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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 modified_lu(q):
 """Perform a modified LU decomposition of a matrix. This takes a matrix q with orthonormal columns, returns l, u, s such that q - s = l * u. Args: q: A two dimensional orthonormal matrix q. Returns: A tuple of a lower triangular matrix l, an upper triangular matrix u, and a a vector representing a diagonal matrix s such that q - s = l * u. """

    q = q.assemble()
    m, b = q.shape[0], q.shape[1]
    S = np.zeros(b)

    q_work = np.copy(q)

    for i in range(b):
        S[i] = -1 * np.sign(q_work[i, i])
        q_work[i, i] -= S[i]
        # Scale ith column of L by diagonal element.
        q_work[(i + 1):m, i] /= q_work[i, i]
        # Perform Schur complement update.
        q_work[(i + 1):m, (i + 1):b] -= np.outer(q_work[(i + 1):m, i],
                                                 q_work[i, (i + 1):b])

    L = np.tril(q_work)
    for i in range(b):
        L[i, i] = 1
    U = np.triu(q_work)[:b, :]
    # TODO(rkn): Get rid of the put below.
    return ray.get(core.numpy_to_dist.remote(ray.put(L))), U, S