def plot_liouville(plotfilename):
E, Lz= -1.25, 0.6
aAS= actionAngleStaeckel(pot=MWPotential2014,c=True,delta=0.5)
#planarOrbit w/ the same energy
o= Orbit([0.8,numpy.sqrt(2.*(E-evalPot(0.8,0.,MWPotential2014)-(Lz/0.8)**2./2.)),Lz/0.8,0.])
#For the orbital period
fo= Orbit([0.8,numpy.sqrt(2.*(E-evalPot(0.8,0.,MWPotential2014)-(Lz/0.8)**2./2.)),Lz/0.8,0.,0.001,0.])
orbt= 2.*numpy.pi/aAS.actionsFreqs(fo)[4]
norb= 200.
nt= 20001
ts= numpy.linspace(0.,norb*orbt,nt)
start= time.time()
integrator= 'dopr54_c'
o.integrate_dxdv([1.,0.,0.,0.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dx= o.getOrbit_dxdv()[:,:]
o.integrate_dxdv([0.,1.,0.,0.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dy= o.getOrbit_dxdv()[:,:]
o.integrate_dxdv([0.,0.,1.,0.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dvx= o.getOrbit_dxdv()[:,:]
o.integrate_dxdv([0.,0.,0.,1.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dvy= o.getOrbit_dxdv()[:,:]
print integrator, time.time()-start
#Calculate Jacobian
jacs= numpy.array([numpy.linalg.det(numpy.array([dx[ii],dy[ii],
dvx[ii],dvy[ii]])) for ii in range(nt)])
breakt= 8.
pts= list(ts[ts < breakt])
pts.extend(list((ts[ts >= breakt])[::10]))
pts= numpy.array(pts)
pjacs= list(jacs[ts < breakt])
pjacs.extend(list((jacs[ts >= breakt])[::10]))
pjacs= numpy.array(pjacs)
print integrator, numpy.mean(jacs)-1.
bovy_plot.bovy_print(fig_width=3.25,fig_height=4.5)
pyplot.subplot(4,1,4)
bovy_plot.bovy_plot(pts/orbt,numpy.fabs(pjacs-1.),color='k',
loglog=True,gcf=True,
xrange=[0.5,norb],
yrange=[10.**-12.,10.**0.],
xlabel=r'$\mathrm{Number\ of\ orbital\ periods}$')
bovy_plot.bovy_text(r'$\texttt{dopr54\_c}$',
top_left=True,size=14.)
bovy_plot.bovy_text(0.1,10.**44.5,
r'$|\mathrm{Determinant\ of\ volume\ transformation}-1|$',
fontsize=16.,
rotation='vertical')
ax= pyplot.gca()
ax.xaxis.set_major_formatter(ticker.FormatStrFormatter(r'$%0.f$'))
ax.yaxis.set_ticks([10.**-12.,10.**-8.,10.**-4.,1.])
nullfmt = NullFormatter() # no labels
other_integrators= ['odeint',
'rk4_c','rk6_c']
for ii,integrator in enumerate(other_integrators):
start= time.time()
o.integrate_dxdv([1.,0.,0.,0.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dx= o.getOrbit_dxdv()[:,:]
o.integrate_dxdv([0.,1.,0.,0.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dy= o.getOrbit_dxdv()[:,:]
o.integrate_dxdv([0.,0.,1.,0.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dvx= o.getOrbit_dxdv()[:,:]
o.integrate_dxdv([0.,0.,0.,1.],ts,MWPotential2014,
method=integrator,
rectIn=True,rectOut=True)
dvy= o.getOrbit_dxdv()[:,:]
print integrator, time.time()-start
jacs= numpy.array([numpy.linalg.det(numpy.array([dx[jj],dy[jj],
dvx[jj],dvy[jj]])) for jj in range(nt)])
pts= list(ts[ts < breakt])
pts.extend(list((ts[ts >= breakt])[::10]))
pts= numpy.array(pts)
pjacs= list(jacs[ts < breakt])
pjacs.extend(list((jacs[ts >= breakt])[::10]))
pjacs= numpy.array(pjacs)
print integrator, numpy.mean(jacs)-1.
pyplot.subplot(4,1,ii+1)
if integrator == 'odeint':
yrange=[10.**-8.,10.**4.]
yticks= [10.**-8.,10.**-4.,1.,10.**4.]
else:
yrange=[10.**-12.,10.**0.]
yticks= [10.**-12.,10.**-8.,10.**-4.,1.]
bovy_plot.bovy_plot(pts/orbt,numpy.fabs(pjacs-1.),color='k',
loglog=True,gcf=True,
xrange=[0.5,norb],
yrange=yrange)
thisax= pyplot.gca()
thisax.xaxis.set_major_formatter(nullfmt)
thisax.yaxis.set_ticks(yticks)
bovy_plot.bovy_text(r'$\texttt{%s}$' % (integrator.replace('_','\_')),
top_left=True,size=14.)
bovy_plot.bovy_end_print(plotfilename)
return None
