Add warning in widening documentation

[linpy.git] / linpy / polyhedra.py

diff --git a/linpy/polyhedra.py b/linpy/polyhedra.py
index 346ffff..9fdf6e7 100644 (file)
--- a/linpy/polyhedra.py
+++ b/linpy/polyhedra.py
@@ -36,21 +36,49 @@ __all__ = [
 
 class Polyhedron(Domain):
     """
 
 class Polyhedron(Domain):
     """

-    Polyhedron class allows users to build and inspect polyherons. Polyhedron inherits from Domain.
+    A convex polyhedron (or simply "polyhedron") is the space defined by a
+    system of linear equalities and inequalities. This space can be
+    unbounded.

     """
     """

+

     __slots__ = (
         '_equalities',
         '_inequalities',
     __slots__ = (
         '_equalities',
         '_inequalities',

-        '_constraints',

         '_symbols',
         '_dimension',
     )
 
     def __new__(cls, equalities=None, inequalities=None):
         """
         '_symbols',
         '_dimension',
     )
 
     def __new__(cls, equalities=None, inequalities=None):
         """

-        Create and return a new Polyhedron from a string or list of equalities and inequalities.
-        """
+        Return a polyhedron from two sequences of linear expressions: equalities
+        is a list of expressions equal to 0, and inequalities is a list of
+        expressions greater or equal to 0. For example, the polyhedron
+        0 <= x <= 2, 0 <= y <= 2 can be constructed with:
+
+        >>> x, y = symbols('x y')
+        >>> square = Polyhedron([], [x, 2 - x, y, 2 - y])
+
+        It may be easier to use comparison operators LinExpr.__lt__(),
+        LinExpr.__le__(), LinExpr.__ge__(), LinExpr.__gt__(), or functions Lt(),
+        Le(), Eq(), Ge() and Gt(), using one of the following instructions:
+
+        >>> x, y = symbols('x y')
+        >>> square = (0 <= x) & (x <= 2) & (0 <= y) & (y <= 2)
+        >>> square = Le(0, x, 2) & Le(0, y, 2)

 
 

+        It is also possible to build a polyhedron from a string.
+
+        >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
+
+        Finally, a polyhedron can be constructed from a GeometricObject
+        instance, calling the GeometricObject.aspolyedron() method. This way, it
+        is possible to compute the polyhedral hull of a Domain instance, i.e.,
+        the convex hull of two polyhedra:
+
+        >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
+        >>> square2 = Polyhedron('2 <= x <= 4, 2 <= y <= 4')
+        >>> Polyhedron(square | square2)
+        """

         if isinstance(equalities, str):
             if inequalities is not None:
                 raise TypeError('too many arguments')
         if isinstance(equalities, str):
             if inequalities is not None:
                 raise TypeError('too many arguments')


@@ -59,59 +87,54 @@ class Polyhedron(Domain):
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return equalities.aspolyhedron()
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return equalities.aspolyhedron()

-        if equalities is None:
-            equalities = []
-        else:
-            for i, equality in enumerate(equalities):
+        sc_equalities = []
+        if equalities is not None:
+            for equality in equalities:

                 if not isinstance(equality, LinExpr):
                     raise TypeError('equalities must be linear expressions')
                 if not isinstance(equality, LinExpr):
                     raise TypeError('equalities must be linear expressions')

-                equalities[i] = equality.scaleint()
-        if inequalities is None:
-            inequalities = []
-        else:
-            for i, inequality in enumerate(inequalities):
+                sc_equalities.append(equality.scaleint())
+        sc_inequalities = []
+        if inequalities is not None:
+            for inequality in inequalities:

                 if not isinstance(inequality, LinExpr):
                     raise TypeError('inequalities must be linear expressions')
                 if not isinstance(inequality, LinExpr):
                     raise TypeError('inequalities must be linear expressions')

-                inequalities[i] = inequality.scaleint()
-        symbols = cls._xsymbols(equalities + inequalities)
-        islbset = cls._toislbasicset(equalities, inequalities, symbols)
+                sc_inequalities.append(inequality.scaleint())
+        symbols = cls._xsymbols(sc_equalities + sc_inequalities)
+        islbset = cls._toislbasicset(sc_equalities, sc_inequalities, symbols)

         return cls._fromislbasicset(islbset, symbols)
 
     @property
     def equalities(self):
         """
         return cls._fromislbasicset(islbset, symbols)
 
     @property
     def equalities(self):
         """

-        Return a list of the equalities in a polyhedron.
+        The tuple of equalities. This is a list of LinExpr instances that are
+        equal to 0 in the polyhedron.

