Lmin, Lmax= 0.01, 10.

if not os.path.exists(savefilename):

#Setup grid

nL, nE= 101,101

Ls= 10.**numpy.linspace(numpy.log10(Lmin),numpy.log10(Lmax),nL)

#Integration times

ts= numpy.linspace(0.,20.,1001)

deltas= numpy.empty((nL,nE))

Einf= evalPot(10.**12.,0.,MWPotential2014)

print Einf

for ii in range(nL):

#Calculate Ec

Rc= rl(MWPotential2014,Ls[ii])

print ii, "Rc = ", Rc*8.

Ec= evalPot(Rc,0.,MWPotential2014)+0.5*Ls[ii]**2./Rc**2.

Es= Ec+(Einf-Ec)*10.**numpy.linspace(-2.,0.,nE)

for jj in range(nE):

#Setup an orbit with this energy and angular momentum

Er= 2.*(Es[jj]-Ec) #Random energy times 2 = vR^2 + vz^2

vR= numpy.sqrt(4./5.*Er)

vz= numpy.sqrt(1./5.*Er)

o= Orbit([Rc,vR,Ls[ii]/Rc,0.,vz,0.])

o.integrate(ts,MWPotential2014,method='symplec4_c')

deltas[ii,jj]= estimateDeltaStaeckel(o.R(ts),o.z(ts),

pot=MWPotential2014)

#Save

save_pickles(savefilename,deltas)

else:

savefile= open(savefilename,'rb')

deltas= pickle.load(savefile)

savefile.close()

#Plot

print numpy.nanmax(deltas)

bovy_plot.bovy_print()

bovy_plot.bovy_dens2d(deltas.T,origin='lower',cmap='jet',

xrange=[numpy.log10(Lmin),numpy.log10(Lmax)],

yrange=[-2,0.],

xlabel=r'$\log_{10} L$',

ylabel=r'$\log_{10}\left(\frac{E-E_c(L)}{E(\infty)-E_c(L)}\right)$',

colorbar=True,shrink=0.78,

zlabel=r'$\mathrm{Approximate\ focal\ length}$',

# interpolation='nearest',

vmin=0.,vmax=0.6)

bovy_plot.bovy_end_print(plotfilename)