X-Git-Url: https://svn.cri.ensmp.fr/git/linpy.git/blobdiff_plain/ce31a1de5082c55b5eed1825ae95d827c55a8b92..9b755b94aa2c8847ffca607de239f5c3bca9984b:/pypol/domains.py

diff --git a/pypol/domains.py b/pypol/domains.py
index 5d98af8..f918e14 100644
--- a/pypol/domains.py
+++ b/pypol/domains.py
@@ -1,14 +1,31 @@
+# Copyright 2014 MINES ParisTech
+#
+# This file is part of Linpy.
+#
+# Linpy is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# Linpy is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with Linpy.  If not, see <http://www.gnu.org/licenses/>.
+
 import ast
 import functools
 import re
+import math
 
 from fractions import Fraction
 
 from . import islhelper
 from .islhelper import mainctx, libisl
-from .geometry import GeometricObject
-from .coordinates import Point
-from .linexprs import Expression, Symbol
+from .linexprs import Expression, Symbol, Rational
+from .geometry import GeometricObject, Point, Vector
 
 
 __all__ = [
@@ -68,11 +85,17 @@ class Domain(GeometricObject):
         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):
+        """
+        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)
@@ -82,18 +105,27 @@ class Domain(GeometricObject):
         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):
+        """
+        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):
+        """
+        Returns true if two sets are equal.
+        """
         symbols = self._xsymbols([self, other])
         islset1 = self._toislset(self.polyhedra, symbols)
         islset2 = other._toislset(other.polyhedra, symbols)
@@ -103,6 +135,9 @@ class Domain(GeometricObject):
         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)
@@ -112,6 +147,9 @@ class Domain(GeometricObject):
         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)
@@ -121,9 +159,15 @@ class Domain(GeometricObject):
         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):
+        """
+        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)
@@ -133,23 +177,31 @@ class Domain(GeometricObject):
         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):
+        """
+        Returns the complement of this set.
+        """
         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):
-        # 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)
@@ -159,7 +211,9 @@ class Domain(GeometricObject):
         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))):
@@ -174,6 +228,9 @@ class Domain(GeometricObject):
         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)):
@@ -189,6 +246,9 @@ class Domain(GeometricObject):
         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)
@@ -199,9 +259,15 @@ class Domain(GeometricObject):
         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 the union of sets as a new set.
+        """
         if len(others) == 0:
             return self
         symbols = self._xsymbols((self,) + others)
@@ -212,12 +278,21 @@ class Domain(GeometricObject):
         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 new set containing all elements in both sets.
+        """
         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)
@@ -225,28 +300,34 @@ class Domain(GeometricObject):
         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 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):
+        """
+        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):
-        #could be useful with large, complicated polyhedrons
-        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
+    def involves_vars(self, vars):
+        """
+        Returns true if a set depends on given dimensions.
+        """
         islset = self._toislset(self.polyhedra, self.symbols)
-        dims = sorted(dims)
+        dims = sorted(vars)
         symbols = sorted(list(self.symbols))
         n = 0
         if len(dims)>0:
@@ -265,8 +346,12 @@ class Domain(GeometricObject):
     _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
+        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)
@@ -287,7 +372,6 @@ class Domain(GeometricObject):
                             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)
                 for symbol, match in zip(self.symbols, matches):
@@ -300,6 +384,9 @@ class Domain(GeometricObject):
         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
@@ -316,6 +403,135 @@ class Domain(GeometricObject):
             points.append(Point(coordinates))
         return points
 
+    @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):
+        """
+        Returns the vertices of the faces of a polyhedra.
+        """
+        faces = []
+        for polyhedron in self.polyhedra:
+            vertices = polyhedron.vertices()
+            for constraint in polyhedron.constraints:
+                face = []
+                for vertex in vertices:
+                    if constraint.subs(vertex.coordinates()) == 0:
+                        face.append(vertex)
+                if len(face) >= 3:
+                    faces.append(face)
+        return faces
+
+    def _plot_2d(self, plot=None, **kwargs):
+        import matplotlib.pyplot as plt
+        from matplotlib.patches import Polygon
+        if plot is None:
+            fig = plt.figure()
+            plot = fig.add_subplot(1, 1, 1)
+        xmin, xmax = plot.get_xlim()
+        ymin, ymax = plot.get_ylim()
+        for polyhedron in self.polyhedra:
+            vertices = polyhedron._sort_polygon_2d(polyhedron.vertices())
+            xys = [tuple(vertex.values()) for vertex in vertices]
+            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.add_patch(Polygon(xys, closed=True, **kwargs))
+        plot.set_xlim(xmin, xmax)
+        plot.set_ylim(ymin, ymax)
+        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_ylim()
+        zmin, zmax = axes.get_zlim()
+        poly_xyzs = []
+        for vertices in self.faces():
+            vertices = self._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 plot of this set.
+        """
+        if not self.isbounded():
+            raise ValueError('domain must be bounded')
+        elif 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 __contains__(self, point):
         for polyhedron in self.polyhedra:
             if point in polyhedron:
@@ -323,6 +539,10 @@ class Domain(GeometricObject):
         return False
 
     def subs(self, symbol, expression=None):
+        """
+        Subsitute the given value into an expression and return the resulting
+        expression.
+        """
         polyhedra = [polyhedron.subs(symbol, expression)
             for polyhedron in self.polyhedra]
         return Domain(*polyhedra)
@@ -439,6 +659,12 @@ class Domain(GeometricObject):
         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
         return 'Or({})'.format(', '.join(strings))
 
+    def _repr_latex_(self):
+        strings = []
+        for polyhedron in self.polyhedra:
+            strings.append('({})'.format(polyhedron._repr_latex_().strip('$')))
+        return '${}$'.format(' \\vee '.join(strings))
+
     @classmethod
     def fromsympy(cls, expr):
         import sympy
@@ -463,6 +689,9 @@ class Domain(GeometricObject):
 
 
 def And(*domains):
+    """
+    Return the intersection of two sets as a new set.
+    """
     if len(domains) == 0:
         from .polyhedra import Universe
         return Universe
@@ -470,6 +699,9 @@ def And(*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
@@ -477,4 +709,7 @@ def Or(*domains):
         return domains[0].union(*domains[1:])
 
 def Not(domain):
+    """
+    Returns the complement of this set.
+    """
     return ~domain