mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-07-27 17:27:43 +00:00
Miha Kralj
67ad6f0cba
Comprehensive refactor across all indicators replacing the periodic ResyncInterval-based drift correction (every 1000 ticks recalculate from scratch) with Kahan compensated summation for running sums. Key changes: - Remove ResyncInterval constants and TickCount fields from all State records - Add Kahan compensation fields (SumComp, SumSqComp, etc.) to State records - Replace naive sum += val - removed with Kahan delta pattern - Remove Resync()/RecalculateSum() methods that did O(N) recalculation - Update batch/SIMD paths to use Kahan compensation instead of resync loops - IIR filters (EMA, REMA, RGMA) simplified: inherently self-correcting - Version bump to 0.8.7 - Build system: README version stamping via Directory.Build.props - Minor doc/test tolerance adjustments for new numerical characteristics Affected modules: channels, core, cycles, dynamics, errors, momentum, oscillators, statistics, trends_FIR, trends_IIR, volatility, volume
554 lines
17 KiB
C#
554 lines
17 KiB
C#
using System.Buffers;
|
|
using System.Runtime.CompilerServices;
|
|
using System.Runtime.InteropServices;
|
|
|
|
namespace QuanTAlib;
|
|
|
|
/// <summary>
|
|
/// Stderr: Standard Error of Regression (Standard Error of the Estimate)
|
|
/// </summary>
|
|
/// <remarks>
|
|
/// Measures the typical distance that observed values fall from the OLS
|
|
/// regression line fitted to the rolling window. Equivalent to the root mean
|
|
/// square of the residuals, scaled by N-2 degrees of freedom (one per
|
|
/// regression coefficient: slope and intercept).
|
|
/// Uses Kahan compensated summation for numerical stability of running regression sums,
|
|
/// eliminating the need for periodic resynchronization.
|
|
///
|
|
/// Formula:
|
|
/// SE = sqrt( SSR / (N - 2) )
|
|
/// SSR = Σ(yᵢ - ŷᵢ)² where ŷᵢ = slope * xᵢ + intercept
|
|
/// slope = (N·Σxy - Σx·Σy) / (N·Σx² - (Σx)²)
|
|
/// intercept = (Σy - slope·Σx) / N
|
|
/// x values: 0, 1, …, N-1 (oldest=0, newest=N-1)
|
|
///
|
|
/// Period minimum is 3 to allow N-2 > 0.
|
|
///
|
|
/// The regression sums Σy and Σxy use O(1) updates identical to LinReg:
|
|
/// ΔΣxy = Σy_prev - N * oldest (when window is full)
|
|
///
|
|
/// The residual sum SSR requires an O(N) walk; there is no known O(1) update
|
|
/// that remains numerically stable for arbitrary inputs.
|
|
///
|
|
/// IsHot: Becomes true when the buffer reaches full period length.
|
|
/// </remarks>
|
|
[SkipLocalsInit]
|
|
public sealed class Stderr : AbstractBase
|
|
{
|
|
private readonly int _period;
|
|
private readonly RingBuffer _buffer;
|
|
private readonly TValuePublishedHandler _handler;
|
|
#pragma warning disable S2933 // _source is mutated in Dispose to release event subscription; cannot be readonly
|
|
private ITValuePublisher? _source;
|
|
#pragma warning restore S2933
|
|
private bool _disposed;
|
|
|
|
// O(1) running regression sums with Kahan compensation
|
|
private double _sumY;
|
|
private double _sumXY;
|
|
private double _p_sumY;
|
|
private double _p_sumXY;
|
|
private double _sumYComp; // Kahan compensation for _sumY
|
