def _bqm_from_2sat(constraint):
"""create a bqm for a constraint with two variables.
bqm will have exactly classical gap 2.
"""
configurations = constraint.configurations
variables = constraint.variables
vartype = constraint.vartype
u, v = constraint.variables
# if all configurations are present, then nothing is infeasible and the bqm is just all
# 0.0s
if len(configurations) == 4:
return dimod.BinaryQuadraticModel.empty(constraint.vartype)
# check if the constraint is irreducible, and if so, build the bqm for its two
# components
components = irreducible_components(constraint)
if len(components) > 1:
const0 = Constraint.from_configurations(
((config[0], ) for config in configurations), (u, ), vartype)
const1 = Constraint.from_configurations(
((config[1], ) for config in configurations), (v, ), vartype)
bqm = _bqm_from_1sat(const0)
bqm.update(_bqm_from_1sat(const1))
return bqm
assert len(
configurations) > 1, "single configurations should be irreducible"
# if it is not irreducible, and there are infeasible configurations, then it is time to
# start building a bqm
bqm = dimod.BinaryQuadraticModel.empty(vartype)
# if the constraint is not irreducible and has two configurations, then it is either eq or ne
if all(operator.eq(*config) for config in configurations):
bqm.add_interaction(u, v, -1, vartype=dimod.SPIN) # equality
elif all(operator.ne(*config) for config in configurations):
bqm.add_interaction(u, v, +1, vartype=dimod.SPIN) # inequality
elif (1, 1) not in configurations:
bqm.add_interaction(u, v, 2, vartype=dimod.BINARY) # penalize (1, 1)
elif (-1, +1) not in configurations and (0, 1) not in configurations:
bqm.add_interaction(u, v, -2, vartype=dimod.BINARY)
bqm.add_variable(v, 2, vartype=dimod.BINARY)
elif (+1, -1) not in configurations and (1, 0) not in configurations:
bqm.add_interaction(u, v, -2, vartype=dimod.BINARY)
bqm.add_variable(u, 2, vartype=dimod.BINARY)
else:
# (0, 0) not in configurations
bqm.add_interaction(u, v, 2, vartype=dimod.BINARY)
bqm.add_variable(u, -2, vartype=dimod.BINARY)
bqm.add_variable(v, -2, vartype=dimod.BINARY)
return bqm
def add_constraint(self, constraint, variables=tuple()):
"""Add a constraint.
Args:
constraint (function/iterable/:obj:`.Constraint`):
Constraint definition in one of the supported formats:
1. Function, with input arguments matching the order and
:attr:`~.ConstraintSatisfactionProblem.vartype` type of the `variables`
argument, that evaluates True when the constraint is satisfied.
2. List explicitly specifying each allowed configuration as a tuple.
3. :obj:`.Constraint` object built either explicitly or by :mod:`dwavebinarycsp.factories`.
variables(iterable):
Variables associated with the constraint. Not required when `constraint` is
a :obj:`.Constraint` object.
Examples:
This example defines a function that evaluates True when the constraint is satisfied.
The function's input arguments match the order and type of the `variables` argument.
>>> csp = dwavebinarycsp.ConstraintSatisfactionProblem(dwavebinarycsp.BINARY)
>>> def all_equal(a, b, c): # works for both dwavebinarycsp.BINARY and dwavebinarycsp.SPIN
... return (a == b) and (b == c)
>>> csp.add_constraint(all_equal, ['a', 'b', 'c'])
>>> csp.check({'a': 0, 'b': 0, 'c': 0})
True
>>> csp.check({'a': 0, 'b': 0, 'c': 1})
False
This example explicitly lists allowed configurations.
>>> csp = dwavebinarycsp.ConstraintSatisfactionProblem(dwavebinarycsp.SPIN)
>>> eq_configurations = {(-1, -1), (1, 1)}
>>> csp.add_constraint(eq_configurations, ['v0', 'v1'])
>>> csp.check({'v0': -1, 'v1': +1})
False
>>> csp.check({'v0': -1, 'v1': -1})
True
This example uses a :obj:`.Constraint` object built by :mod:`dwavebinarycsp.factories`.
>>> import dwavebinarycsp.factories.constraint.gates as gates
>>> csp = dwavebinarycsp.ConstraintSatisfactionProblem(dwavebinarycsp.BINARY)
>>> csp.add_constraint(gates.and_gate(['a', 'b', 'c'])) # add an AND gate
>>> csp.add_constraint(gates.xor_gate(['a', 'c', 'd'])) # add an XOR gate
>>> csp.check({'a': 1, 'b': 0, 'c': 0, 'd': 1})
True
"""
if isinstance(constraint, Constraint):
if variables and (tuple(variables) != constraint.variables):
raise ValueError("mismatched variables and Constraint")
elif isinstance(constraint, Callable):
constraint = Constraint.from_func(constraint, variables,
self.vartype)
elif isinstance(constraint, Iterable):
constraint = Constraint.from_configurations(
constraint, variables, self.vartype)
else:
raise TypeError("Unknown constraint type given")
self.constraints.append(constraint)
for v in constraint.variables:
self.variables[v].append(constraint)