def eval_mean_error_functions(act,ang,n_vec,toy_aa,timeseries,withplot=False):
""" Calculates sqrt(mean(E)) and sqrt(mean(F)) """
Err = np.zeros(6)
NT = len(timeseries)
size = len(ang[6:])/3
UA = ua(toy_aa.T[3:].T,np.ones(3))
fig,axis=None,None
if(withplot):
fig,axis=plt.subplots(3,2)
plt.subplots_adjust(wspace=0.3)
for K in range(3):
ErrJ = np.array([(i[K]-act[K]-2.*np.sum(n_vec.T[K]*act[3:]*np.cos(np.dot(n_vec,i[3:]))))**2 for i in toy_aa])
Err[K] = np.sum(ErrJ)
ErrT = np.array(((ang[K]+timeseries*ang[K+3]-UA.T[K]-2.*np.array([np.sum(ang[6+K*size:6+(K+1)*size]*np.sin(np.sum(n_vec*i,axis=1))) for i in toy_aa.T[3:].T])))**2)
Err[K+3] = np.sum(ErrT)
if(withplot):
axis[K][0].plot(ErrJ,'.')
axis[K][0].set_ylabel(r'$E$'+str(K+1))
axis[K][1].plot(ErrT,'.')
axis[K][1].set_ylabel(r'$F$'+str(K+1))
if(withplot):
for i in range(3):
axis[i][0].set_xlabel(r'$t$')
axis[i][1].set_xlabel(r'$t$')
plt.show()
EJ = np.sqrt(Err[:3]/NT)
ET = np.sqrt(Err[3:]/NT)
return np.array([EJ,ET])
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 eval_mean_error_functions(act,
ang,
n_vec,
toy_aa,
timeseries,
withplot=False):
""" Calculates sqrt(mean(E)) and sqrt(mean(F)) """
Err = np.zeros(6)
NT = len(timeseries)
size = len(ang[6:]) / 3
UA = ua(toy_aa.T[3:].T, np.ones(3))
fig, axis = None, None
if (withplot):
fig, axis = plt.subplots(3, 2)
plt.subplots_adjust(wspace=0.3)
for K in range(3):
ErrJ = np.array([
(i[K] - act[K] - 2. *
np.sum(n_vec.T[K] * act[3:] * np.cos(np.dot(n_vec, i[3:]))))**2
for i in toy_aa
])
Err[K] = np.sum(ErrJ)
ErrT = np.array(
((ang[K] + timeseries * ang[K + 3] - UA.T[K] - 2. * np.array([
np.sum(ang[6 + K * size:6 +
(K + 1) * size] * np.sin(np.sum(n_vec * i, axis=1)))
for i in toy_aa.T[3:].T
])))**2)
Err[K + 3] = np.sum(ErrT)
if (withplot):
axis[K][0].plot(ErrJ, '.')
axis[K][0].set_ylabel(r'$E$' + str(K + 1))
axis[K][1].plot(ErrT, '.')
axis[K][1].set_ylabel(r'$F$' + str(K + 1))
if (withplot):
for i in range(3):
axis[i][0].set_xlabel(r'$t$')
axis[i][1].set_xlabel(r'$t$')
plt.show()
EJ = np.sqrt(Err[:3] / NT)
ET = np.sqrt(Err[3:] / NT)
return np.array([EJ, ET])
(act,ang,n_vec,toy_aa,para),loop = find_actions(results, timeseries, N_matrix = 6, ifloop=True,ifprint = False)
size = len(ang[6:])/3
AA = [np.array([np.sum(ang[6+i*size:6+(i+1)*size]*np.sin(np.sum(n_vec*K,axis=1))) for K in toy_aa.T[3:].T]) for i in range(3)]
# a[0,2].plot((toy_aa.T[3]+2.*AA[0]) % (2.*np.pi) / np.pi,(toy_aa.T[4]+2.*AA[1]) % (2.*np.pi)/ np.pi,'.',markersize=3)
# a[1,2].plot((toy_aa.T[3]+2.*AA[0]) % (2.*np.pi) / np.pi,(toy_aa.T[5]+2.*AA[2]) % (2.*np.pi) / np.pi,'.',markersize=3)
# plt.savefig('LM_test.pdf',bbox_inches='tight')
# exit(0)
toyangles = toy_aa.T[3:6].T/np.pi
MaxRoll = 0.5*Roll
from solver import check_each_direction as ced
from solver import unroll_angles as ua
for i in np.arange(0,MaxRoll,Roll/100.):
(act,ang,n_vec,toy_aa,para),loop = find_actions(results[i:i+Roll], timeseries[:Roll], N_matrix = 6, ifloop=True,ifprint = False)
checks,maxgap = ced(n_vec,ua(toy_aa.T[3:].T,np.ones(3)))
print(checks)
print len(results[i:i+Roll]),act[0],act[1],act[2],ang[3],ang[4],ang[5],ang[0] % (2.*np.pi),ang[1] % (2.*np.pi),ang[2] % (2.*np.pi),' '.join(map(str, loop))
if(len(angles)==0):
angles = ang[:3]%(2.*np.pi)/np.pi
freqs = ang[3:6]
actions = act[:3]
times = timeseries[i]
else:
angles = np.vstack((angles,ang[:3]%(2.*np.pi)/np.pi))
freqs = np.vstack((freqs,ang[3:6]))
actions = np.vstack((actions,act[:3]))
times = np.vstack((times,timeseries[i]))
freqs = freqs/Conv
print(np.mean(actions.T[0]),np.mean(actions.T[1]),np.mean(actions.T[2]))
# a[1,2].plot((toy_aa.T[3]+2.*AA[0]) % (2.*np.pi) / np.pi,(toy_aa.T[5]+2.*AA[2]) % (2.*np.pi) / np.pi,'.',markersize=3)
# plt.savefig('LM_test.pdf',bbox_inches='tight')
# exit(0)
toyangles = toy_aa.T[3:6].T / np.pi
MaxRoll = 0.5 * Roll
from solver import check_each_direction as ced
from solver import unroll_angles as ua
for i in np.arange(0, MaxRoll, Roll / 100.):
(act, ang, n_vec, toy_aa, para), loop = find_actions(results[i:i + Roll],
timeseries[:Roll],
N_matrix=6,
ifloop=True,
ifprint=False)
checks, maxgap = ced(n_vec, ua(toy_aa.T[3:].T, np.ones(3)))
print(checks)
print len(
results[i:i + Roll]
), act[0], act[1], act[2], ang[3], ang[4], ang[5], ang[0] % (
2. * np.pi), ang[1] % (2. * np.pi), ang[2] % (2. * np.pi), ' '.join(
map(str, loop))
if (len(angles) == 0):
angles = ang[:3] % (2. * np.pi) / np.pi
freqs = ang[3:6]
actions = act[:3]
times = timeseries[i]
else:
angles = np.vstack((angles, ang[:3] % (2. * np.pi) / np.pi))
freqs = np.vstack((freqs, ang[3:6]))
actions = np.vstack((actions, act[:3]))
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')
