-import ast
import functools
+import math
import numbers
-import re
from . import islhelper
from .islhelper import mainctx, libisl
-from .linexprs import Expression, Constant
+from .geometry import GeometricObject, Point, Vector
+from .linexprs import Expression, Symbol, Rational
from .domains import Domain
if inequalities is not None:
raise TypeError('too many arguments')
return cls.fromstring(equalities)
- elif isinstance(equalities, Polyhedron):
+ elif isinstance(equalities, GeometricObject):
if inequalities is not None:
raise TypeError('too many arguments')
- return equalities
- elif isinstance(equalities, Domain):
- if inequalities is not None:
- raise TypeError('too many arguments')
- return equalities.polyhedral_hull()
+ 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._toint()
+ 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._toint()
+ inequalities[i] = inequality.scaleint()
symbols = cls._xsymbols(equalities + inequalities)
islbset = cls._toislbasicset(equalities, inequalities, symbols)
return cls._fromislbasicset(islbset, symbols)
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 polyhedral_hull(self):
+ 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:
- islpr = libisl.isl_printer_to_str(mainctx)
constant = libisl.isl_constraint_get_constant_val(islconstraint)
constant = islhelper.isl_val_to_int(constant)
coefficients = {}
- for dim, symbol in enumerate(symbols):
- coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint, libisl.isl_dim_set, dim)
+ 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
@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():
- val = str(coefficient).encode()
- val = libisl.isl_val_read_from_str(mainctx, val)
- sid = symbols.index(symbol)
+ 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, sid, val)
+ libisl.isl_dim_set, index, islval)
if equality.constant != 0:
- val = str(equality.constant).encode()
- val = libisl.isl_val_read_from_str(mainctx, val)
- isleq = libisl.isl_constraint_set_constant_val(isleq, val)
+ 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():
- val = str(coefficient).encode()
- val = libisl.isl_val_read_from_str(mainctx, val)
- sid = symbols.index(symbol)
+ 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, sid, val)
+ libisl.isl_dim_set, index, islval)
if inequality.constant != 0:
- val = str(inequality.constant).encode()
- val = libisl.isl_val_read_from_str(mainctx, val)
- islin = libisl.isl_constraint_set_constant_val(islin, val)
+ 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 _fromast(cls, node):
- 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.BinOp) and isinstance(node.op, ast.BitAnd):
- equalities1, inequalities1 = cls._fromast(node.left)
- equalities2, inequalities2 = cls._fromast(node.right)
- equalities = equalities1 + equalities2
- inequalities = inequalities1 + inequalities2
- return equalities, inequalities
- 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 equalities, inequalities
- raise SyntaxError('invalid syntax')
-
@classmethod
def fromstring(cls, string):
- string = string.strip()
- string = re.sub(r'^\{\s*|\s*\}$', '', string)
- string = re.sub(r'([^<=>])=([^<=>])', r'\1==\2', string)
- string = re.sub(r'(\d+|\))\s*([^\W\d_]\w*|\()', r'\1*\2', string)
- tokens = re.split(r',|;|and|&&|/\\|∧', string, flags=re.I)
- tokens = ['({})'.format(token) for token in tokens]
- string = ' & '.join(tokens)
- tree = ast.parse(string, 'eval')
- equalities, inequalities = cls._fromast(tree)
- return cls(equalities, inequalities)
+ 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():
else:
return 'And({})'.format(', '.join(strings))
- @classmethod
- def _fromsympy(cls, expr):
- import sympy
- equalities = []
- inequalities = []
- if expr.func == sympy.And:
- for arg in expr.args:
- arg_eqs, arg_ins = cls._fromsympy(arg)
- equalities.extend(arg_eqs)
- inequalities.extend(arg_ins)
- elif expr.func == sympy.Eq:
- expr = Expression.fromsympy(expr.args[0] - expr.args[1])
- equalities.append(expr)
+ def _repr_latex_(self):
+ if self.isempty():
+ return '$\\emptyset$'
+ elif self.isuniverse():
+ return '$\\Omega$'
else:
- if expr.func == sympy.Lt:
- expr = Expression.fromsympy(expr.args[1] - expr.args[0] - 1)
- elif expr.func == sympy.Le:
- expr = Expression.fromsympy(expr.args[1] - expr.args[0])
- elif expr.func == sympy.Ge:
- expr = Expression.fromsympy(expr.args[0] - expr.args[1])
- elif expr.func == sympy.Gt:
- expr = Expression.fromsympy(expr.args[0] - expr.args[1] - 1)
- else:
- raise ValueError('non-polyhedral expression: {!r}'.format(expr))
- inequalities.append(expr)
- return equalities, inequalities
+ 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):
- import sympy
- equalities, inequalities = cls._fromsympy(expr)
- return cls(equalities, inequalities)
+ 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.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 isinstance(left, numbers.Rational):
- left = Constant(left)
- elif not isinstance(left, Expression):
- raise TypeError('left must be a a rational number '
- 'or a linear expression')
- if isinstance(right, numbers.Rational):
- right = Constant(right)
- elif not isinstance(right, Expression):
- raise TypeError('right must be a a rational number '
- 'or a linear expression')
+ 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 / blobdiff