# Source code for dimod.utilities

```
# Copyright 2018 D-Wave Systems Inc.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# =============================================================================
import copy
import os
import itertools
from functools import reduce
import numpy as np
from dimod.decorators import lockable_method
__all__ = ['ising_energy',
'qubo_energy',
'ising_to_qubo',
'qubo_to_ising',
'child_structure_dfs',
'get_include',
]
[docs]def ising_energy(sample, h, J, offset=0.0):
"""Calculate the energy for the specified sample of an Ising model.
Energy of a sample for a binary quadratic model is defined as a sum, offset
by the constant energy offset associated with the model, of
the sample multipled by the linear bias of the variable and
all its interactions. For an Ising model,
.. math::
E(\mathbf{s}) = \sum_v h_v s_v + \sum_{u,v} J_{u,v} s_u s_v + c
where :math:`s_v` is the sample, :math:`h_v` is the linear bias, :math:`J_{u,v}`
the quadratic bias (interactions), and :math:`c` the energy offset.
Args:
sample (dict[variable, spin]):
Sample for a binary quadratic model as a dict of form {v: spin, ...},
where keys are variables of the model and values are spins (either -1 or 1).
h (dict[variable, bias]):
Linear biases as a dict of the form {v: bias, ...}, where keys are variables of
the model and values are biases.
J (dict[(variable, variable), bias]):
Quadratic biases as a dict of the form {(u, v): bias, ...}, where keys
are 2-tuples of variables of the model and values are quadratic biases
associated with the pair of variables (the interaction).
offset (numeric, optional, default=0):
Constant offset to be applied to the energy. Default 0.
Returns:
float: The induced energy.
Notes:
No input checking is performed.
Examples:
This example calculates the energy of a sample representing two down spins for
an Ising model of two variables that have positive biases of value 1 and
are positively coupled with an interaction of value 1.
>>> sample = {1: -1, 2: -1}
>>> h = {1: 1, 2: 1}
>>> J = {(1, 2): 1}
>>> dimod.ising_energy(sample, h, J, 0.5)
-0.5
References
----------
`Ising model on Wikipedia <https://en.wikipedia.org/wiki/Ising_model>`_
"""
# add the contribution from the linear biases
for v in h:
offset += h[v] * sample[v]
# add the contribution from the quadratic biases
for v0, v1 in J:
offset += J[(v0, v1)] * sample[v0] * sample[v1]
return offset
[docs]def qubo_energy(sample, Q, offset=0.0):
"""Calculate the energy for the specified sample of a QUBO model.
Energy of a sample for a binary quadratic model is defined as a sum, offset
by the constant energy offset associated with the model, of
the sample multipled by the linear bias of the variable and
all its interactions. For a quadratic unconstrained binary optimization (QUBO)
model,
.. math::
E(\mathbf{x}) = \sum_{u,v} Q_{u,v} x_u x_v + c
where :math:`x_v` is the sample, :math:`Q_{u,v}`
a matrix of biases, and :math:`c` the energy offset.
Args:
sample (dict[variable, spin]):
Sample for a binary quadratic model as a dict of form {v: bin, ...},
where keys are variables of the model and values are binary (either 0 or 1).
Q (dict[(variable, variable), coefficient]):
QUBO coefficients in a dict of form {(u, v): coefficient, ...}, where keys
are 2-tuples of variables of the model and values are biases
associated with the pair of variables. Tuples (u, v) represent interactions
and (v, v) linear biases.
offset (numeric, optional, default=0):
Constant offset to be applied to the energy. Default 0.
Returns:
float: The induced energy.
Notes:
No input checking is performed.
Examples:
This example calculates the energy of a sample representing two zeros for
a QUBO model of two variables that have positive biases of value 1 and
are positively coupled with an interaction of value 1.
>>> sample = {1: 0, 2: 0}
>>> Q = {(1, 1): 1, (2, 2): 1, (1, 2): 1}
>>> dimod.qubo_energy(sample, Q, 0.5)
0.5
References
----------
`QUBO model on Wikipedia <https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization>`_
"""
for v0, v1 in Q:
offset += sample[v0] * sample[v1] * Q[(v0, v1)]
return offset
[docs]def ising_to_qubo(h, J, offset=0.0):
"""Convert an Ising problem to a QUBO problem.
