QuanTAlib/lib/statistics/covariance/Covariance.Tests.cs

using System;
using Xunit;

namespace QuanTAlib.Tests;

public class CovarianceTests
{
    [Fact]
    public void Covariance_CalculatesCorrectly()
    {
        // Arrange
        var cov = new Covariance(3, isPopulation: false);
        
        // Act & Assert
        // 1. Add (1, 2)
        // MeanX = 1, MeanY = 2
        // Cov = 0 (n=1)
        var res1 = cov.Update(1, 2);
        Assert.Equal(0, res1.Value);

        // 2. Add (2, 4)
        // X: {1, 2}, Y: {2, 4}
        // MeanX = 1.5, MeanY = 3
        // Cov = ((1-1.5)(2-3) + (2-1.5)(4-3)) / 1
        //     = ((-0.5)(-1) + (0.5)(1)) / 1
        //     = (0.5 + 0.5) / 1 = 1
        var res2 = cov.Update(2, 4);
        Assert.Equal(1, res2.Value);

        // 3. Add (3, 6)
        // X: {1, 2, 3}, Y: {2, 4, 6}
        // MeanX = 2, MeanY = 4
        // Cov = ((1-2)(2-4) + (2-2)(4-4) + (3-2)(6-4)) / 2
        //     = ((-1)(-2) + 0 + (1)(2)) / 2
        //     = (2 + 2) / 2 = 2
        var res3 = cov.Update(3, 6);
        Assert.Equal(2, res3.Value);

        // 4. Add (4, 8) -> Window slides: {2, 3, 4}, {4, 6, 8}
        // MeanX = 3, MeanY = 6
        // Cov = ((2-3)(4-6) + (3-3)(6-6) + (4-3)(8-6)) / 2
        //     = ((-1)(-2) + 0 + (1)(2)) / 2
        //     = (2 + 2) / 2 = 2
        var res4 = cov.Update(4, 8);
        Assert.Equal(2, res4.Value);
    }

    [Fact]
    public void Covariance_Population_CalculatesCorrectly()
    {
        // Arrange
        var cov = new Covariance(3, isPopulation: true);
        
        // Act & Assert
        cov.Update(1, 2);
        cov.Update(2, 4);
        
        // 3. Add (3, 6)
        // X: {1, 2, 3}, Y: {2, 4, 6}
        // MeanX = 2, MeanY = 4
        // Cov = ((1-2)(2-4) + (2-2)(4-4) + (3-2)(6-4)) / 3
        //     = (2 + 2) / 3 = 4/3
        var res3 = cov.Update(3, 6);
        Assert.Equal(4.0/3.0, res3.Value, precision: 10);
    }

    [Fact]
    public void Covariance_HandlesZeroCovariance()
    {
        // Arrange
        var cov = new Covariance(3);
        
        // Act
        cov.Update(1, 1);
        cov.Update(2, 1);
        var res = cov.Update(3, 1); // Y is constant, variance Y is 0, covariance is 0
        
        // Assert
        Assert.Equal(0, res.Value);
    }

    [Fact]
    public void Covariance_HandlesNegativeCovariance()
    {
        // Arrange
        var cov = new Covariance(3);
        
        // Act
        cov.Update(1, 3);
        cov.Update(2, 2);
        var res = cov.Update(3, 1);
        
        // X: {1, 2, 3}, MeanX = 2
        // Y: {3, 2, 1}, MeanY = 2
        // Cov = ((1-2)(3-2) + (2-2)(2-2) + (3-2)(1-2)) / 2
        //     = ((-1)(1) + 0 + (1)(-1)) / 2
        //     = (-1 - 1) / 2 = -1
        
        // Assert
        Assert.Equal(-1, res.Value);
    }

    [Fact]
    public void Covariance_Resync_Works()
    {
        // Arrange
        var cov = new Covariance(3);
        
        // Act
        // Force many updates to trigger resync (ResyncInterval = 1000)
        // We can't easily force 1000 updates in a simple test without loop, 
        // but we can verify the logic holds for a sequence.
        for (int i = 0; i < 1100; i++)
        {
            cov.Update(i, i * 2);
        }
        
        // Last 3: {1097, 1098, 1099}, {2194, 2196, 2198}
        // This is a perfect linear relationship y = 2x
        // Cov(X, 2X) = 2 * Var(X)
        // Var(X) for {x-1, x, x+1} is:
        // Mean = x
        // SumSqDiff = (-1)^2 + 0 + 1^2 = 2
        // Var = 2 / 2 = 1
        // Cov = 2 * 1 = 2
        
        // Assert
        Assert.Equal(2, cov.Last.Value, precision: 10);
    }

    [Fact]
    public void Covariance_Update_IsNew_False_Works()
    {
        // Arrange
        var cov = new Covariance(3);
        
        // Act
        cov.Update(1, 2);
        cov.Update(2, 4);
        cov.Update(3, 6); // Cov = 2
        
        // Update last bar with new values
        // Change (3, 6) to (4, 8)
        // X: {1, 2, 4}, MeanX = 7/3 = 2.333...
        // Y: {2, 4, 8}, MeanY = 14/3 = 4.666...
        // This is harder to calc manually, let's use the property that it should match adding (4, 8) directly
        
        var res = cov.Update(4, 8, isNew: false);
        
        var cov2 = new Covariance(3);
        cov2.Update(1, 2);
        cov2.Update(2, 4);
        var expected = cov2.Update(4, 8);
        
        // Assert
        Assert.Equal(expected.Value, res.Value, precision: 10);
    }
    
    [Fact]
    public void Covariance_Throws_On_Single_Input()
    {
        var cov = new Covariance(10);
        Assert.Throws<NotSupportedException>(() => cov.Update(new TValue(DateTime.UtcNow, 1)));
        Assert.Throws<NotSupportedException>(() => cov.Update(new TSeries()));
        Assert.Throws<NotSupportedException>(() => cov.Prime(new double[] { 1, 2, 3 }));
    }
}