3d Plot working

diff --git a/examples/diamond.py b/examples/diamond.py
index 5d0de4e..e82581e 100755 (executable)
--- a/examples/diamond.py
+++ b/examples/diamond.py
@@ -2,7 +2,17 @@
 
 from pypol import *
 
 
 from pypol import *
 

-x, y = symbols('x y')
+x, y, z = symbols('x y z')

 diam = Ge(y, x - 1) & Le(y, x + 1) & Ge(y, -x - 1) & Le(y, -x + 1)
 print('diamond:', diam)
 diam = Ge(y, x - 1) & Le(y, x + 1) & Ge(y, -x - 1) & Le(y, -x + 1)
 print('diamond:', diam)

-print('projected on x:', diam.project([y]))
+print() 
+rhom1 = Le(0, x) & Le(x, 3) & Le(0, y) & Le(y, 3) & Le(0, z) & Le(z, 3) \
+& Le(z - 2, x) & Ge(z + 2, x) & Ge(z - 1, -x) & Le(z - 5, -x) \
+& Le(z - 2, y) & Ge(z + 2, y) & Ge(z - 1, -y) & Le(z - 5, -y) \
+& Le(y - 2, x) & Ge(y + 2, x) & Ge(y - 1, -x) & Le(y - 5, -x)
+rhom1.plot()
+rhom2 = rhom1 & Le(x + y + z, 7) & Ge(-2, -x - y - z ) \
+& Le(x + y - z, 4) & Ge(x + y - z, -1) \
+& Le(x - y + z, 4) & Ge(x - y + z, -1) \
+& Le(-x + y + z, 4) & Ge(-x + y + z, -1)
+rhom2.plot()

diff --git a/pypol/domains.py b/pypol/domains.py
index 10d12c5..28ce533 100644 (file)
--- a/pypol/domains.py
+++ b/pypol/domains.py
@@ -67,11 +67,17 @@ class Domain(GeometricObject):
         return self._dimension
 
     def disjoint(self):
         return self._dimension
 
     def disjoint(self):

+        """
+        Returns this set as disjoint.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_make_disjoint(mainctx, islset)
         return self._fromislset(islset, self.symbols)
 
     def isempty(self):
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_make_disjoint(mainctx, islset)
         return self._fromislset(islset, self.symbols)
 
     def isempty(self):

+        """
+        Returns true if this set is an Empty set.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         empty = bool(libisl.isl_set_is_empty(islset))
         libisl.isl_set_free(islset)
         islset = self._toislset(self.polyhedra, self.symbols)
         empty = bool(libisl.isl_set_is_empty(islset))
         libisl.isl_set_free(islset)


@@ -81,18 +87,27 @@ class Domain(GeometricObject):
         return not self.isempty()
 
     def isuniverse(self):
         return not self.isempty()
 
     def isuniverse(self):

+        """
+        Returns true if this set is the Universe set.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         universe = bool(libisl.isl_set_plain_is_universe(islset))
         libisl.isl_set_free(islset)
         return universe
 
     def isbounded(self):
         islset = self._toislset(self.polyhedra, self.symbols)
         universe = bool(libisl.isl_set_plain_is_universe(islset))
         libisl.isl_set_free(islset)
         return universe
 
     def isbounded(self):

+        """
+        Returns true if this set is bounded.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         bounded = bool(libisl.isl_set_is_bounded(islset))
         libisl.isl_set_free(islset)
         return bounded
 
     def __eq__(self, other):
         islset = self._toislset(self.polyhedra, self.symbols)
         bounded = bool(libisl.isl_set_is_bounded(islset))
         libisl.isl_set_free(islset)
         return bounded
 
     def __eq__(self, other):

+        """
+        Returns true if two sets are equal.
+        """

         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = other._toislset(other.polyhedra, symbols)
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = other._toislset(other.polyhedra, symbols)


@@ -102,6 +117,9 @@ class Domain(GeometricObject):
         return equal
 
     def isdisjoint(self, other):
         return equal
 
     def isdisjoint(self, other):

+        """
+        Return True if two sets have a null intersection.
+        """

         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)


@@ -111,6 +129,9 @@ class Domain(GeometricObject):
         return equal
 
     def issubset(self, other):
         return equal
 
     def issubset(self, other):

+        """
+        Report whether another set contains this set.
+        """

         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)


@@ -120,9 +141,15 @@ class Domain(GeometricObject):
         return equal
 
     def __le__(self, other):
         return equal
 
     def __le__(self, other):

+        """
+        Returns true if this set is less than or equal to another set.
+        """

         return self.issubset(other)
 
     def __lt__(self, other):
         return self.issubset(other)
 
     def __lt__(self, other):

+        """
+        Returns true if this set is less than another set.
+        """

         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = self._toislset(other.polyhedra, symbols)