Map an Ising model defined on spins (variables with {-1, +1} values) to quadratic
unconstrained binary optimization (QUBO) formulation :math:`x' Q x` defined over
binary variables (0 or 1 values), where the linear term is contained along the diagonal of Q.
Return matrix Q that defines the model as well as the offset in energy between the two
problem formulations:
.. math::
s' J s + h' s = offset + x' Q x
See :meth:`~dimod.utilities.qubo_to_ising` for the inverse function.
Args:
h (dict[variable, bias]):
Linear biases as a dict of the form {v: bias, ...}, where keys are variables of
the model and values are biases.
J (dict[(variable, variable), bias]):
Quadratic biases as a dict of the form {(u, v): bias, ...}, where keys
are 2-tuples of variables of the model and values are quadratic biases
associated with the pair of variables (the interaction).
offset (numeric, optional, default=0):
Constant offset to be applied to the energy. Default 0.
Returns:
(dict, float): A 2-tuple containing:
dict: QUBO coefficients.
float: New energy offset.
Examples:
This example converts an Ising problem of two variables that have positive
biases of value 1 and are positively coupled with an interaction of value 1
to a QUBO problem and prints the resulting energy offset.
>>> h = {1: 1, 2: 1}
>>> J = {(1, 2): 1}
>>> dimod.ising_to_qubo(h, J, 0.5)[1]
-0.5
"""
# the linear biases are the easiest
q = {(v, v): 2. * bias for v, bias in h.items()}
# next the quadratic biases
for (u, v), bias in J.items():
if bias == 0.0:
continue
q[(u, v)] = 4. * bias
q[(u, u)] = q.setdefault((u, u), 0) - 2. * bias
q[(v, v)] = q.setdefault((v, v), 0) - 2. * bias
# finally calculate the offset
offset += sum(J.values()) - sum(h.values())
return q, offset
[docs]def qubo_to_ising(Q, offset=0.0):
"""Convert a QUBO problem to an Ising problem.
Map a quadratic unconstrained binary optimization (QUBO) problem :math:`x' Q x`
defined over binary variables (0 or 1 values), where the linear term is contained along
the diagonal of Q, to an Ising model defined on spins (variables with {-1, +1} values).
Return h and J that define the Ising model as well as the offset in energy
between the two problem formulations:
.. math::
x' Q x = offset + s' J s + h' s
See :meth:`~dimod.utilities.ising_to_qubo` for the inverse function.
Args:
Q (dict[(variable, variable), coefficient]):
QUBO coefficients in a dict of form {(u, v): coefficient, ...}, where keys
are 2-tuples of variables of the model and values are biases
associated with the pair of variables. Tuples (u, v) represent interactions
and (v, v) linear biases.
offset (numeric, optional, default=0):
Constant offset to be applied to the energy. Default 0.
Returns:
(dict, dict, float): A 3-tuple containing:
dict: Linear coefficients of the Ising problem.
dict: Quadratic coefficients of the Ising problem.
float: New energy offset.
Examples:
This example converts a QUBO problem of two variables that have positive
biases of value 1 and are positively coupled with an interaction of value 1
to an Ising problem, and shows the new energy offset.
>>> Q = {(1, 1): 1, (2, 2): 1, (1, 2): 1}
>>> dimod.qubo_to_ising(Q, 0.5)[2]
1.75
"""
h = {}
J = {}
linear_offset = 0.0
quadratic_offset = 0.0
for (u, v), bias in Q.items():
if u == v:
if u in h:
h[u] += .5 * bias
else:
h[u] = .5 * bias
linear_offset += bias
else:
if bias != 0.0:
J[(u, v)] = .25 * bias
if u in h:
h[u] += .25 * bias
else:
h[u] = .25 * bias
if v in h:
h[v] += .25 * bias
else:
h[v] = .25 * bias
quadratic_offset += bias
offset += .5 * linear_offset + .25 * quadratic_offset
return h, J, offset
def resolve_label_conflict(mapping, old_labels=None, new_labels=None):
"""Resolve a self-labeling conflict by creating an intermediate labeling.
