def test_cloning_cases(self):
g = TypedDiGraph()
g.add_node(10, "agent", {"a": 0})
g.add_node(20, "agent", {"b": 0})
g.add_node(30, "action", {"c": 0})
g.add_edges_from([(10, 30), (20, 30)])
g.set_edge(10, 30, {"x": 0})
g.set_edge(20, 30, {"y": 0})
LHS = TypedDiGraph()
LHS.add_node(1, "agent")
rw = Rewriter(g)
instances = rw.find_matching(LHS)
# simple clone
P1 = TypedDiGraph()
P1.add_node("a", "agent")
P1.add_node("b", "agent")
RHS1 = TypedDiGraph()
RHS1.add_node("x", "agent")
RHS1.add_node("y", "agent")
h1 = Homomorphism(P1, LHS, {"a": 1, "b": 1})
h2 = Homomorphism(P1, RHS1, {"a": "x", "b": "y"})
RHS_instance = rw.apply_rule(instances[0], h1, h2)
# clone merge on the same nodes
RHS2 = TypedGraph()
RHS2.add_node("x", "agent")
h2 = Homomorphism(P1, RHS2, {"a": "x", "b": "x"})
RHS_instance = rw.apply_rule(instances[0], h1, h2)
# clone and merge one with other node
LHS.add_node(2, "agent")
# update matching
instances = rw.find_matching(LHS)
P3 = TypedDiGraph()
P3.add_node("a", "agent")
P3.add_node("b", "agent")
P3.add_node("c", "agent")
RHS3 = TypedDiGraph()
RHS3.add_node("x", "agent")
RHS3.add_node("y", "agent")
h1 = Homomorphism(P3, LHS, {"a": 1, "b": 1, "c": 2})
h2 = Homomorphism(P3, RHS3, {"a": "x", "b": "y", "c": "y"})
RHS_instance = rw.apply_rule(instances[0], h1, h2)
def test_load_graph_undir(self):
__location__ = os.path.realpath(
os.path.join(os.getcwd(), os.path.dirname(__file__)))
filename = os.path.join(__location__, "graph_example.json")
a = TypedGraph()
a.load(filename)
assert_equals(a.nodes(), [1, 2, 3])
assert_edges_undir(a.edges(), [(1, 2), (2, 3), (3, 1)])
assert_equals(a.node[1].type_, "agent")
assert_equals(a.node[2].type_, "agent")
assert_equals(a.node[3].type_, "action")
assert_equals(a.node[1].attrs_, {"u": {1}, "k": {33}})
assert_equals(a.node[2].attrs_, None)
assert_equals(a.node[3].attrs_, {"x": {33, 55, 66}})
def test_load_graph_undir(self):
__location__ = os.path.realpath(
os.path.join(os.getcwd(), os.path.dirname(__file__)))
filename = os.path.join(__location__, "graph_example.json")
a = TypedGraph()
a.load(filename)
assert_equals(a.nodes(), [1, 2, 3])
assert_edges_undir(a.edges(), [(1, 2), (2, 3), (3, 1)])
assert_equals(a.node[1].type_, "agent")
assert_equals(a.node[2].type_, "agent")
assert_equals(a.node[3].type_, "action")
assert_equals(a.node[1].attrs_, {"u": {1}, "k": {33}})
assert_equals(a.node[2].attrs_, None)
assert_equals(a.node[3].attrs_, {"x": {33, 55, 66}})
def final_PBC(h1, h2):
if h1.target_ != h2.source_:
raise ValueError(
"Codomain of homomorphism 1 and domain of homomorphism 2 " +
"don't match, can't do pullback complement")
if not h2.is_monic():
raise ValueError(
"Second homomorphism is not monic, cannot find final pullback complement"
)
if type(h1.target_) == TypedGraph:
res_graph = TypedGraph()
else:
res_graph = TypedDiGraph()
hom1 = {}
hom2 = {}
for node in h2.target_.nodes():
