def sanders_act_ang_freq(t, w, N_max=6):
w2 = w.copy()
loop = classify_orbit(w)
if np.any(loop):
w2[:, 3:] = (w2[:, 3:] * u.kpc / u.Myr).to(u.km / u.s).value
(act, ang, n_vec, toy_aa,
pars), loop2 = genfunc_3d.find_actions(w2,
t / 1000.,
N_matrix=N_max,
ifloop=True)
else:
(act, ang, n_vec, toy_aa,
pars), loop2 = genfunc_3d.find_actions(w2,
t,
N_matrix=N_max,
ifloop=True)
actions = act[:3]
angles = ang[:3]
freqs = ang[3:6]
if np.any(loop):
toy_potential = IsochronePotential(m=pars[0] * 1E11,
b=pars[1],
units=galactic)
actions = (actions * u.kpc * u.km / u.s).to(u.kpc**2 / u.Myr).value
freqs = (freqs / u.Gyr).to(1 / u.Myr).value
else:
toy_potential = HarmonicOscillatorPotential(omega=np.array(pars))
return actions, angles, freqs, toy_potential
def print_freqs(): log = logarithmic() timeseries = np.linspace(0.,500.,2048) ntheta,nphi = 30,30 for i in np.arange(4.,ntheta+1)/(ntheta+1): for j in .5*np.pi*np.arange(15.,nphi+1)/(nphi+1): # if(i>0.9 and j>np.pi*0.45): # if(j>np.pi/4.): # if(i>0.59 and j>np.pi/2.*0.9): print np.arccos(i),j st,ct = np.sin(np.arccos(i)),i sp,cp = np.sin(j),np.cos(j) combo = cp*cp*st*st+sp*sp*st*st/log.qy2+ct*ct/log.qz2 r = np.sqrt((np.exp(1.)-0.1)/combo) initial = np.array([r*cp*st,r*sp*st,r*ct,0.0001,0.0001,0.0001]) # initial = np.array([0.111937987197,0.0104758765442,1.12993449025,0.0001,0.0001,0.0001]) results = odeint(pot.orbit_derivs2,initial,timeseries,args=(log,),rtol=1e-5,atol=1e-5) # print(log.H(initial),log.H(results[-1])) plots(timeseries,results) # freq = find_freqs(timeseries,results) L = find_actions(results, timeseries, N_matrix = 4, ifloop=True,ifprint = False) # if(L==None): # break (act,ang,n_vec,toy_aa,para),loop = L E = eval_mean_error_functions(act,ang,n_vec,toy_aa,timeseries,withplot=False)/np.std(timeseries) # ctas(ang,n_vec,toy_aa,timeseries) # print freq[0],freq[1],freq[2] print ang[3],ang[4],ang[5],initial[0],initial[1],initial[2],act[0],act[1],act[2] #,E[0],E[1],E[2],E[3],E[4],E[5] #,freq[0],freq[1],freq[2] exit()
def sanders_act_ang_freq(t, w, N_max=6):
w2 = w.copy()
loop = classify_orbit(w)
if np.any(loop):
w2[:,3:] = (w2[:,3:]*u.kpc/u.Myr).to(u.km/u.s).value
(act,ang,n_vec,toy_aa,pars),loop2 = genfunc_3d.find_actions(w2, t/1000.,
N_matrix=N_max, ifloop=True)
else:
(act,ang,n_vec,toy_aa,pars),loop2 = genfunc_3d.find_actions(w2, t,
N_matrix=N_max, ifloop=True)
actions = act[:3]
angles = ang[:3]
freqs = ang[3:6]
if np.any(loop):
toy_potential = IsochronePotential(m=pars[0]*1E11, b=pars[1], units=galactic)
actions = (actions*u.kpc*u.km/u.s).to(u.kpc**2/u.Myr).value
freqs = (freqs/u.Gyr).to(1/u.Myr).value
else:
toy_potential = HarmonicOscillatorPotential(omega=np.array(pars))
return actions,angles,freqs,toy_potential
def print_freqs():
log = logarithmic()
timeseries = np.linspace(0., 500., 2048)
ntheta, nphi = 30, 30
for i in np.arange(4., ntheta + 1) / (ntheta + 1):
for j in .5 * np.pi * np.arange(15., nphi + 1) / (nphi + 1):
# if(i>0.9 and j>np.pi*0.45):
# if(j>np.pi/4.):
# if(i>0.59 and j>np.pi/2.*0.9):
print np.arccos(i), j
st, ct = np.sin(np.arccos(i)), i
sp, cp = np.sin(j), np.cos(j)
combo = cp * cp * st * st + sp * sp * st * st / log.qy2 + ct * ct / log.qz2
r = np.sqrt((np.exp(1.) - 0.1) / combo)
initial = np.array(
[r * cp * st, r * sp * st, r * ct, 0.0001, 0.0001, 0.0001])
# initial = np.array([0.111937987197,0.0104758765442,1.12993449025,0.0001,0.0001,0.0001])
results = odeint(pot.orbit_derivs2,
initial,
timeseries,
args=(log, ),
rtol=1e-5,
atol=1e-5)
# print(log.H(initial),log.H(results[-1]))
plots(timeseries, results)
# freq = find_freqs(timeseries,results)
L = find_actions(results,
