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Remove license and add to doc examples
[linpy.git] / linpy / domains.py
diff --git a/linpy/domains.py b/linpy/domains.py
index 21e78db..70e5e4f 100644 (file)
--- a/linpy/domains.py
+++ b/linpy/domains.py
@@ -15,6 +15,13 @@
 # You should have received a copy of the GNU General Public License
 # along with LinPy.  If not, see <http://www.gnu.org/licenses/>.
 
 # 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
 import ast
 import functools
 import re
@@ -36,6 +43,9 @@ __all__ = [
 
 @functools.total_ordering
 class Domain(GeometricObject):
 
 @functools.total_ordering
 class Domain(GeometricObject):
+    """
+    This class represents polyhedral domains, i.e. unions of polyhedra.
+    """
 
     __slots__ = (
         '_polyhedra',
 
     __slots__ = (
         '_polyhedra',
@@ -44,6 +54,9 @@ class Domain(GeometricObject):
     )
 
     def __new__(cls, *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]
         from .polyhedra import Polyhedron
         if len(polyhedra) == 1:
             argument = polyhedra[0]
@@ -74,19 +87,28 @@ class Domain(GeometricObject):
 
     @property
     def polyhedra(self):
 
     @property
     def polyhedra(self):
+        """
+        The tuple of polyhedra which constitute the domain.
+        """
         return self._polyhedra
 
     @property
     def symbols(self):
         return self._polyhedra
 
     @property
     def symbols(self):
+        """
+        The tuple of symbols present in the domain equations.
+        """
         return self._symbols
 
     @property
     def dimension(self):
         return self._symbols
 
     @property
     def dimension(self):
+        """
+        The dimension of the domain, i.e. the number of symbols.
+        """
         return self._dimension
 
         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)
         """
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_make_disjoint(mainctx, islset)
@@ -94,7 +116,7 @@ class Domain(GeometricObject):
 
     def isempty(self):
         """
 
     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))
         """
         islset = self._toislset(self.polyhedra, self.symbols)
         empty = bool(libisl.isl_set_is_empty(islset))
@@ -102,11 +124,14 @@ class Domain(GeometricObject):
         return empty
 
     def __bool__(self):
         return empty
 
     def __bool__(self):
+        """
+        Return True if the domain is non-empty.
+        """
         return not self.isempty()
 
     def isuniverse(self):
         """
         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))
         """
         islset = self._toislset(self.polyhedra, self.symbols)
         universe = bool(libisl.isl_set_plain_is_universe(islset))
@@ -115,7 +140,7 @@ class Domain(GeometricObject):
 
     def isbounded(self):
         """
 
     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))
         """
         islset = self._toislset(self.polyhedra, self.symbols)
         bounded = bool(libisl.isl_set_is_bounded(islset))
@@ -124,7 +149,7 @@ class Domain(GeometricObject):
 
     def __eq__(self, other):
         """
 
     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)
         """
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
@@ -136,7 +161,7 @@ class Domain(GeometricObject):
 
     def isdisjoint(self, other):
         """
 
     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)
         """
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
@@ -148,7 +173,7 @@ class Domain(GeometricObject):
 
     def issubset(self, other):
         """
 
     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)
         """
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
@@ -159,14 +184,12 @@ 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)
         return self.issubset(other)
+    __le__.__doc__ = issubset.__doc__
 
     def __lt__(self, other):
         """
 
     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)
         """
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
@@ -178,21 +201,37 @@ class Domain(GeometricObject):
 
     def complement(self):
         """
 
     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):
         """
         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)
         """
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_remove_redundancies(islset)
@@ -200,7 +239,7 @@ class Domain(GeometricObject):
 
     def aspolyhedron(self):
         """
 
     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)
         """
         from .polyhedra import Polyhedron
         islset = self._toislset(self.polyhedra, self.symbols)
@@ -210,26 +249,27 @@ class Domain(GeometricObject):
     def asdomain(self):
         return self
 
     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))):
         """
         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:
                 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)
                 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):
         """
 
