def test_retrieval(self):
eq = {(-1, -1), (1, 1)}
spec = pm.Specification(nx.path_graph(2), (0, 1), eq, vartype=pm.SPIN)
widget = pm.get_penalty_model(spec)
self.assertEqual(widget.model.linear, {0: 0, 1: 0})
self.assertEqual(widget.model.quadratic, {(0, 1): -1})
def test_relabel_copy(self):
graph = nx.circular_ladder_graph(12)
decision_variables = (0, 2, 5)
feasible_configurations = {(1, 1, 1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
mapping = dict(enumerate('abcdefghijklmnopqrstuvwxyz'))
new_spec = spec.relabel_variables(mapping, inplace=False)
# create a test spec
graph = nx.relabel_nodes(graph, mapping)
decision_variables = (mapping[v] for v in decision_variables)
test_spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
self.assertEqual(new_spec, test_spec)
self.assertEqual(new_spec.ising_linear_ranges, test_spec.ising_linear_ranges)
self.assertEqual(new_spec.ising_quadratic_ranges, test_spec.ising_quadratic_ranges)
def test_relabel_inplace_overlap(self):
graph = nx.circular_ladder_graph(12)
decision_variables = (0, 2, 5)
feasible_configurations = {(1, 1, 1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
mapping = {v: v + 5 for v in graph}
new_spec = spec.relabel_variables(mapping, inplace=True)
def test_relabel_forwards_and_backwards(self):
graph = nx.path_graph(4)
graph.add_edge(0, 2)
decision_variables = (0, 2)
feasible_configurations = {(-1, -1): 0., (+1, +1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
# make another one
graph = nx.path_graph(4)
graph.add_edge(0, 2)
decision_variables = (0, 2)
feasible_configurations = {(-1, -1): 0., (+1, +1): 0.}
original_spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
identity = {v: v for v in graph}
new_label_sets = [(10, 1),
('a', 'b'),
(1, 'b'),
('1', '2', '3', '4'),
('a', 'b', 'c', 'd')]
new_label_sets.extend(itertools.permutations(graph))
for new in new_label_sets:
mapping = dict(enumerate(new))
inv_mapping = {u: v for v, u in mapping.items()}
# apply then invert with inplace=False
copy_spec = spec.relabel_variables(mapping, inplace=False)
inv_copy = copy_spec.relabel_variables(inv_mapping, inplace=False)
self.assertEqual(inv_copy, original_spec)
self.assertEqual(inv_copy.ising_linear_ranges, original_spec.ising_linear_ranges)
self.assertEqual(inv_copy.ising_quadratic_ranges, original_spec.ising_quadratic_ranges)
# apply then invert with inplace=True
spec.relabel_variables(mapping, inplace=True)
if mapping == identity:
self.assertEqual(spec, original_spec)
else:
self.assertNotEqual(spec, original_spec)
spec.relabel_variables(inv_mapping, inplace=True)
self.assertEqual(spec, original_spec)
self.assertEqual(spec.ising_linear_ranges, original_spec.ising_linear_ranges)
self.assertEqual(spec.ising_quadratic_ranges, original_spec.ising_quadratic_ranges)
def test_relabel_forwards_and_backwards(self):
graph = nx.path_graph(4)
graph.add_edge(0, 2)
decision_variables = (0, 2)
feasible_configurations = {(-1, -1): 0., (+1, +1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
linear = {v: 0 for v in graph}
quadratic = {edge: -1 for edge in graph.edges}
model = dimod.BinaryQuadraticModel(linear, quadratic, 0.0, vartype=dimod.SPIN)
widget = pm.PenaltyModel.from_specification(spec, model, 2., -2)
# make another one
graph = nx.path_graph(4)
graph.add_edge(0, 2)
decision_variables = (0, 2)
feasible_configurations = {(-1, -1): 0., (+1, +1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
linear = {v: 0 for v in graph}
quadratic = {edge: -1 for edge in graph.edges}
model = dimod.BinaryQuadraticModel(linear, quadratic, 0.0, vartype=dimod.SPIN)
original_widget = pm.PenaltyModel.from_specification(spec, model, 2., -2)
new_label_sets = [(10, 1),
('a', 'b'),
(1, 'b'),
('1', '2', '3', '4'),
('a', 'b', 'c', 'd')]
new_label_sets.extend(itertools.permutations(graph))
for new in new_label_sets:
mapping = dict(enumerate(new))
inv_mapping = {u: v for v, u in mapping.items()}
# apply then invert with copy=False
widget.relabel_variables(mapping, inplace=True)
