X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/blobdiff_plain/5fa0e7932a1621bee505991475291e43225a4b49..5eca735504be3b7c301e2a1fa37712eb88b4ec64:/pypol/domains.py diff --git a/pypol/domains.py b/pypol/domains.py index a34b75b..cdf2de4 100644 --- a/pypol/domains.py +++ b/pypol/domains.py @@ -1,8 +1,14 @@ +import ast import functools +import re +import math -from . import islhelper +from fractions import Fraction -from .islhelper import mainctx, libisl, isl_set_basic_sets +from . import islhelper +from .islhelper import mainctx, libisl +from .linexprs import Expression, Symbol, Rational +from .geometry import GeometricObject, Point, Vector __all__ = [ @@ -12,7 +18,7 @@ __all__ = [ @functools.total_ordering -class Domain: +class Domain(GeometricObject): __slots__ = ( '_polyhedra', @@ -23,14 +29,14 @@ class Domain: def __new__(cls, *polyhedra): from .polyhedra import Polyhedron if len(polyhedra) == 1: - polyhedron = polyhedra[0] - if isinstance(polyhedron, str): - return cls.fromstring(polyhedron) - elif isinstance(polyhedron, Polyhedron): - return polyhedron + argument = polyhedra[0] + if isinstance(argument, str): + return cls.fromstring(argument) + elif isinstance(argument, GeometricObject): + return argument.aspolyhedron() else: raise TypeError('argument must be a string ' - 'or a Polyhedron instance') + 'or a GeometricObject instance') else: for polyhedron in polyhedra: if not isinstance(polyhedron, Polyhedron): @@ -47,7 +53,7 @@ class Domain: symbols = set() for item in iterator: symbols.update(item.symbols) - return tuple(sorted(symbols)) + return tuple(sorted(symbols, key=Symbol.sortkey)) @property def polyhedra(self): @@ -62,11 +68,17 @@ class Domain: return self._dimension def disjoint(self): + """ + Returns this set as disjoint. + """ islset = self._toislset(self.polyhedra, self.symbols) islset = libisl.isl_set_make_disjoint(mainctx, islset) return self._fromislset(islset, self.symbols) def isempty(self): + """ + Returns true if this set is an Empty set. + """ islset = self._toislset(self.polyhedra, self.symbols) empty = bool(libisl.isl_set_is_empty(islset)) libisl.isl_set_free(islset) @@ -76,18 +88,27 @@ class Domain: return not self.isempty() def isuniverse(self): + """ + Returns true if this set is the Universe set. + """ islset = self._toislset(self.polyhedra, self.symbols) universe = bool(libisl.isl_set_plain_is_universe(islset)) libisl.isl_set_free(islset) return universe def isbounded(self): + """ + Returns true if this set is bounded. + """ islset = self._toislset(self.polyhedra, self.symbols) bounded = bool(libisl.isl_set_is_bounded(islset)) libisl.isl_set_free(islset) return bounded def __eq__(self, other): + """ + Returns true if two sets are equal. + """ symbols = self._xsymbols([self, other]) islset1 = self._toislset(self.polyhedra, symbols) islset2 = other._toislset(other.polyhedra, symbols) @@ -97,6 +118,9 @@ class Domain: return equal def isdisjoint(self, other): + """ + Return True if two sets have a null intersection. + """ symbols = self._xsymbols([self, other]) islset1 = self._toislset(self.polyhedra, symbols) islset2 = self._toislset(other.polyhedra, symbols) @@ -106,6 +130,9 @@ class Domain: return equal def issubset(self, other): + """ + Report whether another set contains this set. + """ symbols = self._xsymbols([self, other]) islset1 = self._toislset(self.polyhedra, symbols) islset2 = self._toislset(other.polyhedra, symbols) @@ -115,9 +142,15 @@ class Domain: return equal def __le__(self, other): + """ + Returns true if this set is less than or equal to another set. + """ return self.issubset(other) def __lt__(self, other): + """ + Returns true if this set is less than another set. + """ symbols = self._xsymbols([self, other]) islset1 = self._toislset(self.polyhedra, symbols) islset2 = self._toislset(other.polyhedra, symbols) @@ -127,39 +160,78 @@ class Domain: return equal