X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/blobdiff_plain/fd990941199581e977b4455345b55f841bbaa05a..1695c920d030869b3a842736fe5bcf963f2ffc52:/pypol/polyhedra.py diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py index ac67cf8..5d1bfa1 100644 --- a/pypol/polyhedra.py +++ b/pypol/polyhedra.py @@ -1,10 +1,12 @@ import functools +import math import numbers from . import islhelper from .islhelper import mainctx, libisl -from .linexprs import Expression, Constant +from .geometry import GeometricObject, Point, Vector +from .linexprs import Expression, Symbol, Rational from .domains import Domain @@ -30,28 +32,24 @@ class Polyhedron(Domain): if inequalities is not None: raise TypeError('too many arguments') return cls.fromstring(equalities) - elif isinstance(equalities, Polyhedron): + elif isinstance(equalities, GeometricObject): if inequalities is not None: raise TypeError('too many arguments') - return equalities - elif isinstance(equalities, Domain): - if inequalities is not None: - raise TypeError('too many arguments') - return equalities.polyhedral_hull() + return equalities.aspolyhedron() if equalities is None: equalities = [] else: for i, equality in enumerate(equalities): if not isinstance(equality, Expression): raise TypeError('equalities must be linear expressions') - equalities[i] = equality._toint() + equalities[i] = equality.scaleint() if inequalities is None: inequalities = [] else: for i, inequality in enumerate(inequalities): if not isinstance(inequality, Expression): raise TypeError('inequalities must be linear expressions') - inequalities[i] = inequality._toint() + inequalities[i] = inequality.scaleint() symbols = cls._xsymbols(equalities + inequalities) islbset = cls._toislbasicset(equalities, inequalities, symbols) return cls._fromislbasicset(islbset, symbols) @@ -73,18 +71,47 @@ 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)) libisl.isl_basic_set_free(islbset) return universe - def polyhedral_hull(self): + 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] + inequalities = [inequality.subs(symbol, expression) + for inequality in self.inequalities] + return Polyhedron(equalities, inequalities) + @classmethod def _fromislbasicset(cls, islbset, symbols): islconstraints = islhelper.isl_basic_set_constraints(islbset) @@ -95,7 +122,8 @@ class Polyhedron(Domain): constant = islhelper.isl_val_to_int(constant) coefficients = {} for index, symbol in enumerate(symbols): - coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint, libisl.isl_dim_set, index) + coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint, + libisl.isl_dim_set, index) coefficient = islhelper.isl_val_to_int(coefficient) if coefficient != 0: coefficients[symbol] = coefficient @@ -171,38 +199,25 @@ class Polyhedron(Domain): else: return 'And({})'.format(', '.join(strings)) - @classmethod - def _fromsympy(cls, expr): - import sympy - equalities = [] - inequalities = [] - if expr.func == sympy.And: - for arg in expr.args: - arg_eqs, arg_ins = cls._fromsympy(arg) - equalities.extend(arg_eqs) - inequalities.extend(arg_ins) - elif expr.func == sympy.Eq: - expr = Expression.fromsympy(expr.args[0] - expr.args[1]) - equalities.append(expr) + def _repr_latex_(self): + if self.isempty(): + return '$\\emptyset$' + elif self.isuniverse(): + return '$\\Omega$' else: - if expr.func == sympy.Lt: - expr = Expression.fromsympy(expr.args[1] - expr.args[0] - 1) - elif expr.func == sympy.Le: - expr = Expression.fromsympy(expr.args[1] - expr.args[0]) - elif expr.func == sympy.Ge: - expr = Expression.fromsympy(expr.args[0] - expr.args[1]) - elif expr.func == sympy.Gt: - expr = Expression.fromsympy(expr.args[0] - expr.args[1] - 1) - else: - raise ValueError('non-polyhedral expression: {!r}'.format(expr)) - inequalities.append(expr) - return equalities, inequalities + 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): - import sympy - equalities, inequalities = cls._fromsympy(expr) - return cls(equalities, inequalities) + domain = Domain.fromsympy(expr) + if not isinstance(domain, Polyhedron): + raise ValueError('non-polyhedral expression: {!r}'.format(expr)) + return domain def tosympy(self): import sympy @@ -213,45 +228,200 @@ 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 = 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(self): + """ + Display 3D plot of set. + """ + import matplotlib.pyplot as plt + import matplotlib.patches as patches + + if len(self.symbols)> 3: + raise TypeError + + elif len(self.symbols) == 2: + import pylab + points = [] + for verts in self.vertices(): + pairs=() + for coordinate, point in verts.coordinates(): + pairs = pairs + (float(point),) + points.append(pairs) + cent=(sum([p[0] for p in points])/len(points),sum([p[1] for p in points])/len(points)) + points.sort(key=lambda p: math.atan2(p[1]-cent[1],p[0]-cent[0])) + pylab.scatter([p[0] for p in points],[p[1] for p in points]) + pylab.gca().add_patch(patches.Polygon(points,closed=True,fill=True)) + pylab.grid() + pylab.show() + + elif len(self.symbols)==3: + from mpl_toolkits.mplot3d import Axes3D + from mpl_toolkits.mplot3d.art3d import Poly3DCollection + faces = self.faces() + fig = plt.figure() + ax = Axes3D(fig) + for face in faces: + points = [] + vertices = Polyhedron._sort_polygon_3d(face) + for verts in vertices: + pairs=() + for coordinate, point in verts.coordinates(): + pairs = pairs + (float(point),) + points.append(pairs) + collection = Poly3DCollection([points], alpha=0.7) + face_color = [0.5, 0.5, 1] # alternative: matplotlib.colors.rgb2hex([0.5, 0.5, 1]) + collection.set_facecolor(face_color) + ax.add_collection3d(collection) + ax.set_xlabel('X') + ax.set_xlim(0, 5) + ax.set_ylabel('Y') + ax.set_ylim(0, 5) + ax.set_zlabel('Z') + ax.set_zlim(0, 5) + plt.grid() + plt.show() + return points + + @classmethod + def limit(cls, faces, variable, lim): + sym = [] + if variable is 'x': + n = 0 + elif variable is 'y': + n = 1 + elif variable is 'z': + n = 2 + for face in faces: + for vert in face: + coordinates = vert.coordinates() + for point in enumerate(coordinates): + coordinates.get(n) + sym.append(points) + if lim == 0: + value = min(sym) + else: + value = max(sym) + return value def _polymorphic(func): @functools.wraps(func) def wrapper(left, right): - if isinstance(left, numbers.Rational): - left = Constant(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 = Constant(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])