test_extmath.py 文件源码

def test_randomized_svd_low_rank_with_noise():
    # Check that extmath.randomized_svd can handle noisy matrices
    n_samples = 100
    n_features = 500
    rank = 5
    k = 10

    # generate a matrix X wity structure approximate rank `rank` and an
    # important noisy component
    X = make_low_rank_matrix(n_samples=n_samples, n_features=n_features,
                             effective_rank=rank, tail_strength=0.1,
                             random_state=0)
    assert_equal(X.shape, (n_samples, n_features))

    # compute the singular values of X using the slow exact method
    _, s, _ = linalg.svd(X, full_matrices=False)

    for normalizer in ['auto', 'none', 'LU', 'QR']:
        # compute the singular values of X using the fast approximate
        # method without the iterated power method
        _, sa, _ = randomized_svd(X, k, n_iter=0,
                                  power_iteration_normalizer=normalizer,
                                  random_state=0)

        # the approximation does not tolerate the noise:
        assert_greater(np.abs(s[:k] - sa).max(), 0.01)

        # compute the singular values of X using the fast approximate
        # method with iterated power method
        _, sap, _ = randomized_svd(X, k,
                                   power_iteration_normalizer=normalizer,
                                   random_state=0)

        # the iterated power method is helping getting rid of the noise:
        assert_almost_equal(s[:k], sap, decimal=3)