|
private double _sumXYComp; // Kahan compensation for _sumXY
|
|
private double _p_sumYComp;
|
|
private double _p_sumXYComp;
|
|
private double _lastVal;
|
|
private double _p_lastVal;
|
|
private double _lastValidValue;
|
|
private double _p_lastValidValue;
|
|
|
|
// Precomputed constants (depend only on period)
|
|
private readonly double _sumX; // 0+1+…+(N-1) = N(N-1)/2
|
|
private readonly double _sumX2; // 0²+…+(N-1)² = (N-1)N(2N-1)/6
|
|
private readonly double _denom; // N·Σx² - (Σx)²
|
|
|
|
public override bool IsHot => _buffer.IsFull;
|
|
|
|
/// <summary>Creates a new Stderr indicator with the specified period.</summary>
|
|
/// <param name="period">Lookback window length. Must be >= 3.</param>
|
|
public Stderr(int period)
|
|
{
|
|
if (period < 3)
|
|
{
|
|
throw new ArgumentException("Period must be at least 3.", nameof(period));
|
|
}
|
|
|
|
_period = period;
|
|
_buffer = new RingBuffer(period);
|
|
Name = $"Stderr({period})";
|
|
WarmupPeriod = period;
|
|
_handler = Handle;
|
|
|
|
// Precompute fixed regression constants
|
|
_sumX = 0.5 * period * (period - 1);
|
|
_sumX2 = (period - 1.0) * period * (2.0 * period - 1.0) / 6.0;
|
|
_denom = period * _sumX2 - _sumX * _sumX;
|
|
}
|
|
|
|
/// <summary>Creates a chaining constructor that subscribes to an upstream publisher.</summary>
|
|
public Stderr(ITValuePublisher source, int period) : this(period)
|
|
{
|
|
_source = source;
|
|
source.Pub += _handler;
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
private void Handle(object? sender, in TValueEventArgs args) => Update(args.Value, args.IsNew);
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
private double GetValidValue(double input)
|
|
{
|
|
if (double.IsFinite(input))
|
|
{
|
|
_lastValidValue = input;
|
|
return input;
|
|
}
|
|
return _lastValidValue;
|
|
}
|
|
|
|
// S4136 suppressed: Update(TSeries) overload follows immediately — all Update overloads are adjacent
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public override TValue Update(TValue input, bool isNew = true)
|
|
{
|
|
if (isNew)
|
|
{
|
|
double val = GetValidValue(input.Value);
|
|
UpdateStateNew(val);
|
|
_p_sumY = _sumY;
|
|
_p_sumXY = _sumXY;
|
|
_p_sumYComp = _sumYComp;
|
|
_p_sumXYComp = _sumXYComp;
|
|
_p_lastVal = _lastVal;
|
|
_p_lastValidValue = _lastValidValue;
|
|
_lastVal = val;
|
|
}
|
|
else
|
|
{
|
|
_lastValidValue = _p_lastValidValue;
|
|
double val = GetValidValue(input.Value);
|
|
|
|
// Restore compensations
|
|
_sumYComp = _p_sumYComp;
|
|
_sumXYComp = _p_sumXYComp;
|
|
|
|
// Correct running sums for newest bar change
|
|
_sumY = _p_sumY - _p_lastVal + val;
|
|
_sumXY = _p_sumXY - (_period - 1) * (_p_lastVal - val);
|
|
// Re-derive sumXY correctly via recalculation to avoid drift on bar corrections
|
|
if (_buffer.Count > 0)
|
|
{
|
|
_buffer.UpdateNewest(val);
|
|
RecalculateSums();
|
|
}
|
|
else
|
|
{
|
|
_buffer.Add(val);
|
|
_sumY = val;
|
|
_sumYComp = 0;
|
|
_sumXY = 0;
|
|
_sumXYComp = 0;
|
|
}
|
|
|
|
_lastVal = val;
|
|
}
|
|
|
|
double result = CalculateStderr();
|
|
|
|
Last = new TValue(input.Time, result);
|
|
PubEvent(Last, isNew);
|
|
return Last;
|
|
}
|
|
|
|
