diff --git a/lang/zh/gklearn/preimage/random_preimage_generator.py b/lang/zh/gklearn/preimage/random_preimage_generator.py
new file mode 100644
index 0000000..cb28519
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+++ b/lang/zh/gklearn/preimage/random_preimage_generator.py
@@ -0,0 +1,389 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Fri May 29 14:29:52 2020
+
+@author: ljia
+"""
+
+import numpy as np
+import time
+import sys
+from tqdm import tqdm
+import multiprocessing
+import networkx as nx
+from multiprocessing import Pool
+from functools import partial
+from gklearn.preimage import PreimageGenerator
+from gklearn.preimage.utils import compute_k_dis
+from gklearn.utils import Timer
+from gklearn.utils.utils import get_graph_kernel_by_name
+# from gklearn.utils.dataset import Dataset
+
+
+class RandomPreimageGenerator(PreimageGenerator):
+	
+	def __init__(self, dataset=None):
+		PreimageGenerator.__init__(self, dataset=dataset)
+		# arguments to set.
+		self.__k = 5 # number of nearest neighbors of phi in D_N.
+		self.__r_max = 10 # maximum number of iterations.
+		self.__l = 500 # numbers of graphs generated for each graph in D_k U {g_i_hat}.
+		self.__alphas = None # weights of linear combinations of points in kernel space.
+		self.__parallel = True
+		self.__n_jobs = multiprocessing.cpu_count()
+		self.__time_limit_in_sec = 0
+		self.__max_itrs = 20
+		# values to compute.
+		self.__runtime_generate_preimage = None
+		self.__runtime_total = None
+		self.__preimage = None
+		self.__best_from_dataset = None
+		self.__k_dis_preimage = None
+		self.__k_dis_dataset = None
+		self.__itrs = 0
+		self.__converged = False # @todo
+		self.__num_updates = 0
+		# values that can be set or to be computed.
+		self.__gram_matrix_unnorm = None
+		self.__runtime_precompute_gm = None
+
+		
+	def set_options(self, **kwargs):
+		self._kernel_options = kwargs.get('kernel_options', {})
+		self._graph_kernel = kwargs.get('graph_kernel', None)
+		self._verbose = kwargs.get('verbose', 2)
+		self.__k = kwargs.get('k', 5)
+		self.__r_max = kwargs.get('r_max', 10)
+		self.__l = kwargs.get('l', 500)
+		self.__alphas = kwargs.get('alphas', None)
+		self.__parallel = kwargs.get('parallel', True)
+		self.__n_jobs = kwargs.get('n_jobs', multiprocessing.cpu_count())
+		self.__time_limit_in_sec = kwargs.get('time_limit_in_sec', 0)
+		self.__max_itrs = kwargs.get('max_itrs', 20)
+		self.__gram_matrix_unnorm = kwargs.get('gram_matrix_unnorm', None)
+		self.__runtime_precompute_gm = kwargs.get('runtime_precompute_gm', None)
+		
+		
+	def run(self):
+		self._graph_kernel = get_graph_kernel_by_name(self._kernel_options['name'], 
+						  node_labels=self._dataset.node_labels,
+						  edge_labels=self._dataset.edge_labels, 
+						  node_attrs=self._dataset.node_attrs,
+						  edge_attrs=self._dataset.edge_attrs,
+						  ds_infos=self._dataset.get_dataset_infos(keys=['directed']),
+						  kernel_options=self._kernel_options)
+		
+		# record start time.
+		start = time.time()
+		
+		# 1. precompute gram matrix.
+		if self.__gram_matrix_unnorm is None:
+			gram_matrix, run_time = self._graph_kernel.compute(self._dataset.graphs, **self._kernel_options)
+			self.__gram_matrix_unnorm = self._graph_kernel.gram_matrix_unnorm
+			end_precompute_gm = time.time()
+			self.__runtime_precompute_gm = end_precompute_gm - start
+		else:
+			if self.__runtime_precompute_gm is None:
+				raise Exception('Parameter "runtime_precompute_gm" must be given when using pre-computed Gram matrix.')
+			self._graph_kernel.gram_matrix_unnorm = self.__gram_matrix_unnorm
+			if self._kernel_options['normalize']:
+				self._graph_kernel.gram_matrix = self._graph_kernel.normalize_gm(np.copy(self.__gram_matrix_unnorm))
+			else:
+				self._graph_kernel.gram_matrix = np.copy(self.__gram_matrix_unnorm)
+			end_precompute_gm = time.time()
+			start -= self.__runtime_precompute_gm
+			
+		# 2. compute k nearest neighbors of phi in D_N.
