--- /dev/null
+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
+
+
+__all__ = [
+ 'Polyhedron',
+ 'Lt', 'Le', 'Eq', 'Ne', 'Ge', 'Gt',
+ 'Empty', 'Universe',
+]
+
+
+class Polyhedron(Domain):
+
+ __slots__ = (
+ '_equalities',
+ '_inequalities',
+ '_constraints',
+ '_symbols',
+ '_dimension',
+ )
+
+ def __new__(cls, equalities=None, inequalities=None):
+ if isinstance(equalities, str):
+ if inequalities is not None:
+ raise TypeError('too many arguments')
+ return cls.fromstring(equalities)
+ elif isinstance(equalities, GeometricObject):
+ if inequalities is not None:
+ raise TypeError('too many arguments')
+ return equalities.aspolyhedron()
+ if equalities is None:
+ equalities = []
+ else:
+ for i, equality in enumerate(equalities):
+ if not isinstance(equality, Expression):
+ raise TypeError('equalities must be linear expressions')
+ equalities[i] = equality.scaleint()
+ if inequalities is None:
+ inequalities = []
+ else:
+ for i, inequality in enumerate(inequalities):
+ if not isinstance(inequality, Expression):
+ raise TypeError('inequalities must be linear expressions')
+ inequalities[i] = inequality.scaleint()
+ symbols = cls._xsymbols(equalities + inequalities)
+ islbset = cls._toislbasicset(equalities, inequalities, symbols)
+ return cls._fromislbasicset(islbset, symbols)
+
+ @property
+ def equalities(self):
+ return self._equalities
+
+ @property
+ def inequalities(self):
+ return self._inequalities
+
+ @property
+ def constraints(self):
+ return self._constraints
+
+ @property
+ def polyhedra(self):
+ return self,
+
+ def disjoint(self):
+ """
+ Return this set as disjoint.
+ """
+ return self
+
+ def isuniverse(self):
+ """
+ Return true if this 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 aspolyhedron(self):
+ """
+ Return polyhedral hull of this 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):
+ 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):
+ if libisl.isl_basic_set_is_empty(islbset):
+ return Empty
+ if libisl.isl_basic_set_is_universe(islbset):
+ return Universe
+ islconstraints = islhelper.isl_basic_set_constraints(islbset)
+ equalities = []
+ inequalities = []
+ for islconstraint in islconstraints:
+ constant = libisl.isl_constraint_get_constant_val(islconstraint)
+ constant = islhelper.isl_val_to_int(constant)
+ coefficients = {}
+ for index, symbol in enumerate(symbols):
+ coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint,
+ libisl.isl_dim_set, index)
+ coefficient = islhelper.isl_val_to_int(coefficient)
+ if coefficient != 0:
+ coefficients[symbol] = coefficient
+ expression = Expression(coefficients, constant)
+ if libisl.isl_constraint_is_equality(islconstraint):
+ equalities.append(expression)
+ else:
+ inequalities.append(expression)
+ libisl.isl_basic_set_free(islbset)
+ self = object().__new__(Polyhedron)
+ self._equalities = tuple(equalities)
+ self._inequalities = tuple(inequalities)
+ self._constraints = tuple(equalities + inequalities)
+ self._symbols = cls._xsymbols(self._constraints)
+ self._dimension = len(self._symbols)
+ return self
+
+ @classmethod
+ def _toislbasicset(cls, equalities, inequalities, symbols):
+ dimension = len(symbols)
+ indices = {symbol: index for index, symbol in enumerate(symbols)}
+ islsp = libisl.isl_space_set_alloc(mainctx, 0, dimension)
+ islbset = libisl.isl_basic_set_universe(libisl.isl_space_copy(islsp))
+ islls = libisl.isl_local_space_from_space(islsp)
+ for equality in equalities:
+ isleq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(islls))
+ for symbol, coefficient in equality.coefficients():
+ islval = str(coefficient).encode()
+ islval = libisl.isl_val_read_from_str(mainctx, islval)
+ index = indices[symbol]
+ isleq = libisl.isl_constraint_set_coefficient_val(isleq,
+ libisl.isl_dim_set, index, islval)
+ if equality.constant != 0:
+ islval = str(equality.constant).encode()
+ islval = libisl.isl_val_read_from_str(mainctx, islval)
+ isleq = libisl.isl_constraint_set_constant_val(isleq, islval)
+ islbset = libisl.isl_basic_set_add_constraint(islbset, isleq)
+ for inequality in inequalities:
+ islin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(islls))
+ for symbol, coefficient in inequality.coefficients():
+ islval = str(coefficient).encode()
+ islval = libisl.isl_val_read_from_str(mainctx, islval)
+ index = indices[symbol]
+ islin = libisl.isl_constraint_set_coefficient_val(islin,
+ libisl.isl_dim_set, index, islval)
+ if inequality.constant != 0:
+ islval = str(inequality.constant).encode()
+ islval = libisl.isl_val_read_from_str(mainctx, islval)
+ islin = libisl.isl_constraint_set_constant_val(islin, islval)
+ islbset = libisl.isl_basic_set_add_constraint(islbset, islin)
+ return islbset
+
+ @classmethod
+ def fromstring(cls, string):
+ domain = Domain.fromstring(string)
+ if not isinstance(domain, Polyhedron):
+ raise ValueError('non-polyhedral expression: {!r}'.format(string))
+ return domain
+
+ def __repr__(self):
+ 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))
+
+ 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):
+ domain = Domain.fromsympy(expr)
+ if not isinstance(domain, Polyhedron):
+ raise ValueError('non-polyhedral expression: {!r}'.format(expr))
+ return domain
+
+ 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)
+
+
+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 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):
+ """
+ Return true if the first set is less than the second.
+ """
+ return Polyhedron([], [right - left - 1])
+
+@_polymorphic
+def Le(left, right):
+ """
+ Return true the first set is less than or equal to the second.
+ """
+ return Polyhedron([], [right - left])
+
+@_polymorphic
+def Eq(left, right):
+ """
+ Return true if the sets are equal.
+ """
+ return Polyhedron([left - right], [])
+
+@_polymorphic
+def Ne(left, right):
+ """
+ Return true if the sets are NOT equal.
+ """
+ return ~Eq(left, right)
+
+@_polymorphic
+def Gt(left, right):
+ """
+ Return true if the first set is greater than the second set.
+ """
+ return Polyhedron([], [left - right - 1])
+
+@_polymorphic
+def Ge(left, right):
+ """
+ Return true if the first set is greater than or equal the second set.
+ """
+ return Polyhedron([], [left - right])
projects / linpy.git / blobdiff