Added some docs

[linpy.git] / pypol / polyhedra.py

diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py
index 2eaa7b5..fe143d4 100644 (file)
--- a/pypol/polyhedra.py
+++ b/pypol/polyhedra.py
@@ -1,4 +1,3 @@
-

 import functools
 import math
 import numbers
 import functools
 import math
 import numbers


@@ -6,9 +5,8 @@ import numbers
 from . import islhelper
 
 from .islhelper import mainctx, libisl
 from . import islhelper
 
 from .islhelper import mainctx, libisl

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

 from .domains import Domain
 
 
 from .domains import Domain
 
 


@@ -58,14 +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


@@ -73,9 +80,15 @@ class Polyhedron(Domain):
         return self,
 
     def disjoint(self):
         return self,
 
     def disjoint(self):

+        """
+        Return a set as disjoint.
+        """

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

+        """
+        Return true if a 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))


@@ -83,6 +96,9 @@ class Polyhedron(Domain):
         return universe
 
     def aspolyhedron(self):
         return universe
 
     def aspolyhedron(self):

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

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


@@ -99,12 +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)


@@ -177,29 +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('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):

+    """
+    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:


@@ -208,123 +262,112 @@ 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)
+class EmptyType(Polyhedron):

 
 

-    @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 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()
+    __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

 
 

-        elif len(self.symbols)==3:
-            return 0
+    def widen(self, other):
+        if not isinstance(other, Polyhedron):
+            raise ValueError('argument must be a Polyhedron instance')
+        return other

 
 

-        return points
+    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):

+    """
+    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):

+    """
+    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):

+    """
+    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):

+    """
+    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):

+    """
+    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):

+    """
+    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([])