Add license to examples

[linpy.git] / examples / squares.py

diff --git a/examples/squares.py b/examples/squares.py
index e140e30..89be192 100755 (executable)
--- a/examples/squares.py
+++ b/examples/squares.py
@@ -1,6 +1,25 @@
 #!/usr/bin/env python3
+#
+# Copyright 2014 MINES ParisTech
+#
+# This file is part of LinPy.
+#
+# LinPy is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# LinPy is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with LinPy.  If not, see <http://www.gnu.org/licenses/>.
 
-from pypol import *
+from linpy import *
+import matplotlib.pyplot as plt
+from matplotlib import pylab
 
 a, x, y, z = symbols('a x y z')
 
@@ -8,25 +27,28 @@ sq1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
 sq2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4)
 sq3 = Le(0, x) & Le(x, 3) & Le(0, y) & Le(y, 3)
 sq4 = Le(1, x) & Le(x, 2) & Le(1, y) & Le(y, 2)
-sq5 = Le(1, x) & Le(x, 2) & Le(1, y) 
-sq6 = Le(1, x) & Le(x, 2) & Le(1, y) & Eq(y, 3)
+sq5 = Le(1, x) & Le(x, 2) & Le(1, y)
+sq6 = Le(1, x) & Le(x, 2) & Le(1, y) & Le(y, 3)
 sq7 = Le(0, x) & Le(x, 2) & Le(0, y) & Eq(z, 2) & Le(a, 3)
-u = Polyhedron([])
-x = sq1 - sq2
+p = Le(2*x+1, y) & Le(-2*x-1, y) & Le(y, 1)
+
+universe = Polyhedron([])
+q = sq1 - sq2
+e = Empty
 
 print('sq1 =', sq1) #print correct square
 print('sq2 =', sq2) #print correct square
 print('sq3 =', sq3) #print correct square
 print('sq4 =', sq4) #print correct square
-print('u =', u) #print correct square
+print('universe =', universe) #print correct square
 print()
-print('¬sq1 =', ~sq1) #test compliment
+print('¬sq1 =', ~sq1) #test complement
 print()
 print('sq1 + sq1 =', sq1 + sq2) #test addition
 print('sq1 + sq2 =', Polyhedron(sq1 + sq2)) #test addition
 print()
-print('u + u =', u + u)#test addition
-print('u - u =', u - u) #test subtraction
+print('universe + universe =', universe + universe)#test addition
+print('universe - universe =', universe - universe) #test subtraction
 print()
 print('sq2 - sq1 =', sq2 - sq1) #test subtraction
 print('sq2 - sq1 =', Polyhedron(sq2 - sq1)) #test subtraction
@@ -39,11 +61,11 @@ print('sq1 ⊔ sq2 =', Polyhedron(sq1 | sq2)) # test convex union
 print()
 print('check if sq1 and sq2 disjoint:', sq1.isdisjoint(sq2)) #should return false
 print()
-print('sq1 disjoint:', sq1.disjoint()) #make disjoint 
+print('sq1 disjoint:', sq1.disjoint()) #make disjoint
 print('sq2 disjoint:', sq2.disjoint()) #make disjoint
 print()
 print('is square 1 universe?:', sq1.isuniverse()) #test if square is universe
-print('is u universe?:', u.isuniverse()) #test if square is universe
+print('is u universe?:', universe.isuniverse()) #test if square is universe
 print()
 print('is sq1 a subset of sq2?:', sq1.issubset(sq2)) #test issubset()
 print('is sq4 less than sq3?:', sq4.__lt__(sq3)) # test lt(), must be a strict subset
@@ -54,16 +76,29 @@ print()
 print('lexographic min of sq2:', sq2.lexmin()) #test lexmax()
 print('lexographic max of sq2:', sq2.lexmax()) #test lexmax()
 print()
-print('Polyhedral hull of sq1 + sq2 is:', x.polyhedral_hull()) #test polyhedral hull, returns same 
-                                                               #value as Polyhedron(sq1 + sq2)
+print('Polyhedral hull of sq1 + sq2 is:', q.aspolyhedron()) #test polyhedral hull
 print()
-print('is sq1 bounded?', sq1.isbounded()) #unbounded should return True
+print('is sq1 bounded?', sq1.isbounded()) #bounded should return True
 print('is sq5 bounded?', sq5.isbounded()) #unbounded should return False
 print()
 print('sq6:', sq6)
-print('sq6 simplified:', sq6.sample())
+print('sample Polyhedron from sq6:', sq6.sample())
+print()
+print('sq7 with out constraints involving y and a', sq7.project([a, z, x, y])) 
 print()
-#print(u.drop_dims(' '))
-print('sq7 with out constraints involving y and a', sq7.drop_dims('y a')) #drops dims that are passed
+print('the verticies for s are:', p.vertices())
+
+
+# plotting the intersection of two squares
+square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
+square2 = Le(1, x) & Le(x, 3) & Le(1, y) & Le(y, 3)
+
+fig = plt.figure()
+plot = fig.add_subplot(1, 1, 1, aspect='equal')
+square1.plot(plot, facecolor='red', alpha=0.3)
+square2.plot(plot, facecolor='blue', alpha=0.3)
 
+squares = Polyhedron(square1 + square2)
+squares.plot(plot, facecolor='blue', alpha=0.3)
 
+pylab.show()