def METHOD_NAME(self, linear_solver):
    m = make_model()
    interface = InteriorPointInterface(m)
    ip_solver = InteriorPointSolver(linear_solver)
    ip_solver.set_interface(interface)
    interface.set_barrier_parameter(1e-1)
    # Evaluate KKT matrix before any iterations
    kkt = interface.evaluate_primal_dual_kkt_matrix()
    reg_coef = ip_solver.factorize(kkt)
    # Expected regularization coefficient:
    self.assertAlmostEqual(reg_coef, 1e-4)
    desired_n_neg_evals = (
        ip_solver.interface.n_eq_constraints()
        + ip_solver.interface.n_ineq_constraints()
    )
    # Expected inertia:
    n_pos_evals, n_neg_evals, n_null_evals = linear_solver.get_inertia()
    self.assertEqual(n_null_evals, 0)
    self.assertEqual(n_neg_evals, desired_n_neg_evals)