# Copyright 2018 Recruit Communications Co., Ltd.
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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# http://www.apache.org/licenses/LICENSE-2.0
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from pyqubo import Array, SubH, Constraint
from pyqubo.integer.integer import IntegerWithPenalty
from pyqubo import WithPenalty, Placeholder
[docs]class OneHotEncInteger(IntegerWithPenalty):
"""One-hot encoded integer. The value that takes :math:`[1, n]` is represented by :math:`\sum_{i=1}^{n}ix_{i}`.
Also we have the penalty function :math:`strength \\times (\sum_{i=1}^{n}x_{i}-1)^2` in the Hamiltonian.
Args:
label (str): Label of the integer.
lower (int): Lower value of the integer.
upper (int): Upper value of the integer.
strength (float/Placeholder): Strength of the constraint.
Examples:
This example is equivalent to the following Hamiltonian.
.. math::
H = \\left(\\left(\sum_{i=1}^{3}ia_{i}+1\\right) - 2\\right)^2 + strength \\times \\left(\sum_{i=1}^{3}a_{i}-1\\right)^2
>>> from pyqubo import OneHotEncInteger
>>> a = OneHotEncInteger("a", (1, 3), strength=5)
>>> H = (a-2)**2
>>> model = H.compile()
>>> bqm = model.to_bqm()
>>> import dimod
>>> sampleset = dimod.ExactSolver().sample(bqm)
>>> decoded_samples = model.decode_sampleset(sampleset)
>>> best_sample = min(decoded_samples, key=lambda s: s.energy)
>>> print(best_sample.subh['a'])
2.0
"""
def __init__(self, label, value_range, strength):
lower, upper = value_range
assert upper > lower, "upper value should be larger than lower value"
assert isinstance(lower, int)
assert isinstance(upper, int)
assert isinstance(strength, int) or isinstance(strength, float) or\
isinstance(strength, Placeholder)
self._num_variables = (upper - lower + 1)
self.array = Array.create(label, shape=self._num_variables, vartype='BINARY')
self.constraint = Constraint((sum(self.array)-1)**2, label=label+"_const", condition=lambda x: x==0)
express = SubH(lower + sum(i*x for i, x in enumerate(self.array)), label=label)
penalty = self.constraint * strength
super().__init__(
label=label,
value_range=value_range,
express=express,
penalty=penalty)
[docs] def equal_to(self, k):
"""Variable representing whether the value is equal to `k`.
Note:
You cannot use this method alone. You should use this variable with the entire integer.
Args:
k (int): Integer value.
Returns:
:class:`Express`
"""
lower, upper = self.value_range
assert isinstance(k, int), "k should be integer"
assert lower <= k <= upper, "This value never takes {}".format(k)
return self.array[k-lower]