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Merge dev into main: v0.8.7 Kahan compensated summation

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Miha Kralj
2026-03-13 22:01:52 -07:00
parent 86a1db286c 67ad6f0cba
commit 9697facfb4
79 changed files with 2923 additions and 2495 deletions
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lib/statistics/correlation/Correlation.cs
+134 -44
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@@ -5,7 +5,8 @@ namespace QuanTAlib;
/// <summary>
/// Correlation: Calculates Pearson's correlation coefficient between two price series
/// using a streaming single-pass algorithm with circular buffers.
/// using a streaming single-pass algorithm with circular buffers and Kahan compensated
/// summation for numerical stability over long streams.
/// </summary>
/// <remarks>
/// The Pearson correlation coefficient measures the linear relationship between two variables.
@@ -37,12 +38,20 @@ public sealed class Correlation : AbstractBase
private double _sumX2, _sumY2;
private double _sumXY;
// Kahan compensation terms
private double _sumXComp, _sumYComp;
private double _sumX2Comp, _sumY2Comp;
private double _sumXYComp;
// Previous compensation state for rollback
private double _p_sumXComp, _p_sumYComp;
private double _p_sumX2Comp, _p_sumY2Comp;
private double _p_sumXYComp;
// Last valid values for NaN handling
private double _lastValidX, _lastValidY;
private double _p_lastValidX, _p_lastValidY;
private int _updateCount;
private const int ResyncInterval = 1000;
private const double Epsilon = 1e-10;
/// <inheritdoc />
@@ -80,11 +89,21 @@ public sealed class Correlation : AbstractBase
{
_p_lastValidX = _lastValidX;
_p_lastValidY = _lastValidY;
_p_sumXComp = _sumXComp;
_p_sumYComp = _sumYComp;
_p_sumX2Comp = _sumX2Comp;
_p_sumY2Comp = _sumY2Comp;
_p_sumXYComp = _sumXYComp;
}
else
{
_lastValidX = _p_lastValidX;
_lastValidY = _p_lastValidY;
_sumXComp = _p_sumXComp;
_sumYComp = _p_sumYComp;
_sumX2Comp = _p_sumX2Comp;
_sumY2Comp = _p_sumY2Comp;
_sumXYComp = _p_sumXYComp;
}
double x = SanitizeX(seriesX.Value);
@@ -117,7 +136,8 @@ public sealed class Correlation : AbstractBase
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public TValue Update(double seriesX, double seriesY, bool isNew = true)
{
return Update(new TValue(DateTime.UtcNow, seriesX), new TValue(DateTime.UtcNow, seriesY), isNew);
DateTime now = DateTime.UtcNow;
return Update(new TValue(now, seriesX), new TValue(now, seriesY), isNew);
}
/// <summary>Not supported. This indicator requires two inputs; use <see cref="Update(TValue, TValue, bool)"/> instead.</summary>
/// <remarks>Not supported for bi-input indicator. Use Update(seriesX, seriesY) instead.</remarks>
@@ -162,27 +182,82 @@ public sealed class Correlation : AbstractBase
{
double oldX = _bufferX.Oldest;
double oldY = _bufferY.Oldest;
_sumX -= oldX;
_sumY -= oldY;
_sumX2 = FusedMultiplyAdd(-oldX, oldX, _sumX2);
_sumY2 = FusedMultiplyAdd(-oldY, oldY, _sumY2);
_sumXY = FusedMultiplyAdd(-oldX, oldY, _sumXY);
// Kahan subtract oldX from _sumX
{
double yk = -oldX - _sumXComp;
double t = _sumX + yk;
_sumXComp = (t - _sumX) - yk;
_sumX = t;
}
// Kahan subtract oldY from _sumY
{
double yk = -oldY - _sumYComp;
double t = _sumY + yk;
_sumYComp = (t - _sumY) - yk;
_sumY = t;
}
// Kahan subtract oldX² from _sumX2
{
double yk = -(oldX * oldX) - _sumX2Comp;
double t = _sumX2 + yk;
_sumX2Comp = (t - _sumX2) - yk;
