X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/blobdiff_plain/22d69753489bdafa3401e54be79b58d9e94225a3..5eca735504be3b7c301e2a1fa37712eb88b4ec64:/pypol/domains.py diff --git a/pypol/domains.py b/pypol/domains.py index 5db1856..cdf2de4 100644 --- a/pypol/domains.py +++ b/pypol/domains.py @@ -1,13 +1,14 @@ 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__ = [ @@ -303,20 +304,13 @@ class Domain(GeometricObject): 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: @@ -361,8 +355,6 @@ class Domain(GeometricObject): 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): @@ -394,6 +386,135 @@ class Domain(GeometricObject): 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: @@ -401,6 +522,10 @@ class Domain(GeometricObject): 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) @@ -521,7 +646,7 @@ class Domain(GeometricObject): 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):