Improved example diamonds.py

[linpy.git] / pypol / polyhedra.py

diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py
index c30fd13..a5048d1 100644 (file)
--- a/pypol/polyhedra.py
+++ b/pypol/polyhedra.py
@@ -5,8 +5,7 @@ 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 .geometry import GeometricObject, Point, Vector

 from .linexprs import Expression, Symbol, Rational
 from .domains import Domain
 
 from .linexprs import Expression, Symbol, Rational
 from .domains import Domain
 


@@ -72,9 +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))


@@ -82,6 +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):


@@ -183,14 +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)


@@ -207,16 +228,26 @@ 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)
+

     @classmethod
     def _sort_polygon_2d(cls, points):
         if len(points) <= 3:
             return points
     @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())
+        o = cls._polygon_inner_point(points)

         angles = {}
         for m in points:
             om = Vector(o, m)
         angles = {}
         for m in points:
             om = Vector(o, m)

-            dx, dy = (coordinate for symbol, coordinates in om.coordinates())
+            dx, dy = (coordinate for symbol, coordinate in om.coordinates())

             angle = math.atan2(dy, dx)
             angles[m] = angle
         return sorted(points, key=angles.get)
             angle = math.atan2(dy, dx)
             angles[m] = angle
         return sorted(points, key=angles.get)


@@ -225,102 +256,159 @@ class Polyhedron(Domain):
     def _sort_polygon_3d(cls, points):
         if len(points) <= 3:
             return points
     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]
+        o = cls._polygon_inner_point(points)
+        a = points[0]

         oa = Vector(o, a)
         oa = Vector(o, a)

-        ob = Vector(o, b)

         norm_oa = oa.norm()
         norm_oa = oa.norm()

-        u = (oa.cross(ob)).asunit()
+        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()
         angles = {a: 0.}
         for m in points[1:]:
             om = Vector(o, m)
             normprod = norm_oa * om.norm()

-            cosinus = oa.dot(om) / normprod
+            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)
 
             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):
+    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_2d(self, plot=None, **kwargs):
+        from matplotlib import pylab

         import matplotlib.pyplot as plt
         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)
+        from matplotlib.axes import Axes
+        from matplotlib.patches import Polygon
+        vertices = self._sort_polygon_2d(self.vertices())
+        xys = [tuple(vertex.values()) for vertex in vertices]
+        if plot is None:

             fig = plt.figure()
             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
+            plot = fig.add_subplot(1, 1, 1)
+            xs, ys = zip(*xys)
+            plot.set_xlim(float(min(xs)), float(max(xs)))
+            plot.set_ylim(float(min(ys)), float(max(ys)))
+        plot.add_patch(Polygon(xys, closed=True, **kwargs))
+        return plot
+
+    def _plot_3d(self, plot=None, **kwargs):
+        import matplotlib.pyplot as plt
+        from mpl_toolkits.mplot3d import Axes3D
+        from mpl_toolkits.mplot3d.art3d import Poly3DCollection
+        if plot is None:
+            fig = plt.figure()
+            axes = Axes3D(fig)
+            xmin, xmax = float('inf'), float('-inf')
+            ymin, ymax = float('inf'), float('-inf')
+            zmin, zmax = float('inf'), float('-inf')
+        else:
+            axes = plot
+        poly_xyzs = []
+        for vertices in self.faces():
+            if len(vertices) == 0:
+                continue
+            vertices = Polyhedron._sort_polygon_3d(vertices)
+            vertices.append(vertices[0])
+            face_xyzs = [tuple(vertex.values()) for vertex in vertices]
+            if plot is None:
+                xs, ys, zs = zip(*face_xyzs)
+                xmin, xmax = min(xmin, float(min(xs))), max(xmax, float(max(xs)))
+                ymin, ymax = min(ymin, float(min(ys))), max(ymax, float(max(ys)))
+                zmin, zmax = min(zmin, float(min(zs))), max(zmax, float(max(zs)))
+            poly_xyzs.append(face_xyzs)
+        collection = Poly3DCollection(poly_xyzs, **kwargs)
+        axes.add_collection3d(collection)
+        if plot is None:
+            axes.set_xlim(xmin, xmax)
+            axes.set_ylim(ymin, ymax)
+            axes.set_zlim(zmin, zmax)
+        return axes
+
+    def plot(self, plot=None, **kwargs):
+        """
+        Display 3D plot of set.
+        """
+        if self.dimension == 2:
+            return self._plot_2d(plot=plot, **kwargs)
+        elif self.dimension == 3:
+            return self._plot_3d(plot=plot, **kwargs)
+        else:
+            raise ValueError('polyhedron must be 2 or 3-dimensional')

 
 
 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])