openerp/tools/graph.py

   1 #!/usr/bin/env python
   2 # -*- coding: utf-8 -*-
   3 ##############################################################################
   4 #
   5 #    OpenERP, Open Source Management Solution
   6 #    Copyright (C) 2004-2009 Tiny SPRL (<http://tiny.be>).
   7 #
   8 #    This program is free software: you can redistribute it and/or modify
   9 #    it under the terms of the GNU Affero General Public License as
  10 #    published by the Free Software Foundation, either version 3 of the
  11 #    License, or (at your option) any later version.
  12 #
  13 #    This program is distributed in the hope that it will be useful,
  14 #    but WITHOUT ANY WARRANTY; without even the implied warranty of
  15 #    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16 #    GNU Affero General Public License for more details.
  17 #
  18 #    You should have received a copy of the GNU Affero General Public License
  19 #    along with this program.  If not, see <http://www.gnu.org/licenses/>.
  20 #
  21 ##############################################################################
  22
  23 import operator
  24 import math
  25
  26 class graph(object):
  27     def __init__(self, nodes, transitions, no_ancester=None):
  28         """Initialize graph's object
  29
  30         @param nodes list of ids of nodes in the graph
  31         @param transitions list of edges in the graph in the form (source_node, destination_node)
  32         @param no_ancester list of nodes with no incoming edges
  33         """
  34
  35         self.nodes = nodes or []
  36         self.edges = transitions or []
  37         self.no_ancester = no_ancester or {}
  38         trans = {}
  39
  40         for t in transitions:
  41             trans.setdefault(t[0], [])
  42             trans[t[0]].append(t[1])
  43         self.transitions = trans
  44         self.result = {}
  45
  46
  47     def init_rank(self):
  48         """Computes rank of the nodes of the graph by finding initial feasible tree
  49         """
  50         self.edge_wt = {}
  51         for link in self.links:
  52             self.edge_wt[link] = self.result[link[1]]['x'] - self.result[link[0]]['x']
  53
  54         tot_node = len(self.partial_order)
  55         #do until all the nodes in the component are searched
  56         while self.tight_tree()<tot_node:
  57             list_node = []
  58             list_edge = []
  59
  60             for node in self.nodes:
  61                 if node not in self.reachable_nodes:
  62                     list_node.append(node)
  63
  64             for edge in self.edge_wt:
  65                  if edge not in self.tree_edges:
  66                     list_edge.append(edge)
  67
  68             slack = 100
  69
  70             for edge in list_edge:
  71                 if ((edge[0] in self.reachable_nodes and edge[1] not in self.reachable_nodes) or
  72                     (edge[1] in self.reachable_nodes and edge[0] not in self.reachable_nodes)):
  73                     if slack > self.edge_wt[edge]-1:
  74                         slack = self.edge_wt[edge]-1
  75                         new_edge = edge
  76
  77             if new_edge[0] not in self.reachable_nodes:
  78                 delta = -(self.edge_wt[new_edge]-1)
  79             else:
  80                 delta = self.edge_wt[new_edge]-1
  81
  82             for node in self.result:
  83                 if node in self.reachable_nodes:
  84                     self.result[node]['x'] += delta
  85
  86             for edge in self.edge_wt:
  87                 self.edge_wt[edge] = self.result[edge[1]]['x'] - self.result[edge[0]]['x']
  88
  89         self.init_cutvalues()
  90
  91
  92     def tight_tree(self):
  93         self.reachable_nodes = []
  94         self.tree_edges = []
  95         self.reachable_node(self.start)
  96         return len(self.reachable_nodes)
  97
  98
  99     def reachable_node(self, node):
 100         """Find the nodes of the graph which are only 1 rank apart from each other
 101         """
 102
 103         if node not in self.reachable_nodes:
 104             self.reachable_nodes.append(node)
 105         for edge in self.edge_wt:
 106             if edge[0]==node:
 107                 if self.edge_wt[edge]==1:
 108                     self.tree_edges.append(edge)
 109                     if edge[1] not in self.reachable_nodes:
 110                         self.reachable_nodes.append(edge[1])
 111                     self.reachable_node(edge[1])
 112
 113
 114     def init_cutvalues(self):
 115         """Initailize cut values of edges of the feasible tree.
