klhztrader/KLHZ.Trader.Core.Math/Declisions/Utils/Statistics.cs

using KLHZ.Trader.Core.Contracts.Messaging.Dtos.Interfaces;
using KLHZ.Trader.Core.Math.Declisions.Dtos;

namespace KLHZ.Trader.Core.Math.Declisions.Utils
{
    public static class Statistics
    {

        public static decimal MeanCount(this ITradeDataItem[] values)
        {
            return values.Sum(x => x.Count) / values.Length;
        }

        public static decimal MeanPrice(this ITradeDataItem[] values)
        {
            return values.Sum(x => x.Price) / values.Length;
        }

        private static (decimal mean, decimal std) CaclSigma(decimal[] values)
        {
            var mean = values.Sum() / values.Length;
            var data = new decimal[values.Length];
            Array.Copy(values, data, data.Length);
            for (int i = 0; i < data.Length; i++)
            {
                var v = data[i] - mean;
                data[i] = v * v;
            }
            var std = System.Math.Pow((double)(data.Sum() / (data.Length - 1)), 0.5);
            return (mean, (decimal)std);
        }

        public static decimal[] ClearNSigmaReqursive(decimal[] values, int depth = 0, int sigmasCount = 3)
        {
            if (values.Length <= 1 || depth > 10) return values;
            var sigmaRes = CaclSigma(values);
            var std = sigmaRes.std;
            var mean = sigmaRes.mean;
            var forRes = new List<decimal>();
            var _3std = sigmasCount * std;
            foreach (var v in values)
            {
                if (System.Math.Abs(mean - v) < _3std)
                {
                    forRes.Add(v);
                }
            }
            if (forRes.Count != values.Length)
            {
                return ClearNSigmaReqursive(forRes.ToArray(), depth + 1);
            }
            else
            {
                return forRes.ToArray();
            }
        }

        public static bool TryCalcTimeWindowsDiff(this ITradeDataItem[] values, TimeSpan boundLeft, TimeSpan boundRight,
            Func<ITradeDataItem, decimal> fieldSelector, bool calcMean, out decimal result, out decimal resultRelative)
        {
            result = default;
            resultRelative = default;
            if (values.Length > 1)
            {
                var shiftTimeR = values.Last().Time - boundRight;
                var shiftTimeL = values.Last().Time - boundLeft;

                var valuesOld = values.Where(b => b.Time < shiftTimeR && b.Time >= shiftTimeL).ToArray();
                var valuesNew = values.Where(b => b.Time >= shiftTimeR).ToArray();

                if (valuesOld.Length > 0 && valuesNew.Length > 0)
                {
                    var valNew = valuesNew.Sum(fieldSelector);
                    var valOld = valuesOld.Sum(fieldSelector);

                    if (calcMean)
                    {
                        valNew = valNew / valuesNew.Length;
                        valOld = valOld / valuesOld.Length;
                    }
                    result = valNew - valOld;
                    resultRelative = (valNew - valOld) / valOld;
                    return true;
                }
            }
            return false;
        }
        public static bool TryCalcTimeDiff(this ITradeDataItem[] values, TimeSpan boundLeft, TimeSpan boundRight,
    Func<ITradeDataItem, decimal> fieldSelector, bool calcMean, out decimal result)
        {
            result = default;
            if (values.Length > 1)
            {
                var shiftTimeR = values.Last().Time - boundRight;
                var shiftTimeL = values.Last().Time - boundLeft;

                var valuesOld = values.Where(b => b.Time < shiftTimeR && b.Time >= shiftTimeL).ToArray();
                var valuesNew = values.Where(b => b.Time >= shiftTimeR).ToArray();

                if (valuesOld.Length > 0 && valuesNew.Length > 0)
                {
                    var valNew = fieldSelector(valuesNew.Last());
                    var valOld = fieldSelector(valuesOld.Last());

