mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-15 00:58:04 +00:00
86fe32a682
Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com> Co-authored-by: aider (openrouter/anthropic/claude-sonnet-4) <aider@aider.chat> Co-authored-by: Warp <agent@warp.dev>
559 lines
18 KiB
C#
559 lines
18 KiB
C#
using System.Runtime.CompilerServices;
|
|
using System.Runtime.InteropServices;
|
|
|
|
namespace QuanTAlib;
|
|
|
|
/// <summary>
|
|
/// QEMA: Quad Exponential Moving Average with Progressive Alphas and Zero-Lag Weighting
|
|
/// </summary>
|
|
/// <remarks>
|
|
/// QEMA uses four cascaded EMAs with progressively increasing alphas (decreasing responsiveness)
|
|
/// and combines them using optimized weights that minimize energy while achieving zero DC lag.
|
|
///
|
|
/// Calculation:
|
|
/// 1. Base alpha: α₁ = 2 / (period + 1)
|
|
/// 2. Progressive alphas: r = (1/α₁)^(1/4), then α₂ = α₁·r, α₃ = α₂·r, α₄ = α₃·r
|
|
/// 3. Four cascaded EMAs: EMA1(input), EMA2(EMA1), EMA3(EMA2), EMA4(EMA3)
|
|
/// 4. Cumulative lags: L₁ = (1-α₁)/α₁, L₂ = L₁ + (1-α₂)/α₂, etc.
|
|
/// 5. Option A weights: Minimize energy subject to Σw=1 and Σw·L=0 (zero DC lag)
|
|
/// 6. Output: w₁·EMA1 + w₂·EMA2 + w₃·EMA3 + w₄·EMA4
|
|
///
|
|
/// O(1) update:
|
|
/// Uses four EMA state accumulators, each with O(1) update complexity.
|
|
///
|
|
/// IsHot:
|
|
/// Becomes true when the slowest EMA (stage 1) has converged to within 5% coverage.
|
|
/// </remarks>
|
|
[SkipLocalsInit]
|
|
public sealed class Qema : AbstractBase
|
|
{
|
|
[StructLayout(LayoutKind.Auto)]
|
|
private record struct EmaState(double Ema, double E, bool IsHot, bool IsCompensated)
|
|
{
|
|
public static EmaState New() => new() { Ema = 0, E = 1.0, IsHot = false, IsCompensated = false };
|
|
}
|
|
|
|
private readonly double _alpha1, _alpha2, _alpha3, _alpha4;
|
|
private readonly double _decay1, _decay2, _decay3, _decay4;
|
|
|
|
private EmaState _state1 = EmaState.New();
|
|
private EmaState _state2 = EmaState.New();
|
|
private EmaState _state3 = EmaState.New();
|
|
private EmaState _state4 = EmaState.New();
|
|
private EmaState _p_state1 = EmaState.New();
|
|
private EmaState _p_state2 = EmaState.New();
|
|
private EmaState _p_state3 = EmaState.New();
|
|
private EmaState _p_state4 = EmaState.New();
|
|
private readonly TValuePublishedHandler _handler;
|
|
|
|
private double _lastValidValue;
|
|
private double _p_lastValidValue;
|
|
|
|
private const double COVERAGE_THRESHOLD = 0.05;
|
|
private const double COMPENSATOR_THRESHOLD = 1e-10;
|
|
private const double DEGENERATE_THRESHOLD = 1e-12;
|
|
|
|
/// <summary>
|
|
/// True when the slowest EMA (stage 1) has warmed up and is providing valid results.
|
|
/// </summary>
|
|
public override bool IsHot => _state1.E <= COVERAGE_THRESHOLD;
|
|
|
|
/// <summary>
|
|
/// Creates QEMA with specified period.
|
|
/// Alpha1 = 2 / (period + 1), with progressive alphas ramped geometrically.
|
|
/// </summary>
|
|
/// <param name="period">Period for base EMA calculation (must be > 0)</param>
|
|
public Qema(int period)
|
|
{
|
|
ArgumentOutOfRangeException.ThrowIfNegativeOrZero(period);
|
|
|
|
_alpha1 = Clamp01(2.0 / (period + 1));
|
|
|
|
// Progressive alpha ramp: r = (1/α₁)^(1/4) → α₂=α₁^(3/4), α₃=α₁^(1/2), α₄=α₁^(1/4)
|
|
double r = Math.Pow(1.0 / _alpha1, 0.25);
|
|
_alpha2 = Clamp01(_alpha1 * r);
|
|
_alpha3 = Clamp01(_alpha2 * r);
|
|
_alpha4 = Clamp01(_alpha3 * r);
|
|
|
|
_decay1 = 1.0 - _alpha1;
|
|
_decay2 = 1.0 - _alpha2;
|
|
_decay3 = 1.0 - _alpha3;
|
|
_decay4 = 1.0 - _alpha4;
|
|
|
|
Name = $"Qema({period})";
|
|
WarmupPeriod = period;
|
|
_handler = Handle;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates QEMA with specified source and period.