def complement(self): + """ + Returns the complement of this set. + """ islset = self._toislset(self.polyhedra, self.symbols) islset = libisl.isl_set_complement(islset) return self._fromislset(islset, self.symbols) def __invert__(self): + """ + Returns the complement of this set. + """ return self.complement() def simplify(self): - # see isl_set_coalesce, isl_set_detect_equalities, - # isl_set_remove_redundancies - # which ones? in which order? - raise NotImplementedError - - def polyhedral_hull(self): - # several types of hull are available - # polyhedral seems to be the more appropriate, to be checked + """ + Returns a set without redundant constraints. + """ + islset = self._toislset(self.polyhedra, self.symbols) + islset = libisl.isl_set_remove_redundancies(islset) + return self._fromislset(islset, self.symbols) + + def aspolyhedron(self): + """ + Returns polyhedral hull of set. + """ from .polyhedra import Polyhedron islset = self._toislset(self.polyhedra, self.symbols) islbset = libisl.isl_set_polyhedral_hull(islset) return Polyhedron._fromislbasicset(islbset, self.symbols) - def project(self, symbols): - # not sure what isl_set_project_out actually doesâ¦ - # use isl_set_drop_constraints_involving_dims instead? - raise NotImplementedError + def asdomain(self): + return self + + def project(self, dims): + """ + Return new set with given dimensions removed. + """ + islset = self._toislset(self.polyhedra, self.symbols) + n = 0 + for index, symbol in reversed(list(enumerate(self.symbols))): + if symbol in dims: + n += 1 + elif n > 0: + islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, index + 1, n) + n = 0 + if n > 0: + islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, 0, n) + dims = [symbol for symbol in self.symbols if symbol not in dims] + return Domain._fromislset(islset, dims) def sample(self): - from .polyhedra import Polyhedron + """ + Returns a single subset of the input. + """ islset = self._toislset(self.polyhedra, self.symbols) - islbset = libisl.isl_set_sample(islset) - return Polyhedron._fromislbasicset(islbset, self.symbols) + islpoint = libisl.isl_set_sample_point(islset) + if bool(libisl.isl_point_is_void(islpoint)): + libisl.isl_point_free(islpoint) + raise ValueError('domain must be non-empty') + point = {} + for index, symbol in enumerate(self.symbols): + coordinate = libisl.isl_point_get_coordinate_val(islpoint, + libisl.isl_dim_set, index) + coordinate = islhelper.isl_val_to_int(coordinate) + point[symbol] = coordinate + libisl.isl_point_free(islpoint) + return point def intersection(self, *others): + """ + Return the intersection of two sets as a new set. + """ if len(others) == 0: return self symbols = self._xsymbols((self,) + others) @@ -170,9 +242,15 @@ class Domain: return self._fromislset(islset1, symbols) def __and__(self, other): + """ + Return the intersection of two sets as a new set. + """ return self.intersection(other) def union(self, *others): + """ + Return the union of sets as a new set. + """ if len(others) == 0: return self symbols = self._xsymbols((self,) + others) @@ -183,12 +261,21 @@ class Domain: return self._fromislset(islset1, symbols) def __or__(self, other): + """ + Return a new set with elements from both sets. + """ return self.union(other) def __add__(self, other): + """ + Return new set containing all elements in both sets. + """ return self.union(other) def difference(self, other): + """ + Return the difference of two sets as a new set. + """ symbols = self._xsymbols([self, other]) islset1 = self._toislset(self.polyhedra, symbols) islset2 = other._toislset(other.polyhedra, symbols) @@ -196,23 +283,258 @@ class Domain: return self._fromislset(islset, symbols) def __sub__(self, other): + """ + Return the difference of two sets as a new set. + """ return self.difference(other) def lexmin(self): + """ + Return a new set containing the lexicographic