pdft.manifolds.OrthogonalManifold

pdft.manifolds.OrthogonalManifold#

class pdft.manifolds.OrthogonalManifold(d=2)[source]#

Bases: object

O(d) for real-valued d×d unitaries (subset of UnitaryManifold).

Implementation: project gradients to the REAL skew-symmetric tangent subspace; Cayley retraction with a real W keeps the tensor real throughout training. Hadamards initialised at canonical form [[1, 1], [1, -1]] / sqrt(2) live in O(2) (det = -1) — the connected component is preserved by retraction, so we stay on the same coset.

Parameters:

d (int)

__init__(d=2)#
Parameters:

d (int)

Return type:

None

Methods

__init__([d])

project(U, G)

retract(U, Xi, alpha, *[, I_batch])

transport(U_old, U_new, v)

Attributes

d

d: int = 2#
project(U, G)[source]#
Parameters:
Return type:

Array

retract(U, Xi, alpha, *, I_batch=None)[source]#
Parameters:
Return type:

Array

transport(U_old, U_new, v)[source]#
Parameters:
Return type:

Array