def plot_Sn_timesamples(PSP):
""" Plots Fig. 5 from Sanders & Binney (2014) """
TT = pot.stackel_triax()
f, a = plt.subplots(2, 1, figsize=[3.32, 3.6])
plt.subplots_adjust(hspace=0.0, top=0.8)
LowestPeriod = 2.0 * np.pi / 38.86564386
Times = np.array([2.0, 4.0, 8.0, 12.0])
Sr = np.arange(2, 14, 2)
# Loop over length of integration window
for i, P, C in zip(Times, [".", "s", "D", "^"], ["k", "r", "b", "g"]):
diffact = np.zeros((len(Sr), 3))
difffreq = np.zeros((len(Sr), 3))
MAXGAPS = np.array([])
# Loop over N_max
for k, j in enumerate(Sr):
NT = choose_NT(j)
timeseries = np.linspace(0.0, i * LowestPeriod, NT)
results = odeint(pot.orbit_derivs2, PSP, timeseries, args=(TT,), rtol=1e-13, atol=1e-13)
act, ang, n_vec, toy_aa, pars = find_actions(results, timeseries, N_matrix=j, ifprint=False, use_box=True)
# Check all modes
checks, maxgap = ced(n_vec, ua(toy_aa.T[3:].T, np.ones(3)))
if len(maxgap) > 0:
maxgap = np.max(maxgap)
else:
maxgap = 0
diffact[k] = act[:3] / TT.action(results[0])
print i, j, print_max_average(n_vec, toy_aa.T[3:].T, act[3:]), str(ang[3:6] - TT.freq(results[0])).replace(
"[", ""
).replace("]", ""), str(np.abs(act[:3] - TT.action(results[0]))).replace("[", "").replace("]", ""), len(
checks
), maxgap
MAXGAPS = np.append(MAXGAPS, maxgap)
difffreq[k] = ang[3:6] / TT.freq(results[0])
size = 15
if P == ".":
size = 30
LW = np.array(map(lambda i: 0.5 + i * 0.5, MAXGAPS))
a[0].scatter(
Sr,
np.log10(np.abs(diffact.T[2] - 1)),
marker=P,
s=size,
color=C,
facecolors="none",
lw=LW,
label=r"$T =\,$" + str(i) + r"$\,T_F$",
)
a[1].scatter(Sr, np.log10(np.abs(difffreq.T[2] - 1)), marker=P, s=size, color=C, facecolors="none", lw=LW)
a[1].get_yticklabels()[-1].set_visible(False)
a[0].set_xticklabels([])
a[0].set_xlim(1, 13)
a[0].set_ylabel(r"$\log_{10}|J_3^\prime/J_{3, \rm true}-1|$")
leg = a[0].legend(loc="upper center", bbox_to_anchor=(0.5, 1.4), ncol=2, scatterpoints=1)
leg.draw_frame(False)
a[1].set_xlim(1, 13)
a[1].set_xlabel(r"$N_{\rm max}$")
a[1].set_ylabel(r"$\log_{10}|\Omega_3^\prime/\Omega_{3,\rm true}-1|$")
plt.savefig("Sn_T_box.pdf", bbox_inches="tight")
def plot3D_stacktriax(initial,final_t,N_MAT,file_output):
""" For producing plots from paper """
# Setup Stackel potential
TT = pot.stackel_triax()
times = choose_NT(N_MAT)
timeseries=np.linspace(0.,final_t,times)
# Integrate orbit
results = odeint(pot.orbit_derivs2,initial,timeseries,args=(TT,),rtol=1e-13,atol=1e-13)
# Find actions, angles and frequencies
(act,ang,n_vec,toy_aa, pars),loop = find_actions(results, timeseries,N_matrix=N_MAT,ifloop=True)
toy_pot = 0
if(loop[2]>0.5 or loop[0]>0.5):
toy_pot = pot.isochrone(par=np.append(pars,0.))