widget.relabel_variables(inv_mapping, inplace=True)
self.assertEqual(widget, original_widget)
# apply then invert with copy=True
copy_widget = widget.relabel_variables(mapping, inplace=False)
inv_copy = copy_widget.relabel_variables(inv_mapping, inplace=False)
self.assertEqual(inv_copy, original_widget)
def test_typical(self):
graph = nx.complete_graph(3)
spec = pm.Specification(graph, [0, 1], {(-1, -1): 0, (+1, +1): 0}, dimod.SPIN)
widget = mip.get_penalty_model(spec)
# some quick test to see that the penalty model propogated in
for v in graph:
self.assertIn(v, widget.model.linear)
for (u, v) in graph.edges:
self.assertIn(u, widget.model.adj[v])
def test_linear_ranges_specified(self):
graph = nx.barbell_graph(4, 16)
decision_variables = (0, 4, 3)
feasible_configurations = {(0, 0, 1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations,
ising_linear_ranges={v: [-v, 2] for v in graph},
vartype=dimod.BINARY)
# check default energy ranges
for v in graph:
self.assertEqual(spec.ising_linear_ranges[v], [-v, 2])
spec = pm.Specification(graph, decision_variables, feasible_configurations,
ising_linear_ranges={v: (-v, 2) for v in graph},
vartype=dimod.BINARY)
# check default energy ranges
for v in graph:
self.assertEqual(spec.ising_linear_ranges[v], [-v, 2])
def test_construction_typical(self):
graph = nx.complete_graph(10)
decision_variables = (0, 4, 5)
feasible_configurations = {(-1, -1, -1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
self.assertEqual(spec.graph, graph) # literally the same object
self.assertEqual(spec.decision_variables, decision_variables)
self.assertEqual(spec.feasible_configurations, feasible_configurations)
self.assertIs(spec.vartype, dimod.SPIN)
def test_relabel(self):
graph = nx.path_graph(3)
decision_variables = (0, 2)
feasible_configurations = {(-1, -1): 0., (+1, +1): 0.}
spec = pm.Specification(graph,
decision_variables,
feasible_configurations,
vartype=dimod.SPIN)
linear = {v: 0 for v in graph}
quadratic = {edge: -1 for edge in graph.edges}
model = dimod.BinaryQuadraticModel(linear,
quadratic,
0.0,
vartype=dimod.SPIN)
widget = pm.PenaltyModel.from_specification(spec, model, 2., -2)
# now set up the same widget with 0 relabelled to 'a'
graph = nx.path_graph(3)
graph = nx.relabel_nodes(graph, {0: 'a'})
decision_variables = ('a', 2)
feasible_configurations = {(-1, -1): 0., (+1, +1): 0.}
spec = pm.Specification(graph,
decision_variables,
feasible_configurations,
vartype=dimod.SPIN)
linear = {v: 0 for v in graph}
quadratic = {edge: -1 for edge in graph.edges}
model = dimod.BinaryQuadraticModel(linear,
quadratic,
0.0,
vartype=dimod.SPIN)
test_widget = pm.PenaltyModel.from_specification(spec, model, 2., -2)
# without copy
new_widget = widget.relabel_variables({0: 'a'}, inplace=False)
self.assertEqual(test_widget, new_widget)
self.assertEqual(new_widget.decision_variables, ('a', 2))
widget.relabel_variables({0: 'a'}, inplace=True)
self.assertEqual(widget, test_widget)
self.assertEqual(widget.decision_variables, ('a', 2))
def test_relabel_inplace(self):
graph = nx.circular_ladder_graph(12)
decision_variables = (0, 2, 5)
feasible_configurations = {(1, 1, 1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
mapping = {i: v for i, v in enumerate('abcdefghijklmnopqrstuvwxyz') if i in graph}
new_spec = spec.relabel_variables(mapping, inplace=True)
self.assertIs(new_spec, spec) # should be the same object
self.assertIs(new_spec.graph, spec.graph)
# create a test spec
graph = nx.relabel_nodes(graph, mapping)
decision_variables = (mapping[v] for v in decision_variables)
test_spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
self.assertEqual(new_spec, test_spec)
self.assertEqual(new_spec.ising_linear_ranges, test_spec.ising_linear_ranges)
self.assertEqual(new_spec.ising_quadratic_ranges, test_spec.ising_quadratic_ranges)
def test_nonzero_configuration(self):
"""MaxGap is currently not supporting non-zero feasible states. This is checking that
non-zero feasible state problems don't get run.