                    result = valNew - valOld;
                    return true;
                }
            }
            return false;
        }
        public static bool TryCalcPirsonCorrelation(this ITradeDataItem[] values, TimeSpan period, out decimal result)
        {
            result = default;
            if (values.Any())
            {
                var shiftTimeDiffs1 = values.Last().Time - period;
                values = values.Where(b => b.Time >= shiftTimeDiffs1).ToArray();
                if (values.Any())
                {
                    var tradevolume_diffMean = values.MeanCount();
                    var dprice_diffMean = values.MeanPrice();
                    var sum1 = (double)values.Sum(d => (d.Value2 - tradevolume_diffMean) * (d.Value - dprice_diffMean));
                    var sum2 = values.Sum(d => (d.Value2 - tradevolume_diffMean) * (d.Value2 - tradevolume_diffMean));
                    var sum3 = values.Sum(d => (d.Value - dprice_diffMean) * (d.Value - dprice_diffMean));
                    if (sum2 != 0 && sum3 != 0)
                    {
                        result = (decimal)(sum1 / System.Math.Sqrt((double)(sum2 * sum3)));
                        return true;
                    }
                }
            }
            return false;
        }

        public static HistItem[] CalcHistogram(ITradeDataItem[] values)
        {
            var result = new Dictionary<decimal, decimal>();
            foreach (var item in values)
            {
                if (!result.TryGetValue(item.Price, out var val))
                {
                    result[item.Price] = 0;
                }
                result[item.Price] = val + 1;
            }
            return result.Select(r => new HistItem() { Value = r.Key, Count = r.Value }).OrderBy(i => i.Value).ToArray();
        }

        public static decimal[] GetParabolaCore(int leverageSize, decimal maxValue = 1)
        {
            var d = new double[2 * leverageSize + 1];
            for (int i = 0; i < d.Length; i++)
            {
                d[i] = -System.Math.Pow((i - leverageSize), 2);
            }

            var min = d.Min();
            var amin = System.Math.Abs(min);
            for (int i = 0; i < d.Length; i++)
            {
                d[i] = (d[i] - min) / amin * (double)maxValue;
            }
            return d.Select(i => (decimal)i).ToArray();
        }

        public static ConvolutionResult[] CalcConvolution(HistItem[] hist, int leverageSize)
        {
            if (hist.Length > 2 * leverageSize + 1)
            {
                var results = new List<ConvolutionResult>();
                var coreSize = 2 * leverageSize + 1;
                for (int shift = 0; shift < hist.Length - coreSize; shift++)
                {
                    var s = 0m;
                    var k = 0;
                    for (int i = 0; i < 2 * leverageSize + 1; i++)
                    {
                        var core = GetParabolaCore(leverageSize, hist[i + shift].Count);
                        s += (hist[i + shift].Count - core[i]) * (hist[i + shift].Count - core[i]);
                        if (i == leverageSize)
                        {
                            k = i + shift;
                        }
                    }
                    s = s / coreSize;
                    s = (decimal)System.Math.Pow((double)s, 0.5d);
                    //s /= coreSum;
                    results.Add(new ConvolutionResult()
                    {
                        Leverage = leverageSize,
                        Sum = s,
                        Value = hist[k].Value,
                        Shift = k,
                    });
                }
                return results.OrderByDescending(r => r.Value).ToArray();
            }
            return Array.Empty<ConvolutionResult>();
        }

        public static void MergeConvolutionResults(List<ConvolutionResult> results, List<ConvolutionResult> mergedResults)
        {
            if (results.Count == 0)
            {
                return;
            }
            var resultsOrdered = results.OrderBy(r => r.Sum).ToList();
            var res = resultsOrdered[0];
            var b1 = res.Shift - res.Leverage;
            var b2 = res.Shift + res.Leverage;
            var forMerge = results.Where(r => r.Shift >= b1 && r.Shift <= b2).ToList();
            res.Sum = forMerge.Sum(r => r.Sum);
            foreach (var m in forMerge)
            {
                results.Remove(m);
            }
            mergedResults.Add(res);
            MergeConvolutionResults(results, mergedResults);
        }
    }
}