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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 ltsa(geom, n_components, eigen_solver='auto', random_state=None, solver_kwds=None):
 """ Perform a Local Tangent Space Alignment analysis on the data. Parameters geom : a Geometry object from megaman.geometry.geometry n_components : integer number of coordinates for the manifold. eigen_solver : {'auto', 'dense', 'arpack', 'lobpcg', or 'amg'} 'auto' : algorithm will attempt to choose the best method for input data 'dense' : use standard dense matrix operations for the eigenvalue decomposition. For this method, M must be an array or matrix type. This method should be avoided for large problems. 'arpack' : use arnoldi iteration in shift-invert mode. For this method, M may be a dense matrix, sparse matrix, or general linear operator. Warning: ARPACK can be unstable for some problems. It is best to try several random seeds in order to check results. 'lobpcg' : Locally Optimal Block Preconditioned Conjugate Gradient Method. A preconditioned eigensolver for large symmetric positive definite (SPD) generalized eigenproblems. 'amg' : AMG requires pyamg to be installed. It can be faster on very large, sparse problems, but may also lead to instabilities. random_state : numpy.RandomState or int, optional The generator or seed used to determine the starting vector for arpack iterations. Defaults to numpy.random. solver_kwds : any additional keyword arguments to pass to the selected eigen_solver Returns ------- embedding : array-like, shape [n_samples, n_components] Embedding vectors. squared_error : float Reconstruction error for the embedding vectors. Equivalent to ``norm(Y - W Y, 'fro')**2``, where W are the reconstruction weights. References * Zhang, Z. & Zha, H. Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. Journal of Shanghai Univ. 8:406 (2004) """

    if geom.X is None:
        raise ValueError("Must pass data matrix X to Geometry")
    (N, d_in) = geom.X.shape
    if n_components > d_in:
        raise ValueError("output dimension must be less than or equal "
                         "to input dimension")
    # get the distance matrix and neighbors list
    if geom.adjacency_matrix is None:
        geom.compute_adjacency_matrix()
    (rows, cols) = geom.adjacency_matrix.nonzero()
    eigen_solver, solver_kwds = check_eigen_solver(eigen_solver, solver_kwds,
                                                   size=geom.adjacency_matrix.shape[0],
                                                   nvec=n_components + 1)
    if eigen_solver != 'dense':
        M = sparse.csr_matrix((N, N))
    else:
        M = np.zeros((N, N))
    for i in range(N):
        neighbors_i = cols[rows == i]
        n_neighbors_i = len(neighbors_i)
        use_svd = (n_neighbors_i > d_in)
        Xi = geom.X[neighbors_i]
        Xi -= Xi.mean(0)
        # compute n_components largest eigenvalues of Xi * Xi^T
        if use_svd:
            v = svd(Xi, full_matrices=True)[0]
        else:
            Ci = np.dot(Xi, Xi.T)
            v = eigh(Ci)[1][:, ::-1]
        Gi = np.zeros((n_neighbors_i, n_components + 1))
        Gi[:, 1:] = v[:, :n_components]
        Gi[:, 0] = 1. / np.sqrt(n_neighbors_i)
        GiGiT = np.dot(Gi, Gi.T)
        nbrs_x, nbrs_y = np.meshgrid(neighbors_i, neighbors_i)
        with warnings.catch_warnings():
            # sparse will complain this is better with lil_matrix but it doesn't work
            warnings.simplefilter("ignore")
            M[nbrs_x, nbrs_y] -= GiGiT
            M[neighbors_i, neighbors_i] += 1
    return null_space(M, n_components, k_skip=1, eigen_solver=eigen_solver,
                      random_state=random_state,solver_kwds=solver_kwds)