from fractions import Fraction
from . import islhelper
-from .islhelper import mainctx, libisl
-from .linexprs import LinExpr, Symbol, Rational
from .geometry import GeometricObject, Point, Vector
+from .islhelper import libisl
+from .linexprs import LinExpr, Symbol
__all__ = [
+ 'And',
'Domain',
- 'And', 'Or', 'Not',
+ 'Not',
+ 'Or',
]
class Domain(GeometricObject):
"""
A domain is a union of polyhedra. Unlike polyhedra, domains allow exact
- computation of union and complementary operations.
+ computation of union, subtraction and complementary operations.
A domain with a unique polyhedron is automatically subclassed as a
Polyhedron instance.
"""
Return a domain from a sequence of polyhedra.
- >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
- >>> square2 = Polyhedron('2 <= x <= 4, 2 <= y <= 4')
- >>> dom = Domain([square, square2])
+ >>> square1 = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
+ >>> square2 = Polyhedron('1 <= x <= 3, 1 <= y <= 3')
+ >>> dom = Domain(square1, square2)
+ >>> dom
+ Or(And(x <= 2, 0 <= x, y <= 2, 0 <= y),
+ And(x <= 3, 1 <= x, y <= 3, 1 <= y))
It is also possible to build domains from polyhedra using arithmetic
- operators Domain.__and__(), Domain.__or__() or functions And() and Or(),
- using one of the following instructions:
+ operators Domain.__or__(), Domain.__invert__() or functions Or() and
+ Not(), using one of the following instructions:
- >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
- >>> square2 = Polyhedron('2 <= x <= 4, 2 <= y <= 4')
- >>> dom = square | square2
- >>> dom = Or(square, square2)
+ >>> dom = square1 | square2
+ >>> dom = Or(square1, square2)
Alternatively, a domain can be built from a string:
- >>> dom = Domain('0 <= x <= 2, 0 <= y <= 2; 2 <= x <= 4, 2 <= y <= 4')
+ >>> dom = Domain('0 <= x <= 2, 0 <= y <= 2; 1 <= x <= 3, 1 <= y <= 3')
Finally, a domain can be built from a GeometricObject instance, calling
the GeometricObject.asdomain() method.
return argument.aspolyhedron()
else:
raise TypeError('argument must be a string '
- 'or a GeometricObject instance')
+ 'or a GeometricObject instance')
else:
for polyhedron in polyhedra:
if not isinstance(polyhedron, Polyhedron):
Return an equivalent domain, whose polyhedra are disjoint.
"""
islset = self._toislset(self.polyhedra, self.symbols)
- islset = libisl.isl_set_make_disjoint(mainctx, islset)
+ islset = libisl.isl_set_make_disjoint(islset)
return self._fromislset(islset, self.symbols)
def coalesce(self):
if symbol in symbols:
n += 1
elif n > 0:
- islset = libisl.isl_set_project_out(islset,
- libisl.isl_dim_set, index + 1, n)
+ islset = libisl.isl_set_project_out(
+ islset, libisl.isl_dim_set, index + 1, n)
n = 0
if n > 0:
- islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, 0, n)
+ islset = libisl.isl_set_project_out(
+ islset, libisl.isl_dim_set, 0, n)
symbols = [symbol for symbol in self.symbols if symbol not in symbols]
return Domain._fromislset(islset, symbols)
raise ValueError('domain must be non-empty')
point = {}
for index, symbol in enumerate(self.symbols):
- coordinate = libisl.isl_point_get_coordinate_val(islpoint,
- libisl.isl_dim_set, index)
+ coordinate = libisl.isl_point_get_coordinate_val(
+ islpoint, libisl.isl_dim_set, index)
coordinate = islhelper.isl_val_to_int(coordinate)
point[symbol] = coordinate
libisl.isl_point_free(islpoint)
Return the intersection of two or more domains as a new domain. As an
alternative, function And() can be used.
"""
- if len(others) == 0:
- return self
- symbols = self._xsymbols((self,) + others)
- islset1 = self._toislset(self.polyhedra, symbols)
+ result = self
for other in others:
- islset2 = other._toislset(other.polyhedra, symbols)
- islset1 = libisl.isl_set_intersect(islset1, islset2)
- return self._fromislset(islset1, symbols)
+ result &= other
+ return result
def __and__(self, other):
- return self.intersection(other)
+ if isinstance(other, Domain):
+ symbols = self._xsymbols([self, other])
+ islset1 = self._toislset(self.polyhedra, symbols)
+ islset2 = other._toislset(other.polyhedra, symbols)
+ islset = libisl.isl_set_intersect(islset1, islset2)
+ return self._fromislset(islset, symbols)
+ return NotImplemented
__and__.__doc__ = intersection.__doc__
def union(self, *others):
Return the union of two or more domains as a new domain. As an
alternative, function Or() can be used.