|
|
/// Subscribes to source.Pub event.
|
|
/// </summary>
|
|
/// <param name="source">Source to subscribe to</param>
|
|
/// <param name="period">Period for base EMA calculation</param>
|
|
public Qema(ITValuePublisher source, int period) : this(period)
|
|
{
|
|
source.Pub += _handler;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates QEMA with specified source TSeries and period.
|
|
/// Primes with historical data and subscribes to updates.
|
|
/// </summary>
|
|
/// <param name="source">Source TSeries</param>
|
|
/// <param name="period">Period for base EMA calculation</param>
|
|
public Qema(TSeries source, int period) : this(period)
|
|
{
|
|
Prime(source.Values);
|
|
if (source.Count > 0)
|
|
{
|
|
Last = new TValue(source.LastTime, Last.Value);
|
|
}
|
|
source.Pub += _handler;
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
private static double Clamp01(double x) => Math.Min(1.0, Math.Max(x, DEGENERATE_THRESHOLD));
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
private static double Lag(double alpha) => (1.0 - alpha) / alpha;
|
|
|
|
private void Handle(object? sender, in TValueEventArgs e) => Update(e.Value, e.IsNew);
|
|
|
|
/// <summary>
|
|
/// Initializes the indicator state using the provided history.
|
|
/// </summary>
|
|
/// <param name="source">Historical data</param>
|
|
/// <param name="step">Optional time step (not used)</param>
|
|
public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
|
|
{
|
|
if (source.Length == 0) return;
|
|
|
|
// Reset state
|
|
_state1 = EmaState.New();
|
|
_state2 = EmaState.New();
|
|
_state3 = EmaState.New();
|
|
_state4 = EmaState.New();
|
|
_p_state1 = EmaState.New();
|
|
_p_state2 = EmaState.New();
|
|
_p_state3 = EmaState.New();
|
|
_p_state4 = EmaState.New();
|
|
_lastValidValue = 0;
|
|
_p_lastValidValue = 0;
|
|
|
|
int len = source.Length;
|
|
double lastValid = 0;
|
|
|
|
// Find first finite value
|
|
for (int i = 0; i < len; i++)
|
|
{
|
|
if (double.IsFinite(source[i]))
|
|
{
|
|
lastValid = source[i];
|
|
break;
|
|
}
|
|
}
|
|
|
|
EmaState s1 = _state1;
|
|
EmaState s2 = _state2;
|
|
EmaState s3 = _state3;
|
|
EmaState s4 = _state4;
|
|
|
|
for (int i = 0; i < len; i++)
|
|
{
|
|
double val = source[i];
|
|
if (double.IsFinite(val))
|
|
lastValid = val;
|
|
else
|
|
val = lastValid;
|
|
|
|
double e1 = ComputeEma(val, _alpha1, _decay1, ref s1);
|
|
double e2 = ComputeEma(e1, _alpha2, _decay2, ref s2);
|
|
double e3 = ComputeEma(e2, _alpha3, _decay3, ref s3);
|
|
ComputeEma(e3, _alpha4, _decay4, ref s4);
|
|
}
|
|
|
|
_state1 = s1;
|
|
_state2 = s2;
|
|
_state3 = s3;
|
|
_state4 = s4;
|
|
_lastValidValue = lastValid;
|
|
|
|
// Calculate final output
|
|
double e1_final = GetCompensated(_state1);
|
|
double e2_final = GetCompensated(_state2);
|
|
double e3_final = GetCompensated(_state3);
|
|
double e4_final = GetCompensated(_state4);
|
|
|
|
var (w1, w2, w3, w4) = ComputeWeights(_alpha1, _alpha2, _alpha3, _alpha4);
|
|
double result = Math.FusedMultiplyAdd(w1, e1_final, Math.FusedMultiplyAdd(w2, e2_final, Math.FusedMultiplyAdd(w3, e3_final, w4 * e4_final)));
|
|
|
|
Last = new TValue(DateTime.MinValue, result);
