Minor improvements in diamonds.py example

[linpy.git] / pypol / polyhedra.py

diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py
index 44826c1..aabe0fd 100644 (file)
--- a/pypol/polyhedra.py
+++ b/pypol/polyhedra.py
@@ -1,10 +1,12 @@
 import functools
 import functools

+import math

 import numbers
 
 from . import islhelper
 
 from .islhelper import mainctx, libisl
 import numbers
 
 from . import islhelper
 
 from .islhelper import mainctx, libisl

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

 from .domains import Domain
 
 
 from .domains import Domain
 
 


@@ -30,28 +32,24 @@ class Polyhedron(Domain):
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return cls.fromstring(equalities)
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return cls.fromstring(equalities)

-        elif isinstance(equalities, Polyhedron):
+        elif isinstance(equalities, GeometricObject):

             if inequalities is not None:
                 raise TypeError('too many arguments')
             if inequalities is not None:
                 raise TypeError('too many arguments')

-            return equalities
-        elif isinstance(equalities, Domain):
-            if inequalities is not None:
-                raise TypeError('too many arguments')
-            return equalities.polyhedral_hull()
+            return equalities.aspolyhedron()

         if equalities is None:
             equalities = []
         else:
             for i, equality in enumerate(equalities):
                 if not isinstance(equality, Expression):
                     raise TypeError('equalities must be linear expressions')
         if equalities is None:
             equalities = []
         else:
             for i, equality in enumerate(equalities):
                 if not isinstance(equality, Expression):
                     raise TypeError('equalities must be linear expressions')

-                equalities[i] = equality._toint()
+                equalities[i] = equality.scaleint()

         if inequalities is None:
             inequalities = []
         else:
             for i, inequality in enumerate(inequalities):
                 if not isinstance(inequality, Expression):
                     raise TypeError('inequalities must be linear expressions')
         if inequalities is None:
             inequalities = []
         else:
             for i, inequality in enumerate(inequalities):
                 if not isinstance(inequality, Expression):
                     raise TypeError('inequalities must be linear expressions')

-                inequalities[i] = inequality._toint()
+                inequalities[i] = inequality.scaleint()

         symbols = cls._xsymbols(equalities + inequalities)
         islbset = cls._toislbasicset(equalities, inequalities, symbols)
         return cls._fromislbasicset(islbset, symbols)
         symbols = cls._xsymbols(equalities + inequalities)
         islbset = cls._toislbasicset(equalities, inequalities, symbols)
         return cls._fromislbasicset(islbset, symbols)


@@ -73,30 +71,59 @@ 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))
         libisl.isl_basic_set_free(islbset)
         return universe
 
         islbset = self._toislbasicset(self.equalities, self.inequalities,
             self.symbols)
         universe = bool(libisl.isl_basic_set_is_universe(islbset))
         libisl.isl_basic_set_free(islbset)
         return universe
 

-    def polyhedral_hull(self):
+    def aspolyhedron(self):
+        """
+        Return polyhedral hull of this set.
+        """

         return self
 
         return self
 

+    def __contains__(self, point):
+        if not isinstance(point, Point):
+            raise TypeError('point must be a Point instance')
+        if self.symbols != point.symbols:
+            raise ValueError('arguments must belong to the same space')
+        for equality in self.equalities:
+            if equality.subs(point.coordinates()) != 0:
+                return False
+        for inequality in self.inequalities:
+            if inequality.subs(point.coordinates()) < 0:
+                return False
+        return True
+
+    def subs(self, symbol, expression=None):
+        equalities = [equality.subs(symbol, expression)
+            for equality in self.equalities]
+        inequalities = [inequality.subs(symbol, expression)
+            for inequality in self.inequalities]
+        return Polyhedron(equalities, inequalities)
+

     @classmethod
     def _fromislbasicset(cls, islbset, symbols):
         islconstraints = islhelper.isl_basic_set_constraints(islbset)
         equalities = []
         inequalities = []
         for islconstraint in islconstraints:
     @classmethod
     def _fromislbasicset(cls, islbset, symbols):
         islconstraints = islhelper.isl_basic_set_constraints(islbset)
         equalities = []
         inequalities = []
         for islconstraint in islconstraints:

-            islpr = libisl.isl_printer_to_str(mainctx)

             constant = libisl.isl_constraint_get_constant_val(islconstraint)
             constant = islhelper.isl_val_to_int(constant)
             coefficients = {}
             for index, symbol in enumerate(symbols):
             constant = libisl.isl_constraint_get_constant_val(islconstraint)
             constant = islhelper.isl_val_to_int(constant)
             coefficients = {}
             for index, symbol in enumerate(symbols):

-                coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint, libisl.isl_dim_set, index)
+                coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint,
+                    libisl.isl_dim_set, index)

                 coefficient = islhelper.isl_val_to_int(coefficient)
                 if coefficient != 0:
                     coefficients[symbol] = coefficient
                 coefficient = islhelper.isl_val_to_int(coefficient)
                 if coefficient != 0:
                     coefficients[symbol] = coefficient


@@ -172,38 +199,25 @@ class Polyhedron(Domain):
             else:
                 return 'And({})'.format(', '.join(strings))
 
             else:
                 return 'And({})'.format(', '.join(strings))
 

-    @classmethod
-    def _fromsympy(cls, expr):
-        import sympy
-        equalities = []
-        inequalities = []
-        if expr.func == sympy.And:
-            for arg in expr.args:
-                arg_eqs, arg_ins = cls._fromsympy(arg)
-                equalities.extend(arg_eqs)
-                inequalities.extend(arg_ins)
-        elif expr.func == sympy.Eq:
-            expr = Expression.fromsympy(expr.args[0] - expr.args[1])
-            equalities.append(expr)
+    def _repr_latex_(self):
+        if self.isempty():
+            return '$\\emptyset$'
+        elif self.isuniverse():
+            return '$\\Omega$'

         else:
         else:

-            if expr.func == sympy.Lt:
-                expr = Expression.fromsympy(expr.args[1] - expr.args[0] - 1)
-            elif expr.func == sympy.Le:
-                expr = Expression.fromsympy(expr.args[1] - expr.args[0])
-            elif expr.func == sympy.Ge:
-                expr = Expression.fromsympy(expr.args[0] - expr.args[1])
-            elif expr.func == sympy.Gt:
-                expr = Expression.fromsympy(expr.args[0] - expr.args[1] - 1)
-            else:
-                raise ValueError('non-polyhedral expression: {!r}'.format(expr))
-            inequalities.append(expr)
-        return equalities, inequalities
+            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):

-        import sympy
-        equalities, inequalities = cls._fromsympy(expr)
-        return cls(equalities, inequalities)
+        domain = Domain.fromsympy(expr)
+        if not isinstance(domain, Polyhedron):
+            raise ValueError('non-polyhedral expression: {!r}'.format(expr))
+        return domain

 
     def tosympy(self):
         import sympy
 
     def tosympy(self):
         import sympy


@@ -214,45 +228,187 @@ 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
+        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)
+
+    @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_2d(self, plot=None, **kwargs):
+        import matplotlib.pyplot as plt
+        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()
+            plot = fig.add_subplot(1, 1, 1)
+        xmin, xmax = plot.get_xlim()
+        ymin, ymax = plot.get_xlim()
+        xs, ys = zip(*xys)
+        xmin, xmax = min(xmin, float(min(xs))), max(xmax, float(max(xs)))
+        ymin, ymax = min(ymin, float(min(ys))), max(ymax, float(max(ys)))
+        plot.set_xlim(xmin, xmax)
+        plot.set_ylim(ymin, ymax)
+        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)
+        else:
+            axes = plot
+        xmin, xmax = axes.get_xlim()
+        ymin, ymax = axes.get_xlim()
+        zmin, zmax = axes.get_xlim()
+        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]
+            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)
+        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 = Constant(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 = Constant(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])