__all__ = [
- 'Expression',
- 'constant', 'symbol', 'symbols',
+ 'Expression', 'Constant', 'Symbol', 'symbols',
'eq', 'le', 'lt', 'ge', 'gt',
'Polyhedron',
'empty', 'universe'
if isinstance(b, Expression):
return func(a, b)
if isinstance(b, numbers.Rational):
- b = constant(b)
+ b = Constant(b)
return func(a, b)
return NotImplemented
return wrapper
@functools.wraps(func)
def wrapper(a, b):
if isinstance(a, numbers.Rational):
- a = constant(a)
+ a = Constant(a)
return func(a, b)
elif isinstance(a, Expression):
return func(a, b)
if constant:
raise TypeError('too many arguments')
return cls.fromstring(coefficients)
- self = super().__new__(cls)
- self._coefficients = {}
if isinstance(coefficients, dict):
coefficients = coefficients.items()
- if coefficients is not None:
- for symbol, coefficient in coefficients:
- if isinstance(symbol, Expression) and symbol.issymbol():
- symbol = str(symbol)
- elif not isinstance(symbol, str):
- raise TypeError('symbols must be strings')
- if not isinstance(coefficient, numbers.Rational):
- raise TypeError('coefficients must be rational numbers')
- if coefficient != 0:
- self._coefficients[symbol] = coefficient
+ if coefficients is None:
+ return Constant(constant)
+ coefficients = [(symbol, coefficient)
+ for symbol, coefficient in coefficients if coefficient != 0]
+ if len(coefficients) == 0:
+ return Constant(constant)
+ elif len(coefficients) == 1 and constant == 0:
+ symbol, coefficient = coefficients[0]
+ if coefficient == 1:
+ return Symbol(symbol)
+ self = object().__new__(cls)
+ self._coefficients = {}
+ for symbol, coefficient in coefficients:
+ if isinstance(symbol, Symbol):
+ symbol = str(symbol)
+ elif not isinstance(symbol, str):
+ raise TypeError('symbols must be strings or Symbol instances')
+ if isinstance(coefficient, Constant):
+ coefficient = coefficient.constant
+ if not isinstance(coefficient, numbers.Rational):
+ raise TypeError('coefficients must be rational numbers or Constant instances')
+ self._coefficients[symbol] = coefficient
+ if isinstance(constant, Constant):
+ constant = constant.constant
if not isinstance(constant, numbers.Rational):
- raise TypeError('constant must be a rational number')
+ raise TypeError('constant must be a rational number or a Constant instance')
self._constant = constant
+ self._symbols = tuple(sorted(self._coefficients))
+ self._dimension = len(self._symbols)
return self
+ @classmethod
+ def fromstring(cls, string):
+ raise NotImplementedError
+ @property
def symbols(self):
- yield from sorted(self._coefficients)
+ return self._symbols
@property
def dimension(self):
- return len(list(self.symbols()))
+ return self._dimension
def coefficient(self, symbol):
- if isinstance(symbol, Expression) and symbol.issymbol():
+ if isinstance(symbol, Symbol):
symbol = str(symbol)
elif not isinstance(symbol, str):
- raise TypeError('symbol must be a string')
+ raise TypeError('symbol must be a string or a Symbol instance')
try:
return self._coefficients[symbol]
except KeyError:
__getitem__ = coefficient
- @property
def coefficients(self):
- for symbol in self.symbols():
+ for symbol in self.symbols:
yield symbol, self.coefficient(symbol)
@property
return self._constant
def isconstant(self):
- return len(self._coefficients) == 0
+ return False
def values(self):
- for symbol in self.symbols():
+ for symbol in self.symbols:
yield self.coefficient(symbol)
yield self.constant
- def values_int(self):
- for symbol in self.symbols():
- return self.coefficient(symbol)
- return int(self.constant)
-
+ @property
def symbol(self):
- if not self.issymbol():
- raise ValueError('not a symbol: {}'.format(self))
- for symbol in self.symbols():
- return symbol
+ raise ValueError('not a symbol: {}'.format(self))
def issymbol(self):
- return len(self._coefficients) == 1 and self._constant == 0
+ return False
def __bool__(self):
- return (not self.isconstant()) or bool(self.constant)
+ True
def __pos__(self):
return self
@_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:
@_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:
@_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
def __str__(self):
string = ''
- symbols = sorted(self.symbols())
i = 0
- for symbol in symbols:
- coefficient = self[symbol]
+ for symbol in self.symbols:
+ coefficient = self.coefficient(symbol)
if coefficient == 1:
if i == 0:
string += symbol
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)
string += '}}, {!r})'.format(self.constant)
return string
- @classmethod
- def fromstring(cls, string):
- raise NotImplementedError
-
@_polymorphic_method
def __eq__(self, other):
# "normal" equality
def __hash__(self):
return hash((self._coefficients, self._constant))
- def _canonify(self):
+ def _toint(self):
lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),
[value.denominator for value in self.values()])
return self * lcm
@_polymorphic_method
def _eq(self, other):
- return Polyhedron(equalities=[(self - other)._canonify()])
+ return Polyhedron(equalities=[(self - other)._toint()])
@_polymorphic_method
def __le__(self, other):
- return Polyhedron(inequalities=[(other - self)._canonify()])
+ return Polyhedron(inequalities=[(other - self)._toint()])
@_polymorphic_method
def __lt__(self, other):
- return Polyhedron(inequalities=[(other - self)._canonify() - 1])
+ return Polyhedron(inequalities=[(other - self)._toint() - 1])
