def make_random(cls, pspace=None, division=None, zero=True,
number_type='float'):
"""Generate a random coherent lower probability."""
# for now this is just a pretty dumb method
pspace = PSpace.make(pspace)
lpr = cls(pspace=pspace, number_type=number_type)
for event in pspace.subsets():
if len(event) == 0:
continue
if len(event) == len(pspace):
continue
gamble = event.indicator(number_type=number_type)
if division is None:
# a number between 0 and len(event) / len(pspace)
lprob = random.random() * len(event) / len(pspace)
else:
# a number between 0 and len(event) / len(pspace)
# but discretized
lprob = Fraction(
random.randint(
0 if zero else 1,
(division * len(event)) // len(pspace)),
division)
# make a copy of lpr
tmplpr = cls(pspace=pspace, mapping=lpr, number_type=number_type)
# set new assignment, and give up if it incurs sure loss
tmplpr.set_lower(gamble, lprob)
if not tmplpr.is_avoiding_sure_loss():
break
else:
lpr.set_lower(gamble, lprob)
# done! return coherent version of it
return lpr.get_coherent()
def __init__(self, pspace, data=None):
self._data = OrderedDict()
self._pspace = PSpace.make(pspace)
# extract data
if isinstance(data, collections.Mapping):
for key, value in data.iteritems():
self[key] = value
elif data is not None:
raise TypeError('data must be a mapping')
def __init__(self, pspace, data=None):
self._data = OrderedDict()
self._pspace = PSpace.make(pspace)
# extract data
if isinstance(data, collections.Mapping):
for key, value in data.iteritems():
self[key] = value
elif data is not None:
raise TypeError('data must be a mapping')
def make_random(cls,
pspace=None,
division=None,
zero=True,
number_type='float'):
"""Generate a random probability mass function.
:param pspace: The possibility space.
:type pspace: |pspacetype|
:param division: If specified, probabilities
will be divisible by this factor.
:type division: :class:`int`
:param zero: Whether to allow for zero probability.
:type zero: :class:`bool`
:param number_type: The number type.
:type number_type: :class:`str`
>>> import random
>>> random.seed(25)
>>> print(Prob.make_random("abcd", division=10))
a : 0.4
b : 0.0
c : 0.1
d : 0.5
>>> random.seed(25)
>>> print(Prob.make_random("abcd", division=10, zero=False))
a : 0.3
b : 0.1
c : 0.2
d : 0.4
"""
pspace = PSpace.make(pspace)
lpr = cls(pspace=pspace, number_type=number_type)
# get a uniform sample from the simplex
probs = [-math.log(random.random()) for omega in pspace]
sum_probs = sum(probs)
probs = [prob / sum_probs for prob in probs]
if division is not None:
# discretize the probabilities
probs = [
int(prob * division + 0.5) + (0 if zero else 1)
for prob in probs
]
# now, again ensure they sum to division
while sum(probs) < division:
probs[random.randrange(len(probs))] += 1
while sum(probs) > division:
while True:
idx = random.randrange(len(probs))
if probs[idx] > (1 if zero else 2):
probs[idx] -= 1
break
# convert to fraction
probs = [fractions.Fraction(prob, division) for prob in probs]
# return the probability
return cls(pspace=pspace, number_type=number_type, prob=probs)
def make_random(cls, pspace=None, division=None, zero=True,
number_type='float'):
"""Generate a random probability mass function.
:param pspace: The possibility space.
:type pspace: |pspacetype|
:param division: If specified, probabilities
will be divisible by this factor.
:type division: :class:`int`
:param zero: Whether to allow for zero probability.
:type zero: :class:`bool`
:param number_type: The number type.
:type number_type: :class:`str`
>>> import random
>>> random.seed(25)
>>> print(Prob.make_random("abcd", division=10))
a : 0.4
b : 0.0
c : 0.1
d : 0.5
>>> random.seed(25)
>>> print(Prob.make_random("abcd", division=10, zero=False))
a : 0.3
b : 0.1
c : 0.2
d : 0.4
"""
pspace = PSpace.make(pspace)
lpr = cls(pspace=pspace, number_type=number_type)
# get a uniform sample from the simplex
probs = [-math.log(random.random()) for omega in pspace]
sum_probs = sum(probs)
probs = [prob / sum_probs for prob in probs]
if division is not None:
# discretize the probabilities
probs = [int(prob * division + 0.5) + (0 if zero else 1)
for prob in probs]
# now, again ensure they sum to division
while sum(probs) < division:
probs[random.randrange(len(probs))] += 1
while sum(probs) > division:
while True:
idx = random.randrange(len(probs))
if probs[idx] > (1 if zero else 2):
probs[idx] -= 1
break
# convert to fraction
probs = [fractions.Fraction(prob, division) for prob in probs]
# return the probability
return cls(pspace=pspace, number_type=number_type, prob=probs)
def make_random(cls,
pspace=None,
division=None,
zero=True,
number_type='float'):
"""Generate a random coherent lower probability.
:param pspace: The possibility space.
:type pspace: |pspacetype|
:param division: If specified, generated numbers
will be divisible by this factor.
:type division: :class:`int`
:param zero: Whether to allow for zero probability.
:type zero: :class:`bool`
:param number_type: The number type.
:type number_type: :class:`str`
.. todo::
Current implementation is highly inefficient. Refactor to use
:meth:`improb.lowprev.lowpoly.LowPoly.make_random` instead.
"""
# for now this is just a pretty dumb method
pspace = PSpace.make(pspace)
lpr = cls(pspace=pspace, number_type=number_type)
for event in pspace.subsets():
if len(event) == 0:
continue
if len(event) == len(pspace):
continue
gamble = event.indicator(number_type=number_type)
if division is None:
# a number between 0 and len(event) / len(pspace)
lprob = random.random() * len(event) / len(pspace)
else:
# a number between 0 and len(event) / len(pspace)
# but discretized
lprob = Fraction(
random.randint(0 if zero else 1,
(division * len(event)) // len(pspace)),
division)
# make a copy of lpr
tmplpr = cls(pspace=pspace, mapping=lpr, number_type=number_type)
# set new assignment, and give up if it incurs sure loss
tmplpr.set_lower(gamble, lprob)
if not tmplpr.is_avoiding_sure_loss():
break
else:
lpr.set_lower(gamble, lprob)
# done! return coherent version of it
return lpr.get_coherent()
def make_random(cls, pspace=None, division=None, zero=True,
number_type='float'):
"""Generate a random coherent lower probability.
:param pspace: The possibility space.
