frame_variations_format

The frontend frame/variations classes: T3Frame (orthogonal frame) + T3Variations.

A (frame, variations) pair is the orthogonal representation of a tangent direction to the fixed-rank T3 manifold (T4S Appendix A). T3Frame.data = (up, down, left, right) = (U, O, P, Q); structural validation runs in __post_init__. t3_orthogonal_representations here returns the frontend objects; the same-named backend function (backend.fv_conversions) returns raw data.

Classes

T3Frame	Frame for frame-variations representation of TuckerTensorTrains
T3Variations	Tuple containing variation cores for frame-variation representations of TuckerTensorTrains.
T3FrameWeights	Diagonal weights defining a metric on the tangent coordinates -- a Grasedyck-Kramer-style

Functions

fv_to_t3(index, frame, variations)	Convert frame-variations representation to TuckerTensorTrain.
t3_orthogonal_representations(x[, ...])	Construct frame-variation representations of TuckerTensorTrain with orthogonal frame.
fv_absorb_weights(variations, weights)	Absorb the metric weights into the variation cores (down->V, up/left/right->H),