else:
toy_pot = pot.harmonic_oscillator(omega=pars[:3])
# Integrate initial condition in toy potential
timeseries_2=np.linspace(0.,2.*final_t,3500)
results_toy = odeint(pot.orbit_derivs2,initial,timeseries_2,args=(toy_pot,))
print "True actions: ", TT.action(results[0])
print "Found actions: ", act[:3]
print "True frequencies: ",TT.freq(results[0])
print "Found frequencies: ",ang[3:6]
# and plot
f,a = plt.subplots(2,3,figsize=[3.32,5.5])
a[0,0] = plt.subplot2grid((3,2), (0, 0))
a[1,0] = plt.subplot2grid((3,2), (0, 1))
a[0,1] = plt.subplot2grid((3,2), (1, 0))
a[1,1] = plt.subplot2grid((3,2), (1, 1))
a[0,2] = plt.subplot2grid((3,2), (2, 0),colspan=2)
plt.subplots_adjust(wspace=0.5,hspace=0.45)
# xy orbit
a[0,0].plot(results.T[0],results.T[1],'k')
a[0,0].set_xlabel(r'$x/{\rm kpc}$')
a[0,0].set_ylabel(r'$y/{\rm kpc}$')
a[0,0].xaxis.set_major_locator(MaxNLocator(5))
# xz orbit
a[1,0].plot(results.T[0],results.T[2],'k')
a[1,0].set_xlabel(r'$x/{\rm kpc}$')
a[1,0].set_ylabel(r'$z/{\rm kpc}$')
a[1,0].xaxis.set_major_locator(MaxNLocator(5))
# toy orbits
a[0,0].plot(results_toy.T[0],results_toy.T[1],'r',alpha=0.2,linewidth=0.3)
a[1,0].plot(results_toy.T[0],results_toy.T[2],'r',alpha=0.2,linewidth=0.3)
# Toy actions
a[0,2].plot(Conv*timeseries,toy_aa.T[0],'k:',label='Toy action')
a[0,2].plot(Conv*timeseries,toy_aa.T[1],'r:')
a[0,2].plot(Conv*timeseries,toy_aa.T[2],'b:')
# Arrows to show approx. actions
arrow_end = a[0,2].get_xlim()[1]
arrowd = 0.08*(arrow_end-a[0,2].get_xlim()[0])
a[0,2].annotate('',(arrow_end+arrowd,act[0]),(arrow_end,act[0]),arrowprops=dict(arrowstyle='<-',color='k'),annotation_clip=False)
a[0,2].annotate('',(arrow_end+arrowd,act[1]),(arrow_end,act[1]),arrowprops=dict(arrowstyle='<-',color='r'),annotation_clip=False)
a[0,2].annotate('',(arrow_end+arrowd,act[2]),(arrow_end,act[2]),arrowprops=dict(arrowstyle='<-',color='b'),annotation_clip=False)
# True actions
a[0,2].plot(Conv*timeseries,TT.action(results[0])[0]*np.ones(len(timeseries)),'k',label='True action')
a[0,2].plot(Conv*timeseries,TT.action(results[0])[1]*np.ones(len(timeseries)),'k')
a[0,2].plot(Conv*timeseries,TT.action(results[0])[2]*np.ones(len(timeseries)),'k')
a[0,2].set_xlabel(r'$t/{\rm Gyr}$')
a[0,2].set_ylabel(r'$J/{\rm kpc\,km\,s}^{-1}$')
leg = a[0,2].legend(loc='upper center',bbox_to_anchor=(0.5,1.2),ncol=3, numpoints = 1)
leg.draw_frame(False)
# Toy angle coverage
a[0,1].plot(toy_aa.T[3]/(np.pi),toy_aa.T[4]/(np.pi),'k.',markersize=0.4)
a[0,1].set_xlabel(r'$\theta_1/\pi$')
a[0,1].set_ylabel(r'$\theta_2/\pi$')
a[1,1].plot(toy_aa.T[3]/(np.pi),toy_aa.T[5]/(np.pi),'k.',markersize=0.4)
a[1,1].set_xlabel(r'$\theta_1/\pi$')
a[1,1].set_ylabel(r'$\theta_3/\pi$')
plt.savefig(file_output,bbox_inches='tight')
return act
def plot3D_stacktriax(initial, final_t, N_MAT, file_output):
""" For producing plots from paper """
# Setup Stackel potential
TT = pot.stackel_triax()
times = choose_NT(N_MAT)
timeseries = np.linspace(0., final_t, times)
# Integrate orbit
results = odeint(pot.orbit_derivs2,
initial,
timeseries,
args=(TT, ),
rtol=1e-13,
atol=1e-13)
# Find actions, angles and frequencies
(act, ang, n_vec, toy_aa, pars), loop = find_actions(results,
timeseries,
N_matrix=N_MAT,
ifloop=True)
toy_pot = 0
if (loop[2] > 0.5 or loop[0] > 0.5):
toy_pot = pot.isochrone(par=np.append(pars, 0.))
