def __init__(self,
group,
inner_product_mat_at_identity=None,
left_or_right='left'):
if inner_product_mat_at_identity is None:
inner_product_mat_at_identity = gs.eye(self.group.dimension)
inner_product_mat_at_identity = gs.to_ndarray(
inner_product_mat_at_identity, to_ndim=3)
mat_shape = inner_product_mat_at_identity.shape
assert mat_shape == (1, ) + (group.dimension, ) * 2, mat_shape
assert left_or_right in ('left', 'right')
eigenvalues = gs.linalg.eigvalsh(inner_product_mat_at_identity)
mask_pos_eigval = gs.greater(eigenvalues, 0.)
n_pos_eigval = gs.sum(gs.cast(mask_pos_eigval, gs.int32))
mask_neg_eigval = gs.less(eigenvalues, 0.)
n_neg_eigval = gs.sum(gs.cast(mask_neg_eigval, gs.int32))
mask_null_eigval = gs.isclose(eigenvalues, 0.)
n_null_eigval = gs.sum(gs.cast(mask_null_eigval, gs.int32))
self.group = group
if inner_product_mat_at_identity is None:
inner_product_mat_at_identity = gs.eye(self.group.dimension)
self.inner_product_mat_at_identity = inner_product_mat_at_identity
self.left_or_right = left_or_right
self.signature = (n_pos_eigval, n_null_eigval, n_neg_eigval)
def __init__(self,
group,
algebra=None,
metric_mat_at_identity=None,
left_or_right='left',
**kwargs):
super(InvariantMetric, self).__init__(dim=group.dim, **kwargs)
self.group = group
self.lie_algebra = algebra
if metric_mat_at_identity is None:
metric_mat_at_identity = gs.eye(self.group.dim)
geomstats.errors.check_parameter_accepted_values(
left_or_right, 'left_or_right', ['left', 'right'])
eigenvalues = gs.linalg.eigvalsh(metric_mat_at_identity)
mask_pos_eigval = gs.greater(eigenvalues, 0.)
n_pos_eigval = gs.sum(gs.cast(mask_pos_eigval, gs.int32))
mask_neg_eigval = gs.less(eigenvalues, 0.)
n_neg_eigval = gs.sum(gs.cast(mask_neg_eigval, gs.int32))
mask_null_eigval = gs.isclose(eigenvalues, 0.)
n_null_eigval = gs.sum(gs.cast(mask_null_eigval, gs.int32))
self.metric_mat_at_identity = metric_mat_at_identity
self.left_or_right = left_or_right
self.signature = (n_pos_eigval, n_null_eigval, n_neg_eigval)
def belongs(self, point):
"""Evaluate if a point belongs to the manifold of beta distributions.
The statistical manifold of beta distributions is the upper right
quadrant of the euclidean 2-plane.
Parameters
----------
point : array-like, shape=[..., 2]
Point to be checked.
Returns
-------
belongs : array-like, shape=[...,]
Boolean indicating whether point represents a beta distribution.
"""
point_dim = point.shape[-1]
belongs = point_dim == self.dim
belongs = gs.logical_and(
belongs, gs.all(gs.greater(point, 0.), axis=-1))
return belongs
def belongs(self, point):
"""Evaluate if a point belongs to the manifold of Dirichlet distributions.
Check that point defines parameters for a Dirichlet distributions,
i.e. belongs to the positive quadrant of the Euclidean space.
Parameters
----------
point : array-like, shape=[..., dim]
Point to be checked.
Returns
-------
belongs : array-like, shape=[...,]
Boolean indicating whether point represents a Dirichlet
distribution.
"""
point_dim = point.shape[-1]
belongs = point_dim == self.dim
belongs = gs.logical_and(
belongs, gs.all(gs.greater(point, 0.), axis=-1))
return belongs
def belongs(self, point, point_type=None):
"""Evaluate if a point belongs to the manifold of beta distributions.
The statistical manifold of beta distributions is the upper right
quadrant of the euclidean 2-plane.
Parameters
----------
point : array-like, shape=[n_samples, 2]
the point of which to check whether it belongs to Beta
Returns
-------
belongs : array-like, shape=[n_samples, 1]
array of booleans indicating whether point belongs the Beta
"""
point = gs.to_ndarray(point, to_ndim=2)
n_points, point_dim = point.shape
belongs = point_dim == self.dim
belongs = gs.to_ndarray(belongs, to_ndim=1)
belongs = gs.tile(belongs, n_points)
belongs = belongs * gs.greater(point, 0).all(axis=1)
return belongs[0] if n_points == 1 else belongs
def __init__(self,
group,
inner_product_mat_at_identity=None,
left_or_right='left'):
self.group = group
if inner_product_mat_at_identity is None:
inner_product_mat_at_identity = gs.eye(self.group.dim)
geomstats.error.check_parameter_accepted_values(
left_or_right, 'left_or_right', ['left', 'right'])
eigenvalues = gs.linalg.eigvalsh(inner_product_mat_at_identity)
mask_pos_eigval = gs.greater(eigenvalues, 0.)
n_pos_eigval = gs.sum(gs.cast(mask_pos_eigval, gs.int32))
mask_neg_eigval = gs.less(eigenvalues, 0.)
n_neg_eigval = gs.sum(gs.cast(mask_neg_eigval, gs.int32))
mask_null_eigval = gs.isclose(eigenvalues, 0.)
n_null_eigval = gs.sum(gs.cast(mask_null_eigval, gs.int32))
self.inner_product_mat_at_identity = inner_product_mat_at_identity
self.left_or_right = left_or_right
self.signature = (n_pos_eigval, n_null_eigval, n_neg_eigval)
