segmentation.cs

/*
 * Copyright (C) 2018 Apple Inc. All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL APPLE INC. OR
 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
 * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 
 */

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using BenchmarkDotNet.Attributes;
using MicroBenchmarks;

namespace JetStream {
    public static class Statistics {
        public static readonly Dictionary<double, double[]> tDistributionByOneSidedProbability = 
            new Dictionary<double, double[]> {
            { 0.9, new [] {
                3.077684, 1.885618, 1.637744, 1.533206, 1.475884, 1.439756, 1.414924, 1.396815, 1.383029, 1.372184,
                1.363430, 1.356217, 1.350171, 1.345030, 1.340606, 1.336757, 1.333379, 1.330391, 1.327728, 1.325341,
                1.323188, 1.321237, 1.319460, 1.317836, 1.316345, 1.314972, 1.313703, 1.312527, 1.311434, 1.310415,
                1.309464, 1.308573, 1.307737, 1.306952, 1.306212, 1.305514, 1.304854, 1.304230, 1.303639, 1.303077,
                1.302543, 1.302035, 1.301552, 1.301090, 1.300649, 1.300228, 1.299825, 1.299439, 1.299069, 1.298714,

                1.298373, 1.298045, 1.297730, 1.297426, 1.297134, 1.296853, 1.296581, 1.296319, 1.296066, 1.295821,
                1.295585, 1.295356, 1.295134, 1.294920, 1.294712, 1.294511, 1.294315, 1.294126, 1.293942, 1.293763,
                1.293589, 1.293421, 1.293256, 1.293097, 1.292941, 1.292790, 1.292643, 1.292500, 1.292360, 1.292224,
                1.292091, 1.291961, 1.291835, 1.291711, 1.291591, 1.291473, 1.291358, 1.291246, 1.291136, 1.291029,
                1.290924, 1.290821, 1.290721, 1.290623, 1.290527, 1.290432, 1.290340, 1.290250, 1.290161, 1.290075 } },
            { 0.95, new [] {
                6.313752, 2.919986, 2.353363, 2.131847, 2.015048, 1.943180, 1.894579, 1.859548, 1.833113, 1.812461,
                1.795885, 1.782288, 1.770933, 1.761310, 1.753050, 1.745884, 1.739607, 1.734064, 1.729133, 1.724718,
                1.720743, 1.717144, 1.713872, 1.710882, 1.708141, 1.705618, 1.703288, 1.701131, 1.699127, 1.697261,
                1.695519, 1.693889, 1.692360, 1.690924, 1.689572, 1.688298, 1.687094, 1.685954, 1.684875, 1.683851,
                1.682878, 1.681952, 1.681071, 1.680230, 1.679427, 1.678660, 1.677927, 1.677224, 1.676551, 1.675905,

                1.675285, 1.674689, 1.674116, 1.673565, 1.673034, 1.672522, 1.672029, 1.671553, 1.671093, 1.670649,
                1.670219, 1.669804, 1.669402, 1.669013, 1.668636, 1.668271, 1.667916, 1.667572, 1.667239, 1.666914,
                1.666600, 1.666294, 1.665996, 1.665707, 1.665425, 1.665151, 1.664885, 1.664625, 1.664371, 1.664125,
                1.663884, 1.663649, 1.663420, 1.663197, 1.662978, 1.662765, 1.662557, 1.662354, 1.662155, 1.661961,
                1.661771, 1.661585, 1.661404, 1.661226, 1.661052, 1.660881, 1.660715, 1.660551, 1.660391, 1.660234 } },
            { 0.975, new [] {
                12.706205, 4.302653, 3.182446, 2.776445, 2.570582, 2.446912, 2.364624, 2.306004, 2.262157, 2.228139,
                2.200985, 2.178813, 2.160369, 2.144787, 2.131450, 2.119905, 2.109816, 2.100922, 2.093024, 2.085963,
                2.079614, 2.073873, 2.068658, 2.063899, 2.059539, 2.055529, 2.051831, 2.048407, 2.045230, 2.042272,
                2.039513, 2.036933, 2.034515, 2.032245, 2.030108, 2.028094, 2.026192, 2.024394, 2.022691, 2.021075,
                2.019541, 2.018082, 2.016692, 2.015368, 2.014103, 2.012896, 2.011741, 2.010635, 2.009575, 2.008559,

