# You should have received a copy of the GNU General Public License
# along with LinPy. If not, see <http://www.gnu.org/licenses/>.
+"""
+Polyhedral domains
+
+This module provides classes and functions to deal with polyhedral
+domains, i.e. unions of polyhedra.
+"""
+
import ast
import functools
import re
@functools.total_ordering
class Domain(GeometricObject):
+ """
+ This class represents polyhedral domains, i.e. unions of polyhedra.
+ """
__slots__ = (
'_polyhedra',
)
def __new__(cls, *polyhedra):
+ """
+ Create and return a new domain from a string or a list of polyhedra.
+ """
from .polyhedra import Polyhedron
if len(polyhedra) == 1:
argument = polyhedra[0]
@property
def polyhedra(self):
+ """
+ The tuple of polyhedra which constitute the domain.
+ """
return self._polyhedra
@property
def symbols(self):
+ """
+ The tuple of symbols present in the domain equations.
+ """
return self._symbols
@property
def dimension(self):
+ """
+ The dimension of the domain, i.e. the number of symbols.
+ """
return self._dimension
- def disjoint(self):
+ def make_disjoint(self):
"""
- Returns this set as disjoint.
+ Return an equivalent domain, whose polyhedra are disjoint.
"""
islset = self._toislset(self.polyhedra, self.symbols)
islset = libisl.isl_set_make_disjoint(mainctx, islset)
def isempty(self):
"""
- Returns true if this set is an Empty set.
+ Return True if the domain is empty.
"""
islset = self._toislset(self.polyhedra, self.symbols)
empty = bool(libisl.isl_set_is_empty(islset))
return empty
def __bool__(self):
+ """
+ Return True if the domain is non-empty.
+ """
return not self.isempty()
def isuniverse(self):
"""
- Returns true if this set is the Universe set.
+ Return True if the domain is universal, i.e. with no constraint.
"""
islset = self._toislset(self.polyhedra, self.symbols)
universe = bool(libisl.isl_set_plain_is_universe(islset))
def isbounded(self):
"""
- Returns true if this set is bounded.
+ Return True if the domain is bounded.
"""
islset = self._toislset(self.polyhedra, self.symbols)
bounded = bool(libisl.isl_set_is_bounded(islset))
def __eq__(self, other):
"""
- Returns true if two sets are equal.
+ Return True if the two domains are equal.
"""
symbols = self._xsymbols([self, other])
islset1 = self._toislset(self.polyhedra, symbols)
def isdisjoint(self, other):
"""
- Return True if two sets have a null intersection.
+ Return True if two domains have a null intersection.
"""
symbols = self._xsymbols([self, other])
islset1 = self._toislset(self.polyhedra, symbols)
def issubset(self, other):
"""
- Report whether another set contains this set.
+ Report whether another domain contains the domain.
"""
symbols = self._xsymbols([self, other])
islset1 = self._toislset(self.polyhedra, symbols)
return equal
def __le__(self, other):
- """
- Returns true if this set is less than or equal to another set.
- """
return self.issubset(other)
+ __le__.__doc__ = issubset.__doc__
def __lt__(self, other):
"""
- Returns true if this set is less than another set.
+ Report whether another domain is contained within the domain.
"""
symbols = self._xsymbols([self, other])
islset1 = self._toislset(self.polyhedra, symbols)
def complement(self):
"""
- Returns the complement of this set.
+ Return the complementary domain of the domain.
"""
islset = self._toislset(self.polyhedra, self.symbols)
islset = libisl.isl_set_complement(islset)
return self._fromislset(islset, self.symbols)
def __invert__(self):
+ return self.complement()
+ __invert__.__doc__ = complement.__doc__
+
+ def coalesce(self):
"""
- Returns the complement of this set.
+ Simplify the representation of the domain by trying to combine pairs of
+ polyhedra into a single polyhedron.
"""
- return self.complement()
+ islset = self._toislset(self.polyhedra, self.symbols)
+ islset = libisl.isl_set_coalesce(islset)
+ return self._fromislset(islset, self.symbols)
- def simplify(self):
+ def detect_equalities(self):
"""
- Returns a set without redundant constraints.
+ Simplify the representation of the domain by detecting implicit
+ equalities.
+ """
+ islset = self._toislset(self.polyhedra, self.symbols)
+ islset = libisl.isl_set_detect_equalities(islset)
+ return self._fromislset(islset, self.symbols)
+
+ def remove_redundancies(self):
+ """
+ Remove redundant constraints in the domain.
"""
islset = self._toislset(self.polyhedra, self.symbols)
islset = libisl.isl_set_remove_redundancies(islset)
def aspolyhedron(self):
"""
- Returns polyhedral hull of set.
+ Return the polyhedral hull of the domain.
"""
from .polyhedra import Polyhedron
islset = self._toislset(self.polyhedra, self.symbols)
def asdomain(self):
return self
- def project(self, dims):
+ def project(self, symbols):
"""
- Return new set with given dimensions removed.
+ Project out the symbols given in arguments.
"""
islset = self._toislset(self.polyhedra, self.symbols)
n = 0
for index, symbol in reversed(list(enumerate(self.symbols))):
- if symbol in dims:
+ 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)
- dims = [symbol for symbol in self.symbols if symbol not in dims]
- return Domain._fromislset(islset, dims)
+ symbols = [symbol for symbol in self.symbols if symbol not in symbols]
+ return Domain._fromislset(islset, symbols)
def sample(self):
"""
- Returns a single subset of the input.
+ Return a sample of the domain.
