/// <summary>
/// Add two positive-definite matrices.
/// </summary>
/// <param name="a">First matrix.</param>
/// <param name="b">Second matrix.</param>
/// <returns>Their sum.</returns>
public static PositiveDefiniteMatrix operator +(PositiveDefiniteMatrix a, PositiveDefiniteMatrix b)
{
PositiveDefiniteMatrix result = (PositiveDefiniteMatrix)a.Clone();
result.SetToSum(result, b);
return(result);
}
/// <summary>
/// Adds a weighted observation
/// </summary>
/// <param name="x"></param>
/// <param name="weight"></param>
public void Add(Matrix x, double weight)
{
// new_mean = mean + w/(count + w)*(x - mean)
// new_var = count/(count + w)*(var + w/(count+w)*(x-mean)*(x-mean)')
Count += weight;
if (Count == 0)
{
return;
}
diff.SetToDifference(x, Mean);
double s = weight / Count;
Mean.SetToSum(1, Mean, s, diff);
diff.SetToElementwiseProduct(diff, diff);
Variance.SetToSum(1 - s, Variance, s * (1 - s), diff);
}
/// <summary>
/// Adds a noisy observation.
/// </summary>
/// <param name="x"></param>
/// <param name="noiseVariance"></param>
/// <param name="weight"></param>
public void Add(Vector x, PositiveDefiniteMatrix noiseVariance, double weight)
{
// new_cov = count/(count + w)*(cov + w/(count+w)*(x-mean)*(x-mean)') + w/(count+w)*noiseVariance
Add(x, weight);
if (count == 0)
{
return;
}
double s = weight / count;
cov.SetToSum(1, cov, s, noiseVariance);
}