-
import functools
import math
import numbers
from . import islhelper
from .islhelper import mainctx, libisl
+from .geometry import GeometricObject, Point, Vector
from .linexprs import Expression, Symbol, Rational
from .domains import Domain
if inequalities is not None:
raise TypeError('too many arguments')
return cls.fromstring(equalities)
- elif isinstance(equalities, Polyhedron):
- if inequalities is not None:
- raise TypeError('too many arguments')
- return equalities
- elif isinstance(equalities, Domain):
+ elif isinstance(equalities, GeometricObject):
if inequalities is not None:
raise TypeError('too many arguments')
return equalities.aspolyhedron()
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):
+ if not isinstance(point, Point):
+ raise TypeError('point must be a Point instance')
+ if self.symbols != point.symbols:
+ raise ValueError('arguments must belong to the same space')
+ for equality in self.equalities:
+ if equality.subs(point.coordinates()) != 0:
+ return False
+ for inequality in self.inequalities:
+ if inequality.subs(point.coordinates()) < 0:
+ return False
+ return True
+
def subs(self, symbol, expression=None):
equalities = [equality.subs(symbol, expression)
for equality in self.equalities]
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 _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 = sum((Vector(point) for point in points)) / len(points)
- o = Point(o.coordinates())
+ o = cls._polygon_inner_point(points)
angles = {}
for m in points:
om = Vector(o, m)
- dx, dy = (coordinate for symbol, coordinates in om.coordinates())
+ dx, dy = (coordinate for symbol, coordinate in om.coordinates())
angle = math.atan2(dy, dx)
angles[m] = angle
return sorted(points, key=angles.get)
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]
+ o = cls._polygon_inner_point(points)
+ a = points[0]
oa = Vector(o, a)
- ob = Vector(o, b)
norm_oa = oa.norm()
- u = (oa.cross(ob)).asunit()
+ 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 = oa.dot(om) / normprod
+ 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 plot(self):
+ 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.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)
+ 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()
- 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
+ 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 _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