# # This file is part of CasADi. # # CasADi -- A symbolic framework for dynamic optimization. # Copyright (C) 2010-2023 Joel Andersson, Joris Gillis, Moritz Diehl, # KU Leuven. All rights reserved. # Copyright (C) 2011-2014 Greg Horn # # CasADi is free software; you can redistribute it and/or # modify it under the terms of the GNU Lesser General Public # License as published by the Free Software Foundation; either # version 3 of the License, or (at your option) any later version. # # CasADi is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU # Lesser General Public License for more details. # # You should have received a copy of the GNU Lesser General Public # License along with CasADi; if not, write to the Free Software # Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA # # from casadi import SX, MX, print_operator import casadi as C try: from pydot import pydot except: try: import pydot except: raise Exception("To use the functionality of casadi.tools.graph, you need to have pydot Installed. Try `easy_install pydot`.") #import ipdb def print_operator_escaped(expr, strs): # replace with {f} to get rid of < or > strs = [ si.replace('<', '{').replace('>', '}') for si in strs ] s = print_operator(expr, strs) # escape < or > s = s.replace('<', r'\<').replace('>', r'\>') # replace {f} with s = s.replace('{', '<').replace('}', '>') return s def hashcompare(self,other): return cmp(hash(self),hash(other)) def equality(self,other): return hash(self)==hash(other) def getDeps(s): deps = [] if not(hasattr(s,'n_dep')): return deps for k in range(s.n_dep()): d = s.dep(k) d.__class__.__cmp__ = hashcompare d.__class__.__eq__ = equality deps.append(d) return deps def addDependency(master,slave,dep={},invdep={}): #print master.__hash__() , " => ", slave.__hash__(), " ", master , " => ", slave if master in dep: dep[master].add(slave) else: dep[master]= set([slave]) if slave in invdep: invdep[slave].add(master) else: invdep[slave] = set([master]) def addDependencies(master,slaves,dep={},invdep={}): for slave in slaves: addDependency(master,slave,dep = dep,invdep = invdep) for slave in slaves: dependencyGraph(slave,dep = dep,invdep = invdep) def is_leaf(s): return s.is_leaf() #return s.is_scalar(True) and (s.is_constant() or s.is_symbolic()) def dependencyGraph(s,dep = {},invdep = {}): if isinstance(s,SX): if s.is_scalar(True): if not(is_leaf(s)): addDependencies(s,getDeps(s),dep = dep,invdep = invdep) else: addDependencies(s,s.nonzeros(),dep = dep,invdep = invdep) elif isinstance(s,MX): addDependencies(s,getDeps(s),dep = dep,invdep = invdep) return (dep,invdep) class DotArtist: sparsitycol = "#eeeeee" def __init__(self,s,dep={},invdep={},graph=None,artists={},**kwargs): self.s = s self.dep = dep self.invdep = invdep self.graph = graph self.artists = artists self.kwargs = kwargs def hasPorts(self): return False def drawSparsity(self,s,id=None,depid=None,graph=None,nzlabels=None): if id is None: id = str(s.__hash__()) if depid is None: depid = str(s.dep(0).__hash__()) if graph is None: graph = self.graph sp = s.sparsity() deps = getDeps(s) if nzlabels is None: nzlabels = list(map(str,list(range(sp.nnz())))) nzlabelcounter = 0 if s.nnz()==s.numel(): graph.add_node(pydot.Node(id,label="%d x %d" % (s.size1(),s.size2()),shape='rectangle',color=self.sparsitycol,style="filled")) else: label = '<' label+="" % (s.size2(), s.dim()) for i in range(s.size1()): label+="" for j in range(s.size2()): k = sp.get_nz(i,j) if k==-1: label+="" else: label+="" % (k,self.sparsitycol,nzlabels[nzlabelcounter]) nzlabelcounter +=1 label+="" label+="
%s
