--- /dev/null
+Domains Module
+==============
+
+.. py:class :: Domain
+
+ .. py:method:: polyhedra(self)
+
+ Return .
+
+Domain Properties
+-----------------
+ .. py:method:: symbols(self)
+
+ Returns a list of the symbols used in a set.
+
+ .. py:method:: dimension(self)
+
+ Returns the number of variables in a set.
+
+ .. py:method:: disjoint(self)
+
+ Returns a set as disjoint.
+
+ .. py:method:: num_parameters(self)
+
+ Returns the total number of parameters, input, output or set dimensions.
+
+ .. py:method:: involves_dims(self, dims)
+
+ Returns true if set depends on given dimensions.
+
+Unary Properties
+----------------
+ .. py:method:: isempty(self)
+
+ Return true is set is an Empty set.
+
+ .. py:method:: isuniverse(self)
+
+ Return true if set is the Universe set.
+
+ .. py:method:: isbounded(self)
+
+ Return true if set is bounded
+
+ .. py:method:: disjoint(self)
+
+ Returns this set as a disjoint set.
+
+Binary Properties
+-----------------
+
+ .. py:method:: isdisjoint(self, other)
+
+ Return true if the intersection of two sets results in an Empty set.
+
+ .. py:method:: issubset(self, other)
+
+ Returns true if one set contains the other set.
+
+ .. py:method:: __eq__(self, other)
+
+ Return true if self == other.
+
+ .. py:method:: __lt__(self, other)
+
+ Return true if self < other.
+
+ .. py:method:: __le__(self, other)
+
+ Return true if self <= other.
+
+ .. py:method:: __gt__(self, other)
+
+ Return true if self > other.
+
+ .. py:method:: __ge__(self, other)
+
+ Return true if self >= other.
+
+
+Unary Operations
+----------------
+
+ .. py:method:: complement(self)
+
+ Return the complement of a set.
+
+ .. py:method:: simplify(self)
+
+ Removes redundant constraints from a set.
+
+ .. py:method:: project(self, dims)
+
+ Return a new set with the given dimensions removed.
+
+ .. py:method:: aspolyhedron(self)
+
+ Return polyhedral hull of a set.
+
+ .. py:method:: asdomain(self)
+
+ Return
+
+ .. py:method:: sample(self)
+
+ Return a single sample subset of a set.
+
+Binary Operations
+-----------------
+
+ .. py:method:: intersection(self)
+
+ Return the intersection of two sets as a new set.
+
+ .. py:method:: union(self)
+
+ Return the union of two sets as a new set.
+
+ .. py:method:: __and__(self, other)
+
+ Return the union of two sets as a new set.
+
+ .. py:method:: __or__(self, other)
+
+ Return the intersection of two sets as a new set.
+
+ .. py:method:: __add__(self, other)
+
+ Return the sum of two sets.
+
+ .. py:method:: difference(self, other)
+
+ Return the difference of two sets.
+
+Lexiographic Operations
+-----------------------
+
+ .. py:method:: lexmin(self)
+
+ Return a new set containing the lexicographic minimum of the elements in the set.
+
+ .. py:method:: lexmax(self)
+
+ Return a new set containing the lexicographic maximum of the elements in the set.
+
+Plot Properties
+---------------
+
+ .. py:method:: points(self)
+
+ Return a list of the points contained in a set.
+
+ .. py:method:: vertices(self)
+
+ Return a list of the verticies of this set.
+
+ .. py:method:: faces(self)
+
+ Return a list of the vertices for each face of a set.
+
+ .. py:method:: plot(self, plot=None, **kwargs)
+
+ Return a plot of the given set.
+
+
+
--- /dev/null
+Domains Module
+==============
+
+.. py:class :: Domain
+
+ .. py:method:: polyhedra(self)
+
+ Return .
+
+Domain Properties
+-----------------
+ .. py:method:: symbols(self)
+
+ Returns a list of the symbols used in a set.
+
+ .. py:method:: dimension(self)
+
+ Returns the number of variables in a set.
+
+ .. py:method:: disjoint(self)
+
+ Returns a set as disjoint.
+
+ .. py:method:: num_parameters(self)
+
+ Returns the total number of parameters, input, output or set dimensions.
+
+ .. py:method:: involves_dims(self, dims)
+
+ Returns true if set depends on given dimensions.