// Update(TSeries) placed adjacent to Update(TValue) per S4136
|
|
public override TSeries Update(TSeries source)
|
|
{
|
|
if (source.Count == 0)
|
|
{
|
|
return [];
|
|
}
|
|
|
|
int len = source.Count;
|
|
// MA0016 — List<T> required for CollectionsMarshal
|
|
var t = new List<long>(len);
|
|
var v = new List<double>(len);
|
|
CollectionsMarshal.SetCount(t, len);
|
|
CollectionsMarshal.SetCount(v, len);
|
|
|
|
var tSpan = CollectionsMarshal.AsSpan(t);
|
|
var vSpan = CollectionsMarshal.AsSpan(v);
|
|
|
|
Batch(source.Values, vSpan, _period);
|
|
source.Times.CopyTo(tSpan);
|
|
|
|
// Reset and prime streaming state from tail
|
|
_buffer.Clear();
|
|
_sumY = 0;
|
|
_sumXY = 0;
|
|
_sumYComp = 0;
|
|
_sumXYComp = 0;
|
|
_lastVal = 0;
|
|
_lastValidValue = 0;
|
|
_p_lastValidValue = 0;
|
|
|
|
int primeStart = Math.Max(0, len - _period);
|
|
for (int i = primeStart; i < len; i++)
|
|
{
|
|
Update(source[i]);
|
|
}
|
|
|
|
Last = new TValue(tSpan[len - 1], vSpan[len - 1]);
|
|
return new TSeries(t, v);
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
private void UpdateStateNew(double val)
|
|
{
|
|
if (_buffer.IsFull)
|
|
{
|
|
double oldest = _buffer.Oldest;
|
|
double prevSumY = _sumY;
|
|
|
|
// O(1) update for sumXY with Kahan compensation
|
|
// ΣXY_new = ΣXY_old - ΣY_old + oldest + (N-1)*val
|
|
{
|
|
double delta = -prevSumY + oldest + (_period - 1) * val;
|
|
double y = delta - _sumXYComp;
|
|
double t = _sumXY + y;
|
|
_sumXYComp = (t - _sumXY) - y;
|
|
_sumXY = t;
|
|
}
|
|
|
|
// O(1) update for sumY with Kahan compensation
|
|
{
|
|
double delta = val - oldest;
|
|
double y = delta - _sumYComp;
|
|
double t = _sumY + y;
|
|
_sumYComp = (t - _sumY) - y;
|
|
_sumY = t;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
_buffer.Add(val);
|
|
|
|
// Kahan add val to sumY
|
|
{
|
|
double y = val - _sumYComp;
|
|
double t = _sumY + y;
|
|
_sumYComp = (t - _sumY) - y;
|
|
_sumY = t;
|
|
}
|
|
|
|
// Recalculate sumXY from scratch during warmup (buffer not yet full)
|
|
_sumXY = 0;
|
|
_sumXYComp = 0;
|
|
var span = _buffer.GetSpan();
|
|
for (int i = 0; i < span.Length; i++)
|
|
{
|
|
// x=0 is oldest (index 0 in ordered span), x=count-1 is newest
|
|
_sumXY = Math.FusedMultiplyAdd(i, span[i], _sumXY);
|
|
}
|
|
return;
|
|
}
|
|
|
|
_buffer.Add(val);
|
|
}
|
|
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
private double CalculateStderr()
|
|
{
|
|
int n = _buffer.Count;
|
|
if (n < 3)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
double sumY = _sumY;
|
|
double sumXY = _sumXY;
|
|
double sumX = (n == _period) ? _sumX : 0.5 * n * (n - 1);
|
|
double sumX2 = (n == _period) ? _sumX2 : (n - 1.0) * n * (2.0 * n - 1.0) / 6.0;
|
|
double denom = (n == _period) ? _denom : n * sumX2 - sumX * sumX;
|
|
|
|
if (denom == 0)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
double slope = (n * sumXY - sumX * sumY) / denom;
|
|
double intercept = (sumY - slope * sumX) / n;
|
|
|
|
// O(N): accumulate residual sum of squares
|
|
double ssr = 0;
|
|
var span = _buffer.GetSpan();
|
|
for (int i = 0; i < span.Length; i++)
|
|
{
|
|
double predicted = Math.FusedMultiplyAdd(slope, i, intercept);
|
|
