-
+import ctypes, ctypes.util
import functools
import numbers
from fractions import Fraction, gcd
+from . import isl, islhelper
+from .isl import libisl, Context, BasicSet
+
__all__ = [
'Expression',
]
+def _polymorphic_method(func):
+ @functools.wraps(func)
+ def wrapper(a, b):
+ if isinstance(b, Expression):
+ return func(a, b)
+ if isinstance(b, numbers.Rational):
+ b = constant(b)
+ return func(a, b)
+ return NotImplemented
+ return wrapper
+
+def _polymorphic_operator(func):
+ # A polymorphic operator should call a polymorphic method, hence we just
+ # have to test the left operand.
+ @functools.wraps(func)
+ def wrapper(a, b):
+ if isinstance(a, numbers.Rational):
+ a = constant(a)
+ return func(a, b)
+ elif isinstance(a, Expression):
+ return func(a, b)
+ raise TypeError('arguments must be linear expressions')
+ return wrapper
+
+
+_main_ctx = Context()
+
+
class Expression:
"""
This class implements linear expressions.
self._constant = constant
return self
+
def symbols(self):
yield from sorted(self._coefficients)
__getitem__ = coefficient
+ @property
def coefficients(self):
for symbol in self.symbols():
yield symbol, self.coefficient(symbol)
yield self.coefficient(symbol)
yield self.constant
+ def values_int(self):
+ for symbol in self.symbols():
+ return self.coefficient(symbol)
+ return int(self.constant)
+
def symbol(self):
if not self.issymbol():
raise ValueError('not a symbol: {}'.format(self))
def __neg__(self):
return self * -1
- def _polymorphic(func):
- @functools.wraps(func)
- def wrapper(self, other):
- if isinstance(other, Expression):
- return func(self, other)
- if isinstance(other, numbers.Rational):
- other = Expression(constant=other)
- return func(self, other)
- return NotImplemented
- return wrapper
-
- @_polymorphic
+ @_polymorphic_method
def __add__(self, other):
- coefficients = dict(self.coefficients())
- for symbol, coefficient in other.coefficients():
+ coefficients = dict(self.coefficients)
+ for symbol, coefficient in other.coefficients:
if symbol in coefficients:
coefficients[symbol] += coefficient
else:
__radd__ = __add__
- @_polymorphic
+ @_polymorphic_method
def __sub__(self, other):
- coefficients = dict(self.coefficients())
- for symbol, coefficient in other.coefficients():
+ coefficients = dict(self.coefficients)
+ for symbol, coefficient in other.coefficients:
if symbol in coefficients:
coefficients[symbol] -= coefficient
else:
constant = self.constant - other.constant
return Expression(coefficients, constant)
- __rsub__ = __sub__
+ def __rsub__(self, other):
+ return -(self - other)
- @_polymorphic
+ @_polymorphic_method
def __mul__(self, other):
if other.isconstant():
- coefficients = dict(self.coefficients())
+ coefficients = dict(self.coefficients)
for symbol in coefficients:
coefficients[symbol] *= other.constant
constant = self.constant * other.constant
__rmul__ = __mul__
- @_polymorphic
+ @_polymorphic_method
def __truediv__(self, other):
if other.isconstant():
coefficients = dict(self.coefficients())
return NotImplemented
def __rtruediv__(self, other):
- if isinstance(other, Rational):
+ if isinstance(other, self):
if self.isconstant():
constant = Fraction(other, self.constant)
return Expression(constant=constant)
elif constant < 0:
constant *= -1
string += ' - {}'.format(constant)
+ if string == '':
+ string = '0'
return string
def _parenstr(self, always=False):
def __repr__(self):
string = '{}({{'.format(self.__class__.__name__)
- for i, (symbol, coefficient) in enumerate(self.coefficients()):
+ for i, (symbol, coefficient) in enumerate(self.coefficients):
if i != 0:
string += ', '
string += '{!r}: {!r}'.format(symbol, coefficient)
def fromstring(cls, string):
raise NotImplementedError
- @_polymorphic
+ @_polymorphic_method
def __eq__(self, other):
# "normal" equality
# see http://docs.sympy.org/dev/tutorial/gotchas.html#equals-signs
[value.denominator for value in self.values()])
return self * lcm
- @_polymorphic
+ @_polymorphic_method
def _eq(self, other):
return Polyhedron(equalities=[(self - other)._canonify()])
- @_polymorphic
+ @_polymorphic_method
def __le__(self, other):
- return Polyhedron(inequalities=[(self - other)._canonify()])
+ return Polyhedron(inequalities=[(other - self)._canonify()])
- @_polymorphic
+ @_polymorphic_method
def __lt__(self, other):
- return Polyhedron(inequalities=[(self - other)._canonify() + 1])
+ return Polyhedron(inequalities=[(other - self)._canonify() - 1])
- @_polymorphic
+ @_polymorphic_method
def __ge__(self, other):
- return Polyhedron(inequalities=[(other - self)._canonify()])
+ return Polyhedron(inequalities=[(self - other)._canonify()])
- @_polymorphic
+ @_polymorphic_method
def __gt__(self, other):
- return Polyhedron(inequalities=[(other - self)._canonify() + 1])
+ return Polyhedron(inequalities=[(self - other)._canonify() - 1])
def constant(numerator=0, denominator=None):
- return Expression(constant=Fraction(numerator, denominator))
+ if denominator is None and isinstance(numerator, numbers.Rational):