"""
graph = nx.complete_graph(3)
spec = pm.Specification(graph, [0, 1], {
(-1, 1): 0,
(-1, -1): -2
}, dimod.SPIN)
with self.assertRaises(ImpossiblePenaltyModel):
maxgap.get_penalty_model(spec)
def test_vartype_specified(self):
graph = nx.complete_graph(12)
decision_variables = (0, 2, 5)
feasible_configurations = {(1, 1, 1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
self.assertIs(spec.vartype, dimod.SPIN)
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.BINARY)
self.assertIs(spec.vartype, dimod.BINARY)
# now set up a spec that can only have one vartype
graph = nx.complete_graph(12)
decision_variables = (0, 2, 5)
feasible_configurations = {(1, 1, -1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
self.assertIs(spec.vartype, dimod.SPIN)
# the feasible_configurations are spin
with self.assertRaises(ValueError):
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.BINARY)
def test_ranges_default(self):
graph = nx.barbell_graph(4, 16)
decision_variables = (0, 4, 3)
feasible_configurations = {(0, 0, 0): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.BINARY)
for v in graph:
self.assertEqual(spec.ising_linear_ranges[v], [-2, 2])
for u, v in graph.edges:
self.assertEqual(spec.ising_quadratic_ranges[u][v], [-1, 1])
self.assertEqual(spec.ising_quadratic_ranges[v][u], [-1, 1])
def test_bad_relabel(self):
graph = nx.path_graph(4)
graph.add_edge(0, 2)
decision_variables = (0, 2)
feasible_configurations = {(-1, -1): 0., (+1, +1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
mapping = {0: 2, 1: 1}
with self.assertRaises(ValueError):
spec.relabel_variables(mapping, inplace=False)
with self.assertRaises(ValueError):
spec.relabel_variables(mapping, inplace=True)
def test_bad_energy_range(self):
graph = nx.path_graph(3)
decision_variables = (0, 2)
feasible_configurations = {(-1, -1): 0., (+1, +1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
linear = {v: -3 for v in graph}
quadratic = {edge: -1 for edge in graph.edges}
model = dimod.BinaryQuadraticModel(linear, quadratic, 0.0, vartype=dimod.SPIN)
with self.assertRaises(ValueError):
widget = pm.PenaltyModel.from_specification(spec, model, 2., -2)
linear = {v: 0 for v in graph}
quadratic = {edge: 5 for edge in graph.edges}
model = dimod.BinaryQuadraticModel(linear, quadratic, 0.0, vartype=dimod.SPIN)
with self.assertRaises(ValueError):
widget = pm.PenaltyModel.from_specification(spec, model, 2., -2)
def gate_model(gate_type, fault=True):
labels, configurations = GATES[gate_type]
if fault:
configurations = fault_gate(configurations, FAULT_GAP)
num_variables = len(next(iter(configurations)))
for size in range(num_variables, num_variables + 4): # reasonable margin
G = nx.complete_graph(size)
nx.relabel_nodes(G, dict(enumerate(labels)), copy=False)
spec = pm.Specification(G, labels, configurations, dimod.SPIN)
try:
pmodel = pm.get_penalty_model(spec)
if pmodel is not None:
return pmodel
except pm.ImpossiblePenaltyModel:
pass
raise ValueError("unable to get the penalty model from factories")
def test_arbitrary_labels_on_k44(self):
dbfile = self.database
graph = nx.Graph()
for i in range(3):
for j in range(3, 6):
graph.add_edge(i, j)
decision_variables = (0, 5)
feasible_configurations = ((0, 0), (1, 1)) # equality
spec = pm.Specification(graph,
decision_variables,
feasible_configurations,
vartype=dimod.BINARY)
linear = {v: 0 for v in graph}
quadratic = {edge: 0 for edge in graph.edges}
if decision_variables in quadratic:
quadratic[decision_variables] = -1
else:
u, v = decision_variables
assert (v, u) in quadratic
quadratic[(v, u)] = -1
model = dimod.BinaryQuadraticModel(linear,
quadratic,
0.0,
