-
+import ast
import functools
import numbers
+import re
from fractions import Fraction, gcd
+from . import isl
+from .isl import libisl
+
__all__ = [
- 'Expression',
- 'constant', 'symbol', 'symbols',
+ 'Expression', 'Constant', 'Symbol', 'symbols',
'eq', 'le', 'lt', 'ge', 'gt',
'Polyhedron',
- 'empty', 'universe'
+ '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)
return wrapper
+_main_ctx = isl.Context()
+
+
class Expression:
"""
This class implements linear expressions.
"""
+ __slots__ = (
+ '_coefficients',
+ '_constant',
+ '_symbols',
+ '_dimension',
+ )
+
def __new__(cls, coefficients=None, constant=0):
if isinstance(coefficients, str):
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 = symbol.name
+ 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 _fromast(cls, node):
+ if isinstance(node, ast.Module) and len(node.body) == 1:
+ return cls._fromast(node.body[0])
+ elif isinstance(node, ast.Expr):
+ return cls._fromast(node.value)
+ elif isinstance(node, ast.Name):
+ return Symbol(node.id)
+ elif isinstance(node, ast.Num):
+ return Constant(node.n)
+ elif isinstance(node, ast.UnaryOp) and isinstance(node.op, ast.USub):
+ return -cls._fromast(node.operand)
+ elif isinstance(node, ast.BinOp):
+ left = cls._fromast(node.left)
+ right = cls._fromast(node.right)
+ if isinstance(node.op, ast.Add):
+ return left + right
+ elif isinstance(node.op, ast.Sub):
+ return left - right
+ elif isinstance(node.op, ast.Mult):
+ return left * right
+ elif isinstance(node.op, ast.Div):
+ return left / right
+ raise SyntaxError('invalid syntax')
+
+ @classmethod
+ def fromstring(cls, string):
+ string = re.sub(r'(\d+|\))\s*([^\W\d_]\w*|\()', r'\1*\2', string)
+ tree = ast.parse(string, 'eval')
+ return cls._fromast(tree)
+
+ @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
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 symbol(self):
- if not self.issymbol():
- raise ValueError('not a symbol: {}'.format(self))
- for symbol in self.symbols():
- return symbol
-
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)
+ return True
def __pos__(self):
return self
constant = self.constant - other.constant
return Expression(coefficients, constant)
- __rsub__ = __sub__
+ def __rsub__(self, other):
+ return -(self - other)
@_polymorphic_method
def __mul__(self, other):
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)
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
string += '}}, {!r})'.format(self.constant)
return string
- @classmethod
- def fromstring(cls, string):
- raise NotImplementedError
-
@_polymorphic_method
def __eq__(self, other):
# "normal" equality
self.constant == other.constant
def __hash__(self):
- return hash((self._coefficients, self._constant))
+ return hash((tuple(sorted(self._coefficients.items())), 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=[(self - other)._canonify()])
+ return Polyhedron(inequalities=[(other - self)._toint()])
@_polymorphic_method
def __lt__(self, other):
- return Polyhedron(inequalities=[(self - other)._canonify() + 1])
+ return Polyhedron(inequalities=[(other - self)._toint() - 1])
@_polymorphic_method
def __ge__(self, other):
- return Polyhedron(inequalities=[(other - self)._canonify()])
+ return Polyhedron(inequalities=[(self - other)._toint()])
@_polymorphic_method
def __gt__(self, other):
- return Polyhedron(inequalities=[(other - self)._canonify() + 1])
+ return Polyhedron(inequalities=[(self - other)._toint() - 1])
+
+ @classmethod
+ def fromsympy(cls, expr):
+ import sympy
+ coefficients = {}
+ constant = 0
+ for symbol, coefficient in expr.as_coefficients_dict().items():
+ coefficient = Fraction(coefficient.p, coefficient.q)
+ if symbol == sympy.S.One:
+ constant = coefficient
+ elif isinstance(symbol, sympy.Symbol):
+ symbol = symbol.name
+ coefficients[symbol] = coefficient
+ else:
+ raise ValueError('non-linear expression: {!r}'.format(expr))
+ return cls(coefficients, constant)
+
+ def tosympy(self):
+ import sympy
+ expr = 0
+ for symbol, coefficient in self.coefficients():
+ term = coefficient * sympy.Symbol(symbol)
+ expr += term
+ expr += self.constant
+ return expr
+
+
+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 __repr__(self):
