def do_fp(h=1e-3,eps=1e-10,debug=False):
q=[1.,2.,10.,5.,2.,2.0,2*np.pi,0,2.]
m,M,k,b,l0,a,om,ph,g = q
debug = False
hop = Hop()
p = hop.P(q,debug)
ph0 = np.pi# - np.pi/(2**2)
phf = ph0 + 20*2*np.pi
t0 = 0.; tf = (phf-ph0)/om
n = np.infty
t = (t0,tf)
j = 2
z = np.array([2.0,2.0])
#j = 1
#z = np.array([0.1,2.0,0.,2.0])
ph = ph0
p.j = j
q = [m,M,k,b,l0,a,om,ph,g]
p.q = q
Zeno = False
import time;
start = time.clock()
trjs = flow(hop, p, h, eps, (t0,tf), z, debug=debug)
#hop.plot(trjs[-10:])
hop.plot(trjs)
xlim = plt.xlim(); ylim = plt.ylim()
plt.xlim(xlim); plt.ylim(ylim)
print "%0.2f sec for sim & plot" % (time.clock() - start)
#dbg()
qq = q[:]
pp = hop.P(qq); pp.j = trjs[-1].p.j
zz = trjs[-1].x[-1]
# Deformation of Poincare section
psi = (lambda t,x : flow(hop,pp,h,eps,(0.,2*t*np.pi/om),x)[-1].x[-1])
# Poincare map
pmap = lambda x : psi(1.,x)
start = time.clock()
# find periodic orbit
z0 = rx.fp(pmap,zz,modes=[1,2])
trjs0 = flow(hop, p, h, eps, (t0,tf), z0)
hop.plot(trjs0,clf=False)
print ' z0 = %s' % z0
# linearize Poincare map
J = rx.jac(pmap,z0)
# compute eigenvalues of P-map
print ' spec J = %s' % ( np.linalg.eigvals(J) )
print '|spec J| = %s' % np.abs( np.linalg.eigvals(J) )
print np.array([(dd,np.abs(np.linalg.eigvals(rx.jac(pmap,z0,d=dd))).max()) for dd in np.logspace(-2,-6,40)])
print "%0.2f sec for fp & jac " % (time.clock() - start)
z = trjs0[-1].x[-1]
sig = np.mod(ph0 + om*(tf-t0),2*np.pi) # == phf
if len(z) == 2:
y,dy = np.array(z)
z = np.array([sig,y,dy])
elif len(z) == 4:
sig,y,dy,x,dx = np.array(z)
z = np.array([sig,y,dy,x,dx])
else:
dbg()
return hop,z,p
def do_pmap(): q=[1.,2.,10.,5.,2.,2.0,2*np.pi,np.pi,2.] m,M,k,b,l0,a,om,ph,g = q debug = False hop = Hop() p = hop.P(q,debug) ph0 = np.pi/2. t0 = ph0*np.pi/om tf = (10*2 + ph0)*np.pi/om n = np.infty t = (t0,tf) j = 1 z = np.array([0.2,1.75,0.,0.]) # nice transient #j = 2 #z = np.array([1.0,0.0]) #z = np.array([1.6,0.6]) #z = np.array([1.4,0.6]) p.j = j h = 1e-2 eps = 1e-12 Zeno = False import time; start = time.clock() trjs = flow(hop, p, h, eps, (t0*om,tf*om), z) #hop.plot(trjs[-10:]) hop.plot(trjs,fn='fig/hoptrj.eps') xlim = plt.xlim(); ylim = plt.ylim() plt.xlim(xlim); plt.ylim(ylim) q0 = q[:]; p0 = hop.P(q0,debug); p0.j = 1; z0 = np.array([0.25,1.75,0.,0.]) hop.sch(3*np.pi/2,[0.25,2.15,0,0],p0,text=True,fn='fig/hopA.eps') #hop.sch(3*np.pi/2,[0.25,2.15,0,0],p0,text=False,fn='fig/hopAplain.eps') p0.j = 2 hop.sch(np.pi/4,[1.5,0],p0,text=True,fn='fig/hopG.eps') #hop.sch(np.pi/4,[1.5,0],p0,text=False,fn='fig/hopGplain.eps') #hop.sch(t0,z,p,text=True,fn='fig/hop.pdf') p0.j = 1 print "%0.2f sec for sim & plot" % (time.clock() - start) qq = q[:] pp = hop.P(qq); pp.j = trjs[-1].p.j zz = trjs[-1].x[-1] # Deformation of Poincare section psi = (lambda t,x : flow(hop,pp,h,eps,(ph0*np.pi,(2*t+ph0)*np.pi),x)[-1].x[-1]) # Poincare map pmap = lambda x : psi(1.,x) start = time.clock() # find periodic orbit z0 = rx.fp(pmap,zz,modes=[1,2]) print ' z0 = %s' % z0 # linearize Poincare map J = rx.jac(pmap,z0) # compute eigenvalues of P-map print ' spec J = %s' % ( np.linalg.eigvals(J) ) print '|spec J| = %s' % np.abs( np.linalg.eigvals(J) ) print 'max |spec J| as a function of perturbation:' #print np.array([(dd,np.abs(np.linalg.eigvals(rx.jac(pmap,z0,d=dd))).max()) for dd in np.logspace(-2,-6,10)]) print "%0.2f sec for fp & jac " % (time.clock() - start)
x = np.array(x)
# don't simulate from invalid initial condition
if p.j == 2 and dp.Lambda(t0,x,p) <= 0:
return np.nan*x
trjs = rx.Euler((t0,tf), x, p, dp, h, eps, n)
if len(trjs[-1].t) <= 2:
trjs = trjs[:-1]
trj = trjs[-1]
s = (tf - trj.t[-2]) / (trj.t[-1]-trj.t[-2])
trj.t[-1] = (1-s)*trj.t[-2] + s*trj.t[-1]
trj.x[-1] = (1-s)*trj.x[-2] + s*trj.x[-1]
return trjs
# Deformation of Poincare section
psi = (lambda t,x : flow(dp,p,h,eps,((0.5+dt)*np.pi,(0.5+dt)*np.pi+2*np.pi*t),x)[-1].x[-1])
# Poincare map
pmap = lambda x : psi(1.,x)
# find periodic orbit
x0 = rx.fp(pmap,x)
# linearize Poincare map
J = rx.jac(pmap,x0)
# compute eigenvalues of P-map
print np.abs(np.linalg.eigvals(J))