def __call__(self, n, **kwargs):
r""" The Watson spherical distribution model.
Parameters
----------
n : array of shape(3) or array of shape(N x 3),
sampled orientations of the Watson distribution.
Returns
-------
Bn: float or array of shape(N),
Probability density at orientations n, given mu and kappa.
"""
odi = kwargs.get('odi', self.odi)
beta_fraction = kwargs.get('beta_fraction', self.beta_fraction)
mu = kwargs.get('mu', self.mu)
psi = kwargs.get('psi', self.psi)
kappa = odi2kappa(odi)
beta = beta_fraction * kappa
mu_cart = utils.unitsphere2cart_1d(mu)
R = utils.rotation_matrix_100_to_theta_phi_psi(mu[0], mu[1], psi)
mu_beta = R.dot(np.r_[0., 1., 0.])
numerator = _probability_bingham(kappa, beta, mu_cart, mu_beta, n)
denominator = 4 * np.pi * self._get_normalization(kappa, beta)
Bn = numerator / denominator
return Bn
def __call__(self, n, **kwargs):
r""" The Watson spherical distribution model [1, 2].
Parameters
----------
n : array of shape(3) or array of shape(N x 3),
sampled orientations of the Watson distribution.
Returns
-------
Wn: float or array of shape(N),
Probability density at orientations n, given mu and kappa.
"""
odi = kwargs.get('odi', self.odi)
mu = kwargs.get('mu', self.mu)
kappa = odi2kappa(odi)
mu_cart = utils.unitsphere2cart_1d(mu)
numerator = np.exp(kappa * np.dot(n, mu_cart)**2)
denominator = 4 * np.pi * special.hyp1f1(0.5, 1.5, kappa)
Wn = numerator / denominator
return Wn