+		if self._verbose >= 2:
+			print('\nstart computing k nearest neighbors of phi in D_N...\n')
+		D_N = self._dataset.graphs
+		if self.__alphas is None:
+			self.__alphas = [1 / len(D_N)] * len(D_N)
+		k_dis_list = [] # distance between g_star and each graph.
+		term3 = 0
+		for i1, a1 in enumerate(self.__alphas):
+			for i2, a2 in enumerate(self.__alphas):
+				term3 += a1 * a2 * self._graph_kernel.gram_matrix[i1, i2]
+		for idx in range(len(D_N)):
+			k_dis_list.append(compute_k_dis(idx, range(0, len(D_N)), self.__alphas, self._graph_kernel.gram_matrix, term3=term3, withterm3=True))
+			
+		# sort.
+		sort_idx = np.argsort(k_dis_list)
+		dis_gs = [k_dis_list[idis] for idis in sort_idx[0:self.__k]] # the k shortest distances.
+		nb_best = len(np.argwhere(dis_gs == dis_gs[0]).flatten().tolist())
+		g0hat_list = [D_N[idx].copy() for idx in sort_idx[0:nb_best]] # the nearest neighbors of phi in D_N
+		self.__best_from_dataset = g0hat_list[0] # get the first best graph if there are muitlple.
+		self.__k_dis_dataset = dis_gs[0]
+		
+		if self.__k_dis_dataset == 0: # get the exact pre-image.
+			end_generate_preimage = time.time()
+			self.__runtime_generate_preimage = end_generate_preimage - end_precompute_gm
+			self.__runtime_total = end_generate_preimage - start
+			self.__preimage = self.__best_from_dataset.copy()	
+			self.__k_dis_preimage = self.__k_dis_dataset
+			if self._verbose:
+				print()
+				print('=============================================================================')
+				print('The exact pre-image is found from the input dataset.')
+				print('-----------------------------------------------------------------------------')
+				print('Distance in kernel space for the best graph from dataset and for preimage:', self.__k_dis_dataset)
+				print('Time to pre-compute Gram matrix:', self.__runtime_precompute_gm)
+				print('Time to generate pre-images:', self.__runtime_generate_preimage)
+				print('Total time:', self.__runtime_total)
+				print('=============================================================================')
+				print()
+			return
+		
+		dhat = dis_gs[0] # the nearest distance
+		Gk = [D_N[ig].copy() for ig in sort_idx[0:self.__k]] # the k nearest neighbors
+		Gs_nearest = [nx.convert_node_labels_to_integers(g) for g in Gk] # [g.copy() for g in Gk]
+		
+		# 3. start iterations.
+		if self._verbose >= 2:
+			print('starting iterations...')
+		gihat_list = []
+		dihat_list = []
+		r = 0
+		dis_of_each_itr = [dhat]
+		if self.__parallel:
+			self._kernel_options['parallel'] = None
+		self.__itrs = 0
+		self.__num_updates = 0
+		timer = Timer(self.__time_limit_in_sec)
+		while not self.__termination_criterion_met(timer, self.__itrs, r):
+			print('\n- r =', r)
+			found = False
+			dis_bests = dis_gs + dihat_list
+			
+			# compute numbers of edges to be inserted/deleted.
+			# @todo what if the log is negetive? how to choose alpha (scalar)?
+			fdgs_list = np.array(dis_bests)
+			if np.min(fdgs_list) < 1: # in case the log is negetive.
+				fdgs_list /= np.min(fdgs_list)
+			fdgs_list = [int(item) for item in np.ceil(np.log(fdgs_list))]
+			if np.min(fdgs_list) < 1: # in case the log is smaller than 1.
+				fdgs_list = np.array(fdgs_list) + 1
+			# expand the number of modifications to increase the possiblity.
+			nb_vpairs_list = [nx.number_of_nodes(g) * (nx.number_of_nodes(g) - 1) for g in (Gs_nearest + gihat_list)]
+			nb_vpairs_min = np.min(nb_vpairs_list)
+			idx_fdgs_max = np.argmax(fdgs_list)
+			fdgs_max_old = fdgs_list[idx_fdgs_max]
+			fdgs_max = fdgs_max_old
+			nb_modif = 1
+			for idx, nb in enumerate(range(nb_vpairs_min, nb_vpairs_min - fdgs_max, -1)):
+				nb_modif *= nb / (fdgs_max - idx)
+			while fdgs_max < nb_vpairs_min and nb_modif < self.__l:
+				fdgs_max += 1
+				nb_modif *= (nb_vpairs_min - fdgs_max + 1) / fdgs_max
+			nb_increase = int(fdgs_max - fdgs_max_old)
+			if nb_increase > 0:
+				fdgs_list += 1
+				
+				
+			for ig, gs in enumerate(Gs_nearest + gihat_list):
+				if self._verbose >= 2:
+					print('-- computing', ig + 1, 'graphs out of', len(Gs_nearest) + len(gihat_list))
+				gnew, dhat, found = self.__generate_l_graphs(gs, fdgs_list[ig], dhat, ig, found, term3)
+						  
+			if found:
+				r = 0
+				gihat_list = [gnew]
+				dihat_list = [dhat]
+			else:
+				r += 1
+				
+			dis_of_each_itr.append(dhat)
+			self.__itrs += 1
+			if self._verbose >= 2:
+				print('Total number of iterations is', self.__itrs, '.')