B_node = keys_by_value(h2.mapping_, node)
if len(B_node) > 0:
mapped_A_nodes = keys_by_value(h1.mapping_, B_node[0])
print(mapped_A_nodes)
for A_node in mapped_A_nodes:
res_graph.add_node(
str(A_node) + "_" + str(node),
h2.target_.node[h2.mapping_[h1.mapping_[A_node]]].type_,
merge_attributes(
h1.source_.node[A_node].attrs_, h2.target_.node[
h2.mapping_[h1.mapping_[A_node]]].attrs_,
"intersection"))
hom1[A_node] = str(A_node) + "_" + str(node)
hom2[str(A_node) + "_" +
str(node)] = h2.mapping_[h1.mapping_[A_node]]
else:
res_graph.add_node(
str(node) + "_", h2.target_.node[node].type_,
h2.target_.node[node].attrs_)
hom2[str(node) + "_"] = node
for s, t in h2.target_.edges():
B_s = keys_by_value(h2.mapping_, s)
B_t = keys_by_value(h2.mapping_, t)
if len(B_s) > 0 and len(B_t) > 0:
mapped_A_ss = keys_by_value(h1.mapping_, B_s[0])
mapped_A_ts = keys_by_value(h1.mapping_, B_t[0])
for A_s in mapped_A_ss:
for A_t in mapped_A_ts:
if res_graph.is_directed():
if hom1[A_s] == hom1[A_t] and (
A_s, A_t) not in h1.source_.edges():
res_graph.add_edge(
hom1[A_s], hom1[A_t],
h2.target_.get_edge(
h2.mapping_[h1.mapping_[A_s]],
h2.mapping_[h1.mapping_[A_t]]))
else:
res_graph.add_edge(
hom1[A_s], hom1[A_t],
merge_attributes(
h1.source_.get_edge(A_s, A_t),
h2.target_.get_edge(
h2.mapping_[h1.mapping_[A_s]],
h2.mapping_[h1.mapping_[A_t]]),
"intersection"))
else:
if hom1[A_s] == hom1[A_t] and (
A_s, A_t) not in h1.source_.edges() and (
A_t, A_s) not in h1.source_.edges():
res_graph.add_edge(
hom1[A_s], hom1[A_t],
h2.target_.get_edge(
h2.mapping_[h1.mapping_[A_s]],
h2.mapping_[h1.mapping_[A_t]]))
pass
else:
res_graph.add_edge(
hom1[A_s], hom1[A_t],
merge_attributes(
h1.source_.get_edge(A_s, A_t),
h2.target_.get_edge(
h2.mapping_[h1.mapping_[A_s]],
h2.mapping_[h1.mapping_[A_t]]),
"intersection"))
else:
if len(B_s) == 0:
sources_to_add = [str(s) + "_"]
else:
mapped_A_ss = keys_by_value(h1.mapping_, B_s[0])
sources_to_add = [hom1[A_s] for A_s in mapped_A_ss]
if len(B_t) == 0:
targets_to_add = [str(t) + "_"]
else:
mapped_A_ts = keys_by_value(h1.mapping_, B_t[0])
targets_to_add = [hom1[A_t] for A_t in mapped_A_ts]
for new_s in sources_to_add:
for new_t in targets_to_add:
res_graph.add_edge(new_s, new_t, h2.target_.edge[s][t])
res_h1 = Homomorphism(h1.source_, res_graph, hom1)
res_h2 = Homomorphism(res_graph, h2.target_, hom2)
return (res_graph, res_h1, res_h2)
def pullback(h1, h2):
""" Given h1 : B -> D; h2 : C -> D returns A, rh1, rh2
with rh1 : A -> B; rh2 : A -> C """
if h1.target_ != h2.target_:
raise ValueError(
"Homomorphisms don't have the same codomain, can't do pullback")
if type(h1.target_) == TypedGraph:
res_graph = TypedGraph()
else:
res_graph = TypedDiGraph()
hom1 = {}
hom2 = {}
for n1 in h1.source_.nodes():
for n2 in h2.source_.nodes():
if not h1.mapping_[n1] in res_graph.nodes():
if h1.mapping_[n1] == h2.mapping_[n2]:
res_graph.add_node(
h1.mapping_[n1],
