X-Git-Url: https://svn.cri.ensmp.fr/git/linpy.git/blobdiff_plain/1c48ba9f3483505f53962731dc58c6c02d785fc4..e2266a6ca10276d2af3065f9e140d994459b92f3:/pypol/polyhedra.py diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py index d181646..aabe0fd 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) @@ -73,30 +71,59 @@ 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) equalities = [] inequalities = [] for islconstraint in islconstraints: - islpr = libisl.isl_printer_to_str(mainctx) constant = libisl.isl_constraint_get_constant_val(islconstraint) constant = islhelper.isl_val_to_int(constant) coefficients = {} - for dim, symbol in enumerate(symbols): - coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint, libisl.isl_dim_set, dim) + for index, symbol in enumerate(symbols): + 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 @@ -117,34 +144,35 @@ class Polyhedron(Domain): @classmethod def _toislbasicset(cls, equalities, inequalities, symbols): dimension = len(symbols) + indices = {symbol: index for index, symbol in enumerate(symbols)} islsp = libisl.isl_space_set_alloc(mainctx, 0, dimension) islbset = libisl.isl_basic_set_universe(libisl.isl_space_copy(islsp)) islls = libisl.isl_local_space_from_space(islsp) for equality in equalities: isleq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(islls)) for symbol, coefficient in equality.coefficients(): - val = str(coefficient).encode() - val = libisl.isl_val_read_from_str(mainctx, val) - sid = symbols.index(symbol) + islval = str(coefficient).encode() + islval = libisl.isl_val_read_from_str(mainctx, islval) + index = indices[symbol] isleq = libisl.isl_constraint_set_coefficient_val(isleq, - libisl.isl_dim_set, sid, val) + libisl.isl_dim_set, index, islval) if equality.constant != 0: - val = str(equality.constant).encode() - val = libisl.isl_val_read_from_str(mainctx, val) - isleq = libisl.isl_constraint_set_constant_val(isleq, val) + islval = str(equality.constant).encode() + islval = libisl.isl_val_read_from_str(mainctx, islval) + isleq = libisl.isl_constraint_set_constant_val(isleq, islval) islbset = libisl.isl_basic_set_add_constraint(islbset, isleq) for inequality in inequalities: islin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(islls)) for symbol, coefficient in inequality.coefficients(): - val = str(coefficient).encode() - val = libisl.isl_val_read_from_str(mainctx, val) - sid = symbols.index(symbol) + islval = str(coefficient).encode() + islval = libisl.isl_val_read_from_str(mainctx, islval) + index = indices[symbol] islin = libisl.isl_constraint_set_coefficient_val(islin, - libisl.isl_dim_set, sid, val) + libisl.isl_dim_set, index, islval) if inequality.constant != 0: - val = str(inequality.constant).encode() - val = libisl.isl_val_read_from_str(mainctx, val) - islin = libisl.isl_constraint_set_constant_val(islin, val) + islval = str(inequality.constant).encode() + islval = libisl.isl_val_read_from_str(mainctx, islval) + islin = libisl.isl_constraint_set_constant_val(islin, islval) islbset = libisl.isl_basic_set_add_constraint(islbset, islin) return islbset @@ -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 +228,187 @@ 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_2d(self, plot=None, **kwargs): + import matplotlib.pyplot as plt + from matplotlib.patches import Polygon + vertices = self._sort_polygon_2d(self.vertices()) + xys = [tuple(vertex.values()) for vertex in vertices] + if plot is None: + fig = plt.figure() + plot = fig.add_subplot(1, 1, 1) + xmin, xmax = plot.get_xlim() + ymin, ymax = plot.get_xlim() + 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.set_xlim(xmin, xmax) + plot.set_ylim(ymin, ymax) + plot.add_patch(Polygon(xys, closed=True, **kwargs)) + 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_xlim() + zmin, zmax = axes.get_xlim() + poly_xyzs = [] + for vertices in self.faces(): + if len(vertices) == 0: + continue + vertices = Polyhedron._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 3D plot of set. + """ + if 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 _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])