+				print('The preimage is updated', self.__num_updates, 'times.')
+				print('The shortest distances for previous iterations are', dis_of_each_itr, '.')
+			
+			
+		# get results and print.
+		end_generate_preimage = time.time()
+		self.__runtime_generate_preimage = end_generate_preimage - end_precompute_gm
+		self.__runtime_total = end_generate_preimage - start
+		self.__preimage = (g0hat_list[0] if len(gihat_list) == 0 else gihat_list[0])
+		self.__k_dis_preimage = dhat
+		if self._verbose:
+			print()
+			print('=============================================================================')
+			print('Finished generation of preimages.')
+			print('-----------------------------------------------------------------------------')
+			print('Distance in kernel space for the best graph from dataset:', self.__k_dis_dataset)
+			print('Distance in kernel space for the preimage:', self.__k_dis_preimage)
+			print('Total number of iterations for optimizing:', self.__itrs)
+			print('Total number of updating preimage:', self.__num_updates)
+			print('Time to pre-compute Gram matrix:', self.__runtime_precompute_gm)
+			print('Time to generate pre-images:', self.__runtime_generate_preimage)
+			print('Total time:', self.__runtime_total)
+			print('=============================================================================')
+			print()	
+			
+			
+	def __generate_l_graphs(self, g_init, fdgs, dhat, ig, found, term3):
+		if self.__parallel:
+			gnew, dhat, found = self.__generate_l_graphs_parallel(g_init, fdgs, dhat, ig, found, term3)
+		else:
+			gnew, dhat, found = self.__generate_l_graphs_series(g_init, fdgs, dhat, ig, found, term3)
+		return gnew, dhat, found
+			
+			
+	def __generate_l_graphs_series(self, g_init, fdgs, dhat, ig, found, term3):
+		gnew = None
+		updated = False
+		for trial in range(0, self.__l):
+			if self._verbose >= 2:
+				print('---', trial + 1, 'trial out of', self.__l)
+
+			gtemp, dnew = self.__do_trial(g_init, fdgs, term3, trial)
+
+			# get the better graph preimage.
+			if dnew <= dhat: # @todo: the new distance is smaller or also equal?
+				if dhat - dnew > 1e-6:
+					if self._verbose >= 2:
+						print('trial =', str(trial))
+						print('\nI am smaller!')
+						print('index (as in D_k U {gihat} =', str(ig))
+						print('distance:', dhat, '->', dnew)
+					updated = True
+				else:
+					if self._verbose >= 2:
+						print('I am equal!') 
+				dhat = dnew
+				gnew = gtemp.copy()
+				found = True # found better or equally good graph.
+		
+		if updated:
+			self.__num_updates += 1
+				
+		return gnew, dhat, found
+	
+	
+	def __generate_l_graphs_parallel(self, g_init, fdgs, dhat, ig, found, term3):
+		gnew = None
+		len_itr = self.__l
+		gnew_list = [None] * len_itr
+		dnew_list = [None] * len_itr
+		itr = range(0, len_itr)
+		n_jobs = multiprocessing.cpu_count()
+		if len_itr < 100 * n_jobs:
+			chunksize = int(len_itr / n_jobs) + 1
+		else:
+			chunksize = 100
+		do_fun = partial(self._generate_graph_parallel, g_init, fdgs, term3)
+		pool = Pool(processes=n_jobs)
+		if self._verbose >= 2:
+			iterator = tqdm(pool.imap_unordered(do_fun, itr, chunksize),
+						desc='Generating l graphs', file=sys.stdout)
+		else:
+			iterator = pool.imap_unordered(do_fun, itr, chunksize)
+		for idx, gnew, dnew in iterator:
+			gnew_list[idx] = gnew
+			dnew_list[idx] = dnew
+		pool.close()
+		pool.join()
+		
+		# check if get the better graph preimage.
+		idx_min = np.argmin(dnew_list)
+		dnew = dnew_list[idx_min]
+		if dnew <= dhat: # @todo: the new distance is smaller or also equal?