|
|
|
|
_p_state1 = _state1;
|
|
_p_state2 = _state2;
|
|
_p_state3 = _state3;
|
|
_p_state4 = _state4;
|
|
_p_lastValidValue = _lastValidValue;
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
private static double GetCompensated(EmaState s)
|
|
{
|
|
if (s.IsCompensated) return s.Ema;
|
|
return s.Ema / (1.0 - s.E);
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
|
|
public override TValue Update(TValue input, bool isNew = true)
|
|
{
|
|
if (isNew)
|
|
{
|
|
_p_state1 = _state1;
|
|
_p_state2 = _state2;
|
|
_p_state3 = _state3;
|
|
_p_state4 = _state4;
|
|
_p_lastValidValue = _lastValidValue;
|
|
}
|
|
else
|
|
{
|
|
_state1 = _p_state1;
|
|
_state2 = _p_state2;
|
|
_state3 = _p_state3;
|
|
_state4 = _p_state4;
|
|
_lastValidValue = _p_lastValidValue;
|
|
}
|
|
|
|
double val = input.Value;
|
|
if (double.IsFinite(val))
|
|
_lastValidValue = val;
|
|
else
|
|
val = _lastValidValue;
|
|
|
|
// Cascaded EMAs
|
|
double e1 = ComputeEma(val, _alpha1, _decay1, ref _state1);
|
|
double e2 = ComputeEma(e1, _alpha2, _decay2, ref _state2);
|
|
double e3 = ComputeEma(e2, _alpha3, _decay3, ref _state3);
|
|
double e4 = ComputeEma(e3, _alpha4, _decay4, ref _state4);
|
|
|
|
// Compute weights and combine
|
|
var (w1, w2, w3, w4) = ComputeWeights(_alpha1, _alpha2, _alpha3, _alpha4);
|
|
double result = Math.FusedMultiplyAdd(w1, e1, Math.FusedMultiplyAdd(w2, e2, Math.FusedMultiplyAdd(w3, e3, w4 * e4)));
|
|
|
|
Last = new TValue(input.Time, result);
|
|
PubEvent(Last, isNew);
|
|
return Last;
|
|
}
|
|
|
|
public override TSeries Update(TSeries source)
|
|
{
|
|
if (source.Count == 0) return [];
|
|
|
|
int len = source.Count;
|
|
List<long> t = new(len);
|
|
List<double> v = new(len);
|
|
CollectionsMarshal.SetCount(t, len);
|
|
CollectionsMarshal.SetCount(v, len);
|
|
|
|
var tSpan = CollectionsMarshal.AsSpan(t);
|
|
var vSpan = CollectionsMarshal.AsSpan(v);
|
|
source.Times.CopyTo(tSpan);
|
|
|
|
var sourceValues = source.Values;
|
|
|
|
EmaState s1 = _state1;
|
|
EmaState s2 = _state2;
|
|
EmaState s3 = _state3;
|
|
EmaState s4 = _state4;
|
|
double lastValid = _lastValidValue;
|
|
|
|
var (w1, w2, w3, w4) = ComputeWeights(_alpha1, _alpha2, _alpha3, _alpha4);
|
|
|
|
for (int i = 0; i < len; i++)
|
|
{
|
|
double val = sourceValues[i];
|
|
if (double.IsFinite(val))
|
|
lastValid = val;
|
|
else
|
|
val = lastValid;
|
|
|
|
double e1 = ComputeEma(val, _alpha1, _decay1, ref s1);
|
|
double e2 = ComputeEma(e1, _alpha2, _decay2, ref s2);
|
|
double e3 = ComputeEma(e2, _alpha3, _decay3, ref s3);
|
|
double e4 = ComputeEma(e3, _alpha4, _decay4, ref s4);
|
|
|
|
vSpan[i] = Math.FusedMultiplyAdd(w1, e1, Math.FusedMultiplyAdd(w2, e2, Math.FusedMultiplyAdd(w3, e3, w4 * e4)));
|
|
}
|
|
|
|
_state1 = s1;
|
|
_state2 = s2;
|
|
_state3 = s3;
|
|
_state4 = s4;
|
|
_p_state1 = s1;
|
|
_p_state2 = s2;
|
|
_p_state3 = s3;
|
|
_p_state4 = s4;
|
|
_lastValidValue = lastValid;
|
|
_p_lastValidValue = lastValid;
|
|
|
|
Last = new TValue(tSpan[len - 1], vSpan[len - 1]);
|
|
return new TSeries(t, v);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Computes the bias-corrected EMA value and updates state.
