Add EmptyType and UniverseType

[linpy.git] / pypol / polyhedra.py

diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py
index db99753..f8d413e 100644 (file)
--- a/pypol/polyhedra.py
+++ b/pypol/polyhedra.py
@@ -1,11 +1,12 @@
-

 import functools
 import functools

+import math

 import numbers
 
 from . import islhelper
 
 from .islhelper import mainctx, libisl
 import numbers
 
 from . import islhelper
 
 from .islhelper import mainctx, libisl

-from .linexprs import Expression, Symbol, Rational
+from .geometry import GeometricObject, Point
+from .linexprs import Expression, Rational

 from .domains import Domain
 
 
 from .domains import Domain
 
 


@@ -31,11 +32,7 @@ class Polyhedron(Domain):
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return cls.fromstring(equalities)
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return cls.fromstring(equalities)

-        elif isinstance(equalities, Polyhedron):
-            if inequalities is not None:
-                raise TypeError('too many arguments')
-            return equalities
-        elif isinstance(equalities, Domain):
+        elif isinstance(equalities, GeometricObject):

             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()


@@ -74,9 +71,15 @@ class Polyhedron(Domain):
         return self,
 
     def disjoint(self):
         return self,
 
     def disjoint(self):

+        """
+        Return this set as disjoint.
+        """

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

+        """
+        Return true if this set 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))


@@ -84,8 +87,24 @@ class Polyhedron(Domain):
         return universe
 
     def aspolyhedron(self):
         return universe
 
     def aspolyhedron(self):

+        """
+        Return polyhedral hull of this set.
+        """

         return self
 
         return self
 

+    def __contains__(self, point):
+        if not isinstance(point, Point):
+            raise TypeError('point must be a Point instance')
+        if self.symbols != point.symbols:
+            raise ValueError('arguments must belong to the same space')
+        for equality in self.equalities:
+            if equality.subs(point.coordinates()) != 0:
+                return False
+        for inequality in self.inequalities:
+            if inequality.subs(point.coordinates()) < 0:
+                return False
+        return True
+

     def subs(self, symbol, expression=None):
         equalities = [equality.subs(symbol, expression)
             for equality in self.equalities]
     def subs(self, symbol, expression=None):
         equalities = [equality.subs(symbol, expression)
             for equality in self.equalities]


@@ -95,6 +114,10 @@ class Polyhedron(Domain):
 
     @classmethod
     def _fromislbasicset(cls, islbset, symbols):
 
     @classmethod
     def _fromislbasicset(cls, islbset, symbols):

+        if libisl.isl_basic_set_is_empty(islbset):
+            return Empty
+        if libisl.isl_basic_set_is_universe(islbset):
+            return Universe

         islconstraints = islhelper.isl_basic_set_constraints(islbset)
         equalities = []
         inequalities = []
         islconstraints = islhelper.isl_basic_set_constraints(islbset)
         equalities = []
         inequalities = []


@@ -165,20 +188,23 @@ class Polyhedron(Domain):
         return domain
 
     def __repr__(self):
         return domain
 
     def __repr__(self):

-        if self.isempty():
-            return 'Empty'
-        elif self.isuniverse():
-            return 'Universe'
+        strings = []
+        for equality in self.equalities:
+            strings.append('Eq({}, 0)'.format(equality))
+        for inequality in self.inequalities:
+            strings.append('Ge({}, 0)'.format(inequality))
+        if len(strings) == 1:
+            return strings[0]

         else:
         else:

-            strings = []
-            for equality in self.equalities:
-                strings.append('0 == {}'.format(equality))
-            for inequality in self.inequalities:
-                strings.append('0 <= {}'.format(inequality))
-            if len(strings) == 1:
-                return strings[0]
-            else:
-                return 'And({})'.format(', '.join(strings))
+            return 'And({})'.format(', '.join(strings))
+
+    def _repr_latex_(self):
+        strings = []
+        for equality in self.equalities:
+            strings.append('{} = 0'.format(equality._repr_latex_().strip('$')))
+        for inequality in self.inequalities:
+            strings.append('{} \\ge 0'.format(inequality._repr_latex_().strip('$')))
+        return '$${}$$'.format(' \\wedge '.join(strings))

 
     @classmethod
     def fromsympy(cls, expr):
 
     @classmethod
     def fromsympy(cls, expr):


@@ -195,88 +221,108 @@ class Polyhedron(Domain):
         for inequality in self.inequalities:
             constraints.append(sympy.Ge(inequality.tosympy(), 0))
         return sympy.And(*constraints)
         for inequality in self.inequalities:
             constraints.append(sympy.Ge(inequality.tosympy(), 0))
         return sympy.And(*constraints)

-    
-    def plot(self):
-        import matplotlib.pyplot as plt
-        from matplotlib.path import Path
-        import matplotlib.patches as patches
-        
-        if len(self.symbols)> 3:
-            raise TypeError
-        
-        elif len(self.symbols) == 2:
-            verts = self.vertices()
-            points = []
-            codes = [Path.MOVETO]   
-            for vert in verts:
-                pairs = ()
-                for sym in sorted(vert, key=Symbol.sortkey):
-                    num = vert.get(sym)
-                    pairs = pairs + (num,)
-                points.append(pairs)
-            points.append((0.0, 0.0))
-            num = len(points)
-            while num > 2:
-                codes.append(Path.LINETO)
-                num = num - 1
-            else:
-                codes.append(Path.CLOSEPOLY)
-            path = Path(points, codes)
-            fig = plt.figure()
-            ax = fig.add_subplot(111)
-            patch = patches.PathPatch(path, facecolor='blue', lw=2)
-            ax.add_patch(patch)
-            ax.set_xlim(-5,5)
-            ax.set_ylim(-5,5)
-            plt.show()
-            
-        elif len(self.symbols)==3:
-            return 0
-            
-        return points
+
+
+class EmptyType(Polyhedron):
+
+    __slots__ = Polyhedron.__slots__
+
+    def __new__(cls):
+        self = object().__new__(cls)
+        self._equalities = (Rational(1),)
+        self._inequalities = ()
+        self._constraints = self._equalities
+        self._symbols = ()
+        self._dimension = 0
+        return self
+
+    def __repr__(self):
+        return 'Empty'
+
+    def _repr_latex_(self):
+        return '$$\\emptyset$$'
+
+Empty = EmptyType()
+
+
+class UniverseType(Polyhedron):
+
+    __slots__ = Polyhedron.__slots__
+
+    def __new__(cls):
+        self = object().__new__(cls)
+        self._equalities = ()
+        self._inequalities = ()
+        self._constraints = ()
+        self._symbols = ()
+        self._dimension = ()
+        return self
+
+    def __repr__(self):
+        return 'Universe'
+
+    def _repr_latex_(self):
+        return '$$\\Omega$$'
+
+Universe = UniverseType()

 
 
 def _polymorphic(func):
     @functools.wraps(func)
     def wrapper(left, right):
 
 
 def _polymorphic(func):
     @functools.wraps(func)
     def wrapper(left, right):

-        if isinstance(left, numbers.Rational):
-            left = Rational(left)
-        elif not isinstance(left, Expression):
-            raise TypeError('left must be a a rational number '
-                'or a linear expression')
-        if isinstance(right, numbers.Rational):
-            right = Rational(right)
-        elif not isinstance(right, Expression):
-            raise TypeError('right must be a a rational number '
-                'or a linear expression')
+        if not isinstance(left, Expression):
+            if isinstance(left, numbers.Rational):
+                left = Rational(left)
+            else:
+                raise TypeError('left must be a a rational number '
+                    'or a linear expression')
+        if not isinstance(right, Expression):
+            if isinstance(right, numbers.Rational):
+                right = Rational(right)
+            else:
+                raise TypeError('right must be a a rational number '
+                    'or a linear expression')

         return func(left, right)
     return wrapper
 
 @_polymorphic
 def Lt(left, right):
         return func(left, right)
     return wrapper
 
 @_polymorphic
 def Lt(left, right):

+    """
+    Return true if the first set is less than the second.
+    """

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

+    """
+    Return true the first set is less than or equal to the second.
+    """

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

+    """
+    Return true if the sets are equal.
+    """

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

+    """
+    Return true if the sets are NOT equal.
+    """

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

+    """
+    Return true if the first set is greater than the second set.
+    """

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

+    """
+    Return true if the first set is greater than or equal the second set.
+    """

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

-
-
-Empty = Eq(1, 0)
-
-Universe = Polyhedron([])