                2.007584, 2.006647, 2.005746, 2.004879, 2.004045, 2.003241, 2.002465, 2.001717, 2.000995, 2.000298,
                1.999624, 1.998972, 1.998341, 1.997730, 1.997138, 1.996564, 1.996008, 1.995469, 1.994945, 1.994437,
                1.993943, 1.993464, 1.992997, 1.992543, 1.992102, 1.991673, 1.991254, 1.990847, 1.990450, 1.990063,
                1.989686, 1.989319, 1.988960, 1.988610, 1.988268, 1.987934, 1.987608, 1.987290, 1.986979, 1.986675,
                1.986377, 1.986086, 1.985802, 1.985523, 1.985251, 1.984984, 1.984723, 1.984467, 1.984217, 1.983972 } },
            { 0.99, new [] {
                31.820516, 6.964557, 4.540703, 3.746947, 3.364930, 3.142668, 2.997952, 2.896459, 2.821438, 2.763769,
                2.718079, 2.680998, 2.650309, 2.624494, 2.602480, 2.583487, 2.566934, 2.552380, 2.539483, 2.527977,
                2.517648, 2.508325, 2.499867, 2.492159, 2.485107, 2.478630, 2.472660, 2.467140, 2.462021, 2.457262,
                2.452824, 2.448678, 2.444794, 2.441150, 2.437723, 2.434494, 2.431447, 2.428568, 2.425841, 2.423257,
                2.420803, 2.418470, 2.416250, 2.414134, 2.412116, 2.410188, 2.408345, 2.406581, 2.404892, 2.403272,

                2.401718, 2.400225, 2.398790, 2.397410, 2.396081, 2.394801, 2.393568, 2.392377, 2.391229, 2.390119,
                2.389047, 2.388011, 2.387008, 2.386037, 2.385097, 2.384186, 2.383302, 2.382446, 2.381615, 2.380807,
                2.380024, 2.379262, 2.378522, 2.377802, 2.377102, 2.376420, 2.375757, 2.375111, 2.374482, 2.373868,
                2.373270, 2.372687, 2.372119, 2.371564, 2.371022, 2.370493, 2.369977, 2.369472, 2.368979, 2.368497,
                2.368026, 2.367566, 2.367115, 2.366674, 2.366243, 2.365821, 2.365407, 2.365002, 2.364606, 2.364217 } },
        };

        public static double oneSidedToTwoSidedProbability (double probability) { return 2 * probability - 1; }
        public static double twoSidedToOneSidedProbability (double probability) { return (1 - (1 - probability) / 2); }

        public static double min (double[] values) {
            var result = values[0];
            for (int i = 1; i < values.Length; i++)
                result = Math.Min(result, values[i]);
            return result;
        }

        public static double max (double[] values) {
            var result = values[0];
            for (int i = 1; i < values.Length; i++)
                result = Math.Max(result, values[i]);
            return result;
        }

        public static double sum (double[] values) {
            double result = 0;
            foreach (var v in values)
                result += v;
            return result;
        }

        public static double mean (double[] values) {
            return sum(values) / values.Length;
        }

        public static double median (double[] values) {
            Array.Sort(values, (a, b) => a.CompareTo(b));
            return values[values.Length / 2];
        }

        public static double squareSum (double[] values) {
            double result = 0;
            foreach (var v in values)
                result += (v * v);
            return result;
        }

        // With sum and sum of squares, we can compute the sample standard deviation in O(1).
        // See https://rniwa.com/2012-11-10/sample-standard-deviation-in-terms-of-sum-and-square-sum-of-samples/
        public static double sampleStandardDeviation (double numberOfSamples, double sum, double squareSum) {
            if (numberOfSamples < 2)
                return 0;
            return Math.Sqrt(squareSum / (numberOfSamples - 1) - sum * sum / (numberOfSamples - 1) / numberOfSamples);
        }

        // Computes the delta d s.t. (mean - d, mean + d) is the confidence interval with the specified probability in O(1).
        public static double confidenceIntervalDelta (double probability, int numberOfSamples, double sum, double squareSum) {
            var oneSidedProbability = twoSidedToOneSidedProbability(probability);

            if (!tDistributionByOneSidedProbability.ContainsKey(oneSidedProbability))
                throw new Exception("Confidence interval not supported");
            if (numberOfSamples - 2 < 0)
                return double.NaN;
            var deltas = tDistributionByOneSidedProbability[oneSidedProbability];
            var degreesOfFreedom = numberOfSamples - 1;
            if (degreesOfFreedom > deltas.Length)
                throw new Exception("We only support up to " + deltas.Length + " degrees of freedom");