double residual = span[i] - predicted;
|
|
ssr = Math.FusedMultiplyAdd(residual, residual, ssr);
|
|
}
|
|
|
|
return Math.Sqrt(ssr / (n - 2.0));
|
|
}
|
|
|
|
private void RecalculateSums()
|
|
{
|
|
_sumY = 0;
|
|
_sumYComp = 0;
|
|
_sumXY = 0;
|
|
_sumXYComp = 0;
|
|
var span = _buffer.GetSpan();
|
|
for (int i = 0; i < span.Length; i++)
|
|
{
|
|
// Kahan add to sumY
|
|
double y = span[i] - _sumYComp;
|
|
double t = _sumY + y;
|
|
_sumYComp = (t - _sumY) - y;
|
|
_sumY = t;
|
|
|
|
_sumXY = Math.FusedMultiplyAdd(i, span[i], _sumXY);
|
|
}
|
|
}
|
|
|
|
/// <summary>Creates a Stderr from a TSeries source and returns result series.</summary>
|
|
public static TSeries Batch(TSeries source, int period)
|
|
{
|
|
var se = new Stderr(period);
|
|
return se.Update(source);
|
|
}
|
|
|
|
/// <summary>Span-based batch calculation. Output length must equal source length.</summary>
|
|
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));
|
|
}
|
|
|
|
if (period < 3)
|
|
{
|
|
throw new ArgumentException("Period must be at least 3.", nameof(period));
|
|
}
|
|
|
|
int len = source.Length;
|
|
if (len == 0)
|
|
{
|
|
return;
|
|
}
|
|
|
|
CalculateScalarCore(source, output, period);
|
|
}
|
|
|
|
public static (TSeries Results, Stderr Indicator) Calculate(TSeries source, int period)
|
|
{
|
|
var indicator = new Stderr(period);
|
|
TSeries results = indicator.Update(source);
|
|
return (results, indicator);
|
|
}
|
|
|
|
public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
|
|
{
|
|
if (source.Length == 0)
|
|
{
|
|
return;
|
|
}
|
|
|
|
_buffer.Clear();
|
|
_sumY = 0;
|
|
_sumXY = 0;
|
|
_sumYComp = 0;
|
|
_sumXYComp = 0;
|
|
_lastVal = 0;
|
|
_lastValidValue = 0;
|
|
_p_lastValidValue = 0;
|
|
|
|
int warmupLength = Math.Min(source.Length, WarmupPeriod);
|
|
int startIndex = source.Length - warmupLength;
|
|
|
|
for (int i = startIndex; i < source.Length; i++)
|
|
{
|
|
Update(new TValue(DateTime.MinValue, source[i]));
|
|
}
|
|
}
|
|
|
|
public override void Reset()
|
|
{
|
|
_buffer.Clear();
|
|
_sumY = 0;
|
|
_sumXY = 0;
|
|
_p_sumY = 0;
|
|
_p_sumXY = 0;
|
|
_sumYComp = 0;
|
|
_sumXYComp = 0;
|
|
_p_sumYComp = 0;
|
|
_p_sumXYComp = 0;
|
|
_lastVal = 0;
|
|
_p_lastVal = 0;
|
|
_lastValidValue = 0;
|
|
_p_lastValidValue = 0;
|
|
Last = default;
|
|
}
|
|
|
|
protected override void Dispose(bool disposing)
|
|
{
|
|
if (!_disposed)
|
|
{
|
|
if (disposing && _source != null)
|
|
{
|
|
_source.Pub -= _handler;
|
|
}
|
|
_disposed = true;
|
|
}
|
|
base.Dispose(disposing);
|
|
}
|
|
|
|
private static void CalculateScalarCore(ReadOnlySpan<double> source, Span<double> output, int period)
|
|
{
|
|
int len = source.Length;
|
|
|
|
const int StackallocThreshold = 256;
|
|
double[]? rented = null;
|
|
scoped Span<double> sanitized;
|
|
if (len <= StackallocThreshold)
|
|
{
|
|
sanitized = stackalloc double[len];
|
|
}
|
|
else
|
|
{
|
|
rented = ArrayPool<double>.Shared.Rent(len);
|
|
sanitized = rented.AsSpan(0, len);
|
|
}
|
|
|
|
try
|
|
{
|
|
double lastValid = 0;
|
|
for (int j = 0; j < len; j++)
|
|
{
|
|
double val = source[j];
|
|
if (!double.IsFinite(val))
|
|
{
|
|
val = lastValid;
|
|
}
|
|
else
|
|
{
|
|
