-
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)
for inequality in self.inequalities:
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 = 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)
+
+ @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
- 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)
+ 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 = 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)
+ 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()
-
- elif len(self.symbols)==3:
- return 0
-
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)
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