New example: Menger sponge, to be plotted

[linpy.git] / pypol / domains.py

diff --git a/pypol/domains.py b/pypol/domains.py
index cd118e8..28ce533 100644 (file)
--- a/pypol/domains.py
+++ b/pypol/domains.py
@@ -5,9 +5,8 @@ import re
 from fractions import Fraction
 
 from . import islhelper
 from fractions import Fraction
 
 from . import islhelper

-from .islhelper import mainctx, libisl, isl_set_basic_sets
-from .geometry import GeometricObject
-from .coordinates import Point
+from .islhelper import mainctx, libisl
+from .geometry import GeometricObject, Point

 from .linexprs import Expression, Symbol
 
 
 from .linexprs import Expression, Symbol
 
 


@@ -68,11 +67,17 @@ class Domain(GeometricObject):
         return self._dimension
 
     def disjoint(self):
         return self._dimension
 
     def disjoint(self):

+        """
+        Returns this set as disjoint.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_make_disjoint(mainctx, islset)
         return self._fromislset(islset, self.symbols)
 
     def isempty(self):
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_make_disjoint(mainctx, islset)
         return self._fromislset(islset, self.symbols)
 
     def isempty(self):

+        """
+        Returns true if this set is an Empty set.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         empty = bool(libisl.isl_set_is_empty(islset))
         libisl.isl_set_free(islset)
         islset = self._toislset(self.polyhedra, self.symbols)
         empty = bool(libisl.isl_set_is_empty(islset))
         libisl.isl_set_free(islset)


@@ -82,18 +87,27 @@ class Domain(GeometricObject):
         return not self.isempty()
 
     def isuniverse(self):
         return not self.isempty()
 
     def isuniverse(self):

+        """
+        Returns true if this set is the Universe set.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         universe = bool(libisl.isl_set_plain_is_universe(islset))
         libisl.isl_set_free(islset)
         return universe
 
     def isbounded(self):
         islset = self._toislset(self.polyhedra, self.symbols)
         universe = bool(libisl.isl_set_plain_is_universe(islset))
         libisl.isl_set_free(islset)
         return universe
 
     def isbounded(self):

+        """
+        Returns true if this set is bounded.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         bounded = bool(libisl.isl_set_is_bounded(islset))
         libisl.isl_set_free(islset)
         return bounded
 
     def __eq__(self, other):
         islset = self._toislset(self.polyhedra, self.symbols)
         bounded = bool(libisl.isl_set_is_bounded(islset))
         libisl.isl_set_free(islset)
         return bounded
 
     def __eq__(self, other):

+        """
+        Returns true if two sets are equal.
+        """

         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = other._toislset(other.polyhedra, symbols)
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = other._toislset(other.polyhedra, symbols)


@@ -103,6 +117,9 @@ class Domain(GeometricObject):
         return equal
 
     def isdisjoint(self, other):
         return equal
 
     def isdisjoint(self, other):

+        """
+        Return True if two sets have a null intersection.
+        """

         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)


@@ -112,6 +129,9 @@ class Domain(GeometricObject):
         return equal
 
     def issubset(self, other):
         return equal
 
     def issubset(self, other):

+        """
+        Report whether another set contains this set.
+        """

         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)


@@ -121,9 +141,15 @@ class Domain(GeometricObject):
         return equal
 
     def __le__(self, other):
         return equal
 
     def __le__(self, other):

+        """
+        Returns true if this set is less than or equal to another set.
+        """

         return self.issubset(other)
 
     def __lt__(self, other):
         return self.issubset(other)
 
     def __lt__(self, other):

+        """
+        Returns true if this set is less than another set.
+        """

         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)


@@ -133,23 +159,31 @@ class Domain(GeometricObject):
         return equal
 
     def complement(self):
         return equal
 
     def complement(self):

+        """
+        Returns the complement of this set.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_complement(islset)
         return self._fromislset(islset, self.symbols)
 
     def __invert__(self):
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_complement(islset)
         return self._fromislset(islset, self.symbols)
 
     def __invert__(self):

+        """
+        Returns the complement of this set.
+        """

         return self.complement()
 
     def simplify(self):
         return self.complement()
 
     def simplify(self):

