# along with LinPy. If not, see <http://www.gnu.org/licenses/>.
import functools
-import math
import numbers
from . import islhelper
-from .islhelper import mainctx, libisl
+from .domains import Domain
from .geometry import GeometricObject, Point
+from .islhelper import libisl, mainctx
from .linexprs import LinExpr, Rational
-from .domains import Domain
__all__ = [
+ 'Empty',
+ 'Eq',
+ 'Ge',
+ 'Gt',
+ 'Le',
+ 'Lt',
+ 'Ne',
'Polyhedron',
- 'Lt', 'Le', 'Eq', 'Ne', 'Ge', 'Gt',
- 'Empty', 'Universe',
+ 'Universe',
]
class Polyhedron(Domain):
"""
A convex polyhedron (or simply "polyhedron") is the space defined by a
- system of linear equalities and inequalities. This space can be unbounded. A
- Z-polyhedron (simply called "polyhedron" in LinPy) is the set of integer
+ system of linear equalities and inequalities. This space can be unbounded.
+ A Z-polyhedron (simply called "polyhedron" in LinPy) is the set of integer
points in a convex polyhedron.
"""
def __new__(cls, equalities=None, inequalities=None):
"""
- Return a polyhedron from two sequences of linear expressions: equalities
- is a list of expressions equal to 0, and inequalities is a list of
- expressions greater or equal to 0. For example, the polyhedron
+ Return a polyhedron from two sequences of linear expressions:
+ equalities is a list of expressions equal to 0, and inequalities is a
+ list of expressions greater or equal to 0. For example, the polyhedron
0 <= x <= 2, 0 <= y <= 2 can be constructed with:
>>> x, y = symbols('x y')
And(0 <= x, x <= 2, 0 <= y, y <= 2)
It may be easier to use comparison operators LinExpr.__lt__(),
- LinExpr.__le__(), LinExpr.__ge__(), LinExpr.__gt__(), or functions Lt(),
- Le(), Eq(), Ge() and Gt(), using one of the following instructions:
+ LinExpr.__le__(), LinExpr.__ge__(), LinExpr.__gt__(), or
+ functions Lt(), Le(), Eq(), Ge() and Gt(), using one of the following
+ instructions:
>>> x, y = symbols('x y')
>>> square1 = (0 <= x) & (x <= 2) & (0 <= y) & (y <= 2)
>>> square1 = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
Finally, a polyhedron can be constructed from a GeometricObject
- instance, calling the GeometricObject.aspolyedron() method. This way, it
- is possible to compute the polyhedral hull of a Domain instance, i.e.,
- the convex hull of two polyhedra:
+ instance, calling the GeometricObject.aspolyedron() method. This way,
+ it is possible to compute the polyhedral hull of a Domain instance,
+ i.e., the convex hull of two polyhedra:
>>> square1 = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
>>> square2 = Polyhedron('1 <= x <= 3, 1 <= y <= 3')
sc_equalities = []
if equalities is not None:
for equality in equalities:
- if not isinstance(equality, LinExpr):
- raise TypeError('equalities must be linear expressions')
- sc_equalities.append(equality.scaleint())
+ if isinstance(equality, LinExpr):
+ sc_equalities.append(equality.scaleint())
+ elif isinstance(equality, numbers.Rational):
+ sc_equalities.append(Rational(equality).scaleint())
+ else:
+ raise TypeError('equalities must be linear expressions '
+ 'or rational numbers')
sc_inequalities = []
if inequalities is not None:
for inequality in inequalities:
- if not isinstance(inequality, LinExpr):
- raise TypeError('inequalities must be linear expressions')
- sc_inequalities.append(inequality.scaleint())
+ if isinstance(inequality, LinExpr):
+ sc_inequalities.append(inequality.scaleint())
+ elif isinstance(inequality, numbers.Rational):
+ sc_inequalities.append(Rational(inequality).scaleint())
+ else:
+ raise TypeError('inequalities must be linear expressions '
+ 'or rational numbers')
symbols = cls._xsymbols(sc_equalities + sc_inequalities)
islbset = cls._toislbasicset(sc_equalities, sc_inequalities, symbols)
return cls._fromislbasicset(islbset, symbols)
def isuniverse(self):
islbset = self._toislbasicset(self.equalities, self.inequalities,
- self.symbols)
+ self.symbols)
universe = bool(libisl.isl_basic_set_is_universe(islbset))
libisl.isl_basic_set_free(islbset)
return universe
def subs(self, symbol, expression=None):
equalities = [equality.subs(symbol, expression)
- for equality in self.equalities]
+ for equality in self.equalities]
inequalities = [inequality.subs(symbol, expression)
- for inequality in self.inequalities]
+ for inequality in self.inequalities]
return Polyhedron(equalities, inequalities)
def asinequalities(self):
@classmethod
def _fromislbasicset(cls, islbset, symbols):
