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)
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)
return faces
def plot(self):
+ """
+ Display 3D plot of set.
+ """
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()
+ 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:
- return 0
-
+ 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.
+ """
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