Python DiGraph.topological_sort方法代码示例

# 需要导入模块: from sage.graphs.digraph import DiGraph [as 别名]
# 或者: from sage.graphs.digraph.DiGraph import topological_sort [as 别名]

#.........这里部分代码省略.........
    and we can compute the Hasse diagram as ::

        sage: L = sage.geometry.cone.Hasse_diagram_from_incidences(
        ...                       atom_to_coatoms, coatom_to_atoms)
        sage: L
        Finite poset containing 8 elements with distinguished linear extension
        sage: for level in L.level_sets(): print(level)
        [((), (0, 1, 2))]
        [((0,), (0, 1)), ((1,), (0, 2)), ((2,), (1, 2))]
        [((0, 1), (0,)), ((0, 2), (1,)), ((1, 2), (2,))]
        [((0, 1, 2), ())]

    For more involved examples see the *source code* of
    :meth:`sage.geometry.cone.ConvexRationalPolyhedralCone.face_lattice` and
    :meth:`sage.geometry.fan.RationalPolyhedralFan._compute_cone_lattice`.
    """
    from sage.graphs.digraph import DiGraph
    from sage.combinat.posets.posets import FinitePoset
    def default_face_constructor(atoms, coatoms, **kwds):
        return (atoms, coatoms)
    if face_constructor is None:
        face_constructor = default_face_constructor
    atom_to_coatoms = [frozenset(atc) for atc in atom_to_coatoms]
    A = frozenset(range(len(atom_to_coatoms)))  # All atoms
    coatom_to_atoms = [frozenset(cta) for cta in coatom_to_atoms]
    C = frozenset(range(len(coatom_to_atoms)))  # All coatoms
    # Comments with numbers correspond to steps in Section 2.5 of the article
    L = DiGraph(1)       # 3: initialize L
    faces = dict()
    atoms = frozenset()
    coatoms = C
    faces[atoms, coatoms] = 0
    next_index = 1
    Q = [(atoms, coatoms)]              # 4: initialize Q with the empty face
    while Q:                            # 5
        q_atoms, q_coatoms = Q.pop()    # 6: remove some q from Q
        q = faces[q_atoms, q_coatoms]
        # 7: compute H = {closure(q+atom) : atom not in atoms of q}
        H = dict()
        candidates = set(A.difference(q_atoms))
        for atom in candidates:
            coatoms = q_coatoms.intersection(atom_to_coatoms[atom])
            atoms = A
            for coatom in coatoms:
                atoms = atoms.intersection(coatom_to_atoms[coatom])
            H[atom] = (atoms, coatoms)
        # 8: compute the set G of minimal sets in H
        minimals = set([])
        while candidates:
            candidate = candidates.pop()
            atoms = H[candidate][0]
            if atoms.isdisjoint(candidates) and atoms.isdisjoint(minimals):
                minimals.add(candidate)
        # Now G == {H[atom] : atom in minimals}
        for atom in minimals:   # 9: for g in G:
            g_atoms, g_coatoms = H[atom]
            if not required_atoms is None:
                if g_atoms.isdisjoint(required_atoms):
                    continue
            if (g_atoms, g_coatoms) in faces:
                g = faces[g_atoms, g_coatoms]
            else:               # 11: if g was newly created
                g = next_index
                faces[g_atoms, g_coatoms] = g
                next_index += 1
                Q.append((g_atoms, g_coatoms))  # 12
            L.add_edge(q, g)                    # 14
    # End of algorithm, now construct a FinitePoset.
    # In principle, it is recommended to use Poset or in this case perhaps
    # even LatticePoset, but it seems to take several times more time
    # than the above computation, makes unnecessary copies, and crashes.
    # So for now we will mimic the relevant code from Poset.