+ if bool(libisl.isl_basic_set_is_empty(islbset)):
+ return Empty
+ if bool(libisl.isl_basic_set_is_universe(islbset)):
+ return Universe
islconstraints = islhelper.isl_basic_set_constraints(islbset)
equalities = []
inequalities = []
constant = islhelper.isl_val_to_int(constant)
coefficients = {}
for index, symbol in enumerate(symbols):
- coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint,
- libisl.isl_dim_set, index)
+ 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
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))
+ isleq = libisl.isl_equality_alloc(
+ libisl.isl_local_space_copy(islls))
for symbol, coefficient in equality.coefficients():
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, index, islval)
+ isleq = libisl.isl_constraint_set_coefficient_val(
+ isleq, libisl.isl_dim_set, index, islval)
if equality.constant != 0:
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))
+ islin = libisl.isl_inequality_alloc(
+ libisl.isl_local_space_copy(islls))
for symbol, coefficient in inequality.coefficients():
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, index, islval)
+ islin = libisl.isl_constraint_set_coefficient_val(
+ islin, libisl.isl_dim_set, index, islval)
if inequality.constant != 0:
islval = str(inequality.constant).encode()
islval = libisl.isl_val_read_from_str(mainctx, islval)
return 'And({})'.format(', '.join(strings))
@classmethod
- def fromsympy(cls, expr):
- domain = Domain.fromsympy(expr)
+ def fromsympy(cls, expression):
+ domain = Domain.fromsympy(expression)
if not isinstance(domain, Polyhedron):
- raise ValueError('non-polyhedral expression: {!r}'.format(expr))
+ raise ValueError('non-polyhedral expression: {!r}'.format(
+ expression))
return domain
def tosympy(self):
def _pseudoconstructor(func):
@functools.wraps(func)
- def wrapper(expr1, expr2, *exprs):
- exprs = (expr1, expr2) + exprs
- for expr in exprs:
- if not isinstance(expr, LinExpr):
- if isinstance(expr, numbers.Rational):
- expr = Rational(expr)
+ def wrapper(expression1, expression2, *expressions):
+ expressions = (expression1, expression2) + expressions
+ for expression in expressions:
+ if not isinstance(expression, LinExpr):
+ if isinstance(expression, numbers.Rational):
+ expression = Rational(expression)
else:
raise TypeError('arguments must be rational numbers '
- 'or linear expressions')
- return func(*exprs)
+ 'or linear expressions')
+ return func(*expressions)
return wrapper
+
@_pseudoconstructor
-def Lt(*exprs):
+def Lt(*expressions):
"""
Create the polyhedron with constraints expr1 < expr2 < expr3 ...
"""
inequalities = []
- for left, right in zip(exprs, exprs[1:]):
+ for left, right in zip(expressions, expressions[1:]):
inequalities.append(right - left - 1)
return Polyhedron([], inequalities)
+
@_pseudoconstructor
-def Le(*exprs):
+def Le(*expressions):
"""
Create the polyhedron with constraints expr1 <= expr2 <= expr3 ...
"""
inequalities = []
- for left, right in zip(exprs, exprs[1:]):
+ for left, right in zip(expressions, expressions[1:]):
inequalities.append(right - left)
return Polyhedron([], inequalities)
+
@_pseudoconstructor
-def Eq(*exprs):
+def Eq(*expressions):
"""
Create the polyhedron with constraints expr1 == expr2 == expr3 ...
"""
equalities = []
- for left, right in zip(exprs, exprs[1:]):
+ for left, right in zip(expressions, expressions[1:]):
equalities.append(left - right)
return Polyhedron(equalities, [])
+
@_pseudoconstructor
-def Ne(*exprs):
+def Ne(*expressions):
"""
Create the domain such that expr1 != expr2 != expr3 ... The result is a
Domain object, not a Polyhedron.
"""
domain = Universe
- for left, right in zip(exprs, exprs[1:]):
+ for left, right in zip(expressions, expressions[1:]):
domain &= ~Eq(left, right)
return domain
+
@_pseudoconstructor
-def Ge(*exprs):
+def Ge(*expressions):
"""
Create the polyhedron with constraints expr1 >= expr2 >= expr3 ...
"""
inequalities = []
- for left, right in zip(exprs, exprs[1:]):
+ for left, right in zip(expressions, expressions[1:]):
inequalities.append(left - right)
return Polyhedron([], inequalities)
+
@_pseudoconstructor
-def Gt(*exprs):
+def Gt(*expressions):
"""
Create the polyhedron with constraints expr1 > expr2 > expr3 ...
"""
inequalities = []
- for left, right in zip(exprs, exprs[1:]):
+ for left, right in zip(expressions, expressions[1:]):
inequalities.append(left - right - 1)
return Polyhedron([], inequalities)
projects / linpy.git / blobdiff