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Miha Kralj
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331 lines
9.7 KiB
C#
331 lines
9.7 KiB
C#
using System.Runtime.CompilerServices;
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using System.Runtime.InteropServices;
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namespace QuanTAlib;
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/// <summary>
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/// CTI: Correlation Trend Indicator (Ehlers, TASC 2020)
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/// </summary>
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/// <remarks>
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/// Measures the Pearson correlation coefficient between the price series and a
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/// perfect linear time index over a rolling window. Output is bounded [-1, +1]:
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/// +1 = perfect uptrend, -1 = perfect downtrend, 0 = no linear trend.
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///
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/// Uses O(1) incremental running sums: ΣY, ΣY², ΣXY. The X-side sums (ΣX, ΣX²)
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/// are analytical closed-form functions of n and never need maintenance.
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///
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/// Incremental ΣXY trick (same as CFO):
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/// When the window slides forward one bar:
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/// ΣXY -= ΣY_before_removal (shifts all position indices down by 1)
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/// ΣXY += (n-1) × y_new (new value enters at highest position)
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///
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/// References:
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/// Ehlers, J.F. (2001). Rocket Science for Traders. Wiley
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/// PineScript reference: cti.pine
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/// </remarks>
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[SkipLocalsInit]
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public sealed class Cti : 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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// Precomputed X-side constants (full-window)
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private readonly double _sx; // period*(period-1)/2
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private readonly double _sxx; // period*(period-1)*(2*period-1)/6
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private readonly double _denomX; // period*sxx - sx*sx (constant, never changes)
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[StructLayout(LayoutKind.Auto)]
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private record struct State(
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double SumY,
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double SumY2,
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double SumXY,
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int Count,
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double LastValid);
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private State _s, _ps;
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private const int ResyncInterval = 1000;
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private int _tickCount;
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/// <summary>
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/// Creates CTI with the specified lookback period.
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/// </summary>
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/// <param name="period">Rolling window length (must be ≥ 2)</param>
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public Cti(int period = 20)
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{
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if (period < 2)
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{
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throw new ArgumentException("Period must be greater than or equal to 2", 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 = $"Cti({period})";
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WarmupPeriod = period;
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_sx = period * (period - 1) / 2.0;
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_sxx = period * (period - 1.0) * (2 * period - 1) / 6.0;
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_denomX = Math.FusedMultiplyAdd(period, _sxx, -_sx * _sx);
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}
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/// <summary>
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/// Creates CTI subscribed to an upstream publisher.
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/// </summary>
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public Cti(ITValuePublisher source, int period = 20) : this(period)
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{
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source.Pub += Handle;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private void Handle(object? sender, in TValueEventArgs e) => Update(e.Value, e.IsNew);
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public override bool IsHot => _buffer.IsFull;
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/// <summary>Period of the indicator.</summary>
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public int Period => _period;
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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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// Sanitize input — substitute last-valid on NaN/Infinity
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if (!double.IsFinite(value))
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{
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value = double.IsFinite(_s.LastValid) ? _s.LastValid : 0.0;
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}
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else
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{
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_s.LastValid = value;
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}
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if (isNew)
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{
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_ps = _s;
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if (_buffer.Count == _buffer.Capacity)
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{
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// Full window: O(1) incremental update
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double oldest = _buffer.Oldest;
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_s.SumY -= oldest;
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_s.SumY2 -= oldest * oldest;
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_s.SumXY -= _s.SumY; // shift all indices down by 1
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_s.SumXY += (_period - 1) * value; // new value at position (n-1)
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}
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else
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{
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// Growing window during warmup
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_s.SumXY += _s.Count * value;
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_s.Count++;
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}
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_s.SumY += value;
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_s.SumY2 = Math.FusedMultiplyAdd(value, value, _s.SumY2);
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_buffer.Add(value);
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_tickCount++;
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if (_buffer.IsFull && _tickCount >= ResyncInterval)
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{
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_tickCount = 0;
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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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_s = _ps;
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_buffer.UpdateNewest(value);
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Resync();
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}
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if (!_buffer.IsFull)
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{
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Last = new TValue(input.Time, 0.0);
