def fast_ordering(self, structure, num_remove_dict, num_to_return=1):
        """
        This method uses the matrix form of ewaldsum to calculate the ewald
        sums of the potential structures. This is on the order of 4 orders of
        magnitude faster when there are large numbers of permutations to
        consider. There are further optimizations possible (doing a smarter
        search of permutations for example), but this wont make a difference
        until the number of permutations is on the order of 30,000.
        """
        self.logger.debug("Performing fast ordering")
        starttime = time.time()
        self.logger.debug("Performing initial ewald sum...")

        ewaldmatrix = EwaldSummation(structure).total_energy_matrix
        self.logger.debug("Ewald sum took {} seconds."
                          .format(time.time() - starttime))
        starttime = time.time()
        m_list = []
        for indices, num in num_remove_dict.items():
            m_list.append([0, num, list(indices), None])

        self.logger.debug("Calling EwaldMinimizer...")
        minimizer = EwaldMinimizer(ewaldmatrix, m_list, num_to_return,
                                   PartialRemoveSitesTransformation.ALGO_FAST)
        self.logger.debug("Minimizing Ewald took {} seconds."
                          .format(time.time() - starttime))

        all_structures = []

        lowest_energy = minimizer.output_lists[0][0]
        num_atoms = sum(structure.composition.values())

        for output in minimizer.output_lists:
            s = structure.copy()
            del_indices = []

            for manipulation in output[1]:
                if manipulation[1] is None:
                    del_indices.append(manipulation[0])
                else:
                    s.replace(manipulation[0], manipulation[1])
            s.remove_sites(del_indices)
            struct = s.get_sorted_structure()
            all_structures.append(
                {"energy": output[0],
                 "energy_above_minimum": (output[0] - lowest_energy)
                    / num_atoms,
                 "structure": struct})

        return all_structures