X-Git-Url: https://svn.cri.ensmp.fr/git/linpy.git/blobdiff_plain/ce985e833f88aed8957c73434198e6bac6bd234e..843dede1d98c459f9761abff5877e0b019fa0155:/pypol/polyhedra.py diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py index db99753..a5d9495 100644 --- a/pypol/polyhedra.py +++ b/pypol/polyhedra.py @@ -1,11 +1,12 @@ - import functools +import math import numbers from . import islhelper from .islhelper import mainctx, libisl -from .linexprs import Expression, Symbol, Rational +from .geometry import GeometricObject, Point +from .linexprs import Expression, Rational from .domains import Domain @@ -31,11 +32,7 @@ class Polyhedron(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() @@ -74,9 +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)) @@ -84,8 +87,24 @@ class Polyhedron(Domain): 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] @@ -172,14 +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) @@ -195,85 +227,65 @@ class Polyhedron(Domain): for inequality in self.inequalities: constraints.append(sympy.Ge(inequality.tosympy(), 0)) return sympy.And(*constraints) - - 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): - 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])