examples/squares.py

   1 #!/usr/bin/env python3
   2
   3 from linpy import *
   4 import matplotlib.pyplot as plt
   5 from matplotlib import pylab
   6
   7 a, x, y, z = symbols('a x y z')
   8
   9 sq1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
  10 sq2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4)
  11 sq3 = Le(0, x) & Le(x, 3) & Le(0, y) & Le(y, 3)
  12 sq4 = Le(1, x) & Le(x, 2) & Le(1, y) & Le(y, 2)
  13 sq5 = Le(1, x) & Le(x, 2) & Le(1, y)
  14 sq6 = Le(1, x) & Le(x, 2) & Le(1, y) & Le(y, 3)
  15 sq7 = Le(0, x) & Le(x, 2) & Le(0, y) & Eq(z, 2) & Le(a, 3)
  16 p = Le(2*x+1, y) & Le(-2*x-1, y) & Le(y, 1)
  17
  18 universe = Polyhedron([])
  19 q = sq1 - sq2
  20 e = Empty
  21
  22 print('sq1 =', sq1) #print correct square
  23 print('sq2 =', sq2) #print correct square
  24 print('sq3 =', sq3) #print correct square
  25 print('sq4 =', sq4) #print correct square
  26 print('universe =', universe) #print correct square
  27 print()
  28 print('¬sq1 =', ~sq1) #test complement
  29 print()
  30 print('sq1 + sq1 =', sq1 + sq2) #test addition
  31 print('sq1 + sq2 =', Polyhedron(sq1 + sq2)) #test addition
  32 print()
  33 print('universe + universe =', universe + universe)#test addition
  34 print('universe - universe =', universe - universe) #test subtraction
  35 print()
  36 print('sq2 - sq1 =', sq2 - sq1) #test subtraction
  37 print('sq2 - sq1 =', Polyhedron(sq2 - sq1)) #test subtraction
  38 print('sq1 - sq1 =', Polyhedron(sq1 - sq1)) #test subtraction
  39 print()
  40 print('sq1 ∩ sq2 =', sq1 & sq2) #test intersection
  41 print('sq1 ∪ sq2 =', sq1 | sq2) #test union
  42 print()
  43 print('sq1 ⊔ sq2 =', Polyhedron(sq1 | sq2)) # test convex union
  44 print()
  45 print('check if sq1 and sq2 disjoint:', sq1.isdisjoint(sq2)) #should return false
  46 print()
  47 print('sq1 disjoint:', sq1.disjoint()) #make disjoint
  48 print('sq2 disjoint:', sq2.disjoint()) #make disjoint
  49 print()
  50 print('is square 1 universe?:', sq1.isuniverse()) #test if square is universe
  51 print('is u universe?:', universe.isuniverse()) #test if square is universe
  52 print()
  53 print('is sq1 a subset of sq2?:', sq1.issubset(sq2)) #test issubset()
  54 print('is sq4 less than sq3?:', sq4.__lt__(sq3)) # test lt(), must be a strict subset
  55 print()
  56 print('lexographic min of sq1:', sq1.lexmin()) #test lexmin()
  57 print('lexographic max of sq1:', sq1.lexmax()) #test lexmin()
  58 print()
  59 print('lexographic min of sq2:', sq2.lexmin()) #test lexmax()
  60 print('lexographic max of sq2:', sq2.lexmax()) #test lexmax()
  61 print()
  62 print('Polyhedral hull of sq1 + sq2 is:', q.aspolyhedron()) #test polyhedral hull
  63 print()
  64 print('is sq1 bounded?', sq1.isbounded()) #bounded should return True
  65 print('is sq5 bounded?', sq5.isbounded()) #unbounded should return False
  66 print()
  67 print('sq6:', sq6)
  68 print('sample Polyhedron from sq6:', sq6.sample())
  69 print()
  70 print('sq7 with out constraints involving y and a', sq7.project([a, z, x, y]))
  71 print()
  72 print('the verticies for s are:', p.vertices())
  73
  74
  75 # plotting the intersection of two squares
  76 square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
  77 square2 = Le(1, x) & Le(x, 3) & Le(1, y) & Le(y, 3)
  78
  79 fig = plt.figure()
  80 plot = fig.add_subplot(1, 1, 1, aspect='equal')
  81 square1.plot(plot, facecolor='red', alpha=0.3)
  82 square2.plot(plot, facecolor='blue', alpha=0.3)
  83
  84 squares = Polyhedron(square1 + square2)
  85 squares.plot(plot, facecolor='blue', alpha=0.3)
  86
  87 pylab.show()