// <copyright file="DescriptiveStatistics.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
// http://mathnetnumerics.codeplex.com
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namespace MathNet.Numerics.Statistics
{
    using System.Collections.Generic;

    /// <summary>
    /// Computes the basic statistics of data set. The class meets the
    /// NIST standard of accuracy for mean, variance, and standard deviation
    /// (the only statistics they provide exact values for) and exceeds them 
    /// in increased accuracy mode.
    /// </summary>
    public class DescriptiveStatistics
    {
        /// <summary>
        /// Initializes a new instance of the <see cref="DescriptiveStatistics"/> class.
        /// </summary>
        /// <param name="data">The sample data.</param>
        public DescriptiveStatistics(IEnumerable<double> data) : this(data, false)
        {
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="DescriptiveStatistics"/> class.
        /// </summary>
        /// <param name="data">The sample data.</param>
        public DescriptiveStatistics(IEnumerable<double?> data) : this(data, false)
        {
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="DescriptiveStatistics"/> class. 
        /// </summary>
        /// <param name="data">The sample data.</param>
        /// <param name="increasedAccuracy">
        /// If set to <c>true</c>, increased accuracy mode used.
        /// Increased accuracy mode uses <see cref="decimal"/> types for internal calculations.
        /// </param>
        /// <remarks>
        /// Don't use increased accuracy for data sets containing large values (in absolute value).
        /// This may cause the calculations to overflow.
        /// </remarks>
        public DescriptiveStatistics(IEnumerable<double> data, bool increasedAccuracy)
        {
            if (increasedAccuracy)
            {
                ComputeHA(data);
            }
            else
            {
                Compute(data);
            }

            Median = data.Median();
            Maximum = data.Maximum();
            Minimum = data.Minimum();
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="DescriptiveStatistics"/> class. 
        /// </summary>
        /// <param name="data">The sample data.</param>
        /// <param name="increasedAccuracy">
        /// If set to <c>true</c>, increased accuracy mode used.
        /// Increased accuracy mode uses <see cref="decimal"/> types for internal calculations.
        /// </param>
        /// <remarks>
        /// Don't use increased accuracy for data sets containing large values (in absolute value).
        /// This may cause the calculations to overflow.
        /// </remarks>
        public DescriptiveStatistics(IEnumerable<double?> data, bool increasedAccuracy)
        {
            if (increasedAccuracy)
            {
                ComputeHA(data);
            }
            else
            {
                Compute(data);
            }

            Median = data.Median();
            Maximum = data.Maximum();
            Minimum = data.Minimum();
        }

        /// <summary>
        /// Gets the size of the sample.
        /// </summary>
        /// <value>The size of the sample.</value>
        public int Count { get; private set; }

        /// <summary>
        /// Gets the sample mean.
        /// </summary>
        /// <value>The sample mean.</value>
        public double Mean { get; private set; }

        /// <summary>
        /// Gets the sample variance.
        /// </summary>
        /// <value>The sample variance.</value>
        public double Variance { get; private set; }

        /// <summary>
        /// Gets the sample standard deviation.
        /// </summary>
        /// <value>The sample standard deviation.</value>
        public double StandardDeviation { get; private set; }

        /// <summary>
        /// Gets the sample skewness.
        /// </summary>
        /// <value>The sample skewness.</value>
        /// <remarks>Returns zero if <see cref="Count"/> is less than three. </remarks>
        public double Skewness { get; private set; }

        /// <summary>
        /// Gets the sample median.
        /// </summary>
        /// <value>The sample median.</value>
        public double Median { get; private set; }

        /// <summary>
        /// Gets the sample kurtosis.
        /// </summary>
        /// <value>The sample kurtosis.</value>
        /// <remarks>Returns zero if <see cref="Count"/> is less than four. </remarks>
        public double Kurtosis { get; private set; }

        /// <summary>
        /// Gets the maximum sample value.
        /// </summary>
        /// <value>The maximum sample value.</value>
        public double Maximum { get; private set; }

        /// <summary>
        /// Gets the minimum sample value.
        /// </summary>
        /// <value>The minimum sample value.</value>
        public double Minimum { get; private set; }

        /// <summary>
        /// Computes descriptive statistics from a stream of data values.
        /// </summary>
        /// <param name="data">A sequence of datapoints.</param>
        private void Compute(IEnumerable<double> data)
        {
            Mean = data.Mean();
            double variance = 0;
            double correction = 0;
            double skewness = 0;
            double kurtosis = 0;
            int n = 0;
            foreach (var xi in data)
            {
                double diff = xi - Mean;
                correction += diff;
                double tmp = diff * diff;
                variance += tmp;
                tmp *= diff;
                skewness += tmp;
                tmp *= diff;
                kurtosis += tmp;
                n++;
            }