:type pspace: |pspacetype|
:param division: If specified, generated numbers
will be divisible by this factor.
:type division: :class:`int`
:param zero: Whether to allow for zero probability.
:type zero: :class:`bool`
:param number_type: The number type.
:type number_type: :class:`str`
.. todo::
Current implementation is highly inefficient. Refactor to use
:meth:`improb.lowprev.lowpoly.LowPoly.make_random` instead.
"""
# for now this is just a pretty dumb method
pspace = PSpace.make(pspace)
lpr = cls(pspace=pspace, number_type=number_type)
for event in pspace.subsets():
if len(event) == 0:
continue
if len(event) == len(pspace):
continue
gamble = event.indicator(number_type=number_type)
if division is None:
# a number between 0 and len(event) / len(pspace)
lprob = random.random() * len(event) / len(pspace)
else:
# a number between 0 and len(event) / len(pspace)
# but discretized
lprob = Fraction(
random.randint(
0 if zero else 1,
(division * len(event)) // len(pspace)),
division)
# make a copy of lpr
tmplpr = cls(pspace=pspace, mapping=lpr, number_type=number_type)
# set new assignment, and give up if it incurs sure loss
tmplpr.set_lower(gamble, lprob)
if not tmplpr.is_avoiding_sure_loss():
break
else:
lpr.set_lower(gamble, lprob)
# done! return coherent version of it
return lpr.get_coherent()
def timeit(n=10, m=10):
k = 10000 // n # number of trials, for timing
gambles = [
dict((i, random.randint(1, m))
for i in xrange(n))
for j in xrange(k)]
pspace = PSpace(n)
s = SetFunction(
pspace=pspace,
number_type='fraction')
# hack so we do not need to fill the set function with data
# (this solves issues when testing for large n)
s._data = defaultdict(lambda: random.randint(-len(pspace), len(pspace)))
t = time.clock()
for gamble in gambles:
s.get_choquet(gamble)
return time.clock() - t
def make_random(cls, pspace=None, division=None, zero=True,
number_type='float'):
"""Generate a random probability mass function.
>>> import random
>>> random.seed(25)
>>> print(Prob.make_random("abcd", division=10))
a : 0.4
b : 0.0
c : 0.1
d : 0.5
>>> random.seed(25)
>>> print(Prob.make_random("abcd", division=10, zero=False))
a : 0.3
b : 0.1
c : 0.2
d : 0.4
"""
pspace = PSpace.make(pspace)
lpr = cls(pspace=pspace, number_type=number_type)
# get a uniform sample from the simplex
probs = [-math.log(random.random()) for omega in pspace]
sum_probs = sum(probs)
probs = [prob / sum_probs for prob in probs]
if division is not None:
# discretize the probabilities
probs = [int(prob * division + 0.5) + (0 if zero else 1)
for prob in probs]
# now, again ensure they sum to division
while sum(probs) < division:
probs[random.randrange(len(probs))] += 1
while sum(probs) > division:
while True:
idx = random.randrange(len(probs))
if probs[idx] > (1 if zero else 2):
probs[idx] -= 1
break
# convert to fraction
probs = [fractions.Fraction(prob, division) for prob in probs]
# return the probability
return cls(pspace=pspace, number_type=number_type, prob=probs)
def __init__(self, pspace, data=None, number_type=None):
"""Construct a set function on the power set of the given
possibility space.
:param pspace: The possibility space.
:type pspace: |pspacetype|
:param data: A mapping that defines the value on each event (missing values default to zero).
:type data: :class:`dict`
"""
if number_type is None:
if data is not None:
number_type = cdd.get_number_type_from_sequences(
data.itervalues())
else:
number_type = 'float'
cdd.NumberTypeable.__init__(self, number_type)
self._pspace = PSpace.make(pspace)
self._data = {}
if data is not None:
for event, value in data.iteritems():
self[event] = value
def __init__(self, pspace, data=None, number_type=None):
"""Construct a set function on the power set of the given
possibility space.
:param pspace: The possibility space.
:type pspace: |pspacetype|
:param data: A mapping that defines the value on each event (missing values default to zero).
:type data: :class:`dict`
"""
if number_type is None:
if data is not None:
number_type = cdd.get_number_type_from_sequences(
data.itervalues())
else:
number_type = 'float'
cdd.NumberTypeable.__init__(self, number_type)
self._pspace = PSpace.make(pspace)
self._data = {}
if data is not None:
for event, value in data.iteritems():
self[event] = value
def make_extreme_n_monotone(cls, pspace, monotonicity=None):
"""Yield extreme lower probabilities with given monotonicity.
.. warning::
Currently this doesn't work very well except for the cases
below.
>>> lprs = list(LowProb.make_extreme_n_monotone('abc', monotonicity=2))
>>> len(lprs)
8
>>> all(lpr.is_coherent() for lpr in lprs)
True
>>> all(lpr.is_n_monotone(2) for lpr in lprs)
True
>>> all(lpr.is_n_monotone(3) for lpr in lprs)
False
>>> lprs = list(LowProb.make_extreme_n_monotone('abc', monotonicity=3))
>>> len(lprs)
7
>>> all(lpr.is_coherent() for lpr in lprs)
True
>>> all(lpr.is_n_monotone(2) for lpr in lprs)
True
>>> all(lpr.is_n_monotone(3) for lpr in lprs)
True
>>> lprs = list(LowProb.make_extreme_n_monotone('abcd', monotonicity=2))
>>> len(lprs)
41
>>> all(lpr.is_coherent() for lpr in lprs)
True
>>> all(lpr.is_n_monotone(2) for lpr in lprs)
True
>>> all(lpr.is_n_monotone(3) for lpr in lprs)
False
>>> all(lpr.is_n_monotone(4) for lpr in lprs)
False
>>> lprs = list(LowProb.make_extreme_n_monotone('abcd', monotonicity=3))
>>> len(lprs)
16
>>> all(lpr.is_coherent() for lpr in lprs)
True
>>> all(lpr.is_n_monotone(2) for lpr in lprs)
True
>>> all(lpr.is_n_monotone(3) for lpr in lprs)
True
>>> all(lpr.is_n_monotone(4) for lpr in lprs)
False
>>> lprs = list(LowProb.make_extreme_n_monotone('abcd', monotonicity=4))
>>> len(lprs)
15
>>> all(lpr.is_coherent() for lpr in lprs)
True
>>> all(lpr.is_n_monotone(2) for lpr in lprs)
True
>>> all(lpr.is_n_monotone(3) for lpr in lprs)
True
>>> all(lpr.is_n_monotone(4) for lpr in lprs)
True
>>> # cddlib hangs on larger possibility spaces
>>> #lprs = list(LowProb.make_extreme_n_monotone('abcde', monotonicity=2))
"""
pspace = PSpace.make(pspace)
# constraint for empty set and full set
matrix = cdd.Matrix(
[[0] + [1 if event.is_false() else 0 for event in pspace.subsets()],
[-1] + [1 if event.is_true() else 0 for event in pspace.subsets()]],
linear=True,
number_type='fraction')
# constraints for monotonicity
constraints = [
dict(constraint) for constraint in
cls.get_constraints_n_monotone(pspace, xrange(1, monotonicity + 1))]
matrix.extend([[0] + [constraint.get(event, 0)
for event in pspace.subsets()]
for constraint in constraints])
matrix.rep_type = cdd.RepType.INEQUALITY
# debug: simplify matrix
#print(pspace, monotonicity) # debug
#print("original:", len(matrix))
#matrix.canonicalize()
#print("new :", len(matrix))
#print(matrix) # debug
# calculate extreme points
poly = cdd.Polyhedron(matrix)
# convert these points back to lower probabilities
#print(poly.get_generators()) # debug
for vert in poly.get_generators():
yield cls(
pspace=pspace,
lprob=dict((event, vert[1 + index])
for index, event in enumerate(pspace.subsets())),
number_type='fraction')
def get_constraints_n_monotone(cls, pspace, monotonicity=None):
"""Yields constraints for lower probabilities with given
monotonicity.