+
+Unary Properties
+----------------
+ .. py:method:: isempty(self)
+
+ Return true is set is an Empty set.
+
+ .. py:method:: isuniverse(self)
+
+ Return true if set is the Universe set.
+
+ .. py:method:: isbounded(self)
+
+ Return true if set is bounded
+
+ .. py:method:: disjoint(self)
+
+ Returns this set as a disjoint set.
+
+Binary Properties
+-----------------
+
+ .. py:method:: isdisjoint(self, other)
+
+ Return true if the intersection of two sets results in an Empty set.
+
+ .. py:method:: issubset(self, other)
+
+ Returns true if one set contains the other set.
+
+ .. py:method:: __eq__(self, other)
+
+ Return true if self == other.
+
+ .. py:method:: __lt__(self, other)
+
+ Return true if self < other.
+
+ .. py:method:: __le__(self, other)
+
+ Return true if self <= other.
+
+ .. py:method:: __gt__(self, other)
+
+ Return true if self > other.
+
+ .. py:method:: __ge__(self, other)
+
+ Return true if self >= other.
+
+
+Unary Operations
+----------------
+
+ .. py:method:: complement(self)
+
+ Return the complement of a set.
+
+ .. py:method:: simplify(self)
+
+ Removes redundant constraints from a set.
+
+ .. py:method:: project(self, dims)
+
+ Return a new set with the given dimensions removed.
+
+ .. py:method:: aspolyhedron(self)
+
+ Return polyhedral hull of a set.
+
+ .. py:method:: asdomain(self)
+
+ Return
+
+ .. py:method:: sample(self)
+
+ Return a single sample subset of a set.
+
+Binary Operations
+-----------------
+
+ .. py:method:: intersection(self)
+
+ Return the intersection of two sets as a new set.
+
+ .. py:method:: union(self)
+
+ Return the union of two sets as a new set.
+
+ .. py:method:: __and__(self, other)
+
+ Return the union of two sets as a new set.
+
+ .. py:method:: __or__(self, other)
+
+ Return the intersection of two sets as a new set.
+
+ .. py:method:: __add__(self, other)
+
+ Return the sum of two sets.
+
+ .. py:method:: difference(self, other)
+
+ Return the difference of two sets.
+
+Lexiographic Operations
+-----------------------
+
+ .. py:method:: lexmin(self)
+
+ Return a new set containing the lexicographic minimum of the elements in the set.
+
+ .. py:method:: lexmax(self)
+
+ Return a new set containing the lexicographic maximum of the elements in the set.
+
+Plot Properties
+---------------
+
+ .. py:method:: points(self)
+
+ Return a list of the points contained in a set.
+
+ .. py:method:: vertices(self)
+
+ Return a list of the verticies of this set.
+
+ .. py:method:: faces(self)
+
+ Return a list of the vertices for each face of a set.
+
+ .. py:method:: plot(self, plot=None, **kwargs)
+
+ Return a plot of the given set.
+
+
+
--- /dev/null
+Geometry Module
+===============
+
+The geometry module is used to obtain information about the points and vertices of a ployhedra.
+
+.. py:class:: Points
+
+This class represents points in space.
+
+ .. py:method:: isorigin(self)
+
+ Return true is given point is the origin.
+
+ .. py:method::
+
+.. py:class:: Vector
+
+This class represents displacements in space.
+
+ .. py:method:: angle(self, other)
+
+ Retrieve the angle required to rotate the vector into the vector passed
+ in argument. The result is an angle in radians, ranging between -pi and
+ pi.
+
+ .. py:method:: cross(self, other)
+
+ Calculate the cross product of two Vector3D structures.
+
+ .. py:method:: dot(self, other)
+
+ Calculate the dot product of two vectors.
+
+ .. py:method:: __trudiv__(self, other)
+
+ Divide the vector by the specified scalar and returns the result as a
+ vector.
+
--- /dev/null
+
+Geometry Module
+===============
+
+The geometry module is used to obtain information about the points and vertices of a ployhedra.
+
+.. py:class:: Points
+
+This class represents points in space.
+
+ .. py:method:: isorigin(self)
+
+ Return true is given point is the origin.
+
+ .. py:method::
+
+.. py:class:: Vector
+
+This class represents displacements in space.
+
+ .. py:method:: angle(self, other)
+
+ Retrieve the angle required to rotate the vector into the vector passed
+ in argument. The result is an angle in radians, ranging between -pi and
+ pi.