+			if dhat - dnew > 1e-6: # @todo: use a proportion and watch out for 0.
+				if self._verbose >= 2:
+					print('I am smaller!')
+					print('index (as in D_k U {gihat}) =', str(ig))
+					print('distance:', dhat, '->', dnew, '\n')
+				self.__num_updates += 1
+			else:
+				if self._verbose >= 2:
+					print('I am equal!') 
+			dhat = dnew
+			gnew = gnew_list[idx_min]
+			found = True # found better graph.
+				
+		return gnew, dhat, found
+		
+		
+	def _generate_graph_parallel(self, g_init, fdgs, term3, itr):
+		trial = itr			
+		gtemp, dnew = self.__do_trial(g_init, fdgs, term3, trial)		
+		return trial, gtemp, dnew
+	
+	
+	def __do_trial(self, g_init, fdgs, term3, trial):
+		# add and delete edges.
+		gtemp = g_init.copy()
+		seed = (trial + int(time.time())) % (2 ** 32 - 1)
+		rdm_state = np.random.RandomState(seed=seed)
+		# which edges to change.
+		# @todo: should we use just half of the adjacency matrix for undirected graphs?
+		nb_vpairs = nx.number_of_nodes(g_init) * (nx.number_of_nodes(g_init) - 1)
+		# @todo: what if fdgs is bigger than nb_vpairs?
+		idx_change = rdm_state.randint(0, high=nb_vpairs, size=(fdgs if 
+									   fdgs < nb_vpairs else nb_vpairs))
+# 		print(idx_change)
+		for item in idx_change:
+			node1 = int(item / (nx.number_of_nodes(g_init) - 1))
+			node2 = (item - node1 * (nx.number_of_nodes(g_init) - 1))
+			if node2 >= node1: # skip the self pair.
+				node2 += 1
+			# @todo: is the randomness correct?
+			if not gtemp.has_edge(node1, node2):
+				gtemp.add_edge(node1, node2)
+			else:
+				gtemp.remove_edge(node1, node2)
+				
+		# compute new distances.
+		kernels_to_gtmp, _ = self._graph_kernel.compute(gtemp, self._dataset.graphs, **self._kernel_options)
+		kernel_gtmp, _ = self._graph_kernel.compute(gtemp, gtemp, **self._kernel_options)
+		if self._kernel_options['normalize']:
+			kernels_to_gtmp = [kernels_to_gtmp[i] / np.sqrt(self.__gram_matrix_unnorm[i, i] * kernel_gtmp) for i in range(len(kernels_to_gtmp))] # normalize 
+			kernel_gtmp = 1
+		# @todo: not correct kernel value
+		gram_with_gtmp = np.concatenate((np.array([kernels_to_gtmp]), np.copy(self._graph_kernel.gram_matrix)), axis=0)
+		gram_with_gtmp = np.concatenate((np.array([[kernel_gtmp] + kernels_to_gtmp]).T, gram_with_gtmp), axis=1)
+		dnew = compute_k_dis(0, range(1, 1 + len(self._dataset.graphs)), self.__alphas, gram_with_gtmp, term3=term3, withterm3=True)
+		
+		return gtemp, dnew
+			
+
+	def get_results(self):
+		results = {}
+		results['runtime_precompute_gm'] = self.__runtime_precompute_gm
+		results['runtime_generate_preimage'] = self.__runtime_generate_preimage
+		results['runtime_total'] = self.__runtime_total
+		results['k_dis_dataset'] = self.__k_dis_dataset
+		results['k_dis_preimage'] = self.__k_dis_preimage
+		results['itrs'] = self.__itrs
+		results['num_updates'] = self.__num_updates
+		return results
+
+
+	def __termination_criterion_met(self, timer, itr, r):
+		if timer.expired() or (itr >= self.__max_itrs if self.__max_itrs >= 0 else False):
+# 			if self.__state == AlgorithmState.TERMINATED:
+# 				self.__state = AlgorithmState.INITIALIZED
+			return True
+		return (r >= self.__r_max if self.__r_max >= 0 else False)
+# 		return converged or (itrs_without_update > self.__max_itrs_without_update if self.__max_itrs_without_update >= 0 else False)
+		
+	
+	@property
+	def preimage(self):
+		return self.__preimage
+	
+	
+	@property
+	def best_from_dataset(self):
+		return self.__best_from_dataset
+	
+		
+	@property
+	def gram_matrix_unnorm(self):
+		return self.__gram_matrix_unnorm
+	
+	@gram_matrix_unnorm.setter
+	def gram_matrix_unnorm(self, value):
+		self.__gram_matrix_unnorm = value
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