compute_orthogonal_representation_ranks#

t3toolbox.backend.ranks.compute_orthogonal_representation_ranks(shape, tucker_ranks, tt_ranks, use_jax=False)#
def compute_orthogonal_representation_ranks(
        shape: typ.Sequence[int], # (N0, ..., N(d-1))
        tucker_ranks: typ.Union[
            typ.Sequence[int], # (n0,...,n(d-1))
            NDArray, # dtype=int, shape=(d,) + stack_shape
        ],
        tt_ranks: typ.Union[
            typ.Sequence[int], # (r0,...,rd)
            NDArray, # dtype=int, shape=(d+1,) + stack_shape
        ],
        use_jax: bool = False,
) -> typ.Tuple[
    typ.Union[
        typ.Tuple[int,...],  # (nU0,...,nU(d-1))
        NDArray,  # dtype=int, shape=(d,) + stack_shape
    ], # up_tucker_ranks
    typ.Union[
        typ.Tuple[int, ...],  # (nD0',...,nD(d-1)')
        NDArray,  # dtype=int, shape=(d,) + stack_shape
    ],  # down_tucker_ranks
    typ.Union[
        typ.Tuple[int,...],  # (rL0',...,rLd')
        NDArray,  # dtype=int, shape=(d+1,) + stack_shape
    ], # left_tt_ranks
    typ.Union[
        typ.Tuple[int, ...],  # (rR0',...,rRd')
        NDArray,  # dtype=int, shape=(d+1,) + stack_shape
    ],  # right_tt_ranks
]:

The ranks the orthogonal-representation sweep (fv_conversions.t3_orthogonal_representations) produces, without running it – the uniform frame masks are built from these, so this recurrence must follow the sweep’s ORDER exactly:

  1. Tucker down-orthogonalization: up_i = min(n_i, N_i);

  2. a LEFT sweep on the original TT bonds: left_{i+1} = min(left_i * up_i, r_{i+1});

  3. a RIGHT sweep over the left-orthogonal chain: right_i = min(left_i, up_i * right_{i+1});

  4. the down cores: down_i = min(up_i, left_i * right_{i+1}).

The boundary bonds are 1 (the sweep squashes the tails). Until 2026-08-22 this ran the paper’s right-then-left order on the original bonds; on minimal-rank structures the two agree, on any non-minimal TT bond they do not, and the uniform frame’s left/down masks were too small (review S1). Host numpy throughout: ranks are static structure (use_jax is accepted for compatibility and ignored).

Parameters:

  • shape (t3toolbox.backend.common.typ.Sequence[int])

  • tucker_ranks (t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[int], NDArray])

  • tt_ranks (t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[int], NDArray])

  • use_jax (bool)

Return type:

t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Tuple[int, …], NDArray], t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Tuple[int, …], NDArray], t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Tuple[int, …], NDArray], t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Tuple[int, …], NDArray]]