@@ -132,23 +159,31 @@ class Domain(GeometricObject):
         return equal
 
     def complement(self):
         return equal
 
     def complement(self):

+        """
+        Returns the complement of this set.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_complement(islset)
         return self._fromislset(islset, self.symbols)
 
     def __invert__(self):
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_complement(islset)
         return self._fromislset(islset, self.symbols)
 
     def __invert__(self):

+        """
+        Returns the complement of this set.
+        """

         return self.complement()
 
     def simplify(self):
         return self.complement()
 
     def simplify(self):

-        #does not change anything in any of the examples
-        #isl seems to do this naturally
+        """
+        Returns a set without redundant constraints.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_remove_redundancies(islset)
         return self._fromislset(islset, self.symbols)
 
     def aspolyhedron(self):
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_remove_redundancies(islset)
         return self._fromislset(islset, self.symbols)
 
     def aspolyhedron(self):

-        # several types of hull are available
-        # polyhedral seems to be the more appropriate, to be checked
+        """
+        Returns polyhedral hull of set.
+        """

         from .polyhedra import Polyhedron
         islset = self._toislset(self.polyhedra, self.symbols)
         islbset = libisl.isl_set_polyhedral_hull(islset)
         from .polyhedra import Polyhedron
         islset = self._toislset(self.polyhedra, self.symbols)
         islbset = libisl.isl_set_polyhedral_hull(islset)


@@ -158,7 +193,9 @@ class Domain(GeometricObject):
         return self
 
     def project(self, dims):
         return self
 
     def project(self, dims):

-        # use to remove certain variables
+        """
+        Return new set with given dimensions removed.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         n = 0
         for index, symbol in reversed(list(enumerate(self.symbols))):
         islset = self._toislset(self.polyhedra, self.symbols)
         n = 0
         for index, symbol in reversed(list(enumerate(self.symbols))):


@@ -173,6 +210,9 @@ class Domain(GeometricObject):
         return Domain._fromislset(islset, dims)
 
     def sample(self):
         return Domain._fromislset(islset, dims)
 
     def sample(self):

+        """
+        Returns a single subset of the input.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         islpoint = libisl.isl_set_sample_point(islset)
         if bool(libisl.isl_point_is_void(islpoint)):
         islset = self._toislset(self.polyhedra, self.symbols)
         islpoint = libisl.isl_set_sample_point(islset)
         if bool(libisl.isl_point_is_void(islpoint)):


@@ -188,6 +228,9 @@ class Domain(GeometricObject):
         return point
 
     def intersection(self, *others):
         return point
 
     def intersection(self, *others):

+        """
+         Return the intersection of two sets as a new set.
+        """

         if len(others) == 0:
             return self
         symbols = self._xsymbols((self,) + others)
         if len(others) == 0:
             return self
         symbols = self._xsymbols((self,) + others)


@@ -198,9 +241,15 @@ class Domain(GeometricObject):
         return self._fromislset(islset1, symbols)
 
     def __and__(self, other):
         return self._fromislset(islset1, symbols)
 
     def __and__(self, other):

+        """
+         Return the intersection of two sets as a new set.
+        """

         return self.intersection(other)
 
     def union(self, *others):
         return self.intersection(other)
 
     def union(self, *others):

+        """
+        Return the union of sets as a new set.
+        """

         if len(others) == 0:
             return self
         symbols = self._xsymbols((self,) + others)
         if len(others) == 0:
             return self
         symbols = self._xsymbols((self,) + others)


@@ -211,12 +260,21 @@ class Domain(GeometricObject):
         return self._fromislset(islset1, symbols)
 
     def __or__(self, other):
         return self._fromislset(islset1, symbols)
 
     def __or__(self, other):

+        """
+        Return a new set with elements from both sets.
+        """

         return self.union(other)
 
     def __add__(self, other):
         return self.union(other)
 
     def __add__(self, other):

+        """
+        Return new set containing all elements in both sets.
+        """

         return self.union(other)
 
     def difference(self, other):
         return self.union(other)
 
     def difference(self, other):

+        """
+        Return the difference of two sets as a new set.
+        """

         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = other._toislset(other.polyhedra, symbols)
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = other._toislset(other.polyhedra, symbols)


@@ -224,26 +282,39 @@ class Domain(GeometricObject):
         return self._fromislset(islset, symbols)
 
     def __sub__(self, other):
         return self._fromislset(islset, symbols)
 
     def __sub__(self, other):

+        """
+        Return the difference of two sets as a new set.
+        """

         return self.difference(other)
 
     def lexmin(self):
         return self.difference(other)
 
     def lexmin(self):

+        """
+        Return a new set containing the lexicographic minimum of the elements in the set.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_lexmin(islset)
         return self._fromislset(islset, self.symbols)
 
     def lexmax(self):
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_lexmin(islset)
         return self._fromislset(islset, self.symbols)
 
     def lexmax(self):