vartype=dimod.SPIN)
pmodel = pm.PenaltyModel.from_specification(spec, model, 2, -1)
# now cache the pmodel to make sure there is something to find
for thingy in itertools.permutations(range(6)):
mapping = dict(enumerate(thingy))
pmodel = pmodel.relabel_variables(mapping, inplace=False)
pmc.cache_penalty_model(pmodel, database=dbfile)
# now relabel some variables
mapping = {1: '1', 2: '2', 3: '3', 4: '4'}
new_spec = spec.relabel_variables(mapping, inplace=True)
# retrieve from the new_spec
# now try to retrieve it
retreived_pmodel = pmc.get_penalty_model(new_spec, database=dbfile)
def test_quadratic_ranges_partially_specified(self):
graph = nx.barbell_graph(4, 16)
decision_variables = (0, 4, 3)
feasible_configurations = {(0, 0, 1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations,
ising_quadratic_ranges={0: {1: [0, 1], 2: [-1, 0]}, 2: {0: [-1, 0]}},
vartype=dimod.BINARY)
ising_quadratic_ranges = spec.ising_quadratic_ranges
for u in ising_quadratic_ranges:
for v in ising_quadratic_ranges[u]:
self.assertIs(ising_quadratic_ranges[u][v], ising_quadratic_ranges[v][u])
for u, v in graph.edges:
self.assertIn(v, ising_quadratic_ranges[u])
self.assertIn(u, ising_quadratic_ranges[v])
self.assertEqual(ising_quadratic_ranges[0][1], [0, 1])
def test_one_variable_insert_retrieve(self):
"""Test case when there is no quadratic contribution (i.e. cache will
receive an empty value for the quadratic contribution)
"""
dbfile = self.database
# generate one variable model (i.e. no quadratic terms)
spec = pm.Specification(graph=nx.complete_graph(1),
decision_variables=[0],
feasible_configurations=[(-1, )],
min_classical_gap=2,
vartype='SPIN')
pmodel = pm.get_penalty_model(spec)
# insert model into cache
pmc.cache_penalty_model(pmodel, database=dbfile)
# retrieve model back from cache
retrieved_model = pmc.get_penalty_model(spec, database=dbfile)
self.assertEqual(pmodel, retrieved_model)
def test_retrieval(self):
# put some stuff in the database
spec = pm.Specification(nx.path_graph(2), (0, 1), {(-1, -1), (1, 1)},
vartype=pm.SPIN)
model = dimod.BinaryQuadraticModel({
0: 0,
1: 0
}, {(0, 1): -1},
0.0,
vartype=pm.SPIN)
widget = pm.PenaltyModel.from_specification(spec, model, 2, -1)
for cache in pm.iter_caches():
cache(widget)
# now try to get it back
new_widget = pm.get_penalty_model(spec)
self.assertEqual(widget, new_widget)
def test_binary_specification(self):
dbfile = self.database
# set up a specification and a corresponding penaltymodel
graph = nx.Graph()
for i in 'abcd':
for j in 'efgh':
graph.add_edge(i, j)
decision_variables = ('a', 'e')
feasible_configurations = ((0, 0), (1, 1)) # equality
spec = pm.Specification(graph,
decision_variables,
feasible_configurations,
vartype=dimod.BINARY)
linear = {v: 0 for v in graph}
quadratic = {edge: 0 for edge in graph.edges}
if decision_variables in quadratic:
quadratic[decision_variables] = -1
else:
u, v = decision_variables
assert (v, u) in quadratic
quadratic[(v, u)] = -1
model = dimod.BinaryQuadraticModel(linear,
quadratic,
0.0,
vartype=dimod.SPIN)
pmodel = pm.PenaltyModel.from_specification(spec, model, 2, -1)
# now cache the pmodel to make sure there is something to find
pmc.cache_penalty_model(pmodel, database=dbfile)
# now try to retrieve it
retreived_pmodel = pmc.get_penalty_model(spec, database=dbfile)
self.assertIs(retreived_pmodel.model.vartype, dimod.BINARY)
# check that the specification is equal to the retreived_pmodel
self.assertTrue(spec.__eq__(retreived_pmodel))
def test_and_on_k44(self):
graph = nx.Graph()
for i in range(3):
for j in range(3, 6):
graph.add_edge(i, j)
decision_variables = (0, 2, 3)
feasible_configurations = AND(2)