lastValid = val;
|
|
}
|
|
sanitized[j] = val;
|
|
}
|
|
|
|
// Precompute constants for full period window
|
|
double sumXFull = 0.5 * period * (period - 1);
|
|
double sumX2Full = (period - 1.0) * period * (2.0 * period - 1.0) / 6.0;
|
|
double denomFull = period * sumX2Full - sumXFull * sumXFull;
|
|
|
|
double sumY = 0;
|
|
double sumXY = 0;
|
|
double sumYComp = 0; // Kahan compensation for sumY
|
|
double sumXYComp = 0; // Kahan compensation for sumXY
|
|
int i = 0;
|
|
|
|
// Warmup: growing window, recompute sums from scratch each bar
|
|
int warmupEnd = Math.Min(period, len);
|
|
for (; i < warmupEnd; i++)
|
|
{
|
|
// Kahan add to sumY
|
|
{
|
|
double y = sanitized[i] - sumYComp;
|
|
double t = sumY + y;
|
|
sumYComp = (t - sumY) - y;
|
|
sumY = t;
|
|
}
|
|
|
|
// Recalculate sumXY with new element appended (oldest=0, newest=i)
|
|
sumXY = 0;
|
|
for (int k = 0; k <= i; k++)
|
|
{
|
|
sumXY = Math.FusedMultiplyAdd(k, sanitized[k], sumXY);
|
|
}
|
|
|
|
int n = i + 1;
|
|
output[i] = (n >= 3) ? CalcStderrFromSums(sanitized, 0, n, sumY, sumXY) : 0;
|
|
}
|
|
|
|
// Reset compensation at transition to sliding window
|
|
sumXYComp = 0;
|
|
|
|
// Sliding window: O(1) sum updates + O(N) residuals
|
|
for (; i < len; i++)
|
|
{
|
|
double oldest = sanitized[i - period];
|
|
double newest = sanitized[i];
|
|
|
|
// O(1) Kahan compensated update for sumXY
|
|
{
|
|
double delta = -sumY + oldest + (period - 1) * newest;
|
|
double y = delta - sumXYComp;
|
|
double t = sumXY + y;
|
|
sumXYComp = (t - sumXY) - y;
|
|
sumXY = t;
|
|
}
|
|
|
|
// O(1) Kahan compensated update for sumY
|
|
{
|
|
double delta = newest - oldest;
|
|
double y = delta - sumYComp;
|
|
double t = sumY + y;
|
|
sumYComp = (t - sumY) - y;
|
|
sumY = t;
|
|
}
|
|
|
|
double slope = (period * sumXY - sumXFull * sumY) / denomFull;
|
|
double intercept = (sumY - slope * sumXFull) / period;
|
|
|
|
double ssr = 0;
|
|
int start = i - period + 1;
|
|
for (int k = 0; k < period; k++)
|
|
{
|
|
double predicted = Math.FusedMultiplyAdd(slope, k, intercept);
|
|
double residual = sanitized[start + k] - predicted;
|
|
ssr = Math.FusedMultiplyAdd(residual, residual, ssr);
|
|
}
|
|
|
|
output[i] = Math.Sqrt(ssr / (period - 2.0));
|
|
}
|
|
}
|
|
finally
|
|
{
|
|
if (rented is not null)
|
|
{
|
|
ArrayPool<double>.Shared.Return(rented);
|
|
}
|
|
}
|
|
}
|
|
|
|
private static double CalcStderrFromSums(ReadOnlySpan<double> sanitized, int start, int n,
|
|
double sumY, double sumXY)
|
|
{
|
|
if (n < 3)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
double sumX = 0.5 * n * (n - 1);
|
|
double sumX2 = (n - 1.0) * n * (2.0 * n - 1.0) / 6.0;
|
|
double denom = n * sumX2 - sumX * sumX;
|
|
|
|
if (denom == 0)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
double slope = (n * sumXY - sumX * sumY) / denom;
|
|
double intercept = (sumY - slope * sumX) / n;
|
|
|
|
double ssr = 0;
|
|
for (int k = 0; k < n; k++)
|
|
{
|
|
double predicted = Math.FusedMultiplyAdd(slope, k, intercept);
|
|
double residual = sanitized[start + k] - predicted;
|
|
ssr = Math.FusedMultiplyAdd(residual, residual, ssr);
|
|
}
|
|
|
|
return Math.Sqrt(ssr / (n - 2.0));
|
|
}
|
|
}
|