/usr/lib/python2.7/dist-packages/ufl/algorithms/graph.py is in python-ufl 1.4.0-1.
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# Copyright (C) 2008-2014 Martin Sandve Alnes
#
# This file is part of UFL.
#
# UFL 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.
#
# UFL 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 UFL. If not, see <http://www.gnu.org/licenses/>.
#
# First added: 2008-12-28
# Last changed: 2012-04-12
from collections import defaultdict
from itertools import imap, izip
from heapq import heapify, heappop, heappush
#from ufl import *
from ufl.algorithms.traversal import fast_pre_traversal
from ufl.algorithms.printing import tree_format
from ufl.algorithms.multifunction import MultiFunction
from ufl.classes import Terminal
# O(n) = O(|V|) = O(|E|), since |E| < c|V| for a fairly small c.
#--- Basic utility functions ---
def lists(n):
return [[] for i in xrange(n)]
def len_items(sequence):
return map(len, sequence)
def join_lines(sequence):
return "\n".join(imap(str, sequence))
def all_is(seq1, seq2):
return all(a is b for (a, b) in izip(seq1, seq2))
def reorder(sequence, ordering):
"Rearrange the items in a sequence."
return [sequence[i] for i in ordering]
#--- Graph building functions ---
def build_graph(expr): # O(n)
"""Build a linearized graph from an UFL Expr.
Returns G = (V, E), with V being a list of
graph nodes (Expr objects) in post traversal
ordering and E being a list of edges. Each edge
is represented as a (i, j) tuple where i and j
are vertex indices into V.
"""
V = []
E = []
handled = {}
#for v in post_traversal(expr):
for v in reversed(list(fast_pre_traversal(expr))):
i = handled.get(v)
if i is None:
i = len(V)
handled[v] = i
V.append(v)
for o in v.operands():
j = handled[o]
e = (i, j)
E.append(e)
G = V, E
return G
def extract_incoming_edges(G): # O(n)
"Build lists of incoming edges to each vertex in a linearized graph."
V, E = G
n = len(V)
Ein = lists(n)
for i, e in enumerate(E):
Ein[e[1]].append(i)
return Ein
def extract_outgoing_edges(G): # O(n)
"Build list of outgoing edges from each vertex in a linearized graph."
V, E = G
n = len(V)
Eout = lists(n)
for i, e in enumerate(E):
Eout[e[0]].append(i)
return Eout
def extract_edges(G): # O(n)
"""Build lists of incoming and outgoing edges
to and from each vertex in a linearized graph.
Returns lists Ein and Eout."""
V, E = G
n = len(V)
Ein = lists(n)
Eout = lists(n)
for i, e in enumerate(E):
a, b = e
Ein[b].append(i)
Eout[a].append(i)
return Ein, Eout
def extract_incoming_vertex_connections(G): # O(n)
"""Build lists of vertices in incoming and outgoing
edges to and from each vertex in a linearized graph.
Returns lists Vin and Vout."""
V, E = G
n = len(V)
Vin = lists(n)
for a, b in E:
Vin[b].append(a)
return Vin
def extract_outgoing_vertex_connections(G): # O(n)
"""Build lists of vertices in incoming and outgoing
edges to and from each vertex in a linearized graph.
Returns lists Vin and Vout."""
V, E = G
n = len(V)
Vout = lists(n)
for a, b in E:
Vout[a].append(b)
return Vout
def extract_vertex_connections(G): # O(n)
"""Build lists of vertices in incoming and outgoing
edges to and from each vertex in a linearized graph.
Returns lists Vin and Vout."""