else:
toy_pot = pot.harmonic_oscillator(omega=pars[:3])
# Integrate initial condition in toy potential
timeseries_2 = np.linspace(0., 2. * final_t, 3500)
results_toy = odeint(pot.orbit_derivs2,
initial,
timeseries_2,
args=(toy_pot, ))
print "True actions: ", TT.action(results[0])
print "Found actions: ", act[:3]
print "True frequencies: ", TT.freq(results[0]) / Conv
print "Found frequencies: ", ang[3:6] / Conv
# and plot
f, a = plt.subplots(2, 3, figsize=[3.32, 5.5])
a[0, 0] = plt.subplot2grid((3, 2), (0, 0))
a[1, 0] = plt.subplot2grid((3, 2), (0, 1))
a[0, 1] = plt.subplot2grid((3, 2), (1, 0))
a[1, 1] = plt.subplot2grid((3, 2), (1, 1))
a[0, 2] = plt.subplot2grid((3, 2), (2, 0), colspan=2)
plt.subplots_adjust(wspace=0.5, hspace=0.45)
# xy orbit
a[0, 0].plot(results.T[0], results.T[1], 'k')
a[0, 0].set_xlabel(r'$x/{\rm kpc}$')
a[0, 0].set_ylabel(r'$y/{\rm kpc}$')
a[0, 0].xaxis.set_major_locator(MaxNLocator(5))
# xz orbit
a[1, 0].plot(results.T[0], results.T[2], 'k')
a[1, 0].set_xlabel(r'$x/{\rm kpc}$')
a[1, 0].set_ylabel(r'$z/{\rm kpc}$')
a[1, 0].xaxis.set_major_locator(MaxNLocator(5))
# toy orbits
a[0, 0].plot(results_toy.T[0],
results_toy.T[1],
'r',
alpha=0.2,
linewidth=0.3)
a[1, 0].plot(results_toy.T[0],
results_toy.T[2],
'r',
alpha=0.2,
linewidth=0.3)
# Toy actions
a[0, 2].plot(Conv * timeseries, toy_aa.T[0], 'k:', label='Toy action')
a[0, 2].plot(Conv * timeseries, toy_aa.T[1], 'r:')
a[0, 2].plot(Conv * timeseries, toy_aa.T[2], 'b:')
# Arrows to show approx. actions
arrow_end = a[0, 2].get_xlim()[1]
arrowd = 0.08 * (arrow_end - a[0, 2].get_xlim()[0])
a[0, 2].annotate('', (arrow_end + arrowd, act[0]), (arrow_end, act[0]),
arrowprops=dict(arrowstyle='<-', color='k'),
annotation_clip=False)
a[0, 2].annotate('', (arrow_end + arrowd, act[1]), (arrow_end, act[1]),
arrowprops=dict(arrowstyle='<-', color='b'),
annotation_clip=False)
a[0, 2].annotate('', (arrow_end + arrowd, act[2]), (arrow_end, act[2]),
arrowprops=dict(arrowstyle='<-', color='r'),
annotation_clip=False)
# True actions
a[0, 2].plot(Conv * timeseries,
TT.action(results[0])[0] * np.ones(len(timeseries)),
'k',
label='True action')
a[0, 2].plot(Conv * timeseries,
TT.action(results[0])[1] * np.ones(len(timeseries)), 'k')
a[0, 2].plot(Conv * timeseries,
TT.action(results[0])[2] * np.ones(len(timeseries)), 'k')
a[0, 2].set_xlabel(r'$t/{\rm Gyr}$')
a[0, 2].set_ylabel(r'$J/{\rm kpc\,km\,s}^{-1}$')
leg = a[0, 2].legend(loc='upper center',
bbox_to_anchor=(0.5, 1.2),
ncol=3,
numpoints=1)
leg.draw_frame(False)