 116         Edges with negative cut-values are removed from the tree to optimize rank assignment
 117         """
 118         self.cut_edges = {}
 119         self.head_nodes = []
 120         i=0
 121
 122         for edge in self.tree_edges:
 123             self.head_nodes = []
 124             rest_edges = []
 125             rest_edges += self.tree_edges
 126             del rest_edges[i]
 127             self.head_component(self.start, rest_edges)
 128             i+=1
 129             positive = 0
 130             negative = 0
 131             for source_node in self.transitions:
 132                 if source_node in self.head_nodes:
 133                     for dest_node in self.transitions[source_node]:
 134                         if dest_node not in self.head_nodes:
 135                             negative+=1
 136                 else:
 137                     for dest_node in self.transitions[source_node]:
 138                         if dest_node in self.head_nodes:
 139                             positive+=1
 140
 141             self.cut_edges[edge] = positive - negative
 142
 143
 144     def head_component(self, node, rest_edges):
 145         """Find nodes which are reachable from the starting node, after removing an edge
 146         """
 147         if node not in self.head_nodes:
 148             self.head_nodes.append(node)
 149
 150             for edge in rest_edges:
 151                 if edge[0]==node:
 152                     self.head_component(edge[1],rest_edges)
 153
 154
 155     def process_ranking(self, node, level=0):
 156         """Computes initial feasible ranking after making graph acyclic with depth-first search
 157         """
 158
 159         if node not in self.result:
 160             self.result[node] = {'y': None, 'x':level, 'mark':0}
 161         else:
 162             if level > self.result[node]['x']:
 163                 self.result[node]['x'] = level
 164
 165         if self.result[node]['mark']==0:
 166             self.result[node]['mark'] = 1
 167             for sec_end in self.transitions.get(node, []):
 168                 self.process_ranking(sec_end, level+1)
 169
 170
 171     def make_acyclic(self, parent, node, level, tree):
 172         """Computes Partial-order of the nodes with depth-first search
 173         """
 174
 175         if node not in self.partial_order:
 176             self.partial_order[node] = {'level':level, 'mark':0}
 177             if parent:
 178                 tree.append((parent, node))
 179
 180         if self.partial_order[node]['mark']==0:
 181             self.partial_order[node]['mark'] = 1
 182             for sec_end in self.transitions.get(node, []):
 183                 self.links.append((node, sec_end))
 184                 self.make_acyclic(node, sec_end, level+1, tree)
 185
 186         return tree
 187
 188
 189     def rev_edges(self, tree):
 190         """reverse the direction of the edges whose source-node-partail_order> destination-node-partail_order
 191         to make the graph acyclic
 192         """
 193         Is_Cyclic = False
 194         i=0
 195         for link in self.links:
 196             src = link[0]
 197             des = link[1]
 198             edge_len = self.partial_order[des]['level'] - self.partial_order[src]['level']
 199             if edge_len < 0:
 200                 del self.links[i]
 201                 self.links.insert(i, (des, src))
 202                 self.transitions[src].remove(des)
 203                 self.transitions.setdefault(des, []).append(src)
 204                 Is_Cyclic = True
 205             elif math.fabs(edge_len) > 1:
 206                 Is_Cyclic = True
 207             i += 1
 208
 209         return Is_Cyclic
 210
 211     def exchange(self, e, f):
 212         """Exchange edges to make feasible-tree optimized
 213         :param e: edge with negative cut-value
 214         :param f: new edge with minimum slack-value
 215         """
 216         del self.tree_edges[self.tree_edges.index(e)]
 217         self.tree_edges.append(f)
 218         self.init_cutvalues()
 219
 220
 221     def enter_edge(self, edge):