minimum of the elements in the set. + """ islset = self._toislset(self.polyhedra, self.symbols) islset = libisl.isl_set_lexmin(islset) return self._fromislset(islset, self.symbols) def lexmax(self): + """ + Return a new set containing the lexicographic maximum of the elements in the set. + """ islset = self._toislset(self.polyhedra, self.symbols) islset = libisl.isl_set_lexmax(islset) return self._fromislset(islset, self.symbols) + + def involves_vars(self, vars): + """ + Returns true if a set depends on given dimensions. + """ + islset = self._toislset(self.polyhedra, self.symbols) + dims = sorted(vars) + symbols = sorted(list(self.symbols)) + n = 0 + if len(dims)>0: + for dim in dims: + if dim in symbols: + first = symbols.index(dims[0]) + n +=1 + else: + first = 0 + else: + return False + value = bool(libisl.isl_set_involves_dims(islset, libisl.isl_dim_set, first, n)) + libisl.isl_set_free(islset) + return value + + _RE_COORDINATE = re.compile(r'\((?P\-?\d+)\)(/(?P\d+))?') + + def vertices(self): + """ + Return a list of vertices for this Polygon. + """ + from .polyhedra import Polyhedron + if not self.isbounded(): + raise ValueError('domain must be bounded') + islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols) + vertices = libisl.isl_basic_set_compute_vertices(islbset); + vertices = islhelper.isl_vertices_vertices(vertices) + points = [] + for vertex in vertices: + expr = libisl.isl_vertex_get_expr(vertex) + coordinates = [] + if islhelper.isl_version < '0.13': + constraints = islhelper.isl_basic_set_constraints(expr) + for constraint in constraints: + constant = libisl.isl_constraint_get_constant_val(constraint) + constant = islhelper.isl_val_to_int(constant) + for index, symbol in enumerate(self.symbols): + coefficient = libisl.isl_constraint_get_coefficient_val(constraint, + libisl.isl_dim_set, index) + coefficient = islhelper.isl_val_to_int(coefficient) + if coefficient != 0: + coordinate = -Fraction(constant, coefficient) + coordinates.append((symbol, coordinate)) + else: + string = islhelper.isl_multi_aff_to_str(expr) + matches = self._RE_COORDINATE.finditer(string) + for symbol, match in zip(self.symbols, matches): + numerator = int(match.group('num')) + denominator = match.group('den') + denominator = 1 if denominator is None else int(denominator) + coordinate = Fraction(numerator, denominator) + coordinates.append((symbol, coordinate)) + points.append(Point(coordinates)) + return points + + def points(self): + """ + Returns the points contained in the set. + """ + if not self.isbounded(): + raise ValueError('domain must be bounded') + from .polyhedra import Universe, Eq + islset = self._toislset(self.polyhedra, self.symbols) + islpoints = islhelper.isl_set_points(islset) + points = [] + for islpoint in islpoints: + coordinates = {} + for index, symbol in enumerate(self.symbols): + coordinate = libisl.isl_point_get_coordinate_val(islpoint, + libisl.isl_dim_set, index) + coordinate = islhelper.isl_val_to_int(coordinate) + coordinates[symbol] = coordinate + 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: + return True + 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) + @classmethod def _fromislset(cls, islset, symbols): from .polyhedra import Polyhedron islset = libisl.isl_set_remove_divs(islset) - islbsets = isl_set_basic_sets(islset) + islbsets = islhelper.isl_set_basic_sets(islset) libisl.isl_set_free(islset) polyhedra = [] for islbset in islbsets: @@ -230,6 +552,7 @@ class Domain: self._dimension = len(self._symbols) return self + @classmethod def _toislset(cls, polyhedra, symbols): polyhedron = polyhedra[0] islbset = polyhedron._toislbasicset(polyhedron.equalities, @@ -242,24 +565,116 @@ class Domain: islset1 = libisl.isl_set_union(islset1, islset2) return islset1 + @classmethod + def _fromast(cls, node): + from .polyhedra import Polyhedron + if isinstance(node, ast.Module) and