_sumX2 = t;
}
// Kahan subtract oldY² from _sumY2
{
double yk = -(oldY * oldY) - _sumY2Comp;
double t = _sumY2 + yk;
_sumY2Comp = (t - _sumY2) - yk;
_sumY2 = t;
}
// Kahan subtract oldX*oldY from _sumXY
{
double yk = -(oldX * oldY) - _sumXYComp;
double t = _sumXY + yk;
_sumXYComp = (t - _sumXY) - yk;
_sumXY = t;
}
}
// Add new values
_bufferX.Add(x);
_bufferY.Add(y);
_sumX += x;
_sumY += y;
_sumX2 = FusedMultiplyAdd(x, x, _sumX2);
_sumY2 = FusedMultiplyAdd(y, y, _sumY2);
_sumXY = FusedMultiplyAdd(x, y, _sumXY);
_updateCount++;
if (_updateCount % ResyncInterval == 0)
// Kahan add x to _sumX
{
Resync();
double yk = x - _sumXComp;
double t = _sumX + yk;
_sumXComp = (t - _sumX) - yk;
_sumX = t;
}
// Kahan add y to _sumY
{
double yk = y - _sumYComp;
double t = _sumY + yk;
_sumYComp = (t - _sumY) - yk;
_sumY = t;
}
// Kahan add x² to _sumX2
{
double yk = (x * x) - _sumX2Comp;
double t = _sumX2 + yk;
_sumX2Comp = (t - _sumX2) - yk;
_sumX2 = t;
}
// Kahan add y² to _sumY2
{
double yk = (y * y) - _sumY2Comp;
double t = _sumY2 + yk;
_sumY2Comp = (t - _sumY2) - yk;
_sumY2 = t;
}
// Kahan add x*y to _sumXY
{
double yk = (x * y) - _sumXYComp;
double t = _sumXY + yk;
_sumXYComp = (t - _sumXY) - yk;
_sumXY = t;
}
}
@@ -199,12 +274,41 @@ public sealed class Correlation : AbstractBase
double oldX = _bufferX.Newest;
double oldY = _bufferY.Newest;
// Update the running sums: remove old, add new (using FMA for consistency with ProcessNewBar)
_sumX = _sumX - oldX + x;
_sumY = _sumY - oldY + y;
_sumX2 = FusedMultiplyAdd(x, x, FusedMultiplyAdd(-oldX, oldX, _sumX2));
_sumY2 = FusedMultiplyAdd(y, y, FusedMultiplyAdd(-oldY, oldY, _sumY2));
_sumXY = FusedMultiplyAdd(x, y, FusedMultiplyAdd(-oldX, oldY, _sumXY));
// Kahan subtract old + add new for _sumX
{
double yk = (-oldX + x) - _sumXComp;
double t = _sumX + yk;
_sumXComp = (t - _sumX) - yk;
_sumX = t;
}
// Kahan subtract old + add new for _sumY
{
double yk = (-oldY + y) - _sumYComp;
double t = _sumY + yk;
_sumYComp = (t - _sumY) - yk;
_sumY = t;
}
// Kahan subtract old² + add new² for _sumX2
{
double yk = (-(oldX * oldX) + (x * x)) - _sumX2Comp;
double t = _sumX2 + yk;
_sumX2Comp = (t - _sumX2) - yk;
_sumX2 = t;
}
// Kahan subtract old² + add new² for _sumY2
{
double yk = (-(oldY * oldY) + (y * y)) - _sumY2Comp;
double t = _sumY2 + yk;
_sumY2Comp = (t - _sumY2) - yk;
_sumY2 = t;
}
// Kahan subtract old*old + add new*new for _sumXY
{
double yk = (-(oldX * oldY) + (x * y)) - _sumXYComp;
double t = _sumXY + yk;
_sumXYComp = (t - _sumXY) - yk;
_sumXY = t;
}
// Update the buffer values
_bufferX.UpdateNewest(x);
@@ -248,25 +352,6 @@ public sealed class Correlation : AbstractBase
return Max(-1.0, Min(1.0, correlation));
}
private void Resync()
{
_sumX = 0;
_sumY = 0;
_sumX2 = 0;
_sumY2 = 0;
_sumXY = 0;
for (int i = 0; i < _bufferX.Count; i++)
{
double x = _bufferX[i];
double y = _bufferY[i];
_sumX += x;
_sumY += y;
_sumX2 = FusedMultiplyAdd(x, x, _sumX2);
_sumY2 = FusedMultiplyAdd(y, y, _sumY2);
_sumXY = FusedMultiplyAdd(x, y, _sumXY);
}
}
/// <summary>Not supported. This indicator requires two input spans.</summary>
public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
{
@@ -285,12 +370,17 @@ public sealed class Correlation : AbstractBase
_sumY2 = 0;
_sumXY = 0;
_sumXComp = 0;
_sumYComp = 0;
_sumX2Comp = 0;
_sumY2Comp = 0;
_sumXYComp = 0;
_lastValidX = 0;
_lastValidY = 0;
_p_lastValidX = 0;
_p_lastValidY = 0;
_updateCount = 0;
Last = default;
}