h1.target_.node[h1.mapping_[n1]].type_,
merge_attributes(h1.source_.node[n1].attrs_,
h2.source_.node[n2].attrs_,
'intersection'))
hom1[h1.mapping_[n1]] = n1
hom2[h2.mapping_[n2]] = n2
for n1 in res_graph.nodes():
for n2 in res_graph.nodes():
if res_graph.is_directed():
if (hom1[n1], hom1[n2]) in h1.source_.edges():
if (hom2[n1], hom2[n2]) in h2.source_.edges():
res_graph.add_edge(n1, n2)
res_graph.set_edge(
n1, n2,
merge_attributes(
h1.source_.get_edge(hom1[n1], hom1[n2]),
h2.source_.get_edge(hom2[n1], hom2[n2]),
'intersection'))
else:
if (hom1[n1], hom1[n2]) in h1.source_.edges() or (
hom1[n2], hom1[n1]) in h1.source_.edges():
if (hom2[n1], hom2[n2]) in h2.source_.edges() or (
hom2[n2], hom2[n1]) in h2.source_.edges():
res_graph.add_edge(n1, n2)
res_graph.set_edge(
n1, n2,
merge_attributes(
h1.source_.get_edge(hom1[n1], hom1[n2]),
h2.source_.get_edge(hom2[n1], hom2[n2]),
'intersection'))
res_h1 = Homomorphism(res_graph, h1.source_, hom1)
res_h2 = Homomorphism(res_graph, h2.source_, hom2)
return res_graph, res_h1, res_h2
def pushout(h1, h2):
if h1.source_ != h2.source_:
raise ValueError(
"Domain of homomorphism 1 and domain of homomorphism 2 " +
"don't match, can't do pushout")
hom1 = {}
hom2 = {}
if type(h1.target_) == TypedGraph:
res_graph = TypedGraph()
else:
res_graph = TypedDiGraph()
for node in h1.source_.nodes():
res_graph.add_node(
str(h1.mapping_[node]) + "_" + str(h2.mapping_[node]),
h1.source_.node[node].type_,
merge_attributes(h1.target_.node[h1.mapping_[node]].attrs_,
h2.target_.node[h2.mapping_[node]].attrs_,
"union"))
hom1[h1.mapping_[node]] =\
str(h1.mapping_[node]) + "_" + str(h2.mapping_[node])
hom2[h2.mapping_[node]] =\
str(h1.mapping_[node]) + "_" + str(h2.mapping_[node])
for s, t in h1.source_.edges():
res_graph.add_edge(
str(h1.mapping_[s]) + "_" + str(h2.mapping_[s]),
str(h1.mapping_[t]) + "_" + str(h2.mapping_[t]),
merge_attributes(
h1.target_.get_edge(h1.mapping_[s], h1.mapping_[t]),
h2.target_.get_edge(h2.mapping_[s], h2.mapping_[t]), "union"))
for node in h1.target_.nodes():
if node not in h1.mapping_.values():
res_graph.add_node(
str(node) + "_", h1.target_.node[node].type_,
h1.target_.node[node].attrs_)
hom1[node] = str(node) + "_"
for node in h2.target_.nodes():
if node not in h2.mapping_.values():
res_graph.add_node(
str(node) + "_", h2.target_.node[node].type_,
h2.target_.node[node].attrs_)
hom2[node] = str(node) + "_"
for s, t in h1.target_.edges():
if s not in h1.mapping_.values() or t not in h1.mapping_.values():
res_graph.add_edge(hom1[s], hom1[t], h1.target_.get_edge(s, t))
if res_graph.is_directed():
if (hom1[s], hom1[t]) not in res_graph.edges():
res_graph.add_edge(hom1[s], hom1[t], h1.target_.get_edge(s, t))
else:
if (hom1[s], hom1[t]) not in res_graph.edges() and (
hom1[t], hom1[s]) not in res_graph.edges():
res_graph.add_edge(hom1[s], hom1[t], h1.target_.get_edge(s, t))
for s, t in h2.target_.edges():
