mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-04 04:07:42 +00:00
Miha Kralj
b3a64f18fa
- Added Ztest class to compute the one-sample t-statistic using sample standard deviation with Bessel correction. - Implemented validation tests for Ztest to ensure accuracy against manual calculations and PineScript. - Updated documentation for Ztest, detailing its mathematical foundation, performance profile, and common pitfalls. - Adjusted NDepend badges to reflect changes in code metrics after implementation. - Updated missing indicators report to reflect the completion of statistical indicators, including ZTEST.
698 lines
22 KiB
C#
698 lines
22 KiB
C#
using System.Buffers;
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using System.Runtime.CompilerServices;
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using System.Runtime.InteropServices;
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using System.Runtime.Intrinsics;
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using System.Runtime.Intrinsics.X86;
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namespace QuanTAlib;
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/// <summary>
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/// JB: Jarque-Bera Test Statistic
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/// </summary>
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/// <remarks>
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/// The Jarque-Bera test measures how far a distribution deviates from normality
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/// by examining skewness and kurtosis. Under the null hypothesis of normality,
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/// JB ~ χ²(2). Large values reject normality.
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///
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/// Formula:
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/// JB = (n / 6) × (S² + EK² / 4)
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/// where S = skewness = m₃ / m₂^(3/2)
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/// EK = excess kurtosis = (m₄ / m₂²) − 3
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/// mₖ = k-th central moment = Σ(xᵢ − x̄)ᵏ / n
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///
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/// O(1) streaming via running sums of x, x², x³, x⁴ with periodic resync
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/// to limit floating-point drift.
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///
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/// Critical values (χ² with 2 df):
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/// 10% → 4.605, 5% → 5.991, 1% → 9.210
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///
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/// IsHot:
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/// Becomes true when the buffer reaches full period length.
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/// </remarks>
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[SkipLocalsInit]
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public sealed class Jb : AbstractBase
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{
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private readonly int _period;
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private readonly RingBuffer _buffer;
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private readonly TValuePublishedHandler _handler;
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private readonly ITValuePublisher? _source;
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private bool _disposed;
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private double _sum;
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private double _sumSq;
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private double _sumCu;
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private double _sumQu;
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private double _p_sum;
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private double _p_sumSq;
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private double _p_sumCu;
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private double _p_sumQu;
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private double _lastValidValue;
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private double _p_lastValidValue;
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private int _updateCount;
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private const int ResyncInterval = 1000;
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private const double Epsilon = 1e-10;
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public override bool IsHot => _buffer.IsFull;
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/// <summary>Creates a new JB indicator with the specified period.</summary>
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/// <param name="period">The lookback period (must be >= 3).</param>
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public Jb(int period)
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{
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if (period < 3)
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{
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throw new ArgumentException("Period must be at least 3.", nameof(period));
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}
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_period = period;
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_buffer = new RingBuffer(period);
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Name = $"Jb({period})";
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WarmupPeriod = period;
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_handler = Handle;
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}
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public Jb(ITValuePublisher source, int period) : this(period)
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{
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_source = source;
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source.Pub += _handler;
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}
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public Jb(TSeries source, int period) : this(period)
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{
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_source = source;
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source.Pub += _handler;
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Prime(source.Values);
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if (source.Count > 0)
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{
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Last = new TValue(source.LastTime, Last.Value);
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}
