examples/squares.py

   1 #!/usr/bin/env python3
   2 #
   3 # Copyright 2014 MINES ParisTech
   4 #
   5 # This file is part of LinPy.
   6 #
   7 # LinPy is free software: you can redistribute it and/or modify
   8 # it under the terms of the GNU General Public License as published by
   9 # the Free Software Foundation, either version 3 of the License, or
  10 # (at your option) any later version.
  11 #
  12 # LinPy is distributed in the hope that it will be useful,
  13 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 # GNU General Public License for more details.
  16 #
  17 # You should have received a copy of the GNU General Public License
  18 # along with LinPy.  If not, see <http://www.gnu.org/licenses/>.
  19
  20 from linpy import *
  21 import matplotlib.pyplot as plt
  22 from matplotlib import pylab
  23
  24 a, x, y, z = symbols('a x y z')
  25
  26 sq1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
  27 sq2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4)
  28 sq3 = Le(0, x) & Le(x, 3) & Le(0, y) & Le(y, 3)
  29 sq4 = Le(1, x) & Le(x, 2) & Le(1, y) & Le(y, 2)
  30 sq5 = Le(1, x) & Le(x, 2) & Le(1, y)
  31 sq6 = Le(1, x) & Le(x, 2) & Le(1, y) & Le(y, 3)
  32 sq7 = Le(0, x) & Le(x, 2) & Le(0, y) & Eq(z, 2) & Le(a, 3)
  33 p = Le(2*x+1, y) & Le(-2*x-1, y) & Le(y, 1)
  34
  35 universe = Polyhedron([])
  36 q = sq1 - sq2
  37 e = Empty
  38
  39 print('sq1 =', sq1) #print correct square
  40 print('sq2 =', sq2) #print correct square
  41 print('sq3 =', sq3) #print correct square
  42 print('sq4 =', sq4) #print correct square
  43 print('universe =', universe) #print correct square
  44 print()
  45 print('¬sq1 =', ~sq1) #test complement
  46 print()
  47 print('sq1 + sq1 =', sq1 + sq2) #test addition
  48 print('sq1 + sq2 =', Polyhedron(sq1 + sq2)) #test addition
  49 print()
  50 print('universe + universe =', universe + universe)#test addition
  51 print('universe - universe =', universe - universe) #test subtraction
  52 print()
  53 print('sq2 - sq1 =', sq2 - sq1) #test subtraction
  54 print('sq2 - sq1 =', Polyhedron(sq2 - sq1)) #test subtraction
  55 print('sq1 - sq1 =', Polyhedron(sq1 - sq1)) #test subtraction
  56 print()
  57 print('sq1 ∩ sq2 =', sq1 & sq2) #test intersection
  58 print('sq1 ∪ sq2 =', sq1 | sq2) #test union
  59 print()
  60 print('sq1 ⊔ sq2 =', Polyhedron(sq1 | sq2)) # test convex union
  61 print()
  62 print('check if sq1 and sq2 disjoint:', sq1.isdisjoint(sq2)) #should return false
  63 print()
  64 print('sq1 disjoint:', sq1.disjoint()) #make disjoint
  65 print('sq2 disjoint:', sq2.disjoint()) #make disjoint
  66 print()
  67 print('is square 1 universe?:', sq1.isuniverse()) #test if square is universe
  68 print('is u universe?:', universe.isuniverse()) #test if square is universe
  69 print()
  70 print('is sq1 a subset of sq2?:', sq1.issubset(sq2)) #test issubset()
  71 print('is sq4 less than sq3?:', sq4.__lt__(sq3)) # test lt(), must be a strict subset
  72 print()
  73 print('lexographic min of sq1:', sq1.lexmin()) #test lexmin()
  74 print('lexographic max of sq1:', sq1.lexmax()) #test lexmin()
  75 print()
  76 print('lexographic min of sq2:', sq2.lexmin()) #test lexmax()
  77 print('lexographic max of sq2:', sq2.lexmax()) #test lexmax()
  78 print()
  79 print('Polyhedral hull of sq1 + sq2 is:', q.aspolyhedron()) #test polyhedral hull
  80 print()
  81 print('is sq1 bounded?', sq1.isbounded()) #bounded should return True
  82 print('is sq5 bounded?', sq5.isbounded()) #unbounded should return False
  83 print()
  84 print('sq6:', sq6)
  85 print('sample Polyhedron from sq6:', sq6.sample())
  86 print()
  87 print('sq7 with out constraints involving y and a', sq7.project([a, z, x, y]))
  88 print()
  89 print('the verticies for s are:', p.vertices())
  90
  91
  92 # plotting the intersection of two squares
  93 square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
  94 square2 = Le(1, x) & Le(x, 3) & Le(1, y) & Le(y, 3)
  95
  96 fig = plt.figure()
  97 plot = fig.add_subplot(1, 1, 1, aspect='equal')
  98 square1.plot(plot, facecolor='red', alpha=0.3)
  99 square2.plot(plot, facecolor='blue', alpha=0.3)
 100
 101 squares = Polyhedron(square1 + square2)
 102 squares.plot(plot, facecolor='blue', alpha=0.3)
 103
 104 pylab.show()