if s not in h2.mapping_.values() or t not in h2.mapping_.values():
res_graph.add_edge(hom2[s], hom2[t], h2.target_.get_edge(s, t))
if res_graph.is_directed():
if (hom2[s], hom2[t]) not in res_graph.edges():
res_graph.add_edge(hom2[s], hom2[t], h2.target_.get_edge(s, t))
else:
if (hom2[s], hom2[t]) not in res_graph.edges() and (
hom2[t], hom2[s]) not in res_graph.edges():
res_graph.add_edge(hom2[s], hom2[t], h2.target_.get_edge(s, t))
res_h1 = Homomorphism(h1.target_, res_graph, hom1)
res_h2 = Homomorphism(h2.target_, res_graph, hom2)
return (res_graph, res_h1, res_h2)
def test_load_export(self):
__location__ = os.path.realpath(
os.path.join(os.getcwd(), os.path.dirname(__file__)))
filename = os.path.join(__location__, "graph_example.json")
a = TypedGraph()
a.load(filename)
out_filename = os.path.join(__location__, "output_graph.json")
a.export(out_filename)
b = TypedGraph()
b.load(out_filename)
assert_equals(a.nodes(), b.nodes())
assert_edges_undir(a.edges(), b.edges())
assert_equals(a.node[3].attrs_, b.node[3].attrs_)
def test_init_with_metamodel_undirected(self):
meta_meta = TypedGraph()
meta_meta.add_node("agent", "node")
meta_meta.add_node("action", "node")
meta_meta.add_edges_from([
("agent", "agent"),
("action", "action"),
("action", "agent")])
meta = TypedGraph(meta_meta)
meta.add_node("protein", "agent")
meta.add_node("region", "agent")
meta.add_node("action", "agent")
meta.add_edges_from([
("protein", "protein", {'a': 1}),
("region", "region"),
("action", "action"),
("protein", "region", {'a': 2}),
("action", "region"),
])
assert_equals(
meta.edge["protein"]["region"],
meta.edge["region"]["protein"])
graph = TypedGraph(meta)
graph.add_nodes_from([
(1, "protein"),
(2, "region"),
(3, "action"),
(4, "region"),
(5, "protein"),
(6, "region"),
(7, "protein")])
graph.add_edge(2, 1, {'x': 1})
graph.add_edge(2, 3, {'x': 2})
graph.add_edge(4, 3, {'x': 3})
graph.add_edge(4, 5, {'x': 4})
graph.add_edge(6, 3, {'x': 5})
graph.add_edge(6, 7, {'x': 6})
assert_equals(graph.edge[1][2], graph.edge[2][1])
def test_rule_to_homomorphism(self):
__location__ = os.path.realpath(
os.path.join(os.getcwd(), os.path.dirname(__file__)))
g = TypedGraph()
g.add_node(1, "action")
g.add_node(2, "agent", {"u": {0, 1}})
g.add_node(3, "agent", {"u": {4}, "name": "Paul"})
g.add_node(4, "action")
g.add_node(5, "agent", {"u": {0}})
g.add_node(6, "agent", {"u": {7}})
g.add_node(7, "agent", {"u": {4}})
g.add_edges_from([(1, 2), (3, 2), (1, 5), (5, 4), (5, 6)])
g.set_edge(1, 2, {"a": {0}})
g.set_edge(2, 3, {"k": {1, 2, 3}})
rw = Rewriter(g)
LHS = TypedGraph()
LHS.add_nodes_from([(1, "action"), (2, "agent"), (3, "agent")])
LHS.node[2].set_attrs({"u": 0})
LHS.add_edges_from([(1, 2), (2, 3)])
LHS.set_edge(2, 3, {"k": {1, 2}})
instances = rw.find_matching(LHS)
rw.add_node_attrs(instances[0], 1, {"u": 55, "x": 0})
h1, h2 = rw.generate_rule(
LHS, """delete_node 1.
