test_extmath.py 文件源码

def test_randomized_svd_low_rank():
    # Check that extmath.randomized_svd is consistent with linalg.svd
    n_samples = 100
    n_features = 500
    rank = 5
    k = 10

    # generate a matrix X of approximate effective rank `rank` and no noise
    # component (very structured signal):
    X = make_low_rank_matrix(n_samples=n_samples, n_features=n_features,
                             effective_rank=rank, tail_strength=0.0,
                             random_state=0)
    assert_equal(X.shape, (n_samples, n_features))

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

    for normalizer in ['auto', 'LU', 'QR']:  # 'none' would not be stable
        # compute the singular values of X using the fast approximate method
        Ua, sa, Va = \
            randomized_svd(X, k, power_iteration_normalizer=normalizer,
                           random_state=0)
        assert_equal(Ua.shape, (n_samples, k))
        assert_equal(sa.shape, (k,))
        assert_equal(Va.shape, (k, n_features))

        # ensure that the singular values of both methods are equal up to the
        # real rank of the matrix
        assert_almost_equal(s[:k], sa)

        # check the singular vectors too (while not checking the sign)
        assert_almost_equal(np.dot(U[:, :k], V[:k, :]), np.dot(Ua, Va))

        # check the sparse matrix representation
        X = sparse.csr_matrix(X)

        # compute the singular values of X using the fast approximate method
        Ua, sa, Va = \
            randomized_svd(X, k, power_iteration_normalizer=normalizer,
                           random_state=0)
        assert_almost_equal(s[:rank], sa[:rank])