V, E = G
n = len(V)
Vin = lists(n)
Vout = lists(n)
for a, b in E:
Vin[b].append(a)
Vout[a].append(b)
return Vin, Vout
#--- Graph class ---
class Graph:
"Graph class which computes connectivity on demand."
def __init__(self, expression):
self._V, self._E = build_graph(expression)
self._Ein = None
self._Eout = None
self._Vin = None
self._Vout = None
def V(self):
return self._V
def E(self):
return self._E
def Ein(self):
if self._Ein is None:
self._Ein = extract_incoming_edges((self._V, self._E))
return self._Ein
def Eout(self):
if self._Eout is None:
self._Eout = extract_outgoing_edges((self._V, self._E))
return self._Eout
def Vin(self):
if self._Vin is None:
self._Vin = extract_incoming_vertex_connections((self._V, self._E))
return self._Vin
def Vout(self):
if self._Vout is None:
self._Vout = extract_outgoing_vertex_connections((self._V, self._E))
return self._Vout
def __iter__(self):
return iter((self._V, self._E))
#--- Graph algorithms ---
def format_graph(G):
V, E = G
lines = ["Graph with %d vertices and %d edges:" % (len(V), sum(map(len, E)))]
lines.extend(("", "Vertices:"))
lines.extend("v%d: \t%s" % (i, v) for (i, v) in enumerate(V))
lines.extend(("", "Edges:"))
lines.extend("e%d: \tv%d -> v%d" % (i, e[0], e[1]) for (i, e) in enumerate(E))
return join_lines(lines)
def find_dependencies(G, targets):
"""Find the set of vertices in a computational
graph that a set of target vertices depend on."""
# G is a graph
V, E = G
n = len(V)
# targets is a sequence of vertex indices
todo = list(targets)
heapify(todo)
keep = [False]*n
while todo:
t = heappop(todo)
if not keep[t]:
keep[t] = True
for edges in Eout[t]:
for e in edges:
heappush(todo, e[1])
return keep
#--- Scheduling algorithms ---
class HeapItem(object):
def __init__(self, incoming, outgoing, i):
self.incoming = incoming
self.outgoing = outgoing
self.i = i
def __lt__(self, other):
a = (self.outgoing[self.i], self.incoming[self.i])
b = (other.outgoing[other.i], other.incoming[other.i])
return a < b
def __le__(self, other):
a = (self.outgoing[self.i], self.incoming[self.i])
b = (other.outgoing[other.i], other.incoming[other.i])
return a <= b
def __eq__(self, other):
a = (self.outgoing[self.i], self.incoming[self.i])
b = (other.outgoing[other.i], other.incoming[other.i])
return a == b
def depth_first_ordering(G):
V, E = G
Vin = G.Vin()
Vout = G.Vout()
Ein_count = len_items(Vin)
Eout_count = len_items(Vout)
# Make a list and a heap of the same items
n = len(V)
q = [HeapItem(Ein_count, Eout_count, i) for i in xrange(n)]
heapify(q)
ordering = []
while q:
item = heappop(q)
iv = item.i
ordering.append(iv)
for i in Vin[iv]:
Eout_count[i] -= 1
# Resort heap, worst case linear time, makes this algorithm O(n^2)... TODO: Not good!
heapify(q)
# TODO: Can later accumulate dependencies as well during dft-like algorithm.
return ordering
#--- Expression tree reconstruction algorithms ---
def rebuild_tree(G):
"""Rebuild expression tree from linearized graph.
Does not touch the input graph. Assumes the graph
is directed, acyclic, and connected, such that there
is only one root node.
"""
V = G.V()
E = G.E()
n = len(V)
Vout = G.Vout()
dfo = depth_first_ordering(G)
subtrees = [None]*n
for i in dfo:
v = V[i]
if not isinstance(v, Terminal):
# Fetch already reconstructed child vertices
# and reconstruct non-terminal node from them
ops = tuple(subtrees[j] for j in Vout[i])
if all_is(ops, v.operands()):
pass
else:
v = v.reconstruct(*ops)
subtrees[i] = v
# Assuming last vertex is the root!
return v
#--- Graph partitoning ---
class StringDependencyDefiner(MultiFunction):
"""Given an expr, returns a frozenset of its dependencies.
