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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 _cart_dists(self, s1, s2, avg_lattice, mask, normalization, lll_frac_tol=None):
 """ Finds a matching in cartesian space. Finds an additional fractional translation vector to minimize RMS distance Args: s1, s2: numpy arrays of fractional coordinates. len(s1) >= len(s2) avg_lattice: Lattice on which to calculate distances mask: numpy array of booleans. mask[i, j] = True indicates that s2[i] cannot be matched to s1[j] normalization (float):
 inverse normalization length Returns: Distances from s2 to s1, normalized by (V/Natom) ^ 1/3 Fractional translation vector to apply to s2. Mapping from s1 to s2, i.e. with numpy slicing, s1[mapping] => s2 """

        if len(s2) > len(s1):
            raise ValueError("s1 must be larger than s2")
        if mask.shape != (len(s2), len(s1)):
            raise ValueError("mask has incorrect shape")

        # vectors are from s2 to s1
        vecs, d_2 = pbc_shortest_vectors(avg_lattice, s2, s1, mask,
                                         return_d2=True,
                                         lll_frac_tol=lll_frac_tol)
        lin = LinearAssignment(d_2)
        s = lin.solution
        short_vecs = vecs[np.arange(len(s)), s]
        translation = np.average(short_vecs, axis=0)
        f_translation = avg_lattice.get_fractional_coords(translation)
        new_d2 = np.sum((short_vecs - translation) ** 2, axis=-1)

        return new_d2 ** 0.5 * normalization, f_translation, s