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private void Handle(object? sender, in TValueEventArgs args) => Update(args.Value, args.IsNew);
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public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
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{
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if (source.Length == 0)
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{
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return;
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}
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_buffer.Clear();
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_sum = 0;
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_sumSq = 0;
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_sumCu = 0;
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_sumQu = 0;
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_lastValidValue = 0;
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_p_lastValidValue = 0;
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_updateCount = 0;
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int warmupLength = Math.Min(source.Length, WarmupPeriod);
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int startIndex = source.Length - warmupLength;
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for (int i = startIndex; i < source.Length; i++)
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{
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Update(new TValue(DateTime.MinValue, source[i]));
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}
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public override TValue Update(TValue input, bool isNew = true)
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{
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double value = input.Value;
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// NaN/Infinity guard — substitute last valid
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if (!double.IsFinite(value))
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{
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value = _lastValidValue;
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}
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else
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{
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if (isNew)
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{
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_p_lastValidValue = _lastValidValue;
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}
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_lastValidValue = value;
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}
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if (isNew)
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{
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// Save state for rollback
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_p_sum = _sum;
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_p_sumSq = _sumSq;
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_p_sumCu = _sumCu;
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_p_sumQu = _sumQu;
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if (_buffer.IsFull)
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{
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double old = _buffer.Oldest;
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double oldSq = old * old;
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_sum -= old;
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_sumSq -= oldSq;
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_sumCu -= oldSq * old;
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_sumQu -= oldSq * oldSq;
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}
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_buffer.Add(value);
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double vSq = value * value;
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_sum += value;
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_sumSq += vSq;
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_sumCu += vSq * value;
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_sumQu += vSq * vSq;
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_updateCount++;
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if (_updateCount % ResyncInterval == 0)
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{
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Resync();
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}
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}
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else
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{
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// Restore previous state
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_lastValidValue = _p_lastValidValue;
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_sum = _p_sum;
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_sumSq = _p_sumSq;
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_sumCu = _p_sumCu;
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_sumQu = _p_sumQu;
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if (_buffer.Count > 0)
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{
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_buffer.UpdateNewest(value);
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Resync();
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}
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else
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{
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_buffer.Add(value);
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double vSq = value * value;
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_sum += value;
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_sumSq += vSq;
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_sumCu += vSq * value;
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_sumQu += vSq * vSq;
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}
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// Re-apply NaN guard for corrected value
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if (double.IsFinite(input.Value))
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{
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_lastValidValue = input.Value;
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}
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}
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double jb = CalculateJbFromSums(_sum, _sumSq, _sumCu, _sumQu, _buffer.Count);
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Last = new TValue(input.Time, jb);
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PubEvent(Last, isNew);
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return Last;
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}
