import ast
import functools
import re
+import math
from fractions import Fraction
from . import islhelper
from .islhelper import mainctx, libisl
-from .geometry import GeometricObject, Point
-from .linexprs import Expression, Symbol
+from .linexprs import Expression, Symbol, Rational
+from .geometry import GeometricObject, Point, Vector
__all__ = [
coordinate = -Fraction(constant, coefficient)
coordinates.append((symbol, coordinate))
else:
-
- # horrible hack, find a cleaner solution
string = islhelper.isl_multi_aff_to_str(expr)
matches = self._RE_COORDINATE.finditer(string)
for symbol, match in zip(self.symbols, matches):
coordinates[symbol] = coordinate
points.append(Point(coordinates))
return points
+
+ @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_2d(self, plot=None, **kwargs):
+ import matplotlib.pyplot as plt
+ from matplotlib.patches import Polygon
+ for polyhedron in self.polyhedra:
+ vertices = polyhedron._sort_polygon_2d(polyhedron.vertices())
+ xys = [tuple(vertex.values()) for vertex in vertices]
+ if plot is None:
+ fig = plt.figure()
+ 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):
+ from .polyhedra import Polyhedron
+ 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 polyhedron in self.polyhedra:
+ for vertices in polyhedron.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 plot of this 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 __contains__(self, point):
for polyhedron in self.polyhedra:
strings = []
for polyhedron in self.polyhedra:
strings.append('({})'.format(polyhedron._repr_latex_().strip('$')))
- return '$${}$$'.format(' \\vee '.join(strings))
+ return '${}$'.format(' \\vee '.join(strings))
@classmethod
def fromsympy(cls, expr):
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
def _repr_latex_(self):
if self.isempty():
- return '$$\\emptyset$$'
+ return '$\\emptyset$'
elif self.isuniverse():
- return '$$\\Omega$$'
+ 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))
+ return '${}$'.format(' \\wedge '.join(strings))
@classmethod
def fromsympy(cls, 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 = 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_2d(self, plot=None, **kwargs):
- import matplotlib.pyplot as plt
- 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()
- 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):
projects / linpy.git / commitdiff