.%s
>" graph.add_node(pydot.Node(id,label=label,shape='plaintext')) graph.add_edge(pydot.Edge(depid,id)) class MXSymbolicArtist(DotArtist): def hasPorts(self): return True def draw(self): s = self.s graph = self.graph sp = s.sparsity() row = sp.row() col = "#990000" if s.nnz() == s.numel() and s.nnz()==1: # The Matrix grid is represented by a html table with 'ports' graph.add_node(pydot.Node(str(self.s.__hash__())+":f0",label=s.name(),shape='rectangle',color=col)) else: # The Matrix grid is represented by a html table with 'ports' label = '<' % col label+="" % (s.size2(),s.name(), s.dim()) for i in range(s.size1()): label+="" for j in range(s.size2()): k = sp.get_nz(i,j) if k==-1: label+="" else: label+="" % (k,i,j,k) label+="" label+="
%s: %s
. (%d,%d | %d)
>" graph.add_node(pydot.Node(str(self.s.__hash__()),label=label,shape='plaintext')) # class MXMappingArtist(DotArtist): # def draw(self): # s = self.s # graph = self.graph # sp = s.sparsity() # row = sp.row() # # Note: due to Mapping restructuring, this is no longer efficient code # deps = getDeps(s) # depind = s.depInd() # nzmap = sum([s.mapping(i) for i in range(len(deps))]) # for k,d in enumerate(deps): # candidates = map(hash,filter(lambda i: i.isMapping(),self.invdep[d])) # candidates.sort() # if candidates[0] == hash(s): # graph.add_edge(pydot.Edge(str(d.__hash__()),"mapinput" + str(d.__hash__()))) # graph = pydot.Cluster('clustertest' + str(s.__hash__()), rank='max', label='Mapping') # self.graph.add_subgraph(graph) # colors = ['#eeeecc','#ccccee','#cceeee','#eeeecc','#eeccee','#cceecc'] # for k,d in enumerate(deps): # spd = d.sparsity() # #ipdb.set_trace() # # The Matrix grid is represented by a html table with 'ports' # candidates = map(hash,filter(lambda i: i.isMapping(),self.invdep[d])) # candidates.sort() # if candidates[0] == hash(s): # label = '<' # if not(d.numel()==1 and d.numel()==d.nnz()): # label+="" % (d.size2(), d.dim()) # for i in range(d.size1()): # label+="" # for j in range(d.size2()): # kk = spd.get_nz(i,j) # if kk==-1: # label+="" # else: # label+="" % (kk,colors[k],kk) # label+="" # label+="
%s
. %d
>" # graph.add_node(pydot.Node("mapinput" + str(d.__hash__()),label=label,shape='plaintext')) # graph.add_edge(pydot.Edge("mapinput" + str(d.__hash__()),str(s.__hash__()))) # # The Matrix grid is represented by a html table with 'ports' # label = '<' # if not(s.numel()==1 and s.numel()==s.nnz()): # label+="" % (s.size2(), s.dim()) # for i in range(s.size1()): # label+="" # for j in range(s.size2()): # k = sp.get_nz(i,j) # if k==-1: # label+="" # else: # label+="" % (k,colors[depind[k]],nzmap[k]) # label+="" # label+="
%s
. %d
>" # graph.add_node(pydot.Node(str(self.s.__hash__()),label=label,shape='plaintext')) class MXEvaluationArtist(DotArtist): def draw(self): s = self.s graph = self.graph sp = s.sparsity() row = sp.row() deps = getDeps(s) f = s.which_function() for k,d in enumerate(deps): graph.add_edge(pydot.Edge(str(d.__hash__()),"funinput" + str(s.__hash__())+ ":f%d" % k,rankdir="LR")) graph = pydot.Cluster(str(s.__hash__()), rank='max', label='Function:\n %s' % f.name()) self.graph.add_subgraph(graph) s = (" %d inputs: |" % f.n_in()) + " | ".join(" %d" % (i,i) for i in range(f.n_in())) graph.add_node(pydot.Node("funinput" + str(self.s.__hash__()),label=s,shape='Mrecord')) s = (" %d outputs: |" % f.n_out())+ " | ".join(" %d" % (i,i) for i in range(f.n_out())) graph.add_node(pydot.Node(str(self.s.__hash__()),label=s,shape='Mrecord')) class MXConstantArtist(DotArtist): def hasPorts(self): return True def draw(self): s = self.s graph = self.graph sp = s.sparsity() row = sp.row() M = s.to_DM() col = "#009900" if s.nnz() == s.numel() and s.nnz() == 1: graph.add_node(pydot.Node(str(self.s.__hash__())+":f0",label=str(M[0,0]),shape='rectangle',color=col)) else: # The Matrix grid is represented by a html table with 'ports' label = '<' % col label+="" % (s.size2(), s.dim()) if not "max_numel" in self.kwargs or s.numel() < self.kwargs["max_numel"]: for i in range(s.size1()): label+="" for j in range(s.size2()): k = sp.get_nz(i,j) if k==-1: label+="" else: label+="" % (k,M[i,j]) label+="" label+="
%s
. %s
>" graph.add_node(pydot.Node(str(self.s.__hash__()),label=label,shape='plaintext')) class MXGenericArtist(DotArtist): def draw(self): k = self.s graph = self.graph dep = getDeps(k) show_sp = not(all([d.sparsity()==k.sparsity() for d in dep])) if show_sp: op = "op" self.drawSparsity(k,depid=op + str(k.__hash__())) else: op = "" if len(dep)>1: # Non-commutative operators are represented by 'record' shapes. # The dependencies have different 'ports' where arrows should arrive. s = print_operator_escaped(self.s,["| | " %i for i in range(len(dep))]) if s.startswith("(|") and s.endswith("|)"): s=s[2:-2] graph.add_node(pydot.Node(op + str(k.__hash__()),label=s,shape='Mrecord')) for i,n in enumerate(dep): graph.add_edge(pydot.Edge(str(n.__hash__()),op + str(k.__hash__())+":f%d" % i)) else: s = print_operator_escaped(k,["."]) self.graph.add_node(pydot.Node(op + str(k.__hash__()),label=s,shape='oval')) for i,n in enumerate(dep): self.graph.add_edge(pydot.Edge(str(n.__hash__()),op + str(k.__hash__()))) class MXGetNonzerosArtist(DotArtist): def draw(self): s = self.s graph = self.graph n = getDeps(s)[0] show_sp = not(s.nnz() == s.numel() and s.nnz() == 1) if show_sp: op = "op" self.drawSparsity(s,depid=op + str(s.__hash__())) else: op = "" sp = s.sparsity() row = sp.row() M = s.mapping() col = "#333333" if s.nnz() == s.numel() and s.nnz() == 1: graph.add_node(pydot.Node(op+str(s.__hash__())+":f0",label="[%s]" % str(M[0,0]),shape='rectangle',style="filled",fillcolor='#eeeeff')) else: # The Matrix grid is represented by a html table with 'ports' label = '<' % col label+="" % (s.size2()) if not "max_nnz" in self.kwargs or s.nnz() < self.kwargs["max_nnz"]: for i in range(s.size1()): label+="" for j in range(s.size2()): k = sp.get_nz(i,j) if k==-1: label+="" else: label+="" % (k,M[i,j]) label+="" label+="
getNonzeros
. %s
>" graph.add_node(pydot.Node(op+str(s.__hash__()),label=label,shape='plaintext')) self.graph.add_edge(pydot.Edge(str(n.__hash__()),op+str(s.__hash__()))) class MXSetNonzerosArtist(DotArtist): def draw(self): s = self.s graph = self.graph entry = getDeps(s)[0] target = getDeps(s)[1] show_sp = not(all([d.sparsity()==s.sparsity() for d in getDeps(s)])) if show_sp: op = "op" self.drawSparsity(s,depid=op + str(s.__hash__())) else: op = "" sp = target.sparsity() row = sp.row() M = list(s.mapping()) Mk = 0 col = "#333333" # The Matrix grid is represented by a html table with 'ports' label = '<' % col label+="" % (s.size2()) for i in range(s.size1()): label+="" for j in range(s.size2()): k = entry.sparsity().get_nz(i,j) if k==-1 or Mk>= len(M) or k != M[Mk]: label+="" if Mk< len(M)-1 and M[Mk]==-1 and k!=-1: Mk+=1 else: label+="" % (Mk,Mk) Mk+=1 label+="" label+="
setNonzeros
. %s
>" graph.add_node(pydot.Node(op+str(s.__hash__()),label=label,shape='plaintext')) self.graph.add_edge(pydot.Edge(str(entry.__hash__()),op+str(s.__hash__())+':entry')) self.graph.add_edge(pydot.Edge(str(target.__hash__()),op+str(s.__hash__()))) class MXAddNonzerosArtist(DotArtist): def draw(self): s = self.s graph = self.graph entry = getDeps(s)[0] target = getDeps(s)[1] show_sp = not(all([d.sparsity()==s.sparsity() for d in getDeps(s)])) if show_sp: op = "op" self.drawSparsity(s,depid=op + str(s.__hash__())) else: op = "" sp = target.sparsity() row = sp.row() M = list(s.mapping()) Mk = 0 col = "#333333" # The Matrix grid is represented by a html table with 'ports' label = '<' % col label+="" % (s.size2()) for i in range(s.size1()): label+="" for j in range(s.size2()): k = sp.get_nz(i,j) if k==-1 or Mk>= len(M) or k != M[Mk]: label+="" if Mk< len(M)-1 and M[Mk]==-1 and k!=-1: Mk+=1 else: label+="" % (Mk,Mk) Mk+=1 label+="" label+="
addNonzeros
. %s
>" graph.add_node(pydot.Node(op+str(s.__hash__()),label=label,shape='plaintext')) self.graph.add_edge(pydot.Edge(str(entry.__hash__()),op+str(s.__hash__())+':entry')) self.graph.add_edge(pydot.Edge(str(target.__hash__()),op+str(s.__hash__()))) class MXOperationArtist(DotArtist): def draw(self): k = self.s graph = self.graph dep = getDeps(k) show_sp = True if k.is_unary() and dep[0].sparsity()==k.sparsity(): show_sp = False if k.is_binary() and dep[0].sparsity()==k.sparsity() and dep[1].sparsity()==k.sparsity(): show_sp = False if show_sp: op = "op" self.drawSparsity(k,depid=op + str(k.__hash__())) else: op = "" if not(k.is_commutative()): # Non-commutative operators are represented by 'record' shapes. # The dependencies have different 'ports' where arrows should arrive. s = print_operator_escaped(self.s,["| | ", " | |"]) if s.startswith("(|") and s.endswith("|)"): s=s[2:-2] graph.add_node(pydot.Node(op + str(k.__hash__()),label=s,shape='Mrecord')) for i,n in enumerate(dep): graph.add_edge(pydot.Edge(str(n.__hash__()),op + str(k.__hash__())+":f%d" % i)) else: # Commutative operators can be represented more compactly as 'oval' shapes. s = print_operator_escaped(k,[".", "."]) if s.startswith("(.") and s.endswith(".)"): s=s[2:-2] if s.startswith("(") and s.endswith(")"): s=s[1:-1] self.graph.add_node(pydot.Node(op + str(k.__hash__()),label=s,shape='oval')) for i,n in enumerate(dep): self.graph.add_edge(pydot.Edge(str(n.__hash__()),op + str(k.__hash__()))) class MXIfTestArtist(DotArtist): def draw(self): k = self.s graph = self.graph dep = getDeps(k) show_sp = True s = " ? | true" graph.add_node(pydot.Node(str(k.__hash__()),label=s,shape='Mrecord')) for i,n in enumerate(dep): graph.add_edge(pydot.Edge(str(n.__hash__()),str(k.__hash__())+":f%d" % i)) class MXDensificationArtist(DotArtist): def draw(self): k = self.s graph = self.graph dep = getDeps(k) self.graph.add_node(pydot.Node(str(k.__hash__()),label="densify(.)",shape='oval')) self.graph.add_edge(pydot.Edge(str(dep[0].__hash__()),str(k.__hash__()))) class MXNormArtist(DotArtist): def draw(self): k = self.s graph = self.graph dep = getDeps(k) s = print_operator_escaped(k,[".", "."]) self.graph.add_node(pydot.Node(str(k.__hash__()),label=s,shape='oval')) self.graph.add_edge(pydot.Edge(str(dep[0].__hash__()),str(k.__hash__()))) class MXEvaluationOutputArtist(DotArtist): def draw(self): k = self.s self.drawSparsity(k,depid=str(hash(k.dep(0))) + ":f%d" % k.which_output()) class MXMultiplicationArtist(DotArtist): def draw(self): k = self.s graph = self.graph dep = getDeps(k) # Non-commutative operators are represented by 'record' shapes. # The dependencies have different 'ports' where arrows should arrive. s = "mul(| | , | | )" graph.add_node(pydot.Node(str(k.__hash__()),label=s,shape='Mrecord')) for i,n in enumerate(dep): graph.add_edge(pydot.Edge(str(n.__hash__()),str(k.__hash__())+":f%d" % i)) class SXArtist(DotArtist): def draw(self): s = self.s graph = self.graph sp = s.sparsity() row = sp.row() # The Matrix grid is represented by a html table with 'ports' label = '<' for i in range(s.size1()): label+="" for j in range(s.size2()): k = sp.get_nz(i,j) if k==-1: label+="" else: sx = s.nz[k] if self.shouldEmbed(sx): label+="" % str(sx) else: self.graph.add_edge(pydot.Edge(str(sx.__hash__()),"%s:f%d" % (str(self.s.__hash__()), k))) label+="" % (k,i,j,k) label+="" label+="
.%s (%d,%d|%d)
>" graph.add_node(pydot.Node(str(self.s.__hash__()),label=label,shape='plaintext')) def shouldEmbed(self,sx): return len(self.invdep[sx]) == 1 and sx.is_leaf() class SXLeafArtist(DotArtist): def draw(self): if len(self.invdep[self.s]) == 1: master = list(self.invdep[self.s])[0] if hasattr(self.artists[master],'shouldEmbed'): if self.artists[master].shouldEmbed(self.s): return style = "solid" # Symbolic nodes are represented box'es if self.s.is_constant(): style = "bold" # Constants are represented by bold box'es self.graph.add_node(pydot.Node(str(self.s.__hash__()),label=str(self.s),shape="box",style=style)) class SXNonLeafArtist(DotArtist): def draw(self): k = self.s graph = self.graph dep = getDeps(k) if not(k.is_commutative()): # Non-commutative operators are represented by 'record' shapes. # The dependencies have different 'ports' where arrows should arrive. if len(dep)==2: s = print_operator_escaped(self.s,["| | ", " | |"]) else: s = print_operator_escaped(self.s,["| | "]) if s.startswith("(|") and s.endswith("|)"): s=s[2:-2] graph.add_node(pydot.Node(str(k.__hash__()),label=s,shape='Mrecord')) for i,n in enumerate(dep): graph.add_edge(pydot.Edge(str(n.__hash__()),str(k.__hash__())+":f%d" % i)) else: # Commutative operators can be represented more compactly as 'oval' shapes. s = print_operator_escaped(k,[".", "."]) if s.startswith("(.") and s.endswith(".)"): s=s[2:-2] if s.startswith("(") and s.endswith(")"): s=s[1:-1] self.graph.add_node(pydot.Node(str(k.__hash__()),label=s,shape='oval')) for i,n in enumerate(dep): self.graph.add_edge(pydot.Edge(str(n.__hash__()),str(k.__hash__()))) def createArtist(node,dep={},invdep={},graph=None,artists={},**kwargs): if isinstance(node,SX): if node.is_scalar(True): if is_leaf(node): return SXLeafArtist(node,dep=dep,invdep=invdep,graph=graph,artists=artists,**kwargs) else: return SXNonLeafArtist(node,dep=dep,invdep=invdep,graph=graph,artists=artists,**kwargs) else: return SXArtist(node,dep=dep,invdep=invdep,graph=graph,artists=artists,**kwargs) elif isinstance(node,MX): if node.is_symbolic(): return MXSymbolicArtist(node,dep=dep,invdep=invdep,graph=graph,artists=artists,**kwargs) elif node.is_binary() or node.is_unary(): return MXOperationArtist(node,dep=dep,invdep=invdep,graph=graph,artists=artists,**kwargs) elif node.is_constant(): return MXConstantArtist(node,dep=dep,invdep=invdep,graph=graph,artists=artists,**kwargs) elif node.is_call(): return MXEvaluationArtist(node,dep=dep,invdep=invdep,graph=graph,artists=artists,**kwargs) elif node.is_output(): return