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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def spectral_layout(data, graph, dim, random_state, metric="euclidean", metric_kwds={}):
 """Given a graph compute the spectral embedding of the graph. This is simply the eigenvectors of the laplacian of the graph. Here we use the normalized laplacian. Parameters data: array of shape (n_samples, n_features) The source data graph: sparse matrix The (weighted) adjacency matrix of the graph as a sparse matrix. dim: int The dimension of the space into which to embed. random_state: numpy RandomState or equivalent A state capable being used as a numpy random state. Returns ------- embedding: array of shape (n_vertices, dim) The spectral embedding of the graph. """

    n_samples = graph.shape[0]
    n_components, labels = scipy.sparse.csgraph.connected_components(graph)

    if n_components > 1:
        warn(
            "Embedding a total of {} separate connected components using meta-embedding (experimental)".format(
                n_components
            )
        )
        return multi_component_layout(
            data,
            graph,
            n_components,
            labels,
            dim,
            random_state,
            metric=metric,
            metric_kwds=metric_kwds,
        )

    diag_data = np.asarray(graph.sum(axis=0))
    # standard Laplacian
    # D = scipy.sparse.spdiags(diag_data, 0, graph.shape[0], graph.shape[0])
    # L = D - graph
    # Normalized Laplacian
    I = scipy.sparse.identity(graph.shape[0], dtype=np.float64)
    D = scipy.sparse.spdiags(
        1.0 / np.sqrt(diag_data), 0, graph.shape[0], graph.shape[0]
    )
    L = I - D * graph * D

    k = dim + 1
    num_lanczos_vectors = max(2 * k + 1, int(np.sqrt(graph.shape[0])))
    try:
        if L.shape[0] < 2000000:
            eigenvalues, eigenvectors = scipy.sparse.linalg.eigsh(
                L,
                k,
                which="SM",
                ncv=num_lanczos_vectors,
                tol=1e-4,
                v0=np.ones(L.shape[0]),
                maxiter=graph.shape[0] * 5,
            )
        else:
            eigenvalues, eigenvectors = scipy.sparse.linalg.lobpcg(
                L,
                random_state.normal(size=(L.shape[0], k)),
                largest=False,
                tol=1e-8
            )
        order = np.argsort(eigenvalues)[1:k]
        return eigenvectors[:, order]
    except scipy.sparse.linalg.ArpackError:
        warn(
            "WARNING: spectral initialisation failed! The eigenvector solver\n"
            "failed. This is likely due to too small an eigengap. Consider\n"
            "adding some noise or jitter to your data.\n\n"
            "Falling back to random initialisation!"
        )
        return random_state.uniform(low=-10.0, high=10.0, size=(graph.shape[0], dim))