How to use the diffcp.cones.parse_cone_dict function in diffcp

A, b, c, cone_dims = utils.least_squares_eq_scs_data(m, n)
        cone_dims.pop("q")
        cone_dims.pop("s")
        cone_dims.pop("ep")
        x, y, s, derivative, adjoint_derivative = cone_prog.solve_and_derivative(
            A, b, c, cone_dims, solver="ECOS")

        # check optimality conditions
        np.testing.assert_allclose(A @ x + s, b, atol=1e-8)
        np.testing.assert_allclose(A.T @ y + c, 0, atol=1e-8)
        np.testing.assert_allclose(s @ y, 0, atol=1e-8)
        np.testing.assert_allclose(s, cone_lib.pi(
            s, cone_lib.parse_cone_dict(cone_dims), dual=False), atol=1e-8)
        np.testing.assert_allclose(y, cone_lib.pi(
            y, cone_lib.parse_cone_dict(cone_dims), dual=True), atol=1e-8)

        x = cp.Variable(10)
        prob = cp.Problem(cp.Minimize(cp.sum_squares(np.random.randn(5, 10) @ x) + np.random.randn(10) @ x), [cp.norm2(x) <= 1, np.random.randn(2, 10) @ x == np.random.randn(2)])
        A, b, c, cone_dims = utils.scs_data_from_cvxpy_problem(prob)
        x, y, s, derivative, adjoint_derivative = cone_prog.solve_and_derivative(
            A, b, c, cone_dims, solver="ECOS")

        # check optimality conditions
        np.testing.assert_allclose(A @ x + s, b, atol=1e-8)
        np.testing.assert_allclose(A.T @ y + c, 0, atol=1e-8)
        np.testing.assert_allclose(s @ y, 0, atol=1e-8)
        np.testing.assert_allclose(s, cone_lib.pi(
            s, cone_lib.parse_cone_dict(cone_dims), dual=False), atol=1e-8)
        np.testing.assert_allclose(y, cone_lib.pi(
            y, cone_lib.parse_cone_dict(cone_dims), dual=True), atol=1e-8)

s, cone_lib.parse_cone_dict(cone_dims), dual=False), atol=1e-8)
        np.testing.assert_allclose(y, cone_lib.pi(
            y, cone_lib.parse_cone_dict(cone_dims), dual=True), atol=1e-8)

        x = cp.Variable(10)
        prob = cp.Problem(cp.Minimize(cp.sum_squares(np.random.randn(5, 10) @ x) + np.random.randn(10) @ x), [cp.norm2(x) <= 1, np.random.randn(2, 10) @ x == np.random.randn(2)])
        A, b, c, cone_dims = utils.scs_data_from_cvxpy_problem(prob)
        x, y, s, derivative, adjoint_derivative = cone_prog.solve_and_derivative(
            A, b, c, cone_dims, solver="ECOS")

        # check optimality conditions
        np.testing.assert_allclose(A @ x + s, b, atol=1e-8)
        np.testing.assert_allclose(A.T @ y + c, 0, atol=1e-8)
        np.testing.assert_allclose(s @ y, 0, atol=1e-8)
        np.testing.assert_allclose(s, cone_lib.pi(
            s, cone_lib.parse_cone_dict(cone_dims), dual=False), atol=1e-8)
        np.testing.assert_allclose(y, cone_lib.pi(
            y, cone_lib.parse_cone_dict(cone_dims), dual=True), atol=1e-8)

elif status != "Solved":
        if raise_on_error:
            raise SolverError("Solver scs returned status %s" % status)
        else:
            result["D"] = None
            result["DT"] = None
            return result

    x = result["x"]
    y = result["y"]
    s = result["s"]

    # pre-compute quantities for the derivative
    m, n = A.shape
    N = m + n + 1
    cones = cone_lib.parse_cone_dict(cone_dict)
    cones_parsed = cone_lib.parse_cone_dict_cpp(cones)
    z = (x, y - s, np.array([1]))
    u, v, w = z

    Q = sparse.bmat([
        [None, A.T, np.expand_dims(c, - 1)],
        [-A, None, np.expand_dims(b, -1)],
        [-np.expand_dims(c, -1).T, -np.expand_dims(b, -1).T, None]
    ])

    D_proj_dual_cone = _diffcp.dprojection(v, cones_parsed, True)
    if mode == "dense":
        Q_dense = Q.todense()
        M = _diffcp.M_dense(Q_dense, cones_parsed, u, v, w)
        MT = M.T
    else: