Package madgraph :: Package core :: Module diagram_generation
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Source Code for Module madgraph.core.diagram_generation

   1  ################################################################################ 
   2  # 
   3  # Copyright (c) 2009 The MadGraph5_aMC@NLO Development team and Contributors 
   4  # 
   5  # This file is a part of the MadGraph5_aMC@NLO project, an application which  
   6  # automatically generates Feynman diagrams and matrix elements for arbitrary 
   7  # high-energy processes in the Standard Model and beyond. 
   8  # 
   9  # It is subject to the MadGraph5_aMC@NLO license which should accompany this  
  10  # distribution. 
  11  # 
  12  # For more information, visit madgraph.phys.ucl.ac.be and amcatnlo.web.cern.ch 
  13  # 
  14  ################################################################################ 
  15  """Classes for diagram generation. Amplitude performs the diagram 
  16  generation, DecayChainAmplitude keeps track of processes with decay 
  17  chains, and MultiProcess allows generation of processes with 
  18  multiparticle definitions. DiagramTag allows to identify diagrams 
  19  based on relevant properties. 
  20  """ 
  21   
  22  import array 
  23  import copy 
  24  import itertools 
  25  import logging 
  26   
  27  import madgraph.core.base_objects as base_objects 
  28  import madgraph.various.misc as misc 
  29  from madgraph import InvalidCmd, MadGraph5Error 
  30   
  31  logger = logging.getLogger('madgraph.diagram_generation') 
32 33 34 -class NoDiagramException(InvalidCmd): pass
35
36 #=============================================================================== 37 # DiagramTag mother class 38 #=============================================================================== 39 40 -class DiagramTag(object):
41 """Class to tag diagrams based on objects with some __lt__ measure, e.g. 42 PDG code/interaction id (for comparing diagrams from the same amplitude), 43 or Lorentz/coupling/mass/width (for comparing AMPs from different MEs). 44 Algorithm: Create chains starting from external particles: 45 1 \ / 6 46 2 /\______/\ 7 47 3_ / | \_ 8 48 4 / 5 \_ 9 49 \ 10 50 gives ((((9,10,id910),8,id9108),(6,7,id67),id910867) 51 (((1,2,id12),(3,4,id34)),id1234), 52 5,id91086712345) 53 where idN is the id of the corresponding interaction. The ordering within 54 chains is based on chain length (depth; here, 1234 has depth 3, 910867 has 55 depth 4, 5 has depht 0), and if equal on the ordering of the chain elements. 56 The determination of central vertex is based on minimizing the chain length 57 for the longest subchain. 58 This gives a unique tag which can be used to identify diagrams 59 (instead of symmetry), as well as identify identical matrix elements from 60 different processes.""" 61
62 - class DiagramTagError(Exception):
63 """Exception for any problems in DiagramTags""" 64 pass
65
66 - def __init__(self, diagram, model=None, ninitial=2):
67 """Initialize with a diagram. Create DiagramTagChainLinks according to 68 the diagram, and figure out if we need to shift the central vertex.""" 69 70 # wf_dict keeps track of the intermediate particles 71 leg_dict = {} 72 # Create the chain which will be the diagram tag 73 for vertex in diagram.get('vertices'): 74 # Only add incoming legs 75 legs = vertex.get('legs')[:-1] 76 lastvx = vertex == diagram.get('vertices')[-1] 77 if lastvx: 78 # If last vertex, all legs are incoming 79 legs = vertex.get('legs') 80 # Add links corresponding to the relevant legs 81 link = DiagramTagChainLink([leg_dict.setdefault(leg.get('number'), 82 DiagramTagChainLink(self.link_from_leg(leg, model))) \ 83 for leg in legs], 84 self.vertex_id_from_vertex(vertex, 85 lastvx, 86 model, 87 ninitial)) 88 # Add vertex to leg_dict if not last one 89 if not lastvx: 90 leg_dict[vertex.get('legs')[-1].get('number')] = link 91 92 # The resulting link is the hypothetical result 93 self.tag = link 94 95 # Now make sure to find the central vertex in the diagram, 96 # defined by the longest leg being as short as possible 97 done = max([l.depth for l in self.tag.links]) == 0 98 while not done: 99 # Identify the longest chain in the tag 100 longest_chain = self.tag.links[0] 101 # Create a new link corresponding to moving one step 102 new_link = DiagramTagChainLink(self.tag.links[1:], 103 self.flip_vertex(\ 104 self.tag.vertex_id, 105 longest_chain.vertex_id, 106 self.tag.links[1:])) 107 # Create a new final vertex in the direction of the longest link 108 other_links = list(longest_chain.links) + [new_link] 109 other_link = DiagramTagChainLink(other_links, 110 self.flip_vertex(\ 111 longest_chain.vertex_id, 112 self.tag.vertex_id, 113 other_links)) 114 115 if other_link.links[0] < self.tag.links[0]: 116 # Switch to new tag, continue search 117 self.tag = other_link 118 else: 119 # We have found the central vertex 120 done = True
121
122 - def get_external_numbers(self):
123 """Get the order of external particles in this tag""" 124 125 return self.tag.get_external_numbers()
126
127 - def diagram_from_tag(self, model):
128 """Output a diagram from a DiagramTag. Note that each daughter 129 class must implement the static functions id_from_vertex_id 130 (if the vertex id is something else than an integer) and 131 leg_from_link (to pass the correct info from an end link to a 132 leg).""" 133 134 # Create the vertices, starting from the final vertex 135 diagram = base_objects.Diagram({'vertices': \ 136 self.vertices_from_link(self.tag, 137 model, 138 True)}) 139 diagram.calculate_orders(model) 140 return diagram
141 142 @classmethod 177 178 @classmethod
179 - def legPDGs_from_vertex_id(cls, vertex_id,model):
180 """Returns the list of external PDGs of the interaction corresponding 181 to this vertex_id.""" 182 183 # In case we have to deal with a regular vertex, we return the list 184 # external PDGs as given by the model information on that integer 185 # vertex id. 186 if (len(vertex_id)>=3 and 'PDGs' in vertex_id[2]): 187 return vertex_id[2]['PDGs'] 188 else: 189 return [part.get_pdg_code() for part in model.get_interaction( 190 cls.id_from_vertex_id(vertex_id)).get('particles')]
191 192 @classmethod
193 - def leg_from_legs(cls,legs, vertex_id, model):
194 """Return a leg from a leg list and the model info""" 195 196 pdgs = list(cls.legPDGs_from_vertex_id(vertex_id, model)) 197 198 # Extract the resulting pdg code from the interaction pdgs 199 for pdg in [leg.get('id') for leg in legs]: 200 pdgs.remove(pdg) 201 202 assert len(pdgs) == 1 203 # Prepare the new leg properties 204 pdg = model.get_particle(pdgs[0]).get_anti_pdg_code() 205 number = min([l.get('number') for l in legs]) 206 # State is False for t-channel, True for s-channel 207 state = (len([l for l in legs if l.get('state') == False]) != 1) 208 # Note that this needs to be done before combining decay chains 209 onshell= False 210 211 return base_objects.Leg({'id': pdg, 212 'number': number, 213 'state': state, 214 'onshell': onshell})
215 216 @classmethod 229 230 @staticmethod 243 244 @staticmethod
245 - def id_from_vertex_id(vertex_id):
246 """Return the numerical vertex id from a link.vertex_id""" 247 248 return vertex_id[0][0]
249 250 @staticmethod
251 - def loop_info_from_vertex_id(vertex_id):
252 """Return the loop_info stored in this vertex id. Notice that the 253 IdentifyME tag does not store the loop_info, but should normally never 254 need access to it.""" 255 256 return vertex_id[2]
257 258 @staticmethod
259 - def reorder_permutation(perm, start_perm):
260 """Reorder a permutation with respect to start_perm. Note that 261 both need to start from 1.""" 262 if perm == start_perm: 263 return range(len(perm)) 264 order = [i for (p,i) in \ 265 sorted([(p,i) for (i,p) in enumerate(perm)])] 266 return [start_perm[i]-1 for i in order]
267 268 @staticmethod 279 280 @staticmethod
281 - def vertex_id_from_vertex(vertex, last_vertex, model, ninitial):
282 """Returns the default vertex id: just the interaction id 283 Note that in the vertex id, like the leg, only the first entry is 284 taken into account in the tag comparison, while the second is for 285 storing information that is not to be used in comparisons and the 286 third for additional info regarding the shrunk loop vertex.""" 287 288 if isinstance(vertex,base_objects.ContractedVertex): 289 # return (vertex.get('id'),(),{'PDGs':vertex.get('PDGs')}) 290 return ((vertex.get('id'),vertex.get('loop_tag')),(), 291 {'PDGs':vertex.get('PDGs')}) 292 else: 293 return ((vertex.get('id'),()),(),{})
294 295 @staticmethod
296 - def flip_vertex(new_vertex, old_vertex, links):
297 """Returns the default vertex flip: just the new_vertex""" 298 return new_vertex
299
300 - def __eq__(self, other):
301 """Equal if same tag""" 302 if type(self) != type(other): 303 return False 304 return self.tag == other.tag
305
306 - def __ne__(self, other):
307 return not self.__eq__(other)
308
309 - def __str__(self):
310 return str(self.tag)
311
312 - def __lt__(self, other):
313 return self.tag < other.tag
314
315 - def __gt__(self, other):
316 return self.tag > other.tag
317 318 __repr__ = __str__
319 405
406 #=============================================================================== 407 # Amplitude 408 #=============================================================================== 409 -class Amplitude(base_objects.PhysicsObject):
410 """Amplitude: process + list of diagrams (ordered) 411 Initialize with a process, then call generate_diagrams() to 412 generate the diagrams for the amplitude 413 """ 414
415 - def default_setup(self):
416 """Default values for all properties""" 417 418 self['process'] = base_objects.Process() 419 self['diagrams'] = None 420 # has_mirror_process is True if the same process but with the 421 # two incoming particles interchanged has been generated 422 self['has_mirror_process'] = False
423
424 - def __init__(self, argument=None):
425 """Allow initialization with Process""" 426 if isinstance(argument, base_objects.Process): 427 super(Amplitude, self).__init__() 428 self.set('process', argument) 429 self.generate_diagrams() 430 elif argument != None: 431 # call the mother routine 432 super(Amplitude, self).__init__(argument) 433 else: 434 # call the mother routine 435 super(Amplitude, self).__init__()
436
437 - def filter(self, name, value):
438 """Filter for valid amplitude property values.""" 439 440 if name == 'process': 441 if not isinstance(value, base_objects.Process): 442 raise self.PhysicsObjectError, \ 443 "%s is not a valid Process object" % str(value) 444 if name == 'diagrams': 445 if not isinstance(value, base_objects.DiagramList): 446 raise self.PhysicsObjectError, \ 447 "%s is not a valid DiagramList object" % str(value) 448 if name == 'has_mirror_process': 449 if not isinstance(value, bool): 450 raise self.PhysicsObjectError, \ 451 "%s is not a valid boolean" % str(value) 452 return True
453
454 - def get(self, name):
455 """Get the value of the property name.""" 456 457 if name == 'diagrams' and self[name] == None: 458 # Have not yet generated diagrams for this process 459 if self['process']: 460 self.generate_diagrams() 461 462 return super(Amplitude, self).get(name)
463 # return Amplitude.__bases__[0].get(self, name) #return the mother routine 464 465
466 - def get_sorted_keys(self):
467 """Return diagram property names as a nicely sorted list.""" 468 469 return ['process', 'diagrams', 'has_mirror_process']
470
471 - def get_number_of_diagrams(self):
472 """Returns number of diagrams for this amplitude""" 473 return len(self.get('diagrams'))
474
475 - def get_amplitudes(self):
476 """Return an AmplitudeList with just this amplitude. 477 Needed for DecayChainAmplitude.""" 478 479 return AmplitudeList([self])
480
481 - def nice_string(self, indent=0):
482 """Returns a nicely formatted string of the amplitude content.""" 483 return self.get('process').nice_string(indent) + "\n" + \ 484 self.get('diagrams').nice_string(indent)
485
486 - def nice_string_processes(self, indent=0):
487 """Returns a nicely formatted string of the amplitude process.""" 488 return self.get('process').nice_string(indent)
489
490 - def get_ninitial(self):
491 """Returns the number of initial state particles in the process.""" 492 return self.get('process').get_ninitial()
493
494 - def has_loop_process(self):
495 """ Returns wether this amplitude has a loop process.""" 496 497 return self.get('process').get('perturbation_couplings')
498
499 - def generate_diagrams(self, returndiag=False, diagram_filter=False):
500 """Generate diagrams. Algorithm: 501 502 1. Define interaction dictionaries: 503 * 2->0 (identity), 3->0, 4->0, ... , maxlegs->0 504 * 2 -> 1, 3 -> 1, ..., maxlegs-1 -> 1 505 506 2. Set flag from_group=true for all external particles. 507 Flip particle/anti particle for incoming particles. 508 509 3. If there is a dictionary n->0 with n=number of external 510 particles, create if possible the combination [(1,2,3,4,...)] 511 with *at least two* from_group==true. This will give a 512 finished (set of) diagram(s) (done by reduce_leglist) 513 514 4. Create all allowed groupings of particles with at least one 515 from_group==true (according to dictionaries n->1): 516 [(1,2),3,4...],[1,(2,3),4,...],..., 517 [(1,2),(3,4),...],...,[(1,2,3),4,...],... 518 (done by combine_legs) 519 520 5. Replace each group with a (list of) new particle(s) with number 521 n = min(group numbers). Set from_group true for these 522 particles and false for all other particles. Store vertex info. 523 (done by merge_comb_legs) 524 525 6. Stop algorithm when at most 2 particles remain. 526 Return all diagrams (lists of vertices). 527 528 7. Repeat from 3 (recursion done by reduce_leglist) 529 530 8. Replace final p=p vertex 531 532 Be aware that the resulting vertices have all particles outgoing, 533 so need to flip for incoming particles when used. 534 535 SPECIAL CASE: For A>BC... processes which are legs in decay 536 chains, we need to ensure that BC... combine first, giving A=A 537 as a final vertex. This case is defined by the Process 538 property is_decay_chain = True. 539 This function can also be called by the generate_diagram function 540 of LoopAmplitudes, in which case the generated diagrams here must not 541 be directly assigned to the 'diagrams' attributed but returned as a 542 DiagramList by the function. This is controlled by the argument 543 returndiag. 544 """ 545 546 process = self.get('process') 547 model = process.get('model') 548 legs = process.get('legs') 549 # Make sure orders is the minimum of orders and overall_orders 550 for key in process.get('overall_orders').keys(): 551 try: 552 process.get('orders')[key] = \ 553 min(process.get('orders')[key], 554 process.get('overall_orders')[key]) 555 except KeyError: 556 process.get('orders')[key] = process.get('overall_orders')[key] 557 558 assert model.get('particles'), \ 559 "particles are missing in model: %s" % model.get('particles') 560 561 assert model.get('interactions'), \ 562 "interactions are missing in model" 563 564 565 res = base_objects.DiagramList() 566 # First check that the number of fermions is even 567 if len(filter(lambda leg: model.get('particle_dict')[\ 568 leg.get('id')].is_fermion(), legs)) % 2 == 1: 569 if not returndiag: 570 self['diagrams'] = res 571 raise InvalidCmd, 'The number of fermion is odd' 572 else: 573 return False, res 574 575 # Then check same number of incoming and outgoing fermions (if 576 # no Majorana particles in model) 577 if not model.get('got_majoranas') and \ 578 len(filter(lambda leg: leg.is_incoming_fermion(model), legs)) != \ 579 len(filter(lambda leg: leg.is_outgoing_fermion(model), legs)): 580 if not returndiag: 581 self['diagrams'] = res 582 raise InvalidCmd, 'The number of of incoming/outcoming fermions are different' 583 else: 584 return False, res 585 586 # Finally check that charge (conserve by all interactions) of the process 587 #is globally conserve for this process. 588 for charge in model.get('conserved_charge'): 589 total = 0 590 for leg in legs: 591 part = model.get('particle_dict')[leg.get('id')] 592 try: 593 value = part.get(charge) 594 except (AttributeError, base_objects.PhysicsObject.PhysicsObjectError): 595 try: 596 value = getattr(part, charge) 597 except AttributeError: 598 value = 0 599 600 if (leg.get('id') != part['pdg_code']) != leg['state']: 601 total -= value 602 else: 603 total += value 604 605 if abs(total) > 1e-10: 606 if not returndiag: 607 self['diagrams'] = res 608 raise InvalidCmd, 'No %s conservation for this process ' % charge 609 return res 610 else: 611 raise InvalidCmd, 'No %s conservation for this process ' % charge 612 return res, res 613 614 if not returndiag: 615 logger.info("Trying %s " % process.nice_string().replace('Process', 'process')) 616 617 # Give numbers to legs in process 618 for i in range(0, len(process.get('legs'))): 619 # Make sure legs are unique 620 leg = copy.copy(process.get('legs')[i]) 621 process.get('legs')[i] = leg 622 if leg.get('number') == 0: 623 leg.set('number', i + 1) 624 625 # Copy leglist from process, so we can flip leg identities 626 # without affecting the original process 627 leglist = self.copy_leglist(process.get('legs')) 628 629 for leg in leglist: 630 631 # For the first step, ensure the tag from_group 632 # is true for all legs 633 leg.set('from_group', True) 634 635 # Need to flip part-antipart for incoming particles, 636 # so they are all outgoing 637 if leg.get('state') == False: 638 part = model.get('particle_dict')[leg.get('id')] 639 leg.set('id', part.get_anti_pdg_code()) 640 641 # Calculate the maximal multiplicity of n-1>1 configurations 642 # to restrict possible leg combinations 643 max_multi_to1 = max([len(key) for key in \ 644 model.get('ref_dict_to1').keys()]) 645 646 647 # Reduce the leg list and return the corresponding 648 # list of vertices 649 650 # For decay processes, generate starting from final-state 651 # combined only as the last particle. This allows to use these 652 # in decay chains later on. 653 is_decay_proc = process.get_ninitial() == 1 654 if is_decay_proc: 655 part = model.get('particle_dict')[leglist[0].get('id')] 656 # For decay chain legs, we want everything to combine to 657 # the initial leg. This is done by only allowing the 658 # initial leg to combine as a final identity. 659 ref_dict_to0 = {(part.get_pdg_code(),part.get_anti_pdg_code()):[0], 660 (part.get_anti_pdg_code(),part.get_pdg_code()):[0]} 661 # Need to set initial leg from_group to None, to make sure 662 # it can only be combined at the end. 663 leglist[0].set('from_group', None) 664 reduced_leglist = self.reduce_leglist(leglist, 665 max_multi_to1, 666 ref_dict_to0, 667 is_decay_proc, 668 process.get('orders')) 669 else: 670 reduced_leglist = self.reduce_leglist(leglist, 671 max_multi_to1, 672 model.get('ref_dict_to0'), 673 is_decay_proc, 674 process.get('orders')) 675 676 #In LoopAmplitude the function below is overloaded such that it 677 #converts back all DGLoopLegs to Legs. In the default tree-level 678 #diagram generation, this does nothing. 679 self.convert_dgleg_to_leg(reduced_leglist) 680 681 if reduced_leglist: 682 for vertex_list in reduced_leglist: 683 res.append(self.create_diagram(base_objects.VertexList(vertex_list))) 684 685 # Record whether or not we failed generation before required 686 # s-channel propagators are taken into account 687 failed_crossing = not res 688 689 # Required s-channels is a list of id-lists. Select the 690 # diagrams where all required s-channel propagators in any of 691 # the lists are present (i.e., the different lists correspond 692 # to "or", while the elements of the list correspond to 693 # "and"). 694 if process.get('required_s_channels') and \ 695 process.get('required_s_channels')[0]: 696 # We shouldn't look at the last vertex in each diagram, 697 # since that is the n->0 vertex 698 lastvx = -1 699 # For decay chain processes, there is an "artificial" 700 # extra vertex corresponding to particle 1=1, so we need 701 # to exclude the two last vertexes. 702 if is_decay_proc: lastvx = -2 703 ninitial = len(filter(lambda leg: leg.get('state') == False, 704 process.get('legs'))) 705 # Check required s-channels for each list in required_s_channels 706 old_res = res 707 res = base_objects.DiagramList() 708 for id_list in process.get('required_s_channels'): 709 res_diags = filter(lambda diagram: \ 710 all([req_s_channel in \ 711 [vertex.get_s_channel_id(\ 712 process.get('model'), ninitial) \ 713 for vertex in diagram.get('vertices')[:lastvx]] \ 714 for req_s_channel in \ 715 id_list]), old_res) 716 # Add diagrams only if not already in res 717 res.extend([diag for diag in res_diags if diag not in res]) 718 719 # Remove all diagrams with a "double" forbidden s-channel propagator 720 # is present. 721 # Note that we shouldn't look at the last vertex in each 722 # diagram, since that is the n->0 vertex 723 if process.get('forbidden_s_channels'): 724 ninitial = len(filter(lambda leg: leg.get('state') == False, 725 process.get('legs'))) 726 if ninitial == 2: 727 res = base_objects.DiagramList(\ 728 filter(lambda diagram: \ 729 not any([vertex.get_s_channel_id(\ 730 process.get('model'), ninitial) \ 731 in process.get('forbidden_s_channels') 732 for vertex in diagram.get('vertices')[:-1]]), 733 res)) 734 else: 735 # split since we need to avoid that the initial particle is forbidden 736 # as well. 737 newres= [] 738 for diagram in res: 739 leg1 = 1 740 #check the latest vertex to see if the leg 1 is inside if it 741 #is we need to inverse the look-up and allow the first s-channel 742 # of the associate particles. 743 vertex = diagram.get('vertices')[-1] 744 if any([l['number'] ==1 for l in vertex.get('legs')]): 745 leg1 = [l['number'] for l in vertex.get('legs') if l['number'] !=1][0] 746 to_loop = range(len(diagram.get('vertices'))-1) 747 if leg1 >1: 748 to_loop.reverse() 749 for i in to_loop: 750 vertex = diagram.get('vertices')[i] 751 if leg1: 752 if any([l['number'] ==leg1 for l in vertex.get('legs')]): 753 leg1 = 0 754 continue 755 if vertex.get_s_channel_id(process.get('model'), ninitial)\ 756 in process.get('forbidden_s_channels'): 757 break 758 else: 759 newres.append(diagram) 760 res = base_objects.DiagramList(newres) 761 762 763 # Mark forbidden (onshell) s-channel propagators, to forbid onshell 764 # generation. 765 if process.get('forbidden_onsh_s_channels'): 766 ninitial = len(filter(lambda leg: leg.get('state') == False, 767 process.get('legs'))) 768 769 verts = base_objects.VertexList(sum([[vertex for vertex \ 770 in diagram.get('vertices')[:-1] 771 if vertex.get_s_channel_id(\ 772 process.get('model'), ninitial) \ 773 in process.get('forbidden_onsh_s_channels')] \ 774 for diagram in res], [])) 775 for vert in verts: 776 # Use onshell = False to indicate that this s-channel is forbidden 777 newleg = copy.copy(vert.get('legs').pop(-1)) 778 newleg.set('onshell', False) 779 vert.get('legs').append(newleg) 780 781 # Set actual coupling orders for each diagram 782 for diagram in res: 783 diagram.calculate_orders(model) 784 785 # Filter the diagrams according to the squared coupling order 786 # constraints and possible the negative one. Remember that OrderName=-n 787 # means that the user wants to include everything up to the N^(n+1)LO 788 # contribution in that order and at most one order can be restricted 789 # in this way. We shall do this only if the diagrams are not asked to 790 # be returned, as it is the case for NLO because it this case the 791 # interference are not necessarily among the diagrams generated here only. 792 if not returndiag and len(res)>0: 793 res = self.apply_squared_order_constraints(res) 794 795 if diagram_filter: 796 res = self.apply_user_filter(res) 797 798 # Replace final id=0 vertex if necessary 799 if not process.get('is_decay_chain'): 800 for diagram in res: 801 vertices = diagram.get('vertices') 802 if len(vertices) > 1 and vertices[-1].get('id') == 0: 803 # Need to "glue together" last and next-to-last 804 # vertex, by replacing the (incoming) last leg of the 805 # next-to-last vertex with the (outgoing) leg in the 806 # last vertex 807 vertices = copy.copy(vertices) 808 lastvx = vertices.pop() 809 nexttolastvertex = copy.copy(vertices.pop()) 810 legs = copy.copy(nexttolastvertex.get('legs')) 811 ntlnumber = legs[-1].get('number') 812 lastleg = filter(lambda leg: leg.get('number') != ntlnumber, 813 lastvx.get('legs'))[0] 814 # Reset onshell in case we have forbidden s-channels 815 if lastleg.get('onshell') == False: 816 lastleg.set('onshell', None) 817 # Replace the last leg of nexttolastvertex 818 legs[-1] = lastleg 819 nexttolastvertex.set('legs', legs) 820 vertices.append(nexttolastvertex) 821 diagram.set('vertices', vertices) 822 823 if res and not returndiag: 824 logger.info("Process has %d diagrams" % len(res)) 825 826 # Trim down number of legs and vertices used to save memory 827 self.trim_diagrams(diaglist=res) 828 829 # Sort process legs according to leg number 830 pertur = 'QCD' 831 if self.get('process')['perturbation_couplings']: 832 pertur = sorted(self.get('process')['perturbation_couplings'])[0] 833 self.get('process').get('legs').sort(pert=pertur) 834 835 # Set diagrams to res if not asked to be returned 836 if not returndiag: 837 self['diagrams'] = res 838 return not failed_crossing 839 else: 840 return not failed_crossing, res
841
842 - def apply_squared_order_constraints(self, diag_list):
843 """Applies the user specified squared order constraints on the diagram 844 list in argument.""" 845 846 res = copy.copy(diag_list) 847 848 # Apply the filtering on constrained amplitude (== and >) 849 # No need to iterate on this one 850 for name, (value, operator) in self['process'].get('constrained_orders').items(): 851 res.filter_constrained_orders(name, value, operator) 852 853 # Iterate the filtering since the applying the constraint on one 854 # type of coupling order can impact what the filtering on a previous 855 # one (relevant for the '==' type of constraint). 856 while True: 857 new_res = res.apply_positive_sq_orders(res, 858 self['process'].get('squared_orders'), 859 self['process']['sqorders_types']) 860 # Exit condition 861 if len(res)==len(new_res): 862 break 863 elif (len(new_res)>len(res)): 864 raise MadGraph5Error( 865 'Inconsistency in function apply_squared_order_constraints().') 866 # Actualizing the list of diagram for the next iteration 867 res = new_res 868 869 870 871 # Now treat the negative squared order constraint (at most one) 872 neg_orders = [(order, value) for order, value in \ 873 self['process'].get('squared_orders').items() if value<0] 874 if len(neg_orders)==1: 875 neg_order, neg_value = neg_orders[0] 876 # Now check any negative order constraint 877 res, target_order = res.apply_negative_sq_order(res, neg_order,\ 878 neg_value, self['process']['sqorders_types'][neg_order]) 879 # Substitute the negative value to this positive one so that 880 # the resulting computed constraints appears in the print out 881 # and at the output stage we no longer have to deal with 882 # negative valued target orders 883 self['process']['squared_orders'][neg_order]=target_order 884 elif len(neg_orders)>1: 885 raise InvalidCmd('At most one negative squared order constraint'+\ 886 ' can be specified, not %s.'%str(neg_orders)) 887 888 return res
889
890 - def apply_user_filter(self, diag_list):
891 """Applies the user specified squared order constraints on the diagram 892 list in argument.""" 893 894 if True: 895 remove_diag = misc.plugin_import('user_filter', 896 'user filter required to be defined in PLUGIN/user_filter.py with the function remove_diag(ONEDIAG) which returns True if the diagram has to be removed', 897 fcts=['remove_diag']) 898 else: 899 #example and simple tests 900 def remove_diag(diag): 901 for vertex in diag['vertices']: #last 902 if vertex['id'] == 0: #special final vertex 903 continue 904 if vertex['legs'][-1]['number'] < 3: #this means T-channel 905 if abs(vertex['legs'][-1]['id']) <6: 906 return True 907 return False
908 909 res = diag_list.__class__() 910 nb_removed = 0 911 for diag in diag_list: 912 if remove_diag(diag): 913 nb_removed +=1 914 else: 915 res.append(diag) 916 917 if nb_removed: 918 logger.warning('Diagram filter is ON and removed %s diagrams for this subprocess.' % nb_removed) 919 920 return res
921 922 923
924 - def create_diagram(self, vertexlist):
925 """ Return a Diagram created from the vertex list. This function can be 926 overloaded by daughter classes.""" 927 return base_objects.Diagram({'vertices':vertexlist})
928
929 - def convert_dgleg_to_leg(self, vertexdoublelist):
930 """ In LoopAmplitude, it converts back all DGLoopLegs into Legs. 931 In Amplitude, there is nothing to do. """ 932 933 return True
934
935 - def copy_leglist(self, legs):
936 """ Simply returns a copy of the leg list. This function is 937 overloaded in LoopAmplitude so that a DGLoopLeg list is returned. 938 The DGLoopLeg has some additional parameters only useful during 939 loop diagram generation""" 940 941 return base_objects.LegList(\ 942 [ copy.copy(leg) for leg in legs ])
943
944 - def reduce_leglist(self, curr_leglist, max_multi_to1, ref_dict_to0, 945 is_decay_proc = False, coupling_orders = None):
946 """Recursive function to reduce N LegList to N-1 947 For algorithm, see doc for generate_diagrams. 948 """ 949 950 # Result variable which is a list of lists of vertices 951 # to be added 952 res = [] 953 954 # Stop condition. If LegList is None, that means that this 955 # diagram must be discarded 956 if curr_leglist is None: 957 return None 958 959 # Extract ref dict information 960 model = self.get('process').get('model') 961 ref_dict_to1 = self.get('process').get('model').get('ref_dict_to1') 962 963 964 # If all legs can be combined in one single vertex, add this 965 # vertex to res and continue. 966 # Special treatment for decay chain legs 967 968 if curr_leglist.can_combine_to_0(ref_dict_to0, is_decay_proc): 969 # Extract the interaction id associated to the vertex 970 971 vertex_ids = self.get_combined_vertices(curr_leglist, 972 copy.copy(ref_dict_to0[tuple(sorted([leg.get('id') for \ 973 leg in curr_leglist]))])) 974 975 final_vertices = [base_objects.Vertex({'legs':curr_leglist, 976 'id':vertex_id}) for \ 977 vertex_id in vertex_ids] 978 # Check for coupling orders. If orders < 0, skip vertex 979 for final_vertex in final_vertices: 980 if self.reduce_orders(coupling_orders, model, 981 [final_vertex.get('id')]) != False: 982 res.append([final_vertex]) 983 # Stop condition 2: if the leglist contained exactly two particles, 984 # return the result, if any, and stop. 985 if len(curr_leglist) == 2: 986 if res: 987 return res 988 else: 989 return None 990 991 # Create a list of all valid combinations of legs 992 comb_lists = self.combine_legs(curr_leglist, 993 ref_dict_to1, max_multi_to1) 994 995 # Create a list of leglists/vertices by merging combinations 996 leg_vertex_list = self.merge_comb_legs(comb_lists, ref_dict_to1) 997 998 # Consider all the pairs 999 for leg_vertex_tuple in leg_vertex_list: 1000 1001 # Remove forbidden particles 1002 if self.get('process').get('forbidden_particles') and \ 1003 any([abs(vertex.get('legs')[-1].get('id')) in \ 1004 self.get('process').get('forbidden_particles') \ 1005 for vertex in leg_vertex_tuple[1]]): 1006 continue 1007 1008 # Check for coupling orders. If couplings < 0, skip recursion. 1009 new_coupling_orders = self.reduce_orders(coupling_orders, 1010 model, 1011 [vertex.get('id') for vertex in \ 1012 leg_vertex_tuple[1]]) 1013 if new_coupling_orders == False: 1014 # Some coupling order < 0 1015 continue 1016 1017 # This is where recursion happens 1018 # First, reduce again the leg part 1019 reduced_diagram = self.reduce_leglist(leg_vertex_tuple[0], 1020 max_multi_to1, 1021 ref_dict_to0, 1022 is_decay_proc, 1023 new_coupling_orders) 1024 # If there is a reduced diagram 1025 if reduced_diagram: 1026 vertex_list_list = [list(leg_vertex_tuple[1])] 1027 vertex_list_list.append(reduced_diagram) 1028 expanded_list = expand_list_list(vertex_list_list) 1029 res.extend(expanded_list) 1030 1031 return res
1032
1033 - def reduce_orders(self, coupling_orders, model, vertex_id_list):
1034 """Return False if the coupling orders for any coupling is < 1035 0, otherwise return the new coupling orders with the vertex 1036 orders subtracted. If coupling_orders is not given, return 1037 None (which counts as success). 1038 WEIGHTED is a special order, which corresponds to the sum of 1039 order hierarchies for the couplings. 1040 We ignore negative constraints as these cannot be taken into 1041 account on the fly but only after generation.""" 1042 1043 if not coupling_orders: 1044 return None 1045 1046 present_couplings = copy.copy(coupling_orders) 1047 for id in vertex_id_list: 1048 # Don't check for identity vertex (id = 0) 1049 if not id: 1050 continue 1051 inter = model.get("interaction_dict")[id] 1052 for coupling in inter.get('orders').keys(): 1053 # Note that we don't consider a missing coupling as a 1054 # constraint 1055 if coupling in present_couplings and \ 1056 present_couplings[coupling]>=0: 1057 # Reduce the number of couplings that are left 1058 present_couplings[coupling] -= \ 1059 inter.get('orders')[coupling] 1060 if present_couplings[coupling] < 0: 1061 # We have too many couplings of this type 1062 return False 1063 # Now check for WEIGHTED, i.e. the sum of coupling hierarchy values 1064 if 'WEIGHTED' in present_couplings and \ 1065 present_couplings['WEIGHTED']>=0: 1066 weight = sum([model.get('order_hierarchy')[c]*n for \ 1067 (c,n) in inter.get('orders').items()]) 1068 present_couplings['WEIGHTED'] -= weight 1069 if present_couplings['WEIGHTED'] < 0: 1070 # Total coupling weight too large 1071 return False 1072 1073 return present_couplings
1074
1075 - def combine_legs(self, list_legs, ref_dict_to1, max_multi_to1):
1076 """Recursive function. Take a list of legs as an input, with 1077 the reference dictionary n-1->1, and output a list of list of 1078 tuples of Legs (allowed combinations) and Legs (rest). Algorithm: 1079 1080 1. Get all n-combinations from list [123456]: [12],..,[23],..,[123],.. 1081 1082 2. For each combination, say [34]. Check if combination is valid. 1083 If so: 1084 1085 a. Append [12[34]56] to result array 1086 1087 b. Split [123456] at index(first element in combination+1), 1088 i.e. [12],[456] and subtract combination from second half, 1089 i.e.: [456]-[34]=[56]. Repeat from 1. with this array 1090 1091 3. Take result array from call to 1. (here, [[56]]) and append 1092 (first half in step b - combination) + combination + (result 1093 from 1.) = [12[34][56]] to result array 1094 1095 4. After appending results from all n-combinations, return 1096 resulting array. Example, if [13] and [45] are valid 1097 combinations: 1098 [[[13]2456],[[13]2[45]6],[123[45]6]] 1099 """ 1100 1101 res = [] 1102 1103 # loop over possible combination lengths (+1 is for range convention!) 1104 for comb_length in range(2, max_multi_to1 + 1): 1105 1106 # Check the considered length is not longer than the list length 1107 if comb_length > len(list_legs): 1108 return res 1109 1110 # itertools.combinations returns all possible combinations 1111 # of comb_length elements from list_legs 1112 for comb in itertools.combinations(list_legs, comb_length): 1113 1114 # Check if the combination is valid 1115 if base_objects.LegList(comb).can_combine_to_1(ref_dict_to1): 1116 1117 # Identify the rest, create a list [comb,rest] and 1118 # add it to res 1119 res_list = copy.copy(list_legs) 1120 for leg in comb: 1121 res_list.remove(leg) 1122 res_list.insert(list_legs.index(comb[0]), comb) 1123 res.append(res_list) 1124 1125 # Now, deal with cases with more than 1 combination 1126 1127 # First, split the list into two, according to the 1128 # position of the first element in comb, and remove 1129 # all elements form comb 1130 res_list1 = list_legs[0:list_legs.index(comb[0])] 1131 res_list2 = list_legs[list_legs.index(comb[0]) + 1:] 1132 for leg in comb[1:]: 1133 res_list2.remove(leg) 1134 1135 # Create a list of type [comb,rest1,rest2(combined)] 1136 res_list = res_list1 1137 res_list.append(comb) 1138 # This is where recursion actually happens, 1139 # on the second part 1140 for item in self.combine_legs(res_list2, 1141 ref_dict_to1, 1142 max_multi_to1): 1143 final_res_list = copy.copy(res_list) 1144 final_res_list.extend(item) 1145 res.append(final_res_list) 1146 1147 return res
1148 1149
1150 - def merge_comb_legs(self, comb_lists, ref_dict_to1):
1151 """Takes a list of allowed leg combinations as an input and returns 1152 a set of lists where combinations have been properly replaced 1153 (one list per element in the ref_dict, so that all possible intermediate 1154 particles are included). For each list, give the list of vertices 1155 corresponding to the executed merging, group the two as a tuple. 1156 """ 1157 1158 res = [] 1159 1160 for comb_list in comb_lists: 1161 1162 reduced_list = [] 1163 vertex_list = [] 1164 1165 for entry in comb_list: 1166 1167 # Act on all leg combinations 1168 if isinstance(entry, tuple): 1169 1170 # Build the leg object which will replace the combination: 1171 # 1) leg ids is as given in the ref_dict 1172 leg_vert_ids = copy.copy(ref_dict_to1[\ 1173 tuple(sorted([leg.get('id') for leg in entry]))]) 1174 # 2) number is the minimum of leg numbers involved in the 1175 # combination 1176 number = min([leg.get('number') for leg in entry]) 1177 # 3) state is final, unless there is exactly one initial 1178 # state particle involved in the combination -> t-channel 1179 if len(filter(lambda leg: leg.get('state') == False, 1180 entry)) == 1: 1181 state = False 1182 else: 1183 state = True 1184 # 4) from_group is True, by definition 1185 1186 # Create and add the object. This is done by a 1187 # separate routine, to allow overloading by 1188 # daughter classes 1189 new_leg_vert_ids = [] 1190 if leg_vert_ids: 1191 new_leg_vert_ids = self.get_combined_legs(entry, 1192 leg_vert_ids, 1193 number, 1194 state) 1195 1196 reduced_list.append([l[0] for l in new_leg_vert_ids]) 1197 1198 1199 # Create and add the corresponding vertex 1200 # Extract vertex ids corresponding to the various legs 1201 # in mylegs 1202 vlist = base_objects.VertexList() 1203 for (myleg, vert_id) in new_leg_vert_ids: 1204 # Start with the considered combination... 1205 myleglist = base_objects.LegList(list(entry)) 1206 # ... and complete with legs after reducing 1207 myleglist.append(myleg) 1208 # ... and consider the correct vertex id 1209 vlist.append(base_objects.Vertex( 1210 {'legs':myleglist, 1211 'id':vert_id})) 1212 1213 vertex_list.append(vlist) 1214 1215 # If entry is not a combination, switch the from_group flag 1216 # and add it 1217 else: 1218 cp_entry = copy.copy(entry) 1219 # Need special case for from_group == None; this 1220 # is for initial state leg of decay chain process 1221 # (see Leg.can_combine_to_0) 1222 if cp_entry.get('from_group') != None: 1223 cp_entry.set('from_group', False) 1224 reduced_list.append(cp_entry) 1225 1226 # Flatten the obtained leg and vertex lists 1227 flat_red_lists = expand_list(reduced_list) 1228 flat_vx_lists = expand_list(vertex_list) 1229 1230 # Combine the two lists in a list of tuple 1231 for i in range(0, len(flat_vx_lists)): 1232 res.append((base_objects.LegList(flat_red_lists[i]), \ 1233 base_objects.VertexList(flat_vx_lists[i]))) 1234 1235 return res
1236
1237 - def get_combined_legs(self, legs, leg_vert_ids, number, state):
1238 """Create a set of new legs from the info given. This can be 1239 overloaded by daughter classes.""" 1240 1241 mylegs = [(base_objects.Leg({'id':leg_id, 1242 'number':number, 1243 'state':state, 1244 'from_group':True}), 1245 vert_id)\ 1246 for leg_id, vert_id in leg_vert_ids] 1247 1248 return mylegs
1249
1250 - def get_combined_vertices(self, legs, vert_ids):
1251 """Allow for selection of vertex ids. This can be 1252 overloaded by daughter classes.""" 1253 1254 return vert_ids
1255
1256 - def trim_diagrams(self, decay_ids=[], diaglist=None):
1257 """Reduce the number of legs and vertices used in memory. 1258 When called by a diagram generation initiated by LoopAmplitude, 1259 this function should not trim the diagrams in the attribute 'diagrams' 1260 but rather a given list in the 'diaglist' argument.""" 1261 1262 legs = [] 1263 vertices = [] 1264 1265 if diaglist is None: 1266 diaglist=self.get('diagrams') 1267 1268 # Flag decaying legs in the core process by onshell = True 1269 process = self.get('process') 1270 for leg in process.get('legs'): 1271 if leg.get('state') and leg.get('id') in decay_ids: 1272 leg.set('onshell', True) 1273 1274 for diagram in diaglist: 1275 # Keep track of external legs (leg numbers already used) 1276 leg_external = set() 1277 for ivx, vertex in enumerate(diagram.get('vertices')): 1278 for ileg, leg in enumerate(vertex.get('legs')): 1279 # Ensure that only external legs get decay flag 1280 if leg.get('state') and leg.get('id') in decay_ids and \ 1281 leg.get('number') not in leg_external: 1282 # Use onshell to indicate decaying legs, 1283 # i.e. legs that have decay chains 1284 leg = copy.copy(leg) 1285 leg.set('onshell', True) 1286 try: 1287 index = legs.index(leg) 1288 except ValueError: 1289 vertex.get('legs')[ileg] = leg 1290 legs.append(leg) 1291 else: # Found a leg 1292 vertex.get('legs')[ileg] = legs[index] 1293 leg_external.add(leg.get('number')) 1294 try: 1295 index = vertices.index(vertex) 1296 diagram.get('vertices')[ivx] = vertices[index] 1297 except ValueError: 1298 vertices.append(vertex)
1299
1300 #=============================================================================== 1301 # AmplitudeList 1302 #=============================================================================== 1303 -class AmplitudeList(base_objects.PhysicsObjectList):
1304 """List of Amplitude objects 1305 """ 1306
1307 - def has_any_loop_process(self):
1308 """ Check the content of all processes of the amplitudes in this list to 1309 see if there is any which defines perturbation couplings. """ 1310 1311 for amp in self: 1312 if amp.has_loop_process(): 1313 return True
1314
1315 - def is_valid_element(self, obj):
1316 """Test if object obj is a valid Amplitude for the list.""" 1317 1318 return isinstance(obj, Amplitude)
1319
1320 #=============================================================================== 1321 # DecayChainAmplitude 1322 #=============================================================================== 1323 -class DecayChainAmplitude(Amplitude):
1324 """A list of amplitudes + a list of decay chain amplitude lists; 1325 corresponding to a ProcessDefinition with a list of decay chains 1326 """ 1327
1328 - def default_setup(self):
1329 """Default values for all properties""" 1330 1331 self['amplitudes'] = AmplitudeList() 1332 self['decay_chains'] = DecayChainAmplitudeList()
1333
1334 - def __init__(self, argument = None, collect_mirror_procs = False, 1335 ignore_six_quark_processes = False, loop_filter=None, diagram_filter=False):
1336 """Allow initialization with Process and with ProcessDefinition""" 1337 1338 if isinstance(argument, base_objects.Process): 1339 super(DecayChainAmplitude, self).__init__() 1340 from madgraph.loop.loop_diagram_generation import LoopMultiProcess 1341 if argument['perturbation_couplings']: 1342 MultiProcessClass=LoopMultiProcess 1343 else: 1344 MultiProcessClass=MultiProcess 1345 if isinstance(argument, base_objects.ProcessDefinition): 1346 self['amplitudes'].extend(\ 1347 MultiProcessClass.generate_multi_amplitudes(argument, 1348 collect_mirror_procs, 1349 ignore_six_quark_processes, 1350 loop_filter=loop_filter, 1351 diagram_filter=diagram_filter)) 1352 else: 1353 self['amplitudes'].append(\ 1354 MultiProcessClass.get_amplitude_from_proc(argument, 1355 loop_filter=loop_filter, 1356 diagram_filter=diagram_filter)) 1357 # Clean decay chains from process, since we haven't 1358 # combined processes with decay chains yet 1359 process = copy.copy(self.get('amplitudes')[0].get('process')) 1360 process.set('decay_chains', base_objects.ProcessList()) 1361 self['amplitudes'][0].set('process', process) 1362 1363 for process in argument.get('decay_chains'): 1364 if process.get('perturbation_couplings'): 1365 raise MadGraph5Error,\ 1366 "Decay processes can not be perturbed" 1367 process.set('overall_orders', argument.get('overall_orders')) 1368 if not process.get('is_decay_chain'): 1369 process.set('is_decay_chain',True) 1370 if not process.get_ninitial() == 1: 1371 raise InvalidCmd,\ 1372 "Decay chain process must have exactly one" + \ 1373 " incoming particle" 1374 self['decay_chains'].append(\ 1375 DecayChainAmplitude(process, collect_mirror_procs, 1376 ignore_six_quark_processes)) 1377 1378 # Flag decaying legs in the core diagrams by onshell = True 1379 decay_ids = sum([[a.get('process').get('legs')[0].get('id') \ 1380 for a in dec.get('amplitudes')] for dec in \ 1381 self['decay_chains']], []) 1382 decay_ids = set(decay_ids) 1383 for amp in self['amplitudes']: 1384 amp.trim_diagrams(decay_ids) 1385 1386 # Check that all decay ids are present in at least some process 1387 for amp in self['amplitudes']: 1388 for l in amp.get('process').get('legs'): 1389 if l.get('id') in decay_ids: 1390 decay_ids.remove(l.get('id')) 1391 1392 if decay_ids: 1393 model = amp.get('process').get('model') 1394 names = [model.get_particle(id).get('name') for id in decay_ids] 1395 1396 logger.warning( 1397 "$RED Decay without corresponding particle in core process found.\n" + \ 1398 "Decay information for particle(s) %s is discarded.\n" % ','.join(names) + \ 1399 "Please check your process definition carefully. \n" + \ 1400 "This warning usually means that you forgot parentheses in presence of subdecay.\n" + \ 1401 "Example of correct syntax: p p > t t~, ( t > w+ b, w+ > l+ vl)") 1402 1403 # Remove unused decays from the process list 1404 for dc in reversed(self['decay_chains']): 1405 for a in reversed(dc.get('amplitudes')): 1406 # Remove the amplitudes from this decay chain 1407 if a.get('process').get('legs')[0].get('id') in decay_ids: 1408 dc.get('amplitudes').remove(a) 1409 if not dc.get('amplitudes'): 1410 # If no amplitudes left, remove the decay chain 1411 self['decay_chains'].remove(dc) 1412 1413 # Finally, write a fat warning if any decay process has 1414 # the decaying particle (or its antiparticle) in the final state 1415 bad_procs = [] 1416 for dc in self['decay_chains']: 1417 for amp in dc.get('amplitudes'): 1418 legs = amp.get('process').get('legs') 1419 fs_parts = [abs(l.get('id')) for l in legs if 1420 l.get('state')] 1421 is_part = [l.get('id') for l in legs if not 1422 l.get('state')][0] 1423 if abs(is_part) in fs_parts: 1424 bad_procs.append(amp.get('process')) 1425 1426 if bad_procs: 1427 logger.warning( 1428 "$RED Decay(s) with particle decaying to itself:\n" + \ 1429 '\n'.join([p.nice_string() for p in bad_procs]) + \ 1430 "\nPlease check your process definition carefully. \n") 1431 1432 1433 elif argument != None: 1434 # call the mother routine 1435 super(DecayChainAmplitude, self).__init__(argument) 1436 else: 1437 # call the mother routine 1438 super(DecayChainAmplitude, self).__init__()
1439
1440 - def filter(self, name, value):
1441 """Filter for valid amplitude property values.""" 1442 1443 if name == 'amplitudes': 1444 if not isinstance(value, AmplitudeList): 1445 raise self.PhysicsObjectError, \ 1446 "%s is not a valid AmplitudeList" % str(value) 1447 if name == 'decay_chains': 1448 if not isinstance(value, DecayChainAmplitudeList): 1449 raise self.PhysicsObjectError, \ 1450 "%s is not a valid DecayChainAmplitudeList object" % \ 1451 str(value) 1452 return True
1453
1454 - def get_sorted_keys(self):
1455 """Return diagram property names as a nicely sorted list.""" 1456 1457 return ['amplitudes', 'decay_chains']
1458 1459 # Helper functions 1460
1461 - def get_number_of_diagrams(self):
1462 """Returns number of diagrams for this amplitude""" 1463 return sum(len(a.get('diagrams')) for a in self.get('amplitudes')) \ 1464 + sum(d.get_number_of_diagrams() for d in \ 1465 self.get('decay_chains'))
1466
1467 - def nice_string(self, indent = 0):
1468 """Returns a nicely formatted string of the amplitude content.""" 1469 mystr = "" 1470 for amplitude in self.get('amplitudes'): 1471 mystr = mystr + amplitude.nice_string(indent) + "\n" 1472 1473 if self.get('decay_chains'): 1474 mystr = mystr + " " * indent + "Decays:\n" 1475 for dec in self.get('decay_chains'): 1476 mystr = mystr + dec.nice_string(indent + 2) + "\n" 1477 1478 return mystr[:-1]
1479
1480 - def nice_string_processes(self, indent = 0):
1481 """Returns a nicely formatted string of the amplitude processes.""" 1482 mystr = "" 1483 for amplitude in self.get('amplitudes'): 1484 mystr = mystr + amplitude.nice_string_processes(indent) + "\n" 1485 1486 if self.get('decay_chains'): 1487 mystr = mystr + " " * indent + "Decays:\n" 1488 for dec in self.get('decay_chains'): 1489 mystr = mystr + dec.nice_string_processes(indent + 2) + "\n" 1490 1491 return mystr[:-1]
1492
1493 - def get_ninitial(self):
1494 """Returns the number of initial state particles in the process.""" 1495 return self.get('amplitudes')[0].get('process').get_ninitial()
1496
1497 - def get_decay_ids(self):
1498 """Returns a set of all particle ids for which a decay is defined""" 1499 1500 decay_ids = [] 1501 1502 # Get all amplitudes for the decay processes 1503 for amp in sum([dc.get('amplitudes') for dc \ 1504 in self['decay_chains']], []): 1505 # For each amplitude, find the initial state leg 1506 decay_ids.append(amp.get('process').get_initial_ids()[0]) 1507 1508 # Return a list with unique ids 1509 return list(set(decay_ids))
1510
1511 - def has_loop_process(self):
1512 """ Returns wether this amplitude has a loop process.""" 1513 return self['amplitudes'].has_any_loop_process()
1514
1515 - def get_amplitudes(self):
1516 """Recursive function to extract all amplitudes for this process""" 1517 1518 amplitudes = AmplitudeList() 1519 1520 amplitudes.extend(self.get('amplitudes')) 1521 for decay in self.get('decay_chains'): 1522 amplitudes.extend(decay.get_amplitudes()) 1523 1524 return amplitudes
1525
1526 1527 #=============================================================================== 1528 # DecayChainAmplitudeList 1529 #=============================================================================== 1530 -class DecayChainAmplitudeList(base_objects.PhysicsObjectList):
1531 """List of DecayChainAmplitude objects 1532 """ 1533
1534 - def is_valid_element(self, obj):
1535 """Test if object obj is a valid DecayChainAmplitude for the list.""" 1536 1537 return isinstance(obj, DecayChainAmplitude)
1538
1539 1540 #=============================================================================== 1541 # MultiProcess 1542 #=============================================================================== 1543 -class MultiProcess(base_objects.PhysicsObject):
1544 """MultiProcess: list of process definitions 1545 list of processes (after cleaning) 1546 list of amplitudes (after generation) 1547 """ 1548
1549 - def default_setup(self):
1550 """Default values for all properties""" 1551 1552 self['process_definitions'] = base_objects.ProcessDefinitionList() 1553 # self['amplitudes'] can be an AmplitudeList or a 1554 # DecayChainAmplitudeList, depending on whether there are 1555 # decay chains in the process definitions or not. 1556 self['amplitudes'] = AmplitudeList() 1557 # Flag for whether to combine IS mirror processes together 1558 self['collect_mirror_procs'] = False 1559 # List of quark flavors where we ignore processes with at 1560 # least 6 quarks (three quark lines) 1561 self['ignore_six_quark_processes'] = [] 1562 # Allow to use the model parameter numerical value for optimization. 1563 #This is currently use for 1->N generation(check mass). 1564 self['use_numerical'] = False
1565
1566 - def __init__(self, argument=None, collect_mirror_procs = False, 1567 ignore_six_quark_processes = [], optimize=False, 1568 loop_filter=None, diagram_filter=None):
1569 """Allow initialization with ProcessDefinition or 1570 ProcessDefinitionList 1571 optimize allows to use param_card information. (usefull for 1-.N)""" 1572 1573 if isinstance(argument, base_objects.ProcessDefinition): 1574 super(MultiProcess, self).__init__() 1575 self['process_definitions'].append(argument) 1576 elif isinstance(argument, base_objects.ProcessDefinitionList): 1577 super(MultiProcess, self).__init__() 1578 self['process_definitions'] = argument 1579 elif argument != None: 1580 # call the mother routine 1581 super(MultiProcess, self).__init__(argument) 1582 else: 1583 # call the mother routine 1584 super(MultiProcess, self).__init__() 1585 1586 self['collect_mirror_procs'] = collect_mirror_procs 1587 self['ignore_six_quark_processes'] = ignore_six_quark_processes 1588 self['use_numerical'] = optimize 1589 self['loop_filter'] = loop_filter 1590 self['diagram_filter'] = diagram_filter # only True/False so far 1591 1592 if isinstance(argument, base_objects.ProcessDefinition) or \ 1593 isinstance(argument, base_objects.ProcessDefinitionList): 1594 # Generate the diagrams 1595 self.get('amplitudes')
1596 1597
1598 - def filter(self, name, value):
1599 """Filter for valid process property values.""" 1600 1601 if name == 'process_definitions': 1602 if not isinstance(value, base_objects.ProcessDefinitionList): 1603 raise self.PhysicsObjectError, \ 1604 "%s is not a valid ProcessDefinitionList object" % str(value) 1605 1606 if name == 'amplitudes': 1607 if not isinstance(value, AmplitudeList): 1608 raise self.PhysicsObjectError, \ 1609 "%s is not a valid AmplitudeList object" % str(value) 1610 1611 if name in ['collect_mirror_procs']: 1612 if not isinstance(value, bool): 1613 raise self.PhysicsObjectError, \ 1614 "%s is not a valid boolean" % str(value) 1615 1616 if name == 'ignore_six_quark_processes': 1617 if not isinstance(value, list): 1618 raise self.PhysicsObjectError, \ 1619 "%s is not a valid list" % str(value) 1620 1621 return True