+
+ .. py:method:: cross(self, other)
+
+ Calculate the cross product of two Vector3D structures.
+
+ .. py:method:: dot(self, other)
+
+ Calculate the dot product of two vectors.
+
+ .. py:method:: __trudiv__(self, other)
+
+ Divide the vector by the specified scalar and returns the result as a
+ vector.
+
Welcome to pypol's documentation!
=================================
-Since Pythagoras, we know that :math:`c = \sqrt{a^2 + b^2}`.
+Pypol is a Python library for symbolic mathematics.
+If you are new to Pypol, start with the Tutorial.
+
+This is the central page for all of SymPy's documentation.
+
Contents:
.. toctree::
:maxdepth: 2
+ install.rst
+ examples.rst
+ modules.rst
-Indices and tables
-==================
-
-* :ref:`genindex`
-* :ref:`modindex`
-* :ref:`search`
--- /dev/null
+.. pypol documentation master file, created by
+ sphinx-quickstart on Wed Jun 25 20:34:21 2014.
+ You can adapt this file completely to your liking, but it should at least
+ contain the root `toctree` directive.
+
+Welcome to pypol's documentation!
+=================================
+
+Pypol is a Python library for symbolic mathematics.
+If you are new to Pypol, start with the Tutorial.
+
+This is the central page for all of SymPy's documentation.
+
+
+Contents:
+
+.. toctree::
+ :maxdepth: 2
+
+ install.rst
+ example.rst
+ modules.rst
+
+
+
--- /dev/null
+.. _installation:
+
+Installation
+------------
+
+Dependencies
+============
+
+Users will first need to install Integer Set Library (isl). The source files of isl are available as a tarball or a git repository. Both
+are available `here`_ .
+
+Source
+======
+
+Git
+===
+
+
+.. _here: http://freshmeat.net/projects/isl/
--- /dev/null
+.. _installation:
+
+Installation
+------------
+
+Dependencies
+============
+
+Users will first need to install Integer Set Library (isl). The source files of isl are available as a tarball or a git repository. Both
+are available `here`_ .
+
+
+
+.. _here: http://freshmeat.net/projects/isl/
--- /dev/null
+Linear Expression Module
+========================
+
+
+This class implements linear expressions.
+
+ .. py:method:: coefficient(self, symbol)
+
+ Return the coefficient value of the given symbol.
+
+ .. py:method:: coefficients(self)
+
+ Return a list of the coefficients of an expression
+
+ .. py:method:: constant(self)
+
+ Return the constant value of an expression.
+
+ .. py:method:: symbols(self)
+
+ Return a list of symbols in an expression.
+
+ .. py:method:: dimension(self)
+
+ Return the number of vriables in an expression.
+
+ .. py:method:: __sub__(self, other)
+
+ Return the difference between two expressions.
+
+ .. py:method:: subs(self, symbol, expression=None)
+
+ Subsitute the given value into an expression and return the resulting expression.
+
+ .. py:method:: fromsympy(self)
+
+ Convert sympy object to an expression.
+
+ .. py:method:: tosympy(self)
+
+ Return an expression as a sympy object.
+
+.. py:class:: Dummy(Symbol)
+
+This class returns a dummy symbol to ensure that each no variables are repeated in an expression
--- /dev/null
+Linear Expression Module
+========================
+
+
+This class implements linear expressions.
+
+ .. py:method:: coefficient(self, symbol)
+
+ Return the coefficient value of the given symbol.
+
+ .. py:method:: coefficients(self)
+
+ Return a list of the coefficients of an expression
+
+ .. py:method:: constant(self)
+
+ Return the constant value of an expression.
+
+ .. py:method:: symbols(self)
+
+ Return a list of symbols in an expression.
+
+ .. py:method:: dimension(self)
+
+ Return the number of vriables in an expression.
+
+ .. py:method:: __sub__(self, other)
+
+ Return the difference between two expressions.
+
+ .. py:method:: subs(self, symbol, expression=None)
+
+ Subsitute the given value into an expression and return the resulting expression.
+
+ .. py:method:: fromsympy(self)
+
+ Convert sympy object to an expression.
+
+ .. py:method:: tosympy(self)
+
+ Return an expression as a sympy object.
