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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 find_all_mappings( self, other_lattice: "Lattice", ltol: float = 1e-5, atol: float = 1, skip_rotation_matrix: bool = False, ) -> Iterator[Tuple["Lattice", Optional[np.ndarray], np.ndarray]]: """ Finds all mappings between current lattice and another lattice. Args: other_lattice (Lattice):
 Another lattice that is equivalent to this one. ltol (float):
 Tolerance for matching lengths. Defaults to 1e-5. atol (float):
 Tolerance for matching angles. Defaults to 1. skip_rotation_matrix (bool):
 Whether to skip calculation of the rotation matrix Yields: (aligned_lattice, rotation_matrix, scale_matrix) if a mapping is found. aligned_lattice is a rotated version of other_lattice that has the same lattice parameters, but which is aligned in the coordinate system of this lattice so that translational points match up in 3D. rotation_matrix is the rotation that has to be applied to other_lattice to obtain aligned_lattice, i.e., aligned_matrix = np.inner(other_lattice, rotation_matrix) and op = SymmOp.from_rotation_and_translation(rotation_matrix) aligned_matrix = op.operate_multi(latt.matrix) Finally, scale_matrix is the integer matrix that expresses aligned_matrix as a linear combination of this lattice, i.e., aligned_matrix = np.dot(scale_matrix, self.matrix) None is returned if no matches are found. """

        (lengths, angles) = other_lattice.lengths_and_angles
        (alpha, beta, gamma) = angles

        frac, dist, _, _ = self.get_points_in_sphere(
            [[0, 0, 0]], [0, 0, 0], max(lengths) * (1 + ltol), zip_results=False
        )
        cart = self.get_cartesian_coords(frac)
        # this can't be broadcast because they're different lengths
        inds = [
            np.logical_and(dist / l < 1 + ltol, dist / l > 1 / (1 + ltol))
            for l in lengths
        ]
        c_a, c_b, c_c = (cart[i] for i in inds)
        f_a, f_b, f_c = (frac[i] for i in inds)
        l_a, l_b, l_c = (np.sum(c ** 2, axis=-1) ** 0.5 for c in (c_a, c_b, c_c))

        def get_angles(v1, v2, l1, l2):
            x = np.inner(v1, v2) / l1[:, None] / l2
            x[x > 1] = 1
            x[x < -1] = -1
            angles = np.arccos(x) * 180.0 / pi
            return angles

        alphab = np.abs(get_angles(c_b, c_c, l_b, l_c) - alpha) < atol
        betab = np.abs(get_angles(c_a, c_c, l_a, l_c) - beta) < atol
        gammab = np.abs(get_angles(c_a, c_b, l_a, l_b) - gamma) < atol

        for i, all_j in enumerate(gammab):
            inds = np.logical_and(
                all_j[:, None], np.logical_and(alphab, betab[i][None, :])
            )
            for j, k in np.argwhere(inds):
                scale_m = np.array((f_a[i], f_b[j], f_c[k]), dtype=np.int)
                if abs(np.linalg.det(scale_m)) < 1e-8:
                    continue

                aligned_m = np.array((c_a[i], c_b[j], c_c[k]))

                if skip_rotation_matrix:
                    rotation_m = None
                else:
                    rotation_m = np.linalg.solve(aligned_m, other_lattice.matrix)

                yield Lattice(aligned_m), rotation_m, scale_m