// <copyright file="Histogram.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
//
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using System;
using System.Collections.Generic;
using System.Runtime.Serialization;
using System.Text;

namespace IStation.Numerics.Statistics
{
    /// <summary>
    /// A <see cref="Histogram"/> consists of a series of <see cref="Bucket"/>s,
    /// each representing a region limited by a lower bound (exclusive) and an upper bound (inclusive).
    /// </summary>
    /// <remarks>
    /// This type declares a DataContract for out of the box ephemeral serialization
    /// with engines like DataContractSerializer, Protocol Buffers and FsPickler,
    /// but does not guarantee any compatibility between versions.
    /// It is not recommended to rely on this mechanism for durable persistence.
    /// </remarks>
    [Serializable]
    [DataContract(Namespace = "urn:IStation/Numerics")]
    public class Bucket : IComparable<Bucket>
#if !NETSTANDARD1_3
        , ICloneable
#endif
    {
        /// <summary>
        /// This <c>IComparer</c> performs comparisons between a point and a bucket.
        /// </summary>
        private sealed class PointComparer : IComparer<Bucket>
        {
            /// <summary>
            /// Compares a point and a bucket. The point will be encapsulated in a bucket with width 0.
            /// </summary>
            /// <param name="bkt1">The first bucket to compare.</param>
            /// <param name="bkt2">The second bucket to compare.</param>
            /// <returns>-1 when the point is less than this bucket, 0 when it is in this bucket and 1 otherwise.</returns>
            public int Compare(Bucket bkt1, Bucket bkt2)
            {
                return bkt2.IsSinglePoint
                    ? -bkt1.Contains(bkt2.UpperBound)
                    : -bkt2.Contains(bkt1.UpperBound);
            }
        }

        private static readonly PointComparer Comparer = new PointComparer();

        /// <summary>
        /// Lower Bound of the Bucket.
        /// </summary>
        [DataMember(Order = 1)]
        public double LowerBound { get; set; }

        /// <summary>
        /// Upper Bound of the Bucket.
        /// </summary>
        [DataMember(Order = 2)]
        public double UpperBound { get; set; }

        /// <summary>
        /// The number of datapoints in the bucket.
        /// </summary>
        /// <remarks>
        /// Value may be NaN if this was constructed as a <see cref="IComparer{Bucket}"/> argument.
        /// </remarks>
        [DataMember(Order = 3)]
        public double Count { get; set; }

        /// <summary>
        /// Initializes a new instance of the Bucket class.
        /// </summary>
        public Bucket(double lowerBound, double upperBound, double count = 0.0)
        {
            if (lowerBound > upperBound)
            {
                throw new ArgumentException("The upper bound must be at least as large as the lower bound.");
            }

            if (count < 0.0)
            {
                throw new ArgumentOutOfRangeException(nameof(count), "Value must be positive.");
            }

            LowerBound = lowerBound;
            UpperBound = upperBound;
            Count = count;
        }

        /// <summary>
        /// Constructs a Bucket that can be used as an argument for a <see cref="IComparer{Bucket}"/>
        /// like <see cref="DefaultPointComparer"/> when performing a Binary search.
        /// </summary>
        /// <param name="targetValue">Value to look for</param>
        public Bucket(double targetValue)
        {
            LowerBound = targetValue;
            UpperBound = targetValue;
            Count = double.NaN;
        }

        /// <summary>
        /// Creates a copy of the Bucket with the lowerbound, upperbound and counts exactly equal.
        /// </summary>
        /// <returns>A cloned Bucket object.</returns>
        public object Clone()
        {
            return new Bucket(LowerBound, UpperBound, Count);
        }

        /// <summary>
        /// Width of the Bucket.
        /// </summary>
        public double Width => UpperBound - LowerBound;

        /// <summary>
        /// True if this is a single point argument for <see cref="IComparer{Bucket}"/>
        /// when performing a Binary search.
        /// </summary>
        private bool IsSinglePoint => double.IsNaN(Count);

        /// <summary>
        /// Default comparer.
        /// </summary>
        public static IComparer<Bucket> DefaultPointComparer => Comparer;

