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__
+
+ 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[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(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[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:
- 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
-
- @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)
@_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