X-Git-Url: https://svn.cri.ensmp.fr/git/linpy.git/blobdiff_plain/1d494bb187b70135df721c13306d7f26fdf33f50..e8ebee616179da727b335a0ef37732ee19c65b43:/pypol/polyhedra.py diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py index 787e965..5d9c287 100644 --- a/pypol/polyhedra.py +++ b/pypol/polyhedra.py @@ -1,12 +1,12 @@ -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 +from .linexprs import Expression, Symbol, Rational from .domains import Domain @@ -32,28 +32,24 @@ class Polyhedron(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) @@ -84,21 +80,41 @@ class Polyhedron(Domain): 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 @@ -119,85 +135,44 @@ class Polyhedron(Domain): @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(): @@ -207,46 +182,20 @@ class Polyhedron(Domain): 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 @@ -257,17 +206,92 @@ class Polyhedron(Domain): constraints.append(sympy.Ge(inequality.tosympy(), 0)) return sympy.And(*constraints) + @classmethod + def _sort_polygon_2d(cls, points): + if len(points) <= 3: + return points + o = sum((Vector(point) for point in points)) / len(points) + o = Point(o.coordinates()) + angles = {} + for m in points: + om = Vector(o, m) + dx, dy = (coordinate for symbol, coordinates 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 = sum((Vector(point) for point in points)) / len(points) + o = Point(o.coordinates()) + a, b = points[:2] + oa = Vector(o, a) + ob = Vector(o, b) + norm_oa = oa.norm() + u = (oa.cross(ob)).asunit() + 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 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')