index 5d1bfa1..9bfc64b 100644 (file)
@@ -1,3 +1,20 @@
+#
+# 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 functools
import math
import numbers
@@ -5,8 +22,8 @@ import numbers
from . import islhelper

from .islhelper import mainctx, libisl
-from .geometry import GeometricObject, Point, Vector
-from .linexprs import Expression, Symbol, Rational
+from .geometry import GeometricObject, Point
+from .linexprs import Expression, Rational
from .domains import Domain

@@ -56,14 +73,23 @@ class Polyhedron(Domain):

@property
def equalities(self):
+        """
+        Return a list of the equalities in a set.
+        """
return self._equalities

@property
def inequalities(self):
+        """
+        Return a list of the inequalities in a set.
+        """
return self._inequalities

@property
def constraints(self):
+        """
+        Return ta list of the constraints of a set.
+        """
return self._constraints

@property
@@ -72,13 +98,13 @@ class Polyhedron(Domain):

def disjoint(self):
"""
-        Return this set as disjoint.
+        Return a set as disjoint.
"""
return self

def isuniverse(self):
"""
-        Return true if this set is the Universe set.
+        Return true if a set is the Universe set.
"""
islbset = self._toislbasicset(self.equalities, self.inequalities,
self.symbols)
@@ -88,7 +114,7 @@ class Polyhedron(Domain):

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

@@ -106,12 +132,41 @@ class Polyhedron(Domain):
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)

+    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)
@@ -184,42 +239,39 @@ class Polyhedron(Domain):
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
else:
-            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
-            else:
-                return 'And({})'.format(', '.join(strings))
+            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))
+        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):
+        """
+        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):
+        """
+        Return an expression as a sympy object.
+        """
import sympy
constraints = []
for equality in self.equalities:
@@ -228,141 +280,55 @@ class Polyhedron(Domain):
constraints.append(sympy.Ge(inequality.tosympy(), 0))
return sympy.And(*constraints)

-    @classmethod
-    def _polygon_inner_point(cls, points):
-        symbols = points.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)
+class EmptyType(Polyhedron):
+
+    __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
+
+    def widen(self, other):
+        if not isinstance(other, Polyhedron):
+            raise ValueError('argument must be a Polyhedron instance')
+        return other
+
+    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()

-    @classmethod
-    def _sort_polygon_3d(cls, points):
-        if len(points) <= 3:
-            return points
-        o = cls._polygon_inner_point(points)
-        a = points
-        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(self):
-        """
-        Display 3D plot of set.
-        """
-        import matplotlib.pyplot as plt
-        import matplotlib.patches as patches
-
-        if len(self.symbols)> 3:
-            raise TypeError
-
-        elif len(self.symbols) == 2:
-            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 for p in points])/len(points),sum([p for p in points])/len(points))
-            points.sort(key=lambda p: math.atan2(p-cent,p-cent))
-            pylab.scatter([p for p in points],[p for p in points])
-            pylab.grid()
-            pylab.show()
-
-        elif len(self.symbols)==3:
-            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.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
-
-    @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)
@@ -385,46 +351,41 @@ def _polymorphic(func):
@_polymorphic
def Lt(left, right):
"""
-    Return true if the first set is less than the second.
+    Assert first set is less than the second set.
"""
return Polyhedron([], [right - left - 1])

@_polymorphic
def Le(left, right):
"""
-    Return true the first set is less than or equal to the second.
+    Assert first set is less than or equal to the second set.
"""
return Polyhedron([], [right - left])

@_polymorphic
def Eq(left, right):
"""
-    Return true if the sets are equal.
+    Assert first set is equal to the second set.
"""
return Polyhedron([left - right], [])

@_polymorphic
def Ne(left, right):
"""
-    Return true if the sets are NOT equal.
+    Assert first set is not equal to the second set.
"""
return ~Eq(left, right)

@_polymorphic
def Gt(left, right):
"""
-    Return true if the first set is greater than the second set.
+    Assert first set is greater than the second set.
"""
return Polyhedron([], [left - right - 1])

@_polymorphic
def Ge(left, right):
"""
-    Return true if the first set is greater than or equal the second set.
+    Assert first set is greater than or equal to the second set.
"""
return Polyhedron([], [left - right])
-
-
-Empty = Eq(1, 0)
-
-Universe = Polyhedron([])