X-Git-Url: https://svn.cri.ensmp.fr/git/linpy.git/blobdiff_plain/d06ab92943ec2e10a2bd798ca7c1b5cea395bf34..2de96003a48ae1ed91c853f38c72374a832824de:/pypol/polyhedra.py?ds=sidebyside diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py index fa2a5c6..b0b5d0e 100644 --- a/pypol/polyhedra.py +++ b/pypol/polyhedra.py @@ -1,9 +1,11 @@ import functools +import math import numbers from . import islhelper from .islhelper import mainctx, libisl +from .geometry import GeometricObject, Point from .linexprs import Expression, Rational from .domains import Domain @@ -30,14 +32,10 @@ class Polyhedron(Domain): if inequalities is not None: raise TypeError('too many arguments') return cls.fromstring(equalities) - elif isinstance(equalities, Polyhedron): + elif isinstance(equalities, GeometricObject): if inequalities is not None: raise TypeError('too many arguments') - return equalities - elif isinstance(equalities, Domain): - if inequalities is not None: - raise TypeError('too many arguments') - return equalities.polyhedral_hull() + return equalities.aspolyhedron() if equalities is None: equalities = [] else: @@ -58,14 +56,23 @@ class Polyhedron(Domain): @property def equalities(self): + """ + Return a list of the equalities in a set. + """ return self._equalities @property def inequalities(self): + """ + Return a list of the inequalities in a set. + """ return self._inequalities @property def constraints(self): + """ + Return ta list of the constraints of a set. + """ return self._constraints @property @@ -73,18 +80,76 @@ class Polyhedron(Domain): return self, def disjoint(self): + """ + Return a set as disjoint. + """ return self def isuniverse(self): + """ + Return true if a set is the Universe set. + """ islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols) universe = bool(libisl.isl_basic_set_is_universe(islbset)) libisl.isl_basic_set_free(islbset) return universe - def polyhedral_hull(self): + def aspolyhedron(self): + """ + Return polyhedral hull of a set. + """ return self + def __contains__(self, point): + if not isinstance(point, Point): + raise TypeError('point must be a Point instance') + if self.symbols != point.symbols: + raise ValueError('arguments must belong to the same space') + for equality in self.equalities: + if equality.subs(point.coordinates()) != 0: + return False + for inequality in self.inequalities: + if inequality.subs(point.coordinates()) < 0: + return False + return True + + def subs(self, symbol, expression=None): + """ + Subsitute the given value into an expression and return the resulting + expression. + """ + equalities = [equality.subs(symbol, expression) + for equality in self.equalities] + inequalities = [inequality.subs(symbol, expression) + for inequality in self.inequalities] + return Polyhedron(equalities, inequalities) + + def _asinequalities(self): + inequalities = list(self.equalities) + inequalities.extend([-expression for expression in self.equalities]) + inequalities.extend(self.inequalities) + return inequalities + + def widen(self, other): + if not isinstance(other, Polyhedron): + raise ValueError('argument must be a Polyhedron instance') + inequalities1 = self._asinequalities() + inequalities2 = other._asinequalities() + inequalities = [] + for inequality1 in inequalities1: + if other <= Polyhedron(inequalities=[inequality1]): + inequalities.append(inequality1) + for inequality2 in inequalities2: + for i in range(len(inequalities1)): + inequalities3 = inequalities1[:i] + inequalities[i + 1:] + inequalities3.append(inequality2) + polyhedron3 = Polyhedron(inequalities=inequalities3) + if self == polyhedron3: + inequalities.append(inequality2) + break + return Polyhedron(inequalities=inequalities) + @classmethod def _fromislbasicset(cls, islbset, symbols): islconstraints = islhelper.isl_basic_set_constraints(islbset) @@ -157,55 +222,39 @@ class Polyhedron(Domain): return domain def __repr__(self): - if self.isempty(): - return 'Empty' - elif self.isuniverse(): - return 'Universe' + strings = [] + for equality in self.equalities: + strings.append('Eq({}, 0)'.format(equality)) + for inequality in