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# AUTO demo pcl
#
# Lorenz system
# compute the EtoP connection via Lin's method
print "\n1st run - continue equilibrium 0 and branches of secondary equilibria"
r1 = run(e='pcl',ICP=['rho'],NDIM=3,ILP=0,ITNW=7,
STOP=['HB1'],UZSTOP={1:31.6},DS=0.1,DSMAX=2.0,
unames={1:'xgamma',2:'ygamma',3:'zgamma',4:'x',5:'y',6:'z',
7:'x+',8:'y+',9:'z+',10:'x-',11:'y-',12:'z-'},
parnames={1:'rho',2:'beta',3:'sigma',
11:'T',12:'mu',13:'h',14:'T+',15:'delta',16:'T-',17:'eps',
21:'sigma+',22:'sigma-',23:'eta',25:'Zx',26:'Zy'})
print "\n2nd run - switch to the periodic orbit and continue in rho up to 24.0579"
r2 = run(r1('HB2'),ICP=['rho','T'],IPS=2,NTST=50,
STOP=[],UZSTOP={'rho':24.0579})
print "\n3rd run - extend the system"
r3 = run(r2('UZ1'),ICP=['mu','h','T'],IPS=4,NDIM=6,NBC=7,NINT=1,
STOP=['BP1'],UZSTOP={},DS=-0.1,DSMIN=1e-7,DSMAX=1.0)
print "\n4th run - normalize the Floquet bundle"
r4 = run(r3('BP1'),ISW=-1,
STOP=[],UZSTOP={'h':1.0},DS=1,DSMIN=1e-5,DSMAX=100)
print "\n5th run - integrate backwards from the periodic orbit"
print "measures the distance to Sigma = { x=10 } in sigma+"
print "UZ point corresponds to an intersection with Sigma"
r5 = run(r4('UZ1'),ICP=['T+','mu','T','sigma+'],ISW=1,NDIM=9,NBC=11,
STOP=['UZ1'],UZR={'sigma+':0},UZSTOP={},DS=1.0)
print "\n6th run - integrate away from the equilibrium up to Sigma"
print "(second UZ is the one we want)"
r6 = run(r5('UZ1'),ICP=['T-','sigma-','T+','mu','T'],NDIM=12,NBC=15,
STOP=['UZ2'],UZR={'sigma-':0})
print "\n7th run - put starting data for Lin vector and Lin gap in"
print "Zx, Zy, Zz and eta"
print "close the gap (with some intermediate solutions)"
r7 = run(r6('UZ2'),ICP=['eta','rho','delta','eps','T-','T+','mu','T'],
NBC=17,NINT=2,NPR=10,THL={'T':0,'T+':0,'T-':0},
STOP=['UZ1'],UZR={'eta':0},DS=-0.01,DSMIN=1e-7,DSMAX=0.1)
save(r7,'closegap')
# plot this, have a look at the solution coordinates 'x-'-vs-'z-' and 'x+'-vs-'z+'
#plot(r7)
#wait()
print "\n8th run - keep the gap closed and continue in rho,beta"
start8 = load(r7('UZ1'),ICP=['rho','beta','delta','eps','T-','T+','mu','T'],
STOP=['LP1'],UZR={'rho':25},UZSTOP={'rho':80},ILP=1,NPR=200,DS=0.1,DSMAX=1)
r8 = merge(run(start8) + run(start8,DS='-'))
save(r8,'cont')
clean()
print "\nDone."
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