            // d = c * S/sqrt(numberOfSamples) where c ~ t-distribution(degreesOfFreedom) and S is the sample standard deviation.
            return deltas[degreesOfFreedom - 1] * sampleStandardDeviation(numberOfSamples, sum, squareSum) / Math.Sqrt(numberOfSamples);
        }

        public static double[] confidenceInterval (double[] values, double probability = 0.95) {
            var sum = Statistics.sum(values);
            var mean = sum / values.Length;
            var delta = confidenceIntervalDelta(probability, values.Length, sum, squareSum(values));
            return new double[] { mean - delta, mean + delta };
        }

        // Welch's t-test (http://en.wikipedia.org/wiki/Welch%27s_t_test)
        public static object testWelchsT (double[] values1, double[] values2, double probability) {
            return computeWelchsT(values1, 0, values1.Length, values2, 0, values2.Length, probability).significantlyDifferent;
        }

        public class ProbabilityRangeForWelchsT {
            public double t;
            public double degreesOfFreedom;
            public double?[] range;
        }

        public static ProbabilityRangeForWelchsT probabilityRangeForWelchsT (double[] values1, double[] values2) {
            var result = computeWelchsT(values1, 0, values1.Length, values2, 0, values2.Length);
            if (Double.IsNaN(result.t) || Double.IsNaN(result.degreesOfFreedom))
                return new ProbabilityRangeForWelchsT {t = Double.NaN, degreesOfFreedom = Double.NaN, range = new double?[] { null, null } };

            double? lowerBound = null;
            double? upperBound = null;
            foreach (var probability in tDistributionByOneSidedProbability.Keys) {
                var twoSidedProbability = oneSidedToTwoSidedProbability(probability);
                var idx = (int)Math.Round(result.degreesOfFreedom - 1);
                if (result.t > tDistributionByOneSidedProbability[probability][idx])
                    lowerBound = twoSidedProbability;
                else if (lowerBound.HasValue) {
                    upperBound = twoSidedProbability;
                    break;
                }
            }
            return new ProbabilityRangeForWelchsT {t = result.t, degreesOfFreedom = result.degreesOfFreedom, range = new [] { lowerBound, upperBound } };
        }

        public class ComputedWelchsT {
            public double t;
            public double degreesOfFreedom;
            public bool significantlyDifferent;
        }

        public static ComputedWelchsT computeWelchsT (double[] values1, int startIndex1, int length1, double[] values2, int startIndex2, int length2, double probability = 0.8) {
            var stat1 = sampleMeanAndVarianceForValues(values1, startIndex1, length1);
            var stat2 = sampleMeanAndVarianceForValues(values2, startIndex2, length2);
            var sumOfSampleVarianceOverSampleSize = stat1.variance / stat1.size + stat2.variance / stat2.size;
            var t = Math.Abs((stat1.mean - stat2.mean) / Math.Sqrt(sumOfSampleVarianceOverSampleSize));

            // http://en.wikipedia.org/wiki/Welch–Satterthwaite_equation
            var degreesOfFreedom = sumOfSampleVarianceOverSampleSize * sumOfSampleVarianceOverSampleSize
                / (stat1.variance * stat1.variance / stat1.size / stat1.size / stat1.degreesOfFreedom
                    + stat2.variance * stat2.variance / stat2.size / stat2.size / stat2.degreesOfFreedom);
            var idx = (int)Math.Round(degreesOfFreedom - 1);
            var minT = tDistributionByOneSidedProbability[twoSidedToOneSidedProbability(probability)][idx];
            return new ComputedWelchsT {
                t = t,
                degreesOfFreedom = degreesOfFreedom,
                significantlyDifferent = t > minT,
            };
        }
        
        public class MeanAndVariance {
            public double mean, variance;
            public double size;
            public double degreesOfFreedom;
        }