clone 2 as 'clone'.
delete_node_attrs 'clone' {'u': 0}.
delete_edge 2 3.
delete_edge_attrs 'clone' 3 {'k': {1}}.
update_edge_attrs 'clone' 3 {'t': 333}.
update_node_attrs 2 {'u': {12, 13}}.
merge ['clone', 3] as 'merged'.
add_node_attrs 'merged' {'m': 1}.
add_node 'new_node' type 'region'.
add_node_attrs 'new_node' {'x': 1}.
add_edge 'new_node' 'merged'.
add_edge_attrs 'merged' 'new_node' {'j': 33}.""")
RHS_instance = rw.apply_rule(instances[0], h1, h2)
plot_instance(rw.graph_,
h2.target_,
RHS_instance,
filename=os.path.join(__location__,
"undir_rule_to_hom_RHS.png"))
def test_undirected_dec_init(self):
__location__ = os.path.realpath(
os.path.join(os.getcwd(), os.path.dirname(__file__)))
g = TypedGraph()
g.add_node(1, "action")
g.add_node(2, "agent", {"u": {0, 1}})
g.add_node(3, "agent", {"u": {4}, "name": "Paul"})
g.add_node(4, "action")
g.add_node(5, "agent", {"u": {0}})
g.add_node(6, "agent", {"u": {7}})
g.add_node(7, "agent", {"u": {4}})
g.add_edges_from([(1, 2), (3, 2), (1, 5), (5, 4), (5, 6)])
g.set_edge(1, 2, {"a": {0}})
g.set_edge(2, 3, {"k": {1, 2, 3}})
rw = Rewriter(g)
LHS = TypedGraph()
LHS.add_nodes_from([(10, "action"), (20, "agent"), (30, "agent")])
LHS.node[20].attrs_ = {"u": {0}}
LHS.add_edges_from([(10, 20), (20, 30)])
LHS.set_edge(20, 30, {"k": {1, 2}})
P = TypedGraph()
P.add_node(100, "agent")
P.add_node(200, "agent", {"u": {0}})
P.add_node(300, "agent")
P.add_edges_from([(300, 100), (200, 300)])
P.set_edge(100, 300, {"k": {1, 2}})
P.set_edge(200, 300, {"k": set()})
RHS = TypedGraph()
RHS.add_node(1000, "region")
RHS.add_node(2000, "agent", {"u": {3}})
RHS.add_node(3000, "agent", {"u": {0, 2}})
RHS.add_edges_from([(1000, 3000), (2000, 3000), (3000, 3000)])
RHS.set_edge(3000, 3000, {"k": {5, 6}})
RHS.set_edge(2000, 3000, {"k": {1, 2, 10}})
RHS.set_edge(1000, 3000, {"a": {12}})
instances = rw.find_matching(LHS)
for i, instance in enumerate(instances):
plot_instance(
rw.graph_, LHS, instance,
os.path.join(__location__, "undir_dec_instance_%d.png" % i))
left_h = Homomorphism(P, LHS, {100: 20, 200: 20, 300: 30})
righ_h = Homomorphism(P, RHS, {100: 2000, 200: 3000, 300: 3000})
RHS_instance = rw.apply_rule(instances[0], left_h, righ_h)
plot_instance(rw.graph_,
RHS,
RHS_instance,
filename=os.path.join(__location__, "undir_dec_RHS.png"))
def test_undirected_imp_init(self):
__location__ = os.path.realpath(
os.path.join(os.getcwd(), os.path.dirname(__file__)))
g = TypedGraph()
g.add_node(1, "agent", {"name": "John"})
g.add_node(2, "action")
g.add_node(3, "agent", {"name": "Paul"})
g.add_edges_from([(1, 2), (3, 2)])
g.set_edge(1, 2, {"a": 0})
rw = Rewriter(g)
LHS = TypedGraph()
LHS.add_nodes_from([(1, "agent"), (2, "action")])
LHS.add_edges_from([(1, 2)])
instances = rw.find_matching(LHS)
for i, instance in enumerate(instances):
plot_instance(
rw.graph_, LHS, instance,
os.path.join(__location__, "undir_instance_%d.png" % i))
