from idea36_catopt_play_category.solver import admm_consensus


def test_admm_consensus_converges_to_average():
    # two agents with objectives 0.5*(x - c)^2 => a=1, b=-c
    c1 = 2.0
    c2 = -1.0
    local = [
        {"a": 1.0, "b": -c1},
        {"a": 1.0, "b": -c2},
    ]

    z, history = admm_consensus(local, rho=1.0, max_iter=500, tol=1e-6)
    # analytic centralized optimum is average of c1 and c2
    expected = (c1 + c2) / 2.0
    assert abs(z - expected) < 1e-3