        public static MeanAndVariance sampleMeanAndVarianceForValues (double[] values, int startIndex, int length) {
            double sum = 0;
            for (var i = 0; i < length; i++)
                sum += values[startIndex + i];
            double squareSum = 0;
            for (var i = 0; i < length; i++)
                squareSum += values[startIndex + i] * values[startIndex + i];
            var sampleMean = sum / length;
            // FIXME: Maybe we should be using the biased sample variance.
            var unbiasedSampleVariance = (squareSum - sum * sum / length) / (length - 1);
            return new MeanAndVariance {
                mean = sampleMean,
                variance = unbiasedSampleVariance,
                size = length,
                degreesOfFreedom = length - 1,
            };
        }

        public static double[] movingAverage (double[] values, int backwardWindowSize, int forwardWindowSize) {
            var averages = new double[values.Length];
            // We use naive O(n^2) algorithm for simplicy as well as to avoid accumulating round-off errors.
            for (var i = 0; i < values.Length; i++) {
                double sum = 0;
                double count = 0;
                for (var j = i - backwardWindowSize; j <= i + forwardWindowSize; j++) {
                    if (j >= 0 && j < values.Length) {
                        sum += values[j];
                        count++;
                    }
                }
                averages[i] = sum / count;
            }
            return averages;
        }

        public static double[] cumulativeMovingAverage (double[] values) {
            var averages = new double[values.Length];
            double sum = 0;
            for (var i = 0; i < values.Length; i++) {
                sum += values[i];
                averages[i] = sum / (double)(i + 1);
            }
            return averages;
        }

        public static object exponentialMovingAverage (double[] values, double smoothingFactor) {
            var averages = new double[values.Length];
            var movingAverage = values[0];
            averages[0] = movingAverage;
            for (var i = 1; i < values.Length; i++) {
                movingAverage = smoothingFactor * values[i] + (1 - smoothingFactor) * movingAverage;
                averages[i] = movingAverage;
            }
            return averages;
        }

        // The return value is the starting indices of each segment.
        public static int[] segmentTimeSeriesGreedyWithStudentsTTest (double[] values, int minLength) {
            if (values.Length < 2)
                return new int[] { 0 };
            var segments = new List<int>();
            recursivelySplitIntoTwoSegmentsAtMaxTIfSignificantlyDifferent(values, 0, values.Length, minLength, segments);
            segments.Add(values.Length);
            return segments.ToArray();
        }

        public static int[] segmentTimeSeriesByMaximizingSchwarzCriterion (double[] values, double segmentCountWeight, int gridLength = 500) {
            // Split the time series into grids since splitIntoSegmentsUntilGoodEnough is O(n^2).
            var totalSegmentation = new List<int> { 0 };
            for (int gridCount = 0, l = (int)Math.Ceiling(values.Length / (double)gridLength); gridCount < l; gridCount++) {

                var gridValues = values.slice(gridCount * gridLength, (gridCount + 1) * gridLength);
                var segmentation = splitIntoSegmentsUntilGoodEnough(gridValues, segmentCountWeight);

                for (var i = 1; i < segmentation.Length - 1; i++)
                    totalSegmentation.Add(gridCount * gridLength + segmentation[i]);
            }

            totalSegmentation.Add(values.Length);

            return totalSegmentation.ToArray();
        }

        public static void recursivelySplitIntoTwoSegmentsAtMaxTIfSignificantlyDifferent (double[] values, int startIndex, int length, int minLength, List<int> segments) {
            double tMax = 0;
            int? argTMax = null;
            for (var i = 1; i < length - 1; i++) {
                var firstLength = i;
                var secondLength = length - i;
                if (firstLength < minLength || secondLength < minLength)
                    continue;
                var result = Statistics.computeWelchsT(values, startIndex, firstLength, values, startIndex + i, secondLength, 0.9);
                if (result.significantlyDifferent && result.t > tMax) {
                    tMax = result.t;
                    argTMax = i;
                }
            }
            if (tMax <= 0) {
                segments.Add(startIndex);
                return;
            }
            recursivelySplitIntoTwoSegmentsAtMaxTIfSignificantlyDifferent(values, startIndex, argTMax.Value, minLength, segments);
            recursivelySplitIntoTwoSegmentsAtMaxTIfSignificantlyDifferent(values, startIndex + argTMax.Value, length - argTMax.Value, minLength, segments);
        }

