from fractions import Fraction, gcd
-from pypol import isl
-from pypol.isl import libisl
+from . import isl
+from .isl import libisl
__all__ = [
This class implements linear expressions.
"""
+ __slots__ = (
+ '_coefficients',
+ '_constant',
+ '_symbols',
+ '_dimension',
+ )
+
def __new__(cls, coefficients=None, constant=0):
if isinstance(coefficients, str):
if constant:
@classmethod
def _fromast(cls, node):
- if isinstance(node, ast.Module):
- assert len(node.body) == 1
+ 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)
return Symbol(node.id)
elif isinstance(node, ast.Num):
return Constant(node.n)
- elif isinstance(node, ast.UnaryOp):
- if isinstance(node.op, ast.USub):
- return -cls._fromast(node.operand)
+ 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)
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.name
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 symbols(names):
if isinstance(names, str):
names = names.replace(',', ' ').split()
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:
return self
@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*|\()', r'\1*\2', string)
- equalities = []
- inequalities = []
- for cstr in re.split(r',|;|and|&&|/\\|∧', string, flags=re.I):
- tree = ast.parse(cstr.strip(), 'eval')
- if not isinstance(tree, ast.Module) or len(tree.body) != 1:
- raise SyntaxError('invalid syntax')
- node = tree.body[0]
- if not isinstance(node, ast.Expr):
- raise SyntaxError('invalid syntax')
- node = node.value
- if not isinstance(node, ast.Compare):
- raise SyntaxError('invalid syntax')
+ def _fromast(cls, node):
+ if isinstance(node, ast.Module) and len(node.body) == 1:
+ return cls._fromast(node.body[0])
+ elif isinstance(node, ast.Expr):
+ return cls._fromast(node.value)
+ elif isinstance(node, ast.BinOp) and isinstance(node.op, ast.BitAnd):
+ equalities1, inequalities1 = cls._fromast(node.left)
+ equalities2, inequalities2 = cls._fromast(node.right)
+ equalities = equalities1 + equalities2
+ inequalities = inequalities1 + inequalities2
+ return equalities, inequalities
+ elif isinstance(node, ast.Compare):
+ equalities = []
+ inequalities = []
left = Expression._fromast(node.left)
for i in range(len(node.ops)):
op = node.ops[i]
elif isinstance(op, ast.Gt):
inequalities.append(left - right - 1)
else:
- raise SyntaxError('invalid syntax')
+ break
left = right
+ else:
+ return equalities, inequalities
+ raise SyntaxError('invalid syntax')
+
+ @classmethod
+ def fromstring(cls, string):
+ string = string.strip()
+ string = re.sub(r'^\{\s*|\s*\}$', '', string)
+ string = re.sub(r'([^<=>])=([^<=>])', r'\1==\2', string)
+ string = re.sub(r'(\d+|\))\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
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):
if self.isempty():
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)
+ 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)
{ [i0, i1] : 2i1 >= -2 - i0 } '''
Empty = eq(0,1)
+
Universe = Polyhedron()
+
if __name__ == '__main__':
- p1 = Polyhedron('2a + 2b + 1 == 0') # empty
- print(p1._toisl())
- p2 = Polyhedron('3x + 2y + 3 == 0') # not empty
- print(p2._toisl())
+ #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