Plot domain added

[linpy.git] / pypol / polyhedra.py

diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py
index 37f16e0..a5d9495 100644 (file)
--- a/pypol/polyhedra.py
+++ b/pypol/polyhedra.py
@@ -6,7 +6,7 @@ from . import islhelper
 
 from .islhelper import mainctx, libisl
 from .geometry import GeometricObject, Point
 
 from .islhelper import mainctx, libisl
 from .geometry import GeometricObject, Point

-from .linexprs import Expression, Symbol, Rational
+from .linexprs import Expression, Rational

 from .domains import Domain
 
 
 from .domains import Domain
 
 


@@ -71,9 +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))


@@ -81,6 +87,9 @@ class Polyhedron(Domain):
         return universe
 
     def aspolyhedron(self):
         return universe
 
     def aspolyhedron(self):

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

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


@@ -182,14 +191,27 @@ class Polyhedron(Domain):
         else:
             strings = []
             for equality in self.equalities:
         else:
             strings = []
             for equality in self.equalities:

-                strings.append('0 == {}'.format(equality))
+                strings.append('Eq({}, 0)'.format(equality))

             for inequality in self.inequalities:
             for inequality in self.inequalities:

-                strings.append('0 <= {}'.format(inequality))
+                strings.append('Ge({}, 0)'.format(inequality))

             if len(strings) == 1:
                 return strings[0]
             else:
                 return 'And({})'.format(', '.join(strings))
 
             if len(strings) == 1:
                 return strings[0]
             else:
                 return 'And({})'.format(', '.join(strings))
 

+    def _repr_latex_(self):
+        if self.isempty():
+            return '$\\emptyset$'
+        elif self.isuniverse():
+            return '$\\Omega$'
+        else:
+            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):
         domain = Domain.fromsympy(expr)
     @classmethod
     def fromsympy(cls, expr):
         domain = Domain.fromsympy(expr)


@@ -206,131 +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)
 

-    @classmethod
-    def _sort_polygon_2d(cls, points):
-        if len(points) <= 3:
-            return points
-        o = sum((Vector(point) for point in points)) / len(points)
-        o = Point(o.coordinates())
-        angles = {}
-        for m in points:
-            om = Vector(o, m)
-            dx, dy = (coordinate for symbol, coordinates in om.coordinates())
-            angle = math.atan2(dy, dx)
-            angles[m] = angle
-        return sorted(points, key=angles.get)
-
-    @classmethod
-    def _sort_polygon_3d(cls, points):
-        if len(points) <= 3:
-            return points
-        o = sum((Vector(point) for point in points)) / len(points)
-        o = Point(o.coordinates())
-        a, b = points[:2]
-        oa = Vector(o, a)
-        ob = Vector(o, b)
-        norm_oa = oa.norm()
-        u = (oa.cross(ob)).asunit()
-        angles = {a: 0.}
-        for m in points[1:]:
-            om = Vector(o, m)
-            normprod = norm_oa * om.norm()
-            cosinus = oa.dot(om) / normprod
-            sinus = u.dot(oa.cross(om)) / normprod
-            angle = math.acos(cosinus)
-            angle = math.copysign(angle, sinus)
-            angles[m] = angle
-        return sorted(points, key=angles.get)
-
-    def faces(self):
-        vertices = self.vertices()
-        faces = []
-        for constraint in self.constraints:
-            face = []
-            for vertex in vertices:
-                if constraint.subs(vertex.coordinates()) == 0:
-                    face.append(vertex)
-            faces.append(face)
-        return faces
-
-    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
-
-

 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])