        /// <summary>
        /// This method check whether a point is contained within this bucket.
        /// </summary>
        /// <param name="x">The point to check.</param>
        /// <returns>
        ///  0 if the point falls within the bucket boundaries;
        /// -1 if the point is smaller than the bucket,
        /// +1 if the point is larger than the bucket.</returns>
        public int Contains(double x)
        {
            if (LowerBound < x)
            {
                if (UpperBound >= x)
                {
                    return 0;
                }

                return 1;
            }

            return -1;
        }

        /// <summary>
        /// Comparison of two disjoint buckets. The buckets cannot be overlapping.
        /// </summary>
        /// <returns>
        ///  0 if <c>UpperBound</c> and <c>LowerBound</c> are bit-for-bit equal
        ///  1 if This bucket is lower that the compared bucket
        /// -1 otherwise
        /// </returns>
        public int CompareTo(Bucket bucket)
        {
            if (UpperBound > bucket.LowerBound && LowerBound < bucket.LowerBound)
            {
                throw new ArgumentException("The two arguments can\'t be compared (maybe they are part of a partial ordering?)");
            }

            if (UpperBound.Equals(bucket.UpperBound)
                && LowerBound.Equals(bucket.LowerBound))
            {
                return 0;
            }

            if (bucket.UpperBound <= LowerBound)
            {
                return 1;
            }

            return -1;
        }

        /// <summary>
        /// Checks whether two Buckets are equal.
        /// </summary>
        /// <remarks>
        /// <c>UpperBound</c> and <c>LowerBound</c> are compared bit-for-bit, but This method tolerates a
        /// difference in <c>Count</c> given by  <seealso cref="Precision.AlmostEqual(double,double)"/>.
        /// </remarks>
        public override bool Equals(object obj)
        {
            if (!(obj is Bucket))
            {
                return false;
            }

            var bucket = (Bucket) obj;
            return LowerBound.Equals(bucket.LowerBound)
                && UpperBound.Equals(bucket.UpperBound)
                && Count.AlmostEqual(bucket.Count);
        }

        /// <summary>
        /// Provides a hash code for this bucket.
        /// </summary>
        public override int GetHashCode()
        {
            return LowerBound.GetHashCode() ^ UpperBound.GetHashCode() ^ Count.GetHashCode();
        }

        /// <summary>
        /// Formats a human-readable string for this bucket.
        /// </summary>
        public override string ToString()
        {
            return "(" + LowerBound + ";" + UpperBound + "] = " + Count;
        }
    }

    /// <summary>
    /// A class which computes histograms of data.
    /// </summary>
    [Serializable]
    [DataContract(Namespace = "urn:IStation/Numerics")]
    public class Histogram
    {
        /// <summary>
        /// Contains all the <c>Bucket</c>s of the <c>Histogram</c>.
        /// </summary>
        [DataMember(Order = 1)]
        private readonly List<Bucket> _buckets;

        /// <summary>
        /// Indicates whether the elements of <c>buckets</c> are currently sorted.
        /// </summary>
        [DataMember(Order = 2)]
        private bool _areBucketsSorted;

        /// <summary>
        /// Initializes a new instance of the Histogram class.
        /// </summary>
        public Histogram()
        {
            _buckets = new List<Bucket>();
            _areBucketsSorted = true;
        }

        /// <summary>
        /// Constructs a Histogram with a specific number of equally sized buckets. The upper and lower bound of the histogram
        /// will be set to the smallest and largest datapoint.
        /// </summary>
        /// <param name="data">The data sequence to build a histogram on.</param>
        /// <param name="nbuckets">The number of buckets to use.</param>
        public Histogram(IEnumerable<double> data, int nbuckets)
            : this()
        {
            if (nbuckets < 1)
            {
                throw new ArgumentOutOfRangeException(nameof(data), "The number of bins in a histogram should be at least 1.");
            }

            double lower = data.Minimum();
            double upper = data.Maximum();
            double width = (upper - lower)/nbuckets;

            if (double.IsNaN(width))
            {
                throw new ArgumentException("Data must contain at least one entry.", nameof(data));
            }

            // Add buckets for each bin; the smallest bucket's lowerbound must be slightly smaller
            // than the minimal element.
            double fNextLowerBound = lower + width;
            AddBucket(new Bucket(lower.Decrement(), fNextLowerBound));
            for (int n = 1; n < nbuckets; n++)
            {
                AddBucket(new Bucket(
                    fNextLowerBound,
                    fNextLowerBound = (lower + (n + 1) * width)));
            }

            AddData(data);
        }

        /// <summary>
        /// Constructs a Histogram with a specific number of equally sized buckets.
        /// </summary>
        /// <param name="data">The data sequence to build a histogram on.</param>
        /// <param name="nbuckets">The number of buckets to use.</param>
        /// <param name="lower">The histogram lower bound.</param>
        /// <param name="upper">The histogram upper bound.</param>
        public Histogram(IEnumerable<double> data, int nbuckets, double lower, double upper)
            : this()
        {
            if (lower > upper)
            {
                throw new ArgumentOutOfRangeException(nameof(upper), "The histogram lower bound must be smaller than the upper bound.");
            }

            if (nbuckets < 1)
            {
                throw new ArgumentOutOfRangeException(nameof(nbuckets), "The number of bins in a histogram should be at least 1.");
            }

            double width = (upper - lower) / nbuckets;

