Source code for geomstats.geometry.landmarks

"""Manifold for sets of landmarks that belong to any given manifold.

Lead author: Nicolas Guigui.

from geomstats.geometry.nfold_manifold import NFoldManifold, NFoldMetric

[docs] class Landmarks(NFoldManifold): """Class for space of landmarks. The landmark space is a product manifold where all manifolds in the product are the same. The default metric is the product metric and is often referred to as the L2 metric. Parameters ---------- ambient_manifold : Manifold Manifold to which landmarks belong. k_landmarks : int Number of landmarks. """ def __init__(self, ambient_manifold, k_landmarks, equip=True): super().__init__( base_manifold=ambient_manifold, n_copies=k_landmarks, equip=equip ) @property def k_landmarks(self): """Number of landmarks.""" return self.n_copies
[docs] @staticmethod def default_metric(): """Metric to equip the space with if equip is True.""" return L2LandmarksMetric
[docs] class L2LandmarksMetric(NFoldMetric): """L2 Riemannian metric on the space of landmarks. This is the NFoldMetric of the n-fold manifold made out of k_landmarks copies of the ambient manifold of each landmark. """