:param pspace: The possibility space.
:type pspace: |pspacetype|
:param monotonicity: Requested level of monotonicity (see
notes below for details).
:type monotonicity: :class:`int` or
:class:`collections.Iterable` of :class:`int`
As described in
:meth:`~improb.setfunction.SetFunction.get_constraints_bba_n_monotone`,
the n-monotonicity constraints on basic belief assignment are:
.. math::
\sum_{B\colon C\subseteq B\subseteq A}m(B)\ge 0
for all :math:`C\subseteq A\subseteq\Omega`, with
:math:`1\le|C|\le n`.
By the Mobius transform, this is equivalent to:
.. math::
\sum_{B\colon C\subseteq B\subseteq A}
\sum_{D\colon D\subseteq B}(-1)^{|B\setminus D|}
\underline{P}(D)\ge 0
Once noted that
.. math::
(C\subseteq B\subseteq A\quad \& \quad D\subseteq B)
\iff
(C\cup D\subseteq B\subseteq A\quad \& \quad D\subseteq A),
we can conveniently rewrite the sum as:
.. math::
\sum_{D\colon D\subseteq A}
\sum_{B\colon C\cup D\subseteq B\subseteq A}(-1)^{|B\setminus D|}
\underline{P}(D)\ge 0
This implementation iterates over all :math:`C\subseteq
A\subseteq\Omega`, with :math:`|C|=n`, and yields each
constraint as an iterable of (event, coefficient) pairs, where
zero coefficients are omitted.
.. note::
As just mentioned, this method returns the constraints
corresponding to the latter equation for :math:`|C|`
equal to *monotonicity*. To get all the
constraints for n-monotonicity, call this method with
*monotonicity=xrange(1, n + 1)*.
The rationale for this approach is that, in case you
already know that (n-1)-monotonicity is satisfied, then
you only need the constraints for *monotonicity=n* to
check for n-monotonicity.
.. note::
The trivial constraints that the empty set must have lower
probability zero, and that the possibility space must have
lower probability one, are not included: so for
*monotonicity=0* this method returns an empty iterator.
>>> pspace = PSpace("abc")
>>> for mono in xrange(1, len(pspace) + 1):
... print("{0} monotonicity:".format(mono))
... print(" ".join("{0:<{1}}".format("".join(i for i in event), len(pspace))
... for event in pspace.subsets()))
... constraints = [
... dict(constraint) for constraint in
... LowProb.get_constraints_n_monotone(pspace, mono)]
... constraints = [
... [constraint.get(event, 0) for event in pspace.subsets()]
... for constraint in constraints]
... for constraint in sorted(constraints):
... print(" ".join("{0:<{1}}".format(value, len(pspace))
... for value in constraint))
1 monotonicity:
a b c ab ac bc abc
-1 0 0 1 0 0 0 0
-1 0 1 0 0 0 0 0
-1 1 0 0 0 0 0 0
0 -1 0 0 0 1 0 0
0 -1 0 0 1 0 0 0
0 0 -1 0 0 0 1 0
0 0 -1 0 1 0 0 0
0 0 0 -1 0 0 1 0
0 0 0 -1 0 1 0 0
0 0 0 0 -1 0 0 1
0 0 0 0 0 -1 0 1
0 0 0 0 0 0 -1 1
2 monotonicity:
a b c ab ac bc abc
0 0 0 1 0 -1 -1 1
0 0 1 0 -1 0 -1 1
0 1 0 0 -1 -1 0 1
1 -1 -1 0 1 0 0 0
1 -1 0 -1 0 1 0 0
1 0 -1 -1 0 0 1 0
3 monotonicity:
a b c ab ac bc abc
-1 1 1 1 -1 -1 -1 1
"""
pspace = PSpace.make(pspace)
# check type
if monotonicity is None:
raise ValueError("specify monotonicity")
elif isinstance(monotonicity, collections.Iterable):
# special case: return it for all values in the iterable
for mono in monotonicity:
for constraint in cls.get_constraints_n_monotone(pspace, mono):
yield constraint
return
elif not isinstance(monotonicity, (int, long)):
raise TypeError("monotonicity must be integer")
# check value
if monotonicity < 0:
raise ValueError("specify a non-negative monotonicity")
if monotonicity == 0:
# don't return constraints in this case
return
# yield all constraints
for event_a in pspace.subsets(size=xrange(monotonicity, len(pspace) + 1)):
for subevent_c in pspace.subsets(event_a, size=monotonicity):
yield (
(subevent_d,
sum((-1) ** len(event_b - subevent_d)
for event_b in pspace.subsets(
event_a, contains=(subevent_d | subevent_c))))
for subevent_d in pspace.subsets(event_a))
def __init__(self, pspace=None, mapping=None,
lprev=None, uprev=None, prev=None,
lprob=None, uprob=None, prob=None,
bba=None, credalset=None, number_type=None):
"""Construct a polyhedral lower prevision on *pspace*.
:param pspace: The possibility space.
:type pspace: |pspacetype|
:param mapping: Mapping from (gamble, event) to (lower prevision, upper prevision).
