circle_bundles.RP1AngleMetric

class circle_bundles.RP1AngleMetric(name='RP1_angle', base_name='RP^1', base_name_latex='\\mathbb{RP}^1')

Bases: object

Geodesic distance on the real projective line \(\mathbb{RP}^1\) using angular coordinates.

The space \(\mathbb{RP}^1\) can be viewed as a circle with antipodal points identified. Angles are therefore taken modulo \(\pi\).

The distance between two angles is

\[d(\theta_1, \theta_2) = \min\left(|\Delta|, \pi - |\Delta|\right), \quad \Delta = (\theta_2 - \theta_1) \bmod \pi.\]

This metric is commonly used when the base variable represents unoriented directions.

Parameters:

• name (str)

• base_name (str)

• base_name_latex (str)

name

Metric identifier (default "RP1_angle").

Type:

str

base_name

Short name of the base space for plots/UI.

Type:

str

base_name_latex

LaTeX symbol used in summaries and tables.

Type:

str

__init__(name='RP1_angle', base_name='RP^1', base_name_latex='\\mathbb{RP}^1')

Parameters:

• name (str)

• base_name (str)

• base_name_latex (str)

Return type:

None

Methods

__init__([name, base_name, base_name_latex])
pairwise(X[, Y])	Compute projective geodesic distances between angle arrays.

Attributes

base_name
base_name_latex
name

pairwise(X, Y=None)

Compute projective geodesic distances between angle arrays.

Parameters:

• X (ndarray) – Array of angles (any real values), shape (n,).

• Y (ndarray | None) – Optional array of angles, shape (m,). If omitted, uses X.

Returns:

Distance matrix of shape (n, m).

Return type:

D