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
@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
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)
def aspolyhedron(self):
"""
- Return polyhedral hull of this set.
+ Return polyhedral hull of a set.
"""
return self
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)
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[0]
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[0]
- 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:
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)
+class EmptyType(Polyhedron):
- @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)
+ __slots__ = Polyhedron.__slots__
- @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 __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()
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([])
projects / linpy.git / blobdiff