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public override TSeries Update(TSeries source)
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{
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if (source.Count == 0)
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{
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return [];
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}
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int len = source.Count;
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var t = new List<long>(len);
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var v = new List<double>(len);
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CollectionsMarshal.SetCount(t, len);
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CollectionsMarshal.SetCount(v, len);
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var tSpan = CollectionsMarshal.AsSpan(t);
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var vSpan = CollectionsMarshal.AsSpan(v);
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Batch(source.Values, vSpan, _period);
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source.Times.CopyTo(tSpan);
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// Reset running state before priming
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_buffer.Clear();
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_sum = 0;
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_sumSq = 0;
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_sumCu = 0;
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_sumQu = 0;
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_lastValidValue = 0;
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_p_lastValidValue = 0;
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_updateCount = 0;
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// Prime the state
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int primeStart = Math.Max(0, len - _period);
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for (int i = primeStart; i < len; i++)
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{
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Update(source[i]);
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}
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Last = new TValue(tSpan[len - 1], vSpan[len - 1]);
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return new TSeries(t, v);
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}
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public static TSeries Batch(TSeries source, int period)
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{
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var jb = new Jb(period);
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return jb.Update(source);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static void Batch(ReadOnlySpan<double> source, Span<double> output, int period)
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{
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if (source.Length != output.Length)
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{
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throw new ArgumentException("Source and output must have the same length.", nameof(output));
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}
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if (period < 3)
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{
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throw new ArgumentException("Period must be at least 3.", nameof(period));
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}
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int len = source.Length;
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if (len == 0)
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{
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return;
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}
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// Try SIMD path for large, clean datasets
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const int SimdThreshold = 256;
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if (len >= SimdThreshold && Avx2.IsSupported && !source.ContainsNonFinite())
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{
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CalculateAvx2Core(source, output, period);
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return;
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}
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// Scalar path
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CalculateScalarCore(source, output, period);
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}
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public static (TSeries Results, Jb Indicator) Calculate(TSeries source, int period)
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{
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var indicator = new Jb(period);
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TSeries results = indicator.Update(source);
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return (results, indicator);
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}
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public override void Reset()
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{
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_buffer.Clear();
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_sum = 0;
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_sumSq = 0;
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_sumCu = 0;
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_sumQu = 0;
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_p_sum = 0;
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_p_sumSq = 0;
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_p_sumCu = 0;
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_p_sumQu = 0;
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_lastValidValue = 0;
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_p_lastValidValue = 0;
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_updateCount = 0;
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Last = default;
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}
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protected override void Dispose(bool disposing)
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{
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if (!_disposed)
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{
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if (disposing && _source != null)
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{
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_source.Pub -= _handler;
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}
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_disposed = true;
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}
