def _aux_log(self, point, sqrt_base_point, inv_sqrt_base_point):
"""Compute the log (auxiliary function).
Parameters
----------
point
sqrt_base_point
inv_sqrt_base_point
Returns
-------
log
"""
point_near_id = gs.matmul(inv_sqrt_base_point, point)
point_near_id = gs.matmul(point_near_id, inv_sqrt_base_point)
point_near_id = GeneralLinear.make_symmetric(point_near_id)
log_at_id = gs.linalg.logm(point_near_id)
log = gs.matmul(sqrt_base_point, log_at_id)
log = gs.matmul(log, sqrt_base_point)
return log
def _aux_exp(self, tangent_vec, sqrt_base_point, inv_sqrt_base_point):
"""Compute the exponential map (auxiliary function).
Parameters
----------
tangent_vec : array-like, shape=[n_samples, n, n]
sqrt_base_point
inv_sqrt_base_point
Returns
-------
exp
"""
tangent_vec_at_id = gs.matmul(inv_sqrt_base_point, tangent_vec)
tangent_vec_at_id = gs.matmul(tangent_vec_at_id, inv_sqrt_base_point)
tangent_vec_at_id = GeneralLinear.make_symmetric(tangent_vec_at_id)
exp_from_id = gs.linalg.expm(tangent_vec_at_id)
exp = gs.matmul(exp_from_id, sqrt_base_point)
exp = gs.matmul(sqrt_base_point, exp)
return exp
def _aux_log(point, sqrt_base_point, inv_sqrt_base_point):
"""Compute the log (auxiliary function).
Parameters
----------
point
sqrt_base_point
inv_sqrt_base_point
Returns
-------
log
"""
point_near_id = gs.einsum('...ij,...jk->...ik', inv_sqrt_base_point,
point)
point_near_id = gs.einsum('...ij,...jk->...ik', point_near_id,
inv_sqrt_base_point)
point_near_id = GeneralLinear.make_symmetric(point_near_id)
log_at_id = SPDMatrices.logm(point_near_id)
log = gs.einsum('...ij,...jk->...ik', sqrt_base_point, log_at_id)
log = gs.einsum('...ij,...jk->...ik', log, sqrt_base_point)
return log
def _aux_exp(tangent_vec, sqrt_base_point, inv_sqrt_base_point):
"""Compute the exponential map (auxiliary function).
Parameters
----------
tangent_vec : array-like, shape=[n_samples, n, n]
sqrt_base_point
inv_sqrt_base_point
Returns
-------
exp
"""
tangent_vec_at_id = gs.einsum('...ij,...jk->...ik',
inv_sqrt_base_point, tangent_vec)
tangent_vec_at_id = gs.einsum('...ij,...jk->...ik', tangent_vec_at_id,
inv_sqrt_base_point)
tangent_vec_at_id = GeneralLinear.make_symmetric(tangent_vec_at_id)
exp_from_id = SymmetricMatrices.expm(tangent_vec_at_id)
exp = gs.einsum('...ij,...jk->...ik', exp_from_id, sqrt_base_point)
exp = gs.einsum('...ij,...jk->...ik', sqrt_base_point, exp)
return exp