Args:
mapping (dict):
A dict mapping the current variable labels to new ones.
old_labels (set, optional, default=None):
The keys of mapping. Can be passed in for performance reasons. These are not checked.
new_labels (set, optional, default=None):
The values of mapping. Can be passed in for performance reasons. These are not checked.
Returns:
tuple: A 2-tuple containing:
dict: A map from the keys of mapping to an intermediate labeling
dict: A map from the intermediate labeling to the values of mapping.
"""
if old_labels is None:
old_labels = set(mapping)
if new_labels is None:
new_labels = set(mapping.values())
# counter will be used to generate the intermediate labels, as an easy optimization
# we start the counter with a high number because often variables are labeled by
# integers starting from 0
counter = itertools.count(2 * len(mapping))
old_to_intermediate = {}
intermediate_to_new = {}
for old, new in mapping.items():
if old == new:
# we can remove self-labels
continue
if old in new_labels or new in old_labels:
# try to get a new unique label
lbl = next(counter)
while lbl in new_labels or lbl in old_labels:
lbl = next(counter)
# add it to the mapping
old_to_intermediate[old] = lbl
intermediate_to_new[lbl] = new
else:
old_to_intermediate[old] = new
# don't need to add it to intermediate_to_new because it is a self-label
return old_to_intermediate, intermediate_to_new
def iter_safe_relabels(mapping, existing):
"""Iterator over "safe" intermediate relabelings.
Args:
mapping (dict):
A map from old labels to new.
existing (set):
A container of existing labels.
Yields:
dict: A "safe" relabelling.
"""
# put the new labels into a set for fast lookup, also ensures that the
# values are valid labels
try:
new_labels = set(mapping.values())
except TypeError:
raise ValueError("mapping targets must be hashable objects")
old_labels = mapping.keys()
for v in new_labels:
if v in existing and v not in old_labels:
msg = ("A variable cannot be relabeled {!r} without also "
"relabeling the existing variable of the same name")
raise ValueError(msg.format(v))
if any(v in new_labels for v in old_labels):
yield from resolve_label_conflict(mapping, old_labels, new_labels)
else:
yield mapping
[docs]def child_structure_dfs(sampler, seen=None):
"""Return the structure of a composed sampler using a depth-first search on its
children.
Args:
sampler (:obj:`.Sampler`):
:class:`.Structured` or composed sampler with at least
one structured child.
seen (set, optional, default=False):
IDs of already checked child samplers.
Returns:
:class:`~collections.namedtuple`: A named tuple of the form
`Structure(nodelist, edgelist, adjacency)`, where the 3-tuple values
are the :attr:`.Structured.nodelist`, :attr:`.Structured.edgelist`
and :attr:`.Structured.adjacency` attributes of the first structured
sampler found.
Raises:
ValueError: If no structured sampler is found.
Examples:
>>> sampler = dimod.TrackingComposite(
... dimod.StructureComposite(
... dimod.ExactSolver(), [0, 1], [(0, 1)]))
>>> print(dimod.child_structure_dfs(sampler).nodelist)
[0, 1]
"""
seen = set() if seen is None else seen
if sampler not in seen:
try:
return sampler.structure
except AttributeError:
# hasattr just tries to access anyway...
pass
seen.add(sampler)
for child in getattr(sampler, 'children', ()): # getattr handles samplers
if child in seen:
continue
try:
return child_structure_dfs(child, seen=seen)
except ValueError:
# tree has no child samplers
pass
raise ValueError("no structured sampler found")
class LockableDict(dict):
"""A dict that can turn writeablity on and off"""
# methods like update, clear etc are not wrappers for __setitem__,
# __delitem__ so they need to be overwritten
@property
def is_writeable(self):
return getattr(self, '_writeable', True)
@is_writeable.setter
def is_writeable(self, b):
self._writeable = bool(b)
@lockable_method
def __setitem__(self, key, value):
return super(LockableDict, self).__setitem__(key, value)
@lockable_method
def __delitem__(self, key):
return super(LockableDict, self).__delitem__(key)
def __deepcopy__(self, memo):
new = type(self)()
memo[id(self)] = new
new.update((copy.deepcopy(key, memo), copy.deepcopy(value, memo))
for key, value in self.items())
new.is_writeable = self.is_writeable
return new
@lockable_method
def clear(self):
return super(LockableDict, self).clear()
@lockable_method
def pop(self, *args, **kwargs):
return super(LockableDict, self).pop(*args, **kwargs)
@lockable_method
def popitem(self):
return super(LockableDict, self).popitem()
@lockable_method
def setdefault(self, *args, **kwargs):
return super(LockableDict, self).setdefault(*args, **kwargs)
@lockable_method
def update(self, *args, **kwargs):
return super(LockableDict, self).update(*args, **kwargs)
def get_include():
"""Return the directory with dimod's header files."""
