geometry.manifolds.sphere.Sphere

class geometry.manifolds.sphere.Sphere(order)

These are hyperspheres of unit radius.

Methods

assert_close(a, b[, atol, msg])	Asserts that two points on the manifold are close to the given tolerance.
belongs_ts(bv)	Checks that a vector vx belongs to the tangent space at the given point base.
embed_in(M, my_point)	Embeds a point on this manifold to the target manifold M.
from_yaml(yaml_structure)	Recovers a value from a Yaml structure.
geodesic(a, b, t)	Returns the point interpolated along the geodesic.
get_dimension()	Returns the intrinsic dimension of this manifold.
normalize(a)	Normalizes the coordinates to the canonical representation for this manifold.
project_from(M, his_point)	Projects a point on a bigger manifold to this manifold.
riemannian_mean(points)	TODO: work out exceptions
tangent_bundle()	Returns the manifold corresponding to the tangent bundle.

belongs
can_convert_to
can_represent
convert_to
distance
embeddable_in
embedding
expmap
friendly
interesting_points
isomorphism
logmap
project_to
project_ts
relations_descriptions
sample_uniform
to_yaml

assert_close(a, b, atol=1e-08, msg=None)

Asserts that two points on the manifold are close to the given tolerance.

atol_geodesic_distance = 1e-08

belongs(x)

Raises an Exception if the point does not belong to this manifold.

This function wraps some checks around belongs_(), which is implemented by the subclasses.

belongs_ts(bv)

Checks that a vector vx belongs to the tangent space at the given point base.

can_convert_to(manifold)

can_represent(manifold)

convert_to(m, my_point)

distance(a, b)

Computes the geodesic distance between two points.

embed_in(M, my_point)

Embeds a point on this manifold to the target manifold M.

embeddable_in(manifold)

static embedding(B, A_to_B, B_to_A, itype='user', steps=None, desc=None)

expmap(bv)

Computes the exponential map from base for the velocity vector v.

This function wraps some checks around expmap_(), which is implemented by the subclasses.

friendly(a)

Returns a friendly description string for a point on the manifold.

from_yaml(yaml_structure)

Recovers a value from a Yaml structure.

geodesic(a, b, t)

Returns the point interpolated along the geodesic.

get_dimension()

Returns the intrinsic dimension of this manifold.

interesting_points()

Returns a list of “interesting points” on this manifold that should be used for testing various properties.

static isomorphism(B, A_to_B, B_to_A, itype='user', steps=None, desc=None)

logmap(base, p)

Computes the logarithmic map from base point base to target b. # XXX: what should we do in the case there is more than one logmap?

norm_rtol = 1e-05

normalize(a)

Normalizes the coordinates to the canonical representation for this manifold. See TorusW.

project_from(M, his_point)

Projects a point on a bigger manifold to this manifold.

project_to(m, my_point)

project_ts(bv)

Projects a vector bv in the ambient space to the tangent space at point base.

relations_descriptions()

riemannian_mean(points)

TODO: work out exceptions

sample_uniform()

tangent_bundle()

Returns the manifold corresponding to the tangent bundle. The default gives a generic implementation. MatrixLieGroup have a different one.

to_yaml(x)