/// <summary>
/// Calculate the mean and covariance of \lambda over all the particles,
/// i.e.
///
/// \text{mean} &= \mu = \sum_i \lambda_i p(i) \nonumber \\
/// \text{mean} &= \sum_i \lambda_i\lambda_i^T p(i) - \mu\mu^T \nonumber
///
/// The result is not returned, but is instead stored in the class to be read using
/// get_mean() and get_covariance().
/// </summary>
public void calculate_mean_and_covariance()
{
// Vector which will store expected value of lambda * lambda^T
// (allows us to do this calculation with one pass through particles)
MatrixFixed ExpectedSquared = new MatrixFixed(PARTICLE_DIMENSION, PARTICLE_DIMENSION);
ExpectedSquared.Fill(0.0f);
// Zero mean vector before filling it up
mean.Fill(0.0f);
foreach (Particle it in particle_vector)
{
mean += it.lambda * it.probability;
ExpectedSquared += it.probability * Vector.OuterProduct(it.lambda, it.lambda);
}
covariance = ExpectedSquared - Vector.OuterProduct(mean, mean);
}