return os.path.join(os.path.dirname(__file__), 'include')
def _astypearrays(arrays, requirements, min_itemsize, allowed_types):
# allowed types can only be numeric for now, see comment below
# todo: allow unsafe with warning controlled by kwarg?
# We need to get the dtype, and as far as I can tell the only way to do
# it for array-like is to actually cast to a numpy array
arrays = [np.asarray(arr) for arr in arrays]
# get the dtype we can promote to
dtype = reduce(np.promote_types, (arr.dtype for arr in arrays))
if not any(np.issubdtype(dtype, type_) for type_ in allowed_types):
# put together an appropriate error message
descriptors = []
if np.floating in allowed_types:
descriptors.append('floating')
if np.integer in allowed_types:
descriptors.append('integer')
elif np.unsignedinteger in allowed_types:
if np.signedinteger in allowed_types:
descriptors.append('integer')
else:
descriptors.append('unsigned integer')
elif np.signedinteger in allowed_types:
descriptors.append('signed integer')
raise TypeError(
"Cannot safely cast arrays to {} (given {})".format(
', '.join(descriptors),
', '.join(arr.dtype.name for arr in arrays)))
if min_itemsize is not None:
if min_itemsize >= 1:
size = str(2**int(np.ceil(np.log2(min_itemsize))))
else:
size = '1'
if np.issubdtype(dtype, np.unsignedinteger):
kind = 'u'
elif np.issubdtype(dtype, np.signedinteger):
kind = 'i'
elif np.issubdtype(dtype, np.floating):
kind = 'f'
else:
# we could instead read this from the type string, but it's kind of
# pandora's box, because there's also structured arrays, complex,
# etc. For now, let's just restrict to numeric.
raise RuntimeError("unexpected dtype")
dtype = np.promote_types(dtype, kind+size)
arrays = tuple(np.require(arr, dtype=dtype, requirements=requirements)
for arr in arrays)
if len(arrays) > 1:
return arrays
else:
return arrays[0]
# Not a public function (yet)
def asintegerarrays(*arrays, requirements=None, min_itemsize=None):
"""Cast the given array(s) to the same integer type.
Not a public function.
This is useful when calling cython functions.
Args:
*arrays (array-like): At least one array-like.
requirements (str/list[str], optional): See :func:`numpy.require`.
min_itemsize (int, optional):
The minimum itemsize (in bytes) for the output arrays.
Returns:
Numpy array(s) satisfying the above requirements. They will all have
the same dtype.
"""
# empty arrays are a problem because numy defaults them to float, so let's
# do a tiny bit of prechecking
arrays = [arr if len(arr) else np.asarray(arr, dtype=np.int8)
for arr in arrays]
if not arrays:
raise TypeError('asintegerarrays() takes at least 1 array (0 given)')
return _astypearrays(arrays, requirements, min_itemsize, [np.integer])
# Not a public function (yet)
def asnumericarrays(*arrays, requirements=None, min_itemsize=None):
"""Cast the given array(s) to the same floating type.
Not a public function.
This is useful when calling cython functions.
Args:
*arrays (array-like): At least one array-like.
requirements (str/list[str], optional): See :func:`numpy.require`.
min_itemsize (int, optional):
The minimum itemsize (in bytes) for the output arrays.
Returns:
Numpy array(s) satisfying the above requirements. They will all have
the same dtype.
"""
if not arrays:
raise TypeError('asnumericarrays() takes at least 1 array (0 given)')
return _astypearrays(arrays, requirements, min_itemsize,
[np.integer, np.floating])
```