        public static int[] splitIntoSegmentsUntilGoodEnough(double[] values, double BirgeAndMassartC = 2.5) {
            if (values.Length < 2)
                return new[] { 0, values.Length };

            var matrix = new SampleVarianceUpperTriangularMatrix(values);

            var SchwarzCriterionBeta = Compat.log1p(values.Length - 1) / values.Length;

            var BirgeAndMassartPenalization = (Func<int, double>)((segmentCount) =>
                segmentCount * (1 + BirgeAndMassartC * Compat.log1p(values.Length / (double)segmentCount - 1))
            );

            int[] segmentation = null;
            var minTotalCost = double.PositiveInfinity;
            var maxK = Math.Min(50, values.Length);

            for (var k = 1; k < maxK; k++) {
                // var start = Date.now();
                var result = findOptimalSegmentation(values, matrix, k);
                var cost = result.cost / (double)values.Length;
                var penalty = SchwarzCriterionBeta * BirgeAndMassartPenalization(k);
                if (cost + penalty < minTotalCost) {
                    minTotalCost = cost + penalty;
                    segmentation = result.segmentation;
                } else
                    maxK = Math.Min(maxK, k + 3);
            }

            return segmentation;
        }

        public static float[][] allocateCostUpperTriangularForSegmentation (double[] values, int segmentCount)
        {
            // Dynamic programming. cost[i][k] = The cost to segmenting values up to i into k segments.
            var cost = new float[values.Length][];
            for (var segmentEnd = 0; segmentEnd < values.Length; segmentEnd++)
                cost[segmentEnd] = new float[segmentCount + 1];
            return cost;
        }

        public static int[][] allocatePreviousNodeForSegmentation(double[] values, int segmentCount)
        {
            // previousNode[i][k] = The start of the last segment in an optimal segmentation that ends at i with k segments.
            var previousNode = new int[values.Length][];
            for (var i = 0; i < values.Length; i++)
                previousNode[i] = new int[segmentCount + 1];
            return previousNode;
        }

        public static bool IsInRange<T> (T[] arr, int index) {
            if (index < 0)
                return false;
            if (index >= arr.Length)
                return false;
            return true;
        }

        public static void findOptimalSegmentationInternal(float[][] cost, int[][] previousNode, double[] values, SampleVarianceUpperTriangularMatrix costMatrix, int segmentCount)
        {
            // The cost of segmenting single value is always 0.
            for (int i = 0; i < cost[0].Length; i++)
                cost[0][i] = 0;
            for (int i = 0; i < previousNode[0].Length; i++)
                previousNode[0][i] = -1;

            for (var segmentStart = 0; segmentStart < values.Length; segmentStart++) {
                var costOfOptimalSegmentationThatEndAtCurrentStart = cost[segmentStart];
                for (var k = 0; k < segmentCount; k++) {
                    var noSegmentationOfLenghtKEndsAtCurrentStart = !IsInRange(previousNode[segmentStart], k);
                    if (noSegmentationOfLenghtKEndsAtCurrentStart)
                        continue;
                    for (var segmentEnd = segmentStart + 1; segmentEnd < values.Length; segmentEnd++) {
                        var costOfOptimalSegmentationOfLengthK = costOfOptimalSegmentationThatEndAtCurrentStart[k];
                        var costOfCurrentSegment = costMatrix.costBetween(segmentStart, segmentEnd);
                        var totalCost = costOfOptimalSegmentationOfLengthK + costOfCurrentSegment;
                        if (!IsInRange(previousNode[segmentEnd], k + 1) || totalCost < cost[segmentEnd][k + 1]) {
                            cost[segmentEnd][k + 1] = (float)totalCost;
                            previousNode[segmentEnd][k + 1] = segmentStart;
                        }
                    }
                }
            }
        }

        public class OptimalSegmentation {
            public int[] segmentation;
            public float cost;
        }

        public static OptimalSegmentation findOptimalSegmentation (double[] values, SampleVarianceUpperTriangularMatrix costMatrix, int segmentCount) {
            var cost = allocateCostUpperTriangularForSegmentation(values, segmentCount);
            var previousNode = allocatePreviousNodeForSegmentation(values, segmentCount);

            findOptimalSegmentationInternal(cost, previousNode, values, costMatrix, segmentCount);

