def testPeriodic(self):
#first decide whether the transpositions compose to an element of G
netTrans = self.netTransposition()
if not self.system.invariant(netTrans):
return False
#next compose the time map with the preserving permutation
Fmap = AffineMap.compose(netTrans.mapRepresentation(), self.map)
#construct the set of constraints for fixed point
A1 = add(Fmap.A, -1.0 * AffineMap.identity(self.system.dim).A)
A2 = add(AffineMap.identity(self.system.dim).A, -1 * Fmap.A)
b2 = Fmap.b
b1 = -1.0 * b2
A = concatenate((A1,A2))
b = concatenate((b1,b2))
cs = ConvexSet(A,b)
FixedPoints = cs.intersect(cs, self.set())
#test feasibility
solution = cvxSolver.solve(FixedPoints)
return (solution['status']=='optimal')
def deserialize(representation):
sequence = []
for p in representation["sequence"]:
sequence.append(Permutation.deserialize(p))
newWord = Word(sequence)
newWord.flips = representation["flips"]
newWord.feasible = representation["feasible"]
newWord.map = AffineMap.deserialize(representation["map"])
newWord.set = ConvexSet.deserialize(representation["set"])
return newWord
def testStrictPeriodic(self, word):
#first decide whether the transpositions compose to identity
netTrans = word.netTransposition()
if not netTrans.isIdentity():
return False
#next, obtain the full poincare map
Fmap = word.map
#construct the set of constraints for fixed point
A1 = add(Fmap.A, -1.0 * AffineMap.identity(self.system.dim).A)
A2 = add(AffineMap.identity(self.system.dim).A, -1 * Fmap.A)
b2 = Fmap.b
b1 = -1.0 * b2
A = concatenate((A1, A2))
b = concatenate((b1, b2))
cs = ConvexSet(A, b)
FixedPoints = cs.intersect(cs, word.set())
#test feasibility
solution = cvxSolver.solve(FixedPoints)
return (solution['status']=='optimal')