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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 cause_repertoire(self, mechanism, purview):
 """Return the cause repertoire of a mechanism over a purview. Args: mechanism (tuple[int]):
 The mechanism for which to calculate the cause repertoire. purview (tuple[int]):
 The purview over which to calculate the cause repertoire. Returns: np.ndarray: The cause repertoire of the mechanism over the purview. .. note:: The returned repertoire is a distribution over purview node states, not the states of the whole network. """

        # If the purview is empty, the distribution is empty; return the
        # multiplicative identity.
        if not purview:
            return np.array([1.0])
        # If the mechanism is empty, nothing is specified about the previous
        # state of the purview; return the purview's maximum entropy
        # distribution.
        if not mechanism:
            return max_entropy_distribution(purview, self.tpm_size)
        # Use a frozenset so the arguments to `_single_node_cause_repertoire`
        # can be hashed and cached.
        purview = frozenset(purview)
        # Preallocate the repertoire with the proper shape, so that
        # probabilities are broadcasted appropriately.
        joint = np.ones(repertoire_shape(purview, self.tpm_size))
        # The cause repertoire is the product of the cause repertoires of the
        # individual nodes.
        joint *= functools.reduce(
            np.multiply, [self._single_node_cause_repertoire(m, purview)
                          for m in mechanism]
        )
        # The resulting joint distribution is over previous states, which are
        # rows in the TPM, so the distribution is a column. The columns of a
        # TPM don't necessarily sum to 1, so we normalize.
        return distribution.normalize(joint)