New translations sylvester_equation.py (French)

lang/fr/gklearn/kernels/sylvester_equation.py

@@ -0,0 +1,245 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Wed Aug 19 17:24:46 2020
+
+@author: ljia
+
+@references: 
+
+	[1] S Vichy N Vishwanathan, Nicol N Schraudolph, Risi Kondor, and Karsten M Borgwardt. Graph kernels. Journal of Machine Learning Research, 11(Apr):1201–1242, 2010.
+"""
+
+import sys
+from tqdm import tqdm
+import numpy as np
+import networkx as nx
+from control import dlyap
+from gklearn.utils.parallel import parallel_gm, parallel_me
+from gklearn.kernels import RandomWalk
+
+
+class SylvesterEquation(RandomWalk):
+	
+	
+	def __init__(self, **kwargs):
+		RandomWalk.__init__(self, **kwargs)
+		
+
+	def _compute_gm_series(self):
+		self._check_edge_weight(self._graphs)
+		self._check_graphs(self._graphs)
+		if self._verbose >= 2:
+			import warnings
+			warnings.warn('All labels are ignored.')
+			
+		lmda = self._weight
+				
+		# compute Gram matrix.
+		gram_matrix = np.zeros((len(self._graphs), len(self._graphs)))		
+		
+		if self._q == None:
+			# don't normalize adjacency matrices if q is a uniform vector. Note
+			# A_wave_list actually contains the transposes of the adjacency matrices.
+			if self._verbose >= 2:
+				iterator = tqdm(self._graphs, desc='compute adjacency matrices', file=sys.stdout)
+			else:
+				iterator = self._graphs
+			A_wave_list = [nx.adjacency_matrix(G, self._edge_weight).todense().transpose() for G in iterator]
+	#		# normalized adjacency matrices
+	#		A_wave_list = []
+	#		for G in tqdm(Gn, desc='compute adjacency matrices', file=sys.stdout):
+	#			A_tilde = nx.adjacency_matrix(G, eweight).todense().transpose()   
+	#			norm = A_tilde.sum(axis=0)
+	#			norm[norm == 0] = 1
+	#			A_wave_list.append(A_tilde / norm)
+
+			if self._p == None: # p is uniform distribution as default.
+				from itertools import combinations_with_replacement
+				itr = combinations_with_replacement(range(0, len(self._graphs)), 2)
+				if self._verbose >= 2:
+					iterator = tqdm(itr, desc='calculating kernels', file=sys.stdout)
+				else:
+					iterator = itr
+					
+				for i, j in iterator:
+					kernel = self.__kernel_do(A_wave_list[i], A_wave_list[j], lmda)
+					gram_matrix[i][j] = kernel
+					gram_matrix[j][i] = kernel
+			
+			else: # @todo
+				pass
+		else: # @todo
+			pass
+				
+		return gram_matrix
+			
+			
+	def _compute_gm_imap_unordered(self):
+		self._check_edge_weight(self._graphs)
+		self._check_graphs(self._graphs)
+		if self._verbose >= 2:
+			import warnings
+			warnings.warn('All labels are ignored.')
+				
+		# compute Gram matrix.
+		gram_matrix = np.zeros((len(self._graphs), len(self._graphs)))		
+		
+		if self._q == None:
+			# don't normalize adjacency matrices if q is a uniform vector. Note
+			# A_wave_list actually contains the transposes of the adjacency matrices.
+			if self._verbose >= 2:
+				iterator = tqdm(self._graphs, desc='compute adjacency matrices', file=sys.stdout)
+			else:
+				iterator = self._graphs
+			A_wave_list = [nx.adjacency_matrix(G, self._edge_weight).todense().transpose() for G in iterator] # @todo: parallel?
+
+			if self._p == None: # p is uniform distribution as default.
+				def init_worker(A_wave_list_toshare):
+					global G_A_wave_list
+					G_A_wave_list = A_wave_list_toshare
+					
+				do_fun = self._wrapper_kernel_do
+					
+				parallel_gm(do_fun, gram_matrix, self._graphs, init_worker=init_worker, 
+							glbv=(A_wave_list,), n_jobs=self._n_jobs, verbose=self._verbose)
+
+			else: # @todo
+				pass
+		else: # @todo
+			pass
+				
+		return gram_matrix
+	
+	
+	def _compute_kernel_list_series(self, g1, g_list):
+		self._check_edge_weight(g_list + [g1])
+		self._check_graphs(g_list + [g1])
+		if self._verbose >= 2:
+			import warnings
+			warnings.warn('All labels are ignored.')
+			
+		lmda = self._weight
+				
+		# compute kernel list.
+		kernel_list = [None] * len(g_list)
+		
+		if self._q == None:
+			# don't normalize adjacency matrices if q is a uniform vector. Note
+			# A_wave_list actually contains the transposes of the adjacency matrices.
