private double density(double x)
{
// Based on the function randVMFMeanDir, available in the
// SphericalDistributionsRand repository under BSD license,
// originally written by Yu-Hui Chen, University of Michigan.
// https://github.com/yuhuichen1015/SphericalDistributionsRand
int p = Dimension;
double g1 = Gamma.Function((p - 1.0) / 2.0);
double g2 = Gamma.Function(1.0 / 2.0);
double bi = Bessel.I(p / 2 - 1, kappa);
double num = Math.Pow(kappa / 2.0, p / 2.0 - 1.0);
double den = g1 * g2 * bi;
double c = num / den;
double a = Math.Exp(kappa * x);
double b = Math.Pow(1.0 - x * x, (p - 3.0) / 2.0);
double y = c * a * b;
return(y);
}
/// <summary>
/// Constructs a Von-Mises Fisher distribution with unit mean.
/// </summary>
///
/// <param name="mean">The mean direction vector (with unit length).</param>
/// <param name="concentration">The concentration value κ (kappa).</param>
///
public VonMisesFisherDistribution(double[] mean, double concentration)
: base(mean.Length)
{
if (concentration < 0)
{
throw new ArgumentOutOfRangeException("concentration", "Concentration parameter kappa must be non-negative.");
}
if (!Norm.Euclidean(mean).IsRelativelyEqual(1, 1e-10))
{
throw new ArgumentOutOfRangeException("mean", "The mean vector must have unit length.");
}
this.mean = mean;
this.kappa = concentration;
int p = Dimension;
double num = Math.Pow(concentration, p / 2 - 1);
double den = Math.Pow(2 * Math.PI, p / 2) * Bessel.I(p / 2 - 1, concentration);
this.constant = num / den;
}