+import ast
+import functools
+import re
+import math
+
+from fractions import Fraction
+
+from . import islhelper
+from .islhelper import mainctx, libisl
+from .linexprs import Expression, Symbol, Rational
+from .geometry import GeometricObject, Point, Vector
+
+
+__all__ = [
+ 'Domain',
+ 'And', 'Or', 'Not',
+]
+
+
+@functools.total_ordering
+class Domain(GeometricObject):
+
+ __slots__ = (
+ '_polyhedra',
+ '_symbols',
+ '_dimension',
+ )
+
+ def __new__(cls, *polyhedra):
+ from .polyhedra import Polyhedron
+ if len(polyhedra) == 1:
+ 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 GeometricObject instance')
+ else:
+ for polyhedron in polyhedra:
+ if not isinstance(polyhedron, Polyhedron):
+ raise TypeError('arguments must be Polyhedron instances')
+ symbols = cls._xsymbols(polyhedra)
+ islset = cls._toislset(polyhedra, symbols)
+ return cls._fromislset(islset, symbols)
+
+ @classmethod
+ def _xsymbols(cls, iterator):
+ """
+ Return the ordered tuple of symbols present in iterator.
+ """
+ symbols = set()
+ for item in iterator:
+ symbols.update(item.symbols)
+ return tuple(sorted(symbols, key=Symbol.sortkey))
+
+ @property
+ def polyhedra(self):
+ return self._polyhedra
+
+ @property
+ def symbols(self):
+ return self._symbols
+
+ @property
+ def dimension(self):
+ 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)
+ return empty
+
+ def __bool__(self):
+ 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)
+ equal = bool(libisl.isl_set_is_equal(islset1, islset2))
+ libisl.isl_set_free(islset1)
+ libisl.isl_set_free(islset2)
+ 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)
+ equal = bool(libisl.isl_set_is_disjoint(islset1, islset2))
+ libisl.isl_set_free(islset1)
+ libisl.isl_set_free(islset2)
+ 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)
+ equal = bool(libisl.isl_set_is_subset(islset1, islset2))
+ libisl.isl_set_free(islset1)
+ libisl.isl_set_free(islset2)
+ 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)
+ equal = bool(libisl.isl_set_is_strict_subset(islset1, islset2))
+ libisl.isl_set_free(islset1)
+ libisl.isl_set_free(islset2)
+ 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):
+ """
+ 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 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):
+ """
+ Returns a single subset of the input.
+ """
+ islset = self._toislset(self.polyhedra, 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)
+ islset1 = self._toislset(self.polyhedra, symbols)
+ for other in others:
+ islset2 = other._toislset(other.polyhedra, symbols)
+ islset1 = libisl.isl_set_intersect(islset1, islset2)
+ 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)
+ islset1 = self._toislset(self.polyhedra, symbols)
+ for other in others:
+ islset2 = other._toislset(other.polyhedra, symbols)
+ islset1 = libisl.isl_set_union(islset1, islset2)
+ 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)
+ islset = libisl.isl_set_subtract(islset1, islset2)
+ 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 num_parameters(self):
+ """
+ Return the total number of parameters, input, output or set dimensions.
+ """
+ islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
+ num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
+ return num
+
+ def involves_dims(self, dims):
+ """
+ Returns true if set depends on given dimensions.
+ """
+ islset = self._toislset(self.polyhedra, self.symbols)
+ dims = sorted(dims)
+ 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'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
+
+ def vertices(self):
+ """
+ Return a list of vertices for this Polygon.
+ """
+ from .polyhedra import Polyhedron
+ 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):
+ 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):
+ 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 = islhelper.isl_set_basic_sets(islset)
+ libisl.isl_set_free(islset)
+ polyhedra = []
+ for islbset in islbsets:
+ polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
+ polyhedra.append(polyhedron)
+ if len(polyhedra) == 0:
+ from .polyhedra import Empty
+ return Empty
+ elif len(polyhedra) == 1:
+ return polyhedra[0]
+ else:
+ self = object().__new__(Domain)
+ self._polyhedra = tuple(polyhedra)
+ self._symbols = cls._xsymbols(polyhedra)
+ self._dimension = len(self._symbols)
+ return self
+
+ @classmethod
+ def _toislset(cls, polyhedra, symbols):
+ polyhedron = polyhedra[0]
+ islbset = polyhedron._toislbasicset(polyhedron.equalities,
+ polyhedron.inequalities, symbols)
+ islset1 = libisl.isl_set_from_basic_set(islbset)
+ for polyhedron in polyhedra[1:]:
+ islbset = polyhedron._toislbasicset(polyhedron.equalities,
+ polyhedron.inequalities, symbols)
+ islset2 = libisl.isl_set_from_basic_set(islbset)
+ 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*\}$')
+ _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
+ _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
+ _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
+ _RE_NOT = re.compile(r'\bnot\b|!|¬')
+ _RE_NUM_VAR = Expression._RE_NUM_VAR
+ _RE_OPERATORS = re.compile(r'(&|\||~)')
+
+ @classmethod
+ def fromstring(cls, string):
+ # remove curly brackets
+ string = cls._RE_BRACES.sub(r'', string)
+ # replace '=' by '=='
+ string = cls._RE_EQ.sub(r'\1==\2', string)
+ # replace 'and', 'or', 'not'
+ string = cls._RE_AND.sub(r' & ', string)
+ string = cls._RE_OR.sub(r' | ', string)
+ string = cls._RE_NOT.sub(r' ~', string)
+ # add implicit multiplication operators, e.g. '5x' -> '5*x'
+ string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
+ # add parentheses to force precedence
+ tokens = cls._RE_OPERATORS.split(string)
+ for i, token in enumerate(tokens):
+ if i % 2 == 0:
+ token = '({})'.format(token)
+ tokens[i] = token
+ string = ''.join(tokens)
+ tree = ast.parse(string, 'eval')
+ return cls._fromast(tree)
+
+ def __repr__(self):
+ assert len(self.polyhedra) >= 2
+ strings = [repr(polyhedron) for polyhedron in self.polyhedra]
+ return 'Or({})'.format(', '.join(strings))
+
+ def _repr_latex_(self):
+ strings = []
+ for polyhedron in self.polyhedra:
+ strings.append('({})'.format(polyhedron._repr_latex_().strip('$')))
+ return '${}$'.format(' \\vee '.join(strings))
+
+ @classmethod
+ def fromsympy(cls, expr):
+ 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):
+ 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
+ else:
+ 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
+ else:
+ return domains[0].union(*domains[1:])
+
+def Not(domain):
+ """
+ Returns the complement of this set.
+ """
+ return ~domain
projects / linpy.git / commitdiff