:type mapping: :class:`collections.Mapping`
:param lprev: Mapping from gamble to lower prevision.
:type lprev: :class:`collections.Mapping`
:param uprev: Mapping from gamble to upper prevision.
:type uprev: :class:`collections.Mapping`
:param prev: Mapping from gamble to precise prevision.
:type prev: :class:`collections.Mapping`
:param lprob: Mapping from event to lower probability.
:type lprob: :class:`collections.Mapping` or :class:`collections.Sequence`
:param uprob: Mapping from event to upper probability.
:type uprob: :class:`collections.Mapping` or :class:`collections.Sequence`
:param prob: Mapping from event to precise probability.
:type prob: :class:`collections.Mapping` or :class:`collections.Sequence`
:param bba: Mapping from event to basic belief assignment (useful for constructing belief functions).
:type bba: :class:`collections.Mapping`
:param credalset: Sequence of probability mass functions.
:type credalset: :class:`collections.Sequence`
:param number_type: The number type. If not specified, it is
determined using
:func:`~cdd.get_number_type_from_sequences` on all
values.
:type number_type: :class:`str`
Generally, you can pass a :class:`dict` as a keyword argument
in order to initialize the lower and upper previsions and/or
probabilities:
>>> print(LowPoly(pspace=3, mapping={
... ((3, 1, 2), True): (1.5, None),
... ((1, 0, -1), (1, 2)): (0.25, 0.3)})) # doctest: +NORMALIZE_WHITESPACE
0 1 2
3.0 1.0 2.0 | 0 1 2 : [1.5 , ]
1.0 0.0 -1.0 | 1 2 : [0.25, 0.3 ]
>>> print(LowPoly(pspace=3,
... lprev={(1, 3, 2): 1.5, (2, 0, -1): 1},
... uprev={(2, 0, -1): 1.9},
... prev={(9, 8, 20): 15},
... lprob={(1, 2): 0.2, (1,): 0.1},
... uprob={(1, 2): 0.3, (0,): 0.9},
... prob={(2,): '0.3'})) # doctest: +NORMALIZE_WHITESPACE
0 1 2
0.0 0.0 1.0 | 0 1 2 : [0.3 , 0.3 ]
0.0 1.0 0.0 | 0 1 2 : [0.1 , ]
0.0 1.0 1.0 | 0 1 2 : [0.2 , 0.3 ]
1.0 0.0 0.0 | 0 1 2 : [ , 0.9 ]
1.0 3.0 2.0 | 0 1 2 : [1.5 , ]
2.0 0.0 -1.0 | 0 1 2 : [1.0 , 1.9 ]
9.0 8.0 20.0 | 0 1 2 : [15.0, 15.0]
A credal set can be specified simply as a list:
>>> print(LowPoly(pspace=3,
... credalset=[['0.1', '0.45', '0.45'],
... ['0.4', '0.3', '0.3'],
... ['0.3', '0.2', '0.5']]))
0 1 2
-10 10 0 | 0 1 2 : [-1, ]
-1 -2 0 | 0 1 2 : [-1, ]
1 1 1 | 0 1 2 : [1 , 1 ]
50/23 40/23 0 | 0 1 2 : [1 , ]
As a special case, for lower/upper/precise probabilities, if
you need to set values on singletons, you can use a list
instead of a dictionary:
>>> print(LowPoly(pspace='abc', lprob=['0.1', '0.2', '0.3'])) # doctest: +NORMALIZE_WHITESPACE
a b c
0 0 1 | a b c : [3/10, ]
0 1 0 | a b c : [1/5 , ]
1 0 0 | a b c : [1/10, ]
If the first argument is a :class:`LowPoly` instance, then it
is copied. For example:
>>> from improb.lowprev.lowprob import LowProb
>>> lpr = LowPoly(pspace='abc', lprob=['0.1', '0.1', '0.1'])
>>> print(lpr)
a b c
0 0 1 | a b c : [1/10, ]
0 1 0 | a b c : [1/10, ]
1 0 0 | a b c : [1/10, ]
>>> lprob = LowProb(lpr)
>>> print(lprob)
a : 1/10
b : 1/10
c : 1/10
"""
def iter_items(obj):
"""Return an iterator over all items of the mapping or the
sequence.
"""
if isinstance(obj, collections.Mapping):
return obj.iteritems()
elif isinstance(obj, collections.Sequence):
if len(obj) < len(self.pspace):
raise ValueError('sequence too short')
return (((omega,), value)
for omega, value in itertools.izip(self.pspace, obj))
else:
raise TypeError(
'expected collections.Mapping or collections.Sequence')
def get_number_type(xprevs, xprobs):
"""Determine number type from arguments."""
# special case: nothing specified, defaults to float
if (all(xprev is None for xprev in xprevs)
and all(xprob is None for xprob in xprobs)):
return 'float'
# inspect all values
for xprev in xprevs:
if xprev is None:
continue
for key, value in xprev.iteritems():
# inspect gamble
if isinstance(key, Gamble):
if key.number_type == 'float':
return 'float'
elif isinstance(key, collections.Sequence):
if cdd.get_number_type_from_sequences(key) == 'float':
return 'float'
elif isinstance(key, collections.Mapping):
if cdd.get_number_type_from_sequences(key.itervalues()) == 'float':
return 'float'
# inspect value(s)
if isinstance(value, collections.Sequence):
if cdd.get_number_type_from_sequences(value) == 'float':
return 'float'
else:
if cdd.get_number_type_from_value(value) == 'float':
return 'float'
for xprob in xprobs:
if xprob is None:
continue
for key, value in iter_items(xprob):
if cdd.get_number_type_from_value(value) == 'float':
return 'float'
# everything is fraction
return 'fraction'
# if first argument is a LowPoly, then override all other arguments
if isinstance(pspace, LowPoly):
mapping = dict(pspace.iteritems())
number_type = pspace.number_type
pspace = pspace.pspace
# initialize everything
self._pspace = PSpace.make(pspace)
if number_type is None:
number_type = get_number_type(
[mapping, lprev, uprev, prev, bba],
[lprob, uprob, prob]
+ (credalset if credalset else []))
cdd.NumberTypeable.__init__(self, number_type)
self._mapping = {}
if mapping:
for key, value in mapping.iteritems():
self[key] = value
if lprev:
for gamble, value in lprev.iteritems():
self.set_lower(gamble, value)
if uprev:
for gamble, value in uprev.iteritems():
self.set_upper(gamble, value)
if prev:
for gamble, value in prev.iteritems():
self.set_precise(gamble, value)
if lprob:
for event, value in iter_items(lprob):
event = self.pspace.make_event(event)
self.set_lower(event, value)
if uprob:
for event, value in iter_items(uprob):
event = self.pspace.make_event(event)
self.set_upper(event, value)
if prob:
for event, value in iter_items(prob):
event = self.pspace.make_event(event)
self.set_precise(event, value)
if bba:
setfunc = SetFunction(
pspace=self.pspace,
data=bba,
number_type=self.number_type)
for event in self.pspace.subsets():
self.set_lower(event, setfunc.get_zeta(event))
if credalset:
# set up polyhedral representation
mat = cdd.Matrix([(['1'] + credalprob) for credalprob in credalset])
mat.rep_type = cdd.RepType.GENERATOR
poly = cdd.Polyhedron(mat)
dualmat = poly.get_inequalities()
#print(mat)
#print(dualmat)
for rownum, row in enumerate(dualmat):
if rownum in dualmat.lin_set:
self.set_precise(row[1:], -row[0])
else:
self.set_lower(row[1:], -row[0])
def make_extreme_n_monotone(cls, pspace, monotonicity=None):
"""Yield extreme lower probabilities with given monotonicity.
