# Buggy code
def spectral_embedding(
    adjacency,
    n_components=8,
    eigen_solver=None,
    random_state=None,
    eigen_tol=0.0,
    norm_laplacian=True,
    drop_first=True,
    mode=None,
):
    """Project the sample on the first eigen vectors of the graph Laplacian.

    The adjacency matrix is used to compute a normalized graph Laplacian
    whose spectrum (especially the eigen vectors associated to the
    smallest eigen values) has an interpretation in terms of minimal
    number of cuts necessary to split the graph into comparably sized
    components.

    This embedding can also 'work' even if the ``adjacency`` variable is
    not strictly the adjacency matrix of a graph but more generally
    an affinity or similarity matrix between samples (for instance the
    heat kernel of a euclidean distance matrix or a k-NN matrix).

    However care must taken to always make the affinity matrix symmetric
    so that the eigen vector decomposition works as expected.

    Parameters
    ----------
    adjacency : array-like or sparse matrix, shape: (n_samples, n_samples)
        The adjacency matrix of the graph to embed.

    n_components : integer, optional
        The dimension of the projection subspace.

    eigen_solver : {None, 'arpack', 'lobpcg', or 'amg'}
        The eigenvalue decomposition strategy to use. AMG requires pyamg
        to be installed. It can be faster on very large, sparse problems,
        but may also lead to instabilities.

    random_state : int seed, RandomState instance, or None (default)
        A pseudo random number generator used for the initialization of the
        lobpcg eigen vectors decomposition when eigen_solver == 'amg'.
        By default, arpack is used.

    eigen_tol : float, optional, default=0.0
        Stopping criterion for eigendecomposition of the Laplacian matrix
        when using arpack eigen_solver.

    drop_first : bool, optional, default=True
        Whether to drop the first eigenvector. For spectral embedding, this
        should be True as the first eigenvector should be constant vector for
        connected graph, but for spectral clustering, this should be kept as
        False to retain the first eigenvector.

    Returns
    -------
    embedding : array, shape=(n_samples, n_components)
        The reduced samples.

    Notes
    -----
    Spectral embedding is most useful when the graph has one connected
    component. If there graph has many components, the first few eigenvectors
    will simply uncover the connected components of the graph.

    References
    ----------
    * http://en.wikipedia.org/wiki/LOBPCG

    * Toward the Optimal Preconditioned Eigensolver: Locally Optimal
      Block Preconditioned Conjugate Gradient Method
      Andrew V. Knyazev
      http://dx.doi.org/10.1137%2FS1064827500366124
    """

    try:
        from pyamg import smoothed_aggregation_solver
    except ImportError:
        if eigen_solver == "amg" or mode == "amg":
            raise ValueError(
                "The eigen_solver was set to 'amg', but pyamg is not available."
            )

    if not mode is None:
        warnings.warn(
            "'mode' was renamed to eigen_solver and will be removed in 0.15.",
            DeprecationWarning,
        )
        eigen_solver = mode

    if eigen_solver is None:
        eigen_solver = "arpack"
    elif not eigen_solver in ("arpack", "lobpcg", "amg"):
        raise ValueError(
            "Unknown value for eigen_solver: '%s'."
            "Should be 'amg', 'arpack', or 'lobpcg'" % eigen_solver
        )

    random_state = check_random_state(random_state)

    n_nodes = adjacency.shape[0]
    # Whether to drop the first eigenvector
    if drop_first:
        n_components = n_components + 1
    # Check that the matrices given is symmetric
    if (
        not sparse.isspmatrix(adjacency)
        and not np.all((adjacency - adjacency.T) < 1e-10)
    ) or (
        sparse.isspmatrix(adjacency)
        and not np.all((adjacency - adjacency.T).data < 1e-10)
    ):
        warnings.warn(
            "Graph adjacency matrix should be symmetric. "
            "Converted to be symmetric by average with its "
            "transpose."
        )
    adjacency = 0.5 * (adjacency + adjacency.T)

    if not _graph_is_connected(adjacency):
        warnings.warn(
            "Graph is not fully connected, spectral embedding may not work as expected."
        )

    laplacian, dd = graph_laplacian(adjacency, normed=norm_laplacian, return_diag=True)
    if (
        eigen_solver == "arpack"
        or eigen_solver != "lobpcg"
        and (not sparse.isspmatrix(laplacian) or n_nodes < 5 * n_components)
    ):
        # lobpcg used with eigen_solver='amg' has bugs for low number of nodes
        # for details see the source code in scipy:
        # https://github.com/scipy/scipy/blob/v0.11.0/scipy/sparse/linalg/eigen
        # /lobpcg/lobpcg.py#L237
        # or matlab:
        # http://www.mathworks.com/matlabcentral/fileexchange/48-lobpcg-m
        laplacian = _set_diag(laplacian, 1)

