shared_geometry

The shared-Tucker-factors (SF-T3) geometry wrapper: shared(base, sharing).

Wraps MANIFOLD / COREWISE (or their uniform twins UNIFORM_MANIFOLD / UNIFORM_COREWISE) so every projection lands on the TIED tangent subspace (one Tucker factor per sharing group) and the retraction stays on the shared set. One principle, two formulas – each geometry ties by orthogonal projection onto ITS tied subspace in ITS metric on ITS coordinates: the manifold geometry’s gauged coordinates carry the frame’s S factors, so its post-pass is the Gram-weighted (SVD-solved) tilted projection; the corewise coordinates are raw factor copies, so its post-pass is the per-group arithmetic mean. Optimizers consume a shared geometry exactly like a base one (t3t.newton_cg(shared_manifold(sharing), 'apply', ww, b, x0)).

Classes

SharedGeometry

The shared (SF-T3) geometry: a base geometry restricted to tied Tucker factors.

Functions

shared(base, sharing)	The shared (SF-T3) geometry over a base geometry: optimize with the Tucker factors tied
shared_manifold(sharing)	shared(MANIFOLD, sharing) -- the shared fixed-rank Riemannian geometry.
shared_corewise(sharing)	shared(COREWISE, sharing) -- the shared core-parameter Euclidean geometry.