.. warning::
Currently this doesn't work very well except for the cases
below.
>>> lprs = list(LowProb.make_extreme_n_monotone('abc', monotonicity=2))
>>> len(lprs)
8
>>> all(lpr.is_coherent() for lpr in lprs)
True
>>> all(lpr.is_n_monotone(2) for lpr in lprs)
True
>>> all(lpr.is_n_monotone(3) for lpr in lprs)
False
>>> lprs = list(LowProb.make_extreme_n_monotone('abc', monotonicity=3))
>>> len(lprs)
7
>>> all(lpr.is_coherent() for lpr in lprs)
True
>>> all(lpr.is_n_monotone(2) for lpr in lprs)
True
>>> all(lpr.is_n_monotone(3) for lpr in lprs)
True
>>> lprs = list(LowProb.make_extreme_n_monotone('abcd', monotonicity=2))
>>> len(lprs)
41
>>> all(lpr.is_coherent() for lpr in lprs)
True
>>> all(lpr.is_n_monotone(2) for lpr in lprs)
True
>>> all(lpr.is_n_monotone(3) for lpr in lprs)
False
>>> all(lpr.is_n_monotone(4) for lpr in lprs)
False
>>> lprs = list(LowProb.make_extreme_n_monotone('abcd', monotonicity=3))
>>> len(lprs)
16
>>> all(lpr.is_coherent() for lpr in lprs)
True
>>> all(lpr.is_n_monotone(2) for lpr in lprs)
True
>>> all(lpr.is_n_monotone(3) for lpr in lprs)
True
>>> all(lpr.is_n_monotone(4) for lpr in lprs)
False
>>> lprs = list(LowProb.make_extreme_n_monotone('abcd', monotonicity=4))
>>> len(lprs)
15
>>> all(lpr.is_coherent() for lpr in lprs)
True
>>> all(lpr.is_n_monotone(2) for lpr in lprs)
True
>>> all(lpr.is_n_monotone(3) for lpr in lprs)
True
>>> all(lpr.is_n_monotone(4) for lpr in lprs)
True
>>> # cddlib hangs on larger possibility spaces
>>> #lprs = list(LowProb.make_extreme_n_monotone('abcde', monotonicity=2))
"""
pspace = PSpace.make(pspace)
# constraint for empty set and full set
matrix = cdd.Matrix([
[0] + [1 if event.is_false() else 0 for event in pspace.subsets()],
[-1] + [1 if event.is_true() else 0 for event in pspace.subsets()]
],
linear=True,
number_type='fraction')
# constraints for monotonicity
constraints = [
dict(constraint) for constraint in cls.get_constraints_n_monotone(
pspace, xrange(1, monotonicity + 1))
]
matrix.extend(
[[0] + [constraint.get(event, 0) for event in pspace.subsets()]
for constraint in constraints])
matrix.rep_type = cdd.RepType.INEQUALITY
# debug: simplify matrix
#print(pspace, monotonicity) # debug
#print("original:", len(matrix))
#matrix.canonicalize()
#print("new :", len(matrix))
#print(matrix) # debug
# calculate extreme points
poly = cdd.Polyhedron(matrix)
# convert these points back to lower probabilities
#print(poly.get_generators()) # debug
for vert in poly.get_generators():
yield cls(pspace=pspace,
lprob=dict(
(event, vert[1 + index])
for index, event in enumerate(pspace.subsets())),
number_type='fraction')
def __init__(self,
pspace=None,
mapping=None,
lprev=None,
uprev=None,
prev=None,
lprob=None,
uprob=None,
prob=None,
bba=None,
credalset=None,
number_type=None):
"""Construct a polyhedral lower prevision on *pspace*.
:param pspace: The possibility space.
:type pspace: |pspacetype|
:param mapping: Mapping from (gamble, event) to (lower prevision, upper prevision).
:type mapping: :class:`collections.Mapping`
:param lprev: Mapping from gamble to lower prevision.
:type lprev: :class:`collections.Mapping`
:param uprev: Mapping from gamble to upper prevision.
:type uprev: :class:`collections.Mapping`
:param prev: Mapping from gamble to precise prevision.
:type prev: :class:`collections.Mapping`
:param lprob: Mapping from event to lower probability.
:type lprob: :class:`collections.Mapping` or :class:`collections.Sequence`
:param uprob: Mapping from event to upper probability.
:type uprob: :class:`collections.Mapping` or :class:`collections.Sequence`
:param prob: Mapping from event to precise probability.
:type prob: :class:`collections.Mapping` or :class:`collections.Sequence`
:param bba: Mapping from event to basic belief assignment (useful for constructing belief functions).
:type bba: :class:`collections.Mapping`
:param credalset: Sequence of probability mass functions.
:type credalset: :class:`collections.Sequence`
:param number_type: The number type. If not specified, it is
determined using
:func:`~cdd.get_number_type_from_sequences` on all
values.