            var segmentEnd = values.Length - 1;
            var segmentation = new int[segmentCount + 1];
            segmentation[segmentCount] = values.Length;

            for (var k = segmentCount; k > 0; k--) {
                if (segmentEnd < 0)
                    break;

                segmentEnd = previousNode[segmentEnd][k];
                segmentation[k - 1] = segmentEnd;
            }

            var costOfOptimalSegmentation = cost[values.Length - 1][segmentCount];

            return new OptimalSegmentation {segmentation = segmentation, cost = costOfOptimalSegmentation};
        }
    }

    public class SampleVarianceUpperTriangularMatrix {
        public float[][] costMatrix;

        public SampleVarianceUpperTriangularMatrix (double[] values) {
            // The cost of segment (i, j].
            costMatrix = new float[values.Length - 1][];
            for (var i = 0; i < values.Length - 1; i++) {
                var remainingValueCount = values.Length - i - 1;
                costMatrix[i] = new float[remainingValueCount];
                var sum = values[i];
                var squareSum = sum * sum;
                costMatrix[i][0] = 0;
                for (var j = i + 1; j < values.Length; j++) {
                    var currentValue = values[j];
                    sum += currentValue;
                    squareSum += currentValue * currentValue;
                    var sampleSize = j - i + 1;
                    var stdev = Statistics.sampleStandardDeviation(sampleSize, sum, squareSum);
                    costMatrix[i][j - i - 1] = (float)(stdev > 0 ? sampleSize * Math.Log(stdev * stdev) : 0);
                }
            }
        }

        public double costBetween (int from, int to) {
            if (from >= this.costMatrix.Length || from == to)
                return 0; // The cost of the segment that starts at the last data point is 0.
            return this.costMatrix[from][to - from - 1];
        }
    }