         """
         return self._equalities
 
     @property
     def inequalities(self):
         """
         """
         return self._equalities
 
     @property
     def inequalities(self):
         """

-        Return a list of the inequalities in a polyhedron.
+        The tuple of inequalities. This is a list of LinExpr instances that are
+        greater or equal to 0 in the polyhedron.

         """
         return self._inequalities
 
     @property
     def constraints(self):
         """
         """
         return self._inequalities
 
     @property
     def constraints(self):
         """

-        Return the list of the constraints of a polyhedron.
+        The tuple of constraints, i.e., equalities and inequalities. This is
+        semantically equivalent to: equalities + inequalities.

         """
         """

-        return self._constraints
+        return self._equalities + self._inequalities

 
     @property
     def polyhedra(self):
         return self,
 
     def make_disjoint(self):
 
     @property
     def polyhedra(self):
         return self,
 
     def make_disjoint(self):

-        """
-        Return a polyhedron as disjoint.
-        """

         return self
 
     def isuniverse(self):
         return self
 
     def isuniverse(self):

-        """
-        Return true if a polyhedron is the Universe set.
-        """

         islbset = self._toislbasicset(self.equalities, self.inequalities,
             self.symbols)
         universe = bool(libisl.isl_basic_set_is_universe(islbset))
         islbset = self._toislbasicset(self.equalities, self.inequalities,
             self.symbols)
         universe = bool(libisl.isl_basic_set_is_universe(islbset))


@@ -119,15 +142,9 @@ class Polyhedron(Domain):
         return universe
 
     def aspolyhedron(self):
         return universe
 
     def aspolyhedron(self):

-        """
-        Return the polyhedral hull of a polyhedron.
-        """

         return self
 
     def __contains__(self, point):
         return self
 
     def __contains__(self, point):

-        """
-        Report whether a polyhedron constains an integer point
-        """

         if not isinstance(point, Point):
             raise TypeError('point must be a Point instance')
         if self.symbols != point.symbols:
         if not isinstance(point, Point):
             raise TypeError('point must be a Point instance')
         if self.symbols != point.symbols:


@@ -141,10 +158,6 @@ class Polyhedron(Domain):
         return True
 
     def subs(self, symbol, expression=None):
         return True
 
     def subs(self, symbol, expression=None):

-        """
-        Subsitute the given value into an expression and return the resulting
-        expression.
-        """

         equalities = [equality.subs(symbol, expression)
             for equality in self.equalities]
         inequalities = [inequality.subs(symbol, expression)
         equalities = [equality.subs(symbol, expression)
             for equality in self.equalities]
         inequalities = [inequality.subs(symbol, expression)


@@ -158,6 +171,12 @@ class Polyhedron(Domain):
         return inequalities
 
     def widen(self, other):
         return inequalities
 
     def widen(self, other):

+        """
+        Compute the standard widening of two polyhedra, à la Halbwachs.
+
+        In its current implementation, this method is slow and should not be
+        used on large polyhedra.
+        """

         if not isinstance(other, Polyhedron):
             raise ValueError('argument must be a Polyhedron instance')
         inequalities1 = self._asinequalities()
         if not isinstance(other, Polyhedron):
             raise ValueError('argument must be a Polyhedron instance')
         inequalities1 = self._asinequalities()


@@ -200,8 +219,7 @@ class Polyhedron(Domain):
         self = object().__new__(Polyhedron)
         self._equalities = tuple(equalities)
         self._inequalities = tuple(inequalities)
         self = object().__new__(Polyhedron)
         self._equalities = tuple(equalities)
         self._inequalities = tuple(inequalities)

-        self._constraints = tuple(equalities + inequalities)
-        self._symbols = cls._xsymbols(self._constraints)
+        self._symbols = cls._xsymbols(self.constraints)

         self._dimension = len(self._symbols)
         return self
 
         self._dimension = len(self._symbols)
         return self
 


@@ -242,9 +260,6 @@ class Polyhedron(Domain):
 
     @classmethod
     def fromstring(cls, string):
 
     @classmethod
     def fromstring(cls, string):

-        """
-        Create and return a Polyhedron from a string.
-        """

         domain = Domain.fromstring(string)
         if not isinstance(domain, Polyhedron):
             raise ValueError('non-polyhedral expression: {!r}'.format(string))
         domain = Domain.fromstring(string)
         if not isinstance(domain, Polyhedron):
             raise ValueError('non-polyhedral expression: {!r}'.format(string))


@@ -261,7 +276,6 @@ class Polyhedron(Domain):
         else:
             return 'And({})'.format(', '.join(strings))
 
         else:
             return 'And({})'.format(', '.join(strings))
 

-

     def _repr_latex_(self):
         strings = []
         for equality in self.equalities:
     def _repr_latex_(self):
         strings = []
         for equality in self.equalities:


@@ -272,18 +286,12 @@ class Polyhedron(Domain):
 
