchecked(System.Random rnd, double[] values, double shape, double scale)
        {
            var exponent = 1.0/shape;
            rnd.NextDoubles(values);
            CommonParallel.For(0, values.Length, 4096, (a, b) =>
            {
                for (int i = a; i < b; i++)
                {
                    values[i] = scale*Math.Pow(-Math.Log(values[i]), exponent);
                }
            });
        }

        /// <summary>
        /// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
        /// </summary>
        /// <param name="shape">The shape (k) of the Weibull distribution. Range: k > 0.</param>
        /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 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.");
            }

            if (x >= 0.0)
            {
                if (x == 0.0 && shape == 1.0)
                {
                    return shape/scale;
                }

                return shape
                       *Math.Pow(x/scale, shape - 1.0)
                       *Math.Exp(-Math.Pow(x, shape)*Math.Pow(scale, -shape))
                       /scale;
            }

            return 0.0;
        }

        /// <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 (k) of the Weibull distribution. Range: k > 0.</param>
        /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 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)
        {
            if (shape <= 0.0 || scale <= 0.0)
            {
                throw new ArgumentException("Invalid parametrization for the distribution.");
            }

            if (x >= 0.0)
            {
                if (x == 0.0 && shape == 1.0)
                {
                    return Math.Log(shape) - Math.Log(scale);
                }

                return Math.Log(shape)
                       + ((shape - 1.0)*Math.Log(x/scale))
                       - (Math.Pow(x, shape)*Math.Pow(scale, -shape))
                       - Math.Log(scale);
            }

            return double.NegativeInfinity;
        }

        /// <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 (k) of the Weibull distribution. Range: k > 0.</param>
        /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 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.");
            }

            if (x < 0.0)
            {
                return 0.0;
            }

            return -SpecialFunctions.ExponentialMinusOne(-Math.Pow(x, shape)*Math.Pow(scale, -shape));
        }

        /// <summary>
        /// Implemented according to: Parameter estimation of the Weibull probability distribution, 1994, Hongzhu Qiao, Chris P. Tsokos
        /// </summary>
        /// <param name="samples"></param>
        /// <param name="randomSource"></param>
        /// <returns>Returns a Weibull distribution.</returns>
        public static Weibull Estimate(IEnumerable<double> samples, System.Random randomSource = null)
        {
            var samp = samples as double[] ?? samples.ToArray();
            double n = samp.Length, s1 = 0, s2 = 0, s3 = 0, previousC = Int32.MinValue, QofC = 0;

            if (n <= 1) throw new Exception("Observations not sufficient");

            // Start values
            double c = 10; double b = 0;

            while (Math.Abs(c - previousC) >= 0.0001)
            {
                s1 = s2 = s3 = 0;
                foreach (double x in samp)
                {
                    if (x > 0)
                    {
                        s1 += Math.Log(x);
                        s2 += Math.Pow(x, c);
                        s3 += Math.Pow(x, c) * Math.Log(x);
                    }
                }
                QofC = n * s2 / (n * s3 - s1 * s2);

                previousC = c;
                c = (c + QofC) / 2;
            }

            foreach (double x in samp)
            {
                if (x > 0)
                {
                    b += Math.Pow(x, c);
                }
            }

            b = Math.Pow(b / n, 1 / c);

            return new Weibull(c, b, randomSource);
        }

        /// <summary>
        /// Generates a sample from the Weibull distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="shape">The shape (k) of the Weibull distribution. Range: k > 0.</param>
        /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 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 Weibull distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="shape">The shape (k) of the Weibull distribution. Range: k > 0.</param>
        /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 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 (k) of the Weibull distribution. Range: k > 0.</param>
        /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 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 Weibull distribution.
        /// </summary>
        /// <param name="shape">The shape (k) of the Weibull distribution. Range: k > 0.</param>
        /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 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 Weibull distribution.
        /// </summary>
        /// <param name="shape">The shape (k) of the Weibull distribution. Range: k > 0.</param>
        /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 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 (k) of the Weibull distribution. Range: k > 0.</param>
        /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 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);
        }
    }
}