geometry.manifolds.torus.Torus

class geometry.manifolds.torus.Torus(n)

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.
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
normalize
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.

belongs(a)

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?

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)