def compute_distance(self, xi: GrassmannPoint, xj: GrassmannPoint):
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)
return np.sqrt(abs(rank_i - rank_j) * np.pi**2 / 4 + np.sum(theta**2))
def compute_distance(self, xi: GrassmannPoint,
xj: GrassmannPoint) -> float:
"""
Compute the Asimov 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)
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.max(theta)
return distance
def compute_distance(self, xi: GrassmannPoint, xj: GrassmannPoint) -> float:
"""
Compute the Projection 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.sum(np.sin(theta) ** 2))
return distance
def compute_distance(self, xi: GrassmannPoint,
xj: GrassmannPoint) -> float:
"""
Compute the Martin 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)
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)
cos_sq = np.cos(theta)**2
float_min = sys.float_info.min
index = np.where(cos_sq < float_min)
cos_sq[index] = float_min
recp = np.reciprocal(cos_sq)
distance = np.sqrt(np.log(np.prod(recp)))
return distance