-        #does not change anything in any of the examples
-        #isl seems to do this naturally
+        """
+        Returns a set without redundant constraints.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_remove_redundancies(islset)
         return self._fromislset(islset, self.symbols)
 
     def aspolyhedron(self):
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_remove_redundancies(islset)
         return self._fromislset(islset, self.symbols)
 
     def aspolyhedron(self):

-        # several types of hull are available
-        # polyhedral seems to be the more appropriate, to be checked
+        """
+        Returns polyhedral hull of set.
+        """

         from .polyhedra import Polyhedron
         islset = self._toislset(self.polyhedra, self.symbols)
         islbset = libisl.isl_set_polyhedral_hull(islset)
         from .polyhedra import Polyhedron
         islset = self._toislset(self.polyhedra, self.symbols)
         islbset = libisl.isl_set_polyhedral_hull(islset)


@@ -159,7 +193,9 @@ class Domain(GeometricObject):
         return self
 
     def project(self, dims):
         return self
 
     def project(self, dims):

-        # use to remove certain variables
+        """
+        Return new set with given dimensions removed.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         n = 0
         for index, symbol in reversed(list(enumerate(self.symbols))):
         islset = self._toislset(self.polyhedra, self.symbols)
         n = 0
         for index, symbol in reversed(list(enumerate(self.symbols))):


@@ -174,6 +210,9 @@ class Domain(GeometricObject):
         return Domain._fromislset(islset, dims)
 
     def sample(self):
         return Domain._fromislset(islset, dims)
 
     def sample(self):

+        """
+        Returns a single subset of the input.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         islpoint = libisl.isl_set_sample_point(islset)
         if bool(libisl.isl_point_is_void(islpoint)):
         islset = self._toislset(self.polyhedra, self.symbols)
         islpoint = libisl.isl_set_sample_point(islset)
         if bool(libisl.isl_point_is_void(islpoint)):


@@ -189,6 +228,9 @@ class Domain(GeometricObject):
         return point
 
     def intersection(self, *others):
         return point
 
     def intersection(self, *others):

+        """
+         Return the intersection of two sets as a new set.
+        """

         if len(others) == 0:
             return self
         symbols = self._xsymbols((self,) + others)
         if len(others) == 0:
             return self
         symbols = self._xsymbols((self,) + others)


@@ -199,9 +241,15 @@ class Domain(GeometricObject):
         return self._fromislset(islset1, symbols)
 
     def __and__(self, other):
         return self._fromislset(islset1, symbols)
 
     def __and__(self, other):

+        """
+         Return the intersection of two sets as a new set.
+        """

         return self.intersection(other)
 
     def union(self, *others):
         return self.intersection(other)
 
     def union(self, *others):

+        """
+        Return the union of sets as a new set.
+        """

         if len(others) == 0:
             return self
         symbols = self._xsymbols((self,) + others)
         if len(others) == 0:
             return self
         symbols = self._xsymbols((self,) + others)


@@ -212,12 +260,21 @@ class Domain(GeometricObject):
         return self._fromislset(islset1, symbols)
 
     def __or__(self, other):
         return self._fromislset(islset1, symbols)
 
     def __or__(self, other):

+        """
+        Return a new set with elements from both sets.
+        """

         return self.union(other)
 
     def __add__(self, other):
         return self.union(other)
 
     def __add__(self, other):

+        """
+        Return new set containing all elements in both sets.
+        """

         return self.union(other)
 
     def difference(self, other):
         return self.union(other)
 
     def difference(self, other):

+        """
+        Return the difference of two sets as a new set.
+        """

         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = other._toislset(other.polyhedra, symbols)
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = other._toislset(other.polyhedra, symbols)


@@ -225,26 +282,39 @@ class Domain(GeometricObject):
         return self._fromislset(islset, symbols)
 
     def __sub__(self, other):
         return self._fromislset(islset, symbols)
 
     def __sub__(self, other):

+        """
+        Return the difference of two sets as a new set.
+        """

         return self.difference(other)
 
     def lexmin(self):
         return self.difference(other)
 
     def lexmin(self):

+        """
+        Return a new set containing the lexicographic minimum of the elements in the set.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_lexmin(islset)
         return self._fromislset(islset, self.symbols)
 
     def lexmax(self):
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_lexmin(islset)
         return self._fromislset(islset, self.symbols)
 
     def lexmax(self):

