compute_manifold_dim

t3toolbox.backend.ranks.compute_manifold_dim(shape, tucker_ranks, tt_ranks)

def compute_manifold_dim(
        shape:          typ.Sequence[int],  # (N0, ..., N(d-1))
        tucker_ranks:   typ.Sequence[int],  # (n0, ..., n(d-1))
        tt_ranks:       typ.Sequence[int],  # (r0, ..., rd)
) -> int:

Dimension of the fixed-rank Tucker tensor train manifold for the given structure.

Computed from the structurally-minimal ranks (gauge already quotiented), so this is the true tangent-space dimension for a minimal-rank base point.

Parameters:

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

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

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

Return type:

int