Added some docs

[linpy.git] / pypol / polyhedra.py

diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py
index 5d1bfa1..fe143d4 100644 (file)
--- a/pypol/polyhedra.py
+++ b/pypol/polyhedra.py
@@ -5,8 +5,8 @@ import numbers
 from . import islhelper
 
 from .islhelper import mainctx, libisl
 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
 
 
 from .domains import Domain
 
 


@@ -56,14 +56,23 @@ class Polyhedron(Domain):
 
     @property
     def equalities(self):
 
     @property
     def equalities(self):

+    """
+    Return a list of the equalities in a set.
+    """

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

+    """
+    Return a list of the inequalities in a set.
+    """

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

+    """
+    Return ta list of the constraints of a set.
+    """

         return self._constraints
 
     @property
         return self._constraints
 
     @property


@@ -72,13 +81,13 @@ class Polyhedron(Domain):
 
     def disjoint(self):
         """
 
     def disjoint(self):
         """

-        Return this set as disjoint.
+        Return a set as disjoint.

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

-        Return true if this set is the Universe set.
+        Return true if a set is the Universe set.

         """
         islbset = self._toislbasicset(self.equalities, self.inequalities,
             self.symbols)
         """
         islbset = self._toislbasicset(self.equalities, self.inequalities,
             self.symbols)


@@ -88,7 +97,7 @@ class Polyhedron(Domain):
 
     def aspolyhedron(self):
         """
 
     def aspolyhedron(self):
         """

-        Return polyhedral hull of this set.
+        Return polyhedral hull of a set.

         """
         return self
 
         """
         return self
 


@@ -106,12 +115,40 @@ 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)
             for inequality in self.inequalities]
         return Polyhedron(equalities, inequalities)
 
         equalities = [equality.subs(symbol, expression)
             for equality in self.equalities]
         inequalities = [inequality.subs(symbol, expression)
             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):
         islconstraints = islhelper.isl_basic_set_constraints(islbset)
     @classmethod
     def _fromislbasicset(cls, islbset, symbols):
         islconstraints = islhelper.isl_basic_set_constraints(islbset)


@@ -184,42 +221,39 @@ 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('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):
 
     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):
 
     @classmethod
     def fromsympy(cls, expr):

+    """
+    Convert a sympy object to an expression.
+    """

         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 an expression as a sympy object. 
+    """

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


@@ -228,141 +262,54 @@ 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 _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)
+class EmptyType(Polyhedron):

 
 

-    @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)
+    __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)
 
 def _polymorphic(func):
     @functools.wraps(func)


@@ -385,46 +332,42 @@ def _polymorphic(func):
 @_polymorphic
 def Lt(left, right):
     """
 @_polymorphic
 def Lt(left, right):
     """

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

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

     """
     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.
+    Assert first set is equal to the second set.

     """
     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.
+    Assert first set is not equal to the second set.

     """
     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.
+    Assert 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.
+    Assert first set is greater than or equal to the second set.

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

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