+++ /dev/null
-import functools
-import math
-import numbers
-
-from . import islhelper
-
-from .islhelper import mainctx, libisl
-from .geometry import GeometricObject, Point, Vector
-from .linexprs import Expression, Symbol, 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)
-
- @classmethod
- def _fromislbasicset(cls, islbset, symbols):
- 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):
- if self.isempty():
- return 'Empty'
- elif self.isuniverse():
- return 'Universe'
- else:
- 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):
- if self.isempty():
- return '$\\emptyset$'
- elif self.isuniverse():
- return '$\\Omega$'
- else:
- 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)
-
- @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):
- vertices = self.vertices()
- faces = []
- for constraint in self.constraints:
- face = []
- for vertex in vertices:
- if constraint.subs(vertex.coordinates()) == 0:
- face.append(vertex)
- faces.append(face)
- return faces
-
- def _plot_2d(self, plot=None, **kwargs):
- from matplotlib import pylab
- import matplotlib.pyplot as plt
- from matplotlib.axes import Axes
- from matplotlib.patches import Polygon
- vertices = self._sort_polygon_2d(self.vertices())
- xys = [tuple(vertex.values()) for vertex in vertices]
- if plot is None:
- fig = plt.figure()
- plot = fig.add_subplot(1, 1, 1)
- xs, ys = zip(*xys)
- plot.set_xlim(float(min(xs)), float(max(xs)))
- plot.set_ylim(float(min(ys)), float(max(ys)))
- plot.add_patch(Polygon(xys, closed=True, **kwargs))
- 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)
- xmin, xmax = float('inf'), float('-inf')
- ymin, ymax = float('inf'), float('-inf')
- zmin, zmax = float('inf'), float('-inf')
- else:
- axes = plot
- poly_xyzs = []
- for vertices in self.faces():
- if len(vertices) == 0:
- continue
- vertices = Polyhedron._sort_polygon_3d(vertices)
- vertices.append(vertices[0])
- face_xyzs = [tuple(vertex.values()) for vertex in vertices]
- if plot is None:
- 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)
- if plot is None:
- axes.set_xlim(xmin, xmax)
- axes.set_ylim(ymin, ymax)
- axes.set_zlim(zmin, zmax)
- return axes
-
- def plot(self, plot=None, **kwargs):
- """
- Display 3D plot of set.
- """
- if 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 _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])
-
-
-Empty = Eq(1, 0)
-
-Universe = Polyhedron([])
projects / linpy.git / blobdiff