-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