import numpy as np
from beartype import beartype
from UQpy.utilities.distances.baseclass.GrassmannianDistance import (
GrassmannianDistance,
)
from UQpy.utilities.GrassmannPoint import GrassmannPoint
[docs]class GeodesicDistance(GrassmannianDistance):
"""
A class to calculate the Geodesic distance between two Grassmann points.
"""
[docs] @beartype
def compute_distance(self, xi: GrassmannPoint, xj: GrassmannPoint) -> float:
"""
Compute the Geodesic distance between two points on the Grassmann manifold.
:param xi: Orthonormal matrix representing the first point.
:param xj: Orthonormal matrix representing the second point.
"""
GrassmannianDistance.check_rows(xi, xj)
rank_i = xi.data.shape[1]
rank_j = xj.data.shape[1]
r = np.dot(xi.data.T, xj.data)
(ui, si, vi) = np.linalg.svd(r, full_matrices=True)
si[np.where(si > 1)] = 1.0
theta = np.arccos(si)
distance = (np.sqrt(abs(rank_i - rank_j) * np.pi ** 2 / 4 + np.sum(theta ** 2)))
return distance