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base.Dispose(disposing);
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}
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/////////////////////////////////////////////////////////////////////////////////////////////////
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// Private helpers
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/////////////////////////////////////////////////////////////////////////////////////////////////
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static double CalculateJbFromSums(double sum, double sumSq, double sumCu, double sumQu, double n)
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{
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if (n < 3)
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{
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return 0;
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}
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double mean = sum / n;
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double meanSq = mean * mean;
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// m₂ = (Σx̲ - Σx²/n) / n
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double m2Numerator = sumSq - (sum * sum) / n;
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if (m2Numerator < Epsilon)
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{
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return 0;
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}
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double m2 = m2Numerator / n;
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if (m2 <= Epsilon)
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{
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return 0;
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}
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// m₃ = (Σx³ - 3·mean·Σx² + 2·n·mean³) / n
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double m3Numerator = sumCu - 3 * mean * sumSq + 2 * n * meanSq * mean;
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double m3 = m3Numerator / n;
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// m₄ = (Σx⁴ - 4·mean·Σx³ + 6·mean²·Σx² - 3·n·mean⁴) / n
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double m4Numerator = sumQu - 4 * mean * sumCu + 6 * meanSq * sumSq - 3 * n * meanSq * meanSq;
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double m4 = m4Numerator / n;
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// Skewness = m₃ / m₂^(3/2)
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double m2Sqrt = Math.Sqrt(m2);
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double skewness = m3 / (m2 * m2Sqrt);
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// Excess Kurtosis = (m₄ / m₂²) - 3
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double excessKurtosis = (m4 / (m2 * m2)) - 3.0;
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// JB = (n/6) × (S² + EK²/4)
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// skipcq: CS-R1140 — FMA for precision in JB formula
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return (n / 6.0) * Math.FusedMultiplyAdd(skewness, skewness, excessKurtosis * excessKurtosis / 4.0);
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}
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private void Resync()
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{
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double sum = 0, sumSq = 0, sumCu = 0, sumQu = 0;
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var span = _buffer.GetSpan();
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for (int i = 0; i < span.Length; i++)
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{
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double val = span[i];
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double vSq = val * val;
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sum += val;
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sumSq += vSq;
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sumCu += vSq * val;
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sumQu += vSq * vSq;
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}
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_sum = sum;
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_sumSq = sumSq;
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_sumCu = sumCu;
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_sumQu = sumQu;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static void CalculateScalarCore(ReadOnlySpan<double> source, Span<double> output, int period)
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{
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int len = source.Length;
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// Pre-process source: replace NaN/Infinity with lastValid so sliding-window
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// subtraction always uses the identical substituted value used during warmup.
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const int StackallocThreshold = 256;
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double[]? rented = null;
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scoped Span<double> sanitized;
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if (len <= StackallocThreshold)
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{
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sanitized = stackalloc double[len];
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}
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else
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{
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rented = ArrayPool<double>.Shared.Rent(len);
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sanitized = rented.AsSpan(0, len);
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}
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try
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{
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double lastValid = 0;
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for (int j = 0; j < len; j++)
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{
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double val = source[j];
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if (!double.IsFinite(val))
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{
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val = lastValid;
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}
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else
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{
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lastValid = val;
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}
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sanitized[j] = val;
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}
