T3Tangent.is_gauged#

t3toolbox.manifold.T3Tangent.is_gauged(atol=1e-09)#
def is_gauged(self, atol: float = 1e-9) -> NDArray:  # bool array, shape = variation stack K+C (scalar unstacked)

True (per stack element) if the variations are gauged with respect to the frame.

Gauge conditions (needed for ManifoldGeometry.inner() / ManifoldGeometry.norm() to equal the Hilbert-Schmidt values; not enforced at construction):

  • einsum('...ia,...ja->...ij', U_i, V_i) = 0 for all i (Tucker variations ⟂ U).

  • einsum('...abi,...abj->...ij', L_i, H_i) = 0 for i = 0..d-2 (TT variations ⟂ L).

These are the gauge conditions (48)-(49), Appendix A.3, of Alger et al. (2026), “Tucker Tensor Train Taylor Series” (arXiv:2603.21141). Per-stack-element bool array (shape = variation stack K+C; scalar when unstacked); reduce with .all() for a single verdict.

Parameters:

atol (float)

Return type:

NDArray