|
|
/// </summary>
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
private static double ComputeEma(double input, double alpha, double decay, ref EmaState state)
|
|
{
|
|
state.Ema = Math.FusedMultiplyAdd(state.Ema, decay, alpha * input);
|
|
|
|
double result;
|
|
if (!state.IsCompensated)
|
|
{
|
|
state.E *= decay;
|
|
|
|
if (!state.IsHot && state.E <= COVERAGE_THRESHOLD)
|
|
state.IsHot = true;
|
|
|
|
if (state.E <= COMPENSATOR_THRESHOLD)
|
|
{
|
|
state.IsCompensated = true;
|
|
result = state.Ema;
|
|
}
|
|
else
|
|
{
|
|
result = state.Ema / (1.0 - state.E);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
result = state.Ema;
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Computes Option A weights for minimum energy with zero DC lag constraint.
|
|
/// Solves: Σw = 1, Σw·L = 0 (δ=0 for zero lag)
|
|
/// </summary>
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
private static (double w1, double w2, double w3, double w4) ComputeWeights(double a1, double a2, double a3, double a4)
|
|
{
|
|
double t1 = Lag(a1);
|
|
double t2 = Lag(a2);
|
|
double t3 = Lag(a3);
|
|
double t4 = Lag(a4);
|
|
|
|
// Cumulative lags
|
|
double L1 = t1;
|
|
double L2 = t1 + t2;
|
|
double L3 = L2 + t3;
|
|
double L4 = L3 + t4;
|
|
|
|
// Option A: min-energy with constraints Σw=1, Σw·L=δ (δ=0)
|
|
double B = L1 + L2 + L3 + L4;
|
|
double C = Math.FusedMultiplyAdd(L1, L1, Math.FusedMultiplyAdd(L2, L2, Math.FusedMultiplyAdd(L3, L3, L4 * L4)));
|
|
double D = Math.FusedMultiplyAdd(4.0, C, -B * B);
|
|
|
|
double w1, w2, w3, w4;
|
|
if (Math.Abs(D) < DEGENERATE_THRESHOLD)
|
|
{
|
|
// Degenerate case (e.g., alpha=1 → all L=0): output is EMA1≈input
|
|
w1 = 1.0;
|
|
w2 = 0.0;
|
|
w3 = 0.0;
|
|
w4 = 0.0;
|
|
}
|
|
else
|
|
{
|
|
double lambda = C / D;
|
|
double mu = -B / D;
|
|
w1 = Math.FusedMultiplyAdd(mu, L1, lambda);
|
|
w2 = Math.FusedMultiplyAdd(mu, L2, lambda);
|
|
w3 = Math.FusedMultiplyAdd(mu, L3, lambda);
|
|
w4 = Math.FusedMultiplyAdd(mu, L4, lambda);
|
|
}
|
|
|
|
return (w1, w2, w3, w4);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates QEMA for the entire series using a new instance.
|
|
/// </summary>
|
|
/// <param name="source">Input series</param>
|
|
/// <param name="period">QEMA period</param>
|
|
/// <returns>QEMA series</returns>
|
|
public static TSeries Batch(TSeries source, int period)
|
|
{
|
|
var qema = new Qema(period);
|
|
return qema.Update(source);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates QEMA in-place using period, writing results to pre-allocated output span.
|
|
/// Zero-allocation method for maximum performance.
