import functools
import re
-from . import islhelper
+from fractions import Fraction
-from .islhelper import mainctx, libisl, isl_set_basic_sets
-from .linexprs import Expression
+from . import islhelper
+from .islhelper import mainctx, libisl
+from .geometry import GeometricObject, Point
+from .linexprs import Expression, Symbol
__all__ = [
@functools.total_ordering
-class Domain:
+class Domain(GeometricObject):
__slots__ = (
'_polyhedra',
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):
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):
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
+ #does not change anything in any of the examples
+ #isl seems to do this naturally
+ islset = self._toislset(self.polyhedra, self.symbols)
+ islset = libisl.isl_set_remove_redundancies(islset)
+ return self._fromislset(islset, self.symbols)
- def polyhedral_hull(self):
+ def aspolyhedron(self):
# several types of hull are available
# polyhedral seems to be the more appropriate, to be checked
from .polyhedra import Polyhedron
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 does…
- # use isl_set_drop_constraints_involving_dims instead?
- raise NotImplementedError
+ def asdomain(self):
+ return self
+
+ def project(self, dims):
+ # use to remove certain variables
+ 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
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):
if len(others) == 0:
islset = libisl.isl_set_lexmax(islset)
return self._fromislset(islset, self.symbols)
+ def num_parameters(self):
+ #could be useful with large, complicated polyhedrons
+ 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):
+ #could be useful with large, complicated polyhedrons
+ 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):
+ #returning list of verticies
+ 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:
+ # horrible hack, find a cleaner solution
+ 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):
+ 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
+
+ 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 = isl_set_basic_sets(islset)
+ islbsets = islhelper.isl_set_basic_sets(islset)
libisl.isl_set_free(islset)
polyhedra = []
for islbset in islbsets:
self._dimension = len(self._symbols)
return self
+ @classmethod
def _toislset(cls, polyhedra, symbols):
polyhedron = polyhedra[0]
islbset = polyhedron._toislbasicset(polyhedron.equalities,
return Polyhedron(equalities, inequalities)
raise SyntaxError('invalid syntax')
+ _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
+ _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
+ _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
+ _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
+ _RE_NOT = re.compile(r'\bnot\b|!|¬')
+ _RE_NUM_VAR = Expression._RE_NUM_VAR
+ _RE_OPERATORS = re.compile(r'(&|\||~)')
+
@classmethod
def fromstring(cls, string):
- # remove brackets
- string = re.sub(r'^\{\s*|\s*\}$', '', string)
+ # remove curly brackets
+ string = cls._RE_BRACES.sub(r'', string)
# replace '=' by '=='
- string = re.sub(r'([^<=>])=([^<=>])', r'\1==\2', string)
+ string = cls._RE_EQ.sub(r'\1==\2', string)
# replace 'and', 'or', 'not'
- string = re.sub(r'\band\b|,|&&|/\\|∧|∩', r' & ', string)
- string = re.sub(r'\bor\b|;|\|\||\\/|∨|∪', r' | ', string)
- string = re.sub(r'\bnot\b|!|¬', r' ~', string)
- tokens = re.split(r'(&|\||~)', string)
+ 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:
- # add implicit multiplication operators, e.g. '5x' -> '5*x'
- token = re.sub(r'(\d+|\))\s*([^\W\d_]\w*|\()', r'\1*\2', token)
token = '({})'.format(token)
tokens[i] = token
string = ''.join(tokens)
- tree = ast.parse(string)
+ tree = ast.parse(string, 'eval')
return cls._fromast(tree)
def __repr__(self):
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):
projects / linpy.git / blobdiff