def benchmark():
"Run few simple benchmarks for extend_hom()."
logging.getLogger().setLevel(logging.DEBUG)
from sage.graphs.graph_generators import graphs
from sage.misc.sage_timeit import sage_timeit
K6 = graphs.CompleteGraph(6)
K2 = graphs.CompleteGraph(2)
K7_6 = graphs.CompleteBipartiteGraph(7, 6)
C16 = graphs.CycleGraph(16)
C13 = graphs.CycleGraph(13)
C5 = graphs.CycleGraph(5)
eh = extend_hom
logging.info(
"All homs K6 -> K6: %s",
sage_timeit("assert len(eh(K6, K6, limit=10000)) == 720",
locals(),
preparse=False))
logging.info(
"All homs K7,6 -> K2: %s",
sage_timeit("assert len(eh(K7_6, K2, limit=10000)) == 2",
locals(),
preparse=False))
logging.info(
"All homs C13 -> C5: %s",
sage_timeit("assert len(eh(C13, C5, limit=10000)) == 7150",
locals(),
preparse=False))
def test():
"Some unit tests"
from sage.graphs.graph_generators import graphs
K2 = graphs.CompleteGraph(2)
K4 = graphs.CompleteGraph(4)
K24 = graphs.CompleteGraph(24)
C4 = graphs.CycleGraph(4)
C16 = graphs.CycleGraph(16)
# parallel_extend_hom
assert len(parallel_extend_hom(K4, K4, limit=100)) == 24
assert parallel_extend_hom(K2, K4, partmap={0:0}, limit=10, onlycount=True) == 3
assert len(parallel_extend_hom(C16, K2, limit=10)) == 2
assert len(parallel_extend_hom(C16, K2, partmap={0:0, 2:1}, limit=10)) == 0
# parallel_extend_hom giving partial mappings
assert len(parallel_extend_hom(C16, C4, partmap={0:0}, order=[0,2,1], limit=100)) == 4
assert len(parallel_extend_hom(C16, C4, partmap={8:0}, order=[0], limit=100)) == 4
assert parallel_extend_hom(C16, C4, partmap={4:1}, order=[], limit=100) == [{4:1}]
assert parallel_extend_hom(C16, C4, order=[], limit=100) == [{}]
# differen branching parameters
assert parallel_extend_hom(C4, K24, branchdepth=[0,0,1], limit=1000000, onlycount=True, check_automorphisms=1) == 11661
assert parallel_extend_hom(C4, K24, branchdepth=[0,1,2,3], limit=1000000, onlycount=True, check_automorphisms=2) == 507
assert (sorted(parallel_extend_hom(C4, K24, branchdepth=[1,0,2,3,2], limit=10000, check_automorphisms=14)) ==
[{0: 1, 1: 0, 2: 1, 3: 0}, {0: 1, 1: 2, 2: 1, 3: 0}, {0: 2, 1: 0, 2: 1, 3: 0}, {0: 3, 1: 2, 2: 1, 3: 0}])
log.info("All tests passed.")
def Cycle(self, n):
"""
Sandpile on the cycle graph with `n` vertices.
INPUT:
- ``n`` -- a non-negative integer
OUTPUT:
- Sandpile
EXAMPLES::
sage: s = sandpiles.Cycle(4)
sage: s.edges()
[(0, 1, 1),
(0, 3, 1),
(1, 0, 1),
(1, 2, 1),
(2, 1, 1),
(2, 3, 1),
(3, 0, 1),
(3, 2, 1)]
"""
return Sandpile(graphs.CycleGraph(n), 0)
def test():
"Run unit tests for the module."
logging.getLogger().setLevel(logging.DEBUG)
from sage.graphs.graph_generators import graphs
K2 = graphs.CompleteGraph(2)
K4 = graphs.CompleteGraph(4)
K24 = graphs.CompleteGraph(24)
C4 = graphs.CycleGraph(4)
C16 = graphs.CycleGraph(16)
# extend_hom
assert len(extend_hom(K4, K4, limit=100)) == 24
assert len(extend_hom(K2, K4, partmap={0: 0}, limit=10)) == 3
assert len(extend_hom(C16, K2, limit=10)) == 2
assert len(extend_hom(C16, K2, partmap={0: 0, 2: 1}, limit=10)) == 0
# extend_hom giving partial mappings
assert len(extend_hom(C16, C4, partmap={0: 0}, order=[0, 2, 1],
limit=100)) == 4
assert len(extend_hom(C16, C4, partmap={8: 0}, order=[0], limit=100)) == 4
assert extend_hom(C16, C4, partmap={4: 1}, order=[], limit=100) == [{4: 1}]
assert extend_hom(C16, C4, order=[], limit=100) == [{}]
# extend_hom only counting
assert extend_hom(K2, K4, partmap={0: 0}, limit=10, onlycount=True) == 3
# Following would probably segfault if actually allocating 1G entries
assert extend_hom(K4, K4, limit=2**30, onlycount=True) == 24
# extend_hom with check_automorphisms
assert len(extend_hom(K4, K4, limit=100, check_automorphisms=1)) == 6
assert len(extend_hom(K4, K4, limit=100, check_automorphisms=2)) == 2
assert len(extend_hom(K4, K4, limit=100, check_automorphisms=3)) == 1
assert len(extend_hom(K4, K4, limit=100, check_automorphisms=4)) == 1
assert len(
extend_hom(K2, K4, partmap={0: 0}, limit=10,
check_automorphisms=1)) == 1
assert len(extend_hom(C16, K2, limit=10, check_automorphisms=1)) == 1
assert len(
extend_hom(C16,
K2,
partmap={
0: 0,
2: 1
},
limit=10,
check_automorphisms=2)) == 0
# This might be slow
assert extend_hom(K24,
K24,
limit=10,
check_automorphisms=42,
onlycount=True) == 1
# find_hom_image
K4c = find_hom_image(K4.disjoint_union(K4))
assert K4.is_isomorphic(K4c)
# find_core
K4d = find_core(K4.disjoint_union(K4).disjoint_union(K4))
assert K4.is_isomorphic(K4d)
# is_hom
for hom in extend_hom(C16, K2, limit=10):
assert is_hom(C16, K2, hom)
assert raises(lambda: is_hom(K2, K2, {0: 0})) # not all vertices mapped
assert raises(lambda: is_hom(K2, K2, {0: 4})) # some vertices outside K2
assert not is_hom(K2, K2, {0: 0, 1: 0}) # creates a loop
logging.info("All tests passed.")