mapping = {0: '0', 1: '1', 2: '2', 3: '3'}
graph = nx.relabel_nodes(graph, mapping)
decision_variables = tuple(mapping[x] for x in decision_variables)
spin_configurations = tuple([tuple([2 * i - 1 for i in b]) for b in feasible_configurations])
spec = pm.Specification(graph, decision_variables, spin_configurations, vartype=dimod.SPIN)
pm0 = mip.get_penalty_model(spec)
self.check_generated_ising_model(pm0.feasible_configurations, pm0.decision_variables,
pm0.model.linear, pm0.model.quadratic, pm0.ground_energy - pm0.model.offset,
pm0.classical_gap)
def gate_model(gate_type, fault=True):
labels, configurations = GATES[gate_type]
if fault:
configurations = fault_gate(configurations, FAULT_GAP)
size = len(next(iter(configurations)))
while True:
G = nx.complete_graph(size)
nx.relabel_nodes(G, dict(enumerate(labels)), copy=False)
spec = pm.Specification(G, labels, configurations, dimod.SPIN)
try:
pmodel = pm.get_penalty_model(spec)
if not pmodel:
raise LookupError("failed to get penalty model from factory")
# print("penalty model fits on K{}".format(size))
break
except pm.ImpossiblePenaltyModel:
# print("penalty model does not fit on K{}".format(size))
size += 1
# print('h: {}'.format(pmodel.model.linear))
# print('J: {}\n'.format(pmodel.model.quadratic))
return pmodel
def test_construction(self):
# build a specification
graph = nx.complete_graph(10)
decision_variables = (0, 4, 5)
feasible_configurations = {(-1, -1, -1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations, vartype=dimod.SPIN)
# build a model
model = dimod.BinaryQuadraticModel({v: 0 for v in graph},
{edge: 0 for edge in graph.edges},
0.0,
vartype=dimod.SPIN)
# build a PenaltyModel explicitly
pm0 = pm.PenaltyModel(graph, decision_variables, feasible_configurations, dimod.SPIN, model, .1, 0)
# build from spec
pm1 = pm.PenaltyModel.from_specification(spec, model, .1, 0)
# should result in equality
self.assertEqual(pm0, pm1)
def test_penalty_model_insert_retrieve(self):
conn = self.clean_connection
graph = nx.path_graph(3)
decision_variables = (0, 2)
feasible_configurations = {(-1, -1): 0., (+1, +1): 0.}
spec = pm.Specification(graph, decision_variables, feasible_configurations, dimod.SPIN)
linear = {v: 0 for v in graph}
quadratic = {edge: -1 for edge in graph.edges}
model = dimod.BinaryQuadraticModel(linear, quadratic, 0.0, vartype=dimod.SPIN)
widget = pm.PenaltyModel.from_specification(spec, model, 2., -2)
with conn as cur:
pmc.insert_penalty_model(cur, widget)
with conn as cur:
pms = list(pmc.iter_penalty_model_from_specification(cur, spec))
self.assertEqual(len(pms), 1)
widget_, = pms
self.assertEqual(widget_, widget)
def test_binary_specification(self):
graph = nx.Graph()
for i in range(4):
for j in range(4, 8):
graph.add_edge(i, j)
decision_variables = (0, 1)
feasible_configurations = ((0, 0), (1, 1)) # equality
spec = pm.Specification(graph,
decision_variables,
feasible_configurations,
vartype=dimod.BINARY)
widget = mip.get_penalty_model(spec)
self.assertIs(widget.model.vartype, dimod.BINARY)
# test the correctness of the widget
energies = {}
for decision_config in itertools.product((0, 1), repeat=2):
energies[decision_config] = float('inf')
for aux_config in itertools.product((0, 1), repeat=6):
sample = dict(enumerate(decision_config + aux_config))
energy = widget.model.energy(sample)
energies[decision_config] = min(energies[decision_config],
energy)
for decision_config, energy in energies.items():
if decision_config in feasible_configurations:
self.assertAlmostEqual(energy, widget.ground_energy)
else:
self.assertGreaterEqual(
energy,
widget.ground_energy + widget.classical_gap - 10**-6)
