-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)
libisl.isl_basic_set_free(islbset)
return universe
- def polyhedral_hull(self):
+ def aspolyhedron(self):
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:
strings = []
for equality in self.equalities:
- strings.append('Eq({}, 0)'.format(equality))
+ strings.append('0 == {}'.format(equality))
for inequality in self.inequalities:
- strings.append('Ge({}, 0)'.format(inequality))
+ strings.append('0 <= {}'.format(inequality))
if len(strings) == 1:
return strings[0]
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)
- 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
-
@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 = oa.dot(om) / normprod
+ 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(self):
+ import matplotlib.pyplot as plt
+ from matplotlib.path import Path
+ import matplotlib.patches as patches
+
+ if len(self.symbols)> 3:
+ raise TypeError
+
+ elif len(self.symbols) == 2:
+ verts = self.vertices()
+ points = []
+ codes = [Path.MOVETO]
+ for vert in verts:
+ pairs = ()
+ for sym in sorted(vert, key=Symbol.sortkey):
+ num = vert.get(sym)
+ pairs = pairs + (num,)
+ points.append(pairs)
+ points.append((0.0, 0.0))
+ num = len(points)
+ while num > 2:
+ codes.append(Path.LINETO)
+ num = num - 1
+ else:
+ codes.append(Path.CLOSEPOLY)
+ path = Path(points, codes)
+ fig = plt.figure()
+ ax = fig.add_subplot(111)
+ patch = patches.PathPatch(path, facecolor='blue', lw=2)
+ ax.add_patch(patch)
+ ax.set_xlim(-5,5)
+ ax.set_ylim(-5,5)
+ plt.show()
+
+ elif len(self.symbols)==3:
+ return 0
+
+ return points
+
def _polymorphic(func):
@functools.wraps(func)
def wrapper(left, right):
if isinstance(left, numbers.Rational):
- left = Constant(left)
+ left = Rational(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)
+ right = Rational(right)
elif not isinstance(right, Expression):
raise TypeError('right must be a a rational number '
'or a linear expression')
projects / linpy.git / blobdiff