"""
islset = self._toislset(self.polyhedra, self.symbols)
islpoint = libisl.isl_set_sample_point(islset)
def intersection(self, *others):
"""
- Return the intersection of two sets as a new set.
+ Return the intersection of two domains as a new domain.
"""
if len(others) == 0:
return self
return self._fromislset(islset1, symbols)
def __and__(self, other):
- """
- Return the intersection of two sets as a new set.
- """
return self.intersection(other)
+ __and__.__doc__ = intersection.__doc__
def union(self, *others):
"""
- Return the union of sets as a new set.
+ Return the union of two domains as a new domain.
"""
if len(others) == 0:
return self
return self._fromislset(islset1, symbols)
def __or__(self, other):
- """
- Return a new set with elements from both sets.
- """
return self.union(other)
+ __or__.__doc__ = union.__doc__
def __add__(self, other):
- """
- Return new set containing all elements in both sets.
- """
return self.union(other)
+ __add__.__doc__ = union.__doc__
def difference(self, other):
"""
- Return the difference of two sets as a new set.
+ Return the difference of two domains as a new domain.
"""
symbols = self._xsymbols([self, other])
islset1 = self._toislset(self.polyhedra, symbols)
return self._fromislset(islset, symbols)
def __sub__(self, other):
- """
- Return the difference of two sets as a new set.
- """
return self.difference(other)
+ __sub__.__doc__ = difference.__doc__
def lexmin(self):
"""
- Return a new set containing the lexicographic minimum of the elements in the set.
+ Return the lexicographic minimum of the elements in the domain.
"""
islset = self._toislset(self.polyhedra, self.symbols)
islset = libisl.isl_set_lexmin(islset)
def lexmax(self):
"""
- Return a new set containing the lexicographic maximum of the elements in the set.
+ Return the lexicographic maximum of the elements in the domain.
"""
islset = self._toislset(self.polyhedra, self.symbols)
islset = libisl.isl_set_lexmax(islset)
return self._fromislset(islset, self.symbols)
-
- def involves_vars(self, vars):
- """
- Returns true if a set depends on given dimensions.
- """
- islset = self._toislset(self.polyhedra, self.symbols)
- dims = sorted(vars)
- symbols = sorted(list(self.symbols))
- n = 0
- if len(dims)>0:
- for dim in dims:
- if dim in symbols:
- first = symbols.index(dims[0])
- n +=1
- else:
- first = 0
- else:
- return False
- value = bool(libisl.isl_set_involves_dims(islset, libisl.isl_dim_set, first, n))
- libisl.isl_set_free(islset)
- return value
-
_RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
def vertices(self):
"""
- Return a list of vertices for this Polygon.
+ Return the vertices of the domain.
"""
from .polyhedra import Polyhedron
if not self.isbounded():
raise ValueError('domain must be bounded')
- islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
+ islbset = self._toislbasicset(self.equalities, self.inequalities,
+ self.symbols)
vertices = libisl.isl_basic_set_compute_vertices(islbset);
vertices = islhelper.isl_vertices_vertices(vertices)
points = []
def points(self):
"""
- Returns the points contained in the set.
+ Return the points with integer coordinates contained in the domain.
"""
if not self.isbounded():
raise ValueError('domain must be bounded')
def faces(self):
"""
- Returns the vertices of the faces of a polyhedra.
+ Return the vertices of the domain, grouped by face.
"""
faces = []
for polyhedron in self.polyhedra:
axes.set_zlim(zmin, zmax)
return axes
-
def plot(self, plot=None, **kwargs):
"""
- Display plot of this set.
+ Plot the domain using matplotlib.
"""
if not self.isbounded():
raise ValueError('domain must be bounded')
raise ValueError('polyhedron must be 2 or 3-dimensional')
def __contains__(self, point):
+ """
+ Return True if point if contained within the domain.
+ """
for polyhedron in self.polyhedra:
if point in polyhedron:
return True
def subs(self, symbol, expression=None):
"""
- Subsitute the given value into an expression and return the resulting
- expression.
+ Subsitute symbol by expression in equations and return the resulting
+ domain.
"""
polyhedra = [polyhedron.subs(symbol, expression)
for polyhedron in self.polyhedra]
@classmethod
def fromstring(cls, string):
+ """
+ Convert a string into a domain.
+ """
# remove curly brackets
string = cls._RE_BRACES.sub(r'', string)
# replace '=' by '=='
return cls._fromast(tree)
def __repr__(self):
+ """
+ Return repr(self).
+ """
assert len(self.polyhedra) >= 2
strings = [repr(polyhedron) for polyhedron in self.polyhedra]
return 'Or({})'.format(', '.join(strings))
@classmethod
def fromsympy(cls, expr):
+ """
+ Convert a SymPy expression into a domain.
+ """
import sympy
from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
funcmap = {
raise ValueError('non-domain expression: {!r}'.format(expr))
def tosympy(self):
+ """
+ Convert a domain into a SymPy expression.
+ """
import sympy
polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
return sympy.Or(*polyhedra)
def And(*domains):
- """
- Return the intersection of two sets as a new set.
- """
if len(domains) == 0:
from .polyhedra import Universe
return Universe
else:
return domains[0].intersection(*domains[1:])
+And.__doc__ = Domain.intersection.__doc__
def Or(*domains):
- """
- Return the union of sets as a new set.
- """
if len(domains) == 0:
from .polyhedra import Empty
return Empty
else:
return domains[0].union(*domains[1:])
+Or.__doc__ = Domain.union.__doc__
def Not(domain):
- """
- Returns the complement of this set.
- """
return ~domain
+Not.__doc__ = Domain.complement.__doc__
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