Implement standard widening
[linpy.git] / pypol / polyhedra.py
index 5d1bfa1..ccb1a8c 100644 (file)
@@ -5,8 +5,8 @@ import numbers
 from . import islhelper
 
 from .islhelper import mainctx, libisl
-from .geometry import GeometricObject, Point, Vector
-from .linexprs import Expression, Symbol, Rational
+from .geometry import GeometricObject, Point
+from .linexprs import Expression, Rational
 from .domains import Domain
 
 
@@ -112,8 +112,37 @@ class Polyhedron(Domain):
             for inequality in self.inequalities]
         return Polyhedron(equalities, inequalities)
 
+    def _asinequalities(self):
+        inequalities = list(self.equalities)
+        inequalities.extend([-expression for expression in self.equalities])
+        inequalities.extend(self.inequalities)
+        return inequalities
+
+    def widen(self, other):
+        if not isinstance(other, Polyhedron):
+            raise ValueError('argument must be a Polyhedron instance')
+        inequalities1 = self._asinequalities()
+        inequalities2 = other._asinequalities()
+        inequalities = []
+        for inequality1 in inequalities1:
+            if other <= Polyhedron(inequalities=[inequality1]):
+                inequalities.append(inequality1)
+        for inequality2 in inequalities2:
+            for i in range(len(inequalities1)):
+                inequalities3 = inequalities1[:i] + inequalities[i + 1:]
+                inequalities3.append(inequality2)
+                polyhedron3 = Polyhedron(inequalities=inequalities3)
+                if self == polyhedron3:
+                    inequalities.append(inequality2)
+                    break
+        return Polyhedron(inequalities=inequalities)
+
     @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 = []
@@ -184,33 +213,23 @@ class Polyhedron(Domain):
         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:
-            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:
-                return 'And({})'.format(', '.join(strings))
+            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))
+        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):
@@ -228,141 +247,55 @@ class Polyhedron(Domain):
             constraints.append(sympy.Ge(inequality.tosympy(), 0))
         return sympy.And(*constraints)
 
-    @classmethod
-    def _polygon_inner_point(cls, points):
-        symbols = points[0].symbols
-        coordinates = {symbol: 0 for symbol in symbols}
-        for point in points:
-            for symbol, coordinate in point.coordinates():
-                coordinates[symbol] += coordinate
-        for symbol in symbols:
-            coordinates[symbol] /= len(points)
-        return Point(coordinates)
 
-    @classmethod
-    def _sort_polygon_2d(cls, points):
-        if len(points) <= 3:
-            return points
-        o = cls._polygon_inner_point(points)
-        angles = {}
-        for m in points:
-            om = Vector(o, m)
-            dx, dy = (coordinate for symbol, coordinate in om.coordinates())
-            angle = math.atan2(dy, dx)
-            angles[m] = angle
-        return sorted(points, key=angles.get)
+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 widen(self, other):
+        if not isinstance(other, Polyhedron):
+            raise ValueError('argument must be a Polyhedron instance')
+        return other
+
+    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()
 
-    @classmethod
-    def _sort_polygon_3d(cls, points):
-        if len(points) <= 3:
-            return points
-        o = cls._polygon_inner_point(points)
-        a = points[0]
-        oa = Vector(o, a)
-        norm_oa = oa.norm()
-        for b in points[1:]:
-            ob = Vector(o, b)
-            u = oa.cross(ob)
-            if not u.isnull():
-                u = u.asunit()
-                break
-        else:
-            raise ValueError('degenerate polygon')
-        angles = {a: 0.}
-        for m in points[1:]:
-            om = Vector(o, m)
-            normprod = norm_oa * om.norm()
-            cosinus = max(oa.dot(om) / normprod, -1.)
-            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):
-        """
-        Display 3D plot of set. 
-        """
-        import matplotlib.pyplot as plt
-        import matplotlib.patches as patches
-
-        if len(self.symbols)> 3:
-            raise TypeError
-
-        elif len(self.symbols) == 2:
-            import pylab
-            points = []  
-            for verts in self.vertices():
-                    pairs=()
-                    for coordinate, point in verts.coordinates():
-                        pairs = pairs + (float(point),)
-                    points.append(pairs)
-            cent=(sum([p[0] for p in points])/len(points),sum([p[1] for p in points])/len(points))
-            points.sort(key=lambda p: math.atan2(p[1]-cent[1],p[0]-cent[0]))
-            pylab.scatter([p[0] for p in points],[p[1] for p in points])
-            pylab.gca().add_patch(patches.Polygon(points,closed=True,fill=True))
-            pylab.grid()
-            pylab.show()
-
-        elif len(self.symbols)==3:
-            from mpl_toolkits.mplot3d import Axes3D
-            from mpl_toolkits.mplot3d.art3d import Poly3DCollection
-            faces = self.faces()
-            fig = plt.figure()
-            ax = Axes3D(fig)
-            for face in faces:
-                points = []
-                vertices = Polyhedron._sort_polygon_3d(face)
-                for verts in vertices:
-                    pairs=()
-                    for coordinate, point in verts.coordinates():
-                        pairs = pairs + (float(point),)
-                    points.append(pairs)
-                collection = Poly3DCollection([points], alpha=0.7)
-                face_color = [0.5, 0.5, 1] # alternative: matplotlib.colors.rgb2hex([0.5, 0.5, 1])
-                collection.set_facecolor(face_color)
-                ax.add_collection3d(collection)
-            ax.set_xlabel('X')   
-            ax.set_xlim(0, 5)
-            ax.set_ylabel('Y')
-            ax.set_ylim(0, 5)
-            ax.set_zlabel('Z')
-            ax.set_zlim(0, 5)
-            plt.grid()      
-            plt.show()
-        return points
-    
-    @classmethod
-    def limit(cls, faces, variable, lim):
-        sym = []
-        if variable is 'x':
-            n = 0
-        elif variable is 'y':
-            n = 1
-        elif variable is 'z':
-            n = 2
-        for face in faces:
-            for vert in face:
-                coordinates = vert.coordinates()
-                for point in enumerate(coordinates):
-                        coordinates.get(n)
-                        sym.append(points)
-        if lim == 0:
-            value = min(sym)
-        else:
-            value = max(sym)
-        return value
 
 def _polymorphic(func):
     @functools.wraps(func)
@@ -423,8 +356,3 @@ def Ge(left, right):
     Return true if the first set is greater than or equal the second set.
     """
     return Polyhedron([], [left - right])
-
-
-Empty = Eq(1, 0)
-
-Universe = Polyhedron([])