+
+.. py:class:: Dummy(Symbol)
+
+This class returns a dummy symbol to ensure that each no variables are repeated in an expression
+
+
+
+
+
+
+
+
+
--- /dev/null
+.. module-docs:
+
+Pypol Module Reference
+======================
+
+There are four main Pypol modules:
+
+.. toctree::
+ :maxdepth: 2
+
+ polyhedra.rst
+ domain.rst
+ linexpr.rst
+ geometry.rst
+
--- /dev/null
+.. module-docs:
+
+Pypol Module Reference
+======================
+
+There are four main Pypol modules:
+
+.. toctree::
+ :maxdepth: 2
+
+ polyhedra.rst
+ domain.rst
+ linexpr.rst
+ geometry.rst
+
--- /dev/null
+Polyhedra Module
+================
+
+.. py:class:: Polyhedron
+
+Polyhedra Properties
+--------------------
+
+ .. py:method:: equalities(self)
+
+ Return a list of the equalities in a set.
+
+ .. py:method:: inequalities(self)
+
+ Return a list of the inequalities in a set.
+
+ .. py:method:: constraints(self)
+
+ Return ta list of the constraints of a set.
+
+Unary Operations
+----------------
+ .. py:method:: disjoint(self)
+
+ Returns this set as a disjoint set.
+
+ .. py:method:: isuniverse(self)
+
+ Return true if this set is the Universe set.
+
+ .. py:method:: aspolyhedron(self)
+
+ Return polyhedral hull of this set.
+
+ .. py:method:: subs(self, symbol, expression=None)
+
+ Subsitute expression into given set and returns the result.
+
+ .. py:method:: Lt(left, right)
+
+ Assert first set is less than the second set.
+
+ .. py:method:: Le(left, right)
+
+ Assert first set is less than or equal to the second set.
+
+ .. py:method:: Eq(left, right)
+
+ Assert first set is equal to the second set.
+
+ .. py:method:: Ne(left, right)
+
+ Assert first set is not equal to the second set.
+
+ .. py:method:: Gt(left, right)
+
+ Assert first set is greater than the second set.
+
+ .. py:method:: Ge(left, right)
+
+ Assert first set is greater than or equal to the second set.
--- /dev/null
+Polyhedra Module
+================
+
+.. py:class:: Polyhedron
+
+Polyhedra Properties
+--------------------
+
+ .. py:method:: equalities(self)
+
+ Return a list of the equalities in a set.
+
+ .. py:method:: inequalities(self)
+
+ Return a list of the inequalities in a set.
+
+ .. py:method:: constraints(self)
+
+ Return ta list of the constraints of a set.
+
+Unary Operations
+----------------
+ .. py:method:: disjoint(self)
+
+ Returns this set as a disjoint set.
+
+ .. py:method:: isuniverse(self)
+
+ Return true if this set is the Universe set.
+
+ .. py:method:: aspolyhedron(self)
+
+ Return polyhedral hull of this set.
+
+ .. py:method:: subs(self, symbol, expression=None)
+
+ Subsitute expression into given set and returns the result.
+
+ .. py:method:: Lt(left, right)
+
+ Assert first set is less than the second set.
+
+ .. py:method:: Le(left, right)
+
+ Assert first set is less than or equal to the second set.
+
+ .. py:method:: Eq(left, right)
+
+ Assert first set is equal to the second set.
+
+ .. py:method:: Ne(left, right)
+
+ Assert first set is not equal to the second set.
+
+ .. py:method:: Gt(left, right)
+
+ Assert first set is greater than the second set.
+
+ .. py:method:: Ge(left, right)
+
+ Assert first set is greater than or equal to the second set.
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)
coordinates[symbol] = coordinate
points.append(Point(coordinates))
return points
-
+
@classmethod
def _polygon_inner_point(cls, points):
symbols = points[0].symbols
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()
axes.set_zlim(zmin, zmax)
return axes
+
def plot(self, plot=None, **kwargs):
"""
Display plot of this set.
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)
--- /dev/null
+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
@property
def equalities(self):
+ """
+ Return a list of the equalities in a set.
+ """
return self._equalities
@property
def inequalities(self):
+ """
+ Return a list of the inequalities in a set.
+ """
return self._inequalities
@property
def constraints(self):
+ """
+ Return ta list of the constraints of a set.
+ """
return self._constraints
@property
def disjoint(self):
"""
- Return this set as disjoint.
+ Return a set as disjoint.
"""
return self
def isuniverse(self):
"""
- Return true if this set is the Universe set.