rw.add_node(instances[0], 'region', 'Europe', {"a": 44})
rw.delete_node(instances[0], 1)
rw.delete_edge(instances[0], 2, 3)
rw.clone(instances[0], 2)
cast_node(rw.graph_, "Europe", "action")
rw.merge(instances[0], ["Europe", 2])
plot_graph(rw.graph_,
filename=os.path.join(__location__, "undir_cloned.png"))
def test_load_export(self):
__location__ = os.path.realpath(
os.path.join(os.getcwd(), os.path.dirname(__file__)))
filename = os.path.join(__location__, "graph_example.json")
a = TypedGraph()
a.load(filename)
out_filename = os.path.join(__location__, "output_graph.json")
a.export(out_filename)
b = TypedGraph()
b.load(out_filename)
assert_equals(a.nodes(), b.nodes())
assert_edges_undir(a.edges(), b.edges())
assert_equals(a.node[3].attrs_, b.node[3].attrs_)
def test_init_with_metamodel_undirected(self):
meta_meta = TypedGraph()
meta_meta.add_node("agent", "node")
meta_meta.add_node("action", "node")
meta_meta.add_edges_from([("agent", "agent"), ("action", "action"),
("action", "agent")])
meta = TypedGraph(meta_meta)
meta.add_node("protein", "agent")
meta.add_node("region", "agent")
meta.add_node("action", "agent")
meta.add_edges_from([
("protein", "protein", {
'a': 1
}),
("region", "region"),
("action", "action"),
("protein", "region", {
'a': 2
}),
("action", "region"),
])
assert_equals(meta.edge["protein"]["region"],
meta.edge["region"]["protein"])
graph = TypedGraph(meta)
graph.add_nodes_from([(1, "protein"), (2, "region"), (3, "action"),
(4, "region"), (5, "protein"), (6, "region"),
(7, "protein")])
graph.add_edge(2, 1, {'x': 1})
graph.add_edge(2, 3, {'x': 2})
graph.add_edge(4, 3, {'x': 3})
graph.add_edge(4, 5, {'x': 4})
graph.add_edge(6, 3, {'x': 5})
graph.add_edge(6, 7, {'x': 6})
assert_equals(graph.edge[1][2], graph.edge[2][1])
def pullback(h1, h2):
""" Given h1 : B -> D; h2 : C -> D returns A, rh1, rh2
with rh1 : A -> B; rh2 : A -> C """
if h1.target_ != h2.target_:
raise ValueError(
"Homomorphisms don't have the same codomain, can't do pullback"
)
if type(h1.target_) == TypedGraph:
res_graph = TypedGraph()
else:
res_graph = TypedDiGraph()
hom1 = {}
hom2 = {}
for n1 in h1.source_.nodes():
for n2 in h2.source_.nodes():
if not h1.mapping_[n1] in res_graph.nodes():
if h1.mapping_[n1] == h2.mapping_[n2]:
res_graph.add_node(
h1.mapping_[n1],
h1.target_.node[h1.mapping_[n1]].type_,
merge_attributes(h1.source_.node[n1].attrs_,
h2.source_.node[n2].attrs_,
'intersection'))
hom1[h1.mapping_[n1]] = n1
hom2[h2.mapping_[n2]] = n2
for n1 in res_graph.nodes():
for n2 in res_graph.nodes():
if res_graph.is_directed():
if (hom1[n1], hom1[n2]) in h1.source_.edges():
if (hom2[n1], hom2[n2]) in h2.source_.edges():
res_graph.add_edge(n1, n2)
res_graph.set_edge(
n1,
n2,
merge_attributes(
h1.source_.get_edge(hom1[n1], hom1[n2]),
h2.source_.get_edge(hom2[n1], hom2[n2]),
'intersection'))
else:
if (hom1[n1], hom1[n2]) in h1.source_.edges() or (hom1[n2], hom1[n1]) in h1.source_.edges():
if (hom2[n1], hom2[n2]) in h2.source_.edges() or (hom2[n2], hom2[n1]) in h2.source_.edges():
res_graph.add_edge(n1, n2)
res_graph.set_edge(
n1,
n2,
merge_attributes(
h1.source_.get_edge(hom1[n1], hom1[n2]),
h2.source_.get_edge(hom2[n1], hom2[n2]),
'intersection'))
res_h1 = Homomorphism(res_graph, h1.source_, hom1)
res_h2 = Homomorphism(res_graph, h2.source_, hom2)
return res_graph, res_h1, res_h2
def final_PBC(h1, h2):
if h1.target_ != h2.source_:
raise ValueError(
"Codomain of homomorphism 1 and domain of homomorphism 2 " +
"don't match, can't do pullback complement"
)
if not h2.is_monic():
raise ValueError(
"Second homomorphism is not monic, cannot find final pullback complement"
)
if type(h1.target_) == TypedGraph:
res_graph = TypedGraph()
else:
res_graph = TypedDiGraph()
hom1 = {}
hom2 = {}
for node in h2.target_.nodes():
B_node = keys_by_value(h2.mapping_, node)
if len(B_node) > 0:
mapped_A_nodes = keys_by_value(h1.mapping_, B_node[0])
print(mapped_A_nodes)
for A_node in mapped_A_nodes:
res_graph.add_node(
str(A_node) + "_" + str(node),
h2.target_.node[h2.mapping_[h1.mapping_[A_node]]].type_,
merge_attributes(
h1.source_.node[A_node].attrs_,
h2.target_.node[h2.mapping_[h1.mapping_[A_node]]].attrs_,
"intersection"
)
)
hom1[A_node] = str(A_node) + "_" + str(node)
hom2[str(A_node) + "_" + str(node)] = h2.mapping_[h1.mapping_[A_node]]
else:
res_graph.add_node(
str(node) + "_",
h2.target_.node[node].type_,
h2.target_.node[node].attrs_
)
hom2[str(node) + "_"] = node
for s, t in h2.target_.edges():
B_s = keys_by_value(h2.mapping_, s)
B_t = keys_by_value(h2.mapping_, t)
if len(B_s) > 0 and len(B_t) > 0:
mapped_A_ss = keys_by_value(h1.mapping_, B_s[0])
mapped_A_ts = keys_by_value(h1.mapping_, B_t[0])
for A_s in mapped_A_ss:
for A_t in mapped_A_ts:
if res_graph.is_directed():
if hom1[A_s] == hom1[A_t] and (A_s, A_t) not in h1.source_.edges():
res_graph.add_edge(
hom1[A_s],
hom1[A_t],
h2.target_.get_edge(
h2.mapping_[h1.mapping_[A_s]],
h2.mapping_[h1.mapping_[A_t]])
)
else:
res_graph.add_edge(
hom1[A_s],
hom1[A_t],
merge_attributes(
h1.source_.get_edge(A_s, A_t),
h2.target_.get_edge(
h2.mapping_[h1.mapping_[A_s]],
h2.mapping_[h1.mapping_[A_t]]),
"intersection"
)
)
else:
if hom1[A_s] == hom1[A_t] and (A_s, A_t) not in h1.source_.edges() and (A_t, A_s) not in h1.source_.edges():
res_graph.add_edge(
hom1[A_s],
hom1[A_t],
h2.target_.get_edge(
h2.mapping_[h1.mapping_[A_s]],
h2.mapping_[h1.mapping_[A_t]])
)
pass
else:
res_graph.add_edge(
hom1[A_s],
hom1[A_t],
merge_attributes(
h1.source_.get_edge(A_s, A_t),
h2.target_.get_edge(
h2.mapping_[h1.mapping_[A_s]],
h2.mapping_[h1.mapping_[A_t]]),
"intersection"
)
)
else:
if len(B_s) == 0:
sources_to_add = [str(s) + "_"]
else:
mapped_A_ss = keys_by_value(h1.mapping_, B_s[0])
sources_to_add = [hom1[A_s] for A_s in mapped_A_ss]