    [BenchmarkCategory(Categories.Runtime)]
    public class TimeSeriesSegmentation {
        public double[] d1 = new double[] { 
            103.63428467218,100.65698512757,103.41681901544,101.73297541769,106.1637181408,98.412208909224,102.1910683922,100.6529954993,100.2060895554,102.79763572285,101.58124402819,104.83646850886,105.68205557779,101.37268411726,101.21856897174,103.29471813954,105.99085083645,104.00152807402,102.5515579466,100.95765471931,101.30414879687,101.28842115694,103.18365782867,104.32770094781,101.04841668133,103.48198436419,100.89825149314,101.96224301484,102.57514127219,101.88941623092,102.55684506087,103.32436792906,102.14059443954,101.34202300433,100.71509510859,102.84019181314,103.90795641251,103.79317123977,102.33281400385,101.05661999771,99.527245552223,104.04756755696,100.08258193089,102.32602929128,101.12649175316,98.59777764562,100.51219905198,100.3384460803,101.15283289168,104.45829696358,103.08640647121,101.15646661427,104.87981301026,102.96022354121,102.91057904096,102.94557493889,104.19286657388,101.49564839627,104.56628696589,102.64328394303,102.98955045659,100.30795615252,101.9596010783,102.7787577747,105.08450703012,105.6083617604,100.58871732306,102.29447246575,103.93156436242,100.15444968522,100.33027723674,99.709998115277,104.77614797428,101.80467295351,103.83722962812,103.8922179754,99.668513176783,103.54088096393,99.79641717842,99.217827453945,100.63604774585,99.397345569613,103.41566155646,102.86730291818,101.3466271856,101.0430581605,101.75352329686,101.79205972782,103.58235064873,102.70955387997,103.513441865,103.55358827182,101.27954344729,100.72000812989,100.50572692724,103.29725364285,99.878238665041,101.33136147166,107.82148653962,106.33087978795,105.76698605645,106.73722912118,105.09474645086,106.93812007831,104.58796212158,108.74454496591,108.77609339631,106.36234738479,107.08594417641,103.14990449109,103.08799682189,106.42944302492,104.95681265496,104.19185455295,103.37266620831,106.88393619713,103.77307460747,107.22959460967,102.92373151821,102.27169909087,105.35352579142,108.55485303073,106.86928831633,107.6604165255,106.08100829687,105.69860408885,104.15919883914,103.43072470928,107.61607415001,105.12730526857,108.26003924405,102.52392958652,103.49742913465,106.40355299133,106.6205839791,103.75599735706,104.02717048675,102.8616712232,107.31403440793,105.71715870348,108.62026687466,103.89002871878,101.02136648518,105.71922937008,107.65246680959,106.90056953891,103.116341753,107.4819154547,104.30217606275,106.2163429931,108.76888355744,106.25769430792,105.62856894786,106.5974802856,107.4572456313,103.76930483468,109.22117086979,103.95101290047,103.04369239044,105.8978020889,108.08880932927,107.09476068374,107.84718462015,104.3185702112,108.58358811573,103.08208736102,106.30281582081,105.5071989199,106.69382657222,105.5661979062,107.55317794727,106.81112895681,103.49181806572,108.11406008626,105.82558000937,110.7280951536,110.57391099468,96.195798803035,98.050055515401,98.34258752078,96.437461839433,107.86695915352,107.50220866371,96.408603678811,96.183884592145,93.874527361487,106.01388920009,106.68752585206,95.748639659824,97.620195660744,95.709384830238,94.844312788627,97.194219302695,95.228621910585,95.299983299732,95.878520884831,95.494218128339,95.721877181905,95.30324004452,93.761957719231,99.052683337698,97.414624016474,98.955647001503,96.944084189531,94.98363688231,97.084748591591,96.56489094851,96.602599613176,99.011103877236,108.56332396293,96.328721476217,112.59520822831,111.4457635202,109.57249840458,112.52658585356,111.79387339089,107.83633335508,110.46783549074,113.07325087266,114.03320142819,108.91999302834,113.28679171319,112.84647681497,112.30446173472,107.70596309315,113.90782983196,110.52702067922,110.77146399218,108.82316306309,112.31704998895,112.04572347677,102.01583120296,102.26933512167,101.04034529285,102.82388967602,103.5215835497,103.60628281381,100.24147995637,102.56920667296,111.65264599649,109.90970916739,110.91610377373,110.86460228468,110.66591901693,110.08877264895,110.07273691588,108.50573934243,111.74386044451,109.613011316,111.00131231439,112.36541199185,107.7696667543,108.22526773007,110.72718495033,110.60353399069,110.27959438874,109.58777079374,111.98279815171,110.36414556569,110.70297309292,111.30023230049,111.53753771801,111.98382518632,105.84905409588,111.46509413983,108.80378506166,108.87305949198,106.71554016504,108.90363691526,110.56509895199,110.36621011006,109.26421997574,110.84819795531,108.01463000771,110.16319399901,110.07964827933,109.98910490708,108.31446832729,108.38910105911,112.30023252646,111.50251919968,109.58690843228,106.49996527433,109.79602509693,96.52144390049,108.95662597735,111.8968272024,110.28041012397,111.55946971612,111.13212900067,109.06043835093,111.0511769347,108.32635458606,107.65798353661,107.34909902585,110.25041961026,109.1718567223,108.03672114421,110.24074486601,107.97075096529,111.3628301031,108.6301339157,103.7289403799,106.60945920642,106.53605315427,103.20148515981,105.11749841121,104.2666389565,103.42858705344,106.1975050171,104.72818386307,106.37807528636,105.02872802439,105.85690151022,105.89551276982,104.0098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
        };

