def group_log(self, point, base_point=None, point_type=None):
"""
Compute the group logarithm of point relative to base_point.
Parameters
----------
point: array-like, shape=[n_samples, {dimension,[n,n]}]
base_point: array-like, shape=[n_samples, {dimension,[n,n]}]
point_type: {'vector', 'matrix'}
Returns
------
tangent_vec: array-like, shape=[n_samples, {dimension,[n,n]}]
"""
if point_type is None:
point_type = self.default_point_type
identity = self.get_identity(point_type=point_type)
if base_point is None:
base_point = identity
if point_type == "vector":
point = gs.to_ndarray(point, to_ndim=2)
base_point = gs.to_ndarray(base_point, to_ndim=2)
if point_type == "matrix":
point = gs.to_ndarray(point, to_ndim=3)
base_point = gs.to_ndarray(base_point, to_ndim=3)
point = self.regularize(point, point_type=point_type)
base_point = self.regularize(base_point, point_type=point_type)
n_points = point.shape[0]
n_base_points = base_point.shape[0]
assert (point.shape == base_point.shape or n_points == 1
or n_base_points == 1)
if n_points == 1:
point = gs.array([point[0]] * n_base_points)
if n_base_points == 1:
base_point = gs.array([base_point[0]] * n_points)
result = gs.cond(
pred=gs.allclose(base_point, identity),
true_fn=lambda: self.group_log_from_identity(
point, point_type=point_type),
false_fn=lambda: self.group_log_not_from_identity(
point, base_point, point_type),
)
return result
def exp(self, tangent_vec, base_point=None, point_type=None):
"""Compute the group exponential at `base_point` of `tangent_vec`.
Parameters
----------
tangent_vec : array-like, shape=[n_samples, {dimension,[n,n]}]
base_point : array-like, shape=[n_samples, {dimension,[n,n]}]
default: self.identity
point_type : str, {'vector', 'matrix'}
default: the default point type
the type of the point
Returns
-------
result : array-like, shape=[n_samples, {dimension,[n,n]}]
The exponentiated tangent vector
"""
if point_type is None:
point_type = self.default_point_type
identity = self.get_identity(point_type=point_type)
identity = self.regularize(identity, point_type=point_type)
if base_point is None:
base_point = identity
base_point = self.regularize(base_point, point_type=point_type)
if point_type == "vector":
tangent_vec = gs.to_ndarray(tangent_vec, to_ndim=2)
base_point = gs.to_ndarray(base_point, to_ndim=2)
if point_type == "matrix":
tangent_vec = gs.to_ndarray(tangent_vec, to_ndim=3)
base_point = gs.to_ndarray(base_point, to_ndim=3)
n_tangent_vecs = tangent_vec.shape[0]
n_base_points = base_point.shape[0]
assert (tangent_vec.shape == base_point.shape or n_tangent_vecs == 1
or n_base_points == 1)
if n_tangent_vecs == 1:
tangent_vec = gs.array([tangent_vec[0]] * n_base_points)
if n_base_points == 1:
base_point = gs.array([base_point[0]] * n_tangent_vecs)
result = gs.cond(pred=gs.allclose(base_point, identity),
true_fn=lambda: self.exp_from_identity(
tangent_vec, point_type=point_type),
false_fn=lambda: self.exp_not_from_identity(
tangent_vec, base_point, point_type))
return result
def group_log(self, point, base_point=None, point_type=None):
"""
Compute the group logarithm at point base_point
of the point point.
"""
if point_type is None:
point_type = self.default_point_type
identity = self.get_identity(point_type=point_type)
if base_point is None:
base_point = identity
if point_type == 'vector':
point = gs.to_ndarray(point, to_ndim=2)
base_point = gs.to_ndarray(base_point, to_ndim=2)
if point_type == 'matrix':
point = gs.to_ndarray(point, to_ndim=3)
base_point = gs.to_ndarray(base_point, to_ndim=3)
point = self.regularize(point, point_type=point_type)
base_point = self.regularize(base_point, point_type=point_type)
n_points = point.shape[0]
n_base_points = base_point.shape[0]
assert (point.shape == base_point.shape or n_points == 1
or n_base_points == 1)
if n_points == 1:
point = gs.array([point[0]] * n_base_points)
if n_base_points == 1:
base_point = gs.array([base_point[0]] * n_points)
result = gs.cond(pred=gs.allclose(base_point, identity),
true_fn=lambda: self.group_log_from_identity(
point, point_type=point_type),
false_fn=lambda: self.group_log_not_from_identity(
point, base_point, point_type))
return result
def group_exp(self, tangent_vec, base_point=None, point_type=None):
"""
Compute the group exponential at point base_point
of tangent vector tangent_vec.
"""
if point_type is None:
point_type = self.default_point_type
identity = self.get_identity(point_type=point_type)
identity = self.regularize(identity, point_type=point_type)
if base_point is None:
base_point = identity
base_point = self.regularize(base_point, point_type=point_type)
if point_type == 'vector':
tangent_vec = gs.to_ndarray(tangent_vec, to_ndim=2)
base_point = gs.to_ndarray(base_point, to_ndim=2)
if point_type == 'matrix':
tangent_vec = gs.to_ndarray(tangent_vec, to_ndim=3)
base_point = gs.to_ndarray(base_point, to_ndim=3)
n_tangent_vecs = tangent_vec.shape[0]
n_base_points = base_point.shape[0]
assert (tangent_vec.shape == base_point.shape or n_tangent_vecs == 1
or n_base_points == 1)
if n_tangent_vecs == 1:
tangent_vec = gs.array([tangent_vec[0]] * n_base_points)
if n_base_points == 1:
base_point = gs.array([base_point[0]] * n_tangent_vecs)
result = gs.cond(pred=gs.allclose(base_point, identity),
true_fn=lambda: self.group_exp_from_identity(
tangent_vec, point_type=point_type),
false_fn=lambda: self.group_exp_not_from_identity(
tangent_vec, base_point, point_type))
return result