+        """
+        Return a new set containing the lexicographic maximum of the elements in the set.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_lexmax(islset)
         return self._fromislset(islset, self.symbols)
 
     def num_parameters(self):
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_lexmax(islset)
         return self._fromislset(islset, self.symbols)
 
     def num_parameters(self):

-        #could be useful with large, complicated polyhedrons
+        """
+        Return the total number of parameters, input, output or set dimensions.
+        """

         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
         num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
         return num
 
     def involves_dims(self, dims):
         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
         num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
         return num
 
     def involves_dims(self, dims):

-        #could be useful with large, complicated polyhedrons
+        """
+        Returns true if set depends on given dimensions.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         dims = sorted(dims)
         symbols = sorted(list(self.symbols))
         islset = self._toislset(self.polyhedra, self.symbols)
         dims = sorted(dims)
         symbols = sorted(list(self.symbols))


@@ -265,8 +335,12 @@ class Domain(GeometricObject):
     _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
 
     def vertices(self):
     _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
 
     def vertices(self):

-        #returning list of verticies
+        """
+        Return a list of vertices for this Polygon.
+        """

         from .polyhedra import Polyhedron
         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);
         vertices = islhelper.isl_vertices_vertices(vertices)
         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
         vertices = libisl.isl_basic_set_compute_vertices(islbset);
         vertices = islhelper.isl_vertices_vertices(vertices)


@@ -287,6 +361,7 @@ class Domain(GeometricObject):
                             coordinate = -Fraction(constant, coefficient)
                             coordinates.append((symbol, coordinate))
             else:
                             coordinate = -Fraction(constant, coefficient)
                             coordinates.append((symbol, coordinate))
             else:

+                

                 # horrible hack, find a cleaner solution
                 string = islhelper.isl_multi_aff_to_str(expr)
                 matches = self._RE_COORDINATE.finditer(string)
                 # horrible hack, find a cleaner solution
                 string = islhelper.isl_multi_aff_to_str(expr)
                 matches = self._RE_COORDINATE.finditer(string)


@@ -300,6 +375,9 @@ class Domain(GeometricObject):
         return points
 
     def points(self):
         return points
 
     def points(self):

+        """
+        Returns the points contained in the set.
+        """

         if not self.isbounded():
             raise ValueError('domain must be bounded')
         from .polyhedra import Universe, Eq
         if not self.isbounded():
             raise ValueError('domain must be bounded')
         from .polyhedra import Universe, Eq


@@ -331,7 +409,7 @@ class Domain(GeometricObject):
     def _fromislset(cls, islset, symbols):
         from .polyhedra import Polyhedron
         islset = libisl.isl_set_remove_divs(islset)
     def _fromislset(cls, islset, symbols):
         from .polyhedra import Polyhedron
         islset = libisl.isl_set_remove_divs(islset)

-        islbsets = isl_set_basic_sets(islset)
+        islbsets = islhelper.isl_set_basic_sets(islset)

         libisl.isl_set_free(islset)
         polyhedra = []
         for islbset in islbsets:
         libisl.isl_set_free(islset)
         polyhedra = []
         for islbset in islbsets:


@@ -439,6 +517,12 @@ class Domain(GeometricObject):
         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
         return 'Or({})'.format(', '.join(strings))
 
         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):
         import sympy
     @classmethod
     def fromsympy(cls, expr):
         import sympy


@@ -463,6 +547,9 @@ class Domain(GeometricObject):
 
 
 def And(*domains):
 
 
 def And(*domains):

+    """
+    Return the intersection of two sets as a new set.
+    """

     if len(domains) == 0:
         from .polyhedra import Universe
         return Universe
     if len(domains) == 0:
         from .polyhedra import Universe
         return Universe


@@ -470,6 +557,9 @@ def And(*domains):
         return domains[0].intersection(*domains[1:])
 
 def Or(*domains):
         return domains[0].intersection(*domains[1:])
 
 def Or(*domains):

+    """
+    Return the union of sets as a new set.
+    """

     if len(domains) == 0:
         from .polyhedra import Empty
         return Empty
     if len(domains) == 0:
         from .polyhedra import Empty
         return Empty


@@ -477,4 +567,7 @@ def Or(*domains):
         return domains[0].union(*domains[1:])
 
 def Not(domain):
         return domains[0].union(*domains[1:])
 
 def Not(domain):

+    """
+    Returns the complement of this set.
+    """

     return ~domain
     return ~domain