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PubEvent(Last, isNew);
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return Last;
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}
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double cti = ComputePearson(_s.SumY, _s.SumY2, _s.SumXY, _period, _sx, _sxx, _denomX);
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Last = new TValue(input.Time, cti);
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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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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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// Replay to sync internal state
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for (int i = 0; i < len; i++)
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{
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Update(new TValue(source.Times[i], source.Values[i]), isNew: true);
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}
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return new TSeries(t, v);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static double ComputePearson(
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double sumY, double sumY2, double sumXY,
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double n, double sx, double sxx, double denomX)
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{
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double denomY = Math.FusedMultiplyAdd(n, sumY2, -sumY * sumY);
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double denom = denomX * denomY;
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if (denom <= 0.0)
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{
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return 0.0;
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}
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double numer = Math.FusedMultiplyAdd(n, sumXY, -sx * sumY);
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return Math.Clamp(numer / Math.Sqrt(denom), -1.0, 1.0);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private void Resync()
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{
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_s.SumY = 0.0;
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_s.SumY2 = 0.0;
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_s.SumXY = 0.0;
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_s.Count = _buffer.Count;
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for (int i = 0; i < _buffer.Count; i++)
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{
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double v = _buffer[i];
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_s.SumY += v;
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_s.SumY2 = Math.FusedMultiplyAdd(v, v, _s.SumY2);
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_s.SumXY = Math.FusedMultiplyAdd(i, v, _s.SumXY);
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}
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}
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public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
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{
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for (int i = 0; i < source.Length; i++)
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{
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Update(new TValue(DateTime.UtcNow, source[i]), isNew: true);
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}
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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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_s = default;
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_ps = default;
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_tickCount = 0;
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Last = default;
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}
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/// <summary>Calculates CTI for an entire TSeries.</summary>
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public static TSeries Batch(TSeries source, int period = 20)
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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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return new TSeries(t, v);
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}
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/// <summary>
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/// Batch CTI calculation using O(1) incremental Pearson correlation.
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static void Batch(ReadOnlySpan<double> source, Span<double> output, int period = 20)
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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 < 2)
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{
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throw new ArgumentException("Period must be greater than or equal to 2", 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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double sx = period * (period - 1) / 2.0;
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double sxx = period * (period - 1.0) * (2 * period - 1) / 6.0;
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double denomX = Math.FusedMultiplyAdd(period, sxx, -sx * sx);
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double sumY = 0.0;
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double sumY2 = 0.0;
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double sumXY = 0.0;
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int count = 0;
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double lastValid = 0.0;
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var buf = new RingBuffer(period);
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for (int i = 0; i < len; i++)
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{
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double val = source[i];
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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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if (buf.Count == buf.Capacity)
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{
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double oldest = buf.Oldest;
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sumY -= oldest;
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sumY2 -= oldest * oldest;
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sumXY -= sumY;
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sumXY += (period - 1) * val;
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}
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else
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{
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sumXY += count * val;
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count++;
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}
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sumY += val;
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sumY2 = Math.FusedMultiplyAdd(val, val, sumY2);
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buf.Add(val);
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if (count < period)
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{
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output[i] = 0.0;
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continue;
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}
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double denomY = Math.FusedMultiplyAdd(period, sumY2, -sumY * sumY);
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double denom = denomX * denomY;
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if (denom <= 0.0)
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{
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output[i] = 0.0;
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continue;
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}
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double numer = Math.FusedMultiplyAdd(period, sumXY, -sx * sumY);
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output[i] = Math.Clamp(numer / Math.Sqrt(denom), -1.0, 1.0);
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}
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}
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/// <summary>Calculates CTI and returns both the series and the live indicator.</summary>
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public static (TSeries Results, Cti Indicator) Calculate(TSeries source, int period = 20)
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{
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var indicator = new Cti(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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}
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