examples/nsad2010.py

   1 #!/usr/bin/env python3
   2
   3 """
   4     This file is part of Linpy.
   5
   6     Linpy is free software: you can redistribute it and/or modify
   7     it under the terms of the GNU General Public License as published by
   8     the Free Software Foundation, either version 3 of the License, or
   9     (at your option) any later version.
  10
  11     Linpy is distributed in the hope that it will be useful,
  12     but WITHOUT ANY WARRANTY; without even the implied warranty of
  13     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14     GNU General Public License for more details.
  15
  16     You should have received a copy of the GNU General Public License
  17     along with Linpy.  If not, see <http://www.gnu.org/licenses/>.
  18 """
  19
  20 from pypol import *
  21
  22
  23 class Transformer:
  24
  25     def __new__(cls, polyhedron, range_symbols, domain_symbols):
  26         self = object().__new__(cls)
  27         self.polyhedron = polyhedron
  28         self.range_symbols = range_symbols
  29         self.domain_symbols = domain_symbols
  30         return self
  31
  32     @property
  33     def symbols(self):
  34         return self.range_symbols + self.domain_symbols
  35
  36     def star(self):
  37         delta_symbols = [symbol.asdummy() for symbol in self.range_symbols]
  38         k = Dummy('k')
  39         polyhedron = self.polyhedron
  40         for x, xprime, dx in zip(self.range_symbols, self.domain_symbols, delta_symbols):
  41             polyhedron &= Eq(dx, xprime - x)
  42         polyhedron = polyhedron.project(self.symbols)
  43         equalities, inequalities = [], []
  44         for equality in polyhedron.equalities:
  45             equality += (k-1) * equality.constant
  46             equalities.append(equality)
  47         for inequality in polyhedron.inequalities:
  48             inequality += (k-1) * inequality.constant
  49             inequalities.append(inequality)
  50         polyhedron = Polyhedron(equalities, inequalities) & Ge(k, 0)
  51         polyhedron = polyhedron.project([k])
  52         for x, xprime, dx in zip(self.range_symbols, self.domain_symbols, delta_symbols):
  53             polyhedron &= Eq(dx, xprime - x)
  54         polyhedron = polyhedron.project(delta_symbols)
  55         return Transformer(polyhedron, self.range_symbols, self.domain_symbols)
  56
  57
  58 if __name__ == '__main__':
  59     i, iprime, j, jprime = symbols("i i' j j'")
  60     transformer = Transformer(Eq(iprime, i + 2) & Eq(jprime, j + 1),
  61         [i, j], [iprime, jprime])
  62     print('T  =', transformer.polyhedron)
  63     print('T* =', transformer.star().polyhedron)
  64
  65 # Copyright 2014 MINES ParisTech