     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)
         """
         islset = self._toislset(self.polyhedra, self.symbols)
         islpoint = libisl.isl_set_sample_point(islset)
@@ -247,7 +287,7 @@ class Domain(GeometricObject):
 
     def intersection(self, *others):
         """
 
     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
         """
         if len(others) == 0:
             return self
@@ -259,14 +299,12 @@ 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)
         return self.intersection(other)
+    __and__.__doc__ = intersection.__doc__
 
     def union(self, *others):
         """
 
     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
         """
         if len(others) == 0:
             return self
@@ -278,20 +316,16 @@ 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)
         return self.union(other)
+    __or__.__doc__ = union.__doc__
 
     def __add__(self, other):
 
     def __add__(self, other):
-        """
-        Return new set containing all elements in both sets.
-        """
         return self.union(other)
         return self.union(other)
+    __add__.__doc__ = union.__doc__
 
     def difference(self, other):
         """
 
     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)
         """
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
@@ -300,14 +334,12 @@ 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)
         return self.difference(other)
+    __sub__.__doc__ = difference.__doc__
 
     def lexmin(self):
         """
 
     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)
         """
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_lexmin(islset)
@@ -315,44 +347,23 @@ class Domain(GeometricObject):
 
     def lexmax(self):
         """
 
     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)
 
         """
         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):
         """
     _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')
         """
         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 = []
         vertices = libisl.isl_basic_set_compute_vertices(islbset);
         vertices = islhelper.isl_vertices_vertices(vertices)
         points = []
@@ -385,7 +396,7 @@ class Domain(GeometricObject):
 
     def points(self):
         """
 
     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')
         """
         if not self.isbounded():
             raise ValueError('domain must be bounded')
@@ -456,7 +467,7 @@ class Domain(GeometricObject):
 
     def faces(self):
         """
 
     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:
         """
         faces = []
         for polyhedron in self.polyhedra:
@@ -518,10 +529,9 @@ class Domain(GeometricObject):
         axes.set_zlim(zmin, zmax)
         return axes
 
         axes.set_zlim(zmin, zmax)
         return axes
 
-
     def plot(self, plot=None, **kwargs):
         """
     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')
         """
         if not self.isbounded():
             raise ValueError('domain must be bounded')
@@ -533,6 +543,9 @@ class Domain(GeometricObject):
             raise ValueError('polyhedron must be 2 or 3-dimensional')
 
     def __contains__(self, point):
             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
         for polyhedron in self.polyhedra:
             if point in polyhedron:
                 return True
@@ -540,8 +553,8 @@ class Domain(GeometricObject):
 
     def subs(self, symbol, expression=None):
         """
 
     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]
         """
         polyhedra = [polyhedron.subs(symbol, expression)
             for polyhedron in self.polyhedra]
@@ -634,6 +647,9 @@ class Domain(GeometricObject):
 
     @classmethod
     def fromstring(cls, string):
 
     @classmethod
     def fromstring(cls, string):
+        """
+        Convert a string into a domain.
+        """
         # remove curly brackets
         string = cls._RE_BRACES.sub(r'', string)
         # replace '=' by '=='
         # remove curly brackets
         string = cls._RE_BRACES.sub(r'', string)
         # replace '=' by '=='
@@ -655,6 +671,9 @@ class Domain(GeometricObject):
         return cls._fromast(tree)
 
     def __repr__(self):
         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))
         assert len(self.polyhedra) >= 2
         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
         return 'Or({})'.format(', '.join(strings))
@@ -667,6 +686,9 @@ class Domain(GeometricObject):
 
     @classmethod
     def fromsympy(cls, expr):
 
     @classmethod
     def fromsympy(cls, expr):
+        """
+        Convert a SymPy expression into a domain.
+        """
         import sympy
         from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
         funcmap = {
         import sympy
         from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
         funcmap = {
@@ -683,33 +705,30 @@ class Domain(GeometricObject):
         raise ValueError('non-domain expression: {!r}'.format(expr))
 
     def tosympy(self):
         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):
         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:])
     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):
 
 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:])
     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):
 
 def Not(domain):
-    """
-    Returns the complement of this set.
-    """
     return ~domain
     return ~domain
+Not.__doc__ = Domain.complement.__doc__
A polyhedral library based on ISL