+ Return true if a set is the Universe set.
"""
islbset = self._toislbasicset(self.equalities, self.inequalities,
self.symbols)
def aspolyhedron(self):
"""
- Return polyhedral hull of this set.
+ Return polyhedral hull of a set.
"""
return self
return True
def subs(self, symbol, expression=None):
+ """
+ Subsitute the given value into an expression and return the resulting expression.
+ """
equalities = [equality.subs(symbol, expression)
for equality in self.equalities]
inequalities = [inequality.subs(symbol, expression)
@classmethod
def _fromislbasicset(cls, islbset, symbols):
- if libisl.isl_basic_set_is_empty(islbset):
- return Empty
- if libisl.isl_basic_set_is_universe(islbset):
- return Universe
islconstraints = islhelper.isl_basic_set_constraints(islbset)
equalities = []
inequalities = []
else:
return 'And({})'.format(', '.join(strings))
+
def _repr_latex_(self):
strings = []
for equality in self.equalities:
@classmethod
def fromsympy(cls, expr):
+ """
+ Convert a sympy object to an expression.
+ """
domain = Domain.fromsympy(expr)
if not isinstance(domain, Polyhedron):
raise ValueError('non-polyhedral expression: {!r}'.format(expr))
return domain
def tosympy(self):
+ """
+ Return an expression as a sympy object.
+ """
import sympy
constraints = []
for equality in self.equalities:
constraints.append(sympy.Ge(inequality.tosympy(), 0))
return sympy.And(*constraints)
-
class EmptyType(Polyhedron):
__slots__ = Polyhedron.__slots__
@_polymorphic
def Lt(left, right):
"""
- Return true if the first set is less than the second.
+ Assert first set is less than the second set.
"""
return Polyhedron([], [right - left - 1])
@_polymorphic
def Le(left, right):
"""
- Return true the first set is less than or equal to the second.
+ Assert first set is less than or equal to the second set.
"""
return Polyhedron([], [right - left])
@_polymorphic
def Eq(left, right):
"""
- Return true if the sets are equal.
+ Assert first set is equal to the second set.
"""
return Polyhedron([left - right], [])
@_polymorphic
def Ne(left, right):
"""
- Return true if the sets are NOT equal.
+ Assert first set is not equal to the second set.
"""
return ~Eq(left, right)
@_polymorphic
def Gt(left, right):
"""
- Return true if the first set is greater than the second set.
+ Assert first set is greater than the second set.
"""
return Polyhedron([], [left - right - 1])
@_polymorphic
def Ge(left, right):
"""
- Return true if the first set is greater than or equal the second set.
+ Assert first set is greater than or equal to the second set.
"""
return Polyhedron([], [left - right])
+
--- /dev/null
+import functools
+import math
+import numbers
+
+from . import islhelper
+
+from .islhelper import mainctx, libisl
+from .geometry import GeometricObject, Point
+from .linexprs import Expression, Rational
+from .domains import Domain
+
+
+__all__ = [
+ 'Polyhedron',
+ 'Lt', 'Le', 'Eq', 'Ne', 'Ge', 'Gt',
+ 'Empty', 'Universe',
+]
+
+
+class Polyhedron(Domain):
+
+ __slots__ = (
+ '_equalities',
+ '_inequalities',
+ '_constraints',
+ '_symbols',
+ '_dimension',
+ )
+
+ def __new__(cls, equalities=None, inequalities=None):
+ if isinstance(equalities, str):
+ if inequalities is not None:
+ raise TypeError('too many arguments')
+ return cls.fromstring(equalities)
+ elif isinstance(equalities, GeometricObject):
+ if inequalities is not None:
+ raise TypeError('too many arguments')
+ return equalities.aspolyhedron()
+ if equalities is None:
+ equalities = []
+ else:
+ for i, equality in enumerate(equalities):
+ if not isinstance(equality, Expression):
+ raise TypeError('equalities must be linear expressions')
+ equalities[i] = equality.scaleint()
+ if inequalities is None:
+ inequalities = []
+ else:
+ for i, inequality in enumerate(inequalities):
+ if not isinstance(inequality, Expression):
+ raise TypeError('inequalities must be linear expressions')
+ inequalities[i] = inequality.scaleint()
+ symbols = cls._xsymbols(equalities + inequalities)
+ islbset = cls._toislbasicset(equalities, inequalities, symbols)
+ return cls._fromislbasicset(islbset, symbols)
+
+ @property
+ def equalities(self):
+ return self._equalities
+
+ @property
+ def inequalities(self):
+ return self._inequalities
+
+ @property
+ def constraints(self):
+ return self._constraints
+
+ @property
+ def polyhedra(self):
+ return self,
+
+ def disjoint(self):
+ """
+ Return this set as disjoint.
