Function solve_on_change_sublinear 

pub fn solve_on_change_sublinear(
    matrix: &dyn Matrix,
    _prev_solution: &[Precision],
    b_new: &[Precision],
    delta: &SparseDelta,
    closure_depth: usize,
    max_terms: usize,
    tolerance: Precision,
) -> Result<Vec<(usize, Precision)>>

SubLinear sibling of IncrementalSolver::solve_on_change. Returns Vec<(usize, Precision)> of (row_index, x_new[row]) for every row in the bounded-depth closure of delta’s support, computed without touching any row outside the closure.

The output is sorted ascending by row index. Callers that need a dense view can scatter the entries into a vector themselves; callers chaining onto contrastive search / find_anomalous_rows_in_subset don’t need to.

Wiring

  closure   = closure::closure_indices(matrix, &delta.indices, closure_depth)
  for i in closure:
      x_new[i] = entry::solve_single_entry_neumann(matrix, b_new, i, max_terms, tolerance)

Caller supplies b_new (the new RHS) directly rather than reconstructing it from b_prev + delta — this is the “I already know what the world looks like now” path. prev_solution is not used by this function: the per-entry Neumann is cold-start from D⁻¹b_new. It’s exposed as a parameter only for API symmetry with solve_on_change and so callers can pre-bind the same shape.

Complexity

O(|closure| · max_terms · branching) — independent of n for sparse DD matrices with bounded max_terms. Pure SubLinear.

Errors

Returns crate::error::SolverError from the inner per-entry calls (InvalidInput on a zero diagonal in the closure; DimensionMismatch on a wrong-sized b_new).

Examples

// We perturbed b at a few indices; tell me the NEW solution at the
// rows that could have changed — and nowhere else.
let new_entries = solve_on_change_sublinear(
    a, prev, b_new, delta,
    /*closure_depth=*/ 4,
    /*max_terms=*/    32,
    /*tolerance=*/    1e-10,
).unwrap();
for (row, val) in new_entries {
    // wake a downstream observer for `row`
}