X-Git-Url: https://svn.cri.ensmp.fr/git/linpy.git/blobdiff_plain/fd990941199581e977b4455345b55f841bbaa05a..3d17926f6a9051fd4b3a2c19b756849103592bd9:/pypol/polyhedra.py?ds=sidebyside diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py index ac67cf8..db99753 100644 --- a/pypol/polyhedra.py +++ b/pypol/polyhedra.py @@ -1,10 +1,11 @@ + import functools import numbers from . import islhelper from .islhelper import mainctx, libisl -from .linexprs import Expression, Constant +from .linexprs import Expression, Symbol, Rational from .domains import Domain @@ -37,21 +38,21 @@ class Polyhedron(Domain): 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) @@ -82,9 +83,16 @@ class Polyhedron(Domain): libisl.isl_basic_set_free(islbset) return universe - def polyhedral_hull(self): + def aspolyhedron(self): return self + 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) @@ -95,7 +103,8 @@ class Polyhedron(Domain): 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 = 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 @@ -163,46 +172,20 @@ 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 @@ -212,18 +195,57 @@ class Polyhedron(Domain): for inequality in self.inequalities: constraints.append(sympy.Ge(inequality.tosympy(), 0)) return sympy.And(*constraints) + + 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')