-import ctypes, ctypes.util
+import ast
import functools
import numbers
+import re
from fractions import Fraction, gcd
'Expression', 'Constant', 'Symbol', 'symbols',
'eq', 'le', 'lt', 'ge', 'gt',
'Polyhedron',
- 'empty', 'universe'
+ 'Empty', 'Universe'
]
This class implements linear expressions.
"""
+ __slots__ = (
+ '_coefficients',
+ '_constant',
+ '_symbols',
+ '_dimension',
+ )
+
def __new__(cls, coefficients=None, constant=0):
if isinstance(coefficients, str):
if constant:
self._coefficients = {}
for symbol, coefficient in coefficients:
if isinstance(symbol, Symbol):
- symbol = str(symbol)
+ symbol = symbol.name
elif not isinstance(symbol, str):
raise TypeError('symbols must be strings or Symbol instances')
if isinstance(coefficient, Constant):
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):
- raise NotImplementedError
+ 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 self.coefficient(symbol)
yield self.constant
- @property
- def symbol(self):
- raise ValueError('not a symbol: {}'.format(self))
-
def issymbol(self):
return False
return '({})'.format(string)
def __repr__(self):
- string = '{}({{'.format(self.__class__.__name__)
- 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
+ return '{}({!r})'.format(self.__class__.__name__, str(self))
@_polymorphic_method
def __eq__(self, other):
def __gt__(self, other):
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):
return bool(self.constant)
def __repr__(self):
- return '{}({!r})'.format(self.__class__.__name__, self._constant)
+ 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.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._symbol = name
+ self._name = name
self._dimension = 1
return self
@property
- def symbol(self):
- return self._symbol
+ def name(self):
+ return self._name
def issymbol(self):
return True
def __repr__(self):
- return '{}({!r})'.format(self.__class__.__name__, self._symbol)
+ 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 symbols(names):
if isinstance(names, str):
@_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:
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):
- raise NotImplementedError
+ 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):
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):
bset = self._toisl()
return bool(libisl.isl_basic_set_is_empty(bset))
def isuniverse(self):
- raise NotImplementedError
+ 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)
constraints.append('{} == 0'.format(constraint))
for constraint in self.inequalities:
constraints.append('{} >= 0'.format(constraint))
- return '{{{}}}'.format(', '.join(constraints))
+ 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:
+ return '{}({!r})'.format(self.__class__.__name__, str(self))
+
+ @classmethod
+ 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)
+
+ 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)
def _toisl(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)
+ 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)
- 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, libisl.isl_dim_set, iden, num) #use 3 for type isl_dim_set
+ 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)
- 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, libisl.isl_dim_set, iden, num) #use 3 for type isl_dim_set
+ 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
@classmethod
- def _fromisl(cls, bset):
+ def _fromisl(cls, bset, symbols):
raise NotImplementedError
equalities = ...
inequalities = ...
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
+ { [i0, i1] : 2i1 >= -2 - i0 } '''
+
+Empty = eq(0,1)
-empty = None #eq(0,1)
-universe = None #Polyhedron()
+Universe = 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._toisl()
- print(bs)
- print('empty ?', p.isempty())
- print('empty ?', eq(0, 1).isempty())
+ #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