MXEvaluationOutputArtist(node,dep=dep,invdep=invdep,graph=graph,artists=artists,**kwargs) elif node.is_norm(): return MXNormArtist(node,dep=dep,invdep=invdep,graph=graph,artists=artists,**kwargs) elif node.is_op(C.OP_GETNONZEROS): return MXGetNonzerosArtist(node,dep=dep,invdep=invdep,graph=graph,artists=artists,**kwargs) elif node.is_op(C.OP_SETNONZEROS): return MXSetNonzerosArtist(node,dep=dep,invdep=invdep,graph=graph,artists=artists,**kwargs) elif node.is_op(C.OP_ADDNONZEROS): return MXAddNonzerosArtist(node,dep=dep,invdep=invdep,graph=graph,artists=artists,**kwargs) else: return MXGenericArtist(node,dep=dep,invdep=invdep,graph=graph,artists=artists,**kwargs) else: raise Exception("Cannot create artist for %s" % str(type(s))) def dotgraph(s,direction="BT",**kwargs): """ Creates and returns a pydot graph structure that represents an SX. direction one of "BT", "LR", "TB", "RL" """ try: def getHashSX(e): if e.is_scalar(True): try: return e.element_hash() except: return SX__hash__backup(e) else: return 0 SX__hash__backup = SX.__hash__ SX.__hash__ = getHashSX # Get the dependencies and inverse dependencies in a dict dep, invdep = dependencyGraph(s,{},{}) allnodes = set(dep.keys()).union(set(invdep.keys())) #print "a", set(dep.keys()), [i.__hash__() for i in dep.keys()] #print "b", set(invdep.keys()), [i.__hash__() for i in invdep.keys()] #print "allnodes", allnodes, [i.__hash__() for i in allnodes] #return None artists = {} graph = pydot.Dot('G', graph_type='digraph',rankdir=direction) for node in allnodes: artists[node] = createArtist(node,dep=dep,invdep=invdep,graph=graph,artists=artists,**kwargs) for artist in artists.values(): if artist is None: continue artist.draw() open('source.dot','w').write(graph.to_string()) finally: SX.__hash__ = SX__hash__backup return graph def dotsave(s,format='ps',filename="temp",direction="RL",**kwargs): """ Make a drawing of an SX and save it. format can be one of: dot canon cmap cmapx cmapx_np dia dot fig gd gd2 gif hpgl imap imap_np ismap jpe jpeg jpg mif mp pcl pdf pic plain plain-ext png ps ps2 raw svg svgz vml vmlz vrml vtx wbmp xdot xlib direction one of "BT", "LR", "TB", "RL" """ g = dotgraph(s,direction=direction,**kwargs) if hasattr(g,'write_'+format): getattr(g,'write_'+format)(filename) else: s = "Unknown format '%s'. Please pick one of the following:\n" % format l = ['dot'] for n in dir(g): if n.startswith("write_"): l.append(n[6:]) s+= " ".join(l) raise Exception(s) def dotdraw(s,direction="RL",**kwargs): """ Make a drawing of an SX and display it. direction one of "BT", "LR", "TB", "RL" """ try: # Check if we have pylab from pylab import imread, imshow,show,figure, axes except: # We don't have pylab, so just write out to file print("casadi.tools.graph.dotdraw: no pylab detected, will not show drawing on screen.") dotgraph(s,direction=direction,**kwargs).write_ps("temp.ps") return if hasattr(show,'__class__') and show.__class__.__name__=='PylabShow': # catch pyreport case, so we have true vector graphics figure_name = '%s%d.%s' % ( show.basename, len(show.figure_list), show.figure_extension ) show.figure_list += (figure_name, ) dotgraph(s,direction=direction,**kwargs).write_pdf(figure_name) print("Here goes figure %s (dotdraw)" % figure_name) else: # Matplotlib does not allow to display vector graphics on screen, # so we fall back to png temp="_temp.png" dotgraph(s,direction=direction,**kwargs).write_png(temp) im = imread(temp) figure() ax = axes([0,0,1,1], frameon=False) ax.set_axis_off() imshow(im) show()