    # Enumeration of graph vertices must be a linear extension of the poset
    new_order = L.topological_sort()
    # Make sure that coatoms are in the end in proper order
    tail = [faces[atoms, frozenset([coatom])]
            for coatom, atoms in enumerate(coatom_to_atoms)]
    tail.append(faces[A, frozenset()])
    new_order = [n for n in new_order if n not in tail] + tail
    # Make sure that atoms are in the beginning in proper order
    head = [0] # We know that the empty face has index 0
    head.extend(faces[frozenset([atom]), coatoms]
                for atom, coatoms in enumerate(atom_to_coatoms)
                if required_atoms is None or atom in required_atoms)
    new_order = head + [n for n in new_order if n not in head]
    # "Invert" this list to a dictionary
    labels = dict()
    for new, old in enumerate(new_order):
        labels[old] = new
    L.relabel(labels)
    # Construct the actual poset elements
    elements = [None] * next_index
    for face, index in faces.items():
        atoms, coatoms = face
        elements[labels[index]] = face_constructor(
                        tuple(sorted(atoms)), tuple(sorted(coatoms)), **kwds)
    D = {i:f for i,f in enumerate(elements)}
    L.relabel(D)
    return FinitePoset(L, elements, key = key)

# 需要导入模块: from sage.graphs.digraph import DiGraph [as 别名]
# 或者: from sage.graphs.digraph.DiGraph import topological_sort [as 别名]
class ParentBigOh(Parent,UniqueRepresentation):
    def __init__(self,ambiant):
        try:
            self._uniformizer = ambiant.uniformizer_name()
        except NotImplementedError:
            raise TypeError("Impossible to determine the name of the uniformizer")
        self._ambiant_space = ambiant
        self._models = DiGraph(loops=False)
        self._default_model = None
        Parent.__init__(self,ambiant.base_ring())
        if self.base_ring() is None:
            self._base_precision = None
        else:
            if self.base_ring() == ambiant:
                self._base_precision = self
            else:
                self._base_precision = ParentBigOh(self.base_ring())

    def __hash__(self):
        return id(self)

    def base_precision(self):
        return self._base_precision

    def precision(self):
        return self._precision

    def default_model(self):
        if self._default_mode is None:
            self.set_default_model()
        return self._default_model
    
    def set_default_model(self,model=None):
        if model is None:
            self._default_model = self._models.topological_sort()[-1]
        else:
            if self._models.has_vertex(model):
                self._default_model = model
            else:
                raise ValueError

    def add_model(self,model):
        from bigoh import BigOh
        if not isinstance(model,list):
            model = [model]
        for m in model:
            if not issubclass(m,BigOh):
                raise TypeError("A precision model must derive from BigOh but '%s' is not"%m)
            self._models.add_vertex(m)

    def delete_model(self,model):
        if isinstance(model,list):
            model = [model]
        for m in model:
            if self._models.has_vertex(m):
                self._models.delete_vertex(m)

    def update_model(self,old,new):
        from bigoh import BigOh
        if self._models.has_vertex(old):
            if not issubclass(new,BigOh):
                raise TypeError("A precision model must derive from BigOh but '%s' is not"%new)
            self._models.relabel({old:new})
        else:
            raise ValueError("Model '%m' does not exist"%old)

    def add_modelconversion(self,domain,codomain,constructor=None,safemode=False):
        if not self._models.has_vertex(domain):
            if safemode: return
            raise ValueError("Model '%s' does not exist"%domain)
        if not self._models.has_vertex(codomain):
            if safemode: return
            raise ValueError("Model '%s' does not exist"%codomain)
        path = self._models.shortest_path(codomain,domain)
        if len(path) > 0:
            raise ValueError("Adding this conversion creates a cycle")
        self._models.add_edge(domain,codomain,constructor)

    def delete_modelconversion(self,domain,codomain):
        if not self._models.has_vertex(domain):
            raise ValueError("Model '%s' does not exist"%domain)
        if not self._models.has_vertex(codomain):
            raise ValueError("Model '%s' does not exist"%codomain)
        if not self._models_has_edge(domain,codomain):
            raise ValueError("No conversion from %s to %s"%(domain,codomain))
        self._modelfs.delete_edge(domain,codomain)

    def uniformizer_name(self):
        return self._uniformizer

    def ambiant_space(self):
        return self._ambiant_space

    # ?!?
    def __call__(self,*args,**kwargs):
        return self._element_constructor_(*args,**kwargs)
    
    def _element_constructor_(self, *args, **kwargs):
        if kwargs.has_key('model'):
            del kwargs['model']
#.........这里部分代码省略.........