Enum WeightField 

pub enum WeightField {
    Identity,
    Factored {
        u: Arc<Array2<f64>>,
        rank: usize,
        p_out: usize,
    },
}

Per-observation behavioral-metric field W_n ∈ ℝ^{p × p}, stored in low-rank factored form W_n = U_n U_n^T with U_n ∈ ℝ^{p × r_n}.

The canonical coordinate is the one where one unit of motion in t is one unit of behavioral change in the output space, so the W_n weighting is load-bearing: the pullback metric is g_n = J_n^T W_n J_n. Storing as U_n lets every contraction in this module run in (J^T U_n)(U_n^T J) order, which is O(p · r · d + r · d²) per row — we never materialize the p × p W_n, which is essential when p (number of observation channels) is large but rank is small (e.g. one or two behavioral dimensions per latent observation).

Identity is the gauge-fix default and corresponds to U_n = I_p so the pullback reduces to the standard J_n^T J_n. Factored stores the per-row U_n blocks contiguously: every row’s factor is p × rank, and rows may share the same rank (uniform-rank case) or vary if the field is data-driven. For the uniform-rank case the storage is (n_obs, p * rank) row-major.

Variants

Identity

W_n = I_p for every n. Reduces to the bare pullback J^T J.

Factored

Per-row low-rank factor U_n ∈ ℝ^{p × rank}. Storage layout: a (n_obs, p * rank) row-major matrix where row n packs U_n in column-major-within-row order U_n[i, k] = u[n, i * rank + k].

Fields

u: Arc<Array2<f64>>

rank: usize

p_out: usize

Implementations

impl WeightField

pub fn project_jac_row_with_u( u_row: &[f64], jac_row: &[f64], p: usize, rank: usize, d: usize, ) -> Array2<f64>

Apply U_n^T J_n for a specific row, given both the row’s J_n flat (p * d) slice and the row’s U_n flat (p * rank) slice. Returns the (rank × d) matrix and its row count.

Trait Implementations

impl Clone for WeightField

fn clone(&self) -> WeightField

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for WeightField

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.