examples/squares.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 a, x, y, z = symbols('a x y z')
  23
  24 sq1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
  25 sq2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4)
  26 sq3 = Le(0, x) & Le(x, 3) & Le(0, y) & Le(y, 3)
  27 sq4 = Le(1, x) & Le(x, 2) & Le(1, y) & Le(y, 2)
  28 sq5 = Le(1, x) & Le(x, 2) & Le(1, y)
  29 sq6 = Le(1, x) & Le(x, 2) & Le(1, y) & Le(y, 3)
  30 sq7 = Le(0, x) & Le(x, 2) & Le(0, y) & Eq(z, 2) & Le(a, 3)
  31 p = Le(2*x+1, y) & Le(-2*x-1, y) & Le(y, 1)
  32
  33
  34 universe = Polyhedron([])
  35 q = sq1 - sq2
  36 e = Empty
  37
  38 print('sq1 =', sq1) #print correct square
  39 print('sq2 =', sq2) #print correct square
  40 print('sq3 =', sq3) #print correct square
  41 print('sq4 =', sq4) #print correct square
  42 print('universe =', universe) #print correct square
  43 print()
  44 print('¬sq1 =', ~sq1) #test complement
  45 print()
  46 print('sq1 + sq1 =', sq1 + sq2) #test addition
  47 print('sq1 + sq2 =', Polyhedron(sq1 + sq2)) #test addition
  48 print()
  49 print('universe + universe =', universe + universe)#test addition
  50 print('universe - universe =', universe - universe) #test subtraction
  51 print()
  52 print('sq2 - sq1 =', sq2 - sq1) #test subtraction
  53 print('sq2 - sq1 =', Polyhedron(sq2 - sq1)) #test subtraction
  54 print('sq1 - sq1 =', Polyhedron(sq1 - sq1)) #test subtraction
  55 print()
  56 print('sq1 ∩ sq2 =', sq1 & sq2) #test intersection
  57 print('sq1 ∪ sq2 =', sq1 | sq2) #test union
  58 print()
  59 print('sq1 ⊔ sq2 =', Polyhedron(sq1 | sq2)) # test convex union
  60 print()
  61 print('check if sq1 and sq2 disjoint:', sq1.isdisjoint(sq2)) #should return false
  62 print()
  63 print('sq1 disjoint:', sq1.disjoint()) #make disjoint
  64 print('sq2 disjoint:', sq2.disjoint()) #make disjoint
  65 print()
  66 print('is square 1 universe?:', sq1.isuniverse()) #test if square is universe
  67 print('is u universe?:', universe.isuniverse()) #test if square is universe
  68 print()
  69 print('is sq1 a subset of sq2?:', sq1.issubset(sq2)) #test issubset()
  70 print('is sq4 less than sq3?:', sq4.__lt__(sq3)) # test lt(), must be a strict subset
  71 print()
  72 print('lexographic min of sq1:', sq1.lexmin()) #test lexmin()
  73 print('lexographic max of sq1:', sq1.lexmax()) #test lexmin()
  74 print()
  75 print('lexographic min of sq2:', sq2.lexmin()) #test lexmax()
  76 print('lexographic max of sq2:', sq2.lexmax()) #test lexmax()
  77 print()
  78 print('Polyhedral hull of sq1 + sq2 is:', q.aspolyhedron()) #test polyhedral hull
  79 print()
  80 print('is sq1 bounded?', sq1.isbounded()) #unbounded should return True
  81 print('is sq5 bounded?', sq5.isbounded()) #unbounded should return False
  82 print()
  83 print('sq6:', sq6)
  84 print('sq6 simplified:', sq6.sample())
  85 print()
  86 print(universe.project([x]))
  87 print('sq7 with out constraints involving y and a', sq7.project([a, z, x, y])) #drops dims that are passed
  88 print()
  89 print('sq1 has {} parameters'.format(sq1.num_parameters()))
  90 print()
  91 print('does sq1 constraints involve x?', sq1.involves_dims([x]))
  92 print()
  93 print('the verticies for s are:', p.vertices())
  94 print()
  95 print(p.plot())
  96
  97 # Copyright 2014 MINES ParisTech