 222         """Finds a new_edge with minimum slack value to replace an edge with negative cut-value
 223
 224         @param edge edge with negative cut-value
 225         """
 226
 227         self.head_nodes = []
 228         rest_edges = []
 229         rest_edges += self.tree_edges
 230         del rest_edges[rest_edges.index(edge)]
 231         self.head_component(self.start, rest_edges)
 232
 233         if edge[1] in self.head_nodes:
 234             l = []
 235             for node in self.result:
 236                 if node not in self.head_nodes:
 237                     l.append(node)
 238             self.head_nodes = l
 239
 240         slack = 100
 241         new_edge = edge
 242         for source_node in self.transitions:
 243             if source_node in self.head_nodes:
 244                 for dest_node in self.transitions[source_node]:
 245                     if dest_node not in self.head_nodes:
 246                         if slack>(self.edge_wt[edge]-1):
 247                             slack = self.edge_wt[edge]-1
 248                             new_edge = (source_node, dest_node)
 249
 250         return new_edge
 251
 252
 253     def leave_edge(self):
 254         """Returns the edge with negative cut_value(if exists)
 255         """
 256         if self.critical_edges:
 257             for edge in self.critical_edges:
 258                 self.cut_edges[edge] = 0
 259
 260         for edge in self.cut_edges:
 261             if self.cut_edges[edge]<0:
 262                 return edge
 263
 264         return None
 265
 266
 267     def finalize_rank(self, node, level):
 268         self.result[node]['x'] = level
 269         for destination in self.optimal_edges.get(node, []):
 270             self.finalize_rank(destination, level+1)
 271
 272
 273     def normalize(self):
 274         """The ranks are normalized by setting the least rank to zero.
 275         """
 276
 277         least_rank = min(map(lambda x: x['x'], self.result.values()))
 278
 279         if least_rank!=0:
 280             for node in self.result:
 281                 self.result[node]['x']-=least_rank
 282
 283
 284     def make_chain(self):
 285         """Edges between nodes more than one rank apart are replaced by chains of unit
 286            length edges between temporary nodes.
 287         """
 288
 289         for edge in self.edge_wt:
 290             if self.edge_wt[edge]>1:
 291                 self.transitions[edge[0]].remove(edge[1])
 292                 start = self.result[edge[0]]['x']
 293                 end = self.result[edge[1]]['x']
 294
 295                 for rank in range(start+1, end):
 296                     if not self.result.get((rank, 'temp'), False):
 297                         self.result[(rank, 'temp')] = {'y': None, 'x': rank, 'mark': 0}
 298
 299                 for rank in range(start, end):
 300                     if start==rank:
 301                         self.transitions[edge[0]].append((rank+1, 'temp'))
 302                     elif rank==end-1:
 303                         self.transitions.setdefault((rank, 'temp'), []).append(edge[1])
 304                     else:
 305                         self.transitions.setdefault((rank, 'temp'), []).append((rank+1, 'temp'))
 306
 307
 308     def init_order(self, node, level):
 309         """Initialize orders the nodes in each rank with depth-first search
 310         """
 311         if not self.result[node]['y']:
 312             self.result[node]['y'] = self.order[level]
 313             self.order[level] += 1
 314
 315         for sec_end in self.transitions.get(node, []):
 316             if node!=sec_end:
 317                 self.init_order(sec_end, self.result[sec_end]['x'])
 318
 319
 320     def order_heuristic(self):
 321         for i in range(12):
 322             self.wmedian()
 323
 324
 325     def wmedian(self):
 326         """Applies median heuristic to find optimzed order of the nodes with in their ranks
 327         """
 328         for level in self.levels:
 329
 330             node_median = []
 331             nodes = self.levels[level]
 332             for node in nodes:
 333                 node_median.append((node, self.median_value(node, level-1)))