"""
- if len(others) == 0:
- return self
- symbols = self._xsymbols((self,) + others)
- islset1 = self._toislset(self.polyhedra, symbols)
+ result = self
for other in others:
- islset2 = other._toislset(other.polyhedra, symbols)
- islset1 = libisl.isl_set_union(islset1, islset2)
- return self._fromislset(islset1, symbols)
+ result |= other
+ return result
def __or__(self, other):
- return self.union(other)
+ if isinstance(other, Domain):
+ symbols = self._xsymbols([self, other])
+ islset1 = self._toislset(self.polyhedra, symbols)
+ islset2 = other._toislset(other.polyhedra, symbols)
+ islset = libisl.isl_set_union(islset1, islset2)
+ return self._fromislset(islset, symbols)
+ return NotImplemented
__or__.__doc__ = union.__doc__
def __add__(self, other):
- return self.union(other)
+ return self | other
__add__.__doc__ = union.__doc__
def difference(self, other):
"""
Return the difference of two domains as a new domain.
"""
- symbols = self._xsymbols([self, other])
- islset1 = self._toislset(self.polyhedra, symbols)
- islset2 = other._toislset(other.polyhedra, symbols)
- islset = libisl.isl_set_subtract(islset1, islset2)
- return self._fromislset(islset, symbols)
+ return self - other
def __sub__(self, other):
- return self.difference(other)
+ if isinstance(other, Domain):
+ symbols = self._xsymbols([self, other])
+ islset1 = self._toislset(self.polyhedra, symbols)
+ islset2 = other._toislset(other.polyhedra, symbols)
+ islset = libisl.isl_set_subtract(islset1, islset2)
+ return self._fromislset(islset, symbols)
+ return NotImplemented
__sub__.__doc__ = difference.__doc__
def lexmin(self):
islset = libisl.isl_set_lexmax(islset)
return self._fromislset(islset, self.symbols)
- _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
+ if islhelper.isl_version >= '0.13':
+ _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
+ else:
+ _RE_COORDINATE = None
def vertices(self):
"""
Return the vertices of the domain, as a list of rational instances of
Point.
"""
- from .polyhedra import Polyhedron
if not self.isbounded():
raise ValueError('domain must be bounded')
islbset = self._toislbasicset(self.equalities, self.inequalities,
- self.symbols)
- vertices = libisl.isl_basic_set_compute_vertices(islbset);
+ self.symbols)
+ vertices = libisl.isl_basic_set_compute_vertices(islbset)
vertices = islhelper.isl_vertices_vertices(vertices)
points = []
for vertex in vertices:
- expr = libisl.isl_vertex_get_expr(vertex)
+ expression = libisl.isl_vertex_get_expr(vertex)
coordinates = []
- if islhelper.isl_version < '0.13':
- constraints = islhelper.isl_basic_set_constraints(expr)
+ if self._RE_COORDINATE is None:
+ constraints = islhelper.isl_basic_set_constraints(expression)
for constraint in constraints:
- constant = libisl.isl_constraint_get_constant_val(constraint)
+ constant = libisl.isl_constraint_get_constant_val(
+ constraint)
constant = islhelper.isl_val_to_int(constant)
for index, symbol in enumerate(self.symbols):
- coefficient = libisl.isl_constraint_get_coefficient_val(constraint,
- libisl.isl_dim_set, index)
+ coefficient = \
+ libisl.isl_constraint_get_coefficient_val(
+ constraint, libisl.isl_dim_set, index)
coefficient = islhelper.isl_val_to_int(coefficient)
if coefficient != 0:
coordinate = -Fraction(constant, coefficient)
coordinates.append((symbol, coordinate))
else:
- string = islhelper.isl_multi_aff_to_str(expr)
+ string = islhelper.isl_multi_aff_to_str(expression)
matches = self._RE_COORDINATE.finditer(string)
for symbol, match in zip(self.symbols, matches):
numerator = int(match.group('num'))
denominator = match.group('den')
- denominator = 1 if denominator is None else int(denominator)
+ denominator = \
+ 1 if denominator is None else int(denominator)
coordinate = Fraction(numerator, denominator)
coordinates.append((symbol, coordinate))
points.append(Point(coordinates))
def points(self):
"""
Return the integer points of a bounded domain, as a list of integer
- instances of Point. If the domain is not bounded, a ValueError exception
- is raised.
+ instances of Point. If the domain is not bounded, a ValueError
+ exception is raised.
