@property
def equalities(self):
+ """
+ Return a list of the equalities in a set.
+ """
return self._equalities
@property
def inequalities(self):
+ """
+ Return a list of the inequalities in a set.
+ """
return self._inequalities
@property
def constraints(self):
+ """
+ Return ta list of the constraints of a set.
+ """
return self._constraints
@property
def disjoint(self):
"""
- Return this set as disjoint.
+ Return a set as disjoint.
"""
return self
def isuniverse(self):
"""
- Return true if this set is the Universe set.
+ Return true if a set is the Universe set.
"""
islbset = self._toislbasicset(self.equalities, self.inequalities,
self.symbols)
def aspolyhedron(self):
"""
- Return polyhedral hull of this set.
+ Return polyhedral hull of a set.
"""
return self
return True
def subs(self, symbol, expression=None):
+ """
+ Subsitute the given value into an expression and return the resulting expression.
+ """
equalities = [equality.subs(symbol, expression)
for equality in self.equalities]
inequalities = [inequality.subs(symbol, expression)
for inequality in self.inequalities]
return Polyhedron(equalities, inequalities)
+ def _asinequalities(self):
+ inequalities = list(self.equalities)
+ inequalities.extend([-expression for expression in self.equalities])
+ inequalities.extend(self.inequalities)
+ return inequalities
+
+ def widen(self, other):
+ if not isinstance(other, Polyhedron):
+ raise ValueError('argument must be a Polyhedron instance')
+ inequalities1 = self._asinequalities()
+ inequalities2 = other._asinequalities()
+ inequalities = []
+ for inequality1 in inequalities1:
+ if other <= Polyhedron(inequalities=[inequality1]):
+ inequalities.append(inequality1)
+ for inequality2 in inequalities2:
+ for i in range(len(inequalities1)):
+ inequalities3 = inequalities1[:i] + inequalities[i + 1:]
+ inequalities3.append(inequality2)
+ polyhedron3 = Polyhedron(inequalities=inequalities3)
+ if self == polyhedron3:
+ inequalities.append(inequality2)
+ break
+ return Polyhedron(inequalities=inequalities)
+
@classmethod
def _fromislbasicset(cls, islbset, symbols):
islconstraints = islhelper.isl_basic_set_constraints(islbset)
return domain
def __repr__(self):
- if self.isempty():
- return 'Empty'
- elif self.isuniverse():
- return 'Universe'
+ strings = []
+ for equality in self.equalities:
+ strings.append('Eq({}, 0)'.format(equality))
+ for inequality in self.inequalities:
+ strings.append('Ge({}, 0)'.format(inequality))
+ if len(strings) == 1:
+ return strings[0]
else:
- strings = []
- for equality in self.equalities:
- strings.append('Eq({}, 0)'.format(equality))
- for inequality in self.inequalities:
- strings.append('Ge({}, 0)'.format(inequality))
- if len(strings) == 1:
- return strings[0]
- else:
- return 'And({})'.format(', '.join(strings))
+ return 'And({})'.format(', '.join(strings))
+
def _repr_latex_(self):
- if self.isempty():
- return '$\\emptyset$'
- elif self.isuniverse():
- return '$\\Omega$'
- else:
- strings = []
- for equality in self.equalities:
- strings.append('{} = 0'.format(equality._repr_latex_().strip('$')))
- for inequality in self.inequalities:
- strings.append('{} \\ge 0'.format(inequality._repr_latex_().strip('$')))
- return '${}$'.format(' \\wedge '.join(strings))
+ strings = []
+ for equality in self.equalities:
+ strings.append('{} = 0'.format(equality._repr_latex_().strip('$')))
+ for inequality in self.inequalities:
+ strings.append('{} \\ge 0'.format(inequality._repr_latex_().strip('$')))
+ return '$${}$$'.format(' \\wedge '.join(strings))
@classmethod
def fromsympy(cls, expr):
+ """
+ Convert a sympy object to an expression.
+ """
domain = Domain.fromsympy(expr)
if not isinstance(domain, Polyhedron):
raise ValueError('non-polyhedral expression: {!r}'.format(expr))
return domain
def tosympy(self):
+ """
+ Return an expression as a sympy object.
+ """
import sympy
constraints = []
for equality in self.equalities:
constraints.append(sympy.Ge(inequality.tosympy(), 0))
return sympy.And(*constraints)
+class EmptyType(Polyhedron):
+
+ __slots__ = Polyhedron.__slots__
+
+ def __new__(cls):
+ self = object().__new__(cls)
+ self._equalities = (Rational(1),)
+ self._inequalities = ()
+ self._constraints = self._equalities
+ self._symbols = ()
+ self._dimension = 0
+ return self
+
+ def widen(self, other):
+ if not isinstance(other, Polyhedron):
+ raise ValueError('argument must be a Polyhedron instance')
+ return other
+
+ def __repr__(self):
+ return 'Empty'
+
+ def _repr_latex_(self):
+ return '$$\\emptyset$$'
+
+Empty = EmptyType()
+
+
+class UniverseType(Polyhedron):
+
+ __slots__ = Polyhedron.__slots__
+
+ def __new__(cls):
+ self = object().__new__(cls)
+ self._equalities = ()
+ self._inequalities = ()
+ self._constraints = ()
+ self._symbols = ()
+ self._dimension = ()
+ return self
+
+ def __repr__(self):
+ return 'Universe'
+
+ def _repr_latex_(self):
+ return '$$\\Omega$$'
+
+Universe = UniverseType()
+
+
def _polymorphic(func):
@functools.wraps(func)
def wrapper(left, right):
@_polymorphic
def Lt(left, right):
"""
- Return true if the first set is less than the second.
+ Assert first set is less than the second set.
"""
return Polyhedron([], [right - left - 1])
@_polymorphic
def Le(left, right):
"""
- Return true the first set is less than or equal to the second.
+ Assert first set is less than or equal to the second set.
"""
return Polyhedron([], [right - left])
@_polymorphic
def Eq(left, right):
"""
- Return true if the sets are equal.
+ Assert first set is equal to the second set.
"""
return Polyhedron([left - right], [])
@_polymorphic
def Ne(left, right):
"""
- Return true if the sets are NOT equal.
+ Assert first set is not equal to the second set.
"""
return ~Eq(left, right)
@_polymorphic
def Gt(left, right):
"""
- Return true if the first set is greater than the second set.
+ Assert first set is greater than the second set.
"""
return Polyhedron([], [left - right - 1])
@_polymorphic
def Ge(left, right):
"""
- Return true if the first set is greater than or equal the second set.
+ Assert first set is greater than or equal to the second set.
"""
return Polyhedron([], [left - right])
-
-Empty = Eq(1, 0)
-
-Universe = Polyhedron([])
projects / linpy.git / blobdiff