:type number_type: :class:`str`
Generally, you can pass a :class:`dict` as a keyword argument
in order to initialize the lower and upper previsions and/or
probabilities:
>>> print(LowPoly(pspace=3, mapping={
... ((3, 1, 2), True): (1.5, None),
... ((1, 0, -1), (1, 2)): (0.25, 0.3)})) # doctest: +NORMALIZE_WHITESPACE
0 1 2
3.0 1.0 2.0 | 0 1 2 : [1.5 , ]
1.0 0.0 -1.0 | 1 2 : [0.25, 0.3 ]
>>> print(LowPoly(pspace=3,
... lprev={(1, 3, 2): 1.5, (2, 0, -1): 1},
... uprev={(2, 0, -1): 1.9},
... prev={(9, 8, 20): 15},
... lprob={(1, 2): 0.2, (1,): 0.1},
... uprob={(1, 2): 0.3, (0,): 0.9},
... prob={(2,): '0.3'})) # doctest: +NORMALIZE_WHITESPACE
0 1 2
0.0 0.0 1.0 | 0 1 2 : [0.3 , 0.3 ]
0.0 1.0 0.0 | 0 1 2 : [0.1 , ]
0.0 1.0 1.0 | 0 1 2 : [0.2 , 0.3 ]
1.0 0.0 0.0 | 0 1 2 : [ , 0.9 ]
1.0 3.0 2.0 | 0 1 2 : [1.5 , ]
2.0 0.0 -1.0 | 0 1 2 : [1.0 , 1.9 ]
9.0 8.0 20.0 | 0 1 2 : [15.0, 15.0]
A credal set can be specified simply as a list:
>>> print(LowPoly(pspace=3,
... credalset=[['0.1', '0.45', '0.45'],
... ['0.4', '0.3', '0.3'],
... ['0.3', '0.2', '0.5']]))
0 1 2
-10 10 0 | 0 1 2 : [-1, ]
-1 -2 0 | 0 1 2 : [-1, ]
1 1 1 | 0 1 2 : [1 , 1 ]
50/23 40/23 0 | 0 1 2 : [1 , ]
As a special case, for lower/upper/precise probabilities, if
you need to set values on singletons, you can use a list
instead of a dictionary:
>>> print(LowPoly(pspace='abc', lprob=['0.1', '0.2', '0.3'])) # doctest: +NORMALIZE_WHITESPACE
a b c
0 0 1 | a b c : [3/10, ]
0 1 0 | a b c : [1/5 , ]
1 0 0 | a b c : [1/10, ]
If the first argument is a :class:`LowPoly` instance, then it
is copied. For example:
>>> from improb.lowprev.lowprob import LowProb
>>> lpr = LowPoly(pspace='abc', lprob=['0.1', '0.1', '0.1'])
>>> print(lpr)
a b c
0 0 1 | a b c : [1/10, ]
0 1 0 | a b c : [1/10, ]
1 0 0 | a b c : [1/10, ]
>>> lprob = LowProb(lpr)
>>> print(lprob)
a : 1/10
b : 1/10
c : 1/10
"""
def iter_items(obj):
"""Return an iterator over all items of the mapping or the
sequence.
"""
if isinstance(obj, collections.Mapping):
return obj.iteritems()
elif isinstance(obj, collections.Sequence):
if len(obj) < len(self.pspace):
raise ValueError('sequence too short')
return (((omega, ), value)
for omega, value in itertools.izip(self.pspace, obj))
else:
raise TypeError(
'expected collections.Mapping or collections.Sequence')
def get_number_type(xprevs, xprobs):
"""Determine number type from arguments."""
# special case: nothing specified, defaults to float
if (all(xprev is None for xprev in xprevs)
and all(xprob is None for xprob in xprobs)):
return 'float'
# inspect all values
for xprev in xprevs:
if xprev is None:
continue
for key, value in xprev.iteritems():
# inspect gamble
if isinstance(key, Gamble):
if key.number_type == 'float':
return 'float'
elif isinstance(key, collections.Sequence):
if cdd.get_number_type_from_sequences(key) == 'float':
return 'float'
elif isinstance(key, collections.Mapping):
if cdd.get_number_type_from_sequences(
key.itervalues()) == 'float':
return 'float'
# inspect value(s)
if isinstance(value, collections.Sequence):
if cdd.get_number_type_from_sequences(
value) == 'float':
return 'float'
else:
if cdd.get_number_type_from_value(value) == 'float':
return 'float'
for xprob in xprobs:
if xprob is None:
continue
for key, value in iter_items(xprob):
if cdd.get_number_type_from_value(value) == 'float':
return 'float'
# everything is fraction
return 'fraction'
# if first argument is a LowPoly, then override all other arguments
if isinstance(pspace, LowPoly):
mapping = dict(pspace.iteritems())
number_type = pspace.number_type
pspace = pspace.pspace
# initialize everything
self._pspace = PSpace.make(pspace)
if number_type is None:
number_type = get_number_type([mapping, lprev, uprev, prev, bba],
[lprob, uprob, prob] +
(credalset if credalset else []))
cdd.NumberTypeable.__init__(self, number_type)
self._mapping = {}
if mapping:
for key, value in mapping.iteritems():
self[key] = value
if lprev:
for gamble, value in lprev.iteritems():
self.set_lower(gamble, value)
if uprev:
for gamble, value in uprev.iteritems():
self.set_upper(gamble, value)
if prev:
for gamble, value in prev.iteritems():
self.set_precise(gamble, value)
if lprob:
for event, value in iter_items(lprob):
event = self.pspace.make_event(event)
self.set_lower(event, value)
if uprob:
for event, value in iter_items(uprob):
event = self.pspace.make_event(event)
self.set_upper(event, value)
if prob:
for event, value in iter_items(prob):
event = self.pspace.make_event(event)
self.set_precise(event, value)
if bba:
setfunc = SetFunction(pspace=self.pspace,
data=bba,
number_type=self.number_type)
for event in self.pspace.subsets():
self.set_lower(event, setfunc.get_zeta(event))
if credalset:
# set up polyhedral representation
mat = cdd.Matrix([(['1'] + credalprob)
for credalprob in credalset])
mat.rep_type = cdd.RepType.GENERATOR
poly = cdd.Polyhedron(mat)
dualmat = poly.get_inequalities()
#print(mat)
#print(dualmat)
for rownum, row in enumerate(dualmat):
if rownum in dualmat.lin_set:
self.set_precise(row[1:], -row[0])
else:
self.set_lower(row[1:], -row[0])
def get_constraints_n_monotone(cls, pspace, monotonicity=None):
"""Yields constraints for lower probabilities with given
monotonicity.
:param pspace: The possibility space.
:type pspace: |pspacetype|
:param monotonicity: Requested level of monotonicity (see
notes below for details).
:type monotonicity: :class:`int` or
:class:`collections.Iterable` of :class:`int`
As described in
:meth:`~improb.setfunction.SetFunction.get_constraints_bba_n_monotone`,
the n-monotonicity constraints on basic belief assignment are:
.. math::
\sum_{B\colon C\subseteq B\subseteq A}m(B)\ge 0
for all :math:`C\subseteq A\subseteq\Omega`, with
:math:`1\le|C|\le n`.