"""
if not self.isbounded():
raise ValueError('domain must be bounded')
- from .polyhedra import Universe, Eq
islset = self._toislset(self.polyhedra, self.symbols)
islpoints = islhelper.isl_set_points(islset)
points = []
for islpoint in islpoints:
coordinates = {}
for index, symbol in enumerate(self.symbols):
- coordinate = libisl.isl_point_get_coordinate_val(islpoint,
- libisl.isl_dim_set, index)
+ coordinate = libisl.isl_point_get_coordinate_val(
+ islpoint, libisl.isl_dim_set, index)
coordinate = islhelper.isl_val_to_int(coordinate)
coordinates[symbol] = coordinate
points.append(Point(coordinates))
elif self.dimension == 3:
return self._plot_3d(plot=plot, **kwargs)
else:
- raise ValueError('polyhedron must be 2 or 3-dimensional')
+ raise ValueError('domain must be two or three-dimensional')
def subs(self, symbol, expression=None):
"""
similar to LinExpr.subs().
"""
polyhedra = [polyhedron.subs(symbol, expression)
- for polyhedron in self.polyhedra]
+ for polyhedron in self.polyhedra]
return Domain(*polyhedra)
@classmethod
@classmethod
def _toislset(cls, polyhedra, symbols):
polyhedron = polyhedra[0]
- islbset = polyhedron._toislbasicset(polyhedron.equalities,
- polyhedron.inequalities, symbols)
+ islbset = polyhedron._toislbasicset(
+ polyhedron.equalities, polyhedron.inequalities, symbols)
islset1 = libisl.isl_set_from_basic_set(islbset)
for polyhedron in polyhedra[1:]:
- islbset = polyhedron._toislbasicset(polyhedron.equalities,
- polyhedron.inequalities, symbols)
+ islbset = polyhedron._toislbasicset(
+ polyhedron.equalities, polyhedron.inequalities, symbols)
islset2 = libisl.isl_set_from_basic_set(islbset)
islset1 = libisl.isl_set_union(islset1, islset2)
return islset1
Create a domain from a string. Raise SyntaxError if the string is not
properly formatted.
"""
- # remove curly brackets
+ # Remove curly brackets.
string = cls._RE_BRACES.sub(r'', string)
- # replace '=' by '=='
+ # Replace '=' by '=='.
string = cls._RE_EQ.sub(r'\1==\2', string)
- # replace 'and', 'or', 'not'
+ # Replace 'and', 'or', 'not'.
string = cls._RE_AND.sub(r' & ', string)
string = cls._RE_OR.sub(r' | ', string)
string = cls._RE_NOT.sub(r' ~', string)
- # add implicit multiplication operators, e.g. '5x' -> '5*x'
+ # Add implicit multiplication operators, e.g. '5x' -> '5*x'.
string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
- # add parentheses to force precedence
+ # Add parentheses to force precedence.
tokens = cls._RE_OPERATORS.split(string)
for i, token in enumerate(tokens):
if i % 2 == 0:
strings = [repr(polyhedron) for polyhedron in self.polyhedra]
return 'Or({})'.format(', '.join(strings))
- def _repr_latex_(self):
- strings = []
- for polyhedron in self.polyhedra:
- strings.append('({})'.format(polyhedron._repr_latex_().strip('$')))
- return '${}$'.format(' \\vee '.join(strings))
-
@classmethod
- def fromsympy(cls, expr):
+ def fromsympy(cls, expression):
"""
- Create a domain from a sympy expression.
+ Create a domain from a SymPy expression.
"""
import sympy
from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
sympy.Eq: Eq, sympy.Ne: Ne,
sympy.Ge: Ge, sympy.Gt: Gt,
}
- if expr.func in funcmap:
- args = [Domain.fromsympy(arg) for arg in expr.args]
- return funcmap[expr.func](*args)
- elif isinstance(expr, sympy.Expr):
- return LinExpr.fromsympy(expr)
- raise ValueError('non-domain expression: {!r}'.format(expr))
+ if expression.func in funcmap:
+ args = [Domain.fromsympy(arg) for arg in expression.args]
+ return funcmap[expression.func](*args)
+ elif isinstance(expression, sympy.Expr):
+ return LinExpr.fromsympy(expression)
+ raise ValueError('non-domain expression: {!r}'.format(expression))
def tosympy(self):
"""
- Convert the domain to a sympy expression.
+ Convert the domain to a SymPy expression.
"""
import sympy
- polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
+ polyhedra = [polyhedron.tosympy() for polyhedron in self.polyhedra]
return sympy.Or(*polyhedra)
return Universe
else:
return domains[0].intersection(*domains[1:])
-And.__doc__ = Domain.intersection.__doc__
+
def Or(*domains):
"""
return Empty
else:
return domains[0].union(*domains[1:])
-Or.__doc__ = Domain.union.__doc__
+
def Not(domain):
"""
Create the complementary domain of the domain given in argument.
"""
return ~domain
-Not.__doc__ = Domain.complement.__doc__
projects / linpy.git / blobdiff