human
Solve the following python programming problem given the following code:
@requires_sklearn_0_15
def test_auto_low_rank():
assistant
#Here is the Python code you requested.

    """Test probabilistic low rank estimators.
    """
    (n_samples, n_features, rank) = (400, 10, 5)
    sigma = 0.1
    def get_data(n_samples, n_features, rank, sigma):
        rng = np.random.RandomState(42)
        W = rng.randn(n_features, n_features)
        X = rng.randn(n_samples, rank)
        (U, _, _) = linalg.svd(W.copy())
        X = np.dot(X, U[:, :rank].T)
        sigmas = ((sigma * rng.rand(n_features)) + (sigma / 2.0))
        X += (rng.randn(n_samples, n_features) * sigmas)
        return X
    X = get_data(n_samples=n_samples, n_features=n_features, rank=rank, sigma=sigma)
    method_params = {'iter_n_components': [4, 5, 6]}
    cv = 3
    n_jobs = 1
    mode = 'factor_analysis'
    rescale = 100000000.0
    X *= rescale
    (est, info) = _auto_low_rank_model(X, mode=mode, n_jobs=n_jobs, method_params=method_params, cv=cv)
    assert_equal(info['best'], rank)
    X = get_data(n_samples=n_samples, n_features=n_features, rank=rank, sigma=sigma)
    method_params = {'iter_n_components': [(n_features + 5)]}
    msg = 'You    are    trying    to    estimate    %i    components    on    matrix    with    %i    features.'
    with warnings.catch_warnings(record=True) as w:
        warnings.simplefilter('always')
        _auto_low_rank_model(X, mode=mode, n_jobs=n_jobs, method_params=method_params, cv=cv)
        assert_equal(len(w), 1)
        assert_equal((msg % ((n_features + 5), n_features)), ('%s' % w[0].message))
    method_params = {'iter_n_components': [(n_features + 5)]}
    assert_raises(ValueError, _auto_low_rank_model, X, mode='foo', n_jobs=n_jobs, method_params=method_params, cv=cv)