1622
1623 - def get(self, name):
1624 """Get the value of the property name.""" 1625 1626 if (name == 'amplitudes') and not self[name]: 1627 for process_def in self.get('process_definitions'): 1628 if process_def.get('decay_chains'): 1629 # This is a decay chain process 1630 # Store amplitude(s) as DecayChainAmplitude 1631 self['amplitudes'].append(\ 1632 DecayChainAmplitude(process_def, 1633 self.get('collect_mirror_procs'), 1634 self.get('ignore_six_quark_processes'), 1635 diagram_filter=self['diagram_filter'])) 1636 else: 1637 self['amplitudes'].extend(\ 1638 self.generate_multi_amplitudes(process_def, 1639 self.get('collect_mirror_procs'), 1640 self.get('ignore_six_quark_processes'), 1641 self['use_numerical'], 1642 loop_filter=self['loop_filter'], 1643 diagram_filter=self['diagram_filter'])) 1644 1645 return MultiProcess.__bases__[0].get(self, name) # call the mother routine
1646
1647 - def get_sorted_keys(self):
1648 """Return process property names as a nicely sorted list.""" 1649 1650 return ['process_definitions', 'amplitudes']
1651 1652 @classmethod
1653 - def generate_multi_amplitudes(cls,process_definition, 1654 collect_mirror_procs = False, 1655 ignore_six_quark_processes = [], 1656 use_numerical=False, 1657 loop_filter=None, 1658 diagram_filter=False):
1659 """Generate amplitudes in a semi-efficient way. 1660 Make use of crossing symmetry for processes that fail diagram 1661 generation, but not for processes that succeed diagram 1662 generation. Doing so will risk making it impossible to 1663 identify processes with identical amplitudes. 1664 """ 1665 assert isinstance(process_definition, base_objects.ProcessDefinition), \ 1666 "%s not valid ProcessDefinition object" % \ 1667 repr(process_definition) 1668 1669 # Set automatic coupling orders 1670 process_definition.set('orders', MultiProcess.\ 1671 find_optimal_process_orders(process_definition, 1672 diagram_filter)) 1673 # Check for maximum orders from the model 1674 process_definition.check_expansion_orders() 1675 1676 processes = base_objects.ProcessList() 1677 amplitudes = AmplitudeList() 1678 1679 # failed_procs and success_procs are sorted processes that have 1680 # already failed/succeeded based on crossing symmetry 1681 failed_procs = [] 1682 success_procs = [] 1683 # Complete processes, for identification of mirror processes 1684 non_permuted_procs = [] 1685 # permutations keeps the permutations of the crossed processes 1686 permutations = [] 1687 1688 # Store the diagram tags for processes, to allow for 1689 # identifying identical matrix elements already at this stage. 1690 model = process_definition['model'] 1691 1692 isids = [leg['ids'] for leg in process_definition['legs'] \ 1693 if leg['state'] == False] 1694 fsids = [leg['ids'] for leg in process_definition['legs'] \ 1695 if leg['state'] == True] 1696 # Generate all combinations for the initial state 1697 1698 for prod in itertools.product(*isids): 1699 islegs = [\ 1700 base_objects.Leg({'id':id, 'state': False}) \ 1701 for id in prod] 1702 1703 # Generate all combinations for the final state, and make 1704 # sure to remove double counting 1705 1706 red_fsidlist = [] 1707 1708 for prod in itertools.product(*fsids): 1709 1710 # Remove double counting between final states 1711 if tuple(sorted(prod)) in red_fsidlist: 1712 continue 1713 1714 red_fsidlist.append(tuple(sorted(prod))); 1715 1716 # Generate leg list for process 1717 leg_list = [copy.copy(leg) for leg in islegs] 1718 1719 leg_list.extend([\ 1720 base_objects.Leg({'id':id, 'state': True}) \ 1721 for id in prod]) 1722 1723 legs = base_objects.LegList(leg_list) 1724 1725 # Check for crossed processes 1726 sorted_legs = sorted([(l,i+1) for (i,l) in \ 1727 enumerate(legs.get_outgoing_id_list(model))]) 1728 permutation = [l[1] for l in sorted_legs] 1729 1730 sorted_legs = array.array('i', [l[0] for l in sorted_legs]) 1731 1732 # Check for six-quark processes 1733 if ignore_six_quark_processes and \ 1734 len([i for i in sorted_legs if abs(i) in \ 1735 ignore_six_quark_processes]) >= 6: 1736 continue 1737 1738 # Check if crossed process has already failed, 1739 # in that case don't check process 1740 if sorted_legs in failed_procs: 1741 continue 1742 1743 # If allowed check mass validity [assume 1->N] 1744 if use_numerical: 1745 # check that final state has lower mass than initial state 1746 initial_mass = abs(model['parameter_dict'][model.get_particle(legs[0].get('id')).get('mass')]) 1747 if initial_mass == 0: 1748 continue 1749 for leg in legs[1:]: 1750 m = model['parameter_dict'][model.get_particle(leg.get('id')).get('mass')] 1751 initial_mass -= abs(m) 1752 if initial_mass.real <= 0: 1753 continue 1754 1755 # Setup process 1756 process = process_definition.get_process_with_legs(legs) 1757 1758 fast_proc = \ 1759 array.array('i',[leg.get('id') for leg in legs]) 1760 if collect_mirror_procs and \ 1761 process_definition.get_ninitial() == 2: 1762 # Check if mirrored process is already generated 1763 mirror_proc = \ 1764 array.array('i', [fast_proc[1], fast_proc[0]] + \ 1765 list(fast_proc[2:])) 1766 try: 1767 mirror_amp = \ 1768 amplitudes[non_permuted_procs.index(mirror_proc)] 1769 except Exception: 1770 # Didn't find any mirror process 1771 pass 1772 else: 1773 # Mirror process found 1774 mirror_amp.set('has_mirror_process', True) 1775 logger.info("Process %s added to mirror process %s" % \ 1776 (process.base_string(), 1777 mirror_amp.get('process').base_string())) 1778 continue 1779 1780 # Check for successful crossings, unless we have specified 1781 # properties that break crossing symmetry 1782 if not process.get('required_s_channels') and \ 1783 not process.get('forbidden_onsh_s_channels') and \ 1784 not process.get('forbidden_s_channels') and \ 1785 not process.get('is_decay_chain'): 1786 try: 1787 crossed_index = success_procs.index(sorted_legs) 1788 # The relabeling of legs for loop amplitudes is cumbersome 1789 # and does not save so much time. It is disable here and 1790 # we use the key 'loop_diagrams' to decide whether 1791 # it is an instance of LoopAmplitude. 1792 if 'loop_diagrams' in amplitudes[crossed_index]: 1793 raise ValueError 1794 except ValueError: 1795 # No crossing found, just continue 1796 pass 1797 else: 1798 # Found crossing - reuse amplitude 1799 amplitude = MultiProcess.cross_amplitude(\ 1800 amplitudes[crossed_index], 1801 process, 1802 permutations[crossed_index], 1803 permutation) 1804 amplitudes.append(amplitude) 1805 success_procs.append(sorted_legs) 1806 permutations.append(permutation) 1807 non_permuted_procs.append(fast_proc) 1808 logger.info("Crossed process found for %s, reuse diagrams." % \ 1809 process.base_string()) 1810 continue 1811 1812 # Create new amplitude 1813 amplitude = cls.get_amplitude_from_proc(process, 1814 loop_filter=loop_filter) 1815 1816 try: 1817 result = amplitude.generate_diagrams(diagram_filter=diagram_filter) 1818 except InvalidCmd as error: 1819 failed_procs.append(sorted_legs) 1820 else: 1821 # Succeeded in generating diagrams 1822 if amplitude.get('diagrams'): 1823 amplitudes.append(amplitude) 1824 success_procs.append(sorted_legs) 1825 permutations.append(permutation) 1826 non_permuted_procs.append(fast_proc) 1827 elif not result: 1828 # Diagram generation failed for all crossings 1829 failed_procs.append(sorted_legs) 1830 1831 # Raise exception if there are no amplitudes for this process 1832 if not amplitudes: 1833 if len(failed_procs) == 1 and 'error' in locals(): 1834 raise error 1835 else: 1836 raise NoDiagramException, \ 1837 "No amplitudes generated from process %s. Please enter a valid process" % \ 1838 process_definition.nice_string() 1839 1840 1841 # Return the produced amplitudes 1842 return amplitudes
1843 1844 @classmethod
1845 - def get_amplitude_from_proc(cls,proc,**opts):
1846 """ Return the correct amplitude type according to the characteristics of 1847 the process proc. The only option that could be specified here is 1848 loop_filter and it is of course not relevant for a tree amplitude.""" 1849 1850 return Amplitude({"process": proc})
1851 1852 1853 @staticmethod
1854 - def find_optimal_process_orders(process_definition, diagram_filter=False):
