Partial constraints

TL;DR

Partial fitting freezes known node-pair occupations, subtracts their contribution from the requested constraints, and fits the parent model on the remaining free support.

Not a separate family

Partial constraints are a support transformation. The inner solver remains the selected ME, B, or W family with the selected constraint layer.

When to use partial fitting

Situation	Why partial helps
Known structural links	keep trusted node pairs fixed
Data integration	combine observed high-confidence pairs with null-model free pairs
Filtering with frozen pairs	avoid treating known occupations as random
Scenario analysis	remove or keep a selected support while preserving totals

Excess constraints

If \(Q\) is the set of frozen pairs and \(r_{ij}\) is the known occupation, then the free outgoing strength is:

\[ s_i^{out,free}=s_i^{out}-\sum_{j:(i,j)\in Q} r_{ij}. \]

Incoming strengths, binary degrees, total binary edges, and total cost are reduced in the same way. Negative excess means the partial problem is infeasible.

Public route

Pass known_source, known_target, and known_rate to fit_model:

partial_fit = fit_model(
    family=ModelFamily.ME,
    constraint=Constraint.STRENGTH_COST,
    strength_out=strength_out,
    strength_in=strength_in,
    target_cost=total_cost,
    coord_x=x,
    coord_y=y,
    known_source=known_source,
    known_target=known_target,
    known_rate=known_rate,
    self_loops=False,
)

partial_fit is a sparse PartialFitResult with source, target, and rate arrays for frozen and fitted free pairs.

Implementation rule

partial fit = compute excess constraints + free support + full family solver

The partial path should not duplicate solver math. Masks, excess computation, and sparse rate-table assembly belong in Rust.