# Toy angle coverage
a[0, 1].plot(toy_aa.T[3] / (np.pi),
toy_aa.T[4] / (np.pi),
'k.',
markersize=0.4)
a[0, 1].set_xlabel(r'$\theta_1/\pi$')
a[0, 1].set_ylabel(r'$\theta_2/\pi$')
a[1, 1].plot(toy_aa.T[3] / (np.pi),
toy_aa.T[5] / (np.pi),
'k.',
markersize=0.4)
a[1, 1].set_xlabel(r'$\theta_1/\pi$')
a[1, 1].set_ylabel(r'$\theta_3/\pi$')
plt.savefig(file_output, bbox_inches='tight')
return act
def plot_Sn_timesamples(PSP):
""" Plots Fig. 5 from Sanders & Binney (2014) """
TT = pot.stackel_triax()
f, a = plt.subplots(2, 1, figsize=[3.32, 3.6])
plt.subplots_adjust(hspace=0., top=0.8)
LowestPeriod = 2. * np.pi / 38.86564386
Times = np.array([2., 4., 8., 12.])
Sr = np.arange(2, 14, 2)
# Loop over length of integration window
for i, P, C in zip(Times, ['.', 's', 'D', '^'], ['k', 'r', 'b', 'g']):
diffact = np.zeros((len(Sr), 3))
difffreq = np.zeros((len(Sr), 3))
MAXGAPS = np.array([])
# Loop over N_max
for k, j in enumerate(Sr):
NT = choose_NT(j)
timeseries = np.linspace(0., i * LowestPeriod, NT)
results = odeint(pot.orbit_derivs2,
PSP,
timeseries,
args=(TT, ),
rtol=1e-13,
atol=1e-13)
act, ang, n_vec, toy_aa, pars = find_actions(results,
timeseries,
N_matrix=j,
ifprint=False,
use_box=True)
# Check all modes
checks, maxgap = ced(n_vec, ua(toy_aa.T[3:].T, np.ones(3)))
if len(maxgap) > 0:
maxgap = np.max(maxgap)
else:
maxgap = 0
diffact[k] = act[:3] / TT.action(results[0])
print i, j, print_max_average(
n_vec, toy_aa.T[3:].T,
act[3:]), str(ang[3:6] - TT.freq(results[0])).replace(
'[', '').replace(']', ''), str(
np.abs(act[:3] - TT.action(results[0]))).replace(
'[', '').replace(']', ''), len(checks), maxgap
MAXGAPS = np.append(MAXGAPS, maxgap)
difffreq[k] = ang[3:6] / TT.freq(results[0])
size = 15
if (P == '.'):
size = 30
LW = np.array(map(lambda i: 0.5 + i * 0.5, MAXGAPS))
a[0].scatter(Sr,
np.log10(np.abs(diffact.T[2] - 1)),
marker=P,
s=size,
color=C,
facecolors="none",
lw=LW,
label=r'$T =\,$' + str(i) + r'$\,T_F$')
a[1].scatter(Sr,
np.log10(np.abs(difffreq.T[2] - 1)),
marker=P,
s=size,
color=C,
facecolors="none",
lw=LW)
a[1].get_yticklabels()[-1].set_visible(False)
a[0].set_xticklabels([])
a[0].set_xlim(1, 13)
a[0].set_ylabel(r"$\log_{10}|J_3^\prime/J_{3, \rm true}-1|$")
leg = a[0].legend(loc='upper center',
bbox_to_anchor=(0.5, 1.4),
ncol=2,
scatterpoints=1)
leg.draw_frame(False)
a[1].set_xlim(1, 13)
a[1].set_xlabel(r'$N_{\rm max}$')
a[1].set_ylabel(r"$\log_{10}|\Omega_3^\prime/\Omega_{3,\rm true}-1|$")
plt.savefig('Sn_T_box.pdf', bbox_inches='tight')