+ return Expression(constant=numerator)
+ else:
+ return Expression(constant=Fraction(numerator, denominator))
def symbol(name):
if not isinstance(name, str):
return (symbol(name) for name in names)
-def _operator(func):
- @functools.wraps(func)
- def wrapper(a, b):
- if isinstance(a, numbers.Rational):
- a = constant(a)
- if isinstance(b, numbers.Rational):
- b = constant(b)
- if isinstance(a, Expression) and isinstance(b, Expression):
- return func(a, b)
- raise TypeError('arguments must be linear expressions')
- return wrapper
-
-@_operator
+@_polymorphic_operator
def eq(a, b):
return a._eq(b)
-@_operator
+@_polymorphic_operator
def le(a, b):
return a <= b
-@_operator
+@_polymorphic_operator
def lt(a, b):
return a < b
-@_operator
+@_polymorphic_operator
def ge(a, b):
return a >= b
-@_operator
+@_polymorphic_operator
def gt(a, b):
return a > b
def inequalities(self):
yield from self._inequalities
+ @property
+ def constant(self):
+ return self._constant
+
+ def isconstant(self):
+ return len(self._coefficients) == 0
+
+ def isempty(self):
+ return bool(libisl.isl_basic_set_is_empty(self._bset))
+
def constraints(self):
yield from self.equalities
yield from self.inequalities
def symbols(self):
s = set()
for constraint in self.constraints():
- s.update(constraint.symbols)
- yield from sorted(s)
+ s.update(constraint.symbols())
+ return sorted(s)
@property
def dimension(self):
def __bool__(self):
# return false if the polyhedron is empty, true otherwise
- raise NotImplementedError
+ if self._equalities or self._inequalities:
+ return False
+ else:
+ return True
def __contains__(self, value):
# is the value in the polyhedron?
def __eq__(self, other):
raise NotImplementedError
- def isempty(self):
- return self == empty
+ def is_empty(self):
+ return
def isuniverse(self):
return self == universe
def issuperset(self, other):
# test whether every element in other is in the polyhedron
+ for value in other:
+ if value == self.constraints():
+ return True
+ else:
+ return False
raise NotImplementedError
def __ge__(self, other):
for constraint in self.equalities:
constraints.append('{} == 0'.format(constraint))
for constraint in self.inequalities:
- constraints.append('{} <= 0'.format(constraint))
+ constraints.append('{} >= 0'.format(constraint))
return '{{{}}}'.format(', '.join(constraints))
def __repr__(self):
def fromstring(cls, string):
raise NotImplementedError
-
-empty = le(1, 0)
-
-universe = Polyhedron()
+ def _symbolunion(self, *others):
+ symbols = set(self.symbols())
+ for other in others:
+ symbols.update(other.symbols())
+ return sorted(symbols)
+
+ def _to_isl(self, symbols=None):
+ if symbols is None:
+ symbols = self.symbols()
+ num_coefficients = len(symbols)
+ space = libisl.isl_space_set_alloc(_main_ctx, 0, num_coefficients)
+ bset = libisl.isl_basic_set_universe(libisl.isl_space_copy(space))
+ ls = libisl.isl_local_space_from_space(space)
+ ceq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(ls))
+ cin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(ls))
+ '''if there are equalities/inequalities, take each constant and coefficient and add as a constraint to the basic set'''
+ if list(self.equalities): #check if any equalities exist
+ for eq in self.equalities:
+ coeff_eq = dict(eq.coefficients)
+ if eq.constant:
+ value = eq.constant
+ ceq = libisl.isl_constraint_set_constant_si(ceq, value)
+ for eq in coeff_eq:
+ num = coeff_eq.get(eq)
+ iden = symbols.index(eq)
+ ceq = libisl.isl_constraint_set_coefficient_si(ceq, islhelper.isl_dim_set, iden, num) #use 3 for type isl_dim_set
+ bset = libisl.isl_basic_set_add_constraint(bset, ceq)
+ if list(self.inequalities): #check if any inequalities exist
+ for ineq in self.inequalities:
+ coeff_in = dict(ineq.coefficients)
+ if ineq.constant:
+ value = ineq.constant
+ cin = libisl.isl_constraint_set_constant_si(cin, value)
+ for ineq in coeff_in:
+ num = coeff_in.get(ineq)
+ iden = symbols.index(ineq)
+ cin = libisl.isl_constraint_set_coefficient_si(cin, islhelper.isl_dim_set, iden, num) #use 3 for type isl_dim_set
+ bset = libisl.isl_basic_set_add_constraint(bset, cin)
+ bset = BasicSet(bset)
+ return bset
+
+ def from_isl(self, bset):
+ '''takes basic set in isl form and puts back into python version of polyhedron
+ isl example code gives isl form as:
+ "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}")
+ our printer is giving form as:
+ b'{ [i0] : 1 = 0 }' '''
+ #bset = self
+ if self._equalities:
+ constraints = libisl.isl_basic_set_equalities_matrix(bset, 3)
+ elif self._inequalities:
+ constraints = libisl.isl_basic_set_inequalities_matrix(bset, 3)
+ print(constraints)
+ return constraints
+
+empty = None #eq(0,1)
+universe = None #Polyhedron()
+
+if __name__ == '__main__':
+ ex1 = Expression(coefficients={'a': 1, 'x': 2}, constant=2)
+ ex2 = Expression(coefficients={'a': 3 , 'b': 2}, constant=3)
+ p = Polyhedron(inequalities=[ex1, ex2])
+ bs = p._to_isl()
+ print(bs)
projects / linpy.git / blobdiff