len(node.body) == 1: + return cls._fromast(node.body[0]) + elif isinstance(node, ast.Expr): + return cls._fromast(node.value) + elif isinstance(node, ast.UnaryOp): + domain = cls._fromast(node.operand) + if isinstance(node.operand, ast.invert): + return Not(domain) + elif isinstance(node, ast.BinOp): + domain1 = cls._fromast(node.left) + domain2 = cls._fromast(node.right) + if isinstance(node.op, ast.BitAnd): + return And(domain1, domain2) + elif isinstance(node.op, ast.BitOr): + return Or(domain1, domain2) + elif isinstance(node, ast.Compare): + equalities = [] + inequalities = [] + left = Expression._fromast(node.left) + for i in range(len(node.ops)): + op = node.ops[i] + right = Expression._fromast(node.comparators[i]) + if isinstance(op, ast.Lt): + inequalities.append(right - left - 1) + elif isinstance(op, ast.LtE): + inequalities.append(right - left) + elif isinstance(op, ast.Eq): + equalities.append(left - right) + elif isinstance(op, ast.GtE): + inequalities.append(left - right) + elif isinstance(op, ast.Gt): + inequalities.append(left - right - 1) + else: + break + left = right + else: + return Polyhedron(equalities, inequalities) + raise SyntaxError('invalid syntax') + + _RE_BRACES = re.compile(r'^\{\s*|\s*\}\$') + _RE_EQ = re.compile(r'([^<=>])=([^<=>])') + _RE_AND = re.compile(r'\band\b|,|&&|/\\|â§|â©') + _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|â¨|âª') + _RE_NOT = re.compile(r'\bnot\b|!|Â¬') + _RE_NUM_VAR = Expression._RE_NUM_VAR + _RE_OPERATORS = re.compile(r'(&|\||~)') + @classmethod def fromstring(cls, string): - raise NotImplementedError + # remove curly brackets + string = cls._RE_BRACES.sub(r'', string) + # replace '=' by '==' + string = cls._RE_EQ.sub(r'\1==\2', string) + # replace 'and', 'or', 'not' + string = cls._RE_AND.sub(r' & ', string) + string = cls._RE_OR.sub(r' | ', string) + string = cls._RE_NOT.sub(r' ~', string) + # add implicit multiplication operators, e.g. '5x' -> '5*x' + string = cls._RE_NUM_VAR.sub(r'\1*\2', string) + # add parentheses to force precedence + tokens = cls._RE_OPERATORS.split(string) + for i, token in enumerate(tokens): + if i % 2 == 0: + token = '({})'.format(token) + tokens[i] = token + string = ''.join(tokens) + tree = ast.parse(string, 'eval') + return cls._fromast(tree) def __repr__(self): assert len(self.polyhedra) >= 2 strings = [repr(polyhedron) for polyhedron in self.polyhedra] return 'Or({})'.format(', '.join(strings)) + def _repr_latex_(self): + strings = [] + for polyhedron in self.polyhedra: + strings.append('({})'.format(polyhedron._repr_latex_().strip('\$'))) + return '\${}\$'.format(' \\vee '.join(strings)) + @classmethod def fromsympy(cls, expr): - raise NotImplementedError + import sympy + from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt + funcmap = { + sympy.And: And, sympy.Or: Or, sympy.Not: Not, + sympy.Lt: Lt, sympy.Le: Le, + sympy.Eq: Eq, sympy.Ne: Ne, + sympy.Ge: Ge, sympy.Gt: Gt, + } + if expr.func in funcmap: + args = [Domain.fromsympy(arg) for arg in expr.args] + return funcmap[expr.func](*args) + elif isinstance(expr, sympy.Expr): + return Expression.fromsympy(expr) + raise ValueError('non-domain expression: {!r}'.format(expr)) def tosympy(self): - raise NotImplementedError + import sympy + polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra] + return sympy.Or(*polyhedra) def And(*domains): + """ + Return the intersection of two sets as a new set. + """ if len(domains) == 0: from .polyhedra import Universe return Universe @@ -267,6 +682,9 @@ def And(*domains): return domains[0].intersection(*domains[1:]) def Or(*domains): + """ + Return the union of sets as a new set. + """ if len(domains) == 0: from .polyhedra import Empty return Empty @@ -274,4 +692,7 @@ def Or(*domains): return domains[0].union(*domains[1:]) def Not(domain): + """ + Returns the complement of this set. + """ return ~domain