X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/blobdiff_plain/a157f7c947533f4be375e55f78adfa3dae7eeef7..9e103619134c8839d143951c5b814bab500fcdcf:/pypol/linear.py diff --git a/pypol/linear.py b/pypol/linear.py index a562a3f..e6d442e 100644 --- a/pypol/linear.py +++ b/pypol/linear.py @@ -1,19 +1,19 @@ -import ctypes, ctypes.util +import ast import functools import numbers +import re from fractions import Fraction, gcd -from . import isl -from .isl import libisl +from pypol import isl +from pypol.isl import libisl __all__ = [ - 'Expression', - 'constant', 'symbol', 'symbols', + 'Expression', 'Constant', 'Symbol', 'symbols', 'eq', 'le', 'lt', 'ge', 'gt', 'Polyhedron', - 'empty', 'universe' + 'Empty', 'Universe' ] @@ -23,7 +23,7 @@ def _polymorphic_method(func): 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 @@ -34,7 +34,7 @@ def _polymorphic_operator(func): @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) @@ -50,32 +50,82 @@ 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): return self._symbols @@ -85,10 +135,10 @@ class Expression: 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: @@ -105,30 +155,18 @@ class Expression: return self._constant def isconstant(self): - return len(self._coefficients) == 0 + return False def values(self): 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 - 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 @@ -139,7 +177,7 @@ class Expression: @_polymorphic_method def __add__(self, other): coefficients = dict(self.coefficients()) - for symbol, coefficient in other.coefficients: + for symbol, coefficient in other.coefficients(): if symbol in coefficients: coefficients[symbol] += coefficient else: @@ -152,7 +190,7 @@ class Expression: @_polymorphic_method def __sub__(self, other): coefficients = dict(self.coefficients()) - for symbol, coefficient in other.coefficients: + for symbol, coefficient in other.coefficients(): if symbol in coefficients: coefficients[symbol] -= coefficient else: @@ -205,8 +243,8 @@ class Expression: def __str__(self): string = '' 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 @@ -255,10 +293,6 @@ class Expression: string += '}}, {!r})'.format(self.constant) return string - @classmethod - def fromstring(cls, string): - raise NotImplementedError - @_polymorphic_method def __eq__(self, other): # "normal" equality @@ -268,7 +302,7 @@ class Expression: self.constant == other.constant def __hash__(self): - return hash((self._coefficients, self._constant)) + return hash((tuple(sorted(self._coefficients.items())), self._constant)) def _toint(self): lcm = functools.reduce(lambda a, b: a*b // gcd(a, b), @@ -296,42 +330,91 @@ class Expression: return Polyhedron(inequalities=[(self - other)._toint() - 1]) -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)) +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 __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) + +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 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._name) 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: @@ -339,6 +422,13 @@ 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: @@ -370,6 +460,55 @@ class Polyhedron: 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|&&|/\\|â§', 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): return self._equalities @@ -378,9 +517,6 @@ class Polyhedron: def inequalities(self): return self._inequalities - def isempty(self): - return bool(libisl.isl_basic_set_is_empty(self._bset)) - @property def constraints(self): return self._constraints @@ -401,26 +537,42 @@ class 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 @@ -430,6 +582,10 @@ class 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): @@ -455,10 +611,13 @@ class Polyhedron: 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) @@ -472,14 +631,15 @@ class Polyhedron: 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) - - @classmethod - def fromstring(cls, string): - raise NotImplementedError + 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) def _symbolunion(self, *others): symbols = set(self.symbols) @@ -487,67 +647,59 @@ class Polyhedron: 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 - 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 from_isl(cls, 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 }' ''' + def _fromisl(cls, bset, symbols): raise NotImplementedError equalities = ... inequalities = ... return cls(equalities, inequalities) - #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 + '''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) -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._to_isl() - print(bs) + p1 = Polyhedron('2a + 2b + 1 == 0') # empty + print(p1._toisl()) + p2 = Polyhedron('3x + 2y + 3 == 0') # not empty + print(p2._toisl())