+        """
+        Return a new set containing the lexicographic maximum of the elements in the set.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_lexmax(islset)
         return self._fromislset(islset, self.symbols)
 
     def num_parameters(self):
         islset = self._toislset(self.polyhedra, self.symbols)
         islset = libisl.isl_set_lexmax(islset)
         return self._fromislset(islset, self.symbols)
 
     def num_parameters(self):

-        #could be useful with large, complicated polyhedrons
+        """
+        Return the total number of parameters, input, output or set dimensions.
+        """

         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
         num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
         return num
 
     def involves_dims(self, dims):
         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
         num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
         return num
 
     def involves_dims(self, dims):

-        #could be useful with large, complicated polyhedrons
+        """
+        Returns true if set depends on given dimensions.
+        """

         islset = self._toislset(self.polyhedra, self.symbols)
         dims = sorted(dims)
         symbols = sorted(list(self.symbols))
         islset = self._toislset(self.polyhedra, self.symbols)
         dims = sorted(dims)
         symbols = sorted(list(self.symbols))


@@ -264,8 +335,12 @@ class Domain(GeometricObject):
     _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
 
     def vertices(self):
     _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
 
     def vertices(self):

-        #returning list of verticies
+        """
+        Return a list of vertices for this Polygon.
+        """

         from .polyhedra import Polyhedron
         from .polyhedra import Polyhedron

+        if not self.isbounded():
+            raise ValueError('domain must be bounded')

         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
         vertices = libisl.isl_basic_set_compute_vertices(islbset);
         vertices = islhelper.isl_vertices_vertices(vertices)
         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
         vertices = libisl.isl_basic_set_compute_vertices(islbset);
         vertices = islhelper.isl_vertices_vertices(vertices)


@@ -286,6 +361,7 @@ class Domain(GeometricObject):
                             coordinate = -Fraction(constant, coefficient)
                             coordinates.append((symbol, coordinate))
             else:
                             coordinate = -Fraction(constant, coefficient)
                             coordinates.append((symbol, coordinate))
             else:

+                

                 # horrible hack, find a cleaner solution
                 string = islhelper.isl_multi_aff_to_str(expr)
                 matches = self._RE_COORDINATE.finditer(string)
                 # horrible hack, find a cleaner solution
                 string = islhelper.isl_multi_aff_to_str(expr)
                 matches = self._RE_COORDINATE.finditer(string)


@@ -299,6 +375,9 @@ class Domain(GeometricObject):
         return points
 
     def points(self):
         return points
 
     def points(self):

+        """
+        Returns the points contained in the set.
+        """

         if not self.isbounded():
             raise ValueError('domain must be bounded')
         from .polyhedra import Universe, Eq
         if not self.isbounded():
             raise ValueError('domain must be bounded')
         from .polyhedra import Universe, Eq


@@ -468,6 +547,9 @@ class Domain(GeometricObject):
 
 
 def And(*domains):
 
 
 def And(*domains):

+    """
+    Return the intersection of two sets as a new set.
+    """

     if len(domains) == 0:
         from .polyhedra import Universe
         return Universe
     if len(domains) == 0:
         from .polyhedra import Universe
         return Universe


@@ -475,6 +557,9 @@ def And(*domains):
         return domains[0].intersection(*domains[1:])
 
 def Or(*domains):
         return domains[0].intersection(*domains[1:])
 
 def Or(*domains):

+    """
+    Return the union of sets as a new set.
+    """

     if len(domains) == 0:
         from .polyhedra import Empty
         return Empty
     if len(domains) == 0:
         from .polyhedra import Empty
         return Empty


@@ -482,4 +567,7 @@ def Or(*domains):
         return domains[0].union(*domains[1:])
 
 def Not(domain):
         return domains[0].union(*domains[1:])
 
 def Not(domain):

+    """
+    Returns the complement of this set.
+    """

     return ~domain
     return ~domain

diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py
index 6b5f9ab..5d1bfa1 100644 (file)
--- a/pypol/polyhedra.py
+++ b/pypol/polyhedra.py
@@ -71,9 +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))


@@ -81,6 +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):


@@ -263,7 +272,7 @@ class Polyhedron(Domain):
         for m in points[1:]:
             om = Vector(o, m)
             normprod = norm_oa * om.norm()
         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)
             sinus = u.dot(oa.cross(om)) / normprod
             angle = math.acos(cosinus)
             angle = math.copysign(angle, sinus)


@@ -282,44 +291,78 @@ class Polyhedron(Domain):
         return faces
 
     def plot(self):
         return faces
 
     def plot(self):

+        """
+        Display 3D plot of set. 
+        """

         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:
         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()
+            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:
 
         elif len(self.symbols)==3:

-            return 0
-
+            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
         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)


@@ -341,26 +384,44 @@ def _polymorphic(func):
 
 @_polymorphic
 def Lt(left, right):
 
 @_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])