def _default_gradient_descent(points, metric, weights, max_iter, point_type,
epsilon, verbose):
"""Perform default gradient descent."""
if point_type == 'vector':
points = gs.to_ndarray(points, to_ndim=2)
einsum_str = 'n,nj->j'
if point_type == 'matrix':
points = gs.to_ndarray(points, to_ndim=3)
einsum_str = 'n,nij->ij'
n_points = gs.shape(points)[0]
if weights is None:
weights = gs.ones((n_points, ))
mean = points[0]
if n_points == 1:
return mean
sum_weights = gs.sum(weights)
sq_dists_between_iterates = []
iteration = 0
sq_dist = 0.
var = 0.
while iteration < max_iter:
var_is_0 = gs.isclose(var, 0.)
sq_dist_is_small = gs.less_equal(sq_dist, epsilon * var)
condition = ~gs.logical_or(var_is_0, sq_dist_is_small)
if not (condition or iteration == 0):
break
logs = metric.log(point=points, base_point=mean)
tangent_mean = gs.einsum(einsum_str, weights, logs)
tangent_mean /= sum_weights
estimate_next = metric.exp(tangent_vec=tangent_mean, base_point=mean)
sq_dist = metric.squared_dist(estimate_next, mean)
sq_dists_between_iterates.append(sq_dist)
var = variance(points=points,
weights=weights,
metric=metric,
base_point=estimate_next,
point_type=point_type)
mean = estimate_next
iteration += 1
if iteration == max_iter:
logging.warning('Maximum number of iterations {} reached. '
'The mean may be inaccurate'.format(max_iter))
if verbose:
logging.info('n_iter: {}, final variance: {}, final dist: {}'.format(
iteration, var, sq_dist))
return mean
def projection(self, point, atol=gs.atol):
"""Project a point in ambient space to the parameter set.
The parameter is floored to `gs.atol` if it is negative
and to '1-gs.atol' if it is greater than 1.
Parameters
----------
point : array-like, shape=[...,]
Point in ambient space.
atol : float
Tolerance to evaluate positivity.
Returns
-------
projected : array-like, shape=[...,]
Projected point.
"""
point = gs.cast(gs.array(point), dtype=gs.float32)
projected = gs.where(
gs.logical_or(point < atol, point > 1 - atol),
(1 - atol) * gs.cast(
(point > 1 - atol), gs.float32) + atol * gs.cast(
(point < atol), gs.float32),
point,
)
return gs.squeeze(projected)
def while_loop_cond(iteration, mean, var, sq_dist):
result = ~gs.logical_or(gs.isclose(var, 0.),
gs.less_equal(sq_dist, epsilon * var))
return result[0, 0] or iteration == 0
def _default_gradient_descent(points, metric, weights, max_iter, point_type,
epsilon, initial_step_size, verbose):
"""Perform default gradient descent."""
if point_type == 'vector':
points = gs.to_ndarray(points, to_ndim=2)
einsum_str = 'n,nj->j'
else:
points = gs.to_ndarray(points, to_ndim=3)
einsum_str = 'n,nij->ij'
n_points = gs.shape(points)[0]
if weights is None:
weights = gs.ones((n_points, ))
mean = points[0]
if n_points == 1:
return mean
sum_weights = gs.sum(weights)
sq_dists_between_iterates = []
iteration = 0
sq_dist = 0.
var = 0.
norm_old = gs.linalg.norm(points)
step = initial_step_size
while iteration < max_iter:
logs = metric.log(point=points, base_point=mean)
var = gs.sum(
metric.squared_norm(logs, mean) * weights) / gs.sum(weights)
tangent_mean = gs.einsum(einsum_str, weights, logs)
tangent_mean /= sum_weights
norm = gs.linalg.norm(tangent_mean)
sq_dist = metric.squared_norm(tangent_mean, mean)
sq_dists_between_iterates.append(sq_dist)
var_is_0 = gs.isclose(var, 0.)
sq_dist_is_small = gs.less_equal(sq_dist, epsilon * metric.dim)
condition = ~gs.logical_or(var_is_0, sq_dist_is_small)
if not (condition or iteration == 0):
break
estimate_next = metric.exp(step * tangent_mean, mean)
mean = estimate_next
iteration += 1
if norm < norm_old:
norm_old = norm
elif norm > norm_old:
step = step / 2.
if iteration == max_iter:
logging.warning('Maximum number of iterations {} reached. '
'The mean may be inaccurate'.format(max_iter))
if verbose:
logging.info('n_iter: {}, final variance: {}, final dist: {}'.format(
iteration, var, sq_dist))
return mean