+ if self.constant.denominator == 1:
+ return '{}({!r})'.format(self.__class__.__name__, self.constant)
+ else:
+ return '{}({!r}, {!r})'.format(self.__class__.__name__,
+ self.constant.numerator, self.constant.denominator)
+
+ @classmethod
+ def fromsympy(cls, expr):
+ import sympy
+ if isinstance(expr, sympy.Rational):
+ return cls(expr.p, expr.q)
+ elif isinstance(expr, numbers.Rational):
+ return cls(expr)
+ else:
+ raise TypeError('expr must be a sympy.Rational instance')
+
+
+class Symbol(Expression):
+
+ __slots__ = Expression.__slots__ + (
+ '_name',
+ )
+
+ def __new__(cls, name):
+ if isinstance(name, Symbol):
+ name = name.name
+ 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._name = name
+ self._dimension = 1
+ return self
+
+ @property
+ def name(self):
+ return self._name
+
+ def issymbol(self):
+ return True
+
+ def __repr__(self):
+ return '{}({!r})'.format(self.__class__.__name__, self._name)
+
+ @classmethod
+ def fromsympy(cls, expr):
+ import sympy
+ if isinstance(expr, sympy.Symbol):
+ return cls(expr.name)
+ else:
+ raise TypeError('expr must be a sympy.Symbol instance')
-def symbol(name):
- if not isinstance(name, str):
- raise TypeError('name must be a string')
- return Expression(coefficients={name: 1})
def symbols(names):
if isinstance(names, str):
names = names.replace(',', ' ').split()
- return (symbol(name) for name in names)
+ return (Symbol(name) for name in names)
@_polymorphic_operator
def eq(a, b):
- return a._eq(b)
+ return a.__eq__(b)
@_polymorphic_operator
def le(a, b):
- return a <= b
+ return a.__le__(b)
@_polymorphic_operator
def lt(a, b):
- return a < b
+ return a.__lt__(b)
@_polymorphic_operator
def ge(a, b):
- return a >= b
+ return a.__ge__(b)
@_polymorphic_operator
def gt(a, b):
- return a > b
+ return a.__gt__(b)
class Polyhedron:
This class implements polyhedrons.
"""
+ __slots__ = (
+ '_equalities',
+ '_inequalities',
+ '_constraints',
+ '_symbols',
+ )
+
def __new__(cls, equalities=None, inequalities=None):
if isinstance(equalities, str):
if inequalities is not None:
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 _fromast(cls, node):
+ if isinstance(node, ast.Module) and len(node.body) == 1:
+ return cls._fromast(node.body[0])
+ elif isinstance(node, ast.Expr):
+ return cls._fromast(node.value)
+ elif isinstance(node, ast.BinOp) and isinstance(node.op, ast.BitAnd):
+ equalities1, inequalities1 = cls._fromast(node.left)
+ equalities2, inequalities2 = cls._fromast(node.right)
+ equalities = equalities1 + equalities2
+ inequalities = inequalities1 + inequalities2
+ return equalities, inequalities
+ elif isinstance(node, ast.Compare):
+ equalities = []
+ inequalities = []
+ left = Expression._fromast(node.left)
+ for i in range(len(node.ops)):
+ op = node.ops[i]
+ right = Expression._fromast(node.comparators[i])
+ if isinstance(op, ast.Lt):
+ inequalities.append(right - left - 1)
+ elif isinstance(op, ast.LtE):
+ inequalities.append(right - left)
+ elif isinstance(op, ast.Eq):
+ equalities.append(left - right)
+ elif isinstance(op, ast.GtE):
+ inequalities.append(left - right)
+ elif isinstance(op, ast.Gt):
+ inequalities.append(left - right - 1)
+ else:
+ break
+ left = right
+ else:
+ return equalities, inequalities
+ raise SyntaxError('invalid syntax')
+
+ @classmethod
+ def fromstring(cls, string):
+ string = string.strip()
+ string = re.sub(r'^\{\s*|\s*\}$', '', string)
+ string = re.sub(r'([^<=>])=([^<=>])', r'\1==\2', string)
+ string = re.sub(r'(\d+|\))\s*([^\W\d_]\w*|\()', r'\1*\2', string)
+ tokens = re.split(r',|;|and|&&|/\\|∧', string, flags=re.I)
+ tokens = ['({})'.format(token) for token in tokens]
+ string = ' & '.join(tokens)
+ tree = ast.parse(string, 'eval')
+ equalities, inequalities = cls._fromast(tree)
+ return cls(equalities, inequalities)
+
@property
def equalities(self):
- yield from self._equalities
+ return self._equalities
@property
def inequalities(self):
- yield from self._inequalities
+ return self._inequalities
+ @property
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)
- yield from 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
- raise NotImplementedError
+ return not self.is_empty()
def __contains__(self, value):