Possible dependency values are:
"c" - depends on runtime information like the cell, local<->global coordinate mappings, facet normals, or coefficients
"x" - depends on local coordinates
"v%d" % i - depends on argument i, for i in [0,rank)
"""
def __init__(self, argument_deps = None, coefficient_deps = None):
MultiFunction.__init__(self)
if argument_deps is None:
argument_deps = {}
if coefficient_deps is None:
coefficient_deps = {}
self.argument_deps = argument_deps
self.coefficient_deps = coefficient_deps
def expr(self, o):
return frozenset()
def argument(self, x):
default = frozenset(("v%d" % x.number(), "x")) # TODO: This is missing the part, but this code is ready for deletion anyway?
return self.argument_deps.get(x, default)
def coefficient(self, x):
default = frozenset(("c", "x"))
return self.coefficient_deps.get(x, default)
def constant(self, x):
default = frozenset(("c",))
return self.coefficient_deps.get(x, default)
def geometric_quantity(self, x):
deps = frozenset(("c", "x",))
return deps
def facet_normal(self, o):
deps = frozenset(("c",))
# Enabling coordinate dependency for higher order geometries
# (not handled anywhere else though, so consider this experimental)
#if o.has_higher_degree_cell_geometry():
# deps = deps | frozenset(("x",))
return deps
def spatial_derivative(self, o): # TODO: What about (basis) functions of which derivatives are constant? Should special-case spatial_derivative in partition().
deps = frozenset(("c",))
# Enabling coordinate dependency for higher order geometries (not handled anywhere else though).
#if o.has_higher_degree_cell_geometry():
# deps = deps | frozenset(("x",))
return deps
dd = StringDependencyDefiner()
def string_set_criteria(v, keys):
# Using sets of ufl objects
key = dd(v)
for k in keys:
key |= k
return frozenset(key)
def partition(G, criteria=string_set_criteria):
V, E = G
n = len(V)
Vout = G.Vout()
partitions = defaultdict(list)
keys = [None]*n
for iv, v in enumerate(V):
# Get keys from all outgoing edges
edge_keys = [keys[ii] for ii in Vout[iv]]
# Calculate key for this vertex
key = criteria(v, edge_keys)
# Store mappings from key to vertex and back
partitions[key].append(iv)
keys[iv] = key
return partitions, keys
#--- Test code ---
def test_expr():
from ufl import triangle, FiniteElement, TestFunction, TrialFunction, Coefficient
element = FiniteElement("CG", triangle, 1)
v = TestFunction(element)
u = TrialFunction(element)
f = Coefficient(element)
g = Coefficient(element)
expr = (f+g)*u.dx(0)*(g-1)*v
return expr
if __name__ == "__main__":
expr = test_expr()
G = Graph(expr)
V, E = G
n = len(V)
Ein = G.Ein()
Eout = G.Eout()
print
print "Entire graph:"
for iv, v in enumerate(V):
print "Vertex %03d: %s" % (iv, v)
for ie, e in enumerate(E):
print "Edge %03d: %s" % (ie, e)
for iv, eout in enumerate(Eout):
print "Edges out for vertex %03d: %s" % (iv, eout)
for iv, ein in enumerate(Ein):
print "Edges in for vertex %03d: %s" % (iv, ein)
print
from ufl.common import sstr
partitions, keys = partition(G, string_set_criteria)
for k in partitions:
print
print "Partition with key", sstr(k)
for iv in partitions[k]:
print "Vertex %03d: %s" % (iv, V[iv])
if __name__ == "__main_":
expr = test_expr()
G = Graph(expr)
V, E = G
e2 = rebuild_tree(G)
Ein = G.Ein()
Eout = G.Eout()
Ein_count = len_items(Ein)
Eout_count = len_items(Eout)
dfo = depth_first_ordering(G)
print
print "expr:"
print expr
print
print "e2:"
print e2
print
print tree_format(expr)
print
print format_graph(G)
print
print "Ein:"
print join_lines(Ein)
print
print "Eout:"
print join_lines(Eout)
print
print "Ein_count:"
print join_lines(Ein_count)
print
print "Eout_count:"
print join_lines(Eout_count)
print
print "dfo:"
print join_lines(reorder(V, dfo))
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