 334
 335             sort_list = sorted(node_median, key=operator.itemgetter(1))
 336
 337             new_list = [tuple[0] for tuple in sort_list]
 338
 339             self.levels[level] = new_list
 340             order = 0
 341             for node in nodes:
 342                 self.result[node]['y'] = order
 343                 order +=1
 344
 345
 346     def median_value(self, node, adj_rank):
 347         """Returns median value of a vertex , defined as the median position of the adjacent vertices
 348
 349         @param node node to process
 350         @param adj_rank rank 1 less than the node's rank
 351         """
 352         adj_nodes = self.adj_position(node, adj_rank)
 353         l = len(adj_nodes)
 354         m = l/2
 355
 356         if l==0:
 357             return -1.0
 358         elif l%2 == 1:
 359             return adj_nodes[m]#median of the middle element
 360         elif l==2:
 361             return (adj_nodes[0]+adj_nodes[1])/2
 362         else:
 363             left = adj_nodes[m-1] - adj_nodes[0]
 364             right = adj_nodes[l-1] - adj_nodes[m]
 365             return ((adj_nodes[m-1]*right) + (adj_nodes[m]*left))/(left+right)
 366
 367
 368     def adj_position(self, node, adj_rank):
 369         """Returns list of the present positions of the nodes adjacent to node in the given adjacent rank.
 370
 371         @param node node to process
 372         @param adj_rank rank 1 less than the node's rank
 373         """
 374
 375         pre_level_nodes = self.levels.get(adj_rank, [])
 376         adj_nodes = []
 377
 378         if pre_level_nodes:
 379             for src in pre_level_nodes:
 380                 if self.transitions.get(src) and node in self.transitions[src]:
 381                     adj_nodes.append(self.result[src]['y'])
 382
 383         return adj_nodes
 384
 385
 386     def preprocess_order(self):
 387         levels = {}
 388
 389         for r in self.partial_order:
 390             l = self.result[r]['x']
 391             levels.setdefault(l,[])
 392             levels[l].append(r)
 393
 394         self.levels = levels
 395
 396
 397     def graph_order(self):
 398         """Finds actual-order of the nodes with respect to maximum number of nodes in a rank in component
 399         """
 400         mid_pos = 0.0
 401         max_level = max(map(lambda x: len(x), self.levels.values()))
 402
 403         for level in self.levels:
 404             if level:
 405                 no = len(self.levels[level])
 406                 factor = (max_level - no) * 0.10
 407                 list = self.levels[level]
 408                 list.reverse()
 409
 410                 if no%2==0:
 411                     first_half = list[no/2:]
 412                     factor = -factor
 413                 else:
 414                     first_half = list[no/2+1:]
 415                     if max_level==1:#for the case when horizontal graph is there
 416                         self.result[list[no/2]]['y'] = mid_pos + (self.result[list[no/2]]['x']%2 * 0.5)
 417                     else:
 418                         self.result[list[no/2]]['y'] = mid_pos + factor
 419
 420                 last_half = list[:no/2]
 421
 422                 i=1
 423                 for node in first_half:
 424                     self.result[node]['y'] = mid_pos - (i + factor)
 425                     i += 1
 426
 427                 i=1
 428                 for node in last_half:
 429                     self.result[node]['y'] = mid_pos + (i + factor)
 430                     i += 1
 431             else:
 432                 self.max_order += max_level+1
 433                 mid_pos = self.result[self.start]['y']
 434
 435
 436     def tree_order(self, node, last=0):
 437         mid_pos = self.result[node]['y']
 438         l = self.transitions.get(node, [])
 439         l.reverse()
 440         no = len(l)
 441
 442         rest = no%2
 443         first_half = l[no/2+rest:]
 444         last_half = l[:no/2]
 445
 446         for i, child in enumerate(first_half):
 447             self.result[child]['y'] = mid_pos - (i+1 - (0 if rest else 0.5))
 448
