ocs-rs — exact, matrix-free optimum contribution selection

Python bindings for the Rust support-first OCS solver.

Optimum contribution selection (OCS) chooses how much each candidate contributes to the next generation: maximise genetic gain bᵀc subject to a cap on the mean coancestry of the offspring, cᵀGc ≤ k, with non-negative contributions summing to one — or, in the sexed form, to one half per sex.

Exact, not heuristic. The solver returns the global optimum of the (convex) OCS program, certified by the KKT conditions at termination — verified against optiSel, a conic interior-point solver (agreement 1e-8) and an independent numerical reference (1.5e-14). Scope: continuous contributions under a single coancestry constraint; it does not do integer mate allocation.

Matrix-free. It never forms the dense n×n relationship matrix: the kinship products come straight from the genotype matrix as Gc = εc + Z(Zᵀc)/s. That is what lets it solve instances whose dense matrix (≈12 GiB at n = 40 000) will not fit in memory, and why the cost follows the (tiny) active support and the marker count rather than n².

On real marker panels it reaches the same optimum as optiSel 90–2280× faster.

Install

pip install maturin
maturin develop --release        # from bindings/python/ in the repository

(A PyPI release will follow; for now build from source.)

Quickstart

import numpy as np
import ocs_rs

# Z : (n, m) genotypes centred by twice the allele frequencies
# s : VanRaden scale 2 Σ p(1-p)  —  ocs_rs.vanraden_scale(p) computes it
res = ocs_rs.solve(Z, b, k=0.03, s=s, male=male)

print(res)                # OcsResult(status='Solved', |support|=17, gain=..., ...)
print(res.support)        # the handful of selected candidates
print(res.c[res.support]) # their contributions

API

solve(Z, b, k, *, s, ridge=1e-5, male=None, caps=None, max_iter=10_000, tol=1e-9)

Returns an OcsResult with c, support, gain, quad, iterations, products and status ("Solved" means KKT-optimal; only then are c/gain usable).

Links

• Source, manuscript and reproduction scripts: https://github.com/Adelagric/ocs-rs
• Archived release: https://doi.org/10.5281/zenodo.20746987

MIT licence.