By the Mobius transform, this is equivalent to:
.. math::
\sum_{B\colon C\subseteq B\subseteq A}
\sum_{D\colon D\subseteq B}(-1)^{|B\setminus D|}
\underline{P}(D)\ge 0
Once noted that
.. math::
(C\subseteq B\subseteq A\quad \& \quad D\subseteq B)
\iff
(C\cup D\subseteq B\subseteq A\quad \& \quad D\subseteq A),
we can conveniently rewrite the sum as:
.. math::
\sum_{D\colon D\subseteq A}
\sum_{B\colon C\cup D\subseteq B\subseteq A}(-1)^{|B\setminus D|}
\underline{P}(D)\ge 0
This implementation iterates over all :math:`C\subseteq
A\subseteq\Omega`, with :math:`|C|=n`, and yields each
constraint as an iterable of (event, coefficient) pairs, where
zero coefficients are omitted.
.. note::
As just mentioned, this method returns the constraints
corresponding to the latter equation for :math:`|C|`
equal to *monotonicity*. To get all the
constraints for n-monotonicity, call this method with
*monotonicity=xrange(1, n + 1)*.
The rationale for this approach is that, in case you
already know that (n-1)-monotonicity is satisfied, then
you only need the constraints for *monotonicity=n* to
check for n-monotonicity.
.. note::
The trivial constraints that the empty set must have lower
probability zero, and that the possibility space must have
lower probability one, are not included: so for
*monotonicity=0* this method returns an empty iterator.
>>> pspace = PSpace("abc")
>>> for mono in xrange(1, len(pspace) + 1):
... print("{0} monotonicity:".format(mono))
... print(" ".join("{0:<{1}}".format("".join(i for i in event), len(pspace))
... for event in pspace.subsets()))
... constraints = [
... dict(constraint) for constraint in
... LowProb.get_constraints_n_monotone(pspace, mono)]
... constraints = [
... [constraint.get(event, 0) for event in pspace.subsets()]
... for constraint in constraints]
... for constraint in sorted(constraints):
... print(" ".join("{0:<{1}}".format(value, len(pspace))
... for value in constraint))
1 monotonicity:
a b c ab ac bc abc
-1 0 0 1 0 0 0 0
-1 0 1 0 0 0 0 0
-1 1 0 0 0 0 0 0
0 -1 0 0 0 1 0 0
0 -1 0 0 1 0 0 0
0 0 -1 0 0 0 1 0
0 0 -1 0 1 0 0 0
0 0 0 -1 0 0 1 0
0 0 0 -1 0 1 0 0
0 0 0 0 -1 0 0 1
0 0 0 0 0 -1 0 1
0 0 0 0 0 0 -1 1
2 monotonicity:
a b c ab ac bc abc
0 0 0 1 0 -1 -1 1
0 0 1 0 -1 0 -1 1
0 1 0 0 -1 -1 0 1
1 -1 -1 0 1 0 0 0
1 -1 0 -1 0 1 0 0
1 0 -1 -1 0 0 1 0
3 monotonicity:
a b c ab ac bc abc
-1 1 1 1 -1 -1 -1 1
"""
pspace = PSpace.make(pspace)
# check type
if monotonicity is None:
raise ValueError("specify monotonicity")
elif isinstance(monotonicity, collections.Iterable):
# special case: return it for all values in the iterable
for mono in monotonicity:
for constraint in cls.get_constraints_n_monotone(pspace, mono):
yield constraint
return
elif not isinstance(monotonicity, (int, long)):
raise TypeError("monotonicity must be integer")
# check value
if monotonicity < 0:
raise ValueError("specify a non-negative monotonicity")
if monotonicity == 0:
# don't return constraints in this case
return
# yield all constraints
for event_a in pspace.subsets(size=xrange(monotonicity,
len(pspace) + 1)):
for subevent_c in pspace.subsets(event_a, size=monotonicity):
yield ((subevent_d,
sum((-1)**len(event_b - subevent_d)
for event_b in pspace.subsets(
event_a, contains=(subevent_d | subevent_c))))
for subevent_d in pspace.subsets(event_a))
def get_constraints_bba_n_monotone(cls, pspace, monotonicity=None):
"""Yields constraints for basic belief assignments with given
monotonicity.
:param pspace: The possibility space.
:type pspace: |pspacetype|
:param monotonicity: Requested level of monotonicity (see
notes below for details).
:type monotonicity: :class:`int` or
:class:`collections.Iterable` of :class:`int`
This follows the algorithm described in Proposition 2 (for
1-monotonicity) and Proposition 4 (for n-monotonicity) of
*Chateauneuf and Jaffray, 1989. Some characterizations of
lower probabilities and other monotone capacities through the
use of Mobius inversion. Mathematical Social Sciences 17(3),
pages 263-283*:
A set function :math:`s` defined on the power set of
:math:`\Omega` is :math:`n`-monotone if and only if its Mobius
transform :math:`m` satisfies:
.. math::
m(\emptyset)=0, \qquad\sum_{A\subseteq\Omega} m(A)=1,
and
.. math::
\sum_{B\colon C\subseteq B\subseteq A} m(B)\ge 0
for all :math:`C\subseteq A\subseteq\Omega`, with
:math:`1\le|C|\le n`.
This implementation iterates over all :math:`C\subseteq
A\subseteq\Omega`, with :math:`|C|=n`, and yields each
constraint as an iterable of the events :math:`\{B\colon
C\subseteq B\subseteq A\}`. For example, you can then check
the constraint by summing over this iterable.
.. note::
As just mentioned, this method returns the constraints
corresponding to the latter equation for :math:`|C|`
equal to *monotonicity*. To get all the
constraints for n-monotonicity, call this method with
*monotonicity=xrange(1, n + 1)*.
The rationale for this approach is that, in case you
already know that (n-1)-monotonicity is satisfied, then
you only need the constraints for *monotonicity=n* to
check for n-monotonicity.
.. note::
The trivial constraints that the empty set must have mass
zero, and that the masses must sum to one, are not
included: so for *monotonicity=0* this method returns an
empty iterator.
