// <copyright file="MovingStatistics.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2015 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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using System.Collections.Generic;
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namespace IStation.Numerics.Statistics
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{
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/// <summary>
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/// Running statistics over a window of data, allows updating by adding values.
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/// </summary>
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public class MovingStatistics
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{
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readonly double[] _oldValues;
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readonly int _windowSize;
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long _count;
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long _totalCountOffset;
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int _lastIndex;
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int _lastNaNTimeToLive;
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int _lastPosInfTimeToLive;
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int _lastNegInfTimeToLive;
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double _m1;
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double _m2;
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double _max = double.NegativeInfinity;
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double _min = double.PositiveInfinity;
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public MovingStatistics(int windowSize)
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{
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if (windowSize < 1)
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{
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throw new ArgumentException(string.Format("Value must be positive."), nameof(windowSize));
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}
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_windowSize = windowSize;
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_oldValues = new double[_windowSize];
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}
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public MovingStatistics(int windowSize, IEnumerable<double> values)
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: this(windowSize)
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{
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PushRange(values);
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}
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public int WindowSize => _windowSize;
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/// <summary>
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/// Gets the total number of samples.
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/// </summary>
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public long Count => _totalCountOffset + _count;
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/// <summary>
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/// Returns the minimum value in the sample data.
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/// Returns NaN if data is empty or if any entry is NaN.
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/// </summary>
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public double Minimum
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{
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get
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{
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if (_lastNaNTimeToLive > 0)
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{
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return double.NaN;
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}
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if (_lastNegInfTimeToLive > 0)
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{
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return double.NegativeInfinity;
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}
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return (_count > 0 || _lastPosInfTimeToLive > 0) ? _min : double.NaN;
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}
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}
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/// <summary>
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/// Returns the maximum value in the sample data.
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/// Returns NaN if data is empty or if any entry is NaN.
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/// </summary>
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public double Maximum
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{
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get
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{
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if (_lastNaNTimeToLive > 0)
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{
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return double.NaN;
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}
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if (_lastPosInfTimeToLive > 0)
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{
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return double.PositiveInfinity;
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}
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return (_count > 0 || _lastNegInfTimeToLive > 0) ? _max : double.NaN;
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}
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}
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/// <summary>
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/// Evaluates the sample mean, an estimate of the population mean.
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/// Returns NaN if data is empty or if any entry is NaN.
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/// </summary>
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public double Mean
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{
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get
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{
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if (_lastNaNTimeToLive > 0 || (_lastPosInfTimeToLive > 0 && _lastNegInfTimeToLive > 0))
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{
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return double.NaN;
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}
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if (_lastPosInfTimeToLive > 0)
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{
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return double.PositiveInfinity;
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}
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if (_lastNegInfTimeToLive > 0)
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{
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return double.NegativeInfinity;
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}
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return _count == 0 ? double.NaN : _m1;
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}
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}
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/// <summary>
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/// Estimates the unbiased population variance from the provided samples.
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/// On a dataset of size N will use an N-1 normalizer (Bessel's correction).
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/// Returns NaN if data has less than two entries or if any entry is NaN.
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/// </summary>
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public double Variance
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{
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get
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{
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if (_lastNaNTimeToLive > 0 || _lastNegInfTimeToLive > 0)
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{
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return double.NaN;
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}
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if (_lastPosInfTimeToLive > 0)
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{
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return double.PositiveInfinity;
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}
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return _count < 2 ? double.NaN : _m2 / (_count - 1);
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}
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}
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/// <summary>
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/// Evaluates the variance from the provided full population.
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/// On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset.
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/// Returns NaN if data is empty or if any entry is NaN.
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/// </summary>
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public double PopulationVariance
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{
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get
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{
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if (_lastNaNTimeToLive > 0 || _lastNegInfTimeToLive > 0)
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{
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return double.NaN;
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}
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if (_lastPosInfTimeToLive > 0)
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{
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return double.PositiveInfinity;
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}
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return _count < 2 ? double.NaN : _m2 / _count;
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}
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}
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/// <summary>
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/// Estimates the unbiased population standard deviation from the provided samples.
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/// On a dataset of size N will use an N-1 normalizer (Bessel's correction).
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/// Returns NaN if data has less than two entries or if any entry is NaN.
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/// </summary>
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public double StandardDeviation
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{
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get
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{
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if (_lastNaNTimeToLive > 0 || _lastNegInfTimeToLive > 0)
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{
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return double.NaN;
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}
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if (_lastPosInfTimeToLive > 0)
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{
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return double.PositiveInfinity;
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}
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return _count < 2 ? double.NaN : Math.Sqrt(_m2 / (_count - 1));
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}
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}
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/// <summary>
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/// Evaluates the standard deviation from the provided full population.
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/// On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset.
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/// Returns NaN if data is empty or if any entry is NaN.
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/// </summary>
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public double PopulationStandardDeviation
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{
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get
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{
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if (_lastNaNTimeToLive > 0 || _lastNegInfTimeToLive > 0)
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{
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return double.NaN;
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}
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if (_lastPosInfTimeToLive > 0)
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{
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return double.PositiveInfinity;
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}
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return _count < 2 ? double.NaN : Math.Sqrt(_m2 / _count);
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}
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}
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/// <summary>
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/// Update the running statistics by adding another observed sample (in-place).
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/// </summary>
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public void Push(double value)
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{
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DecrementTimeToLive();
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if (double.IsNaN(value))
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{
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_lastNaNTimeToLive = _windowSize;
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Reset(double.PositiveInfinity, double.NegativeInfinity);
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return;
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}
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if (double.IsPositiveInfinity(value))
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{
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_lastPosInfTimeToLive = _windowSize;
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Reset(_min, double.NegativeInfinity);
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return;
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}
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if (double.IsNegativeInfinity(value))
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{
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_lastNegInfTimeToLive = _windowSize;
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Reset(double.PositiveInfinity, _max);
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return;
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}
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if (_count < _windowSize)
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{
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_oldValues[_count] = value;
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_count++;
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var d = value - _m1;
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var s = d / _count;
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var t = d * s * (_count - 1);
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_m1 += s;
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_m2 += t;
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if (value < _min)
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{
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_min = value;
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}
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if (value > _max)
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{
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_max = value;
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}
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}
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else
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{
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var oldValue = _oldValues[_lastIndex];
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var d = value - oldValue;
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var s = d / _count;
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var oldM1 = _m1;
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_m1 += s;
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var x = (value - _m1 + oldValue - oldM1);
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var t = d * x;
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_m2 += t;
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_oldValues[_lastIndex] = value;
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_lastIndex++;
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if (_lastIndex == WindowSize)
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{
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_lastIndex = 0;
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}
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_max = value > _max ? value : _oldValues.Maximum();
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_min = value < _min ? value : _oldValues.Minimum();
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}
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}
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/// <summary>
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/// Update the running statistics by adding a sequence of observed sample (in-place).
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/// </summary>
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public void PushRange(IEnumerable<double> values)
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{
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foreach (var value in values)
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{
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Push(value);
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}
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}
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private void DecrementTimeToLive()
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{
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if (_lastNaNTimeToLive > 0)
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{
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_lastNaNTimeToLive--;
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}
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if (_lastPosInfTimeToLive > 0)
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{
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_lastPosInfTimeToLive--;
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}
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if (_lastNegInfTimeToLive > 0)
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{
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_lastNegInfTimeToLive--;
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}
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}
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private void Reset(double min, double max)
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{
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_totalCountOffset += _count + 1;
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_count = 0;
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_m1 = 0;
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_max = max;
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_min = min;
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}
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}
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}
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