Plot domain added

[linpy.git] / pypol / polyhedra.py

diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py
index ac67cf8..a5d9495 100644 (file)
--- a/pypol/polyhedra.py
+++ b/pypol/polyhedra.py
@@ -1,10 +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, Constant
+from .geometry import GeometricObject, Point
+from .linexprs import Expression, Rational

 from .domains import Domain
 
 
 from .domains import Domain
 
 


@@ -30,28 +32,24 @@ 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):
+        elif isinstance(equalities, GeometricObject):

             if inequalities is not None:
                 raise TypeError('too many arguments')
             if inequalities is not None:
                 raise TypeError('too many arguments')

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

         if equalities is None:
             equalities = []
         else:
             for i, equality in enumerate(equalities):
                 if not isinstance(equality, Expression):
                     raise TypeError('equalities must be linear expressions')
         if equalities is None:
             equalities = []
         else:
             for i, equality in enumerate(equalities):
                 if not isinstance(equality, Expression):
                     raise TypeError('equalities must be linear expressions')

-                equalities[i] = equality._toint()
+                equalities[i] = equality.scaleint()

         if inequalities is None:
             inequalities = []
         else:
             for i, inequality in enumerate(inequalities):
                 if not isinstance(inequality, Expression):
                     raise TypeError('inequalities must be linear expressions')
         if inequalities is None:
             inequalities = []
         else:
             for i, inequality in enumerate(inequalities):
                 if not isinstance(inequality, Expression):
                     raise TypeError('inequalities must be linear expressions')

-                inequalities[i] = inequality._toint()
+                inequalities[i] = inequality.scaleint()

         symbols = cls._xsymbols(equalities + inequalities)
         islbset = cls._toislbasicset(equalities, inequalities, symbols)
         return cls._fromislbasicset(islbset, symbols)
         symbols = cls._xsymbols(equalities + inequalities)
         islbset = cls._toislbasicset(equalities, inequalities, symbols)
         return cls._fromislbasicset(islbset, symbols)


@@ -73,18 +71,47 @@ 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))
         libisl.isl_basic_set_free(islbset)
         return universe
 
         islbset = self._toislbasicset(self.equalities, self.inequalities,
             self.symbols)
         universe = bool(libisl.isl_basic_set_is_universe(islbset))
         libisl.isl_basic_set_free(islbset)
         return universe
 

-    def polyhedral_hull(self):
+    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]
+        inequalities = [inequality.subs(symbol, expression)
+            for inequality in self.inequalities]
+        return Polyhedron(equalities, inequalities)
+

     @classmethod
     def _fromislbasicset(cls, islbset, symbols):
         islconstraints = islhelper.isl_basic_set_constraints(islbset)
     @classmethod
     def _fromislbasicset(cls, islbset, symbols):
         islconstraints = islhelper.isl_basic_set_constraints(islbset)


@@ -95,7 +122,8 @@ class Polyhedron(Domain):
             constant = islhelper.isl_val_to_int(constant)
             coefficients = {}
             for index, symbol in enumerate(symbols):
             constant = islhelper.isl_val_to_int(constant)
             coefficients = {}
             for index, symbol in enumerate(symbols):

-                coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint, libisl.isl_dim_set, index)
+                coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint,
+                    libisl.isl_dim_set, index)

                 coefficient = islhelper.isl_val_to_int(coefficient)
                 if coefficient != 0:
                     coefficients[symbol] = coefficient
                 coefficient = islhelper.isl_val_to_int(coefficient)
                 if coefficient != 0:
                     coefficients[symbol] = coefficient


@@ -171,38 +199,25 @@ class Polyhedron(Domain):
             else:
                 return 'And({})'.format(', '.join(strings))
 
             else:
                 return 'And({})'.format(', '.join(strings))
 

-    @classmethod
-    def _fromsympy(cls, expr):
-        import sympy
-        equalities = []
-        inequalities = []
-        if expr.func == sympy.And:
-            for arg in expr.args:
-                arg_eqs, arg_ins = cls._fromsympy(arg)
-                equalities.extend(arg_eqs)
-                inequalities.extend(arg_ins)
-        elif expr.func == sympy.Eq:
-            expr = Expression.fromsympy(expr.args[0] - expr.args[1])
-            equalities.append(expr)
+    def _repr_latex_(self):
+        if self.isempty():
+            return '$\\emptyset$'
+        elif self.isuniverse():
+            return '$\\Omega$'

         else:
         else:

-            if expr.func == sympy.Lt:
-                expr = Expression.fromsympy(expr.args[1] - expr.args[0] - 1)
-            elif expr.func == sympy.Le:
-                expr = Expression.fromsympy(expr.args[1] - expr.args[0])
-            elif expr.func == sympy.Ge:
-                expr = Expression.fromsympy(expr.args[0] - expr.args[1])
-            elif expr.func == sympy.Gt:
-                expr = Expression.fromsympy(expr.args[0] - expr.args[1] - 1)
-            else:
-                raise ValueError('non-polyhedral expression: {!r}'.format(expr))
-            inequalities.append(expr)
-        return equalities, inequalities
+            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):

-        import sympy
-        equalities, inequalities = cls._fromsympy(expr)
-        return cls(equalities, inequalities)
+        domain = Domain.fromsympy(expr)
+        if not isinstance(domain, Polyhedron):
+            raise ValueError('non-polyhedral expression: {!r}'.format(expr))
+        return domain

 
     def tosympy(self):
         import sympy
 
     def tosympy(self):
         import sympy


@@ -213,45 +228,64 @@ class Polyhedron(Domain):
             constraints.append(sympy.Ge(inequality.tosympy(), 0))
         return sympy.And(*constraints)
 
             constraints.append(sympy.Ge(inequality.tosympy(), 0))
         return sympy.And(*constraints)
 

-

 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 = Constant(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 = Constant(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])