if len(B_t) == 0:
targets_to_add = [str(t) + "_"]
else:
mapped_A_ts = keys_by_value(h1.mapping_, B_t[0])
targets_to_add = [hom1[A_t] for A_t in mapped_A_ts]
for new_s in sources_to_add:
for new_t in targets_to_add:
res_graph.add_edge(
new_s,
new_t,
h2.target_.edge[s][t])
res_h1 = Homomorphism(h1.source_, res_graph, hom1)
res_h2 = Homomorphism(res_graph, h2.target_, hom2)
return (res_graph, res_h1, res_h2)
def pushout(h1, h2):
if h1.source_ != h2.source_:
raise ValueError(
"Domain of homomorphism 1 and domain of homomorphism 2 " +
"don't match, can't do pushout"
)
hom1 = {}
hom2 = {}
if type(h1.target_) == TypedGraph:
res_graph = TypedGraph()
else:
res_graph = TypedDiGraph()
for node in h1.source_.nodes():
res_graph.add_node(
str(h1.mapping_[node]) + "_" + str(h2.mapping_[node]),
h1.source_.node[node].type_,
merge_attributes(
h1.target_.node[h1.mapping_[node]].attrs_,
h2.target_.node[h2.mapping_[node]].attrs_,
"union"
)
)
hom1[h1.mapping_[node]] =\
str(h1.mapping_[node]) + "_" + str(h2.mapping_[node])
hom2[h2.mapping_[node]] =\
str(h1.mapping_[node]) + "_" + str(h2.mapping_[node])
for s, t in h1.source_.edges():
res_graph.add_edge(
str(h1.mapping_[s]) + "_" + str(h2.mapping_[s]),
str(h1.mapping_[t]) + "_" + str(h2.mapping_[t]),
merge_attributes(
h1.target_.get_edge(h1.mapping_[s], h1.mapping_[t]),
h2.target_.get_edge(h2.mapping_[s], h2.mapping_[t]),
"union"
)
)
for node in h1.target_.nodes():
if node not in h1.mapping_.values():
res_graph.add_node(
str(node) + "_",
h1.target_.node[node].type_,
h1.target_.node[node].attrs_
)
hom1[node] = str(node) + "_"
for node in h2.target_.nodes():
if node not in h2.mapping_.values():
res_graph.add_node(
str(node) + "_",
h2.target_.node[node].type_,
h2.target_.node[node].attrs_
)
hom2[node] = str(node) + "_"
for s, t in h1.target_.edges():
if s not in h1.mapping_.values() or t not in h1.mapping_.values():
res_graph.add_edge(
hom1[s],
hom1[t],
h1.target_.get_edge(s, t)
)
if res_graph.is_directed():
if (hom1[s], hom1[t]) not in res_graph.edges():
res_graph.add_edge(
hom1[s],
hom1[t],
h1.target_.get_edge(s, t)
)
else:
if (hom1[s], hom1[t]) not in res_graph.edges() and (hom1[t], hom1[s]) not in res_graph.edges():
res_graph.add_edge(
hom1[s],
hom1[t],
h1.target_.get_edge(s, t)
)
for s, t in h2.target_.edges():
if s not in h2.mapping_.values() or t not in h2.mapping_.values():
res_graph.add_edge(
hom2[s],
hom2[t],
h2.target_.get_edge(s, t)
)
if res_graph.is_directed():
if (hom2[s], hom2[t]) not in res_graph.edges():
res_graph.add_edge(
hom2[s],
hom2[t],
h2.target_.get_edge(s, t)
)
else:
if (hom2[s], hom2[t]) not in res_graph.edges() and (hom2[t], hom2[s]) not in res_graph.edges():
res_graph.add_edge(
hom2[s],
hom2[t],
h2.target_.get_edge(s, t)
)
res_h1 = Homomorphism(h1.target_, res_graph, hom1)
res_h2 = Homomorphism(h2.target_, res_graph, hom2)
return (res_graph, res_h1, res_h2)