+++ /dev/null
-# Copyright 2014 MINES ParisTech
-#
-# This file is part of Linpy.
-#
-# Linpy is free software: you can redistribute it and/or modify
-# it under the terms of the GNU General Public License as published by
-# the Free Software Foundation, either version 3 of the License, or
-# (at your option) any later version.
-#
-# Linpy is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-# GNU General Public License for more details.
-#
-# You should have received a copy of the GNU General Public License
-# along with Linpy. If not, see <http://www.gnu.org/licenses/>.
-
-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 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
- def polyhedra(self):
- 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 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)
- 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):
- """
- 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:
- 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):
- """
- 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])
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