def test_typical(self):
dbfile = self.database
# insert a penalty model
graph = nx.path_graph(3)
decision_variables = (0, 2)
feasible_configurations = {(-1, -1): 0., (+1, +1): 0.}
spec = pm.Specification(graph, decision_variables,
feasible_configurations, dimod.SPIN)
linear = {v: 0 for v in graph}
quadratic = {edge: -1 for edge in graph.edges}
model = dimod.BinaryQuadraticModel(linear,
quadratic,
0.0,
vartype=dimod.SPIN)
widget = pm.PenaltyModel.from_specification(spec, model, 2., -2)
# cache the penaltymodel
pmc.cache_penalty_model(widget, database=dbfile)
# retrieve it
widget_ = pmc.get_penalty_model(spec, database=dbfile)
self.assertEqual(widget_, widget)
@author: ahaemm
'''
import penaltymodel.core as pm
import networkx as nx
import dimod
from penaltymodel.cache.interface import cache_penalty_model
### create penalty model for the [(1,0), (0,0), (0,1)] constraint between x_i_t, x_j_k;
variables = ['i_t', 'j_k']
feasible_configs = {(1, 0), (0, 0), (0, 1)}
graph = nx.Graph()
graph.add_edges_from([('i_t', 'j_k')])
spec = pm.Specification(graph, variables, feasible_configs, dimod.BINARY)
qubo = dimod.BinaryQuadraticModel({
'i_t': 0.,
'j_k': 0.
}, {('i_t', 'j_k'): 1.}, 0.0, dimod.BINARY)
ground_energy = qubo.energy({'i_t': 1., 'j_k': 0.})
print(ground_energy)
pModel = pm.PenaltyModel.from_specification(spec, qubo, 2, 0)
cache_penalty_model(
pModel,
'c:\\Users\\ahaemm\\workspace\\dwave\\env\\data\\dwave-penaltymodel-cache\\penaltymodel_cache_v0.4.0.db'
)
### t = 2, t' = 1,2,3
def stitch(csp, min_classical_gap=2.0, max_graph_size=8):
"""Build a binary quadratic model with minimal energy levels at solutions to the specified constraint satisfaction
problem.
Args:
csp (:obj:`.ConstraintSatisfactionProblem`):
Constraint satisfaction problem.
min_classical_gap (float, optional, default=2.0):
Minimum energy gap from ground. Each constraint violated by the solution increases
the energy level of the binary quadratic model by at least this much relative
to ground energy.
max_graph_size (int, optional, default=8):
Maximum number of variables in the binary quadratic model that can be used to
represent a single constraint.
Returns:
:class:`~dimod.BinaryQuadraticModel`
Notes:
For a `min_classical_gap` > 2 or constraints with more than two variables, requires
access to factories from the penaltymodel_ ecosystem to construct the binary quadratic
model.
.. _penaltymodel: https://github.com/dwavesystems/penaltymodel
Examples:
This example creates a binary-valued constraint satisfaction problem
with two constraints, :math:`a = b` and :math:`b \\ne c`, and builds
a binary quadratic model such that
each constraint violation by a solution adds the default minimum energy gap.
>>> import operator
>>> csp = dwavebinarycsp.ConstraintSatisfactionProblem(dwavebinarycsp.BINARY)
>>> csp.add_constraint(operator.eq, ['a', 'b']) # a == b
>>> csp.add_constraint(operator.ne, ['b', 'c']) # b != c
>>> bqm = dwavebinarycsp.stitch(csp)
Variable assignments that satisfy the CSP above, violate one, then two constraints,
produce energy increases of the default minimum classical gap:
>>> bqm.energy({'a': 0, 'b': 0, 'c': 1}) # doctest: +SKIP
-2.0
>>> bqm.energy({'a': 0, 'b': 0, 'c': 0}) # doctest: +SKIP
0.0
>>> bqm.energy({'a': 1, 'b': 0, 'c': 0}) # doctest: +SKIP
2.0
This example creates a binary-valued constraint satisfaction problem
with two constraints, :math:`a = b` and :math:`b \\ne c`, and builds
a binary quadratic model with a minimum energy gap of 4.
Note that in this case the conversion to binary quadratic model adds two
ancillary variables that must be minimized over when solving.
