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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_local_maximum(self, input_sample, N, num_params, k_choices, num_groups=None):
 """Find the most different trajectories in the input sample using a local approach An alternative by Ruano et al. (2012) for the brute force approach as originally proposed by Campolongo et al. (2007). The method should improve the speed with which an optimal set of trajectories is found tremendously for larger sample sizes. Arguments --------- input_sample : np.ndarray N : int The number of trajectories num_params : int The number of factors k_choices : int The number of optimal trajectories to return num_groups : int, default=None The number of groups Returns ------- list """

        distance_matrix = self.compute_distance_matrix(input_sample, N,
                                                       num_params, num_groups,
                                                       local_optimization=True)

        tot_indices_list = []
        tot_max_array = np.zeros(k_choices - 1)

        # Loop over `k_choices`, i starts at 1
        for i in range(1, k_choices):
            indices_list = []
            row_maxima_i = np.zeros(len(distance_matrix))

            row_nr = 0
            for row in distance_matrix:
                indices = tuple(row.argsort()[-i:][::-1]) + (row_nr,)
                row_maxima_i[row_nr] = self.sum_distances(
                    indices, distance_matrix)
                indices_list.append(indices)
                row_nr += 1

            # Find the indices belonging to the maximum distance
            i_max_ind = self.get_max_sum_ind(indices_list, row_maxima_i, i, 0)

            # Loop 'm' (called loop 'k' in Ruano)
            m_max_ind = i_max_ind
            # m starts at 1
            m = 1

            while m <= k_choices - i - 1:
                m_ind = self.add_indices(m_max_ind, distance_matrix)

                m_maxima = np.zeros(len(m_ind))

                for n in range(0, len(m_ind)):
                    m_maxima[n] = self.sum_distances(m_ind[n], distance_matrix)

                m_max_ind = self.get_max_sum_ind(m_ind, m_maxima, i, m)

                m += 1

            tot_indices_list.append(m_max_ind)
            tot_max_array[i -
                          1] = self.sum_distances(m_max_ind, distance_matrix)

        tot_max = self.get_max_sum_ind(
            tot_indices_list, tot_max_array, "tot", "tot")
        return sorted(list(tot_max))