def squared_dist(self, point_a, point_b, **kwargs):
"""Compute squared distance associated with the binomial Fisher Rao metric.
Parameters
----------
point_a : array-like, shape=[...,]
Point representing a binomial distribution (probability of success).
point_b : array-like, shape=[...,] (same shape as point_a)
Point representing a binomial distribution (probability of success).
Returns
-------
squared_dist : array-like, shape=[...,]
Squared distance between points point_a and point_b.
"""
return (4 * self.n_draws *
(gs.arcsin(gs.sqrt(point_a)) - gs.arcsin(gs.sqrt(point_b)))**2)
def tait_bryan_angles_from_quaternion_intrinsic_zyx(self, quaternion):
assert self.n == 3, ('The quaternion representation'
' and the Tait-Bryan angles representation'
' do not exist'
' for rotations in %d dimensions.' % self.n)
quaternion = gs.to_ndarray(quaternion, to_ndim=2)
w, x, y, z = gs.hsplit(quaternion, 4)
angle_1 = gs.arctan2(y * z + w * x, 1. / 2. - (x**2 + y**2))
angle_2 = gs.arcsin(-2. * (x * z - w * y))
angle_3 = gs.arctan2(x * y + w * z, 1. / 2. - (y**2 + z**2))
tait_bryan_angles = gs.concatenate([angle_3, angle_2, angle_1], axis=1)
return tait_bryan_angles
def tait_bryan_angles_from_quaternion_intrinsic_xyz(self, quaternion):
assert self.n == 3, ('The quaternion representation'
' and the Tait-Bryan angles representation'
' do not exist'
' for rotations in %d dimensions.' % self.n)
quaternion = gs.to_ndarray(quaternion, to_ndim=2)
w, x, y, z = gs.hsplit(quaternion, 4)
angle_3 = gs.arctan2(2. * (x * y + w * z),
w * w + x * x - y * y - z * z)
angle_2 = gs.arcsin(-2. * (x * z - w * y))
angle_1 = gs.arctan2(2. * (y * z + w * x),
w * w - x * x - y * y + z * z)
tait_bryan_angles = gs.concatenate([angle_1, angle_2, angle_3], axis=1)
return tait_bryan_angles
def tait_bryan_angles_from_quaternion_intrinsic_zyx(quaternion):
"""Convert quaternion to tait bryan representation of order zyx.
Parameters
----------
quaternion : array-like, shape=[..., 4]
Returns
-------
tait_bryan_angles : array-like, shape=[..., 3]
"""
w, x, y, z = gs.hsplit(quaternion, 4)
angle_1 = gs.arctan2(y * z + w * x, 1. / 2. - (x**2 + y**2))
angle_2 = gs.arcsin(-2. * (x * z - w * y))
angle_3 = gs.arctan2(x * y + w * z, 1. / 2. - (y**2 + z**2))
tait_bryan_angles = gs.concatenate([angle_1, angle_2, angle_3], axis=1)
return tait_bryan_angles
def tait_bryan_angles_from_quaternion_intrinsic_xyz(quaternion):
"""Convert quaternion to tait bryan representation of order xyz.
Parameters
----------
quaternion : array-like, shape=[..., 4]
Returns
-------
tait_bryan_angles : array-like, shape=[..., 3]
"""
w, x, y, z = gs.hsplit(quaternion, 4)
angle_1 = gs.arctan2(2. * (-x * y + w * z),
w * w + x * x - y * y - z * z)
angle_2 = gs.arcsin(2 * (x * z + w * y))
angle_3 = gs.arctan2(2. * (-y * z + w * x),
w * w + z * z - x * x - y * y)
tait_bryan_angles = gs.concatenate([angle_1, angle_2, angle_3], axis=1)
return tait_bryan_angles