 449             if self.transitions.get(child, False):
 450                 if last:
 451                     self.result[child]['y'] = last + len(self.transitions[child])/2 + 1
 452                 last = self.tree_order(child, last)
 453
 454         if rest:
 455             mid_node = l[no/2]
 456             self.result[mid_node]['y'] = mid_pos
 457
 458             if self.transitions.get(mid_node, False):
 459                 if last:
 460                     self.result[mid_node]['y'] = last + len(self.transitions[mid_node])/2 + 1
 461                 if node!=mid_node:
 462                     last = self.tree_order(mid_node)
 463             else:
 464                 if last:
 465                     self.result[mid_node]['y'] = last + 1
 466             self.result[node]['y'] = self.result[mid_node]['y']
 467             mid_pos = self.result[node]['y']
 468
 469         i=1
 470         last_child = None
 471         for child in last_half:
 472             self.result[child]['y'] = mid_pos + (i - (0 if rest else 0.5))
 473             last_child = child
 474             i += 1
 475             if self.transitions.get(child, False):
 476                 if last:
 477                     self.result[child]['y'] = last + len(self.transitions[child])/2 + 1
 478                 if node!=child:
 479                     last = self.tree_order(child, last)
 480
 481         if last_child:
 482             last = self.result[last_child]['y']
 483
 484         return last
 485
 486
 487     def process_order(self):
 488         """Finds actual-order of the nodes with respect to maximum number of nodes in a rank in component
 489         """
 490
 491         if self.Is_Cyclic:
 492             max_level = max(map(lambda x: len(x), self.levels.values()))
 493
 494             if max_level%2:
 495                 self.result[self.start]['y'] = (max_level+1)/2 + self.max_order + (self.max_order and 1)
 496             else:
 497                 self.result[self.start]['y'] = max_level /2 + self.max_order + (self.max_order and 1)
 498
 499             self.graph_order()
 500
 501         else:
 502             self.result[self.start]['y'] = 0
 503             self.tree_order(self.start, 0)
 504             min_order = math.fabs(min(map(lambda x: x['y'], self.result.values())))
 505
 506             index = self.start_nodes.index(self.start)
 507             same = False
 508
 509             roots  = []
 510             if index>0:
 511                 for start in self.start_nodes[:index]:
 512                     same = True
 513                     for edge in self.tree_list[start][1:]:
 514                         if edge in self.tree_list[self.start]:
 515                             continue
 516                         else:
 517                             same = False
 518                             break
 519                     if same:
 520                         roots.append(start)
 521
 522             if roots:
 523                 min_order += self.max_order
 524             else:
 525                 min_order += self.max_order + 1
 526
 527             for level in self.levels:
 528                 for node in self.levels[level]:
 529                     self.result[node]['y'] += min_order
 530
 531             if roots:
 532                 roots.append(self.start)
 533                 one_level_el = self.tree_list[self.start][0][1]
 534                 base = self.result[one_level_el]['y']# * 2 / (index + 2)
 535
 536
 537                 no = len(roots)
 538                 first_half = roots[:no/2]
 539
 540                 if no%2==0:
 541                     last_half = roots[no/2:]
 542                 else:
 543                     last_half = roots[no/2+1:]
 544
 545                 factor = -math.floor(no/2)
 546                 for start in first_half:
 547                     self.result[start]['y'] = base + factor
 548                     factor += 1
 549
 550                 if no%2:
 551                     self.result[roots[no/2]]['y'] = base + factor
 552                 factor +=1
 553
 554                 for start in last_half:
 555                     self.result[start]['y'] = base + factor