     @classmethod
     def fromsympy(cls, expr):
 
     @classmethod
     def fromsympy(cls, expr):

-        """
-        Convert a sympy object to a polyhedron.
-        """

         domain = Domain.fromsympy(expr)
         if not isinstance(domain, Polyhedron):
             raise ValueError('non-polyhedral expression: {!r}'.format(expr))
         return domain
 
     def tosympy(self):
         domain = Domain.fromsympy(expr)
         if not isinstance(domain, Polyhedron):
             raise ValueError('non-polyhedral expression: {!r}'.format(expr))
         return domain
 
     def tosympy(self):

-        """
-        Return a polyhedron as a sympy object.
-        """

         import sympy
         constraints = []
         for equality in self.equalities:
         import sympy
         constraints = []
         for equality in self.equalities:


@@ -294,6 +302,9 @@ class Polyhedron(Domain):
 
 
 class EmptyType(Polyhedron):
 
 
 class EmptyType(Polyhedron):

+    """
+    The empty polyhedron, whose set of constraints is not satisfiable.
+    """

 
     __slots__ = Polyhedron.__slots__
 
 
     __slots__ = Polyhedron.__slots__
 


@@ -301,7 +312,6 @@ class EmptyType(Polyhedron):
         self = object().__new__(cls)
         self._equalities = (Rational(1),)
         self._inequalities = ()
         self = object().__new__(cls)
         self._equalities = (Rational(1),)
         self._inequalities = ()

-        self._constraints = self._equalities

         self._symbols = ()
         self._dimension = 0
         return self
         self._symbols = ()
         self._dimension = 0
         return self


@@ -321,6 +331,10 @@ Empty = EmptyType()
 
 
 class UniverseType(Polyhedron):
 
 
 class UniverseType(Polyhedron):

+    """
+    The universe polyhedron, whose set of constraints is always satisfiable,
+    i.e. is empty.
+    """

 
     __slots__ = Polyhedron.__slots__
 
 
     __slots__ = Polyhedron.__slots__
 


@@ -328,7 +342,6 @@ class UniverseType(Polyhedron):
         self = object().__new__(cls)
         self._equalities = ()
         self._inequalities = ()
         self = object().__new__(cls)
         self._equalities = ()
         self._inequalities = ()

-        self._constraints = ()

         self._symbols = ()
         self._dimension = ()
         return self
         self._symbols = ()
         self._dimension = ()
         return self


@@ -363,41 +376,42 @@ def _polymorphic(func):
 @_polymorphic
 def Lt(left, right):
     """
 @_polymorphic
 def Lt(left, right):
     """

-    Returns a Polyhedron instance with a single constraint as left less than right.
+    Create the polyhedron with constraints expr1 < expr2 < expr3 ...

     """
     return Polyhedron([], [right - left - 1])
 
 @_polymorphic
 def Le(left, right):
     """
     """
     return Polyhedron([], [right - left - 1])
 
 @_polymorphic
 def Le(left, right):
     """

-    Returns a Polyhedron instance with a single constraint as left less than or equal to right.
+    Create the polyhedron with constraints expr1 <= expr2 <= expr3 ...

     """
     return Polyhedron([], [right - left])
 
 @_polymorphic
 def Eq(left, right):
     """
     """
     return Polyhedron([], [right - left])
 
 @_polymorphic
 def Eq(left, right):
     """

-    Returns a Polyhedron instance with a single constraint as left equal to right.
+    Create the polyhedron with constraints expr1 == expr2 == expr3 ...

     """
     return Polyhedron([left - right], [])
 
 @_polymorphic
 def Ne(left, right):
     """
     """
     return Polyhedron([left - right], [])
 
 @_polymorphic
 def Ne(left, right):
     """

-    Returns a Polyhedron instance with a single constraint as left not equal to right.
+    Create the domain such that expr1 != expr2 != expr3 ... The result is a
+    Domain, not a Polyhedron.

     """
     return ~Eq(left, right)
 
 @_polymorphic
 def Gt(left, right):
     """
     """
     return ~Eq(left, right)
 
 @_polymorphic
 def Gt(left, right):
     """

-    Returns a Polyhedron instance with a single constraint as left greater than right.
+    Create the polyhedron with constraints expr1 > expr2 > expr3 ...

     """
     return Polyhedron([], [left - right - 1])
 
 @_polymorphic
 def Ge(left, right):
     """
     """
     return Polyhedron([], [left - right - 1])
 
 @_polymorphic
 def Ge(left, right):
     """

-    Returns a Polyhedron instance with a single constraint as left greater than or equal to right.
+    Create the polyhedron with constraints expr1 >= expr2 >= expr3 ...

     """
     return Polyhedron([], [left - right])
     """
     return Polyhedron([], [left - right])