+ """
+ return self
+
+ def isuniverse(self):
+ """
+ Return true if this set is the Universe set.
+ """
+ islbset = self._toislbasicset(self.equalities, self.inequalities,
+ self.symbols)
+ universe = bool(libisl.isl_basic_set_is_universe(islbset))
+ libisl.isl_basic_set_free(islbset)
+ return universe
+
+ def aspolyhedron(self):
+ """
+ Return polyhedral hull of this set.
+ """
+ return self
+
+ def __contains__(self, point):
+ if not isinstance(point, Point):
+ raise TypeError('point must be a Point instance')
+ if self.symbols != point.symbols:
+ raise ValueError('arguments must belong to the same space')
+ for equality in self.equalities:
+ if equality.subs(point.coordinates()) != 0:
+ return False
+ for inequality in self.inequalities:
+ if inequality.subs(point.coordinates()) < 0:
+ return False
+ return True
+
+ def subs(self, symbol, expression=None):
+ equalities = [equality.subs(symbol, expression)
+ for equality in self.equalities]
+ inequalities = [inequality.subs(symbol, expression)
+ for inequality in self.inequalities]
+ return Polyhedron(equalities, inequalities)
+
+ def _asinequalities(self):
+ inequalities = list(self.equalities)
+ inequalities.extend([-expression for expression in self.equalities])
+ inequalities.extend(self.inequalities)
+ return inequalities
+
+ def widen(self, other):
+ if not isinstance(other, Polyhedron):
+ raise ValueError('argument must be a Polyhedron instance')
+ inequalities1 = self._asinequalities()
+ inequalities2 = other._asinequalities()
+ inequalities = []
+ for inequality1 in inequalities1:
+ if other <= Polyhedron(inequalities=[inequality1]):
+ inequalities.append(inequality1)
+ for inequality2 in inequalities2:
+ for i in range(len(inequalities1)):
+ inequalities3 = inequalities1[:i] + inequalities[i + 1:]
+ inequalities3.append(inequality2)
+ polyhedron3 = Polyhedron(inequalities=inequalities3)
+ if self == polyhedron3:
+ inequalities.append(inequality2)
+ break
+ return Polyhedron(inequalities=inequalities)
+
+ @classmethod
+ def _fromislbasicset(cls, islbset, symbols):
+ if libisl.isl_basic_set_is_empty(islbset):
+ return Empty
+ if libisl.isl_basic_set_is_universe(islbset):
+ return Universe
+ islconstraints = islhelper.isl_basic_set_constraints(islbset)
+ equalities = []
+ inequalities = []
+ for islconstraint in islconstraints:
+ constant = libisl.isl_constraint_get_constant_val(islconstraint)
+ 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 = islhelper.isl_val_to_int(coefficient)
+ if coefficient != 0:
+ coefficients[symbol] = coefficient
+ expression = Expression(coefficients, constant)
+ if libisl.isl_constraint_is_equality(islconstraint):
+ equalities.append(expression)
+ else:
+ inequalities.append(expression)
+ libisl.isl_basic_set_free(islbset)
+ self = object().__new__(Polyhedron)
+ self._equalities = tuple(equalities)
+ self._inequalities = tuple(inequalities)
+ self._constraints = tuple(equalities + inequalities)
+ self._symbols = cls._xsymbols(self._constraints)
+ self._dimension = len(self._symbols)
+ return self
+
+ @classmethod
+ def _toislbasicset(cls, equalities, inequalities, symbols):
+ dimension = len(symbols)
+ indices = {symbol: index for index, symbol in enumerate(symbols)}
+ islsp = libisl.isl_space_set_alloc(mainctx, 0, dimension)
+ 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))
+ 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)
+ 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))
+ 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)
+ if inequality.constant != 0:
+ islval = str(inequality.constant).encode()
+ islval = libisl.isl_val_read_from_str(mainctx, islval)
+ islin = libisl.isl_constraint_set_constant_val(islin, islval)
