SharedGeometry.retract

t3toolbox.shared_geometry.SharedGeometry.retract(p, shared_data=None)

def retract(self, p, shared_data=None):

The shared retraction: stays on the shared set exactly (one factor array per group; on the uniform layer, one factor content at every group mode).

Manifold bases: the TIED doubled-rank embedding (the group’s common ambient direction is recovered from the tied coordinates by the companion’s clipped solve) truncated by the grouped T3-SVD. Corewise bases: mean-tie then the additive retraction. Safe mode requires the base preconditions, tied frame factors, and (manifold) tied tangent coordinates – an untied tangent would be silently tied-projected by the embedding’s solve, which is almost never what the caller meant.