|
|
/// </summary>
|
|
/// <param name="source">Input values</param>
|
|
/// <param name="output">Output span (must be same length as source)</param>
|
|
/// <param name="period">QEMA period (must be > 0)</param>
|
|
[MethodImpl(MethodImplOptions.AggressiveOptimization)]
|
|
public static void Batch(ReadOnlySpan<double> source, Span<double> output, int period)
|
|
{
|
|
if (source.Length != output.Length)
|
|
throw new ArgumentException("Source and output must have the same length", nameof(output));
|
|
ArgumentOutOfRangeException.ThrowIfNegativeOrZero(period);
|
|
|
|
if (source.Length == 0) return;
|
|
|
|
double alpha1 = Clamp01(2.0 / (period + 1));
|
|
double r = Math.Pow(1.0 / alpha1, 0.25);
|
|
double alpha2 = Clamp01(alpha1 * r);
|
|
double alpha3 = Clamp01(alpha2 * r);
|
|
double alpha4 = Clamp01(alpha3 * r);
|
|
|
|
double decay1 = 1.0 - alpha1;
|
|
double decay2 = 1.0 - alpha2;
|
|
double decay3 = 1.0 - alpha3;
|
|
double decay4 = 1.0 - alpha4;
|
|
|
|
double lastValid = 0;
|
|
|
|
// Find first finite value
|
|
for (int i = 0; i < source.Length; i++)
|
|
{
|
|
if (double.IsFinite(source[i]))
|
|
{
|
|
lastValid = source[i];
|
|
break;
|
|
}
|
|
}
|
|
|
|
// EMA states
|
|
double ema1_val = 0, ema1_e = 1.0;
|
|
bool ema1_compensated = false;
|
|
double ema2_val = 0, ema2_e = 1.0;
|
|
bool ema2_compensated = false;
|
|
double ema3_val = 0, ema3_e = 1.0;
|
|
bool ema3_compensated = false;
|
|
double ema4_val = 0, ema4_e = 1.0;
|
|
bool ema4_compensated = false;
|
|
|
|
var (w1, w2, w3, w4) = ComputeWeights(alpha1, alpha2, alpha3, alpha4);
|
|
|
|
for (int i = 0; i < source.Length; i++)
|
|
{
|
|
double val = source[i];
|
|
if (double.IsFinite(val))
|
|
lastValid = val;
|
|
else
|
|
val = lastValid;
|
|
|
|
// EMA1
|
|
ema1_val = Math.FusedMultiplyAdd(ema1_val, decay1, alpha1 * val);
|
|
double e1;
|
|
if (!ema1_compensated)
|
|
{
|
|
ema1_e *= decay1;
|
|
if (ema1_e <= COMPENSATOR_THRESHOLD)
|
|
{
|
|
ema1_compensated = true;
|
|
e1 = ema1_val;
|
|
}
|
|
else
|
|
{
|
|
e1 = ema1_val / (1.0 - ema1_e);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
e1 = ema1_val;
|
|
}
|
|
|
|
// EMA2
|
|
ema2_val = Math.FusedMultiplyAdd(ema2_val, decay2, alpha2 * e1);
|
|
double e2;
|
|
if (!ema2_compensated)
|
|
{
|
|
ema2_e *= decay2;
|
|
if (ema2_e <= COMPENSATOR_THRESHOLD)
|
|
{
|
|
ema2_compensated = true;
|
|
e2 = ema2_val;
|
|
}
|
|
else
|
|
{
|
|
e2 = ema2_val / (1.0 - ema2_e);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
e2 = ema2_val;
|
|
}
|
|
|
|
// EMA3
|
|
ema3_val = Math.FusedMultiplyAdd(ema3_val, decay3, alpha3 * e2);
|
|
double e3;
|
|
if (!ema3_compensated)
|
|
{
|
|
ema3_e *= decay3;
|
|
if (ema3_e <= COMPENSATOR_THRESHOLD)
|
|
{
|
|
ema3_compensated = true;
|
|
e3 = ema3_val;
|
|
}
|
|
else
|
|
{
|
|
e3 = ema3_val / (1.0 - ema3_e);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
e3 = ema3_val;
|
|
}
|
|
|
|
// EMA4
|
|
ema4_val = Math.FusedMultiplyAdd(ema4_val, decay4, alpha4 * e3);
|
|
double e4;
|
|
if (!ema4_compensated)
|
|
{
|
|
ema4_e *= decay4;
|
|
if (ema4_e <= COMPENSATOR_THRESHOLD)
|
|
{
|
|
ema4_compensated = true;
|
|
e4 = ema4_val;
|
|
}
|
|
else
|
|
{
|
|
e4 = ema4_val / (1.0 - ema4_e);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
e4 = ema4_val;
|
|
}
|
|
|
|
output[i] = Math.FusedMultiplyAdd(w1, e1, Math.FusedMultiplyAdd(w2, e2, Math.FusedMultiplyAdd(w3, e3, w4 * e4)));
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Resets the QEMA state.
|
|
/// </summary>
|
|
public override void Reset()
|
|
{
|
|
_state1 = EmaState.New();
|
|
_state2 = EmaState.New();
|
|
_state3 = EmaState.New();
|
|
_state4 = EmaState.New();
|
|
_p_state1 = EmaState.New();
|
|
_p_state2 = EmaState.New();
|
|
_p_state3 = EmaState.New();
|
|
_p_state4 = EmaState.New();
|
|
_lastValidValue = 0;
|
|
_p_lastValidValue = 0;
|
|
Last = default;
|
|
}
|
|
}
|