# is the value in the polyhedron?
raise NotImplementedError
def __eq__(self, other):
- raise NotImplementedError
+ # works correctly when symbols is not passed
+ # should be equal if values are the same even if symbols are different
+ bset = self._toisl()
+ other = other._toisl()
+ return bool(libisl.isl_basic_set_plain_is_equal(bset, other))
def isempty(self):
- return self == empty
+ bset = self._toisl()
+ return bool(libisl.isl_basic_set_is_empty(bset))
def isuniverse(self):
- return self == universe
+ bset = self._toisl()
+ return bool(libisl.isl_basic_set_is_universe(bset))
def isdisjoint(self, other):
# return true if the polyhedron has no elements in common with other
- raise NotImplementedError
+ #symbols = self._symbolunion(other)
+ bset = self._toisl()
+ other = other._toisl()
+ return bool(libisl.isl_set_is_disjoint(bset, other))
def issubset(self, other):
- raise NotImplementedError
+ # check if self(bset) is a subset of other
+ symbols = self._symbolunion(other)
+ bset = self._toisl(symbols)
+ other = other._toisl(symbols)
+ return bool(libisl.isl_set_is_strict_subset(other, bset))
def __le__(self, other):
return self.issubset(other)
def __lt__(self, other):
- raise NotImplementedError
+ symbols = self._symbolunion(other)
+ bset = self._toisl(symbols)
+ other = other._toisl(symbols)
+ return bool(libisl.isl_set_is_strict_subset(other, bset))
def issuperset(self, other):
# test whether every element in other is in the polyhedron
return self.issuperset(other)
def __gt__(self, other):
+ symbols = self._symbolunion(other)
+ bset = self._toisl(symbols)
+ other = other._toisl(symbols)
+ bool(libisl.isl_set_is_strict_subset(other, bset))
raise NotImplementedError
def union(self, *others):
def __and__(self, other):
return self.intersection(other)
- def difference(self, *others):
- # return a new polyhedron with elements in the polyhedron that are not
- # in the others
- raise NotImplementedError
+ def difference(self, other):
+ # return a new polyhedron with elements in the polyhedron that are not in the other
+ symbols = self._symbolunion(other)
+ bset = self._toisl(symbols)
+ other = other._toisl(symbols)
+ difference = libisl.isl_set_subtract(bset, other)
+ return difference
def __sub__(self, other):
return self.difference(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):
- equalities = list(self.equalities)
- inequalities = list(self.inequalities)
- return '{}(equalities={!r}, inequalities={!r})' \
- ''.format(self.__class__.__name__, equalities, inequalities)
+ if self.isempty():
+ return 'Empty'
+ elif self.isuniverse():
+ return 'Universe'
+ else:
+ equalities = list(self.equalities)
+ inequalities = list(self.inequalities)
+ return '{}(equalities={!r}, inequalities={!r})' \
+ ''.format(self.__class__.__name__, equalities, inequalities)
@classmethod
- def fromstring(cls, string):
- raise NotImplementedError
+ def _fromsympy(cls, expr):
+ import sympy
+ equalities = []
+ inequalities = []
+ if expr.func == sympy.And:
+ for arg in expr.args:
+ arg_eqs, arg_ins = cls._fromsympy(arg)
+ equalities.extend(arg_eqs)
+ inequalities.extend(arg_ins)
+ elif expr.func == sympy.Eq:
+ expr = Expression.fromsympy(expr.args[0] - expr.args[1])
+ equalities.append(expr)
+ else:
+ if expr.func == sympy.Lt:
+ expr = Expression.fromsympy(expr.args[1] - expr.args[0] - 1)
+ elif expr.func == sympy.Le:
+ expr = Expression.fromsympy(expr.args[1] - expr.args[0])
+ elif expr.func == sympy.Ge:
+ expr = Expression.fromsympy(expr.args[0] - expr.args[1])
+ elif expr.func == sympy.Gt:
+ expr = Expression.fromsympy(expr.args[0] - expr.args[1] - 1)
+ else:
+ raise ValueError('non-polyhedral expression: {!r}'.format(expr))
+ inequalities.append(expr)
+ return equalities, inequalities
+ @classmethod
+ def fromsympy(cls, expr):
+ import sympy
+ equalities, inequalities = cls._fromsympy(expr)
+ return cls(equalities, inequalities)
-empty = le(1, 0)
+ def tosympy(self):
+ import sympy
+ constraints = []
+ for equality in self.equalities:
+ constraints.append(sympy.Eq(equality.tosympy(), 0))
+ for inequality in self.inequalities:
+ constraints.append(sympy.Ge(inequality.tosympy(), 0))
+ return sympy.And(*constraints)
+
+ def _symbolunion(self, *others):
+ symbols = set(self.symbols)
+ for other in others:
+ symbols.update(other.symbols)
+ return sorted(symbols)
+
+ def _toisl(self, symbols=None):
+ if symbols is None:
+ symbols = self.symbols
+ dimension = len(symbols)
+ space = libisl.isl_space_set_alloc(_main_ctx, 0, dimension)
+ bset = libisl.isl_basic_set_universe(libisl.isl_space_copy(space))
+ ls = libisl.isl_local_space_from_space(space)
+ for equality in self.equalities:
+ ceq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(ls))
+ for symbol, coefficient in equality.coefficients():
+ val = str(coefficient).encode()
+ val = libisl.isl_val_read_from_str(_main_ctx, val)
+ dim = symbols.index(symbol)
+ ceq = libisl.isl_constraint_set_coefficient_val(ceq, libisl.isl_dim_set, dim, val)
+ if equality.constant != 0:
+ val = str(equality.constant).encode()
+ val = libisl.isl_val_read_from_str(_main_ctx, val)
+ ceq = libisl.isl_constraint_set_constant_val(ceq, val)
+ bset = libisl.isl_basic_set_add_constraint(bset, ceq)
+ for inequality in self.inequalities:
+ cin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(ls))
+ for symbol, coefficient in inequality.coefficients():
+ val = str(coefficient).encode()
+ val = libisl.isl_val_read_from_str(_main_ctx, val)
+ dim = symbols.index(symbol)
+ cin = libisl.isl_constraint_set_coefficient_val(cin, libisl.isl_dim_set, dim, val)
+ if inequality.constant != 0:
+ val = str(inequality.constant).encode()
+ val = libisl.isl_val_read_from_str(_main_ctx, val)
+ cin = libisl.isl_constraint_set_constant_val(cin, val)
+ bset = libisl.isl_basic_set_add_constraint(bset, cin)
+ bset = isl.BasicSet(bset)
+ return bset
-universe = Polyhedron()
+ @classmethod
+ def _fromisl(cls, bset, symbols):
+ 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:
+ { [i0, i1] : 2i1 >= -2 - i0 } '''
+
+Empty = eq(0,1)
+
+Universe = Polyhedron()
+
+
+if __name__ == '__main__':
+ #p = Polyhedron('2a + 2b + 1 == 0') # empty
+ p = Polyhedron('3x + 2y + 3 == 0, y == 0') # not empty
+ ip = p._toisl()
+ print(ip)
+ print(ip.constraints())
projects / linpy.git / blobdiff