timeseries,
N_matrix=4,
ifloop=True,
ifprint=False)
# if(L==None):
# break
(act, ang, n_vec, toy_aa, para), loop = L
E = eval_mean_error_functions(
act, ang, n_vec, toy_aa, timeseries,
withplot=False) / np.std(timeseries)
# ctas(ang,n_vec,toy_aa,timeseries)
# print freq[0],freq[1],freq[2]
print ang[3], ang[4], ang[5], initial[0], initial[1], initial[
2], act[0], act[1], act[
2] #,E[0],E[1],E[2],E[3],E[4],E[5] #,freq[0],freq[1],freq[2]
exit()
a[1,0].set_ylabel(r'$z/{\rm kpc}$')
a[0,1].set_xlabel(r'$t/{\rm Gyr}$')
a[0,1].set_ylabel(r"$(J_1'-\langle J_1'\rangle )/{\rm kpc\,km\,s}^{-1}$")
a[1,1].set_xlabel(r'$t/{\rm Gyr}$')
a[1,1].set_ylabel(r"$(\Omega_1'-\langle\Omega_1'\rangle )/1000\,{\rm Gyr}^{-1}$")
a[0,2].set_xlabel(r'$\theta_1/\pi$')
a[0,2].set_ylabel(r'$\theta_2/\pi$')
a[1,2].set_xlabel(r'$\theta_1/\pi$')
a[1,2].set_ylabel(r'$\theta_3/\pi$')
times = np.array([])
angles = np.array([])
toyangles = np.array([])
actions = np.array([])
freqs= np.array([])
(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)))
a[1, 1].set_xlabel(r'$t/{\rm Gyr}$')
a[1,
1].set_ylabel(r"$(\Omega_1'-\langle\Omega_1'\rangle )/1000\,{\rm Gyr}^{-1}$")
a[0, 2].set_xlabel(r'$\theta_1/\pi$')
a[0, 2].set_ylabel(r'$\theta_2/\pi$')
a[1, 2].set_xlabel(r'$\theta_1/\pi$')
a[1, 2].set_ylabel(r'$\theta_3/\pi$')
times = np.array([])
angles = np.array([])
toyangles = np.array([])
actions = np.array([])
freqs = np.array([])
(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
def rotate_coords(X): xy = LM.invcoordrot(X[0],X[1]) vxvy = LM.invcoordrot(X[3],X[4]) return np.array([xy[0],xy[1],X[2],vxvy[0],vxvy[1],X[5]]) def unrotate_coords(X): xy = LM.coordrot(X[0],X[1]) vxvy = LM.coordrot(X[3],X[4]) return np.array([xy[0],xy[1],X[2],vxvy[0],vxvy[1],X[5]]) for i in datae: results = np.array([rotate_coords(p) for p in odeint(pot.orbit_derivs2,i,timeseries,args=(LM,),rtol=1e-10,atol=1e-10)]) L = find_actions(results,timeseries,N_matrix=6,ifprint=False) (act,ang,n_vec,toy_aa,para) = L checks,maxgap = ced(n_vec,ua(toy_aa.T[3:].T,np.ones(3))) TMAX = 1000 counter = 0 while(len(checks)>0 and counter<10): # print(checks) if(np.any(maxgap<0.)): TMAX=TMAX*2. results = np.array([rotate_coords(p) for p in odeint(pot.orbit_derivs2,initial,np.linspace(0.,10.,TMAX),args=(LM,),rtol=1e-10,atol=1e-10)]) L = find_actions(results, np.linspace(0.,10.,TMAX), N_matrix = 6, ifprint = False) else: results2 = np.array([rotate_coords(p) for p in odeint(pot.orbit_derivs2,unrotate_coords(results[-1]),timeseries,args=(LM,),rtol=1e-10,atol=1e-10)]) results = np.vstack((results,results2)) L = find_actions(results, np.linspace(0.,len(results)/100.,len(results)), N_matrix = 6, ifprint = False) (act,ang,n_vec,toy_aa,para) = L
initial = np.array([xy[0], xy[1], zlittle, pxpy[0], pxpy[1], pz])
results = np.array([
rotate_coords(p) for p in odeint(pot.orbit_derivs2,
initial,
timeseries,
args=(LM, ),
rtol=1e-10,
atol=1e-10)
])
# results_long = np.array([rotate_coords(p) for p in odeint(pot.orbit_derivs2,initial,timeseries_long,args=(LM,),rtol=1e-5,atol=1e-5)])
# loop = assess_angmom(results_long)
# LL = np.any(loop>0)
# BOX = not LL
L = find_actions(results,
timeseries,
N_matrix=6,
ifloop=True,
ifprint=False)
if (L == None):
print LM.H(initial), i, px, pz, loop
continue
(act, ang, n_vec, toy_aa, para), loop = L
# print(eval_mean_error_functions(act,ang,n_vec,toy_aa,timeseries,withplot=True))
checks, maxgap = ced(n_vec, ua(toy_aa.T[3:].T, np.ones(3)))
TMAX = 1000
counter = 0
while (len(checks) > 0 and counter < 10):
# print(checks)
if (np.any(maxgap < 0.)):
