New example: Menger sponge, to be plotted

[linpy.git] / pypol / domains.py

diff --git a/pypol/domains.py b/pypol/domains.py
index a2650e4..28ce533 100644 (file)
--- a/pypol/domains.py
+++ b/pypol/domains.py
@@ -2,9 +2,11 @@ import ast
 import functools
 import re
 
 import functools
 import re
 

-from . import islhelper
+from fractions import Fraction

 
 

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

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


@@ -15,7 +17,7 @@ __all__ = [
 
 
 @functools.total_ordering
 
 
 @functools.total_ordering

-class Domain:
+class Domain(GeometricObject):

 
     __slots__ = (
         '_polyhedra',
 
     __slots__ = (
         '_polyhedra',


@@ -26,14 +28,14 @@ class Domain:
     def __new__(cls, *polyhedra):
         from .polyhedra import Polyhedron
         if len(polyhedra) == 1:
     def __new__(cls, *polyhedra):
         from .polyhedra import Polyhedron
         if len(polyhedra) == 1:

-            polyhedron = polyhedra[0]
-            if isinstance(polyhedron, str):
-                return cls.fromstring(polyhedron)
-            elif isinstance(polyhedron, Polyhedron):
-                return polyhedron
+            argument = polyhedra[0]
+            if isinstance(argument, str):
+                return cls.fromstring(argument)
+            elif isinstance(argument, GeometricObject):
+                return argument.aspolyhedron()

             else:
                 raise TypeError('argument must be a string '
             else:
                 raise TypeError('argument must be a string '

-                    'or a Polyhedron instance')
+                    'or a GeometricObject instance')

         else:
             for polyhedron in polyhedra:
                 if not isinstance(polyhedron, Polyhedron):
         else:
             for polyhedron in polyhedra:
                 if not isinstance(polyhedron, Polyhedron):


@@ -65,11 +67,17 @@ class Domain:
         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)


@@ -79,18 +87,27 @@ class Domain:
         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)


@@ -100,6 +117,9 @@ class Domain:
         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)


@@ -109,6 +129,9 @@ class Domain:
         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)


@@ -118,9 +141,15 @@ class Domain:
         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)


@@ -130,30 +159,43 @@ class Domain:
         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)
 
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_remove_redundancies(islset)
         return self._fromislset(islset, self.symbols)
 

-    def polyhedral_hull(self):
-        # several types of hull are available
-        # polyhedral seems to be the more appropriate, to be checked
+    def aspolyhedron(self):
+        """
+        Returns polyhedral hull of set.
+        """

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

-    def project_out(self, dims):
-        # use to remove certain variables
+    def asdomain(self):
+        return self
+
+    def project(self, dims):
+        """
+        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))):


@@ -168,12 +210,27 @@ class Domain:
         return Domain._fromislset(islset, dims)
 
     def sample(self):
         return Domain._fromislset(islset, dims)
 
     def sample(self):

-        from .polyhedra import Polyhedron
+        """
+        Returns a single subset of the input.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         islset = self._toislset(self.polyhedra, self.symbols)

-        islbset = libisl.isl_set_sample(islset)
-        return Polyhedron._fromislbasicset(islbset, self.symbols)
+        islpoint = libisl.isl_set_sample_point(islset)
+        if bool(libisl.isl_point_is_void(islpoint)):
+            libisl.isl_point_free(islpoint)
+            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 = islhelper.isl_val_to_int(coordinate)
+            point[symbol] = coordinate
+        libisl.isl_point_free(islpoint)
+        return point

 
     def intersection(self, *others):
 
     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)


@@ -184,9 +241,15 @@ class Domain:
         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)


@@ -197,12 +260,21 @@ class Domain:
         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)


@@ -210,26 +282,39 @@ class Domain:
         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)
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_lexmax(islset)
         return self._fromislset(islset, self.symbols)

-    
+

     def num_parameters(self):
     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
         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):
     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))


@@ -238,20 +323,93 @@ class Domain:
             for dim in dims:
                 if dim in symbols:
                     first = symbols.index(dims[0])
             for dim in dims:
                 if dim in symbols:
                     first = symbols.index(dims[0])

-                    n +=1  
+                    n +=1

                 else:
                     first = 0
                 else:
                     first = 0

-        else: 
-            return False            
+        else:
+            return False

         value = bool(libisl.isl_set_involves_dims(islset, libisl.isl_dim_set, first, n))
         libisl.isl_set_free(islset)
         return value
 
         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.
+        """
+        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)
+        points = []
+        for vertex in vertices:
+            expr = libisl.isl_vertex_get_expr(vertex)
+            coordinates = []
+            if islhelper.isl_version < '0.13':
+                constraints = islhelper.isl_basic_set_constraints(expr)
+                for constraint in constraints:
+                    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 = islhelper.isl_val_to_int(coefficient)
+                        if coefficient != 0:
+                            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)
+                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)
+                    coordinate = Fraction(numerator, denominator)
+                    coordinates.append((symbol, coordinate))
+            points.append(Point(coordinates))
+        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
+        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 = islhelper.isl_val_to_int(coordinate)
+                coordinates[symbol] = coordinate
+            points.append(Point(coordinates))
+        return points
+
+    def __contains__(self, point):
+        for polyhedron in self.polyhedra:
+            if point in polyhedron:
+                return True
+        return False
+
+    def subs(self, symbol, expression=None):
+        polyhedra = [polyhedron.subs(symbol, expression)
+            for polyhedron in self.polyhedra]
+        return Domain(*polyhedra)
+

     @classmethod
     def _fromislset(cls, islset, symbols):
         from .polyhedra import Polyhedron
         islset = libisl.isl_set_remove_divs(islset)
     @classmethod
     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:


@@ -269,6 +427,7 @@ class Domain:
             self._dimension = len(self._symbols)
             return self
 
             self._dimension = len(self._symbols)
             return self
 

+    @classmethod

     def _toislset(cls, polyhedra, symbols):
         polyhedron = polyhedra[0]
         islbset = polyhedron._toislbasicset(polyhedron.equalities,
     def _toislset(cls, polyhedra, symbols):
         polyhedron = polyhedra[0]
         islbset = polyhedron._toislbasicset(polyhedron.equalities,


@@ -358,6 +517,12 @@ class Domain:
         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


@@ -382,6 +547,9 @@ class Domain:
 
 
 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


@@ -389,6 +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


@@ -396,4 +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