geometry.tangent_bundle

geometry.tangent_bundle(M, X, d=2, centers=None)

Estimates the tangent bundle of a range space (X,M) via local PCA.

This function estimates the d-dimensional tangent spaces of neighborhoods in X given by ranges in M. This may be interpreted as evaluating the logarithm between the centers and points in the local neighborhood in the direction given by the principle directions.

Parameters

Name	Type	Description	Default
M	sparray	Sparse matrix whose columns represent subsets of X.	required
X	np.ndarray	coordinates of the range space.	required
d	int	dimension of the tangent space.	2
centers	Optional[np.ndarray]	points to center the tangent space estimates. If None, each neighborhoods is centered around its average.	None

Returns

Type	Description
dict	list of tangent pairs, i.e. base points paired with tangent vector.