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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 preprocess(S, coloring_method=None):
 """Preprocess splitting functions. Parameters S : csr_matrix Strength of connection matrix method : string Algorithm used to compute the vertex coloring: * 'MIS' - Maximal Independent Set * 'JP' - Jones-Plassmann (parallel) * 'LDF' - Largest-Degree-First (parallel) Returns ------- weights: ndarray Weights from a graph coloring of G S : csr_matrix Strength matrix with ones T : csr_matrix transpose of S G : csr_matrix union of S and T Notes ----- Performs the following operations: - Checks input strength of connection matrix S - Replaces S.data with ones - Creates T = S.T in CSR format - Creates G = S union T in CSR format - Creates random weights - Augments weights with graph coloring (if use_color == True) """

    if not isspmatrix_csr(S):
        raise TypeError('expected csr_matrix')

    if S.shape[0] != S.shape[1]:
        raise ValueError('expected square matrix, shape=%s' % (S.shape,))

    N = S.shape[0]
    S = csr_matrix((np.ones(S.nnz, dtype='int8'), S.indices, S.indptr),
                   shape=(N, N))
    T = S.T.tocsr()  # transpose S for efficient column access

    G = S + T  # form graph (must be symmetric)
    G.data[:] = 1

    weights = np.ravel(T.sum(axis=1))  # initial weights
    # weights -= T.diagonal()          # discount self loops

    if coloring_method is None:
        weights = weights + sp.rand(len(weights))
    else:
        coloring = vertex_coloring(G, coloring_method)
        num_colors = coloring.max() + 1
        weights = weights + (sp.rand(len(weights)) + coloring)/num_colors

    return (weights, G, S, T)