        public double[] d2 = new double[] { 
            372535296,382377984,391487488,372695040,384020480,388427776,385986560,401125376,389529600,394014720,383983616,383504384,388804608,391004160,379936768,390008832,392830976,385937408,386101248,391065600,383262720,383717376,405553152,411299840,395431936,400896000,411578368,413659136,393289728,397176832,415444992,383922176,380809216,402214912,420286464,408412160,392343552,406532096,405950464,405266432,405266432,399302656,392708096,403107840,396943360,413351936,394735616,414461952,391102464,415363072,394797056,394432512,399646720,393465856,395780096,395829248,393895936,420745216,401338368,396079104,407846912,401051648,396705792,396345344,401694720,395808768,408088576,393785344,400572416,392282112,397897728,393547776,394969088,398417920,409014272,394620928,401031168,402567168,399011840,398532608,410574848,391426048,419282944,415105024,400883712,399093760,398114816,408608768,408432640,394809344,410787840,394522624,392658944,394158080,409600000,415043584,396181504,413138944,392978432,390225920,396677120,405676032,403087360,405594112,399937536,395894784,394608640,398200832,406245376,392458240,418922496,401690624,389500928,411136000,386760704,413073408,385392640,394715136,389586944,395960320,392036352,387768320,381210624,405696512,389230592,384266240,392065024,397029376,408678400,385114112,388362240,395304960,383799296,384253952,383303680,396394496,402731008,401383424,394399744,410091520,393256960,408727552,390725632,388235264,395939840,390950912,385069056,387432448,399179776,390594560,391823360,408346624,394641408,403292160,395751424,381997056,396726272,386023424,402124800,382537728,391188480,398589952,382857216,403599360,390873088,394309632,397361152,383676416,380076032,385716224,401346560,399822848,399826944,381673472,398479360,385056768,377995264,376963072,391421952,376049664,392478720,399884288,376856576,393891840,376143872,384397312,395837440,392298496,374730752,383254528,385105920,400908288,387526656,377487360,388812800,381935616,385187840,377909248,376717312,391622656,376836096,384651264,377069568,379535360,382607360,378822656,395116544,378396672,380440576,399740928,381788160,397438976,390111232,386150400,379228160,375971840,385290240,383262720,377401344,398135296,386297856,384110592,386359296,383848448,385998848,376852480,384012288,384344064,399777792,396468224,376623104,375128064,387264512,375648256,392667136,389255168,373874688,386101248,382988288,390455296,397877248,389328896,404615168,383582208,386965504,384815104,381370368,384880640,383262720,383463424,374714368,385224704,376725504,387416064,384774144,383967232,386433024,386834432,392900608,383627264,383184896,375844864,388706304,387858432,394989568,385040384,379428864,376778752,388112384,382734336,402206720,376815616,377913344,380018688,382402560,381964288,382722048,396218368,386211840,380309504,381325312,390418432,383815680,398917632,384167936,377221120,384434176,385839104,395571200,379887616,376418304,380084224,385200128,378437632,378007552,391417856,391852032,376610816,390393856,380276736,386224128,376111104,384335872,377425920,379564032,400736256,376180736,382963712,385146880,385929216,377671680,379469824,398663680,381931520,379908096,375885824,383655936,384159744,379043840,380432384,380719104,377397248,377303040,381177856,396369920,377040896,379293696,382693376,390258688,377618432,381018112,379682816,386469888,385335296,376221696,378331136,388902912,376958976,370102272,377380864,370663424,385691648,378560512,397266944,370716672,377184256,392278016,377294848,369430528,370847744,378265600,370515968,387846144,371118080,375603200,375427072,370831360,377589760,371916800,368480256,369254400,399187968,394952704,371372032,369049600,370802688,370241536,370724864,376610816,379260928,387842048,375123968,369745920,371642368,366592000,374640640,366833664,368275456,367886336,392151040,374788096,382320640,399278080,394911744,370671616,383025152,379637760,372101120,379641856,378572800,381874176,401866752,391942144,388337664,397881344,381849600,381624320,388698112,393519104,400277504,384905216,392511488,383672320,384270336,393269248,390021120,383795200,391340032,390000640,400314368,398553088,392880128,391102464,392032256,394575872,387489792,385622016,388419584,394289152,384110592,393973760,392511488,385220608,387932160,386142208,399581184,391589888,385613824,384352256,421908480,395427840,390283264,389324800,392372224,385978368,389001216,389984256,392323072,386953216,387043328,412049408,385286144,401416192,385998848,386850816,389926912,387919872,390127616,385937408,385949696,402853888,385982464,387874816,391024640,389029888,385191936,399749120,392933376,388321280,390909952,385171456,395223040,405741568,386252800,392491008,405037056,411389952,385073152,385007616,392638464,391790592,385249280,391319552,405843968,416309248,392921088,409276416,386154496,385003520,401702912,395935744,386121728,400613376,394919936,387952640,383307776,385748992,399876096,402923520,393531392,396890112,393920512,385622016,385769472,393744384,384585728,392798208,394072064,384020480,386056192,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
        };

        [Benchmark]
        public void MaximizeSchwarzCriterion() {
            const double segmentCountWeight = 2.5;
            const int gridLength = 500;
            var data = new [] { d1, d2 };

            foreach (var d in data)
                Statistics.segmentTimeSeriesByMaximizingSchwarzCriterion(d, segmentCountWeight, gridLength);
        }
    }
}