self.inequalities: + strings.append('Ge({}, 0)'.format(inequality)) + if len(strings) == 1: + return strings[0] else: - strings = [] - for equality in self.equalities: - strings.append('Eq({}, 0)'.format(equality)) - for inequality in self.inequalities: - strings.append('Ge({}, 0)'.format(inequality)) - if len(strings) == 1: - return strings[0] - else: - return 'And({})'.format(', '.join(strings)) + return 'And({})'.format(', '.join(strings)) - @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 + + def _repr_latex_(self): + strings = [] + for equality in self.equalities: + strings.append('{} = 0'.format(equality._repr_latex_().strip('$'))) + for inequality in self.inequalities: + strings.append('{} \\ge 0'.format(inequality._repr_latex_().strip('$'))) + return '$${}$$'.format(' \\wedge '.join(strings)) @classmethod def fromsympy(cls, expr): - import sympy - equalities, inequalities = cls._fromsympy(expr) - return cls(equalities, inequalities) + """ + Convert a sympy object to an expression. + """ + domain = Domain.fromsympy(expr) + if not isinstance(domain, Polyhedron): + raise ValueError('non-polyhedral expression: {!r}'.format(expr)) + return domain def tosympy(self): + """ + Return an expression as a sympy object. + """ import sympy constraints = [] for equality in self.equalities: @@ -214,48 +263,112 @@ class Polyhedron(Domain): constraints.append(sympy.Ge(inequality.tosympy(), 0)) return sympy.And(*constraints) +class EmptyType(Polyhedron): + + __slots__ = Polyhedron.__slots__ + + def __new__(cls): + self = object().__new__(cls) + self._equalities = (Rational(1),) + self._inequalities = () + self._constraints = self._equalities + self._symbols = () + self._dimension = 0 + return self + + def widen(self, other): + if not isinstance(other, Polyhedron): + raise ValueError('argument must be a Polyhedron instance') + return other + + def __repr__(self): + return 'Empty' + + def _repr_latex_(self): + return '$$\\emptyset$$' + +Empty = EmptyType() + + +class UniverseType(Polyhedron): + + __slots__ = Polyhedron.__slots__ + + def __new__(cls): + self = object().__new__(cls) + self._equalities = () + self._inequalities = () + self._constraints = () + self._symbols = () + self._dimension = () + return self + + def __repr__(self): + return 'Universe' + + def _repr_latex_(self): + return '$$\\Omega$$' + +Universe = UniverseType() + def _polymorphic(func): @functools.wraps(func) def wrapper(left, right): - if isinstance(left, numbers.Rational): - left = Rational(left) - elif not isinstance(left, Expression): - raise TypeError('left must be a a rational number ' - 'or a linear expression') - if isinstance(right, numbers.Rational): - right = Rational(right) - elif not isinstance(right, Expression): - raise TypeError('right must be a a rational number ' - 'or a linear expression') + if not isinstance(left, Expression): + if isinstance(left, numbers.Rational): + left = Rational(left) + else: + raise TypeError('left must be a a rational number ' + 'or a linear expression') + if not isinstance(right, Expression): + if isinstance(right, numbers.Rational): + right = Rational(right) + else: + raise TypeError('right must be a a rational number ' + 'or a linear expression') return func(left, right) return wrapper @_polymorphic def Lt(left, right): + """ + Assert first set is less than the second set. + """ return Polyhedron([], [right - left - 1]) @_polymorphic def Le(left, right): + """ + Assert first set is less than or equal to the second set. + """ return Polyhedron([], [right - left]) @_polymorphic def Eq(left, right): + """ + Assert first set is equal to the second set. + """ return Polyhedron([left - right], []) @_polymorphic def Ne(left, right): + """ + Assert first set is not equal to the second set. + """ return ~Eq(left, right) @_polymorphic def Gt(left, right): + """ + Assert first set is greater than the second set. + """ return Polyhedron([], [left - right - 1]) @_polymorphic def Ge(left, right): + """ + Assert first set is greater than or equal to the second set. + """ return Polyhedron([], [left - right]) - -Empty = Eq(1, 0) - -Universe = Polyhedron([])