tv_operations

Tangent-variations operations on raw (frame, variations) data.

tv_to_t3 (the tangent SUM over variation terms – vs fv_conversions.fv_to_t3’s single term), tv_to_dense, the orthogonal/oblique gauge projections, the tangent-space projections of t3/dense operands, tv_retract, tv_gauge_residual, and the tangent/frame stack converters.

Functions

tv_to_dense(frame, variations[, include_shift])	Form the dense tensor represented by a frame-variations tangent vector.
tv_orthogonal_gauge_projection(frame, variations)	Project the variations onto the gauge-satisfying subspace (orthogonal projection).
tv_oblique_gauge_projection(frame, variations)	Project the variations onto the gauge-satisfying subspace while preserving the tangent vector.
tv_to_t3(frame, variations[, include_shift])	Doubled-rank Tucker tensor train representing a frame-variations tangent vector.
tv_project_t3_onto_tangent_space(frame, x)	Orthogonal projection of a Tucker tensor train onto the tangent space at an orthogonal frame.
tv_project_dense_onto_tangent_space(frame, Z)	Orthogonal projection of a dense tensor onto the tangent space at an orthogonal frame.
tv_unstack_tangent_stack(frame, variations)	Peel the tangent stack V off the variations, returning a V-shaped tree of variation-data.
tv_stack_tangent_stack(variations_tree)	Stack a V-shaped tree of variation-data over the tangent stack V (outermost).
tv_unstack_frame_stack(frame, variations)	Peel the frame stack G off both the frame and the variations, returning a G-shaped tree whose
tv_stack_frame_stack(paired_tree)	Stack a G-shaped tree of (frame_data, variations_data) pairs over the frame stack G.
tv_gauge_residual(frame, variations)	Max violation of the gauge conditions for a tangent vector, per stack element.
tv_retract(frame, variations)	Retract a frame-variations tangent vector onto the fixed-rank manifold.