ranks

Rank bookkeeping: minimal/continuation ranks, manifold dimension, rank-spec normalization.

Mostly cheap structural integer arithmetic – bare minimal_ranks means the structural notion, per the naming convention; the SVD-based numerically_minimal checkers live with their operations – plus edge condition-number diagnostics.

Functions

normalize_max_ranks(spec, length)	Normalize a max-rank specification to a per-position tuple.
compute_minimal_ranks(shape, tucker_ranks, tt_ranks[, ...])	Find minimal ranks for a generic Tucker tensor train with a given structure.
edge_condition_numbers(tucker_singular_values, ...)	Edge condition numbers kappa_i = sigma_{i,1} / sigma_{i,r_i} of the matrix unfoldings.
compute_continuation_ranks(shape, ...[, tau, n_chunk, ...])	Rank-continuation update: choose new ranks from the current iterate's unfolding singular values.
compute_raw_sweep_ranks(shape, tucker_ranks, tt_ranks, ...)	Ranks the T3-SVD sweep produces under hard rank caps -- i.e. the ranks t3svd returns (it does
compute_orthogonal_representation_ranks(shape, ...[, ...])	Find ranks that would be produced by sweeping orthogonalization, except without actually doing it.
compute_manifold_dim(shape, tucker_ranks, tt_ranks)	Dimension of the fixed-rank Tucker tensor train manifold for the given structure.
frame_has_minimal_ranks(shape, up_ranks, down_ranks, ...)	True if a T3Frame with these (redundant) ranks is structurally minimal.