def METHOD_NAME(state, request):
    old_state = request.getfixturevalue(state)
    new_nevals = 5
    # some new data
    x = np.zeros([new_nevals, old_state.input_dim])
    y = np.ones(new_nevals)
    integral = Normal(0, 1)
    gram = np.eye(new_nevals)
    gram_cho_factor = (np.eye(new_nevals), False)
    kernel_means = np.ones(new_nevals)
    kernel = ExpQuad(input_shape=(old_state.input_dim,))
    scale_sq = 1.7
    # previously no data given
    s = BQState.from_new_data(
        kernel=kernel,
        scale_sq=scale_sq,
        nodes=x,
        fun_evals=y,
        integral_belief=integral,
        prev_state=old_state,
        gram=gram,
        gram_cho_factor=gram_cho_factor,
        kernel_means=kernel_means,
    )
    # types
    assert isinstance(s.kernel, Kernel)
    assert isinstance(s.measure, IntegrationMeasure)
    assert isinstance(s.kernel_embedding, KernelEmbedding)
    assert isinstance(s.nodes, np.ndarray)
    assert isinstance(s.fun_evals, np.ndarray)
    assert isinstance(s.gram, np.ndarray)
    assert isinstance(s.gram_cho_factor[0], np.ndarray)
    assert isinstance(s.gram_cho_factor[1], bool)
    assert isinstance(s.kernel_means, np.ndarray)
    assert isinstance(s.integral_belief, Normal)
    assert isinstance(s.previous_integral_beliefs, tuple)
    # shapes
    assert s.nodes.shape == (new_nevals, s.input_dim)
    assert s.fun_evals.shape == (new_nevals,)
    assert len(s.previous_integral_beliefs) == 1
    assert s.gram.shape == (new_nevals, new_nevals)
    assert s.gram_cho_factor[0].shape == (new_nevals, new_nevals)
    assert s.kernel_means.shape == (new_nevals,)
    # values
    assert s.input_dim == s.measure.input_dim
    assert s.scale_sq == scale_sq