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double sum = 0, sumSq = 0, sumCu = 0, sumQu = 0;
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int i = 0;
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// Warmup phase
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int warmupEnd = Math.Min(period, len);
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for (; i < warmupEnd; i++)
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{
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double val = sanitized[i];
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double vSq = val * val;
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sum += val;
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sumSq += vSq;
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sumCu += vSq * val;
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sumQu += vSq * vSq;
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output[i] = CalculateJbFromSums(sum, sumSq, sumCu, sumQu, i + 1);
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}
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// Sliding window phase
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int tickCount = period;
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for (; i < len; i++)
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{
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double val = sanitized[i];
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double oldVal = sanitized[i - period];
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double vSq = val * val;
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double oSq = oldVal * oldVal;
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sum = sum - oldVal + val;
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sumSq = sumSq - oSq + vSq;
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sumCu = sumCu - (oSq * oldVal) + (vSq * val);
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sumQu = sumQu - (oSq * oSq) + (vSq * vSq);
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output[i] = CalculateJbFromSums(sum, sumSq, sumCu, sumQu, period);
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tickCount++;
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if (tickCount >= ResyncInterval)
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{
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tickCount = 0;
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ResyncFromSanitized(sanitized, i, period, ref sum, ref sumSq, ref sumCu, ref sumQu);
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}
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}
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}
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finally
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{
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if (rented is not null)
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{
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ArrayPool<double>.Shared.Return(rented);
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}
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}
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static void ResyncFromSanitized(ReadOnlySpan<double> sanitized, int endIndex, int period,
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ref double sum, ref double sumSq, ref double sumCu, ref double sumQu)
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{
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double s = 0, sSq = 0, sCu = 0, sQu = 0;
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int startIdx = endIndex - period + 1;
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for (int k = 0; k < period; k++)
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{
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double v = sanitized[startIdx + k];
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double vSq = v * v;
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s += v;
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sSq += vSq;
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sCu += vSq * v;
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sQu += vSq * vSq;
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}
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sum = s;
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sumSq = sSq;
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sumCu = sCu;
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sumQu = sQu;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static void WarmupJb(int period, ref double srcRef, ref double outRef,
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out double sum, out double sumSq, out double sumCu, out double sumQu)
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{
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sum = 0; sumSq = 0; sumCu = 0; sumQu = 0;
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for (int i = 0; i < period; i++)
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{
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double val = Unsafe.Add(ref srcRef, i);
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double vSq = val * val;
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sum += val;
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sumSq += vSq;
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sumCu += vSq * val;
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sumQu += vSq * vSq;
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Unsafe.Add(ref outRef, i) = CalculateJbFromSums(sum, sumSq, sumCu, sumQu, i + 1);
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}
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}
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[MethodImpl(MethodImplOptions.AggressiveOptimization)]
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private static void CalculateAvx2Core(ReadOnlySpan<double> source, Span<double> output, int period)
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{
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int len = source.Length;
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const int VectorWidth = 4;
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ref double srcRef = ref MemoryMarshal.GetReference(source);
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ref double outRef = ref MemoryMarshal.GetReference(output);
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WarmupJb(period, ref srcRef, ref outRef, out double sum, out double sumSq, out double sumCu, out double sumQu);
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if (len <= period)
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{
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return;
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}
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double invN = 1.0 / period;
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double n = period;
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var vInvN = Vector256.Create(invN);
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var vN = Vector256.Create(n);
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var vThree = Vector256.Create(3.0);
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var vTwo = Vector256.Create(2.0);
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var vFour = Vector256.Create(4.0);
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var vSix = Vector256.Create(6.0);
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var vEpsilon = Vector256.Create(Epsilon);
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var vZero = Vector256<double>.Zero;
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int simdEnd = period + ((len - period) / VectorWidth) * VectorWidth;
|
||
int tickCount = period;
|
||
|
||
for (int i = period; i < simdEnd; i += VectorWidth)
|
||
{
|
||
var vNew = Vector256.LoadUnsafe(ref Unsafe.Add(ref srcRef, i));
|
||
var vOld = Vector256.LoadUnsafe(ref Unsafe.Add(ref srcRef, i - period));
|
||
|
||
// Deltas for Sum
|
||
var vDelta = Avx.Subtract(vNew, vOld);
|
||
|
||
// Deltas for SumSq
|
||
var vNewSq = Avx.Multiply(vNew, vNew);
|
||
var vOldSq = Avx.Multiply(vOld, vOld);
|
||
var vDeltaSq = Avx.Subtract(vNewSq, vOldSq);
|
||
|
||
// Deltas for SumCu
|
||
var vNewCu = Avx.Multiply(vNewSq, vNew);
|
||
var vOldCu = Avx.Multiply(vOldSq, vOld);
|
||
var vDeltaCu = Avx.Subtract(vNewCu, vOldCu);
|
||
|
||
// Deltas for SumQu
|
||
var vNewQu = Avx.Multiply(vNewSq, vNewSq);
|
||
var vOldQu = Avx.Multiply(vOldSq, vOldSq);
|
||
var vDeltaQu = Avx.Subtract(vNewQu, vOldQu);
|
||
|
||
// Prefix sums for Sum
|
||
var vShift1 = Avx2.Permute4x64(vDelta.AsUInt64(), 0b_10_01_00_00).AsDouble(); // skipcq: CS-R1131
|
||
vShift1 = Avx.Blend(vZero, vShift1, 0b_1110);
|
||
var vP1 = Avx.Add(vDelta, vShift1);
|
||
var vShift2 = Avx2.Permute4x64(vP1.AsUInt64(), 0b_01_00_00_00).AsDouble(); // skipcq: CS-R1131
|
||
vShift2 = Avx.Blend(vZero, vShift2, 0b_1100);
|
||
var vSums = Avx.Add(Vector256.Create(sum), Avx.Add(vP1, vShift2));
|
||
|
||
// Prefix sums for SumSq
|
||
var vShiftSq1 = Avx2.Permute4x64(vDeltaSq.AsUInt64(), 0b_10_01_00_00).AsDouble(); // skipcq: CS-R1131
|
||
vShiftSq1 = Avx.Blend(vZero, vShiftSq1, 0b_1110);
|
||
var vP1Sq = Avx.Add(vDeltaSq, vShiftSq1);
|
||
var vShiftSq2 = Avx2.Permute4x64(vP1Sq.AsUInt64(), 0b_01_00_00_00).AsDouble(); // skipcq: CS-R1131
|
||
vShiftSq2 = Avx.Blend(vZero, vShiftSq2, 0b_1100);
|
||
var vSumSqs = Avx.Add(Vector256.Create(sumSq), Avx.Add(vP1Sq, vShiftSq2));
|
||
|
||
// Prefix sums for SumCu
|
||
var vShiftCu1 = Avx2.Permute4x64(vDeltaCu.AsUInt64(), 0b_10_01_00_00).AsDouble(); // skipcq: CS-R1131
|
||
vShiftCu1 = Avx.Blend(vZero, vShiftCu1, 0b_1110);
|
||
var vP1Cu = Avx.Add(vDeltaCu, vShiftCu1);
|
||
var vShiftCu2 = Avx2.Permute4x64(vP1Cu.AsUInt64(), 0b_01_00_00_00).AsDouble(); // skipcq: CS-R1131
|
||
vShiftCu2 = Avx.Blend(vZero, vShiftCu2, 0b_1100);
|
||
var vSumCus = Avx.Add(Vector256.Create(sumCu), Avx.Add(vP1Cu, vShiftCu2));
|
||
|
||
// Prefix sums for SumQu
|
||
var vShiftQu1 = Avx2.Permute4x64(vDeltaQu.AsUInt64(), 0b_10_01_00_00).AsDouble(); // skipcq: CS-R1131
|
||
vShiftQu1 = Avx.Blend(vZero, vShiftQu1, 0b_1110);
|
||
var vP1Qu = Avx.Add(vDeltaQu, vShiftQu1);
|
||
var vShiftQu2 = Avx2.Permute4x64(vP1Qu.AsUInt64(), 0b_01_00_00_00).AsDouble(); // skipcq: CS-R1131
|
||
vShiftQu2 = Avx.Blend(vZero, vShiftQu2, 0b_1100);
|
||
var vSumQus = Avx.Add(Vector256.Create(sumQu), Avx.Add(vP1Qu, vShiftQu2));
|
||
|
||
// Calculate JB for 4 lanes
|
||
var vMean = Avx.Multiply(vSums, vInvN);
|
||
var vMeanSq = Avx.Multiply(vMean, vMean);
|
||
var vMeanCu = Avx.Multiply(vMeanSq, vMean);
|
||
var vMeanQu = Avx.Multiply(vMeanSq, vMeanSq);
|
||
|
||
// m₂ = (SumSq − Sum²/n) / n
|
||
var vSumSquared = Avx.Multiply(vSums, vSums);
|
||
var vM2Num = Fma.IsSupported
|
||
? Fma.MultiplyAddNegated(vSumSquared, vInvN, vSumSqs)
|
||
: Avx.Subtract(vSumSqs, Avx.Multiply(vSumSquared, vInvN));
|
||
vM2Num = Avx.Max(vZero, vM2Num);
|
||
var vM2 = Avx.Multiply(vM2Num, vInvN);
|
||
|
||
// m₃ = (SumCu − 3·mean·SumSq + 2·n·mean³) / n
|
||
var vTerm3_2 = Avx.Multiply(vThree, Avx.Multiply(vMean, vSumSqs));
|
||
var vNMeanCu = Avx.Multiply(vN, vMeanCu);
|
||
var vM3Num = Fma.IsSupported
|
||
? Fma.MultiplyAdd(vTwo, vNMeanCu, Avx.Subtract(vSumCus, vTerm3_2))
|
||
: Avx.Add(Avx.Subtract(vSumCus, vTerm3_2), Avx.Multiply(vTwo, vNMeanCu));
|
||
var vM3 = Avx.Multiply(vM3Num, vInvN);
|
||
|
||
// m₄ = (SumQu − 4·mean·SumCu + 6·mean²·SumSq − 3·n·mean⁴) / n
|
||
var vTerm4_1 = Avx.Multiply(vFour, Avx.Multiply(vMean, vSumCus));
|
||
var vTerm4_2 = Avx.Multiply(vSix, Avx.Multiply(vMeanSq, vSumSqs));
|
||
var vTerm4_3 = Avx.Multiply(vThree, Avx.Multiply(vN, vMeanQu));
|
||
var vM4Num = Avx.Add(Avx.Subtract(Avx.Subtract(vSumQus, vTerm4_1), vTerm4_3), vTerm4_2);
|
||
var vM4 = Avx.Multiply(vM4Num, vInvN);
|
||
|
||
// Skewness = m₃ / (m₂ · √m₂)
|
||
var vM2Sqrt = Avx.Sqrt(vM2);
|
||
var vSkewDenom = Avx.Multiply(vM2, vM2Sqrt);
|
||
var vSkew = Avx.Divide(vM3, vSkewDenom);
|
||
|
||
// Excess Kurtosis = (m₄ / m₂²) − 3
|
||
var vM2Sq = Avx.Multiply(vM2, vM2);
|
||
var vKurt = Avx.Subtract(Avx.Divide(vM4, vM2Sq), vThree);
|
||
|
||
// JB = (n/6) × (S² + EK²/4)
|
||
var vSkewSq = Avx.Multiply(vSkew, vSkew);
|
||
var vKurtSq = Avx.Multiply(vKurt, vKurt);
|
||
var vKurtTerm = Avx.Divide(vKurtSq, vFour);
|
||
var vJbInner = Avx.Add(vSkewSq, vKurtTerm);
|
||
var vNOver6 = Avx.Divide(vN, vSix);
|
||
var vJb = Avx.Multiply(vNOver6, vJbInner);
|
||
|
||
// Mask: zero out where m₂ is too small
|
||
var vMask = Avx.Compare(vM2, vEpsilon, FloatComparisonMode.OrderedGreaterThanNonSignaling);
|
||
vJb = Avx.BlendVariable(vZero, vJb, vMask);
|
||
|
||
// Clamp negative JB to zero (numerical noise)
|
||
vJb = Avx.Max(vZero, vJb);
|
||
|
||
vJb.StoreUnsafe(ref Unsafe.Add(ref outRef, i));
|
||
|
||
sum = vSums.GetElement(3);
|
||
sumSq = vSumSqs.GetElement(3);
|
||
sumCu = vSumCus.GetElement(3);
|
||
sumQu = vSumQus.GetElement(3);
|
||
|
||
tickCount += VectorWidth;
|
||
if (tickCount >= ResyncInterval)
|
||
{
|
||
tickCount = 0;
|
||
double s = 0, sSq = 0, sCu = 0, sQu = 0;
|
||
int startIdx = i + VectorWidth - period;
|
||
for (int k = 0; k < period; k++)
|
||
{
|
||
double v = Unsafe.Add(ref srcRef, startIdx + k);
|
||
double v2 = v * v;
|
||
s += v;
|
||
sSq += v2;
|
||
sCu += v2 * v;
|
||
sQu += v2 * v2;
|
||
}
|
||
sum = s;
|
||
sumSq = sSq;
|
||
sumCu = sCu;
|
||
sumQu = sQu;
|
||
}
|
||
}
|
||
|
||
// Scalar tail
|
||
for (int i = simdEnd; i < len; i++)
|
||
{
|
||
double val = Unsafe.Add(ref srcRef, i);
|
||
double oldVal = Unsafe.Add(ref srcRef, i - period);
|
||
double vSq = val * val;
|
||
double oSq = oldVal * oldVal;
|
||
|
||
sum = sum - oldVal + val;
|
||
sumSq = sumSq - oSq + vSq;
|
||
sumCu = sumCu - (oSq * oldVal) + (vSq * val);
|
||
sumQu = sumQu - (oSq * oSq) + (vSq * vSq);
|
||
|
||
Unsafe.Add(ref outRef, i) = CalculateJbFromSums(sum, sumSq, sumCu, sumQu, n);
|
||
}
|
||
}
|
||
}
|