        # Here we'll use shift-invert mode for fast eigenvalues
        # (see http://docs.scipy.org/doc/scipy/reference/tutorial/arpack.html
        #  for a short explanation of what this means)
        # Because the normalized Laplacian has eigenvalues between 0 and 2,
        # I - L has eigenvalues between -1 and 1.  ARPACK is most efficient
        # when finding eigenvalues of largest magnitude (keyword which='LM')
        # and when these eigenvalues are very large compared to the rest.
        # For very large, very sparse graphs, I - L can have many, many
        # eigenvalues very near 1.0.  This leads to slow convergence.  So
        # instead, we'll use ARPACK's shift-invert mode, asking for the
        # eigenvalues near 1.0.  This effectively spreads-out the spectrum
        # near 1.0 and leads to much faster convergence: potentially an
        # orders-of-magnitude speedup over simply using keyword which='LA'
        # in standard mode.
        try:
            lambdas, diffusion_map = eigsh(
                -laplacian, k=n_components, sigma=1.0, which="LM", tol=eigen_tol
            )
            embedding = diffusion_map.T[n_components::-1] * dd
        except RuntimeError:
            # When submatrices are exactly singular, an LU decomposition
            # in arpack fails. We fallback to lobpcg
            eigen_solver = "lobpcg"

    if eigen_solver == "amg":
        # Use AMG to get a preconditioner and speed up the eigenvalue
        # problem.
        if not sparse.issparse(laplacian):
            warnings.warn("AMG works better for sparse matrices")
        laplacian = laplacian.astype(np.float)  # lobpcg needs native floats
        laplacian = _set_diag(laplacian, 1)
        ml = smoothed_aggregation_solver(atleast2d_or_csr(laplacian))
        M = ml.aspreconditioner()
        X = random_state.rand(laplacian.shape[0], n_components + 1)
        X[:, 0] = dd.ravel()
        lambdas, diffusion_map = lobpcg(laplacian, X, M=M, tol=1.0e-12, largest=False)
        embedding = diffusion_map.T * dd
        if embedding.shape[0] == 1:
            raise ValueError

    elif eigen_solver == "lobpcg":
        laplacian = laplacian.astype(np.float)  # lobpcg needs native floats
        if n_nodes < 5 * n_components + 1:
            # see note above under arpack why lobpcg has problems with small
            # number of nodes
            # lobpcg will fallback to symeig, so we short circuit it
            if sparse.isspmatrix(laplacian):
                laplacian = laplacian.toarray()
            lambdas, diffusion_map = symeig(laplacian)
            embedding = diffusion_map.T[:n_components] * dd
        else:
            # lobpcg needs native floats
            laplacian = laplacian.astype(np.float)
            laplacian = _set_diag(laplacian, 1)
            # We increase the number of eigenvectors requested, as lobpcg
            # doesn't behave well in low dimension
            X = random_state.rand(laplacian.shape[0], n_components + 1)
            X[:, 0] = dd.ravel()
            lambdas, diffusion_map = lobpcg(
                laplacian, X, tol=1e-15, largest=False, maxiter=2000
            )
            embedding = diffusion_map.T[:n_components] * dd
            if embedding.shape[0] == 1:
                raise ValueError
    if drop_first:
        return embedding[1:n_components].T
    else:
        return embedding[:n_components].T


