def test_angle_to_extrinsic(self):
space = Hypersphere(1)
point = gs.pi / 4
result = space.angle_to_extrinsic(point)
expected = gs.array([1., 1.]) / gs.sqrt(2.)
self.assertAllClose(result, expected)
point = gs.array([1. / 3, 0.]) * gs.pi
result = space.angle_to_extrinsic(point)
expected = gs.array([[1. / 2, gs.sqrt(3.) / 2], [1., 0.]])
self.assertAllClose(result, expected)
def test_extrinsic_to_angle_inverse(self):
space = Hypersphere(1)
point = space.random_uniform()
angle = space.extrinsic_to_angle(point)
result = space.angle_to_extrinsic(angle)
self.assertAllClose(result, point)
space = Hypersphere(1, default_coords_type='intrinsic')
angle = space.random_uniform()
extrinsic = space.angle_to_extrinsic(angle)
result = space.extrinsic_to_angle(extrinsic)
self.assertAllClose(result, angle)
def fit(self, X, y=None, weights=None):
"""Compute the empirical Frechet mean.
Parameters
----------
X : {array-like, sparse matrix}, shape=[..., {dim, [n, n]}]
Training input samples.
y : array-like, shape=[...,] or [..., n_outputs]
Target values (class labels in classification, real numbers in
regression).
Ignored.
weights : array-like, shape=[...,]
Weights associated to the points.
Optional, default: None.
Returns
-------
self : object
Returns self.
"""
metric_str = self.metric.__str__()
is_linear_metric = (
"EuclideanMetric" in metric_str
or "MatricesMetric" in metric_str
or "MinkowskiMetric" in metric_str
)
if "HypersphereMetric" in metric_str and self.metric.dim == 1:
mean = Hypersphere.angle_to_extrinsic(_circle_mean(X))
error.check_parameter_accepted_values(
self.method, "method", ["default", "adaptive", "batch"]
)
if is_linear_metric:
mean = linear_mean(points=X, weights=weights, point_type=self.point_type)
elif self.method == "default":
mean = _default_gradient_descent(
points=X,
weights=weights,
metric=self.metric,
max_iter=self.max_iter,
initial_step_size=self.lr,
point_type=self.point_type,
epsilon=self.epsilon,
verbose=self.verbose,
)
elif self.method == "adaptive":
mean = _adaptive_gradient_descent(
points=X,
weights=weights,
metric=self.metric,
max_iter=self.max_iter,
point_type=self.point_type,
epsilon=self.epsilon,
verbose=self.verbose,
initial_tau=self.lr,
)
elif self.method == "batch":
mean = _batch_gradient_descent(
points=X,
weights=weights,
metric=self.metric,
lr=self.lr,
epsilon=self.epsilon,
max_iter=self.max_iter,
point_type=self.point_type,
verbose=self.verbose,
)
self.estimate_ = mean
return self
