X-Git-Url: https://svn.cri.ensmp.fr/git/linpy.git/blobdiff_plain/2bad3743bd25bbcfe12db50e2b18ab8d070f2354..843dede1d98c459f9761abff5877e0b019fa0155:/pypol/polyhedra.py?ds=sidebyside diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py index e745d7d..a5d9495 100644 --- a/pypol/polyhedra.py +++ b/pypol/polyhedra.py @@ -5,8 +5,8 @@ import numbers 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 @@ -71,9 +71,15 @@ class Polyhedron(Domain): 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)) @@ -81,6 +87,9 @@ class Polyhedron(Domain): return universe def aspolyhedron(self): + """ + Return polyhedral hull of this set. + """ return self def __contains__(self, point): @@ -182,14 +191,27 @@ class Polyhedron(Domain): 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) @@ -206,108 +228,6 @@ class Polyhedron(Domain): 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 = oa.dot(om) / normprod - 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): - 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() - - elif len(self.symbols)==3: - return 0 - - return points - - def _polymorphic(func): @functools.wraps(func) def wrapper(left, right): @@ -328,26 +248,44 @@ def _polymorphic(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])