# Traceback (IndexError)
======================================================================
ERROR: sklearn.tests.test_common.test_regressors_train('RANSACRegressor', <class 'sklearn.linear_model.ransac.RANSACRegr
essor'>, array([[-0.44836249, -0.47282444, -1.20608008, ..., -0.75500806,
----------------------------------------------------------------------
Traceback (most recent call last):
File "C:\Python27\lib\site-packages\nose\case.py", line 197, in runTest
self.test(*self.arg)
File "C:\Python27\lib\site-packages\sklearn\tests\test_common.py", line 850, in check_regressors_train
assert_raises(ValueError, regressor.fit, X, y[:-1])
File "C:\Python27\lib\unittest\case.py", line 473, in assertRaises
callableObj(*args, **kwargs)
File "C:\Python27\lib\site-packages\sklearn\linear_model\ransac.py", line 261, in fit
y_subset = y[subset_idxs]
IndexError: index 199 is out of bounds for axis 0 with size 199

# Fixed code
def spectral_embedding(
    adjacency,
    n_components=8,
    eigen_solver=None,
    random_state=None,
    eigen_tol=0.0,
    norm_laplacian=True,
    drop_first=True,
    mode=None,
):
    """Project the sample on the first eigen vectors of the graph Laplacian.

    The adjacency matrix is used to compute a normalized graph Laplacian
    whose spectrum (especially the eigen vectors associated to the
    smallest eigen values) has an interpretation in terms of minimal
    number of cuts necessary to split the graph into comparably sized
    components.

    This embedding can also 'work' even if the ``adjacency`` variable is
    not strictly the adjacency matrix of a graph but more generally
    an affinity or similarity matrix between samples (for instance the
    heat kernel of a euclidean distance matrix or a k-NN matrix).

    However care must taken to always make the affinity matrix symmetric
    so that the eigen vector decomposition works as expected.

    Parameters
    ----------
    adjacency : array-like or sparse matrix, shape: (n_samples, n_samples)
        The adjacency matrix of the graph to embed.

    n_components : integer, optional
        The dimension of the projection subspace.

    eigen_solver : {None, 'arpack', 'lobpcg', or 'amg'}
        The eigenvalue decomposition strategy to use. AMG requires pyamg
        to be installed. It can be faster on very large, sparse problems,
        but may also lead to instabilities.

    random_state : int seed, RandomState instance, or None (default)
        A pseudo random number generator used for the initialization of the
        lobpcg eigen vectors decomposition when eigen_solver == 'amg'.
        By default, arpack is used.

    eigen_tol : float, optional, default=0.0
        Stopping criterion for eigendecomposition of the Laplacian matrix
        when using arpack eigen_solver.

    drop_first : bool, optional, default=True
        Whether to drop the first eigenvector. For spectral embedding, this
        should be True as the first eigenvector should be constant vector for
        connected graph, but for spectral clustering, this should be kept as
        False to retain the first eigenvector.

    Returns
    -------
    embedding : array, shape=(n_samples, n_components)
        The reduced samples.

    Notes
    -----
    Spectral embedding is most useful when the graph has one connected
    component. If there graph has many components, the first few eigenvectors
    will simply uncover the connected components of the graph.

    References
    ----------
    * http://en.wikipedia.org/wiki/LOBPCG

    * Toward the Optimal Preconditioned Eigensolver: Locally Optimal
      Block Preconditioned Conjugate Gradient Method
      Andrew V. Knyazev
      http://dx.doi.org/10.1137%2FS1064827500366124
    """

    try:
        from pyamg import smoothed_aggregation_solver
    except ImportError:
        if eigen_solver == "amg" or mode == "amg":
            raise ValueError(
                "The eigen_solver was set to 'amg', but pyamg is not available."
            )

    if not mode is None:
        warnings.warn(
            "'mode' was renamed to eigen_solver and will be removed in 0.15.",
            DeprecationWarning,
        )
        eigen_solver = mode

    if eigen_solver is None:
        eigen_solver = "arpack"
    elif not eigen_solver in ("arpack", "lobpcg", "amg"):
        raise ValueError(
            "Unknown value for eigen_solver: '%s'."
            "Should be 'amg', 'arpack', or 'lobpcg'" % eigen_solver
        )

    random_state = check_random_state(random_state)

    n_nodes = adjacency.shape[0]
    # Whether to drop the first eigenvector
    if drop_first:
        n_components = n_components + 1
    # Check that the matrices given is symmetric
    if (
        not sparse.isspmatrix(adjacency)
        and not np.all((adjacency - adjacency.T) < 1e-10)
    ) or (
        sparse.isspmatrix(adjacency)
        and not np.all((adjacency - adjacency.T).data < 1e-10)
    ):
        warnings.warn(
            "Graph adjacency matrix should be symmetric. "
            "Converted to be symmetric by average with its "
            "transpose."
        )
    adjacency = 0.5 * (adjacency + adjacency.T)