            Count = n;
            Variance = (variance - (correction * correction / n)) / (n - 1);
            StandardDeviation = System.Math.Sqrt(Variance);
            if (Variance != 0)
            {
                if (n > 2)
                {
                    Skewness = (double)n / ((n - 1) * (n - 2)) * (skewness / (Variance * StandardDeviation));
                }

                if (n > 3)
                {
                    Kurtosis = (((double)n * (n + 1))
                                / ((n - 1) * (n - 2) * (n - 3))
                                * (kurtosis / (Variance * Variance)))
                               - ((3.0 * (n - 1) * (n - 1)) / ((n - 2) * (n - 3)));
                }
            }
        }

        /// <summary>
        /// Computes descriptive statistics from a stream of nullable data values.
        /// </summary>
        /// <param name="data">A sequence of datapoints.</param>
        private void Compute(IEnumerable<double?> data)
        {
            Mean = data.Mean();
            double variance = 0;
            double correction = 0;
            double skewness = 0;
            double kurtosis = 0;
            int n = 0;
            foreach (var xi in data)
            {
                if (xi.HasValue)
                {
                    double diff = xi.Value - Mean;
                    double tmp = diff * diff;
                    correction += diff;
                    variance += tmp;
                    tmp *= diff;
                    skewness += tmp;
                    tmp *= diff;
                    kurtosis += tmp;
                    n++;
                }
            }

            Count = n;
            if (n > 0)
            {
                Variance = (variance - (correction * correction / n)) / (n - 1);
                StandardDeviation = System.Math.Sqrt(Variance);
                if (Variance != 0)
                {
                    if (n > 2)
                    {
                        Skewness = (double)n / ((n - 1) * (n - 2)) * (skewness / (Variance * StandardDeviation));
                    }

                    if (n > 3)
                    {
                        Kurtosis = (((double)n * (n + 1))
                                    / ((n - 1) * (n - 2) * (n - 3))
                                    * (kurtosis / (Variance * Variance)))
                                   - ((3.0 * (n - 1) * (n - 1)) / ((n - 2) * (n - 3)));
                    }
                }
            }
        }

        /// <summary>
        /// Computes descriptive statistics from a stream of data values using high accuracy.
        /// </summary>
        /// <param name="data">A sequence of datapoints.</param>
        private void ComputeHA(IEnumerable<double> data)
        {
            Mean = data.Mean();
            decimal mean = (decimal)Mean;
            decimal variance = 0;
            decimal correction = 0;
            decimal skewness = 0;
            decimal kurtosis = 0;
            int n = 0;
            foreach (decimal xi in data)
            {
                decimal diff = xi - mean;
                decimal tmp = diff * diff;
                correction += diff;
                variance += tmp;
                tmp *= diff;
                skewness += tmp;
                tmp *= diff;
                kurtosis += tmp;
                n++;
            }

            Count = n;
            Variance = (double)(variance - (correction * correction / n)) / (n - 1);
            StandardDeviation = System.Math.Sqrt(Variance);
            if (Variance != 0)
            {
                if (n > 2)
                {
                    Skewness = (double)n / ((n - 1) * (n - 2)) * ((double)skewness / (Variance * StandardDeviation));
                }

                if (n > 3)
                {
                    Kurtosis = (((double)n * (n + 1))
                                / ((n - 1) * (n - 2) * (n - 3))
                                * ((double)kurtosis / (Variance * Variance)))
                               - ((3.0 * (n - 1) * (n - 1)) / ((n - 2) * (n - 3)));
                }
            }
        }

        /// <summary>
        /// Computes descriptive statistics from a stream of nullable data values using high accuracy.
        /// </summary>
        /// <param name="data">A sequence of datapoints.</param>
        private void ComputeHA(IEnumerable<double?> data)
        {
            Mean = data.Mean();
            decimal mean = (decimal)Mean;
            decimal variance = 0;
            decimal correction = 0;
            decimal skewness = 0;
            decimal kurtosis = 0;
            int n = 0;
            foreach (decimal? xi in data)
            {
                if (xi.HasValue)
                {
                    decimal diff = xi.Value - mean;
                    decimal tmp = diff * diff;
                    correction += diff;
                    variance += tmp;
                    tmp *= diff;
                    skewness += tmp;
                    tmp *= diff;
                    kurtosis += tmp;
                    n++;
                }
            }

            Count = n;
            if (n > 0)
            {
                Variance = (double)(variance - (correction * correction / n)) / (n - 1);
                StandardDeviation = System.Math.Sqrt(Variance);
                if (Variance != 0)
                {
                    if (n > 2)
                    {
                        Skewness = (double)n / ((n - 1) * (n - 2)) * ((double)skewness / (Variance * StandardDeviation));
                    }

                    if (n > 3)
                    {
                        Kurtosis = (((double)n * (n + 1))
                                    / ((n - 1) * (n - 2) * (n - 3))
                                    * ((double)kurtosis / (Variance * Variance)))
                                   - ((3.0 * (n - 1) * (n - 1)) / ((n - 2) * (n - 3)));
                    }
                }
            }
        }
    }
}