from .islhelper import mainctx, libisl
from .geometry import GeometricObject, Point
-from .linexprs import Expression, Symbol, Rational
+from .linexprs import Expression, Rational
from .domains import Domain
return self,
def disjoint(self):
+ """
+ Return this set as disjoint.
+ """
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))
return universe
def aspolyhedron(self):
+ """
+ Return polyhedral hull of this set.
+ """
return self
def __contains__(self, point):
else:
strings = []
for equality in self.equalities:
- strings.append('0 == {}'.format(equality))
+ strings.append('Eq({}, 0)'.format(equality))
for inequality in self.inequalities:
- strings.append('0 <= {}'.format(inequality))
+ strings.append('Ge({}, 0)'.format(inequality))
if len(strings) == 1:
return strings[0]
else:
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))
+
@classmethod
def fromsympy(cls, expr):
domain = Domain.fromsympy(expr)
constraints.append(sympy.Ge(inequality.tosympy(), 0))
return sympy.And(*constraints)
- @classmethod
- def _sort_polygon_2d(cls, points):
- if len(points) <= 3:
- return points
- o = sum((Vector(point) for point in points)) / len(points)
- o = Point(o.coordinates())
- angles = {}
- for m in points:
- om = Vector(o, m)
- dx, dy = (coordinate for symbol, coordinates 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 = sum((Vector(point) for point in points)) / len(points)
- o = Point(o.coordinates())
- a, b = points[:2]
- oa = Vector(o, a)
- ob = Vector(o, b)
- norm_oa = oa.norm()
- u = (oa.cross(ob)).asunit()
- angles = {a: 0.}
- for m in points[1:]:
- om = Vector(o, m)
- normprod = norm_oa * om.norm()
- cosinus = oa.dot(om) / normprod
- 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):
- 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:
- 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()
-
- elif len(self.symbols)==3:
- return 0
-
- return points
-
-
def _polymorphic(func):
@functools.wraps(func)
def wrapper(left, right):
- if isinstance(left, numbers.Rational):
- left = Rational(left)
- elif not isinstance(left, Expression):
- raise TypeError('left must be a a rational number '
- 'or a linear expression')
- if isinstance(right, numbers.Rational):
- right = Rational(right)
- elif not isinstance(right, Expression):
- raise TypeError('right must be a a rational number '
- 'or a linear expression')
+ if not isinstance(left, Expression):
+ if isinstance(left, numbers.Rational):
+ left = Rational(left)
+ else:
+ raise TypeError('left must be a a rational number '
+ 'or a linear expression')
+ if not isinstance(right, Expression):
+ if isinstance(right, numbers.Rational):
+ right = Rational(right)
+ else:
+ raise TypeError('right must be a a rational number '
+ 'or a linear expression')
return func(left, right)
return wrapper
@_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 true the first set is less than or equal to the second.
+ """
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 true if the sets are NOT equal.
+ """
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 true if the first set is greater than or equal the second set.
+ """
return Polyhedron([], [left - right])
projects / linpy.git / blobdiff