uniform_manifold_ops

t3toolbox.backend.uniform_fitting.uniform_manifold_ops(x0_data)

def uniform_manifold_ops(
        x0_data:  typ.Tuple,   # UniformTuckerTensorTrain.data = (tk_sc, tt_sc, shape, (tucker_mask, tt_mask))
) -> bopt.GeometryOps:         # the uniform manifold geometry ops (masks of x0's fixed rank closed over)

The uniform manifold GeometryOps at x0’s fixed rank – the raw-supercore twin of t3toolbox.uniform_manifold.UNIFORM_MANIFOLD.

frame = the orthonormal frame (ufv_conversions.ut3_orthogonal_representations()); project = the gauge projection Pi; retract = the manifold (doubled-rank, mask-truncated) retraction; inner = the masked coordinate dot (utv_operations.utv_corewise_inner(), the check-free twin of UNIFORM_MANIFOLD.inner – equal to Hilbert-Schmidt on this orthonormal, gauged frame). All masks are loop-invariant at x0’s rank and closed over here.

Parameters:

x0_data (t3toolbox.backend.common.typ.Tuple)

Return type:

GeometryOps