/// <summary>
/// Construct a new Gaussian object given its parameters.
/// </summary>
/// <param name="mean">Gaussian mean value.</param>
/// <param name="covariance">Gaussian covariance matrix.</param>
/// <param name="weight">Gaussian coefficient in the mixture.</param>
public Gaussian(double[] mean, double[][] covariance, double weight)
{
Mean = mean;
Covariance = covariance;
CovarianceDeterminant = covariance.PseudoDeterminant();
CovarianceInverse = covariance.PseudoInverse();
Weight = (!double.IsNaN(weight)) ? weight : 0;
Multiplier = Math.Pow(2 * Math.PI, -mean.Length / 2) / Math.Sqrt(CovarianceDeterminant);
CanonicalVector = CovarianceInverse.Multiply(Mean);
}
/// <summary>
/// Obtain the squared Mahalanobis distance between the gaussian distribution and a point.
/// </summary>
/// <param name="point">Point in R^N space.</param>
/// <returns>Squared distance between distribution and point.</returns>
public double SquareMahalanobis(double[] point)
{
double[] diff = Mean.Subtract(point);
return(diff.InnerProduct(CovarianceInverse.Multiply(diff)));
}
/// <summary>
/// Evaluate the logarithm of the gaussian component, although without the weight multiplication.
/// </summary>
/// <param name="x">Evaluation point.</param>
/// <returns>Distribution density.</returns>
public double LogEvaluate(double[] x)
{
double[] diff = x.Subtract(Mean);
return(Math.Log(Multiplier) - 0.5 * diff.InnerProduct(CovarianceInverse.Multiply(diff)));
}
/// <summary>
/// Evaluate the gaussian component, although without the weight multiplication.
/// </summary>
/// <param name="x">Evaluation point.</param>
/// <returns>Distribution density.</returns>
public double Evaluate(double[] x)
{
double[] diff = x.Subtract(Mean);
//return Multiplier * ApproximateNegExp(0.5 * diff.InnerProduct(CovarianceInverse.Multiply(diff)));
return(Multiplier * Math.Exp(-0.5 * diff.InnerProduct(CovarianceInverse.Multiply(diff))));
}