    if not _graph_is_connected(adjacency):
        warnings.warn(
            "Graph is not fully connected, spectral embedding may not work as expected."
        )

    laplacian, dd = graph_laplacian(adjacency, normed=norm_laplacian, return_diag=True)
    if (
        eigen_solver == "arpack"
        or eigen_solver != "lobpcg"
        and (not sparse.isspmatrix(laplacian) or n_nodes < 5 * n_components)
    ):
        # lobpcg used with eigen_solver='amg' has bugs for low number of nodes
        # for details see the source code in scipy:
        # https://github.com/scipy/scipy/blob/v0.11.0/scipy/sparse/linalg/eigen
        # /lobpcg/lobpcg.py#L237
        # or matlab:
        # http://www.mathworks.com/matlabcentral/fileexchange/48-lobpcg-m
        laplacian = _set_diag(laplacian, 1)

        # Here we'll use shift-invert mode for fast eigenvalues
        # (see http://docs.scipy.org/doc/scipy/reference/tutorial/arpack.html
        #  for a short explanation of what this means)
        # Because the normalized Laplacian has eigenvalues between 0 and 2,
        # I - L has eigenvalues between -1 and 1.  ARPACK is most efficient
        # when finding eigenvalues of largest magnitude (keyword which='LM')
        # and when these eigenvalues are very large compared to the rest.
        # For very large, very sparse graphs, I - L can have many, many
        # eigenvalues very near 1.0.  This leads to slow convergence.  So
        # instead, we'll use ARPACK's shift-invert mode, asking for the
        # eigenvalues near 1.0.  This effectively spreads-out the spectrum
        # near 1.0 and leads to much faster convergence: potentially an
        # orders-of-magnitude speedup over simply using keyword which='LA'
        # in standard mode.
        try:
            lambdas, diffusion_map = eigsh(
                -laplacian, k=n_components, sigma=1.0, which="LM", tol=eigen_tol
            )
            embedding = diffusion_map.T[n_components::-1] * dd
        except RuntimeError:
            # When submatrices are exactly singular, an LU decomposition
            # in arpack fails. We fallback to lobpcg
            eigen_solver = "lobpcg"

    if eigen_solver == "amg":
        # Use AMG to get a preconditioner and speed up the eigenvalue
        # problem.
        if not sparse.issparse(laplacian):
            warnings.warn("AMG works better for sparse matrices")
        laplacian = laplacian.astype(np.float)  # lobpcg needs native floats
        laplacian = _set_diag(laplacian, 1)
        ml = smoothed_aggregation_solver(atleast2d_or_csr(laplacian))
        M = ml.aspreconditioner()
        X = random_state.rand(laplacian.shape[0], n_components + 1)
        X[:, 0] = dd.ravel()
        lambdas, diffusion_map = lobpcg(laplacian, X, M=M, tol=1.0e-12, largest=False)
        embedding = diffusion_map.T * dd
        if embedding.shape[0] == 1:
            raise ValueError

    elif eigen_solver == "lobpcg":
        laplacian = laplacian.astype(np.float)  # lobpcg needs native floats
        if n_nodes < 5 * n_components + 1:
            # see note above under arpack why lobpcg has problems with small
            # number of nodes
            # lobpcg will fallback to eigh, so we short circuit it
            if sparse.isspmatrix(laplacian):
                laplacian = laplacian.toarray()
            lambdas, diffusion_map = eigh(laplacian)
            embedding = diffusion_map.T[:n_components] * dd
        else:
            # lobpcg needs native floats
            laplacian = laplacian.astype(np.float)
            laplacian = _set_diag(laplacian, 1)
            # We increase the number of eigenvectors requested, as lobpcg
            # doesn't behave well in low dimension
            X = random_state.rand(laplacian.shape[0], n_components + 1)
            X[:, 0] = dd.ravel()
            lambdas, diffusion_map = lobpcg(
                laplacian, X, tol=1e-15, largest=False, maxiter=2000
            )
            embedding = diffusion_map.T[:n_components] * dd
            if embedding.shape[0] == 1:
                raise ValueError
    if drop_first:
        return embedding[1:n_components].T
    else:
        return embedding[:n_components].T