@_polymorphic_method
def __ge__(self, other):
- return Polyhedron(inequalities=[(self - other)._canonify()])
+ return Polyhedron(inequalities=[(self - other)._toint()])
@_polymorphic_method
def __gt__(self, other):
- return Polyhedron(inequalities=[(self - other)._canonify() - 1])
+ return Polyhedron(inequalities=[(self - other)._toint() - 1])
+
+
+class Constant(Expression):
+
+ def __new__(cls, numerator=0, denominator=None):
+ self = object().__new__(cls)
+ if denominator is None:
+ if isinstance(numerator, numbers.Rational):
+ self._constant = numerator
+ elif isinstance(numerator, Constant):
+ self._constant = numerator.constant
+ else:
+ raise TypeError('constant must be a rational number or a Constant instance')
+ else:
+ self._constant = Fraction(numerator, denominator)
+ self._coefficients = {}
+ self._symbols = ()
+ self._dimension = 0
+ return self
+ def isconstant(self):
+ return True
-def constant(numerator=0, denominator=None):
- if denominator is None and isinstance(numerator, numbers.Rational):
- return Expression(constant=numerator)
- else:
- return Expression(constant=Fraction(numerator, denominator))
+ def __bool__(self):
+ return bool(self.constant)
-def symbol(name):
- if not isinstance(name, str):
- raise TypeError('name must be a string')
- return Expression(coefficients={name: 1})
+ def __repr__(self):
+ return '{}({!r})'.format(self.__class__.__name__, self._constant)
+
+
+class Symbol(Expression):
+
+ def __new__(cls, name):
+ if isinstance(name, Symbol):
+ name = name.symbol
+ elif not isinstance(name, str):
+ raise TypeError('name must be a string or a Symbol instance')
+ self = object().__new__(cls)
+ self._coefficients = {name: 1}
+ self._constant = 0
+ self._symbols = tuple(name)
+ self._symbol = name
+ self._dimension = 1
+ return self
+
+ @property
+ def symbol(self):
+ return self._symbol
+
+ def issymbol(self):
+ return True
+
+ def __repr__(self):
+ return '{}({!r})'.format(self.__class__.__name__, self._symbol)
def symbols(names):
if isinstance(names, str):
raise TypeError('non-integer constraint: '
'{} == 0'.format(constraint))
self._equalities.append(constraint)
+ self._equalities = tuple(self._equalities)
self._inequalities = []
if inequalities is not None:
for constraint in inequalities:
raise TypeError('non-integer constraint: '
'{} <= 0'.format(constraint))
self._inequalities.append(constraint)
+ self._inequalities = tuple(self._inequalities)
+ self._constraints = self._equalities + self._inequalities
+ self._symbols = set()
+ for constraint in self._constraints:
+ self.symbols.update(constraint.symbols)
+ self._symbols = tuple(sorted(self._symbols))
return self
+ @classmethod
+ def fromstring(cls, string):
+ raise NotImplementedError
+
@property
def equalities(self):
- yield from self._equalities
+ return self._equalities
@property
def inequalities(self):
- yield from self._inequalities
+ return 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
+ return self._constraints
+ @property
def symbols(self):
- s = set()
- for constraint in self.constraints():
- s.update(constraint.symbols())
- return sorted(s)
+ return self._symbols
@property
def dimension(self):
- return len(self.symbols())
+ return len(self.symbols)
def __bool__(self):
- # return false if the polyhedron is empty, true otherwise
- if self._equalities or self._inequalities:
- return False
- else:
- return True
+ return not self.is_empty()
def __contains__(self, value):
# is the value in the polyhedron?
def __eq__(self, other):
raise NotImplementedError
- def is_empty(self):
- return
+ def isempty(self):
+ bset = self._toisl()
+ return bool(libisl.isl_basic_set_is_empty(bset))
def isuniverse(self):
- return self == universe
+ raise NotImplementedError
def isdisjoint(self, other):
# return true if the polyhedron has no elements in common with other
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):
return '{}(equalities={!r}, inequalities={!r})' \
''.format(self.__class__.__name__, equalities, inequalities)
- @classmethod
- def fromstring(cls, string):
- raise NotImplementedError
-
def _symbolunion(self, *others):
- symbols = set(self.symbols())
+ symbols = set(self.symbols)
for other in others:
- symbols.update(other.symbols())
+ symbols.update(other.symbols)
return sorted(symbols)
- def _to_isl(self, symbols=None):
+ def _toisl(self, symbols=None):
if symbols is None:
- symbols = self.symbols()
+ 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))
'''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)
+ coeff_eq = dict(eq.coefficients())
if eq.constant:
value = eq.constant
ceq = libisl.isl_constraint_set_constant_si(ceq, value)
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)
+ coeff_in = dict(ineq.coefficients())
if ineq.constant:
value = ineq.constant
cin = libisl.isl_constraint_set_constant_si(cin, value)
bset = isl.BasicSet(bset)
return bset
- def from_isl(self, bset):
- '''takes basic set in isl form and puts back into python version of polyhedron
+ @classmethod
+ def _fromisl(cls, bset):
+ raise NotImplementedError
+ equalities = ...
+ inequalities = ...
+ return cls(equalities, inequalities)
+ '''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
+ # 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()
+ bs = p._toisl()
print(bs)
+ print('empty ?', p.isempty())
+ print('empty ?', eq(0, 1).isempty())
projects / linpy.git / blobdiff