+			A_wave_1 = nx.adjacency_matrix(g1, self._edge_weight).todense().transpose()
+			if self._verbose >= 2:
+				iterator = tqdm(range(len(g_list)), desc='compute adjacency matrices', file=sys.stdout)
+			else:
+				iterator = range(len(g_list))
+			A_wave_list = [nx.adjacency_matrix(G, self._edge_weight).todense().transpose() for G in iterator]
+
+			if self._p == None: # p is uniform distribution as default.
+				if self._verbose >= 2:
+					iterator = tqdm(range(len(g_list)), desc='calculating kernels', file=sys.stdout)
+				else:
+					iterator = range(len(g_list))
+					
+				for i in iterator:
+					kernel = self.__kernel_do(A_wave_1, A_wave_list[i], lmda)
+					kernel_list[i] = kernel
+			
+			else: # @todo
+				pass
+		else: # @todo
+			pass
+				
+		return kernel_list
+	
+	
+	def _compute_kernel_list_imap_unordered(self, g1, g_list):
+		self._check_edge_weight(g_list + [g1])
+		self._check_graphs(g_list + [g1])
+		if self._verbose >= 2:
+			import warnings
+			warnings.warn('All labels are ignored.')
+				
+		# compute kernel list.
+		kernel_list = [None] * len(g_list)
+		
+		if self._q == None:
+			# don't normalize adjacency matrices if q is a uniform vector. Note
+			# A_wave_list actually contains the transposes of the adjacency matrices.
+			A_wave_1 = nx.adjacency_matrix(g1, self._edge_weight).todense().transpose()
+			if self._verbose >= 2:
+				iterator = tqdm(range(len(g_list)), desc='compute adjacency matrices', file=sys.stdout)
+			else:
+				iterator = range(len(g_list))
+			A_wave_list = [nx.adjacency_matrix(G, self._edge_weight).todense().transpose() for G in iterator] # @todo: parallel?
+
+			if self._p == None: # p is uniform distribution as default.
+				def init_worker(A_wave_1_toshare, A_wave_list_toshare):
+					global G_A_wave_1, G_A_wave_list
+					G_A_wave_1 = A_wave_1_toshare
+					G_A_wave_list = A_wave_list_toshare
+
+				do_fun = self._wrapper_kernel_list_do	
+				
+				def func_assign(result, var_to_assign):	
+					var_to_assign[result[0]] = result[1]
+				itr = range(len(g_list))
+				len_itr = len(g_list)
+				parallel_me(do_fun, func_assign, kernel_list, itr, len_itr=len_itr,
+					init_worker=init_worker, glbv=(A_wave_1, A_wave_list), method='imap_unordered', 
+					n_jobs=self._n_jobs, itr_desc='calculating kernels', verbose=self._verbose)
+			
+			else: # @todo
+				pass
+		else: # @todo
+			pass
+				
+		return kernel_list
+
+
+	def _wrapper_kernel_list_do(self, itr):
+		return itr, self._kernel_do(G_A_wave_1, G_A_wave_list[itr], self._weight)
+	
+	
+	def _compute_single_kernel_series(self, g1, g2):
+		self._check_edge_weight([g1] + [g2])
+		self._check_graphs([g1] + [g2])
+		if self._verbose >= 2:
+			import warnings
+			warnings.warn('All labels are ignored.')
+			
+		lmda = self._weight
+		
+		if self._q == None:
+			# don't normalize adjacency matrices if q is a uniform vector. Note
+			# A_wave_list actually contains the transposes of the adjacency matrices.
+			A_wave_1 = nx.adjacency_matrix(g1, self._edge_weight).todense().transpose()
+			A_wave_2 = nx.adjacency_matrix(g2, self._edge_weight).todense().transpose()
+			if self._p == None: # p is uniform distribution as default.
+				kernel = self.__kernel_do(A_wave_1, A_wave_2, lmda)
+			else: # @todo
+				pass
+		else: # @todo
+			pass
+				
+		return kernel		
+	
+	
+	def __kernel_do(self, A_wave1, A_wave2, lmda):
+		
+		S = lmda * A_wave2
+		T_t = A_wave1
+		# use uniform distribution if there is no prior knowledge.
+		nb_pd = len(A_wave1) * len(A_wave2)
+		p_times_uni = 1 / nb_pd
+		M0 = np.full((len(A_wave2), len(A_wave1)), p_times_uni)
+		X = dlyap(S, T_t, M0)
+		X = np.reshape(X, (-1, 1), order='F')
+		# use uniform distribution if there is no prior knowledge.
+		q_times = np.full((1, nb_pd), p_times_uni)
+		return np.dot(q_times, X)
+	
+	
+	def _wrapper_kernel_do(self, itr):
+		i = itr[0]
+		j = itr[1]
+		return i, j, self.__kernel_do(G_A_wave_list[i], G_A_wave_list[j], self._weight)