+ islbset = libisl.isl_basic_set_add_constraint(islbset, islin)
+ return islbset
+
+ @classmethod
+ def fromstring(cls, string):
+ domain = Domain.fromstring(string)
+ if not isinstance(domain, Polyhedron):
+ raise ValueError('non-polyhedral expression: {!r}'.format(string))
+ return domain
+
+ def __repr__(self):
+ strings = []
+ for equality in self.equalities:
+ strings.append('Eq({}, 0)'.format(equality))
+ for inequality in self.inequalities:
+ strings.append('Ge({}, 0)'.format(inequality))
+ if len(strings) == 1:
+ return strings[0]
+ else:
+ return 'And({})'.format(', '.join(strings))
+
+ def _repr_latex_(self):
+ strings = []
+ for equality in self.equalities:
+ strings.append('{} = 0'.format(equality._repr_latex_().strip('$')))
+ for inequality in self.inequalities:
+ strings.append('{} \\ge 0'.format(inequality._repr_latex_().strip('$')))
+ return '$${}$$'.format(' \\wedge '.join(strings))
+
+ @classmethod
+ def fromsympy(cls, expr):
+ domain = Domain.fromsympy(expr)
+ if not isinstance(domain, Polyhedron):
+ raise ValueError('non-polyhedral expression: {!r}'.format(expr))
+ return domain
+
+ def tosympy(self):
+ import sympy
+ constraints = []
+ for equality in self.equalities:
+ constraints.append(sympy.Eq(equality.tosympy(), 0))
+ for inequality in self.inequalities:
+ constraints.append(sympy.Ge(inequality.tosympy(), 0))
+ return sympy.And(*constraints)
+
+
+class EmptyType(Polyhedron):
+
+ __slots__ = Polyhedron.__slots__
+
+ def __new__(cls):
+ self = object().__new__(cls)
+ self._equalities = (Rational(1),)
+ self._inequalities = ()
+ self._constraints = self._equalities
+ self._symbols = ()
+ self._dimension = 0
+ return self
+
+ def widen(self, other):
+ if not isinstance(other, Polyhedron):
+ raise ValueError('argument must be a Polyhedron instance')
+ return other
+
+ def __repr__(self):
+ return 'Empty'
+
+ def _repr_latex_(self):
+ return '$$\\emptyset$$'
+
+Empty = EmptyType()
+
+
+class UniverseType(Polyhedron):
+
+ __slots__ = Polyhedron.__slots__
+
+ def __new__(cls):
+ self = object().__new__(cls)
+ self._equalities = ()
+ self._inequalities = ()
+ self._constraints = ()
+ self._symbols = ()
+ self._dimension = ()
+ return self
+
+ def __repr__(self):
+ return 'Universe'
+
+ def _repr_latex_(self):
+ return '$$\\Omega$$'
+
+Universe = UniverseType()
+
+
+def _polymorphic(func):
+ @functools.wraps(func)
+ def wrapper(left, right):
+ if not isinstance(left, Expression):
+ if isinstance(left, numbers.Rational):
+ left = Rational(left)
+ else:
+ raise TypeError('left must be a a rational number '
+ 'or a linear expression')
+ if not isinstance(right, Expression):
+ if isinstance(right, numbers.Rational):
+ right = Rational(right)
+ else:
+ raise TypeError('right must be a a rational number '
+ 'or a linear expression')
+ return func(left, right)
+ return wrapper
+
+@_polymorphic
+def Lt(left, right):
+ """
+ Return true if the first set is less than the second.
+ """
+ return Polyhedron([], [right - left - 1])
+
+@_polymorphic
+def Le(left, right):
+ """
+ Return true the first set is less than or equal to the second.
+ """
+ return Polyhedron([], [right - left])
+
+@_polymorphic
+def Eq(left, right):
+ """
+ Return true if the sets are equal.
+ """
+ return Polyhedron([left - right], [])
+
+@_polymorphic
+def Ne(left, right):
+ """
+ Return true if the sets are NOT equal.
+ """
+ return ~Eq(left, right)
+
+@_polymorphic
+def Gt(left, right):
+ """
+ Return true if the first set is greater than the second set.
+ """
+ return Polyhedron([], [left - right - 1])
+
+@_polymorphic
+def Ge(left, right):
+ """
+ Return true if the first set is greater than or equal the second set.
+ """
+ return Polyhedron([], [left - right])
projects / linpy.git / commitdiff