 556                     factor += 1
 557
 558             self.max_order = max(map(lambda x: x['y'], self.result.values()))
 559
 560     def find_starts(self):
 561         """Finds other start nodes of the graph in the case when graph is disconneted
 562         """
 563         rem_nodes = []
 564         for node in self.nodes:
 565             if not self.partial_order.get(node):
 566                 rem_nodes.append(node)
 567         cnt = 0
 568         while True:
 569             if len(rem_nodes)==1:
 570                 self.start_nodes.append(rem_nodes[0])
 571                 break
 572             else:
 573                 count = 0
 574                 new_start = rem_nodes[0]
 575                 largest_tree = []
 576
 577                 for node in rem_nodes:
 578                     self.partial_order = {}
 579                     tree = self.make_acyclic(None, node, 0, [])
 580                     if len(tree)+1 > count:
 581                         count = len(tree) + 1
 582                         new_start = node
 583                         largest_tree = tree
 584                 else:
 585                     if not largest_tree:
 586                         new_start = rem_nodes[0]
 587                         rem_nodes.remove(new_start)
 588
 589                 self.start_nodes.append(new_start)
 590
 591
 592                 for edge in largest_tree:
 593                     if edge[0] in rem_nodes:
 594                         rem_nodes.remove(edge[0])
 595                     if edge[1] in rem_nodes:
 596                         rem_nodes.remove(edge[1])
 597
 598                 if not rem_nodes:
 599                     break
 600
 601
 602     def rank(self):
 603         """Finds the optimized rank of the nodes using Network-simplex algorithm
 604         """
 605         self.levels = {}
 606         self.critical_edges = []
 607         self.partial_order = {}
 608         self.links = []
 609         self.Is_Cyclic = False
 610
 611         self.tree_list[self.start] = self.make_acyclic(None, self.start, 0, [])
 612         self.Is_Cyclic = self.rev_edges(self.tree_list[self.start])
 613         self.process_ranking(self.start)
 614         self.init_rank()
 615
 616         #make cut values of all tree edges to 0 to optimize feasible tree
 617         e = self.leave_edge()
 618
 619         while e :
 620             f = self.enter_edge(e)
 621             if e==f:
 622                 self.critical_edges.append(e)
 623             else:
 624                 self.exchange(e,f)
 625             e = self.leave_edge()
 626
 627         #finalize rank using optimum feasible tree
 628 #        self.optimal_edges = {}
 629 #        for edge in self.tree_edges:
 630 #            source = self.optimal_edges.setdefault(edge[0], [])
 631 #            source.append(edge[1])
 632
 633 #        self.finalize_rank(self.start, 0)
 634
 635         #normalization
 636         self.normalize()
 637         for edge in self.edge_wt:
 638             self.edge_wt[edge] = self.result[edge[1]]['x'] - self.result[edge[0]]['x']
 639
 640     def order_in_rank(self):
 641         """Finds optimized order of the nodes within their ranks using median heuristic
 642         """
 643
 644         self.make_chain()
 645         self.preprocess_order()
 646         self.order = {}
 647         max_rank = max(map(lambda x: x, self.levels.keys()))
 648
 649         for i in range(max_rank+1):
 650             self.order[i] = 0
 651
 652         self.init_order(self.start, self.result[self.start]['x'])
 653
 654         for level in self.levels:
 655             self.levels[level].sort(lambda x, y: cmp(self.result[x]['y'], self.result[y]['y']))
 656
 657         self.order_heuristic()
 658         self.process_order()
 659
 660     def process(self, starting_node):
 661         """Process the graph to find ranks and order of the nodes
 662
 663         @param starting_node node from where to start the graph search
 664         """
 665
 666         self.start_nodes = starting_node or []
 667         self.partial_order = {}
 668         self.links = []
 669         self.tree_list = {}
 670
 671         if self.nodes:
 672             if self.start_nodes:
 673                 #add dummy edges to the nodes which does not have any incoming edges
 674                 tree = self.make_acyclic(None, self.start_nodes[0], 0, [])
 675
 676                 for node in self.no_ancester:
 677                     for sec_node in self.transitions.get(node, []):
 678                         if sec_node in self.partial_order.keys():
 679                             self.transitions[self.start_nodes[0]].append(node)
 680                             break
 681
 682                 self.partial_order = {}
 683                 tree = self.make_acyclic(None, self.start_nodes[0], 0, [])
 684
 685
 686             # if graph is disconnected or no start-node is given
 687             #than to find starting_node for each component of the node
 688             if len(self.nodes) > len(self.partial_order):
 689                 self.find_starts()
 690
 691             self.max_order = 0
 692             #for each component of the graph find ranks and order of the nodes
 693             for s in self.start_nodes:
 694                 self.start = s
 695                 self.rank()   # First step:Netwoek simplex algorithm
 696                 self.order_in_rank()    #Second step: ordering nodes within ranks
 697
 698
 699     def __str__(self):
 700         result = ''
 701         for l in self.levels:
 702             result += 'PosY: ' + str(l) + '\n'
 703             for node in self.levels[l]:
 704                 result += '\tPosX: '+ str(self.result[node]['y']) + '  - Node:' + str(node) + "\n"
 705         return result
 706
 707
 708     def scale(self, maxx, maxy, nwidth=0, nheight=0, margin=20):
 709         """Computes actual co-ordiantes of the nodes
 710         """
 711
 712             #for flat edges ie. source an destination nodes are on the same rank
 713         for src in self.transitions:
 714             for des in self.transitions[src]:
 715                 if self.result[des]['x'] - self.result[src]['x'] == 0:
 716                     self.result[src]['x'] += 0.08
 717                     self.result[des]['x'] -= 0.08
 718
 719         factorX = maxx + nheight
 720         factorY = maxy + nwidth
 721
 722         for node in self.result:
 723             self.result[node]['y'] = (self.result[node]['y']) * factorX + margin
 724             self.result[node]['x'] = (self.result[node]['x']) * factorY + margin
 725
 726
 727     def result_get(self):
 728         return self.result
 729
 730 if __name__=='__main__':
 731     starting_node = ['profile']  # put here nodes with flow_start=True
 732     nodes = ['project','account','hr','base','product','mrp','test','profile']
 733     transitions = [
 734         ('profile','mrp'),
 735         ('mrp','project'),
 736         ('project','product'),
 737         ('mrp','hr'),
 738         ('mrp','test'),
 739         ('project','account'),
 740         ('project','hr'),
 741         ('product','base'),
 742         ('account','product'),
 743         ('account','test'),
 744         ('account','base'),
 745         ('hr','base'),
 746         ('test','base')
 747     ]
 748
 749     radius = 20
 750     g = graph(nodes, transitions)
 751     g.process(starting_node)
 752     g.scale(radius*3,radius*3, radius, radius)
 753
 754     from PIL import Image
 755     from PIL import ImageDraw
 756     img = Image.new("RGB", (800, 600), "#ffffff")
 757     draw = ImageDraw.Draw(img)
 758
 759     result = g.result_get()
 760     node_res = {}
 761     for node in nodes:
 762         node_res[node] = result[node]
 763
 764     for name,node in node_res.items():
 765
 766         draw.arc( (int(node['y']-radius), int(node['x']-radius),int(node['y']+radius), int(node['x']+radius) ), 0, 360, (128,128,128))
 767         draw.text( (int(node['y']),  int(node['x'])), str(name),  (128,128,128))
 768
 769
 770     for t in transitions:
 771         draw.line( (int(node_res[t[0]]['y']), int(node_res[t[0]]['x']),int(node_res[t[1]]['y']),int(node_res[t[1]]['x'])),(128,128,128) )
 772     img.save("graph.png", "PNG")
 773
 774
 775 # vim:expandtab:smartindent:tabstop=4:softtabstop=4:shiftwidth=4:
 776