>>> pspace = "abc"
>>> for mono in xrange(1, len(pspace) + 1):
... print("{0} monotonicity:".format(mono))
... print(" ".join("{0:<{1}}".format("".join(i for i in event), len(pspace))
... for event in PSpace(pspace).subsets()))
... constraints = SetFunction.get_constraints_bba_n_monotone(pspace, mono)
... constraints = [set(constraint) for constraint in constraints]
... constraints = [[1 if event in constraint else 0
... for event in PSpace(pspace).subsets()]
... for constraint in constraints]
... for constraint in sorted(constraints):
... print(" ".join("{0:<{1}}"
... .format(value, len(pspace))
... for value in constraint))
1 monotonicity:
a b c ab ac bc abc
0 0 0 1 0 0 0 0
0 0 0 1 0 0 1 0
0 0 0 1 0 1 0 0
0 0 0 1 0 1 1 1
0 0 1 0 0 0 0 0
0 0 1 0 0 0 1 0
0 0 1 0 1 0 0 0
0 0 1 0 1 0 1 1
0 1 0 0 0 0 0 0
0 1 0 0 0 1 0 0
0 1 0 0 1 0 0 0
0 1 0 0 1 1 0 1
2 monotonicity:
a b c ab ac bc abc
0 0 0 0 0 0 1 0
0 0 0 0 0 0 1 1
0 0 0 0 0 1 0 0
0 0 0 0 0 1 0 1
0 0 0 0 1 0 0 0
0 0 0 0 1 0 0 1
3 monotonicity:
a b c ab ac bc abc
0 0 0 0 0 0 0 1
"""
pspace = PSpace.make(pspace)
# check type
if monotonicity is None:
raise ValueError("specify monotonicity")
elif isinstance(monotonicity, collections.Iterable):
# special case: return it for all values in the iterable
for mono in monotonicity:
for constraint in cls.get_constraints_bba_n_monotone(
pspace, mono):
yield constraint
return
elif not isinstance(monotonicity, (int, long)):
raise TypeError("monotonicity must be integer")
# check value
if monotonicity < 0:
raise ValueError("specify a non-negative monotonicity")
if monotonicity == 0:
# don't return constraints in this case
return
# yield all constraints
for event in pspace.subsets(size=xrange(monotonicity,
len(pspace) + 1)):
for subevent in pspace.subsets(event, size=monotonicity):
yield pspace.subsets(event, contains=subevent)
def __init__(self, pspace, number_type=None):
if number_type is None:
number_type = 'float'
cdd.NumberTypeable.__init__(self, number_type)
self._pspace = PSpace.make(pspace)
def get_constraints_bba_n_monotone(cls, pspace, monotonicity=None):
"""Yields constraints for basic belief assignments with given
monotonicity.
:param pspace: The possibility space.
:type pspace: |pspacetype|
:param monotonicity: Requested level of monotonicity (see
notes below for details).
:type monotonicity: :class:`int` or
:class:`collections.Iterable` of :class:`int`
This follows the algorithm described in Proposition 2 (for
1-monotonicity) and Proposition 4 (for n-monotonicity) of
*Chateauneuf and Jaffray, 1989. Some characterizations of
lower probabilities and other monotone capacities through the
use of Mobius inversion. Mathematical Social Sciences 17(3),
pages 263-283*:
A set function :math:`s` defined on the power set of
:math:`\Omega` is :math:`n`-monotone if and only if its Mobius
transform :math:`m` satisfies:
.. math::
m(\emptyset)=0, \qquad\sum_{A\subseteq\Omega} m(A)=1,
and
.. math::
\sum_{B\colon C\subseteq B\subseteq A} m(B)\ge 0
for all :math:`C\subseteq A\subseteq\Omega`, with
:math:`1\le|C|\le n`.
This implementation iterates over all :math:`C\subseteq
A\subseteq\Omega`, with :math:`|C|=n`, and yields each
constraint as an iterable of the events :math:`\{B\colon
C\subseteq B\subseteq A\}`. For example, you can then check
the constraint by summing over this iterable.
.. note::
As just mentioned, this method returns the constraints
corresponding to the latter equation for :math:`|C|`
equal to *monotonicity*. To get all the
constraints for n-monotonicity, call this method with
*monotonicity=xrange(1, n + 1)*.
The rationale for this approach is that, in case you
already know that (n-1)-monotonicity is satisfied, then
you only need the constraints for *monotonicity=n* to
check for n-monotonicity.
.. note::
The trivial constraints that the empty set must have mass
zero, and that the masses must sum to one, are not
included: so for *monotonicity=0* this method returns an
empty iterator.
>>> pspace = "abc"
>>> for mono in xrange(1, len(pspace) + 1):
... print("{0} monotonicity:".format(mono))
... print(" ".join("{0:<{1}}".format("".join(i for i in event), len(pspace))
... for event in PSpace(pspace).subsets()))
... constraints = SetFunction.get_constraints_bba_n_monotone(pspace, mono)
... constraints = [set(constraint) for constraint in constraints]
... constraints = [[1 if event in constraint else 0
... for event in PSpace(pspace).subsets()]
... for constraint in constraints]
... for constraint in sorted(constraints):
... print(" ".join("{0:<{1}}"
... .format(value, len(pspace))
... for value in constraint))
1 monotonicity:
a b c ab ac bc abc
0 0 0 1 0 0 0 0
0 0 0 1 0 0 1 0
0 0 0 1 0 1 0 0
0 0 0 1 0 1 1 1
0 0 1 0 0 0 0 0
0 0 1 0 0 0 1 0
0 0 1 0 1 0 0 0
0 0 1 0 1 0 1 1
0 1 0 0 0 0 0 0
0 1 0 0 0 1 0 0
0 1 0 0 1 0 0 0
0 1 0 0 1 1 0 1
2 monotonicity:
a b c ab ac bc abc
0 0 0 0 0 0 1 0
0 0 0 0 0 0 1 1
0 0 0 0 0 1 0 0
0 0 0 0 0 1 0 1
0 0 0 0 1 0 0 0
0 0 0 0 1 0 0 1
3 monotonicity:
a b c ab ac bc abc
0 0 0 0 0 0 0 1
"""
pspace = PSpace.make(pspace)
# check type
if monotonicity is None:
raise ValueError("specify monotonicity")
elif isinstance(monotonicity, collections.Iterable):
# special case: return it for all values in the iterable
for mono in monotonicity:
for constraint in cls.get_constraints_bba_n_monotone(pspace, mono):
yield constraint
return
elif not isinstance(monotonicity, (int, long)):
raise TypeError("monotonicity must be integer")
# check value
if monotonicity < 0:
raise ValueError("specify a non-negative monotonicity")
if monotonicity == 0:
# don't return constraints in this case
return
# yield all constraints
for event in pspace.subsets(size=xrange(monotonicity, len(pspace) + 1)):
for subevent in pspace.subsets(event, size=monotonicity):
yield pspace.subsets(event, contains=subevent)