>>> import operator
>>> import itertools
>>> csp = dwavebinarycsp.ConstraintSatisfactionProblem(dwavebinarycsp.BINARY)
>>> csp.add_constraint(operator.eq, ['a', 'b']) # a == b
>>> csp.add_constraint(operator.ne, ['b', 'c']) # b != c
>>> bqm = dwavebinarycsp.stitch(csp, min_classical_gap=4.0)
>>> list(bqm) # doctest: +SKIP
['a', 'aux1', 'aux0', 'b', 'c']
Variable assignments that satisfy the CSP above, violate one, then two constraints,
produce energy increases of the specified minimum classical gap:
>>> min([bqm.energy({'a': 0, 'b': 0, 'c': 1, 'aux0': aux0, 'aux1': aux1}) for
... aux0, aux1 in list(itertools.product([0, 1], repeat=2))]) # doctest: +SKIP
-6.0
>>> min([bqm.energy({'a': 0, 'b': 0, 'c': 0, 'aux0': aux0, 'aux1': aux1}) for
... aux0, aux1 in list(itertools.product([0, 1], repeat=2))]) # doctest: +SKIP
-2.0
>>> min([bqm.energy({'a': 1, 'b': 0, 'c': 0, 'aux0': aux0, 'aux1': aux1}) for
... aux0, aux1 in list(itertools.product([0, 1], repeat=2))]) # doctest: +SKIP
2.0
This example finds for the previous example the minimum graph size.
>>> import operator
>>> csp = dwavebinarycsp.ConstraintSatisfactionProblem(dwavebinarycsp.BINARY)
>>> csp.add_constraint(operator.eq, ['a', 'b']) # a == b
>>> csp.add_constraint(operator.ne, ['b', 'c']) # b != c
>>> for n in range(8, 1, -1):
... try:
... bqm = dwavebinarycsp.stitch(csp, min_classical_gap=4.0, max_graph_size=n)
... except dwavebinarycsp.exceptions.ImpossibleBQM:
... print(n+1)
...
3
"""
# ensure we have penaltymodel factory available
try:
dwavebinarycsp.assert_penaltymodel_factory_available()
except AssertionError as e:
raise RuntimeError(e)
def aux_factory():
for i in count():
yield 'aux{}'.format(i)
aux = aux_factory()
bqm = dimod.BinaryQuadraticModel.empty(csp.vartype)
# developer note: we could cache them and relabel, for now though let's do the simple thing
# penalty_models = {}
for const in csp.constraints:
configurations = const.configurations
if len(const.variables) > max_graph_size:
msg = (
"The given csp contains a constraint {const} with {num_var} variables. "
"This cannot be mapped to a graph with {max_graph_size} nodes. "
"Consider checking whether your constraint is irreducible."
"").format(const=const,
num_var=len(const.variables),
max_graph_size=max_graph_size)
raise ImpossibleBQM(msg)
pmodel = None
if len(const) == 0:
# empty constraint
continue
# at the moment, penaltymodel-cache cannot handle 1-variable PMs, so
# we handle that case here
if min_classical_gap <= 2.0 and len(
const) == 1 and max_graph_size >= 1:
bqm.update(_bqm_from_1sat(const))
continue
# developer note: we could cache them and relabel, for now though let's do the simple thing
# if configurations in penalty_models:
# raise NotImplementedError
for G in iter_complete_graphs(const.variables, max_graph_size + 1,
aux):
# construct a specification
spec = pm.Specification(graph=G,
decision_variables=const.variables,
feasible_configurations=configurations,
min_classical_gap=min_classical_gap,
vartype=csp.vartype)
# try to use the penaltymodel ecosystem
try:
pmodel = pm.get_penalty_model(spec)
except pm.ImpossiblePenaltyModel:
# hopefully adding more variables will make it possible
continue
if pmodel.classical_gap >= min_classical_gap:
break
# developer note: we could cache them and relabel, for now though let's do the simple thing
# penalty_models[configurations] = pmodel
else:
msg = ("No penalty model can be built for constraint {}".format(
const))
raise ImpossibleBQM(msg)
bqm.update(pmodel.model)
return bqm
def test_construction_empty(self):
spec = pm.Specification(nx.Graph(), [], {}, dimod.SPIN)
self.assertEqual(len(spec), 0)
