+# Copyright 2014 MINES ParisTech
+#
+# This file is part of Linpy.
+#
+# Linpy is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# Linpy is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with Linpy. If not, see <http://www.gnu.org/licenses/>.
+
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__ = [
islset = libisl.isl_set_lexmax(islset)
return self._fromislset(islset, self.symbols)
- def num_parameters(self):
- """
- Return the total number of parameters, input, output or set dimensions.
- """
- islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
- num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
- return num
- def involves_dims(self, dims):
+ def involves_vars(self, vars):
"""
- Returns true if set depends on given dimensions.
+ Returns true if a set depends on given dimensions.
"""
islset = self._toislset(self.polyhedra, self.symbols)
- dims = sorted(dims)
+ dims = sorted(vars)
symbols = sorted(list(self.symbols))
n = 0
if len(dims)>0:
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):
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):
+ """
+ Returns the vertices of the faces of a polyhedra.
+ """
+ faces = []
+ for polyhedron in self.polyhedra:
+ vertices = polyhedron.vertices()
+ for constraint in polyhedron.constraints:
+ face = []
+ for vertex in vertices:
+ if constraint.subs(vertex.coordinates()) == 0:
+ face.append(vertex)
+ if len(face) >= 3:
+ faces.append(face)
+ return faces
+
+ def _plot_2d(self, plot=None, **kwargs):
+ import matplotlib.pyplot as plt
+ from matplotlib.patches import Polygon
+ if plot is None:
+ fig = plt.figure()
+ plot = fig.add_subplot(1, 1, 1)
+ xmin, xmax = plot.get_xlim()
+ ymin, ymax = plot.get_ylim()
+ for polyhedron in self.polyhedra:
+ vertices = polyhedron._sort_polygon_2d(polyhedron.vertices())
+ xys = [tuple(vertex.values()) for vertex in vertices]
+ 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.add_patch(Polygon(xys, closed=True, **kwargs))
+ plot.set_xlim(xmin, xmax)
+ plot.set_ylim(ymin, ymax)
+ 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_ylim()
+ zmin, zmax = axes.get_zlim()
+ poly_xyzs = []
+ for vertices in self.faces():
+ vertices = self._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 not self.isbounded():
+ raise ValueError('domain must be bounded')
+ elif 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:
if point in polyhedron:
return False
def subs(self, symbol, expression=None):
+ """
+ Subsitute the given value into an expression and return the resulting
+ expression.
+ """
polyhedra = [polyhedron.subs(symbol, expression)
for polyhedron in self.polyhedra]
return Domain(*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):
projects / linpy.git / blobdiff