            // Add buckets for each bin.
            for (int n = 0; n < nbuckets; n++)
            {
                AddBucket(new Bucket(lower + n * width, lower + (n + 1) * width));
            }

            AddData(data);
        }

        /// <summary>
        /// Add one data point to the histogram. If the datapoint falls outside the range of the histogram,
        /// the lowerbound or upperbound will automatically adapt.
        /// </summary>
        /// <param name="d">The datapoint which we want to add.</param>
        public void AddData(double d)
        {
            // Sort if needed.
            LazySort();

            if (d <= LowerBound)
            {
                // Make the lower bound just slightly smaller than the datapoint so it is contained in this bucket.
                _buckets[0].LowerBound = d.Decrement();
                _buckets[0].Count++;
            }
            else if (d > UpperBound)
            {
                _buckets[BucketCount - 1].UpperBound = d;
                _buckets[BucketCount - 1].Count++;
            }
            else
            {
                _buckets[GetBucketIndexOf(d)].Count++;
            }
        }

        /// <summary>
        /// Add a sequence of data point to the histogram. If the datapoint falls outside the range of the histogram,
        /// the lowerbound or upperbound will automatically adapt.
        /// </summary>
        /// <param name="data">The sequence of datapoints which we want to add.</param>
        public void AddData(IEnumerable<double> data)
        {
            foreach (double d in data)
            {
                AddData(d);
            }
        }

        /// <summary>
        /// Adds a <c>Bucket</c> to the <c>Histogram</c>.
        /// </summary>
        public void AddBucket(Bucket bucket)
        {
            _buckets.Add(bucket);
            _areBucketsSorted = false;
        }

        /// <summary>
        /// Sort the buckets if needed.
        /// </summary>
        private void LazySort()
        {
            if (!_areBucketsSorted)
            {
                _buckets.Sort();
                _areBucketsSorted = true;
            }
        }

        /// <summary>
        /// Returns the <c>Bucket</c> that contains the value <c>v</c>.
        /// </summary>
        /// <param name="v">The point to search the bucket for.</param>
        /// <returns>A copy of the bucket containing point <paramref name="v"/>.</returns>
        public Bucket GetBucketOf(double v)
        {
            return (Bucket) _buckets[GetBucketIndexOf(v)].Clone();
        }

        /// <summary>
        /// Returns the index in the <c>Histogram</c> of the <c>Bucket</c>
        /// that contains the value <c>v</c>.
        /// </summary>
        /// <param name="v">The point to search the bucket index for.</param>
        /// <returns>The index of the bucket containing the point.</returns>
        public int GetBucketIndexOf(double v)
        {
            // Sort if needed.
            LazySort();

            // Binary search for the bucket index.
            int index = _buckets.BinarySearch(new Bucket(v), Bucket.DefaultPointComparer);

            if (index < 0)
            {
                throw new ArgumentException("The histogram does not contain the value.");
            }

            return index;
        }

        /// <summary>
        /// Returns the lower bound of the histogram.
        /// </summary>
        public double LowerBound
        {
            get
            {
                LazySort();
                return _buckets[0].LowerBound;
            }
        }

        /// <summary>
        /// Returns the upper bound of the histogram.
        /// </summary>
        public double UpperBound
        {
            get
            {
                LazySort();
                return _buckets[_buckets.Count - 1].UpperBound;
            }
        }

        /// <summary>
        /// Gets the <c>n</c>'th bucket.
        /// </summary>
        /// <param name="n">The index of the bucket to be returned.</param>
        /// <returns>A copy of the <c>n</c>'th bucket.</returns>
        public Bucket this[int n]
        {
            get
            {
                LazySort();
                return (Bucket) _buckets[n].Clone();
            }
        }

        /// <summary>
        /// Gets the number of buckets.
        /// </summary>
        public int BucketCount => _buckets.Count;

        /// <summary>
        /// Gets the total number of datapoints in the histogram.
        /// </summary>
        public double DataCount
        {
            get
            {
                double totalCount = 0;

                for (int i = 0; i < BucketCount; i++)
                {
                    totalCount += this[i].Count;
                }

                return totalCount;
            }
        }

        /// <summary>
        /// Prints the buckets contained in the <see cref="Histogram"/>.
        /// </summary>
        public override string ToString()
        {
            var sb = new StringBuilder();
            foreach (Bucket b in _buckets)
            {
                sb.Append(b);
            }

            return sb.ToString();
        }
    }
}