1855 """Find the minimal WEIGHTED order for this set of processes. 1856 1857 The algorithm: 1858 1859 1) Check the coupling hierarchy of the model. Assign all 1860 particles to the different coupling hierarchies so that a 1861 particle is considered to be in the highest hierarchy (i.e., 1862 with lowest value) where it has an interaction. 1863 1864 2) Pick out the legs in the multiprocess according to the 1865 highest hierarchy represented (so don't mix particles from 1866 different hierarchy classes in the same multiparticles!) 1867 1868 3) Find the starting maximum WEIGHTED order as the sum of the 1869 highest n-2 weighted orders 1870 1871 4) Pick out required s-channel particle hierarchies, and use 1872 the highest of the maximum WEIGHTED order from the legs and 1873 the minimum WEIGHTED order extracted from 2*s-channel 1874 hierarchys plus the n-2-2*(number of s-channels) lowest 1875 leg weighted orders. 1876 1877 5) Run process generation with the WEIGHTED order determined 1878 in 3)-4) - # final state gluons, with all gluons removed from 1879 the final state 1880 1881 6) If no process is found, increase WEIGHTED order by 1 and go 1882 back to 5), until we find a process which passes. Return that 1883 order. 1884 1885 7) Continue 5)-6) until we reach (n-2)*(highest hierarchy)-1. 1886 If still no process has passed, return 1887 WEIGHTED = (n-2)*(highest hierarchy) 1888 """ 1889 1890 assert isinstance(process_definition, base_objects.ProcessDefinition), \ 1891 "%s not valid ProcessDefinition object" % \ 1892 repr(process_definition) 1893 1894 processes = base_objects.ProcessList() 1895 amplitudes = AmplitudeList() 1896 1897 # If there are already couplings defined, return 1898 if process_definition.get('orders') or \ 1899 process_definition.get('overall_orders') or \ 1900 process_definition.get('NLO_mode')=='virt': 1901 return process_definition.get('orders') 1902 1903 # If this is a decay process (and not a decay chain), return 1904 if process_definition.get_ninitial() == 1 and not \ 1905 process_definition.get('is_decay_chain'): 1906 return process_definition.get('orders') 1907 1908 logger.info("Checking for minimal orders which gives processes.") 1909 logger.info("Please specify coupling orders to bypass this step.") 1910 1911 # Calculate minimum starting guess for WEIGHTED order 1912 max_order_now, particles, hierarchy = \ 1913 process_definition.get_minimum_WEIGHTED() 1914 coupling = 'WEIGHTED' 1915 1916 model = process_definition.get('model') 1917 1918 # Extract the initial and final leg ids 1919 isids = [leg['ids'] for leg in \ 1920 filter(lambda leg: leg['state'] == False, process_definition['legs'])] 1921 fsids = [leg['ids'] for leg in \ 1922 filter(lambda leg: leg['state'] == True, process_definition['legs'])] 1923 1924 max_WEIGHTED_order = \ 1925 (len(fsids + isids) - 2)*int(model.get_max_WEIGHTED()) 1926 # get the definition of the WEIGHTED 1927 hierarchydef = process_definition['model'].get('order_hierarchy') 1928 tmp = [] 1929 hierarchy = hierarchydef.items() 1930 hierarchy.sort() 1931 for key, value in hierarchydef.items(): 1932 if value>1: 1933 tmp.append('%s*%s' % (value,key)) 1934 else: 1935 tmp.append('%s' % key) 1936 wgtdef = '+'.join(tmp) 1937 # Run diagram generation with increasing max_order_now until 1938 # we manage to get diagrams 1939 while max_order_now < max_WEIGHTED_order: 1940 logger.info("Trying coupling order WEIGHTED<=%d: WEIGTHED IS %s" % (max_order_now, wgtdef)) 1941 1942 oldloglevel = logger.level 1943 logger.setLevel(logging.WARNING) 1944 1945 # failed_procs are processes that have already failed 1946 # based on crossing symmetry 1947 failed_procs = [] 1948 # Generate all combinations for the initial state 1949 for prod in apply(itertools.product, isids): 1950 islegs = [ base_objects.Leg({'id':id, 'state': False}) \ 1951 for id in prod] 1952 1953 # Generate all combinations for the final state, and make 1954 # sure to remove double counting 1955 1956 red_fsidlist = [] 1957 1958 for prod in apply(itertools.product, fsids): 1959 1960 # Remove double counting between final states 1961 if tuple(sorted(prod)) in red_fsidlist: 1962 continue 1963 1964 red_fsidlist.append(tuple(sorted(prod))); 1965 1966 # Remove gluons from final state if QCD is among 1967 # the highest coupling hierarchy 1968 nglue = 0 1969 if 21 in particles[0]: 1970 nglue = len([id for id in prod if id == 21]) 1971 prod = [id for id in prod if id != 21] 1972 1973 # Generate leg list for process 1974 leg_list = [copy.copy(leg) for leg in islegs] 1975 1976 leg_list.extend([\ 1977 base_objects.Leg({'id':id, 'state': True}) \ 1978 for id in prod]) 1979 1980 legs = base_objects.LegList(leg_list) 1981 1982 # Set summed coupling order according to max_order_now 1983 # subtracting the removed gluons 1984 coupling_orders_now = {coupling: max_order_now - \ 1985 nglue * model['order_hierarchy']['QCD']} 1986 1987 # Setup process 1988 process = base_objects.Process({\ 1989 'legs':legs, 1990 'model':model, 1991 'id': process_definition.get('id'), 1992 'orders': coupling_orders_now, 1993 'required_s_channels': \ 1994 process_definition.get('required_s_channels'), 1995 'forbidden_onsh_s_channels': \ 1996 process_definition.get('forbidden_onsh_s_channels'), 1997 'sqorders_types': \ 1998 process_definition.get('sqorders_types'), 1999 'squared_orders': \ 2000 process_definition.get('squared_orders'), 2001 'split_orders': \ 2002 process_definition.get('split_orders'), 2003 'forbidden_s_channels': \ 2004 process_definition.get('forbidden_s_channels'), 2005 'forbidden_particles': \ 2006 process_definition.get('forbidden_particles'), 2007 'is_decay_chain': \ 2008 process_definition.get('is_decay_chain'), 2009 'overall_orders': \ 2010 process_definition.get('overall_orders'), 2011 'split_orders': \ 2012 process_definition.get('split_orders')}) 2013 2014 # Check for couplings with given expansion orders 2015 process.check_expansion_orders() 2016 2017 # Check for crossed processes 2018 sorted_legs = sorted(legs.get_outgoing_id_list(model)) 2019 # Check if crossed process has already failed 2020 # In that case don't check process 2021 if tuple(sorted_legs) in failed_procs and not process_definition.get('forbidden_s_channels'): 2022 continue 2023 2024 amplitude = Amplitude({'process': process}) 2025 try: 2026 amplitude.generate_diagrams(diagram_filter=diagram_filter) 2027 except InvalidCmd, error: 2028 failed_procs.append(tuple(sorted_legs)) 2029 else: 2030 if amplitude.get('diagrams'): 2031 # We found a valid amplitude. Return this order number 2032 logger.setLevel(oldloglevel) 2033 return {coupling: max_order_now} 2034 else: 2035 failed_procs.append(tuple(sorted_legs)) 2036 # No processes found, increase max_order_now 2037 max_order_now += 1 2038 logger.setLevel(oldloglevel) 2039 2040 # If no valid processes found with nfinal-1 couplings, return maximal 2041 return {coupling: max_order_now}
2042 2043 @staticmethod
2044 - def cross_amplitude(amplitude, process, org_perm, new_perm):
2045 """Return the amplitude crossed with the permutation new_perm""" 2046 # Create dict from original leg numbers to new leg numbers 2047 perm_map = dict(zip(org_perm, new_perm)) 2048 # Initiate new amplitude 2049 new_amp = copy.copy(amplitude) 2050 # Number legs 2051 for i, leg in enumerate(process.get('legs')): 2052 leg.set('number', i+1) 2053 # Set process 2054 new_amp.set('process', process) 2055 # Now replace the leg numbers in the diagrams 2056 diagrams = base_objects.DiagramList([d.renumber_legs(perm_map, 2057 process.get('legs'),) for \ 2058 d in new_amp.get('diagrams')]) 2059 new_amp.set('diagrams', diagrams) 2060 new_amp.trim_diagrams() 2061 2062 # Make sure to reset mirror process 2063 new_amp.set('has_mirror_process', False) 2064 2065 return new_amp
2066
2067 #=============================================================================== 2068 # Global helper methods 2069 #=============================================================================== 2070 2071 -def expand_list(mylist):
2072 """Takes a list of lists and elements and returns a list of flat lists. 2073 Example: [[1,2], 3, [4,5]] -> [[1,3,4], [1,3,5], [2,3,4], [2,3,5]] 2074 """ 2075 2076 # Check that argument is a list 2077 assert isinstance(mylist, list), "Expand_list argument must be a list" 2078 2079 res = [] 2080 2081 tmplist = [] 2082 for item in mylist: 2083 if isinstance(item, list): 2084 tmplist.append(item) 2085 else: 2086 tmplist.append([item]) 2087 2088 for item in apply(itertools.product, tmplist): 2089 res.append(list(item)) 2090 2091 return res
2092
2093 -def expand_list_list(mylist):
2094 """Recursive function. Takes a list of lists and lists of lists 2095 and returns a list of flat lists. 2096 Example: [[1,2],[[4,5],[6,7]]] -> [[1,2,4,5], [1,2,6,7]] 2097 """ 2098 2099 res = [] 2100 2101 if not mylist or len(mylist) == 1 and not mylist[0]: 2102 return [[]] 2103 2104 # Check the first element is at least a list 2105 assert isinstance(mylist[0], list), \ 2106 "Expand_list_list needs a list of lists and lists of lists" 2107 2108 # Recursion stop condition, one single element 2109 if len(mylist) == 1: 2110 if isinstance(mylist[0][0], list): 2111 return mylist[0] 2112 else: 2113 return mylist 2114 2115 if isinstance(mylist[0][0], list): 2116 for item in mylist[0]: 2117 # Here the recursion happens, create lists starting with 2118 # each element of the first item and completed with 2119 # the rest expanded 2120 for rest in expand_list_list(mylist[1:]): 2121 reslist = copy.copy(item) 2122 reslist.extend(rest) 2123 res.append(reslist) 2124 else: 2125 for rest in expand_list_list(mylist[1:]): 2126 reslist = copy.copy(mylist[0]) 2127 reslist.extend(rest) 2128 res.append(reslist) 2129 2130 2131 return res
2132